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<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/2312.16525">arXiv:2312.16525</a> <span> [<a href="https://arxiv.org/pdf/2312.16525">pdf</a>, <a href="https://arxiv.org/format/2312.16525">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> Diagnosis of Small-world Bias in Random Graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Argyris%2C+G">Georgios Argyris</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="2312.16525v1-abstract-short" style="display: inline;"> Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now consider duplicating this network onto another paper with a slight bias-a fraction of its links (approximately 1/10) undergo rearrangement. If we shuffle the two paper… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.16525v1-abstract-full').style.display = 'inline'; document.getElementById('2312.16525v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.16525v1-abstract-full" style="display: none;"> Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now consider duplicating this network onto another paper with a slight bias-a fraction of its links (approximately 1/10) undergo rearrangement. If we shuffle the two papers, how can we distinguish the pure random graph from the biased one? Results: In response to this challenge, we propose a novel metric called Randomness Index (RI). The closer the metric to zero is, the higher degree of randomness in the graph. The RI can distinguish between dense small-world networks and dense random graphs; a distinction which is impossible by conventional small-world properties like clustering coefficient and average path length. To validate its effectiveness, we apply the RI to temporal correlation networks of stock indices. Our findings reveal a reduction in randomness during global economic recession periods. Conclusion: The RI emerges as a powerful metric capable of characterizing small-world topology, especially in scenarios where other network measures fail. Beyond its utility in network analysis, the RI is promising for change-point (anomaly) detection in dynamical systems studied by means of multivariate time series. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.16525v1-abstract-full').style.display = 'none'; document.getElementById('2312.16525v1-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 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/2206.15169">arXiv:2206.15169</a> <span> [<a href="https://arxiv.org/pdf/2206.15169">pdf</a>, <a href="https://arxiv.org/format/2206.15169">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Logic in Computer Science">cs.LO</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"> Minimization of Dynamical Systems over Monoids </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Argyris%2C+G">Georgios Argyris</a>, <a href="/search/cs?searchtype=author&query=Lafuente%2C+A+L">Alberto Lluch Lafuente</a>, <a href="/search/cs?searchtype=author&query=Robayo%2C+A+L">Alexander Leguizamon Robayo</a>, <a href="/search/cs?searchtype=author&query=Tribastone%2C+M">Mirco Tribastone</a>, <a href="/search/cs?searchtype=author&query=Tschaikowski%2C+M">Max Tschaikowski</a>, <a href="/search/cs?searchtype=author&query=Vandin%2C+A">Andrea Vandin</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="2206.15169v3-abstract-short" style="display: inline;"> Quantitative notions of bisimulation are well-known tools for the minimization of dynamical models such as Markov chains and ordinary differential equations (ODEs). In \emph{forward bisimulations}, each state in the quotient model represents an equivalence class and the dynamical evolution gives the overall sum of its members in the original model. Here we introduce generalized forward bisimulatio… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.15169v3-abstract-full').style.display = 'inline'; document.getElementById('2206.15169v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.15169v3-abstract-full" style="display: none;"> Quantitative notions of bisimulation are well-known tools for the minimization of dynamical models such as Markov chains and ordinary differential equations (ODEs). In \emph{forward bisimulations}, each state in the quotient model represents an equivalence class and the dynamical evolution gives the overall sum of its members in the original model. Here we introduce generalized forward bisimulation (GFB) for dynamical systems over commutative monoids and develop a partition refinement algorithm to compute the coarsest one. When the monoid is $(\mathbb{R}, +)$, we recover probabilistic bisimulation for Markov chains and more recent forward bisimulations for nonlinear ODEs. Using $(\mathbb{R}, \cdot)$ we get nonlinear reductions for discrete-time dynamical systems and ODEs where each variable in the quotient model represents the product of original variables in the equivalence class. When the domain is a finite set such as the Booleans $\mathbb{B}$, we can apply GFB to Boolean networks (BN), a widely used dynamical model in computational biology. Using a prototype implementation of our minimization algorithm for GFB, we find disjunction- and conjunction-preserving reductions on 60 BN from two well-known repositories, and demonstrate the obtained analysis speed-ups. We also provide the biological interpretation of the reduction obtained for two selected BN, and we show how GFB enables the analysis of a large one that could not be analyzed otherwise. Using a randomized version of our algorithm we find product-preserving (therefore non-linear) reductions on 21 dynamical weighted networks from the literature that could not be handled by the exact algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.15169v3-abstract-full').style.display = 'none'; document.getElementById('2206.15169v3-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 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 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">Accepted at Thirty-Eighth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2023</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.15476">arXiv:2106.15476</a> <span> [<a href="https://arxiv.org/pdf/2106.15476">pdf</a>, <a href="https://arxiv.org/format/2106.15476">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computational Engineering, Finance, and Science">cs.CE</span> </div> </div> <p class="title is-5 mathjax"> Reducing Boolean Networks with Backward Boolean Equivalence </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Argyris%2C+G">Georgios Argyris</a>, <a href="/search/cs?searchtype=author&query=Lafuente%2C+A+L">Alberto Lluch Lafuente</a>, <a href="/search/cs?searchtype=author&query=Tribastone%2C+M">Mirco Tribastone</a>, <a href="/search/cs?searchtype=author&query=Tschaikowski%2C+M">Max Tschaikowski</a>, <a href="/search/cs?searchtype=author&query=Vandin%2C+A">Andrea Vandin</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="2106.15476v2-abstract-short" style="display: inline;"> Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium to large BNs due to the state-space explosion problem. We propose a novel reduction technique called \emph{Backward Boolean Equivalence} (BBE), which preserves some properties of interest of BNs. In particular, reduced BNs provide a compact representation b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.15476v2-abstract-full').style.display = 'inline'; document.getElementById('2106.15476v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.15476v2-abstract-full" style="display: none;"> Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium to large BNs due to the state-space explosion problem. We propose a novel reduction technique called \emph{Backward Boolean Equivalence} (BBE), which preserves some properties of interest of BNs. In particular, reduced BNs provide a compact representation by grouping variables that, if initialized equally, are always updated equally. The resulting reduced state space is a subset of the original one, restricted to identical initialization of grouped variables. The corresponding trajectories of the original BN can be exactly restored. We show the effectiveness of BBE by performing a large-scale validation on the whole GINsim BN repository. In selected cases, we show how our method enables analyses that would be otherwise intractable. Our method complements, and can be combined with, other reduction methods found in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.15476v2-abstract-full').style.display = 'none'; document.getElementById('2106.15476v2-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 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </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"> <div 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