IA Scholar Query: Distributed exact weighted all-pairs shortest paths in near-linear time.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
https://scholar.archive.org/work/vlqa6rnsa5d3vnpa3qeaizot6a
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in the same way. 2. The computational aspects of lattice-based cryptosystem are usually simple to understand and fairly easy to implement in practice. 3. Lattice-based cryptosystems have lower encryption/decryption computational complexities compared to popular cryptosystems that are based on the integer factorisation or the discrete logarithm problems. 4. Lattice-based cryptosystems enjoy strong worst-case hardness security proofs based on approximate versions of known NP-hard lattice problems. 5. Lattice-based cryptosystems are believed to be good candidates for post-quantum cryptography, since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best-known classical (non-quantum) algorithms, unlike for integer factorisation and (elliptic curve) discrete logarithm problems. 6. Last but not least, interesting structures in lattice problems have led to significant advances in Homomorphic Encryption, a new research area with wide-ranging applications.Yang Li, Kee Siong Ng, Michael Purcellwork_vlqa6rnsa5d3vnpa3qeaizot6aWed, 28 Sep 2022 00:00:00 GMTReal Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
https://scholar.archive.org/work/n4z24erzazc2finedtc73ycz2e
We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real time evolution of a non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as L=40, far beyond exact diagonalisability, though only for short evolution times t≲ 1. We identify discontinuities of the density of states as one of the key problems in the MC simulations and propose to calculate some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements the density of states is found highly non-smooth and therefore the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real time simulations with discrete degrees of freedom.Pavel Buividovich, Johann Ostmeyerwork_n4z24erzazc2finedtc73ycz2eWed, 28 Sep 2022 00:00:00 GMTArtificial Intelligence and Advanced Materials
https://scholar.archive.org/work/tkf566mg6zf77a7xan6anloxvu
Artificial intelligence is gaining strength and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems and processes can be devised and optimized thanks to machine learning techniques and such progress can be turned into in-novative computing platforms. Future materials scientists will profit from understanding how machine learning can boost the conception of advanced materials. This review covers aspects of computation from the fundamentals to directions taken and repercussions produced by compu-tation to account for the origins, procedures and applications of artificial intelligence. Machine learning and its methods are reviewed to provide basic knowledge on its implementation and its potential. The materials and systems used to implement artificial intelligence with electric charges are finding serious competition from other information carrying and processing agents. The impact these techniques are having on the inception of new advanced materials is so deep that a new paradigm is developing where implicit knowledge is being mined to conceive materi-als and systems for functions instead of finding applications to found materials. How far this trend can be carried is hard to fathom as exemplified by the power to discover unheard of mate-rials or physical laws buried in data.Cefe Lópezwork_tkf566mg6zf77a7xan6anloxvuWed, 28 Sep 2022 00:00:00 GMTStellar population of the Rosette Nebula and NGC 2244: application of the probabilistic random forest
https://scholar.archive.org/work/vkdgs5altzetdbyia7nqhaheae
(Abridged) In this work, we study the 2.8x2.6 deg2 region in the emblematic Rosette Nebula, centred at the young cluster NGC 2244, with the aim of constructing the most reliable candidate member list to date, determining various structural and kinematic parameters, and learning about the past and the future of the region. Starting from a catalogue containing optical to mid-infrared photometry, as well as positions and proper motions from Gaia EDR3, we apply the Probabilistic Random Forest algorithm and derive membership probability for each source. Based on the list of almost 3000 probable members, of which about a third are concentrated within the radius of 20' from the centre of NGC 2244, we identify various clustered sources and stellar concentrations, and estimate the average distance of 1489+-37 pc (entire region), 1440+-32 pc (NGC 2244) and 1525+-36 pc (NGC 2237). The masses, extinction, and ages are derived by SED fitting, and the internal dynamic is assessed via proper motions relative to the mean proper motion of NGC 2244. NGC 2244 is showing a clear expansion pattern, with an expansion velocity that increases with radius. Its IMF is well represented by two power laws (dN/dM∝M^-α), with slopes α= 1.05+-0.02 for the mass range 0.2 - 1.5 MSun, and α= 2.3+-0.3 for the mass range 1.5 - 20 MSun, in agreement with other star forming regions. The mean age of the region is 2 Myr. We find evidence for the difference in ages between NGC 2244 and the region associated with the molecular cloud, which appears slightly younger. The velocity dispersion of NGC 2244 is well above the virial velocity dispersion derived from the total mass (1000+-70 MSun) and half-mass radius (3.4+-0.2 pc). From the comparison to other clusters and to numerical simulations, we conclude that NGC 2244 may be unbound, and possibly even formed in a super-virial state.Koraljka Muzic, Victor Almendros-Abad, Herve Bouy, Karolina Kubiak, Karla Pena Ramirez, Alberto Krone-Martins, Andre Moitinho, Miguel Conceicaowork_vkdgs5altzetdbyia7nqhaheaeTue, 27 Sep 2022 00:00:00 GMTTesting Explanations of Short Baseline Neutrino Anomalies
https://scholar.archive.org/work/ojolauja4fe3doblxx4sl4cr4e
The experimental observation of neutrino oscillations profoundly impacted the physics of neutrinos, from being well understood theoretically to requiring new physics beyond the standard model of particle physics. Indeed, the mystery of neutrino masses implies the presence of new particles never observed before, often called sterile neutrinos, as they would not undergo standard weak interactions. And while neutrino oscillation measurements entered the precision era, reaching percent-level precision, many experimental results show significant discrepancies with the standard model, at baselines much shorter than typical oscillation baselines, like LSND, MiniBooNE, gallium experiments, and reactor antineutrino measurements. These short baseline anomalies could be explained by the addition of a light sterile neutrino, with mass in the 1-10 eV range, however, in strong tension with many null experimental observations. Other explanations that rely on sterile neutrinos with masses in the 1-500 MeV could resolve the tension. Here we test both classes of models. On the one hand, we look for datasets collected at a short baseline which can constrain heavy sterile neutrino models. We find that the minimal model is fully constrained, but several extensions of this model could weaken the current constraint and be tested with current and future datasets. On the other hand, we test the presence of neutrino oscillations at short baselines, induced by a light sterile state, with the data collected by the MicroBooNE experiment, a liquid argon time projection chamber specifically designed to resolve the details of each neutrino interaction. We report null results from both analyses, further constraining the space of possible explanations for the short baseline anomalies. If new physics lies behind the short baseline anomaly puzzle, it is definitely not described by a simple model.Nicolò Foppianiwork_ojolauja4fe3doblxx4sl4cr4eTue, 27 Sep 2022 00:00:00 GMTIt's a Wrap! Visualisations that Wrap Around Cylindrical, Toroidal, or Spherical Topologies
https://scholar.archive.org/work/akpvfdnu2fhgdjsfxa25kjeu2a
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart's boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less "flat" and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data. Subsequently, we investigate a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data's underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.Kun-Ting Chenwork_akpvfdnu2fhgdjsfxa25kjeu2aTue, 27 Sep 2022 00:00:00 GMTSingularity formation in the incompressible Euler equation in finite and infinite time
https://scholar.archive.org/work/p4ictrnchvgjbefqnuk3w4rn3q
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given through the lens of infinite-dimensional dynamical systems, and various open problems are listed and discussed.Theodore D. Drivas, Tarek M. Elgindiwork_p4ictrnchvgjbefqnuk3w4rn3qTue, 27 Sep 2022 00:00:00 GMTPrinciples Of Heliophysics: a textbook on the universal processes behind planetary habitability
https://scholar.archive.org/work/v2zqk34khrabtaqqb3zmwqkhpa
Heliophysics is the system science of the physical connections between the Sun and the solar system. As the physics of the local cosmos, it embraces space weather and planetary habitability. The wider view of comparative heliophysics forms a template for conditions in exoplanetary systems and provides a view over time of the aging Sun and its magnetic activity, of the heliosphere in different settings of the interstellar medium and subject to stellar impacts, of the space physics over evolving planetary dynamos, and of the long-term influence on planetary atmospheres by stellar radiation and wind. Based on a series of NASA-funded summer schools for early-career researchers, this textbook is intended for students in physical sciences in later years of their university training and for beginning graduate students in fields of solar, stellar, (exo-)planetary, and planetary-system sciences. The book emphasizes universal processes from a perspective that draws attention to what provides Earth (and similar (exo-)planets) with a relatively stable setting in which life as we know it could thrive. The text includes 200 "Activities" in the form of exercises, explorations, literature readings, "what if" challenges, and group discussion topics; many of the Activities provide additional information complementing the main text. Solutions and discussions are included in an Appendix for a selection of the exercises.Karel Schrijver, Fran Bagenal, Tim Bastian, Juerg Beer, Mario Bisi, Tom Bogdan, Steve Bougher, David Boteler, Dave Brain, Guy Brasseur, Don Brownlee, Paul Charbonneau, Ofer Cohen, Uli Christensen, Tom Crowley, Debrah Fischer, Terry Forbes, Tim Fuller-Rowell, Marina Galand, Joe Giacalone, George Gloeckler, Jack Gosling, Janet Green, Nick Gross, Steve Guetersloh, Viggo Hansteen, Lee Hartmann, Mihaly Horanyi, Hugh Hudson, Norbert Jakowski, Randy Jokipii, Margaret Kivelson, Dietmar Krauss-Varban, Norbert Krupp, Judith Lean, Jeff Linsky, Dana Longcope, Daniel Marsh, Mark Miesch, Mark Moldwin, Luke Moore, Sten Odenwald, Merav Opher, Rachel Osten, Matthias Rempel, Hauke Schmidt, George Siscoe, Dave Siskind, Chuck Smith, Stan Solomon, Tom Stallard, Sabine Stanley, Jan Sojka, Kent Tobiska, Frank Toffoletto, Alan Tribble, Vytenis Vasyliunas, Richard Walterscheid, Ji Wang, Brian Wood, Tom Woods, Neal Zappwork_v2zqk34khrabtaqqb3zmwqkhpaTue, 27 Sep 2022 00:00:00 GMTTurbulence, Coherence and Collapse: Three Phases for Core Evolution
https://scholar.archive.org/work/hhoxvvjanvgyblv2hmgpfdwoly
We study the formation, evolution and collapse of dense cores by tracking structures in a magnetohydrodynamic simulation of a star-forming cloud. We identify cores using the dendrogram algorithm and utilize machine learning techniques, including Neural Gas prototype learning and Fuzzy c-means clustering, to analyze the density and velocity dispersion profiles of cores together with six bulk properties. We produce a 2-d visualization using a Uniform Manifold Approximation and Projection (UMAP), which facilitates the connection between physical properties and three partially-overlapping phases: i) unbound turbulent structures (Phase I), ii) coherent cores that have low turbulence (Phase II), and iii) bound cores, many of which become protostellar (Phase III). Within Phase II we identify a population of long-lived coherent cores that reach a quasi-equilibrium state. Most prestellar cores form in Phase II and become protostellar after evolving into Phase III. Due to the turbulent cloud environment, the initial core properties do not uniquely predict the eventual evolution, i.e., core evolution is stochastic, and cores follow no one evolutionary path. The phase lifetimes are 1.0±0.1×10^5 yr, 1.3±0.2×10^5 yr, and 1.8±0.3×10^5 yr for Phase I, II, and III, respectively. We compare our results to NH_3 observations of dense cores. Known coherent cores predominantly map into Phase II, while most turbulent pressure-confined cores map to Phase I or III. We predict that a significant fraction of observed starless cores have unresolved coherent regions and that ≳ 20 Measurements of core radial profiles, in addition to the usual bulk properties, will enable more accurate predictions of core evolution.Stella S. R. Offner, Josh Taylor, Carleen Markey, Hope How-Huan Chen, Jaime E. Pineda, Alyssa A. Goodman, Andreas Burkert, Adam Ginsburg, Spandan Choudhurywork_hhoxvvjanvgyblv2hmgpfdwolyMon, 26 Sep 2022 00:00:00 GMTOptimization problems in graphs with locational uncertainty
https://scholar.archive.org/work/gswwrkoycrbexdtpahixxxpwrm
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are NP-hard even when the feasible sets consist either of all spanning trees or of all s-t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem.Marin Bougeret, Jérémy Omer, Michael Posswork_gswwrkoycrbexdtpahixxxpwrmMon, 26 Sep 2022 00:00:00 GMTHierarchical Cyclic Pursuit: Algebraic Curves Containing the Laplacian Spectra
https://scholar.archive.org/work/vud3fnhivncvfgv7umt4ow4pha
The paper addresses the problem of multi-agent communication in networks with regular directed ring structure. These can be viewed as hierarchical extensions of the classical cyclic pursuit topology. We show that the spectra of the corresponding Laplacian matrices allow exact localization on the complex plane. Furthermore, we derive a general form of the characteristic polynomial of such matrices, analyze the algebraic curves its roots belong to, and propose a way to obtain their closed-form equations. In combination with frequency domain consensus criteria for high-order SISO linear agents, these curves enable one to analyze the feasibility of consensus in networks with varying number of agents.Sergei E. Parsegov, Pavel Yu. Chebotarev, Pavel S. Shcherbakov, Federico M. Ibáñezwork_vud3fnhivncvfgv7umt4ow4phaSun, 25 Sep 2022 00:00:00 GMTThe Solar System: Nature and mechanics
https://scholar.archive.org/work/wrhqx6363zhjtmsoybtwo64sua
Origin, mechanics and properties of the Solar System are analysed in the framework of the Complete Relativity theory (by the same author). According to Complete Relativity, everything is relative. Any apparent absolutism (notably invariance to scale of dimensional constants, absolute elementariness, invariance to time) is an illusion stemming from limits imposed by [or on] polarized observers that will inevitably lead to misinterpretation of phenomena (another illusion) occurring on non-directly observable scales or even observable but distant scales in space or time. If everything is relative, reference frames will exist where particles are planets and where planets are living beings. Earth is, therefore, analysed here in more detail, both as a particle and, as a living evolving being (of, hypothesized, extremely introverted intelligence). The analysis confirms the postulates and hypotheses of the theory (ie. existence of discrete vertical energy levels) with a significant degree of confidence. During the analysis, some new hypotheses have emerged. These are discussed and confirmed with various degrees of confidence. To increase confidence or refute some hypotheses, experimental verification is necessary. Main conclusions that stem from my research and are further confirmed in this paper are: universes are, indeed, completely relative, Solar System is a scaled (inflated, in some interpretations) Carbon isotope with a nucleus in a condensed (bosonic) state and components in various vertically excited states, life is common everywhere, albeit extroverted complex forms are present on planetary surfaces only during planetary neurogenesis, anthropogenic climate change is only a part (trigger from one perspective) of bigger global changes, major extinction events on a surface of a planet are relative extinctions, a regular part of transformation and transfer of life in the process of planetary neurogenesis.Mario Ljubičićwork_wrhqx6363zhjtmsoybtwo64suaSun, 25 Sep 2022 00:00:00 GMTElastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework
https://scholar.archive.org/work/cdjnlyopgfbv3drot6pf7wkcce
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic distances between parametrized or unparametrized immersed surfaces represented as 3D meshes. Building on this, we develop tools for the statistical shape analysis of sets of surfaces, including methods for estimating Karcher means and performing tangent PCA on shape populations, and for computing parallel transport along paths of surfaces. Our proposed approach fundamentally relies on a relaxed variational formulation for the geodesic matching problem via the use of varifold fidelity terms, which enable us to enforce reparametrization independence when computing geodesics between unparametrized surfaces, while also yielding versatile algorithms that allow us to compare surfaces with varying sampling or mesh structures. Importantly, we demonstrate how our relaxed variational framework can be extended to tackle partially observed data. The different benefits of our numerical pipeline are illustrated over various examples, synthetic and real.Emmanuel Hartman, Yashil Sukurdeep, Eric Klassen, Nicolas Charon, Martin Bauerwork_cdjnlyopgfbv3drot6pf7wkcceSun, 25 Sep 2022 00:00:00 GMTEnsembles of Realistic Power Distribution Networks
https://scholar.archive.org/work/5suepn52ubemjan7pqppjppoz4
The power grid is going through significant changes with the introduction of renewable energy sources and incorporation of smart grid technologies. These rapid advancements necessitate new models and analyses to keep up with the various emergent phenomena they induce. A major prerequisite of such work is the acquisition of well-constructed and accurate network datasets for the power grid infrastructure. In this paper, we propose a robust, scalable framework to synthesize power distribution networks which resemble their physical counterparts for a given region. We use openly available information about interdependent road and building infrastructures to construct the networks. In contrast to prior work based on network statistics, we incorporate engineering and economic constraints to create the networks. Additionally, we provide a framework to create ensembles of power distribution networks to generate multiple possible instances of the network for a given region. The comprehensive dataset consists of nodes with attributes such as geo-coordinates, type of node (residence, transformer, or substation), and edges with attributes such as geometry, type of line (feeder lines, primary or secondary) and line parameters. For validation, we provide detailed comparisons of the generated networks with actual distribution networks. The generated datasets represent realistic test systems (as compared to standard IEEE test cases) that can be used by network scientists to analyze complex events in power grids and to perform detailed sensitivity and statistical analyses over ensembles of networks.Rounak Meyur, Anil Vullikanti, Samarth Swarup, Henning Mortveit, Virgilio Centeno, Arun Phadke, H. Vincent Poor, Madhav Marathework_5suepn52ubemjan7pqppjppoz4Sat, 24 Sep 2022 00:00:00 GMTDeterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity Certificates
https://scholar.archive.org/work/finy2wwnkrhdpag6u6gmmpy46m
This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in polylog(n) rounds in weighted graphs. Concretely, our algorithm outputs a spanning subgraph with only n+o(n) edges in which the pairwise distances are stretched by a factor of at most O(log n · 2^O(log^* n)). We provide a polylog(n)-round deterministic distributed algorithm that computes a spanner with stretch (2k-1) and O(nk + n^1 + 1/klog k) edges in unweighted graphs and with O(n^1 + 1/k k) edges in weighted graphs. We present the first polylog(n)-round randomized distributed algorithm that computes a sparse connectivity certificate. For an n-node graph G, a certificate for connectivity k is a spanning subgraph H that is k-edge-connected if and only if G is k-edge-connected, and this subgraph H is called sparse if it has O(nk) edges. Our algorithm achieves a sparsity of (1 + o(1))nk edges, which is within a 2(1 + o(1)) factor of the best possible.Marcel Bezdrighin, Michael Elkin, Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, Václav Rozhoňwork_finy2wwnkrhdpag6u6gmmpy46mFri, 23 Sep 2022 00:00:00 GMTUndirected (1+ε)-Shortest Paths via Minor-Aggregates: Near-Optimal Deterministic Parallel Distributed Algorithms
https://scholar.archive.org/work/avgfthkhgzgltjmalqqxpw37rq
This paper presents near-optimal deterministic parallel and distributed algorithms for computing (1+ε)-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this and other shortest-path problems to Õ(1) Minor-Aggregations. A Minor-Aggregation computes an aggregate (e.g., max or sum) of node-values for every connected component of some subgraph. Our reduction immediately implies: Optimal deterministic parallel (PRAM) algorithms with Õ(1) depth and near-linear work. Universally-optimal deterministic distributed (CONGEST) algorithms, whenever deterministic Minor-Aggregate algorithms exist. For example, an optimal Õ(HopDiameter(G))-round deterministic CONGEST algorithm for excluded-minor networks. Several novel tools developed for the above results are interesting in their own right: A local iterative approach for reducing shortest path computations "up to distance D" to computing low-diameter decompositions "up to distance D/2". Compared to the recursive vertex-reduction approach of [Li20], our approach is simpler, suitable for distributed algorithms, and eliminates many derandomization barriers. A simple graph-based Õ(1)-competitive ℓ_1-oblivious routing based on low-diameter decompositions that can be evaluated in near-linear work. The previous such routing [ZGY+20] was n^o(1)-competitive and required n^o(1) more work. A deterministic algorithm to round any fractional single-source transshipment flow into an integral tree solution. The first distributed algorithms for computing Eulerian orientations.Václav Rozhoň and Christoph Grunau and Bernhard Haeupler and Goran Zuzic and Jason Liwork_avgfthkhgzgltjmalqqxpw37rqFri, 23 Sep 2022 00:00:00 GMTCombinatorial optimization and reasoning with graph neural networks
https://scholar.archive.org/work/dszclpgdgfgzrnd562tfbceni4
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at optimization and machine learning researchers.Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, Petar Veličkovićwork_dszclpgdgfgzrnd562tfbceni4Fri, 23 Sep 2022 00:00:00 GMTNonlocal Wasserstein Distance: Metric and Asymptotic Properties
https://scholar.archive.org/work/k7nch26zj5dedk46ushzw3xhkm
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where paths are solutions of the continuity equation and the action is the kinetic energy. Here we consider a fundamental modification of the framework where the paths are solutions of nonlocal (jump) continuity equations and the action is a nonlocal kinetic energy. The resulting nonlocal Wasserstein distances are relevant to fractional diffusions and Wasserstein distances on graphs. We characterize the basic properties of the distance and obtain sharp conditions on the (jump) kernel specifying the nonlocal transport that determine whether the topology metrized is the weak or the strong topology. A key result of the paper are the quantitative comparisons between the nonlocal and local Wasserstein distance.Dejan Slepčev, Andrew Warrenwork_k7nch26zj5dedk46ushzw3xhkmThu, 22 Sep 2022 00:00:00 GMTIntegrated and Coordinated Relief Logistics Planning Under Uncertainty for Relief Logistics Operations
https://scholar.archive.org/work/kydxk7lhnrdpbl3vbh5jzmuina
In this thesis, we explore three critical emergency logistics problems faced by healthcare and humanitarian relief service providers for short-term post-disaster management. In the first manuscript, we investigate various integration mechanisms (fully integrated horizontal-vertical, horizontal, and vertical resource sharing mechanisms) following a natural disaster for a multi-type whole blood-derived platelets, multi-patient logistics network. The goal is to reduce the amount of shortage and wastage of multi-blood-group of platelets in the response phase of relief logistics operations. To solve the logistics model for a large scale problem, we develop a hybrid exact solution approach involving an augmented epsilon-constraint and Lagrangian relaxation algorithms and demonstrate the model's applicability for a case study of an earthquake. Due to uncertainty in the number of injuries needing multi-type blood-derived platelets, we apply a robust optimization version of the proposed model which captures the expected performance of the system. The results show that the performance of the platelets logistics network under coordinated and integrated mechanisms better control the level of shortage and wastage compared with that of a non-integrated network. In the second manuscript, we propose a two-stage casualty evacuation model that involves routing of patients with different injury levels during wildfires. The first stage deals with field hospital selection and the second stage determines the number of patients that can be transferred to the selected hospitals or shelters via different routes of the evacuation network. The goal of this model is to reduce the evacuation response time, which ultimately increase the number of evacuated people from evacuation assembly points under limited time windows. To solve the model for large-scale problems, we develop a two-step meta-heuristic algorithm. To consider multiple sources of uncertainty, a flexible robust approach considering the worst-case and expected performance of the [...]Afshin Kamyabniya, University, Mywork_kydxk7lhnrdpbl3vbh5jzmuinaThu, 22 Sep 2022 00:00:00 GMTLayered character models for fast physics-based simulation
https://scholar.archive.org/work/e2u77bn53fd65kfxyzs6sycpmq
This thesis presents two different layered character models that are ready to be used in physics-based simulations, in particular they enable convincing character animations in real-time. We start by introducing a two-layered model consisting of rigid bones and an elastic soft tissue layer that is efficiently constructed from a surface mesh of the character and its underlying skeleton. Building on this model, we introduce Fast Projective Skinning, a novel approach for physics-based character skinning. While maintaining real-time performance it overcomes the well-known artifacts of commonly used geometric skinning approaches. It further enables dynamic effects and resolves local and global self-collisions. In particular, our method neither requires skinning weights, which are often expensive to compute or tedious to hand-tune, nor a complex volumetric tessellation, which fails for many real-world input meshes due to self-intersections. By developing a custom-tailored GPU implementation and a high-quality upsampling method, our ap- proach is the first skinning method capable of detecting and handling arbitrary global collisions in real-time. In the second part of the thesis, we extend the idea of a simplified two-layered volumetric model by developing an anatomically plausible three-layered representation of human virtual characters. Starting with an anatomy model of the male and female body, we show how to generate a layered body template for both sexes. It is composed of three surfaces for bones, muscles and skin enclosing the volumetric skeleton, muscles and fat tissues. Utilizing the simple structure of these templates, we show how to fit them to the surface scan of a person in just a few seconds. Our approach includes a data-driven method for estimating the amount of muscle mass and fat mass from a surface scan, which provides more accurate fits to the variety of human body shapes compared to previous approaches. Additionally, we demonstrate how to efficiently embed fine-scale anatomical details, such as high [...]Martin Komaritzan, Technische Universität Dortmundwork_e2u77bn53fd65kfxyzs6sycpmqThu, 22 Sep 2022 00:00:00 GMT