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u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_13866338" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/13866338" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="38d5441bd19c68f04b0317db633aeff3" rel="nofollow" data-download="{"attachment_id":44862702,"asset_id":13866338,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/44862702/download_file?st=MTczMjQ0NjM4OSw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="32952593" href="https://unige-it1.academia.edu/EnricoPuppo">Enrico Puppo</a><script data-card-contents-for-user="32952593" type="text/json">{"id":32952593,"first_name":"Enrico","last_name":"Puppo","domain_name":"unige-it1","page_name":"EnricoPuppo","display_name":"Enrico Puppo","profile_url":"https://unige-it1.academia.edu/EnricoPuppo?f_ri=132593","photo":"/images/s65_no_pic.png"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-13866338">+1</span><div class="hidden js-additional-users-13866338"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/LeilaFloriani">Leila Floriani</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-13866338'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-13866338').html(); 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Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform","downloadable_attachments":[{"id":44862702,"asset_id":13866338,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":32952593,"first_name":"Enrico","last_name":"Puppo","domain_name":"unige-it1","page_name":"EnricoPuppo","display_name":"Enrico Puppo","profile_url":"https://unige-it1.academia.edu/EnricoPuppo?f_ri=132593","photo":"/images/s65_no_pic.png"},{"id":32771595,"first_name":"Leila","last_name":"Floriani","domain_name":"independent","page_name":"LeilaFloriani","display_name":"Leila Floriani","profile_url":"https://independent.academia.edu/LeilaFloriani?f_ri=132593","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":30718,"name":"Level Of Detail (LOD)","url":"https://www.academia.edu/Documents/in/Level_Of_Detail_LOD_?f_ri=132593","nofollow":false},{"id":132593,"name":"Piecewise Linear","url":"https://www.academia.edu/Documents/in/Piecewise_Linear?f_ri=132593","nofollow":false},{"id":993289,"name":"Multi Resolution Transform","url":"https://www.academia.edu/Documents/in/Multi_Resolution_Transform?f_ri=132593","nofollow":false},{"id":1268803,"name":"Terrain Modeling","url":"https://www.academia.edu/Documents/in/Terrain_Modeling?f_ri=132593","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_19060911" data-work_id="19060911" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/19060911/Marginal_rates_and_two_dimensional_level_curves_in_DEA">Marginal rates and two-dimensional level curves in DEA</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/19060911" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a932aaae830eb49baa855e89dab2f18b" rel="nofollow" data-download="{"attachment_id":40408767,"asset_id":19060911,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/40408767/download_file?st=MTczMjQ0NjM4OSw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="39232486" href="https://independent.academia.edu/DanRosen6">Dan Rosen</a><script data-card-contents-for-user="39232486" type="text/json">{"id":39232486,"first_name":"Dan","last_name":"Rosen","domain_name":"independent","page_name":"DanRosen6","display_name":"Dan Rosen","profile_url":"https://independent.academia.edu/DanRosen6?f_ri=132593","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_19060911 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="19060911"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 19060911, container: ".js-paper-rank-work_19060911", }); 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We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_8089979" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/8089979" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="764ed5db43451bb30fec2609d3f2b905" rel="nofollow" data-download="{"attachment_id":34540335,"asset_id":8089979,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/34540335/download_file?st=MTczMjQ0NjM4OSw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="15654611" href="https://vnu-vn.academia.edu/NgocMaiTran">Ngoc Mai Tran</a><script data-card-contents-for-user="15654611" type="text/json">{"id":15654611,"first_name":"Ngoc Mai","last_name":"Tran","domain_name":"vnu-vn","page_name":"NgocMaiTran","display_name":"Ngoc Mai Tran","profile_url":"https://vnu-vn.academia.edu/NgocMaiTran?f_ri=132593","photo":"https://0.academia-photos.com/15654611/4229910/4922629/s65_ngoc_mai.tran.jpg"}</script></span></span></li><li class="js-paper-rank-work_8089979 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="8089979"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 8089979, container: ".js-paper-rank-work_8089979", }); 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We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.","downloadable_attachments":[{"id":34540335,"asset_id":8089979,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":15654611,"first_name":"Ngoc Mai","last_name":"Tran","domain_name":"vnu-vn","page_name":"NgocMaiTran","display_name":"Ngoc Mai Tran","profile_url":"https://vnu-vn.academia.edu/NgocMaiTran?f_ri=132593","photo":"https://0.academia-photos.com/15654611/4229910/4922629/s65_ngoc_mai.tran.jpg"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=132593","nofollow":false},{"id":37345,"name":"Discrete Mathematics","url":"https://www.academia.edu/Documents/in/Discrete_Mathematics?f_ri=132593","nofollow":false},{"id":132593,"name":"Piecewise 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The objective is to propose a dynamical gradient neural network, which employs a penalty function approach with time varying coefficients for the solution of the problem which is known to be NP-hard. After the appropriate energy function was constructed, the dynamics are defined by steepest gradient descent on the energy function. The proposed neural network system is composed of two maximum neural networks, three piecewise linear and one log-sigmoid network all of which interact with each other. The motivation for using maximum networks is to reduce the network complexity and to obtain a simplified energy function. To overcome the tradeoff problem encountered in using the penalty function approach, a time varying penalty coefficient methodology is proposed to be used during simulation experiments. Simulation results of the proposed approach on a scheduling problem indicate that the proposed coupled network yields an optimal solution which makes it attractive for applications of larger sized problems.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/3091495" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="09953720ddb663cec16aebb2a7119e74" rel="nofollow" data-download="{"attachment_id":50470247,"asset_id":3091495,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/50470247/download_file?st=MTczMjQ0NjM4OSw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="3554126" href="https://independent.academia.edu/AnastasiaNizikova">Anastasia Nizikova</a><script data-card-contents-for-user="3554126" type="text/json">{"id":3554126,"first_name":"Anastasia","last_name":"Nizikova","domain_name":"independent","page_name":"AnastasiaNizikova","display_name":"Anastasia Nizikova","profile_url":"https://independent.academia.edu/AnastasiaNizikova?f_ri=132593","photo":"https://0.academia-photos.com/3554126/1227180/1533941/s65_anastasia.nizikova.jpg"}</script></span></span></li><li class="js-paper-rank-work_3091495 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="3091495"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 3091495, container: ".js-paper-rank-work_3091495", }); 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The objective is to propose a dynamical gradient neural network, which employs a penalty function approach with time varying coefficients for the solution of the problem which is known to be NP-hard. After the appropriate energy function was constructed, the dynamics are defined by steepest gradient descent on the energy function. The proposed neural network system is composed of two maximum neural networks, three piecewise linear and one log-sigmoid network all of which interact with each other. The motivation for using maximum networks is to reduce the network complexity and to obtain a simplified energy function. To overcome the tradeoff problem encountered in using the penalty function approach, a time varying penalty coefficient methodology is proposed to be used during simulation experiments. Simulation results of the proposed approach on a scheduling problem indicate that the proposed coupled network yields an optimal solution which makes it attractive for applications of larger sized problems.","downloadable_attachments":[{"id":50470247,"asset_id":3091495,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":3554126,"first_name":"Anastasia","last_name":"Nizikova","domain_name":"independent","page_name":"AnastasiaNizikova","display_name":"Anastasia Nizikova","profile_url":"https://independent.academia.edu/AnastasiaNizikova?f_ri=132593","photo":"https://0.academia-photos.com/3554126/1227180/1533941/s65_anastasia.nizikova.jpg"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering?f_ri=132593","nofollow":false},{"id":26066,"name":"Neural Network","url":"https://www.academia.edu/Documents/in/Neural_Network?f_ri=132593","nofollow":false},{"id":80414,"name":"Mathematical 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Linear","url":"https://www.academia.edu/Documents/in/Piecewise_Linear?f_ri=132593","nofollow":false},{"id":181850,"name":"Approximation","url":"https://www.academia.edu/Documents/in/Approximation?f_ri=132593","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33558384 coauthored" data-work_id="33558384" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/33558384/A_digital_implementation_of_2D_Hindmarsh_Rose_neuron">A digital implementation of 2D Hindmarsh--Rose neuron</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Different architectures and techniques have developed in the neuromorphic field to mimic and investigate the activity of biological neural networks. This paper presents a set of piece-wise linear approximations of a two-dimensional... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_33558384" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Different architectures and techniques have developed in the neuromorphic field to mimic and investigate the activity of biological neural networks. This paper presents a set of piece-wise linear approximations of a two-dimensional Hindmarsh--Rose neuron model for digital circuit implementation to achieve higher speeds and lower hardware costs in large-scale implementation of the biological neural networks. The performance of the model was evaluated with a time domain signal error. Synthesis and hardware implementation on a field-programmable gate array, as a proof of concept, indicates that the proposed model reproduces several neuronal behaviors similar to the original model with higher performance and considerably lower implementation costs.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/33558384" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="513fbebd22c795936ed5fba91788c0b7" rel="nofollow" data-download="{"attachment_id":53585133,"asset_id":33558384,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/53585133/download_file?st=MTczMjQ0NjM4OSw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="3665866" href="https://uwindsor.academia.edu/MoslemHeidarpur">Moslem Heidarpur</a><script data-card-contents-for-user="3665866" type="text/json">{"id":3665866,"first_name":"Moslem","last_name":"Heidarpur","domain_name":"uwindsor","page_name":"MoslemHeidarpur","display_name":"Moslem Heidarpur","profile_url":"https://uwindsor.academia.edu/MoslemHeidarpur?f_ri=132593","photo":"https://0.academia-photos.com/3665866/11890984/13251172/s65_mslm.hdpr.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-33558384">+2</span><div class="hidden js-additional-users-33558384"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://carleton-ca.academia.edu/ArashAhmadi">Arash Ahmadi</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/NabeehKandalaft">Nabeeh Kandalaft</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-33558384'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-33558384').html(); 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This paper presents a set of piece-wise linear approximations of a two-dimensional Hindmarsh--Rose neuron model for digital circuit implementation to achieve higher speeds and lower hardware costs in large-scale implementation of the biological neural networks. The performance of the model was evaluated with a time domain signal error. Synthesis and hardware implementation on a field-programmable gate array, as a proof of concept, indicates that the proposed model reproduces several neuronal behaviors similar to the original model with higher performance and considerably lower implementation costs.","downloadable_attachments":[{"id":53585133,"asset_id":33558384,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":3665866,"first_name":"Moslem","last_name":"Heidarpur","domain_name":"uwindsor","page_name":"MoslemHeidarpur","display_name":"Moslem Heidarpur","profile_url":"https://uwindsor.academia.edu/MoslemHeidarpur?f_ri=132593","photo":"https://0.academia-photos.com/3665866/11890984/13251172/s65_mslm.hdpr.jpg"},{"id":1838194,"first_name":"Arash","last_name":"Ahmadi","domain_name":"carleton-ca","page_name":"ArashAhmadi","display_name":"Arash 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u-mb0x js-work-card work_1617017 coauthored" data-work_id="1617017" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/1617017/Integrating_a_Piecewise_Linear_Representation_Method_and_a_Neural_Network_Model_for_Stock_Trading_Points_Prediction">Integrating a Piecewise Linear Representation Method and a Neural Network Model for Stock Trading Points Prediction</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Recently, the piecewise linear representation (PLR) method has been applied to the stock market for pattern matching. As such, similar patterns can be retrieved from historical data and future prices of the stock can be predicted... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_1617017" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Recently, the piecewise linear representation (PLR) method has been applied to the stock market for pattern matching. As such, similar patterns can be retrieved from historical data and future prices of the stock can be predicted according to the patterns retrieved. In this paper, a different approach is taken by applying PLR to decompose historical data into different segments. As a result, temporary turning points (trough or peak) of the historical stock data can be detected and inputted to the backpropagation neural network (BPN) for supervised training of the model. After this, a new set of test data can trigger the model when a buy or sell point is detected by BPN. An intelligent PLR (IPLR) model is further developed by integrating the genetic algorithm with the PLR to iteratively improve the threshold value of the PLR. Thus, it further increases the profitability of the model. The proposed system is tested on three different types of stocks, i.e., uptrend, steady, and downtrend. The experimental results show that the IPLR approach can make significant amounts of profit on stocks with different variations. In conclusion, the proposed system is very effective and encouraging in that it predicts the future trading points of a specific stock.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/1617017" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="4b7cfb51338baffcb3fcf1404f706ed9" rel="nofollow" data-download="{"attachment_id":15953224,"asset_id":1617017,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/15953224/download_file?st=MTczMjQ0NjM5MCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="564288" href="https://yzu.academia.edu/peichannchang">pei-chann chang</a><script data-card-contents-for-user="564288" type="text/json">{"id":564288,"first_name":"pei-chann","last_name":"chang","domain_name":"yzu","page_name":"peichannchang","display_name":"pei-chann chang","profile_url":"https://yzu.academia.edu/peichannchang?f_ri=132593","photo":"https://0.academia-photos.com/564288/1533531/1863022/s65_pei-chann.chang.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-1617017">+2</span><div class="hidden js-additional-users-1617017"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://yzu.academia.edu/ChinFan">Chin-YUAN Fan</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/ChenhaoLiu">Chen-hao Liu</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-1617017'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-1617017').html(); 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As such, similar patterns can be retrieved from historical data and future prices of the stock can be predicted according to the patterns retrieved. In this paper, a different approach is taken by applying PLR to decompose historical data into different segments. As a result, temporary turning points (trough or peak) of the historical stock data can be detected and inputted to the backpropagation neural network (BPN) for supervised training of the model. After this, a new set of test data can trigger the model when a buy or sell point is detected by BPN. An intelligent PLR (IPLR) model is further developed by integrating the genetic algorithm with the PLR to iteratively improve the threshold value of the PLR. Thus, it further increases the profitability of the model. The proposed system is tested on three different types of stocks, i.e., uptrend, steady, and downtrend. The experimental results show that the IPLR approach can make significant amounts of profit on stocks with different variations. In conclusion, the proposed system is very effective and encouraging in that it predicts the future trading points of a specific stock.","downloadable_attachments":[{"id":15953224,"asset_id":1617017,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":564288,"first_name":"pei-chann","last_name":"chang","domain_name":"yzu","page_name":"peichannchang","display_name":"pei-chann chang","profile_url":"https://yzu.academia.edu/peichannchang?f_ri=132593","photo":"https://0.academia-photos.com/564288/1533531/1863022/s65_pei-chann.chang.jpg"},{"id":38938139,"first_name":"Chin-YUAN","last_name":"Fan","domain_name":"yzu","page_name":"ChinFan","display_name":"Chin-YUAN Fan","profile_url":"https://yzu.academia.edu/ChinFan?f_ri=132593","photo":"https://0.academia-photos.com/38938139/13555820/14728792/s65_chin.fan.jpg"},{"id":50891135,"first_name":"Chen-hao","last_name":"Liu","domain_name":"independent","page_name":"ChenhaoLiu","display_name":"Chen-hao 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u-pv7x u-mb0x js-work-card work_21440159" data-work_id="21440159" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/21440159/Teaching_Introduction_to_electrical_and_computer_engineering_in_context">Teaching "Introduction to electrical and computer engineering" in context</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/21440159" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a 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js-work-link" href="https://www.academia.edu/8875795/Characterizing_Convexity_of_a_Function_by_Its_Fr%C3%A9chet_and_Limiting_Second_Order_Subdifferentials">Characterizing Convexity of a Function by Its Fréchet and Limiting Second-Order Subdifferentials</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The Fréchet and limiting second-order subdifferentials of a proper lower semicontinuous convex function $\varphi: \mathbb R^n\rightarrow\bar{\mathbb R}$ have a property called the positive semi-definiteness (PSD)—in analogy with the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_8875795" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The Fréchet and limiting second-order subdifferentials of a proper lower semicontinuous convex function $\varphi: \mathbb R^n\rightarrow\bar{\mathbb R}$ have a property called the positive semi-definiteness (PSD)—in analogy with the notion of positive semi-definiteness of symmetric real matrices. In general, the PSD is insufficient for ensuring the convexity of an arbitrary lower semicontinuous function φ. However, if φ is a C 1,1 function then the PSD property of one of the second-order subdifferentials is a complete characterization of the convexity of φ. The same assertion is valid for C 1 functions of one variable. The limiting second-order subdifferential can recognize the convexity/nonconvexity of piecewise linear functions and of separable piecewise C 2 functions, while its Fréchet counterpart cannot.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/8875795" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="97a41ddd14abb502ae13f34a53ef1b86" rel="nofollow" data-download="{"attachment_id":47970102,"asset_id":8875795,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/47970102/download_file?st=MTczMjQ0NjM5MCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="19452113" href="https://icst-vn.academia.edu/DoanChieu">Doan Chieu</a><script data-card-contents-for-user="19452113" type="text/json">{"id":19452113,"first_name":"Doan","last_name":"Chieu","domain_name":"icst-vn","page_name":"DoanChieu","display_name":"Doan Chieu","profile_url":"https://icst-vn.academia.edu/DoanChieu?f_ri=132593","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_8875795 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="8875795"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 8875795, container: ".js-paper-rank-work_8875795", }); 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In general, the PSD is insufficient for ensuring the convexity of an arbitrary lower semicontinuous function φ. However, if φ is a C 1,1 function then the PSD property of one of the second-order subdifferentials is a complete characterization of the convexity of φ. The same assertion is valid for C 1 functions of one variable. The limiting second-order subdifferential can recognize the convexity/nonconvexity of piecewise linear functions and of separable piecewise C 2 functions, while its Fréchet counterpart cannot.","downloadable_attachments":[{"id":47970102,"asset_id":8875795,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":19452113,"first_name":"Doan","last_name":"Chieu","domain_name":"icst-vn","page_name":"DoanChieu","display_name":"Doan Chieu","profile_url":"https://icst-vn.academia.edu/DoanChieu?f_ri=132593","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=132593","nofollow":false},{"id":132593,"name":"Piecewise Linear","url":"https://www.academia.edu/Documents/in/Piecewise_Linear?f_ri=132593","nofollow":false},{"id":347272,"name":"Second Order","url":"https://www.academia.edu/Documents/in/Second_Order?f_ri=132593","nofollow":false}]}, }) } 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href="https://www.academia.edu/20872225/Tangential_thickness_of_manifolds">Tangential thickness of manifolds</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_20872225" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently large dimension are isomorphic in the given category. This paper studies such questions when the dimensions of the Euclidean space do not satisfy such a condition, mainly for topological manifolds homotopy equivalent to lens spaces with odd prime order fundamental groups. In particular, complete information is obtained for homotopy lens spaces in most dimensions when the Euclidean space is even dimensional. The proofs use basic techniques from surgery theory and a variety of results from homotopy theory, including results of Cohen, Moore and Neisendorfer related to finite exponents of certain unstable homotopy groups.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/20872225" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="7b9b34c5ea9d4168cad4acf8fac978d5" rel="nofollow" data-download="{"attachment_id":41607520,"asset_id":20872225,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/41607520/download_file?st=MTczMjQ0NjM5MCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="23625315" href="https://ucriverside.academia.edu/ReinhardSchultz">Reinhard Schultz</a><script data-card-contents-for-user="23625315" type="text/json">{"id":23625315,"first_name":"Reinhard","last_name":"Schultz","domain_name":"ucriverside","page_name":"ReinhardSchultz","display_name":"Reinhard Schultz","profile_url":"https://ucriverside.academia.edu/ReinhardSchultz?f_ri=132593","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_20872225 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="20872225"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 20872225, container: ".js-paper-rank-work_20872225", }); 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