Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

{"title":"Ensemble of weak spectral total-variation learners: a PET-CT case study.","authors":"Anna Rosenberg, John Kennedy, Zohar Keidar, Yehoshua Y Zeevi, Guy Gilboa","doi":"10.1098/rsta.2024.0236","DOIUrl":"https://doi.org/10.1098/rsta.2024.0236","url":null,"abstract":"<p><p>Solving computer vision problems through machine learning, one often encounters lack of sufficient training data. To mitigate this, we propose the use of ensembles of weak learners based on spectral total-variation (STV) features (Gilboa G. 2014 A total variation spectral framework for scale and texture analysis. <i>SIAM J. Imaging Sci</i>. <b>7</b>, 1937-1961. (doi:10.1137/130930704)). The features are related to nonlinear eigenfunctions of the total-variation subgradient and can characterize well textures at various scales. It was shown (Burger M, Gilboa G, Moeller M, Eckardt L, Cremers D. 2016 Spectral decompositions using one-homogeneous functionals. <i>SIAM J. Imaging Sci</i>. <b>9</b>, 1374-1408. (doi:10.1137/15m1054687)) that, in the one-dimensional case, orthogonal features are generated, whereas in two dimensions the features are empirically lowly correlated. Ensemble learning theory advocates the use of lowly correlated weak learners. We thus propose here to design ensembles using learners based on STV features. To show the effectiveness of this paradigm, we examine a hard real-world medical imaging problem: the predictive value of computed tomography (CT) data for high uptake in positron emission tomography (PET) for patients suspected of skeletal metastases. The database consists of 457 scans with 1524 unique pairs of registered CT and PET slices. Our approach is compared with deep-learning methods and to radiomics features, showing STV learners perform best (AUC=[Formula: see text]), compared with neural nets (AUC=[Formula: see text]) and radiomics (AUC=[Formula: see text]). We observe that fine STV scales in CT images are especially indicative of the presence of high uptake in PET.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240236"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Connections between sequential Bayesian inference and evolutionary dynamics.","authors":"Sahani Pathiraja, Philipp Wacker","doi":"10.1098/rsta.2024.0241","DOIUrl":"10.1098/rsta.2024.0241","url":null,"abstract":"<p><p>It has long been posited that there is a connection between the dynamical equations describing evolutionary processes in biology and sequential Bayesian learning methods. This manuscript describes new research in which this precise connection is rigorously established in the continuous time setting. Here we focus on a partial differential equation known as the Kushner-Stratonovich equation describing the evolution of the posterior density in time. Of particular importance is a piecewise smooth approximation of the observation path from which the discrete time filtering equations, which are shown to converge to a Stratonovich interpretation of the Kushner-Stratonovich equation. This smooth formulation will then be used to draw precise connections between nonlinear stochastic filtering and replicator-mutator dynamics. Additionally, gradient flow formulations will be investigated as well as a form of replicator-mutator dynamics that is shown to be beneficial for the misspecified model filtering problem. It is hoped this work will spur further research into exchanges between sequential learning and evolutionary biology and to inspire new algorithms in filtering and sampling.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240241"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12152925/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization.","authors":"Martin Burger, Samira Kabri, Yury Korolev, Tim Roith, Lukas Weigand","doi":"10.1098/rsta.2024.0233","DOIUrl":"10.1098/rsta.2024.0233","url":null,"abstract":"<p><p>The aim of this article is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform distributions pose a number of challenging mathematical questions. We focus on a special case that admits a gradient flow formulation in the spaces of probability measures on the unit sphere under a special metric, which allows us to give at least partial answers in a rigorous way. The arising mathematical problems resemble those recently studied in aggregation equations but with additional challenges emerging from restricting the dynamics to the sphere and the particular form of the interaction energy. We provide a rigorous framework for studying the gradient flow, which also suggests a possible metric geometry to study the general case (i.e. one that is not described by a gradient flow). We further analyse the stationary points of the induced self-attention dynamics. The latter are related to stationary points of the interaction energy in the Wasserstein geometry, and we further discuss energy minimizers and maximizers in different parameter settings.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240233"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12152857/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attraction-repulsion swarming: a generalized framework of t-SNE via force normalization and tunable interactions.","authors":"Jingcheng Lu, Jeff Calder","doi":"10.1098/rsta.2024.0234","DOIUrl":"https://doi.org/10.1098/rsta.2024.0234","url":null,"abstract":"<p><p>We propose a new method for data visualization based on attraction-repulsion swarming (ARS) dynamics, which we call ARS visualization. ARS is a generalized framework that is based on viewing the t-distributed stochastic neighbour embedding (t-SNE) visualization technique as a swarm of interacting agents driven by attraction and repulsion. Motivated by recent developments in swarming, we modify the t-SNE dynamics to include a normalization by the <i>total influence</i>, which results in better posed dynamics in which we can use a data size independent time step (of [Formula: see text]) and a simple gradient descent iteration. ARS also includes the ability to separately tune the attraction and repulsion kernels, which gives the user control over the tightness within clusters and the spacing between them in the visualization. In contrast with t-SNE, our proposed ARS data visualization method is not gradient descent on the Kullback-Leibler (KL) divergence, and can be viewed solely as an interacting particle system driven by attraction and repulsion forces, which illustrates that the KL divergence is not an essential part of the t-SNE algorithm. We provide theoretical results illustrating how the choice of interaction kernel affects the dynamics, and experimental results to validate our method and compare to t-SNE on the MNIST, Cifar-10, SVHN and NORB datasets.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240234"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Counting the number of stationary solutions of partial differential equations via infinite dimensional sampling.","authors":"Martin Kolodziejczyk, Michela Ottobre, Gideon Simpson","doi":"10.1098/rsta.2024.0239","DOIUrl":"https://doi.org/10.1098/rsta.2024.0239","url":null,"abstract":"<p><p>This paper is concerned with the problem of counting solutions of stationary nonlinear Partial Differential Equations (PDEs) when the PDE is known to admit more than one solution. We suggest tackling the problem via a sampling-based approach. The method allows one to find solutions that are stable, in the sense that they are stable equilibria of the associated time-dependent PDE. We test our proposed methodology on the McKean-Vlasov PDE, more precisely on the problem of determining the number of stationary solutions of the McKean-Vlasov equation.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240239"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Partial differential equations in data science.","authors":"Andrea L Bertozzi, Nadejda Drenska, Jonas Latz, Matthew Thorpe","doi":"10.1098/rsta.2024.0249","DOIUrl":"10.1098/rsta.2024.0249","url":null,"abstract":"<p><p>The advent of artificial intelligence and machine learning has led to significant technological and scientific progress, but also to new challenges. Partial differential equations, usually used to model systems in the sciences, have shown to be useful tools in a variety of tasks in the data sciences, be it just as physical models to describe physical data, as more general models to replace or construct artificial neural networks, or as analytical tools to analyse stochastic processes appearing in the training of machine-learning models. This article acts as an introduction of a theme issue covering synergies and intersections of partial differential equations and data science. We briefly review some aspects of these synergies and intersections in this article and end with an editorial foreword to the issue.This article is part of the theme issue 'Partial differential equations in data science'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2298","pages":"20240249"},"PeriodicalIF":4.3,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12162097/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144226172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Direct measurement of non-thermal microwave effects on bacterial growth and redox dynamics using a novel high-throughput waveguide applicator.","authors":"Angharad Miles, Adrian Porch, Heungjae Choi, Steve Cripps, Helen Brown, Catrin Williams","doi":"10.1098/rsta.2024.0073","DOIUrl":"10.1098/rsta.2024.0073","url":null,"abstract":"<p><p>A high-throughput microwave applicator has been designed and characterized to investigate microwave interactions with biological systems. When operated in the TE₁₀ mode, this rectangular waveguide enabled simultaneous exposure of 96 biological samples to a quantifiable electric field (<i>E</i> field) at 2.45 GHz. Optimized electric probe transitions efficiently couple power (up to 50 W) into and out of the waveguide, achieving a voltage transmission coefficient (S₂₁) near unity (0 dB) and a voltage reflection coefficient (S₁₁) below 0.01 ( less than -20 dB). The growth dynamics of <i>Staphylococcus aureus</i> bacteria were analysed after non-thermal, microsecond-pulsed microwave exposure at 25 W r.m.s. of microwave power for 24 h. Post-exposure, <i>S. aureus</i> exhibited significantly higher optical density measurements and growth rates than thermal controls. Fluorescent probes directed towards key redox indicators revealed that microwave exposure altered the cellular redox state. This study provides new insights into the non-thermal effects of pulsed 2.45 GHz microwaves on <i>S. aureus</i> growth dynamics and characterizes a novel high-throughput platform for further exploration of fundamental microwave effects on biological systems.This article is part of the theme discussion meeting issue 'Microwave science in sustainable technologies'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2297","pages":"20240073"},"PeriodicalIF":4.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12096104/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144120415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microwave power sources for industrial, scientific and medical applications.","authors":"Steve Cripps","doi":"10.1098/rsta.2024.0069","DOIUrl":"10.1098/rsta.2024.0069","url":null,"abstract":"<p><p>The industrial, scientific and medical (ISM) sector has been a growth area in recent years for applications of microwave engineering. These applications include various forms of heating and more controversial uses that exploit so-called 'non-thermal' effects of microwave exposure on biological and chemical samples. Given the non-thermal nature of these effects, the microwave power source may be adequate in pulsed, rather than continuous form. This paper will not attempt to address the questions surrounding the provenance of such effects but will discuss the challenges presented to the microwave circuit designer in delivering substantial amounts of microwave power, both continuous and pulsed, to targets that vary in size and microwave impedance properties. ISM applications may represent a large new market for radio frequency power amplifier (RFPA) products that may utilize alternative technologies and design approaches over those that have evolved for the conventional microwave applications such as telecommunications and radar.This article is part of the discussion meeting issue 'Microwave science in sustainability'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2297","pages":"20240069"},"PeriodicalIF":4.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12096102/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144120434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microwaves in clean energy technologies.","authors":"Samuel Hefford, Michael Barter, M Usman Azam, Bhupinder Singh, Georgios Dimitrakis, Xiangyu Jie, Peter Edwards, Daniel R Slocombe","doi":"10.1098/rsta.2024.0394","DOIUrl":"10.1098/rsta.2024.0394","url":null,"abstract":"<p><p>Energy in the microwave spectrum is increasingly applied in clean energy technologies. This review discusses recent innovations using microwave fields in hydrogen production and synthesis of new battery materials, highlighting the unique properties of microwave heating. Key innovations include microwave-assisted hydrogen generation from water, hydrocarbons and ammonia and the synthesis of high-performance anode and cathode materials. Microwave-assisted catalytic water splitting using Gd-doped ceria achieves efficient hydrogen production below 250°C. For hydrocarbons, advanced microwave-active catalysts Fe-Ni alloys and ruthenium nanoparticles enable high conversion rates and hydrogen yields. In ammonia synthesis, microwaves reduce the energy demands of the Haber-Bosch process and enhance hydrogen production efficiency using catalysts such as ruthenium and Co₂Mo₃N. In battery technology, microwave-assisted synthesis of cathode materials like LiFePO₄ and LiNi_0.5Mn_1.5O₄ yields high-purity materials with superior electrochemical performance. Developing nanostructured and composite materials, including graphene-based anodes, significantly improves battery capacities and cycling stability. The ability of microwave technology to provide rapid, selective heating and enhance reaction rates offers significant advancements in clean energy technologies. Ongoing research continues to bridge theoretical understanding and practical applications, driving further innovations in this field. This review aims to highlight recent advances in clean energy technologies based upon the novel use of microwave energy. The potential impact of these emerging applications is now being fully understood in areas that are critical to achieving net zero and can contribute to the decarbonization of key sectors. Notable in this landscape are the sectors of hydrogen fuel and battery technologies. This review examines the role of microwaves in these areas.This article is part of the discussion meeting issue 'Microwave science in sustainability'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2297","pages":"20240394"},"PeriodicalIF":4.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12096106/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144120440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Low to near-zero CO₂ production of hydrogen from fossil fuels: critical role of microwave-initiated catalysis.","authors":"Xiangyu Jie, Daniel R Slocombe, Adrian Porch, Tiancun Xiao, Sergio González-Cortés, Saud Aldrees, Jon R Dilworth, Benzhen Yao, Martin-Owen Jones, Vladimir Kuznetsov, Peter P Edwards","doi":"10.1098/rsta.2024.0061","DOIUrl":"10.1098/rsta.2024.0061","url":null,"abstract":"&lt;p&gt;&lt;p&gt;Presently, there is no single, clear route for the near-term production of the huge volumes of CO&lt;sub&gt;2&lt;/sub&gt;-free hydrogen necessary for the global transition to any type of hydrogen economy. All conventional routes to produce hydrogen from hydrocarbon fossil fuels (notably natural gas) involve the production-and hence the emission-of CO&lt;sub&gt;2&lt;/sub&gt;, most notably in the steam methane reforming (SMR) process. Our recent studies have highlighted another route; namely, the critical role played by the microwave-initiated catalytic pyrolysis, decomposition or deconstruction of fossil hydrocarbon fuels to produce hydrogen with low to near-zero CO&lt;sub&gt;2&lt;/sub&gt; emissions together with high-value solid nanoscale carbonaceous materials. These innovations have been applied, firstly to wax, then methane, crude oil, diesel, then biomass and most recently Saudi Arabian light crude oil, as well as plastics waste. Microwave catalysis has therefore now emerged as a highly effective route for the rapid and effective production of hydrogen and high-value carbon nanomaterials co-products, in many cases accompanied by low to near-zero CO&lt;sub&gt;2&lt;/sub&gt; emissions. Underpinning all of these advances has been the important concept from solid state physics of the so-called Size-Induced-Metal-Insulator Transition (SIMIT) in mesoscale or mesoscopic particles of catalysts. The mesoscale refers to a range of physical scale in-between the micro- and the macro-scale of matter (Huang W, Li J and Edwards PP, 2018, Mesoscience: exploring the common principle at mesoscale, &lt;i&gt;Natl. Sci. Rev&lt;/i&gt;. &lt;b&gt;5&lt;/b&gt;, 321-326 (doi:10.1093/nsr/nwx083)). We highlight here that the actual physical size of the mesoscopic catalyst particles, located close to the SIMIT, is the primary cause of their enhanced microwave absorption and rapid heating of particles to initiate the catalytic-and highly selective-breaking of carbon-hydrogen bonds in fossil hydrocarbons and plastics to produce clean hydrogen and nanoscale carbonaceous materials. Importantly, also, since the surrounding 'bath' of hydrocarbons is cooler than the microwave-heated catalytic particles themselves, the produced neutral hydrogen molecule can quickly diffuse from the active sites. This important feature of microwave heating thereby minimizes undesirable side reactions, a common feature of conventional thermal heating in heterogeneous catalysis. The low to near-zero CO&lt;sub&gt;2&lt;/sub&gt; production of hydrogen via microwave-initiated decomposition or cracking of abundant hydrocarbon fossil fuels may be an interim, viable alternative to the conventional, widely-used SMR, that a highly efficient process, but unfortunately associated with the emission of vast quantities of CO&lt;sub&gt;2&lt;/sub&gt;. Microwave-initiated catalytic decomposition also opens up the intriguing possibility of using distributed methane in the current natural gas structure to produce hydrogen and high-value solid carbon at either central or distributed sites. That approach will","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2297","pages":"20240061"},"PeriodicalIF":4.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12096099/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144120425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}