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u-fw700 u-mr5x u-pr5x u-borderColorGrayLight u-borderRight1"><a href="https://cityu-hk.academia.edu/"><span class="u-linkUnstyled u-tcGrayDarkest">City University of Hong Kong</span></a></span><h1 class="u-m0x u-fw300 u-fs24 u-displayInline">School of Data Science</h1></div><div class="u-floatRight u-mt1x"></div></div></div></div></div><div class="TabbedNavigation"><div class="container"><div class="row"><div class="col-xs-12 clearfix"><ul class="nav u-m0x u-p0x list-inline"><li class="u-floatLeft u-pr5x u-mr5x u-borderColorGrayLight u-borderRight1"><a href="https://cityu-hk.academia.edu/"><span><i class="fa fa-arrow-left"></i>  All Departments</span></a></li><li class="u-floatLeft active"><a href="https://cityu-hk.academia.edu/Departments/School_of_Data_Science/Documents">10 Papers</a></li><li class="u-floatLeft"><a href="https://cityu-hk.academia.edu/Departments/School_of_Data_Science">47 Researchers</a></li></ul></div></div></div></div><div class="container"><div class="row"><div 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})();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_113508252" data-work_id="113508252" 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/113508252/Estimating_the_most_probable_transition_time_for_stochastic_dynamical_systems">Estimating the most probable transition time for stochastic dynamical systems</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems with non-vanishing Brownian noise. Instead of minimizing the Onsager–Machlup action functional, we... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_113508252" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems with non-vanishing Brownian noise. Instead of minimizing the Onsager–Machlup action functional, we examine the maximum probability that the solution process of the system stays in a neighbourhood (or a tube) of a transition path, in order to characterize the most probable transition path. We first establish the exponential decay lower bound and a power law decay upper bound for the maximum of this probability. Based on these estimates, we further derive the lower and upper bounds for the most probable transition time, under suitable conditions. Finally, we illustrate our results in simple stochastic dynamical systems, and highlight the relation with some relevant works.</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/113508252" 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="1536d0f227ac9396e8294a77497dce73" rel="nofollow" data-download="{"attachment_id":110449596,"asset_id":113508252,"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/110449596/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&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="280720005" href="https://cityu-hk.academia.edu/YuanfeiHuang">Yuanfei Huang</a><script data-card-contents-for-user="280720005" type="text/json">{"id":280720005,"first_name":"Yuanfei","last_name":"Huang","domain_name":"cityu-hk","page_name":"YuanfeiHuang","display_name":"Yuanfei Huang","profile_url":"https://cityu-hk.academia.edu/YuanfeiHuang","photo":"https://0.academia-photos.com/280720005/129046720/118444638/s65_yuanfei.huang.png"}</script></span></span></li><li class="js-paper-rank-work_113508252 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="113508252"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 113508252, container: ".js-paper-rank-work_113508252", }); 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Instead of minimizing the Onsager–Machlup action functional, we examine the maximum probability that the solution process of the system stays in a neighbourhood (or a tube) of a transition path, in order to characterize the most probable transition path. We first establish the exponential decay lower bound and a power law decay upper bound for the maximum of this probability. Based on these estimates, we further derive the lower and upper bounds for the most probable transition time, under suitable conditions. Finally, we illustrate our results in simple stochastic dynamical systems, and highlight the relation with some relevant works.","publication":"Nonlinearity","publication_with_fallback":"Nonlinearity","downloadable_attachments":[{"id":110449596,"asset_id":113508252,"asset_type":"Work","always_allow_download":false,"scribd_thumbnail_url":"https://attachments.academia-assets.com/110449596/thumbnails/1.jpg","download_url":"https://d1wqtxts1xzle7.cloudfront.net/110449596/2006.10979v1-libre.pdf?1705305117=\u0026response-content-disposition=attachment%3B+filename%3DEstimating_the_most_probable_transition.pdf\u0026Expires=1732672157\u0026Signature=IFW-zZgdhR2lMykUwExH6yGiKWHriAS-EjKdxosnAw9xwJkPS3jTZd6L1E7mVZmaH8b-ElBEArs-odhRf~gTAlMbImnnOlNp1ACyGVauSs-ct3so-834wHkOJw~9UC8Dp~wBJzpjw4hafpy6hFyOn17r-kEorqHgTwEa~tMlB5KgixWb-azkVZayGssiKl7rjJeSfh-af0B9GzxA1JYBuCWo95j5adR1yWW12LXVPaAISCHKr5wjmg~uAVqM94AeAhdCjpCD7F6j3sW3Bsg5M52ev7N2MyJuIZb3FTz2DYAEC~tY5rhoGFBeK2HbHZWy4q13B8pPgRDEp4B1RJ0Eng__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA","download_file_url":"https://www.academia.edu/attachments/110449596/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&","full_thumbnail_url":"https://0.academia-photos.com/attachment_thumbnails/110449596/mini_magick20240115-1-atwisv.png?1705300924"}],"downloadable_attachments_with_full_thumbnails":[{"id":110449596,"asset_id":113508252,"asset_type":"Work","always_allow_download":false,"scribd_thumbnail_url":"https://attachments.academia-assets.com/110449596/thumbnails/1.jpg","download_url":"https://d1wqtxts1xzle7.cloudfront.net/110449596/2006.10979v1-libre.pdf?1705305117=\u0026response-content-disposition=attachment%3B+filename%3DEstimating_the_most_probable_transition.pdf\u0026Expires=1732672157\u0026Signature=IFW-zZgdhR2lMykUwExH6yGiKWHriAS-EjKdxosnAw9xwJkPS3jTZd6L1E7mVZmaH8b-ElBEArs-odhRf~gTAlMbImnnOlNp1ACyGVauSs-ct3so-834wHkOJw~9UC8Dp~wBJzpjw4hafpy6hFyOn17r-kEorqHgTwEa~tMlB5KgixWb-azkVZayGssiKl7rjJeSfh-af0B9GzxA1JYBuCWo95j5adR1yWW12LXVPaAISCHKr5wjmg~uAVqM94AeAhdCjpCD7F6j3sW3Bsg5M52ev7N2MyJuIZb3FTz2DYAEC~tY5rhoGFBeK2HbHZWy4q13B8pPgRDEp4B1RJ0Eng__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA","download_file_url":"https://www.academia.edu/attachments/110449596/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&","full_thumbnail_url":"https://0.academia-photos.com/attachment_thumbnails/110449596/mini_magick20240115-1-atwisv.png?1705300924"}],"has_pdf":true,"has_fulltext":true,"page_count":28,"ordered_authors":[{"id":280720005,"first_name":"Yuanfei","last_name":"Huang","domain_name":"cityu-hk","page_name":"YuanfeiHuang","display_name":"Yuanfei Huang","profile_url":"https://cityu-hk.academia.edu/YuanfeiHuang","photo":"https://0.academia-photos.com/280720005/129046720/118444638/s65_yuanfei.huang.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics","nofollow":false},{"id":16460,"name":"Statistical Physics","url":"https://www.academia.edu/Documents/in/Statistical_Physics","nofollow":false},{"id":136128,"name":"Brownian Motion","url":"https://www.academia.edu/Documents/in/Brownian_Motion"},{"id":228362,"name":"Stochastic differential equation","url":"https://www.academia.edu/Documents/in/Stochastic_differential_equation"},{"id":779767,"name":"Nonlinearity","url":"https://www.academia.edu/Documents/in/Nonlinearity"}],"publication_year":2021,"publication_year_with_fallback":2021,"paper_rank":null,"all_time_views":0,"active_discussion":{}}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_113508279" data-work_id="113508279" 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/113508279/Modelling_brain_wide_neuronal_morphology_via_rooted_Cayley_trees">Modelling brain-wide neuronal morphology via rooted Cayley trees</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_113508279" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.</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/113508279" 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="78c087e744060a01008fbce03453770f" rel="nofollow" data-download="{"attachment_id":110449592,"asset_id":113508279,"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/110449592/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&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="280720005" href="https://cityu-hk.academia.edu/YuanfeiHuang">Yuanfei Huang</a><script data-card-contents-for-user="280720005" type="text/json">{"id":280720005,"first_name":"Yuanfei","last_name":"Huang","domain_name":"cityu-hk","page_name":"YuanfeiHuang","display_name":"Yuanfei Huang","profile_url":"https://cityu-hk.academia.edu/YuanfeiHuang","photo":"https://0.academia-photos.com/280720005/129046720/118444638/s65_yuanfei.huang.png"}</script></span></span></li><li class="js-paper-rank-work_113508279 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="113508279"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 113508279, container: ".js-paper-rank-work_113508279", }); 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$(".js-view-count[data-work-id=113508279]").text(description); $(".js-view-count-work_113508279").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_113508279").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="113508279"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="161" href="https://www.academia.edu/Documents/in/Neuroscience">Neuroscience</a>, <script data-card-contents-for-ri="161" type="text/json">{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="7710" href="https://www.academia.edu/Documents/in/Biology">Biology</a>, <script data-card-contents-for-ri="7710" type="text/json">{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="26327" href="https://www.academia.edu/Documents/in/Medicine">Medicine</a><script data-card-contents-for-ri="26327" type="text/json">{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=113508279]'), work: {"id":113508279,"title":"Modelling brain-wide neuronal morphology via rooted Cayley trees","created_at":"2024-01-14T22:41:13.343-08:00","owner_id":280720005,"url":"https://www.academia.edu/113508279/Modelling_brain_wide_neuronal_morphology_via_rooted_Cayley_trees","slug":"Modelling_brain_wide_neuronal_morphology_via_rooted_Cayley_trees","dom_id":"work_113508279","summary":"Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.","publication":"Scientific Reports","publication_with_fallback":"Scientific Reports","downloadable_attachments":[{"id":110449592,"asset_id":113508279,"asset_type":"Work","always_allow_download":false,"scribd_thumbnail_url":"https://attachments.academia-assets.com/110449592/thumbnails/1.jpg","download_url":"https://d1wqtxts1xzle7.cloudfront.net/110449592/s41598-018-34050-1-libre.pdf?1705305126=\u0026response-content-disposition=attachment%3B+filename%3DModelling_brain_wide_neuronal_morphology.pdf\u0026Expires=1732672157\u0026Signature=YRLVxBr15aMp3aMy1WC9Cry~D1EprRGoycRSYB9PLWDHnDWSoTuBJu7OMZJE0jePRH2k6H9tYj0Fh~a7jo2U3TN9wYGSOPK-64s4caqgCrD6TIF-fV7iNd8zjXIRxrVOC4rbok6LYEpFrCScfeRcZ8AqnOkk5b2V~V1sSYv2kOEsxdk-kOreRcSyZC~BTqsbmnYmEZFSUuHaRjzwgOJicVw7wLnNUlxSZiFMZanVW49mX4p~WyJz9qIZkz-IpWHIP2LyAPF80mdZrbejRbyoZBmWSP3QJzHuvdNblBOGYQcQlZiNbbYkr1TwzirnnDWRe4daPzHfHtPOgtpCnRReow__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA","download_file_url":"https://www.academia.edu/attachments/110449592/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&","full_thumbnail_url":"https://0.academia-photos.com/attachment_thumbnails/110449592/mini_magick20240115-1-rnolq5.png?1705300918"}],"downloadable_attachments_with_full_thumbnails":[{"id":110449592,"asset_id":113508279,"asset_type":"Work","always_allow_download":false,"scribd_thumbnail_url":"https://attachments.academia-assets.com/110449592/thumbnails/1.jpg","download_url":"https://d1wqtxts1xzle7.cloudfront.net/110449592/s41598-018-34050-1-libre.pdf?1705305126=\u0026response-content-disposition=attachment%3B+filename%3DModelling_brain_wide_neuronal_morphology.pdf\u0026Expires=1732672157\u0026Signature=YRLVxBr15aMp3aMy1WC9Cry~D1EprRGoycRSYB9PLWDHnDWSoTuBJu7OMZJE0jePRH2k6H9tYj0Fh~a7jo2U3TN9wYGSOPK-64s4caqgCrD6TIF-fV7iNd8zjXIRxrVOC4rbok6LYEpFrCScfeRcZ8AqnOkk5b2V~V1sSYv2kOEsxdk-kOreRcSyZC~BTqsbmnYmEZFSUuHaRjzwgOJicVw7wLnNUlxSZiFMZanVW49mX4p~WyJz9qIZkz-IpWHIP2LyAPF80mdZrbejRbyoZBmWSP3QJzHuvdNblBOGYQcQlZiNbbYkr1TwzirnnDWRe4daPzHfHtPOgtpCnRReow__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA","download_file_url":"https://www.academia.edu/attachments/110449592/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&","full_thumbnail_url":"https://0.academia-photos.com/attachment_thumbnails/110449592/mini_magick20240115-1-rnolq5.png?1705300918"}],"has_pdf":true,"has_fulltext":true,"page_count":10,"ordered_authors":[{"id":280720005,"first_name":"Yuanfei","last_name":"Huang","domain_name":"cityu-hk","page_name":"YuanfeiHuang","display_name":"Yuanfei Huang","profile_url":"https://cityu-hk.academia.edu/YuanfeiHuang","photo":"https://0.academia-photos.com/280720005/129046720/118444638/s65_yuanfei.huang.png"}],"research_interests":[{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience","nofollow":false},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics","nofollow":false},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology","nofollow":false},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine","nofollow":false},{"id":85916,"name":"Theoretical Morphology (in Biology)","url":"https://www.academia.edu/Documents/in/Theoretical_Morphology_in_Biology_"},{"id":473565,"name":"Neuron","url":"https://www.academia.edu/Documents/in/Neuron"}],"publication_year":2018,"publication_year_with_fallback":2018,"paper_rank":null,"all_time_views":2,"active_discussion":{}}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_63319793" data-work_id="63319793" 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/63319793/Restatement_and_Question_Generation_for_Counsellor_Chatbot">Restatement and Question Generation for Counsellor Chatbot</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Amidst rising mental health needs in society, virtual agents are increasingly deployed in counselling. In order to give pertinent advice, counsellors must first gain an understanding of the issues at hand by eliciting sharing from the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_63319793" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Amidst rising mental health needs in society, virtual agents are increasingly deployed in counselling. In order to give pertinent advice, counsellors must first gain an understanding of the issues at hand by eliciting sharing from the counsellee. It is thus important for the counsellor chatbot to encourage the user to open up and talk. One way to sustain the conversation flow is to acknowledge the counsellee’s key points by restating them, or probing them further with questions. This paper applies models from two closely related NLP tasks — summarization and question generation — to restatement and question generation in the counselling context. We conducted experiments on a manually annotated dataset of Cantonese post-reply pairs on topics related to loneliness, academic anxiety and test anxiety. We obtained the best performance in both restatement and question generation by fine-tuning BertSum, a state-of-the-art summarization model, with the in-domain manual dataset augmented wit...</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/63319793" 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="ea998140a1e8c5caea797338c7664673" rel="nofollow" data-download="{"attachment_id":75789734,"asset_id":63319793,"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/75789734/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&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="124326311" href="https://cityu-hk.academia.edu/BaikunLiang">Baikun Liang</a><script data-card-contents-for-user="124326311" type="text/json">{"id":124326311,"first_name":"Baikun","last_name":"Liang","domain_name":"cityu-hk","page_name":"BaikunLiang","display_name":"Baikun Liang","profile_url":"https://cityu-hk.academia.edu/BaikunLiang","photo":"https://0.academia-photos.com/124326311/31810882/29034934/s65_baikun.liang.jpg"}</script></span></span></li><li class="js-paper-rank-work_63319793 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="63319793"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 63319793, container: ".js-paper-rank-work_63319793", }); });</script></li><li class="js-percentile-work_63319793 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 63319793; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_63319793"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_63319793 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="63319793"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 63319793; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=63319793]").text(description); $(".js-view-count-work_63319793").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_63319793").removeClass('hidden') })</script></div></li></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_47897750 coauthored" data-work_id="47897750" 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/47897750/ANOVA_MOP_ANOVA_Decomposition_for_Multiobjective_Optimization">ANOVA-MOP: ANOVA Decomposition for Multiobjective Optimization</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_47897750" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive functions, but this does not reduce the dimension of the search domain nor mitigate the curse of dimensionality effects. The dimension of the search domain can be reduced by functional anova decomposition involving Sobol' sensitivity indices. This approach allows one to rank decision variables according to their impact on the objective function values. On the basis of the sparsity of effects principle, typically only a small number of decision variables significantly affects an objective function. Therefore, neglecting the variables with the smallest impact should lead to an acceptably accurate and simpler metamodel for the original problem. This appealing strategy has been applied only to single-objective optimization problems so far. Given a high-dimensional optimization problem with multiple objectives, a method called anova-mop is proposed for defining a number of independent low-dimensional subproblems with a smaller number of objectives. The method allows one to define approximated solutions for the original problem by suitably combining the solutions of the subproblems. The quality of the approximated solutions and both practical and theoretical aspects related to decision making are discussed.</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/47897750" 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="bab5133161dedb595202e21a86676afc" rel="nofollow" data-download="{"attachment_id":81811182,"asset_id":47897750,"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/81811182/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&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="14666669" href="https://independent.academia.edu/AlbertoLovison">Alberto Lovison</a><script data-card-contents-for-user="14666669" type="text/json">{"id":14666669,"first_name":"Alberto","last_name":"Lovison","domain_name":"independent","page_name":"AlbertoLovison","display_name":"Alberto Lovison","profile_url":"https://independent.academia.edu/AlbertoLovison","photo":"https://0.academia-photos.com/14666669/3990052/4660974/s65_alberto.lovison.jpg_oh_be60aed6d4509174a262621d9850119a_oe_54421a0e___gda___1414161895_769528a3b0cd34e82621fee539f17217"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-47897750">+2</span><div class="hidden js-additional-users-47897750"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://cityu-hk.academia.edu/MatthiasTan">Matthias Tan</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/MohammadTabatabaei15">Mohammad Tabatabaei</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-47897750'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-47897750').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_47897750 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="47897750"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 47897750, container: ".js-paper-rank-work_47897750", }); });</script></li><li class="js-percentile-work_47897750 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 47897750; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_47897750"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_47897750 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="47897750"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 47897750; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=47897750]").text(description); $(".js-view-count-work_47897750").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_47897750").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="47897750"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="556845" href="https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics">Numerical Analysis and Computational Mathematics</a><script data-card-contents-for-ri="556845" type="text/json">{"id":556845,"name":"Numerical Analysis and Computational Mathematics","url":"https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=47897750]'), work: {"id":47897750,"title":"ANOVA-MOP: ANOVA Decomposition for Multiobjective Optimization","created_at":"2021-05-03T01:25:54.989-07:00","owner_id":14666669,"url":"https://www.academia.edu/47897750/ANOVA_MOP_ANOVA_Decomposition_for_Multiobjective_Optimization","slug":"ANOVA_MOP_ANOVA_Decomposition_for_Multiobjective_Optimization","dom_id":"work_47897750","summary":"Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive functions, but this does not reduce the dimension of the search domain nor mitigate the curse of dimensionality effects. The dimension of the search domain can be reduced by functional anova decomposition involving Sobol' sensitivity indices. This approach allows one to rank decision variables according to their impact on the objective function values. On the basis of the sparsity of effects principle, typically only a small number of decision variables significantly affects an objective function. Therefore, neglecting the variables with the smallest impact should lead to an acceptably accurate and simpler metamodel for the original problem. This appealing strategy has been applied only to single-objective optimization problems so far. Given a high-dimensional optimization problem with multiple objectives, a method called anova-mop is proposed for defining a number of independent low-dimensional subproblems with a smaller number of objectives. The method allows one to define approximated solutions for the original problem by suitably combining the solutions of the subproblems. 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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/72855007/Residual_Distillation_Towards_Portable_Deep_Neural_Networks_without_Shortcuts">Residual Distillation: Towards Portable Deep Neural Networks without Shortcuts</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">By transferring both features and gradients between different layers, shortcut connections explored by ResNets allow us to effectively train very deep neural networks up to hundreds of layers. However, the additional computation costs... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_72855007" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">By transferring both features and gradients between different layers, shortcut connections explored by ResNets allow us to effectively train very deep neural networks up to hundreds of layers. However, the additional computation costs induced by those shortcuts are often overlooked. For example, during online inference, the shortcuts in ResNet-50 account for about 40 percent of the entire memory usage on feature maps, because the features in the preceding layers cannot be released until the subsequent calculation is completed. In this work, for the first time, we consider training the CNN models with shortcuts and deploying them without. In particular, we propose a novel joint-training framework to train plain CNN by leveraging the gradients of the ResNet counterpart. During forward step, the feature maps of the early stages of plain CNN are passed through later stages of both itself and the ResNet counterpart to calculate the loss. During backpropagation, gradients calculated from ...</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/72855007" 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="4bacd2d025f1a924cd2e0efdbbede664" rel="nofollow" data-download="{"attachment_id":81614325,"asset_id":72855007,"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/81614325/download_file?st=MTczMjg1ODc3Niw4LjIyMi4yMDguMTQ2&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="216372697" href="https://cityu-hk.academia.edu/MatthiasTan">Matthias Tan</a><script data-card-contents-for-user="216372697" type="text/json">{"id":216372697,"first_name":"Matthias","last_name":"Tan","domain_name":"cityu-hk","page_name":"MatthiasTan","display_name":"Matthias Tan","profile_url":"https://cityu-hk.academia.edu/MatthiasTan","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_72855007 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="72855007"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 72855007, container: ".js-paper-rank-work_72855007", }); });</script></li><li class="js-percentile-work_72855007 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 72855007; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_72855007"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_72855007 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="72855007"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 72855007; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=72855007]").text(description); $(".js-view-count-work_72855007").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_72855007").removeClass('hidden') })</script></div></li></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_72855008" data-work_id="72855008" 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/72855008/Hierarchical_Neural_Architecture_Search_via_Operator_Clustering">Hierarchical Neural Architecture Search via Operator Clustering</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 efficiency of automatic neural architecture design has been significantly improved by gradient-based search methods such as DARTS. However, recent literature has brought doubt to the generalization ability of DARTS, arguing... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_72855008" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Recently, the efficiency of automatic neural architecture design has been significantly improved by gradient-based search methods such as DARTS. However, recent literature has brought doubt to the generalization ability of DARTS, arguing that DARTS performs poorly when the search space is changed, i.e, when different set of candidate operators are used. Regularization techniques such as early stopping have been proposed to partially solve this problem. In this paper, we tackle this problem from a different perspective by identifying two contributing factors to the collapse of DARTS when the search space changes: (1) the correlation of similar operators incurs unfavorable competition among them and makes their relative importance score unreliable and (2) the optimization complexity gap between the proxy search stage and the final training. Based on these findings, we propose a new hierarchical search algorithm. With its operator clustering and optimization complexity match, the algor...</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/72855008" 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="ac53a7047175ae38d375f0fd43f9932c" rel="nofollow" data-download="{"attachment_id":81614327,"asset_id":72855008,"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/81614327/download_file?st=MTczMjg1ODc3Nyw4LjIyMi4yMDguMTQ2&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="216372697" href="https://cityu-hk.academia.edu/MatthiasTan">Matthias Tan</a><script data-card-contents-for-user="216372697" type="text/json">{"id":216372697,"first_name":"Matthias","last_name":"Tan","domain_name":"cityu-hk","page_name":"MatthiasTan","display_name":"Matthias Tan","profile_url":"https://cityu-hk.academia.edu/MatthiasTan","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_72855008 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="72855008"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 72855008, container: ".js-paper-rank-work_72855008", }); 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