Philosophical transactions. Series A, Mathematical, physical, and engineering sciences最新文献

{"title":"Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations.","authors":"Jason Dykes,&nbsp;Alfie Abdul-Rahman,&nbsp;Daniel Archambault,&nbsp;Benjamin Bach,&nbsp;Rita Borgo,&nbsp;Min Chen,&nbsp;Jessica Enright,&nbsp;Hui Fang,&nbsp;Elif E Firat,&nbsp;Euan Freeman,&nbsp;Tuna Gönen,&nbsp;Claire Harris,&nbsp;Radu Jianu,&nbsp;Nigel W John,&nbsp;Saiful Khan,&nbsp;Andrew Lahiff,&nbsp;Robert S Laramee,&nbsp;Louise Matthews,&nbsp;Sibylle Mohr,&nbsp;Phong H Nguyen,&nbsp;Alma A M Rahat,&nbsp;Richard Reeve,&nbsp;Panagiotis D Ritsos,&nbsp;Jonathan C Roberts,&nbsp;Aidan Slingsby,&nbsp;Ben Swallow,&nbsp;Thomas Torsney-Weir,&nbsp;Cagatay Turkay,&nbsp;Robert Turner,&nbsp;Franck P Vidal,&nbsp;Qiru Wang,&nbsp;Jo Wood,&nbsp;Kai Xu","doi":"10.1098/rsta.2021.0299","DOIUrl":"https://doi.org/10.1098/rsta.2021.0299","url":null,"abstract":"<p><p>We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210299"},"PeriodicalIF":5.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9376715/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40613055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bayesian emulation and history matching of JUNE.","authors":"I Vernon,&nbsp;J Owen,&nbsp;J Aylett-Bullock,&nbsp;C Cuesta-Lazaro,&nbsp;J Frawley,&nbsp;A Quera-Bofarull,&nbsp;A Sedgewick,&nbsp;D Shi,&nbsp;H Truong,&nbsp;M Turner,&nbsp;J Walker,&nbsp;T Caulfield,&nbsp;K Fong,&nbsp;F Krauss","doi":"10.1098/rsta.2022.0039","DOIUrl":"https://doi.org/10.1098/rsta.2022.0039","url":null,"abstract":"<p><p>We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20220039"},"PeriodicalIF":5.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9376712/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40613059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reformulating the susceptible-infectious-removed model in terms of the number of detected cases: well-posedness of the observational model.","authors":"Eduard Campillo-Funollet,&nbsp;Hayley Wragg,&nbsp;James Van Yperen,&nbsp;Duc-Lam Duong,&nbsp;Anotida Madzvamuse","doi":"10.1098/rsta.2021.0306","DOIUrl":"https://doi.org/10.1098/rsta.2021.0306","url":null,"abstract":"<p><p>Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible-infectious-recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210306"},"PeriodicalIF":5.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9376718/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40613127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On space-time structure and the Universe: some issues of concept and principle.","authors":"Naresh Dadhich","doi":"10.1098/rsta.2021.0405","DOIUrl":"https://doi.org/10.1098/rsta.2021.0405","url":null,"abstract":"<p><p>In this discourse, we would like to discuss some issues of concept and principle in the context of the following three aspects. One, how [Formula: see text] arises as a constant of space-time structure on the same footing as the velocity of light. These are the two constants innate to space-time without reference to any force or dynamics whatsoever, and are interwoven in the geometry of 'free' homogeneous space-time. Two, how does the vacuum energy gravitate? Could its gravitational interaction in principle be included in general relativity or a new theory of quantum space-time/gravity would be required? Finally, we would like to raise the fundamental question: How does the Universe physically expand? Since there does not lie anything outside into which it can expand, instead it has to expand on its own-maybe by creating new space-time out of nothing at each instant and at every location! Thus not only was the Universe created at some instant in the past marking the beginning in the Big Bang, it is in fact being created continuously at each epoch as it expands. We thus need quantum theory of space-time/gravity for fully understanding the working of the Universe. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210405"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40479002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How inflationary gravitons affect gravitational radiation.","authors":"L Tan,&nbsp;N C Tsamis,&nbsp;R P Woodard","doi":"10.1098/rsta.2021.0187","DOIUrl":"https://doi.org/10.1098/rsta.2021.0187","url":null,"abstract":"<p><p>We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary [Formula: see text]-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21 cm cosmology. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210187"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40570208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gravity beyond Einstein? Yes, but in which direction?","authors":"Demosthenes Kazanas,&nbsp;Demetrios Papadopoulos,&nbsp;Dimitris Christodoulou","doi":"10.1098/rsta.2021.0367","DOIUrl":"https://doi.org/10.1098/rsta.2021.0367","url":null,"abstract":"<p><p>We present qualitative arguments in favour of an extension of the theory of the gravitational interaction beyond that resulting from the Hilbert-Einstein action. To this end, we consider a locally conformal invariant theory of gravity, discussed some 30 years ago by Mannheim and Kazanas. We discuss its exact solution of the static, spherically symmetric configurations and, based on these, we revisit some of the outstanding problems associated with gravity, high energy interactions and sketch potential resolutions within the conformal gravity framework. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210367"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9251483/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40570211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higgs effect without lunch.","authors":"C W Erickson,&nbsp;Rahim Leung,&nbsp;K S Stelle","doi":"10.1098/rsta.2021.0184","DOIUrl":"https://doi.org/10.1098/rsta.2021.0184","url":null,"abstract":"<p><p>Reduction in effective space-time dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wave function factors depend non-trivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a 'covert' pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. The Stueckelberg mode remains in the theory as a propagating scalar degree of freedom from a dimensionally reduced perspective, but it is not 'eaten' in a mass-generating mechanism. At leading order, it also makes no contribution to the conserved energy; for this reason, it may be called a (non-ghost) 'phantom'. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210184"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9251485/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40479005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Limitations of an effective field theory treatment of early Universe cosmology.","authors":"Robert Brandenberger","doi":"10.1098/rsta.2021.0178","DOIUrl":"https://doi.org/10.1098/rsta.2021.0178","url":null,"abstract":"<p><p>Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations to the applicability of effective field theory techniques in describing early Universe cosmology. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210178"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40570209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Brane-world singularities and asymptotics of five-dimensional bulk fluids.","authors":"I Antoniadis,&nbsp;S Cotsakis,&nbsp;I Klaoudatou","doi":"10.1098/rsta.2021.0180","DOIUrl":"https://doi.org/10.1098/rsta.2021.0180","url":null,"abstract":"<p><p>We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a 'perfect fluid' with an equation of state [Formula: see text], where [Formula: see text] is the 'pressure' and [Formula: see text] is the 'density' of the fluid, depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane for [Formula: see text] or of AdS branes for [Formula: see text]. More cases can be found by gluing two regular brunches of solutions at the position of the brane. However, only a flat brane for [Formula: see text] leads to finite Planck mass on the brane and thus localizes gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane and a range of [Formula: see text], which is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state of the form [Formula: see text] with [Formula: see text] and [Formula: see text]. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210180"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40479001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An <i>S</i>-matrix approach to gravitational-wave physics.","authors":"Pierre Vanhove","doi":"10.1098/rsta.2021.0181","DOIUrl":"https://doi.org/10.1098/rsta.2021.0181","url":null,"abstract":"<p><p>The detection of gravitational waves emitted by binary systems has opened a new astronomical window into the Universe. We describe recent advances in the field of scattering amplitudes applied to the post-Minkowskian expansion, and the extraction of the effective two-body gravitational potential. The techniques presented here apply to any effective field theory of gravity and are not restricted to four-dimensional Einstein gravity. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210181"},"PeriodicalIF":5.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40479003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}