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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Franci, A"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.00798">arXiv:2410.00798</a> <span> [<a href="https://arxiv.org/pdf/2410.00798">pdf</a>, <a href="https://arxiv.org/format/2410.00798">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Fast-and-flexible decision-making with modulatory interactions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Moreno-Morton%2C+R">Rodrigo Moreno-Morton</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.00798v1-abstract-short" style="display: inline;"> Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent decision-making. In this work we introduce modulatory, that is, multiplicative, in contrast to additive, interactions in a nonlinear opinion dynamics model of fas… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.00798v1-abstract-full').style.display = 'inline'; document.getElementById('2410.00798v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.00798v1-abstract-full" style="display: none;"> Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent decision-making. In this work we introduce modulatory, that is, multiplicative, in contrast to additive, interactions in a nonlinear opinion dynamics model of fast-and-flexible decision-making. The original model is nonlinear because network interactions, although additive, are saturated. Modulatory interactions introduce an extra source of nonlinearity that greatly enriches the model decision-making behavior in a mathematically tractable way. Modulatory interactions are widespread in both biological and social decision-making networks; our model provides new tools to understand the role of these interactions in networked decision-making and to engineer them in artificial systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.00798v1-abstract-full').style.display = 'none'; document.getElementById('2410.00798v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 4 figures, submitted to American Control Conference 2025</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37G99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.12420">arXiv:2409.12420</a> <span> [<a href="https://arxiv.org/pdf/2409.12420">pdf</a>, <a href="https://arxiv.org/format/2409.12420">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> Spatially-invariant opinion dynamics on the circle </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Amorim%2C+G">Giovanna Amorim</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.12420v2-abstract-short" style="display: inline;"> We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.12420v2-abstract-full').style.display = 'inline'; document.getElementById('2409.12420v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.12420v2-abstract-full" style="display: none;"> We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.12420v2-abstract-full').style.display = 'none'; document.getElementById('2409.12420v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.04324">arXiv:2401.04324</a> <span> [<a href="https://arxiv.org/pdf/2401.04324">pdf</a>, <a href="https://arxiv.org/format/2401.04324">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Adaptation and Self-Organizing Systems">nlin.AO</span> </div> </div> <p class="title is-5 mathjax"> Collective rhythm design in coupled mixed-feedback systems through dominance and bifurcations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Juarez-Alvarez%2C+O">Omar Juarez-Alvarez</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.04324v3-abstract-short" style="display: inline;"> The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper is to extend the mixed-feedback oscillation design framework to networks. To this aim, we introduce a network model of coupled mixed-feedback systems, ask under… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.04324v3-abstract-full').style.display = 'inline'; document.getElementById('2401.04324v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.04324v3-abstract-full" style="display: none;"> The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper is to extend the mixed-feedback oscillation design framework to networks. To this aim, we introduce a network model of coupled mixed-feedback systems, ask under which conditions it exhibits a collective oscillatory rhythm, and if, and how, this rhythm can be shaped by network design. In the proposed network model, node dynamics are nonlinear and defined by a tractable realization of the mixed-feedback structure. Coupling between nodes is also nonlinear and defined by a tractable abstraction of synaptic coupling between neurons. We derive constructive conditions under which the spectral properties of the network adjacency matrix fully and explicitly determine both the emergence of a stable network rhythm and its detailed rhythmic profile, i.e., the pattern of relative oscillation amplitudes and phase differences. Our theoretical developments are grounded on ideas from dominant systems and bifurcation theory. They provide a new framework for the analysis and design of nonlinear network rhythms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.04324v3-abstract-full').style.display = 'none'; document.getElementById('2401.04324v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 6 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.06395">arXiv:2312.06395</a> <span> [<a href="https://arxiv.org/pdf/2312.06395">pdf</a>, <a href="https://arxiv.org/format/2312.06395">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Robotics">cs.RO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Threshold Decision-Making Dynamics Adaptive to Physical Constraints and Changing Environment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Amorim%2C+G">Giovanna Amorim</a>, <a href="/search/math?searchtype=author&query=Santos%2C+M">Mar铆a Santos</a>, <a href="/search/math?searchtype=author&query=Park%2C+S">Shinkyu Park</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.06395v3-abstract-short" style="display: inline;"> We propose a threshold decision-making framework for controlling the physical dynamics of an agent switching between two spatial tasks. Our framework couples a nonlinear opinion dynamics model that represents the evolution of an agent's preference for a particular task with the physical dynamics of the agent. We prove the bifurcation that governs the behavior of the coupled dynamics. We show by me… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.06395v3-abstract-full').style.display = 'inline'; document.getElementById('2312.06395v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.06395v3-abstract-full" style="display: none;"> We propose a threshold decision-making framework for controlling the physical dynamics of an agent switching between two spatial tasks. Our framework couples a nonlinear opinion dynamics model that represents the evolution of an agent's preference for a particular task with the physical dynamics of the agent. We prove the bifurcation that governs the behavior of the coupled dynamics. We show by means of the bifurcation behavior how the coupled dynamics are adaptive to the physical constraints of the agent. We also show how the bifurcation can be modulated to allow the agent to switch tasks based on thresholds adaptive to environmental conditions. We illustrate the benefits of the approach through a decentralized multi-robot task allocation application for trash collection. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.06395v3-abstract-full').style.display = 'none'; document.getElementById('2312.06395v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.02755">arXiv:2308.02755</a> <span> [<a href="https://arxiv.org/pdf/2308.02755">pdf</a>, <a href="https://arxiv.org/format/2308.02755">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Multi-topic belief formation through bifurcations over signed social networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2308.02755v2-abstract-short" style="display: inline;"> We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our model accounts for the effects of a structured belief system, self-appraisal, internal biases, and various sources of cognitive dissonance posited by recent theories in social psychology. We prove that agents become opinionated as a consequence of a bifurcation. W… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.02755v2-abstract-full').style.display = 'inline'; document.getElementById('2308.02755v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.02755v2-abstract-full" style="display: none;"> We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our model accounts for the effects of a structured belief system, self-appraisal, internal biases, and various sources of cognitive dissonance posited by recent theories in social psychology. We prove that agents become opinionated as a consequence of a bifurcation. We analyze how the balance of social network effects in the model controls the nature of the bifurcation and, therefore, the belief-forming limit-set solutions. Our analysis provides constructive conditions on how multi-stable network belief equilibria and belief oscillations emerging at a belief-forming bifurcation depend on the communication network graph and belief system network graph. Our model and analysis provide new theoretical insights on the dynamics of social systems and a new principled framework for designing decentralized decision-making on engineered networks in the presence of structured relationships among alternatives. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.02755v2-abstract-full').style.display = 'none'; document.getElementById('2308.02755v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 7 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.00353">arXiv:2210.00353</a> <span> [<a href="https://arxiv.org/pdf/2210.00353">pdf</a>, <a href="https://arxiv.org/format/2210.00353">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> </div> <p class="title is-5 mathjax"> Sustained oscillations in multi-topic belief dynamics over signed networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.00353v2-abstract-short" style="display: inline;"> We study the dynamics of belief formation on multiple interconnected topics in networks of agents with a shared belief system. We establish sufficient conditions and necessary conditions under which sustained oscillations of beliefs arise on the network in a Hopf bifurcation and characterize the role of the communication graph and the belief system graph in shaping the relative phase and amplitude… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.00353v2-abstract-full').style.display = 'inline'; document.getElementById('2210.00353v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.00353v2-abstract-full" style="display: none;"> We study the dynamics of belief formation on multiple interconnected topics in networks of agents with a shared belief system. We establish sufficient conditions and necessary conditions under which sustained oscillations of beliefs arise on the network in a Hopf bifurcation and characterize the role of the communication graph and the belief system graph in shaping the relative phase and amplitude patterns of the oscillations. Additionally, we distinguish broad classes of graphs that exhibit such oscillations from those that do not. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.00353v2-abstract-full').style.display = 'none'; document.getElementById('2210.00353v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 6 figures, accepted for publication in the 2023 American Control Conference proceedings</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.14893">arXiv:2206.14893</a> <span> [<a href="https://arxiv.org/pdf/2206.14893">pdf</a>, <a href="https://arxiv.org/format/2206.14893">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Breaking indecision in multi-agent, multi-option dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Golubitsky%2C+M">Martin Golubitsky</a>, <a href="/search/math?searchtype=author&query=Stewart%2C+I">Ian Stewart</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.14893v1-abstract-short" style="display: inline;"> How does a group of agents break indecision when deciding about options with qualities that are hard to distinguish? Biological and artificial multi-agent systems, from honeybees and bird flocks to bacteria, robots, and humans, often need to overcome indecision when choosing among options in situations in which the performance or even the survival of the group are at stake. Breaking indecision is… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.14893v1-abstract-full').style.display = 'inline'; document.getElementById('2206.14893v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.14893v1-abstract-full" style="display: none;"> How does a group of agents break indecision when deciding about options with qualities that are hard to distinguish? Biological and artificial multi-agent systems, from honeybees and bird flocks to bacteria, robots, and humans, often need to overcome indecision when choosing among options in situations in which the performance or even the survival of the group are at stake. Breaking indecision is also important because in a fully indecisive state agents are not biased toward any specific option and therefore the agent group is maximally sensitive and prone to adapt to inputs and changes in its environment. Here, we develop a mathematical theory to study how decisions arise from the breaking of indecision. Our approach is grounded in both equivariant and network bifurcation theory. We model decision from indecision as synchrony-breaking in influence networks in which each node is the value assigned by an agent to an option. First, we show that three universal decision behaviors, namely, deadlock, consensus, and dissensus, are the generic outcomes of synchrony-breaking bifurcations from a fully synchronous state of indecision in influence networks. Second, we show that all deadlock and consensus value patterns and some dissensus value patterns are predicted by the symmetry of the influence networks. Third, we show that there are also many `exotic' dissensus value patterns. These patterns are predicted by network architecture, but not by network symmetries, through a new synchrony-breaking branching lemma. This is the first example of exotic solutions in an application. Numerical simulations of a novel influence network model illustrate our theoretical results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.14893v1-abstract-full').style.display = 'none'; document.getElementById('2206.14893v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">36 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.12009">arXiv:2203.12009</a> <span> [<a href="https://arxiv.org/pdf/2203.12009">pdf</a>, <a href="https://arxiv.org/format/2203.12009">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Molecular Networks">q-bio.MN</span> </div> </div> <p class="title is-5 mathjax"> Control of Multistability through Local Sensitivity Analysis: Application to Cellular Decision-making Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Moreno-Morton%2C+R">Rodrigo Moreno-Morton</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.12009v2-abstract-short" style="display: inline;"> Control of multistable dynamical system has important applications, from physics to biology. Here, we attack this problem from the perspective of local sensitivity analysis. We develop sensitivity rules to control properties of continuous-time multistable dynamics with simple attractors, namely, the relative size and depth of their basins of attraction. Our parameter control signal is computationa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.12009v2-abstract-full').style.display = 'inline'; document.getElementById('2203.12009v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.12009v2-abstract-full" style="display: none;"> Control of multistable dynamical system has important applications, from physics to biology. Here, we attack this problem from the perspective of local sensitivity analysis. We develop sensitivity rules to control properties of continuous-time multistable dynamics with simple attractors, namely, the relative size and depth of their basins of attraction. Our parameter control signal is computationally cheap and provides counter-intuitive information about the sensitive parameters to be manipulated in an experimental setting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.12009v2-abstract-full').style.display = 'none'; document.getElementById('2203.12009v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Gave an in-depth discussion of and added references to the theory in Section III. Slight change of structure in Control Strategies. Slight changes to figures and discussion of example systems</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.11703">arXiv:2203.11703</a> <span> [<a href="https://arxiv.org/pdf/2203.11703">pdf</a>, <a href="https://arxiv.org/format/2203.11703">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1109/LCSYS.2022.3185981">10.1109/LCSYS.2022.3185981 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Switching transformations for decentralized control of opinion patterns in signed networks: application to dynamic task allocation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Amorim%2C+G">Giovanna Amorim</a>, <a href="/search/math?searchtype=author&query=Santos%2C+M">Maria Santos</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.11703v2-abstract-short" style="display: inline;"> We propose a new decentralized design method to control opinion patterns on signed networks of agents making decisions about two options and to switch the network from any opinion pattern to a new desired one. Our method relies on switching transformations, which switch the sign of an agent's opinion at a stable equilibrium by flipping the sign of its local interactions with its neighbors. The glo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.11703v2-abstract-full').style.display = 'inline'; document.getElementById('2203.11703v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.11703v2-abstract-full" style="display: none;"> We propose a new decentralized design method to control opinion patterns on signed networks of agents making decisions about two options and to switch the network from any opinion pattern to a new desired one. Our method relies on switching transformations, which switch the sign of an agent's opinion at a stable equilibrium by flipping the sign of its local interactions with its neighbors. The global dynamical behavior of the switched network can be predicted rigorously when the original, and thus the witched, networks are structurally balanced. Structural balance ensures that the network dynamics are monotone, which makes the study of the basin of attraction of the various opinion patterns amenable to rigorous analysis through monotone systems theory. We illustrate the utility of the approach through scenarios motivated by multi-robot coordination and dynamic task allocation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.11703v2-abstract-full').style.display = 'none'; document.getElementById('2203.11703v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2109.13932">arXiv:2109.13932</a> <span> [<a href="https://arxiv.org/pdf/2109.13932">pdf</a>, <a href="https://arxiv.org/format/2109.13932">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Chaotic Dynamics">nlin.CD</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> </div> </div> <p class="title is-5 mathjax"> In-phase oscillations from the cooperation of cellular and network positive feedback in synaptically-coupled oscillators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Juarez-Alvarez%2C+O">Omar Juarez-Alvarez</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2109.13932v2-abstract-short" style="display: inline;"> We study the emergent dynamics of a network of synaptically coupled slow-fast oscillators. Synaptic coupling provides a network-level positive feedback mechanism that cooperates with cellular-level positive feedback to ignite in-phase network oscillations. Using analytical bifurcation analysis, we prove that the Perron-Frobenius eigenvector of the network adjacency matrix fully controls the oscill… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.13932v2-abstract-full').style.display = 'inline'; document.getElementById('2109.13932v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2109.13932v2-abstract-full" style="display: none;"> We study the emergent dynamics of a network of synaptically coupled slow-fast oscillators. Synaptic coupling provides a network-level positive feedback mechanism that cooperates with cellular-level positive feedback to ignite in-phase network oscillations. Using analytical bifurcation analysis, we prove that the Perron-Frobenius eigenvector of the network adjacency matrix fully controls the oscillation pattern locally in a neighborhood of a Hopf bifurcation. Besides shifting the focus from the spectral properties of the network Laplacian matrix to the network adjacency matrix, we discuss other key differences between synaptic and diffusive coupling. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.13932v2-abstract-full').style.display = 'none'; document.getElementById('2109.13932v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 3 figures, Conference on Decision and Control 2021</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.06917">arXiv:2108.06917</a> <span> [<a href="https://arxiv.org/pdf/2108.06917">pdf</a>, <a href="https://arxiv.org/format/2108.06917">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Miranda-Villatoro%2C+F">Felix Miranda-Villatoro</a>, <a href="/search/math?searchtype=author&query=Casta%C3%B1os%2C+F">Fernando Casta帽os</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.06917v2-abstract-short" style="display: inline;"> Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear complementarity systems. Mimicking the program that led to the foundation of bifurcation theory in smooth maps, we introduce a novel notion of equivalence between li… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.06917v2-abstract-full').style.display = 'inline'; document.getElementById('2108.06917v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.06917v2-abstract-full" style="display: none;"> Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear complementarity systems. Mimicking the program that led to the foundation of bifurcation theory in smooth maps, we introduce a novel notion of equivalence between linear complementarity problems that sets the basis for a theory of bifurcations in a large class of nonsmooth maps, including, but not restricted to, steadystate bifurcations in linear complementarity systems. Our definition exploits the rich geometry of linear complementarity problems and leads to constructive algebraic conditions for identifying and classifying the nonsmooth singularities associated with nonsmooth bifurcations. We thoroughly illustrate our theory on an extended applied example, the design of bistability in an electrical network, and a more theoretical one, the identification and classification of all possible equivalence classes in two-dimensional linear complementarity problems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.06917v2-abstract-full').style.display = 'none'; document.getElementById('2108.06917v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.00966">arXiv:2108.00966</a> <span> [<a href="https://arxiv.org/pdf/2108.00966">pdf</a>, <a href="https://arxiv.org/format/2108.00966">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Tuning Cooperative Behavior in Games with Nonlinear Opinion Dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Park%2C+S">Shinkyu Park</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Kawakatsu%2C+M">Mari Kawakatsu</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.00966v3-abstract-short" style="display: inline;"> We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agent opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.00966v3-abstract-full').style.display = 'inline'; document.getElementById('2108.00966v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.00966v3-abstract-full" style="display: none;"> We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agent opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others (reciprocity), network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.00966v3-abstract-full').style.display = 'none'; document.getElementById('2108.00966v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.02583">arXiv:2106.02583</a> <span> [<a href="https://arxiv.org/pdf/2106.02583">pdf</a>, <a href="https://arxiv.org/format/2106.02583">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> </div> </div> <p class="title is-5 mathjax"> Feedback design of spatially-distributed filters with tunable resolution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.02583v1-abstract-short" style="display: inline;"> We derive gain-tuning rules for the positive and negative spatial-feedback loops of a spatially-distributed filter to change the resolution of its spatial band-pass characteristic accordingly to a wavelet zoom, while preserving temporal stability. The filter design is inspired by the canonical spatial feedback structure of the primary visual cortex and is motivated by understanding attentional con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.02583v1-abstract-full').style.display = 'inline'; document.getElementById('2106.02583v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.02583v1-abstract-full" style="display: none;"> We derive gain-tuning rules for the positive and negative spatial-feedback loops of a spatially-distributed filter to change the resolution of its spatial band-pass characteristic accordingly to a wavelet zoom, while preserving temporal stability. The filter design is inspired by the canonical spatial feedback structure of the primary visual cortex and is motivated by understanding attentional control of visual resolution. Besides biology, our control-theoretical design strategy is relevant for the development of neuromorphic multiresolution distributed sensors through the feedback interconnection of elementary spatial transfer functions and gain tuning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.02583v1-abstract-full').style.display = 'none'; document.getElementById('2106.02583v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.14764">arXiv:2103.14764</a> <span> [<a href="https://arxiv.org/pdf/2103.14764">pdf</a>, <a href="https://arxiv.org/ps/2103.14764">ps</a>, <a href="https://arxiv.org/format/2103.14764">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1109/CDC45484.2021.9683650">10.1109/CDC45484.2021.9683650 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Control of Agreement and Disagreement Cascades with Distributed Inputs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Sorochkin%2C+T">Timothy Sorochkin</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.14764v1-abstract-short" style="display: inline;"> For a group of autonomous communicating agents, the ability to distinguish a meaningful input from disturbance, and come to collective agreement or disagreement in response to that input, is paramount for carrying out coordinated objectives. In this work we study how a cascade of opinion formation spreads through a group of networked decision-makers in response to a distributed input signal. Using… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.14764v1-abstract-full').style.display = 'inline'; document.getElementById('2103.14764v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.14764v1-abstract-full" style="display: none;"> For a group of autonomous communicating agents, the ability to distinguish a meaningful input from disturbance, and come to collective agreement or disagreement in response to that input, is paramount for carrying out coordinated objectives. In this work we study how a cascade of opinion formation spreads through a group of networked decision-makers in response to a distributed input signal. Using a nonlinear opinion dynamics model with dynamic feedback modulation of an attention parameter, we show how the triggering of an opinion cascade and the collective decision itself depend on both the distributed input and the node agreement and disagreement centrality, determined by the spectral properties of the network graph. We further show how the attention dynamics introduce an implicit threshold that distinguishes between distributed inputs that trigger cascades and ones that are rejected as disturbance. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.14764v1-abstract-full').style.display = 'none'; document.getElementById('2103.14764v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 4 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.12223">arXiv:2103.12223</a> <span> [<a href="https://arxiv.org/pdf/2103.12223">pdf</a>, <a href="https://arxiv.org/format/2103.12223">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11721-021-00190-w">10.1007/s11721-021-00190-w <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Analysis and control of agreement and disagreement opinion cascades </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Park%2C+S">Shinkyu Park</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.12223v1-abstract-short" style="display: inline;"> We introduce and analyze a continuous time and state-space model of opinion cascades on networks of large numbers of agents that form opinions about two or more options. By leveraging our recent results on the emergence of agreement and disagreement states, we introduce novel tools to analyze and control agreement and disagreement opinion cascades. New notions of agreement and disagreement central… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.12223v1-abstract-full').style.display = 'inline'; document.getElementById('2103.12223v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.12223v1-abstract-full" style="display: none;"> We introduce and analyze a continuous time and state-space model of opinion cascades on networks of large numbers of agents that form opinions about two or more options. By leveraging our recent results on the emergence of agreement and disagreement states, we introduce novel tools to analyze and control agreement and disagreement opinion cascades. New notions of agreement and disagreement centrality, which depend only on network structure, are shown to be key to characterizing the nonlinear behavior of agreement and disagreement opinion formation and cascades. Our results are relevant for the analysis and control of opinion cascades in real-world networks, including biological, social and artificial networks, and for the design of opinion-forming behaviors in robotic swarms. We illustrate an application of our model to a multi-robot task-allocation problem and discuss extensions and future directions opened by our modeling framework. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.12223v1-abstract-full').style.display = 'none'; document.getElementById('2103.12223v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.13600">arXiv:2009.13600</a> <span> [<a href="https://arxiv.org/pdf/2009.13600">pdf</a>, <a href="https://arxiv.org/format/2009.13600">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.23919/ACC50511.2021.9482811">10.23919/ACC50511.2021.9482811 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Patterns of Nonlinear Opinion Formation on Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Matthews%2C+A">Ayanna Matthews</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.13600v2-abstract-short" style="display: inline;"> When communicating agents form opinions about a set of possible options, agreement and disagreement are both possible outcomes. Depending on the context, either can be desirable or undesirable. We show that for nonlinear opinion dynamics on networks, and a variety of network structures, the spectral properties of the underlying adjacency matrix fully characterize the occurrence of either agreement… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.13600v2-abstract-full').style.display = 'inline'; document.getElementById('2009.13600v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.13600v2-abstract-full" style="display: none;"> When communicating agents form opinions about a set of possible options, agreement and disagreement are both possible outcomes. Depending on the context, either can be desirable or undesirable. We show that for nonlinear opinion dynamics on networks, and a variety of network structures, the spectral properties of the underlying adjacency matrix fully characterize the occurrence of either agreement or disagreement. We further show how the corresponding eigenvector centrality, as well as any symmetry in the network, informs the resulting patterns of opinion formation and agent sensitivity to input that triggers opinion cascades. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.13600v2-abstract-full').style.display = 'none'; document.getElementById('2009.13600v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 4 figures; accepted to appear in 2021 American Control Conference proceedings</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.04332">arXiv:2009.04332</a> <span> [<a href="https://arxiv.org/pdf/2009.04332">pdf</a>, <a href="https://arxiv.org/format/2009.04332">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1109/TAC.2022.3159527">10.1109/TAC.2022.3159527 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Nonlinear Opinion Dynamics with Tunable Sensitivity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.04332v3-abstract-short" style="display: inline;"> We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models. For a group of agents that communicate opinions over a network… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.04332v3-abstract-full').style.display = 'inline'; document.getElementById('2009.04332v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.04332v3-abstract-full" style="display: none;"> We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models. For a group of agents that communicate opinions over a network, these behaviors include multistable agreement and disagreement, tunable sensitivity to input, robustness to disturbance, flexible transition between patterns of opinions, and opinion cascades. We derive network-dependent tuning rules to robustly control the system behavior and we design state-feedback dynamics for the model parameters to make the behavior adaptive to changing external conditions.} The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.04332v3-abstract-full').style.display = 'none'; document.getElementById('2009.04332v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.03774">arXiv:1911.03774</a> <span> [<a href="https://arxiv.org/pdf/1911.03774">pdf</a>, <a href="https://arxiv.org/format/1911.03774">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> </div> </div> <p class="title is-5 mathjax"> A notion of equivalence for linear complementarity problems with application to the design of non-smooth bifurcations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Casta%C3%B1os%2C+F">Fernando Casta帽os</a>, <a href="/search/math?searchtype=author&query=Miranda-Villatoro%2C+F">F茅lix Miranda-Villatoro</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.03774v2-abstract-short" style="display: inline;"> Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to analyze, classify, and design non-smooth bifurcat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.03774v2-abstract-full').style.display = 'inline'; document.getElementById('1911.03774v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.03774v2-abstract-full" style="display: none;"> Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to analyze, classify, and design non-smooth bifurcations in linear complementarity problems and their interconnection. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.03774v2-abstract-full').style.display = 'none'; document.getElementById('1911.03774v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Submitted to the IFAC 2020 World Congress</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37G05; 37G10; 37E99; 93C10; 93A30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.05765">arXiv:1909.05765</a> <span> [<a href="https://arxiv.org/pdf/1909.05765">pdf</a>, <a href="https://arxiv.org/format/1909.05765">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantitative Methods">q-bio.QM</span> </div> </div> <p class="title is-5 mathjax"> A model-independent theory of consensus and dissensus decision making </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Golubitsky%2C+M">Martin Golubitsky</a>, <a href="/search/math?searchtype=author&query=Bizyaeva%2C+A">Anastasia Bizyaeva</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1909.05765v2-abstract-short" style="display: inline;"> We develop a model-independent framework to study the dynamics of decision-making in opinion networks for an arbitrary number of agents and an arbitrary number of options. Model-independence means that the analysis is not performed on a specific set of equations, in contrast to classical approaches to decision making that fix a specific model and analyze it. Rather, the general features of decisio… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.05765v2-abstract-full').style.display = 'inline'; document.getElementById('1909.05765v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.05765v2-abstract-full" style="display: none;"> We develop a model-independent framework to study the dynamics of decision-making in opinion networks for an arbitrary number of agents and an arbitrary number of options. Model-independence means that the analysis is not performed on a specific set of equations, in contrast to classical approaches to decision making that fix a specific model and analyze it. Rather, the general features of decision making in dynamical opinion networks can be derived starting from empirically testable hypotheses about the deciding agents, the available options, and the interactions among them. After translating these empirical hypotheses into algebraic ones, we use the tools of equivariant bifurcation theory to uncover model-independent properties of dynamical opinion networks. The model-independent results are illustrated on a novel analytical model that is constructed by plugging a generic sigmoidal nonlinearity, modeling boundedness of opinions and opinion perception, into the model-independent equivariant structure. Our analysis reveals richer and more flexible opinion-formation behavior as compared to model-dependent approaches. For instance, analysis reveals the possibility of switching between consensus and various forms of dissensus by modulation of the level of agent cooperativity and without requiring any particular ad-hoc interaction topology (e.g., structural balance). From a theoretical viewpoint, we prove new results in equivariant bifurcation theory. We construct an exhaustive list of axial subgroups for the action of $\ES_n \times \ES_3$ on $\R^{n-1}\otimes\R^{2}$. We also generalize this list to the action of $\ES_n \times \ES_k$ on $\R^{n-1}\otimes \R^{k-1}$, i.e., for $n$ agents and $k$ options, although without proving that in this case the list is exhaustive. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.05765v2-abstract-full').style.display = 'none'; document.getElementById('1909.05765v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.07117">arXiv:1812.07117</a> <span> [<a href="https://arxiv.org/pdf/1812.07117">pdf</a>, <a href="https://arxiv.org/format/1812.07117">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1080/03080188.2018.1544806">10.1080/03080188.2018.1544806 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Social decision-making driven by artistic explore-exploit tension </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ozcimder%2C+K">Kayhan Ozcimder</a>, <a href="/search/math?searchtype=author&query=Dey%2C+B">Biswadip Dey</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Lazier%2C+R">Rebecca Lazier</a>, <a href="/search/math?searchtype=author&query=Trueman%2C+D">Daniel Trueman</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.07117v1-abstract-short" style="display: inline;"> We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier e… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.07117v1-abstract-full').style.display = 'inline'; document.getElementById('1812.07117v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.07117v1-abstract-full" style="display: none;"> We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.07117v1-abstract-full').style.display = 'none'; document.getElementById('1812.07117v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> K. Ozcimder, B. Dey, A. Franci, R. Lazier, D. Trueman, and N. E. Leonard (2018): Social decision-making driven by artistic explore-exploit tension, Interdisciplinary Science Reviews </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.06700">arXiv:1802.06700</a> <span> [<a href="https://arxiv.org/pdf/1802.06700">pdf</a>, <a href="https://arxiv.org/format/1802.06700">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Cellular switches orchestrate rhythmic circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1802.06700v1-abstract-short" style="display: inline;"> Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate such circuits. The cellular switch makes the circuits reconfigurable, robust, adaptable, and externally controllable. Without this cellular mechanism, the circui… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.06700v1-abstract-full').style.display = 'inline'; document.getElementById('1802.06700v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.06700v1-abstract-full" style="display: none;"> Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate such circuits. The cellular switch makes the circuits reconfigurable, robust, adaptable, and externally controllable. Without this cellular mechanism, the circuits rhythms entirely rely on specific tunings of the synaptic connectivity, which makes them rigid, fragile, and difficult to control externally. We illustrate those properties on the much studied architecture of a small network controlling both the pyloric and gastric rhythms of crabs. The cellular switch is provided by a slow negative conductance often neglected in mathematical modeling of central pattern generators. We propose that this conductance is simple to model and key to computational studies of rhythmic circuit neuromodulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.06700v1-abstract-full').style.display = 'none'; document.getElementById('1802.06700v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1711.11578">arXiv:1711.11578</a> <span> [<a href="https://arxiv.org/pdf/1711.11578">pdf</a>, <a href="https://arxiv.org/format/1711.11578">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Multi-agent decision-making dynamics inspired by honeybees </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Gray%2C+R">Rebecca Gray</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Srivastava%2C+V">Vaibhav Srivastava</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1711.11578v2-abstract-short" style="display: inline;"> When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation an… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.11578v2-abstract-full').style.display = 'inline'; document.getElementById('1711.11578v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1711.11578v2-abstract-full" style="display: none;"> When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multi-agent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological models of decision-making. Using tools of nonlinear dynamics we show how the designed agent-based dynamics recover the high performing value-sensitive decision-making of the honeybees and rigorously connect investigation of mechanisms of animal group decision-making to systematic, bio-inspired control of multi-agent network systems. We further present a distributed adaptive bifurcation control law and prove how it enhances the network decision-making performance beyond that observed in swarms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.11578v2-abstract-full').style.display = 'none'; document.getElementById('1711.11578v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.00664">arXiv:1707.00664</a> <span> [<a href="https://arxiv.org/pdf/1707.00664">pdf</a>, <a href="https://arxiv.org/format/1707.00664">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Robust and tunable bursting requires slow positive feedback </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.00664v2-abstract-short" style="display: inline;"> We highlight that the robustness and tunability of a bursting model critically relies on currents that provide slow positive feedback to the membrane potential. Such currents have the ability of making the total conductance of the circuit negative in a time scale that is termed slow because intermediate between the fast time scale of the spike upstroke and the ultraslow time scale of even slower a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.00664v2-abstract-full').style.display = 'inline'; document.getElementById('1707.00664v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.00664v2-abstract-full" style="display: none;"> We highlight that the robustness and tunability of a bursting model critically relies on currents that provide slow positive feedback to the membrane potential. Such currents have the ability of making the total conductance of the circuit negative in a time scale that is termed slow because intermediate between the fast time scale of the spike upstroke and the ultraslow time scale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.00664v2-abstract-full').style.display = 'none'; document.getElementById('1707.00664v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.05820">arXiv:1611.05820</a> <span> [<a href="https://arxiv.org/pdf/1611.05820">pdf</a>, <a href="https://arxiv.org/format/1611.05820">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> On-line detection of qualitative dynamical changes in nonlinear systems: the resting-oscillation case </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Tang%2C+Y">Ying Tang</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Postoyan%2C+R">Romain Postoyan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.05820v3-abstract-short" style="display: inline;"> Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a nonlinear system. The approach is thought for systems characterized by i) large parameter variability and redundancy, ii) a small number of possible robust, qualita… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.05820v3-abstract-full').style.display = 'inline'; document.getElementById('1611.05820v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.05820v3-abstract-full" style="display: none;"> Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a nonlinear system. The approach is thought for systems characterized by i) large parameter variability and redundancy, ii) a small number of possible robust, qualitatively different dynamical behaviors and, iii) the presence of sharply different characteristic timescales. These properties are omnipresent in neurosciences and hamper quantitative modeling and fitting of experimental data. As a result, novel control theoretical strategies are needed to face neuroscience challenges like on-line epileptic seizure detection. The proposed approach aims at detecting the current dynamical behavior of the system and whether a qualitative change is likely to occur without quantitatively fitting any model nor asymptotically estimating any parameter. We talk of qualitative detection. We rely on the qualitative properties of the system dynamics, extracted via singularity and singular perturbation theories, to design low dimensional qualitative detectors. We introduce this concept on a general class of singularly perturbed systems and then solve the problem for an analytically tractable class of two-dimensional systems with a single unknown sigmoidal nonlinearity and two sharply separated timescales. Numerical results are provided to show the performance of the designed qualitative detector. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.05820v3-abstract-full').style.display = 'none'; document.getElementById('1611.05820v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1608.03908">arXiv:1608.03908</a> <span> [<a href="https://arxiv.org/pdf/1608.03908">pdf</a>, <a href="https://arxiv.org/format/1608.03908">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.neucom.2016.08.099">10.1016/j.neucom.2016.08.099 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Implementing robust neuromodulation in neuromorphic circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Casta%C3%B1os%2C+F">Fernando Casta帽os</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1608.03908v1-abstract-short" style="display: inline;"> We introduce a methodology to implement the physiological transition {between distinct neuronal spiking modes} in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by the same geometry {and exhibiting the same input--output properties as} high-dimensional electrophysiological neuron models. {Preliminary} experimental results… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.03908v1-abstract-full').style.display = 'inline'; document.getElementById('1608.03908v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1608.03908v1-abstract-full" style="display: none;"> We introduce a methodology to implement the physiological transition {between distinct neuronal spiking modes} in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by the same geometry {and exhibiting the same input--output properties as} high-dimensional electrophysiological neuron models. {Preliminary} experimental results highlight the robustness of the approach in real-world applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.03908v1-abstract-full').style.display = 'none'; document.getElementById('1608.03908v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> 2017 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Neurocomputing, 233:3 - 13, April 2017 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.08938">arXiv:1510.08938</a> <span> [<a href="https://arxiv.org/pdf/1510.08938">pdf</a>, <a href="https://arxiv.org/format/1510.08938">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> A three-scale model of spatio-temporal bursting </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.08938v2-abstract-short" style="display: inline;"> We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winge… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.08938v2-abstract-full').style.display = 'inline'; document.getElementById('1510.08938v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.08938v2-abstract-full" style="display: none;"> We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winged cusp. The modulation of spatio-temporal bursting in such a model naturally translates into paths in the universal unfolding of the winged-cusp. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.08938v2-abstract-full').style.display = 'none'; document.getElementById('1510.08938v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 July, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1506.02010">arXiv:1506.02010</a> <span> [<a href="https://arxiv.org/pdf/1506.02010">pdf</a>, <a href="https://arxiv.org/format/1506.02010">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1109/CDC.2016.7798982">10.1109/CDC.2016.7798982 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Singularly perturbed phase response curves </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sacr%C3%A9%2C+P">Pierre Sacr茅</a>, <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1506.02010v2-abstract-short" style="display: inline;"> In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the meth… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.02010v2-abstract-full').style.display = 'inline'; document.getElementById('1506.02010v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1506.02010v2-abstract-full" style="display: none;"> In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the methodology by deriving semi-analytic formula for the (finite) phase response curve of generic planar relaxation oscillators to impulses and square pulses of finite duration and verify its goodness numerically on the FitzHugh-Nagumo model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.02010v2-abstract-full').style.display = 'none'; document.getElementById('1506.02010v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.08526">arXiv:1503.08526</a> <span> [<a href="https://arxiv.org/pdf/1503.08526">pdf</a>, <a href="https://arxiv.org/format/1503.08526">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> A Realization Theory for Bio-inspired Collective Decision-Making </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Srivastava%2C+V">Vaibhav Srivastava</a>, <a href="/search/math?searchtype=author&query=Leonard%2C+N+E">Naomi Ehrich Leonard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1503.08526v3-abstract-short" style="display: inline;"> The collective decision-making exhibited by animal groups provides enormous inspiration for multi-agent control system design as it embodies several features that are desirable in engineered networks, including robustness and adaptability, low computational effort, and an intrinsically decentralized architecture. However, many of the mechanistic models for collective decision-making are described… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.08526v3-abstract-full').style.display = 'inline'; document.getElementById('1503.08526v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.08526v3-abstract-full" style="display: none;"> The collective decision-making exhibited by animal groups provides enormous inspiration for multi-agent control system design as it embodies several features that are desirable in engineered networks, including robustness and adaptability, low computational effort, and an intrinsically decentralized architecture. However, many of the mechanistic models for collective decision-making are described at the population-level abstraction and are challenging to implement in an engineered system. We develop simple and easy-to-implement models of opinion dynamics that realize the empirically observed collective decision-making behavior as well as the behavior predicted by existing models of animal groups. Using methods from Lyapunov analysis, singularity theory, and monotone dynamical systems, we rigorously investigate the steady-state decision-making behavior of our models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.08526v3-abstract-full').style.display = 'none'; document.getElementById('1503.08526v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 March, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1409.5560">arXiv:1409.5560</a> <span> [<a href="https://arxiv.org/pdf/1409.5560">pdf</a>, <a href="https://arxiv.org/format/1409.5560">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Realization of nonlinear behaviors from organizing centers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1409.5560v1-abstract-short" style="display: inline;"> Borrowing the concept of organizing center from singularity theory, the paper proposes a methodology to realize nonlinear behaviors such as switches, relaxation oscillators, or bursters from core circuits that reveal the fundamental role of monotonicity and feedback in their robustness and modulation. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1409.5560v1-abstract-full" style="display: none;"> Borrowing the concept of organizing center from singularity theory, the paper proposes a methodology to realize nonlinear behaviors such as switches, relaxation oscillators, or bursters from core circuits that reveal the fundamental role of monotonicity and feedback in their robustness and modulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1409.5560v1-abstract-full').style.display = 'none'; document.getElementById('1409.5560v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2014. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1305.7364">arXiv:1305.7364</a> <span> [<a href="https://arxiv.org/pdf/1305.7364">pdf</a>, <a href="https://arxiv.org/format/1305.7364">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Modeling the modulation of neuronal bursting: a singularity theory approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1305.7364v3-abstract-short" style="display: inline;"> Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scales attractors in the neighborhood of high-codimension singularities. We detect a three-time scale bursting attractor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.7364v3-abstract-full').style.display = 'inline'; document.getElementById('1305.7364v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1305.7364v3-abstract-full" style="display: none;"> Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scales attractors in the neighborhood of high-codimension singularities. We detect a three-time scale bursting attractor in the universal unfolding of the winged cusp singularity and discuss the physiological relevance of the bifurcation and unfolding parameters in determining a physiological modulation of bursting. The results suggest generality and simplicity in the organizing role of the winged cusp singularity for the global dynamics of conductance based models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.7364v3-abstract-full').style.display = 'none'; document.getElementById('1305.7364v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 November, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2013. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1209.6445">arXiv:1209.6445</a> <span> [<a href="https://arxiv.org/pdf/1209.6445">pdf</a>, <a href="https://arxiv.org/ps/1209.6445">ps</a>, <a href="https://arxiv.org/format/1209.6445">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1371/journal.pcbi.1003040">10.1371/journal.pcbi.1003040 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A Balance Equation Determines a Switch in Neuronal Excitability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Seutin%2C+V">Vincent Seutin</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1209.6445v2-abstract-short" style="display: inline;"> We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.6445v2-abstract-full').style.display = 'inline'; document.getElementById('1209.6445v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1209.6445v2-abstract-full" style="display: none;"> We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.6445v2-abstract-full').style.display = 'none'; document.getElementById('1209.6445v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 September, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2012. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.5686">arXiv:1204.5686</a> <span> [<a href="https://arxiv.org/pdf/1204.5686">pdf</a>, <a href="https://arxiv.org/format/1204.5686">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> </div> </div> <p class="title is-5 mathjax"> An organizing center in a planar model of neuronal excitability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.5686v1-abstract-short" style="display: inline;"> The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.5686v1-abstract-full').style.display = 'inline'; document.getElementById('1204.5686v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.5686v1-abstract-full" style="display: none;"> The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.5686v1-abstract-full').style.display = 'none'; document.getElementById('1204.5686v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1112.2588">arXiv:1112.2588</a> <span> [<a href="https://arxiv.org/pdf/1112.2588">pdf</a>, <a href="https://arxiv.org/format/1112.2588">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neurons and Cognition">q-bio.NC</span> </div> </div> <p class="title is-5 mathjax"> A Novel Phase Portrait to Understand Neuronal Excitability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Franci%2C+A">Alessio Franci</a>, <a href="/search/math?searchtype=author&query=Drion%2C+G">Guillaume Drion</a>, <a href="/search/math?searchtype=author&query=Seutin%2C+V">Vincent Seutin</a>, <a href="/search/math?searchtype=author&query=Sepulchre%2C+R">Rodolphe Sepulchre</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1112.2588v1-abstract-short" style="display: inline;"> Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained the cor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.2588v1-abstract-full').style.display = 'inline'; document.getElementById('1112.2588v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1112.2588v1-abstract-full" style="display: none;"> Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained the core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of Fitzugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexication of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which the calcium conductance controls the two distinct firing modes of thalamocortical neurons. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.2588v1-abstract-full').style.display = 'none'; document.getElementById('1112.2588v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2011. </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> 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