Journal articles on the topic 'Entropy optimal transport'
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Tong, Qijun, and Kei Kobayashi. "Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions." Entropy 23, no. 3 (March 3, 2021): 302. http://dx.doi.org/10.3390/e23030302.
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The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.
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Bonafini, Mauro, and Bernhard Schmitzer. "Domain decomposition for entropy regularized optimal transport." Numerische Mathematik 149, no. 4 (November 19, 2021): 819–70. http://dx.doi.org/10.1007/s00211-021-01245-0.
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AbstractWe study Benamou’s domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove linear convergence of the algorithm with respect to the Kullback–Leibler divergence and illustrate the (potentially very slow) rates with numerical examples. On problems with sufficient geometric structure (such as Wasserstein distances between images) we expect much faster convergence. We then discuss important aspects of a computationally efficient implementation, such as adaptive sparsity, a coarse-to-fine scheme and parallelization, paving the way to numerically solving large-scale optimal transport problems. We demonstrate efficient numerical performance for computing the Wasserstein-2 distance between 2D images and observe that, even without parallelization, domain decomposition compares favorably to applying a single efficient implementation of the Sinkhorn algorithm in terms of runtime, memory and solution quality.
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Bao, Han, and Shinsaku Sakaue. "Sparse Regularized Optimal Transport with Deformed q-Entropy." Entropy 24, no. 11 (November 10, 2022): 1634. http://dx.doi.org/10.3390/e24111634.
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Optimal transport is a mathematical tool that has been a widely used to measure the distance between two probability distributions. To mitigate the cubic computational complexity of the vanilla formulation of the optimal transport problem, regularized optimal transport has received attention in recent years, which is a convex program to minimize the linear transport cost with an added convex regularizer. Sinkhorn optimal transport is the most prominent one regularized with negative Shannon entropy, leading to densely supported solutions, which are often undesirable in light of the interpretability of transport plans. In this paper, we report that a deformed entropy designed by q-algebra, a popular generalization of the standard algebra studied in Tsallis statistical mechanics, makes optimal transport solutions supported sparsely. This entropy with a deformation parameter q interpolates the negative Shannon entropy (q=1) and the squared 2-norm (q=0), and the solution becomes more sparse as q tends to zero. Our theoretical analysis reveals that a larger q leads to a faster convergence when optimized with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In summary, the deformation induces a trade-off between the sparsity and convergence speed.
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Essid, Montacer, Debra F. Laefer, and Esteban G. Tabak. "Adaptive optimal transport." Information and Inference: A Journal of the IMA 8, no. 4 (May 16, 2019): 789–816. http://dx.doi.org/10.1093/imaiai/iaz008.
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AbstractAn adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu $ and $\nu $, known only through a finite set of independent samples $(x_i)_{i=1..n}$ and $(y_j)_{j=1..m}$. The methodology automatically creates features that adapt to the data, thus avoiding reliance on a priori knowledge of the distributions underlying the data. Specifically, instead of a discrete point-by-point assignment, the new procedure seeks an optimal map $T(x)$ defined for all $x$, minimizing the Kullback–Leibler divergence between $(T(x_i))$ and the target $(y_j)$. The relative entropy is given a sample-based, variational characterization, thereby creating an adversarial setting: as one player seeks to push forward one distribution to the other, the second player develops features that focus on those areas where the two distributions fail to match. The procedure solves local problems that seek the optimal transfer between consecutive, intermediate distributions between $\mu $ and $\nu $. As a result, maps of arbitrary complexity can be built by composing the simple maps used for each local problem. Displaced interpolation is used to guarantee global from local optimality. The procedure is illustrated through synthetic examples in one and two dimensions.
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PEYRÉ, GABRIEL, LÉNAÏC CHIZAT, FRANÇOIS-XAVIER VIALARD, and JUSTIN SOLOMON. "Quantum entropic regularization of matrix-valued optimal transport." European Journal of Applied Mathematics 30, no. 6 (September 28, 2017): 1079–102. http://dx.doi.org/10.1017/s0956792517000274.
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This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This “quantum” formulation of optimal transport (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy. We propose a quantum-entropic regularization of the resulting convex optimization problem, which can be solved efficiently using an iterative scaling algorithm. This method is a generalization of the celebrated Sinkhorn algorithm to the quantum setting of PSD matrices. We extend this formulation and the quantum Sinkhorn algorithm to compute barycentres within a collection of input tensor fields. We illustrate the usefulness of the proposed approach on applications to procedural noise generation, anisotropic meshing, diffusion tensor imaging and spectral texture synthesis.
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Santambrogio, Filippo. "Dealing with moment measures via entropy and optimal transport." Journal of Functional Analysis 271, no. 2 (July 2016): 418–36. http://dx.doi.org/10.1016/j.jfa.2016.04.009.
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Gentil, Ivan, Christian Léonard, and Luigia Ripani. "About the analogy between optimal transport and minimal entropy." Annales de la faculté des sciences de Toulouse Mathématiques 26, no. 3 (2017): 569–600. http://dx.doi.org/10.5802/afst.1546.
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Mihelich, M., D. Faranda, B. Dubrulle, and D. Paillard. "Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy." Nonlinear Processes in Geophysics 22, no. 2 (March 25, 2015): 187–96. http://dx.doi.org/10.5194/npg-22-187-2015.
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Abstract. We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy, seen as functions of a parameter f connected to the jump probability, admit a unique maximum denoted fmaxEP and fmaxKS. The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this paper is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation from equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of those adopted by Paltridge and climatologists working on maximum entropy production (N ≈ 10–100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second-order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non-equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.
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Mihelich, M., D. Faranda, B. Dubrulle, and D. Paillard. "Statistical optimization for passive scalar transport: maximum entropy production vs. maximum Kolmogorov–Sinay entropy." Nonlinear Processes in Geophysics Discussions 1, no. 2 (November 18, 2014): 1691–713. http://dx.doi.org/10.5194/npgd-1-1691-2014.
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Abstract. We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists (N ≈ 10 ~ 100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.
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Islas, Carlos, Pablo Padilla, and Marco Antonio Prado. "Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach." Entropy 22, no. 11 (October 29, 2020): 1231. http://dx.doi.org/10.3390/e22111231.
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We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.
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Bazaluk, Oleg, Sergiy Kotenko, and Vitalii Nitsenko. "Entropy as an Objective Function of Optimization Multimodal Transportations." Entropy 23, no. 8 (July 24, 2021): 946. http://dx.doi.org/10.3390/e23080946.
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This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks.
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Carlen, Eric A., and Jan Maas. "Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems." Journal of Statistical Physics 178, no. 2 (November 27, 2019): 319–78. http://dx.doi.org/10.1007/s10955-019-02434-w.
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AbstractWe study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $$C^*$$ C ∗ -algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral gap estimates.
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Datta, Nilanjana, and Cambyse Rouzé. "Relating Relative Entropy, Optimal Transport and Fisher Information: A Quantum HWI Inequality." Annales Henri Poincaré 21, no. 7 (February 5, 2020): 2115–50. http://dx.doi.org/10.1007/s00023-020-00891-8.
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Le, Xuan Hoang Khoa, Hakan F. Oztop, Fatih Selimefendigil, and Mikhail A. Sheremet. "Entropy Analysis of the Thermal Convection of Nanosuspension within a Chamber with a Heat-Conducting Solid Fin." Entropy 24, no. 4 (April 7, 2022): 523. http://dx.doi.org/10.3390/e24040523.
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Heat transport augmentation in closed chambers can be achieved using nanofluids and extended heat transfer surfaces. This research is devoted to the computational analysis of natural convection energy transport and entropy emission within a closed region, with isothermal vertical borders and a heat-conducting solid fin placed on the hot border. Horizontal walls were assumed to be adiabatic. Control relations written using non-primitive variables with experimentally based correlations for nanofluid properties were computed by the finite difference technique. The impacts of the fin size, fin position, and nanoadditive concentration on energy transfer performance and entropy production were studied. It was found that location of the long fin near the bottom wall allowed for the intensification of convective heat transfer within the chamber. Moreover, this position was characterized by high entropy generation. Therefore, the minimization of the entropy generation can define the optimal location of the heat-conducting fin using the obtained results. An addition of nanoparticles reduced the heat transfer strength and minimized the entropy generation.
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An, Dongsheng, Na Lei, Xiaoyin Xu, and Xianfeng Gu. "Efficient Optimal Transport Algorithm by Accelerated Gradient Descent." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10119–28. http://dx.doi.org/10.1609/aaai.v36i9.21251.
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Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly challenging. Recently, methods based on the Sinkhorn algorithm add an entropy regularizer to the prime problem and get a trade off between efficiency and accuracy. In this paper, we propose a novel algorithm to further improve the efficiency and accuracy based on Nesterov's smoothing technique. Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which finally smooths the original non-smooth Kantorovich dual functional. The smooth Kantorovich functional can be optimized by the fast proximal gradient algorithm (FISTA) efficiently. Theoretically, the computational complexity of the proposed method is lower than current estimation of the Sinkhorn algorithm in terms of the precision. Empirically, compared with the Sinkhorn algorithm, our experimental results demonstrate that the proposed method achieves faster convergence and better accuracy with the same parameter.
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Dupuis, Paul, and Yixiang Mao. "Formulation and properties of a divergence used to compare probability measures without absolute continuity." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 10. http://dx.doi.org/10.1051/cocv/2022002.
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This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. Also included are examples of computation and approximation of the divergence, and the demonstration of properties that are useful when one quantifies model uncertainty.
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Liero, Matthias, Alexander Mielke, and Giuseppe Savaré. "Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures." Inventiones mathematicae 211, no. 3 (December 14, 2017): 969–1117. http://dx.doi.org/10.1007/s00222-017-0759-8.
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Wang, Shuchan, Photios A. Stavrou, and Mikael Skoglund. "Generalizations of Talagrand Inequality for Sinkhorn Distance Using Entropy Power Inequality." Entropy 24, no. 2 (February 21, 2022): 306. http://dx.doi.org/10.3390/e24020306.
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The distance that compares the difference between two probability distributions plays a fundamental role in statistics and machine learning. Optimal transport (OT) theory provides a theoretical framework to study such distances. Recent advances in OT theory include a generalization of classical OT with an extra entropic constraint or regularization, called entropic OT. Despite its convenience in computation, entropic OT still lacks sufficient theoretical support. In this paper, we show that the quadratic cost in entropic OT can be upper-bounded using entropy power inequality (EPI)-type bounds. First, we prove an HWI-type inequality by making use of the infinitesimal displacement convexity of the OT map. Second, we derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expressions. These two new inequalities are shown to generalize two previous results obtained by Bolley et al. and Bai et al. Using the new Talagrand-type inequalities, we also show that the geometry observed by Sinkhorn distance is smoothed in the sense of measure concentration. Finally, we corroborate our results with various simulation studies.
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Bigot, Jérémie, Elsa Cazelles, and Nicolas Papadakis. "Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications." Electronic Journal of Statistics 13, no. 2 (2019): 5120–50. http://dx.doi.org/10.1214/19-ejs1637.
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Li, Haifeng, Jun Liu, Li Cui, Haiyang Huang, and Xue-Cheng Tai. "Volume preserving image segmentation with entropy regularized optimal transport and its applications in deep learning." Journal of Visual Communication and Image Representation 71 (August 2020): 102845. http://dx.doi.org/10.1016/j.jvcir.2020.102845.
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Dechant, Andreas. "Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes." Journal of Physics A: Mathematical and Theoretical 55, no. 9 (February 3, 2022): 094001. http://dx.doi.org/10.1088/1751-8121/ac4ac0.
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Abstract We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is driven by conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph via continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model.
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Bhatia, Rajendra, Tanvi Jain, and Yongdo Lim. "Strong convexity of sandwiched entropies and related optimization problems." Reviews in Mathematical Physics 30, no. 09 (September 25, 2018): 1850014. http://dx.doi.org/10.1142/s0129055x18500149.
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We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrized version of the classical fidelity). These are crucial for establishing global linear convergence of the gradient projection algorithm for optimization problems for these functions. The case of the classical fidelity is of special interest for the multimarginal optimal transport problem (the [Formula: see text]-coupling problem) for Gaussian measures.
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Juretić, Davor, Juraj Simunić, and Željana Bonačić Lošić. "Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications." Entropy 21, no. 8 (July 29, 2019): 743. http://dx.doi.org/10.3390/e21080743.
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Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.
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Hobbs, Bruce E., and Alison Ord. "The mechanics of granitoid systems and maximum entropy production rates." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 53–93. http://dx.doi.org/10.1098/rsta.2009.0202.
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A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10 4 –10 7 years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson–Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient ‘ponds’ of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic–viscous at high temperatures to elastic–plastic–viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate.
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Stoilova, Svetla. "An approach for choosing the optimal route and type of transport for freight carriage using Compromise programming." MATEC Web of Conferences 234 (2018): 06002. http://dx.doi.org/10.1051/matecconf/201823406002.
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This study elaborates a methodology for choosing a transport strategy based on the selection of the optimal route and type of transport. The research examines carriage by containers and includes two ways of transportation: by container block trains and by trucks. The methodology consists of three steps. The first step defines the determination of alternatives routes and criteria for assessment. Eight criteria have been studied: environmental protection; economic criteria; additional transportation fare; the duration of transportation; transhipment operations; security; reliability; stability. In the second step three approaches have been used and compared to determine the weights of the criteria: the Shannon entropy method, which is based on information from data, expert assessments by means of the Analytic hierarchy process (AHP) method and the Decision Making Trial and Evaluation Laboratory (DEMATEL) method. The third step determines the optimal solution based on the Compromise programming method. The methodology is approbated for routes from the railway and road network of Bulgaria. The results show that the criteria with the greatest impact are: the economic criteria; the duration of transportation and environmental protection. It was found out that the technologies that include rail transport are the best variant of transportation. The presented methodology could be used for choosing transportation for other destinations in the transport network.
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Dong, Sheng, Jibiao Zhou, and Changxi Ma. "Design of a Network Optimization Platform for the Multivehicle Transportation of Hazardous Materials." International Journal of Environmental Research and Public Health 17, no. 3 (February 10, 2020): 1104. http://dx.doi.org/10.3390/ijerph17031104.
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With economic development, the volume of hazardous materials is increasing, and the potential risks to human beings and the natural environment are expanding. Road transportation has become the main mode of transportation for hazardous materials. Because of the specific characteristics of hazardous materials, if an accident occurs in the transportation process, it often causes mass casualties, serious property and socioeconomic damage, and damage to the ecological environment. Hence, transportation is an important part of the life cycle of hazardous materials. This paper designs an optimization platform for multidestination, multiterminal, and multivehicle networks that transport hazardous materials. The logistics module in TransCAD software is used to construct this platform. By identifying the effective transportation routes considering the transportation risk, sensitive target population, and transportation time of each road section, the entropy method can be used to fuse and obtain the comprehensive impedance value of each road section. Finally, the optimal transportation network of hazardous materials was obtained by the transportation network optimization algorithm in TransCAD. The platform can display the optimal transport program with data windows, text, and maps. The research results provide a reference for relevant departments to scientifically manage the transport of hazardous materials.
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Lindgren, Jussi. "Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach." Entropy 22, no. 11 (November 12, 2020): 1283. http://dx.doi.org/10.3390/e22111283.
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This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.
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Dolbeault, Jean, and Xingyu Li. "φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations." Mathematical Models and Methods in Applied Sciences 28, no. 13 (December 6, 2018): 2637–66. http://dx.doi.org/10.1142/s0218202518500574.
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This paper is devoted to [Formula: see text]-entropies applied to Fokker–Planck and kinetic Fokker–Planck equations in the whole space, with confinement. The so-called [Formula: see text]-entropies are Lyapunov functionals which typically interpolate between Gibbs entropies and [Formula: see text] estimates. We review some of their properties in the case of diffusion equations of Fokker–Planck type, give new and simplified proofs, and then adapt these methods to a kinetic Fokker–Planck equation acting on a phase space with positions and velocities. At kinetic level, since the diffusion only acts on the velocity variable, the transport operator plays an essential role in the relaxation process. Here we adopt the [Formula: see text] point of view and establish a sharp decay rate. Rather than giving general but quantitatively vague estimates, our goal here is to consider simple cases, benchmark available methods and obtain sharp estimates on a key example. Some [Formula: see text]-entropies give rise to improved entropy–entropy production inequalities and, as a consequence, to faster decay rates for entropy estimates of solutions to non-degenerate diffusion equations. We prove that faster entropy decay also holds at kinetic level away from equilibrium and that optimal decay rates are achieved only in asymptotic regimes.
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Koehl, Patrice, Marc Delarue, and Henri Orland. "Computing the Gromov-Wasserstein Distance between Two Surface Meshes Using Optimal Transport." Algorithms 16, no. 3 (February 28, 2023): 131. http://dx.doi.org/10.3390/a16030131.
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The Gromov-Wasserstein (GW) formalism can be seen as a generalization of the optimal transport (OT) formalism for comparing two distributions associated with different metric spaces. It is a quadratic optimization problem and solving it usually has computational costs that can rise sharply if the problem size exceeds a few hundred points. Recently fast techniques based on entropy regularization have being developed to solve an approximation of the GW problem quickly. There are issues, however, with the numerical convergence of those regularized approximations to the true GW solution. To circumvent those issues, we introduce a novel strategy to solve the discrete GW problem using methods taken from statistical physics. We build a temperature-dependent free energy function that reflects the GW problem’s constraints. To account for possible differences of scales between the two metric spaces, we introduce a scaling factor s in the definition of the energy. From the extremum of the free energy, we derive a mapping between the two probability measures that are being compared, as well as a distance between those measures. This distance is equal to the GW distance when the temperature goes to zero. The optimal scaling factor itself is obtained by minimizing the free energy with respect to s. We illustrate our approach on the problem of comparing shapes defined by unstructured triangulations of their surfaces. We use several synthetic and “real life” datasets. We demonstrate the accuracy and automaticity of our approach in non-rigid registration of shapes. We provide numerical evidence that there is a strong correlation between the GW distances computed from low-resolution, surface-based representations of proteins and the analogous distances computed from atomistic models of the same proteins.
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Li, Yunqiang, Silvia-Laura Pintea, and Jan C. van Gemert. "Equal Bits: Enforcing Equally Distributed Binary Network Weights." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 2 (June 28, 2022): 1491–99. http://dx.doi.org/10.1609/aaai.v36i2.20039.
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Binary networks are extremely efficient as they use only two symbols to define the network: {+1, −1}. One can make the prior distribution of these symbols a design choice. The recent IR-Net of Qin et al. argues that imposing a Bernoulli distribution with equal priors (equal bit ratios) over the binary weights leads to maximum entropy and thus minimizes information loss. However, prior work cannot precisely control the binary weight distribution during training, and therefore cannot guarantee maximum entropy. Here, we show that quantizing using optimal transport can guarantee any bit ratio, including equal ratios. We investigate experimentally that equal bit ratios are indeed preferable and show that our method leads to optimization benefits. We show that our quantization method is effective when compared to state-of-the-art binarization methods, even when using binary weight pruning. Our code is available at https://github.com/liyunqianggyn/Equal-Bits-BNN.
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Hussain, Muzamil, Jifeng Cui, Umer Farooq, Mohammed Elamin Ahmed Rabie, and Taseer Muhammad. "Nonsimilar Modeling and Numerical Simulations of Electromagnetic Radiative Flow of Nanofluid with Entropy Generation." Mathematical Problems in Engineering 2022 (February 1, 2022): 1–20. http://dx.doi.org/10.1155/2022/4272566.
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Electromagnetic water/CNTs nanofluid flow across a convectively heated moving surface is reported in this communication. Aspect of thermal radiations is considered for heat transport analysis. The concept of nonsimilar boundary layer is executed to simplify the convoluted mathematical expressions. Also, an entropy generation model is considered since its reduction minimizes the loss of available energy, which improves thermal efficiency. The governing model is reduced to a dimensionless system by using an appropriate nonsimilarity transformation. The numerical solution for the velocity and temperature profiles has been obtained by implementing local nonsimilarity via finite difference based Matlab algorithm bvp4c for various quantities of the main emerging parameters. The outcomes are depicted in tabular and graphical formats to analyze impacts of different geometrical, thermophysical, and dynamical factors on temperature, velocity, frictional drag, entropy generation (EG), Nusselt number, and the Bejan number. The temperature profile is seen to rise with Biot number and thermal radiation. Higher radiation parameters and nanoparticle concentrations cause an increase in entropy generation. Horizontal plate with the wedge angle m = 0 is the optimal geometry for minimizing entropy generation. The increase in the values electric field parameter leads to the rise in the skin friction coefficient. Also, Nusselt number declines when magnetic parameter and Eckert number are increase. The authors discussed the local nonsimilarity approach for simulating the dimensionless nonsimilar structure. To the best of authors’ knowledge, no such study has yet been published in the literature. To show the originality of results, the current numerical findings are compared with the published research for some limiting cases and are found to be in excellent alignment. This study could be useful for examining the impacts of nanofluids in a thermal transport analysis.
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Yang, Fan, Zhongbin Li, Yiping Cai, Dongjin Jiang, Fangping Tang, and Shengjie Sun. "Numerical Study for Flow Loss Characteristic of an Axial-Flow Pump as Turbine via Entropy Production Analysis." Processes 10, no. 9 (August 26, 2022): 1695. http://dx.doi.org/10.3390/pr10091695.
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Low-head vertical axial-flow pump as turbine (PAT) devices play a vital part in the development of clean energy for hydropower in plain areas. The traditional method of evaluating the flow loss in hydraulic machinery is calculated by the pressure drop method, the limitation of which is that the location of the occurrence of large losses cannot be accurately determined. In this paper, entropy production theory is introduced to evaluate the irreversible losses in the axial-flow PAT from the perspective of the second law of thermodynamics. A three-dimensional model of the axial-flow PAT is established and solved numerically using the Reynolds time-averaged equation, and the turbulence model is adopted as Shear Stress Transport–Curvature Correction (SST-CC) model. The validity of the entropy production theory to evaluate the energy loss distribution of the axial-flow PAT is illustrated by comparing the flow loss calculated by the pressure drop and the entropy production theory, respectively. The entropy production by turbulent dissipative dominates the total entropy production in the whole flow conduit, and the turbulent dissipative entropy accounts for the smallest percentage of the whole conduit entropy production at the optimal working condition Qbep, which is 51%. The impeller and the dustpan-shaped conduit are the essential sources of hydraulic loss in the entire flow conduit of the axial-flow PAT, and most of the energy loss of the impeller occurs at the blade leading edge, the trailing edge, and the flow separation zone near the suction surface. The energy loss of the dustpan-shaped conduit results from the high-speed flow from the impeller outlet to dustpan-shaped conduit to form a vortex, backflow and other chaotic flow patterns. Flow impact, flow separation, vortex and backflow are the main causes of high entropy production and energy loss.
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An, Yongkai, Yanxiang Zhang, and Xueman Yan. "An Integrated Bayesian and Machine Learning Approach Application to Identification of Groundwater Contamination Source Parameters." Water 14, no. 15 (August 7, 2022): 2447. http://dx.doi.org/10.3390/w14152447.
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The identification of groundwater contamination source parameters is an important prerequisite for the control and risk assessment of groundwater contamination. This study developed an innovative approach for the optimal design of observation well locations and the high-precision identification of groundwater contamination source parameters. The approach involves Bayesian theory and integrates Markov Chain Monte Carlo, Bayesian design, information entropy, machine learning, and surrogate modeling. The optimal observation well locations are determined by information entropy, which is adopted to mine valuable information about unknown groundwater contamination source parameters from measurements of contaminant concentration according to Bayesian design. After determining the optimal observation well locations, the identification of groundwater contamination source parameters is implemented through a Bayesian-based Differential Evolution Adaptive Metropolis with Discrete Sampling–Markov Chain Monte Carlo approach. However, the processes of both determination and identification are time-consuming because the original simulation model (that is, the contaminant transport model) needs to be invoked multiple times. To overcome this challenge, a machine learning approach, that is, Multi-layer Perceptron, is used to build a surrogate model for the original simulation model, which can greatly accelerate the determination and identification processes. Finally, two hypothetical numerical case studies involving homogeneous and heterogeneous cases are used to verify the performance of the proposed approach. The results show that the optimal design of observation well locations and high-precision identification of groundwater contamination source parameters can be implemented accurately and effectively by using the proposed approach. In summary, this study highlights that the integrated Bayesian and machine learning approach provides a promising solution for high-precision identification of groundwater contamination source parameters.
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Sciacovelli, Adriano, and Vittorio Verda. "Entropy generation analysis for the design optimization of solid oxide fuel cells." International Journal of Numerical Methods for Heat & Fluid Flow 21, no. 5 (June 14, 2011): 535–58. http://dx.doi.org/10.1108/09615531111135819.
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PurposeThe aim of this paper is to investigate performance improvements of a monolithic solid oxide fuel cell geometry through an entropy generation analysis.Design/methodology/approachThe analysis of entropy generation rates makes it possible to identify the phenomena that cause the main irreversibilities in the fuel cell, to understand their causes and to propose changes in the design and operation of the system. The various contributions to entropy generation are analyzed separately in order to identify which geometrical parameters should be considered as the independent variables in the optimization procedure. The local entropy generation rates are obtained through 3D numerical calculations, which account for the heat, mass, momentum, species and current transport. The system is then optimized in order to minimize the overall entropy generation and increase efficiency.FindingsIn the optimized geometry, the power density is increased by about 10 per cent compared to typical designs. In addition, a 20 per cent reduction in the fuel cell volume can be achieved with less than a 1 per cent reduction in the power density with respect to the optimal design.Research limitations/implicationsThe physical model is based on a simple composition of the reactants, which also implies that no chemical reactions (water gas shift, methane steam reforming, etc.) take place in the fuel cell. Nevertheless, the entire procedure could be applied in the case of different gas compositions.Practical implicationsEntropy generation analysis allows one to identify the geometrical parameters that are expected to play important roles in the optimization process and thus to reduce the free independent variables that have to be considered. This information may also be used for design improvement purposes.Originality/valueIn this paper, entropy generation analysis is used for a multi‐physics problem that involves various irreversible terms, with the double use of this physical quantity: as a guide to select the most relevant design geometrical quantities to be modified and as objective function to be minimized in the optimization process.
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Wang, Y., W. Xu, H. Yin, Y. Zhang, and H. S. Dou. "Numerical study on the influence of pre-swirl angle on internal flow characteristics of centrifugal pumps." AIP Advances 12, no. 4 (April 1, 2022): 045019. http://dx.doi.org/10.1063/5.0085903.
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The effect of inlet pre-swirl on the performance of a centrifugal pump is studied by numerical simulation. The governing equations are Navier–Stokes equations and the shear stress transport k–ω turbulence model. The numerical results show that the optimal operating point moves from the low flow region to the high flow region as the pre-swirl angle shifts from positive to negative. It is found by contours of Omega–Liutex that the positive pre-swirl angle is able to weaken the vortex on the blade suction and reduce the energy dissipation. On both the 0.5Q0 and 1.2Q0 operating conditions, the proportion of entropy production loss in the impeller and volute is about 60% and 30%, respectively. As the pre-swirl angle changes from negative to positive, the entropy production loss in the inlet and outlet pipes increases slowly, and the entropy production loss in the volute and impeller shows a decreasing trend and the peak area of entropy loss moves toward the outlet. Under the four pre-swirl angles, the main frequency is always the passing frequency of the blade. The pre-swirl angle affects the pressure fluctuation at the main frequency but has little effect at the secondary frequency. The change in velocity pulsation amplitude in the impeller in the positive pre-swirl angle is smaller than that in the negative pre-swirl angle. As a result, for the positive pre-swirl angle, the turbulent kinetic energy density in the impeller is low, and the energy loss is low, compared with negative pre-swirl. Under the low flow condition (0.5Q0), the change in velocity pulsation amplitude in the inertial range of the energy spectrum under negative pre-swirl is greater than that under positive pre-swirl.
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Zhiwei, Guo, Wang Chihang, Qian Zhongdong, Luo Xianwu, and Xia Weipeng. "Suppression of hump characteristic for a pump-turbine using leading-edge protuberance." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 234, no. 2 (June 4, 2019): 187–94. http://dx.doi.org/10.1177/0957650919854638.
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The application of wave guide vanes with bio-inspired leading-edge protuberances to the hump characteristic of a pump-turbine is examined in this study. Numerical simulation with a shear-stress transport turbulence model is used to calculate the three-dimensional flow in a pump-turbine in pumping mode. Three tubercle amplitudes of 0.02c, 0.04c, and 0.08c (c is chord length), and three spanwise wavenumbers (2/s, 4/s and 8/s, s is the length of span) for guide vanes are especially considered. The results obtained show that the simulated performances of original guide vanes are found to be in good qualitative agreement with experimental data, supporting the validation of the computational fluid dynamics method. For different wave guide vanes with leading-edge protuberances, it is shown that the hump characteristic of the pump-turbine in pumping mode is effectively improved. This is due to improved flow fields below the tongue in view of entropy production and vector field. The energy loss can be clearly compared through the entropy distribution for different locations of the guide vanes, and it is improved for the wave guide vanes with bio-inspired leading-edge protuberances. For current pump-turbine, the optimal amplitude and wavenumber are found to be around 0.04c and 4/s.
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Panchenko, Sergii, Tatyana Butko, Аndrii Prokhorchenko, Larisa Parkhomenko, and Oleg Zhurba. "Development of Rational Rail Network Topology for High-Speed and Conventional Trains Based on Bacterial Foraging Optimization." International Journal of Engineering & Technology 7, no. 4.3 (September 15, 2018): 217. http://dx.doi.org/10.14419/ijet.v7i4.3.19790.
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Development of projects on higher speeds of passenger trains on the world railways requires investigation into the balanced combination of routes for high-speed and conventional trains considering railway network topology. The objective of the study is consideration of railway network peculiarities regarding transportation demand by designing a mathematical model to find an optimal passenger train flow distribution. In order to formalize the process of a simultaneous search for the rail passenger network topology and determination of the most probable distribution within the formed train flow network for high-speed and conventional trains it has been proposed to use a criterion as a system entropy adapted to the rail passenger-oriented transportation. The concept of entropy is based on isomorphism in systems, which allows monitoring and implementing the link between a micro and macro level in the passenger transportation system. To solve the mathematical model the authors have used an optimization method based on Bacterial Foraging Optimization (BFO). The implementation of the mathematical model based on BFO will make it possible to theoretically substantiate the efficiency of existing and promising projects on higher speeds of passenger trains on the rail transport regarding adaptation of the network topology to transportation demand.
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Hajihosseini, Morteza, Payam Amini, Dan Voicu, Irina Dinu, and Saumyadipta Pyne. "Geostatistical Modeling and Heterogeneity Analysis of Tumor Molecular Landscape." Cancers 14, no. 21 (October 25, 2022): 5235. http://dx.doi.org/10.3390/cancers14215235.
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Intratumor heterogeneity (ITH) is associated with therapeutic resistance and poor prognosis in cancer patients, and attributed to genetic, epigenetic, and microenvironmental factors. We developed a new computational platform, GATHER, for geostatistical modeling of single cell RNA-seq data to synthesize high-resolution and continuous gene expression landscapes of a given tumor sample. Such landscapes allow GATHER to map the enriched regions of pathways of interest in the tumor space and identify genes that have spatial differential expressions at locations representing specific phenotypic contexts using measures based on optimal transport. GATHER provides new applications of spatial entropy measures for quantification and objective characterization of ITH. It includes new tools for insightful visualization of spatial transcriptomic phenomena. We illustrate the capabilities of GATHER using real data from breast cancer tumor to study hallmarks of cancer in the phenotypic contexts defined by cancer associated fibroblasts.
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Lacker, Daniel. "A non-exponential extension of Sanov’s theorem via convex duality." Advances in Applied Probability 52, no. 1 (March 2020): 61–101. http://dx.doi.org/10.1017/apr.2019.52.
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AbstractThis work is devoted to a vast extension of Sanov’s theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a number of probabilistic limit theorems and asymptotics. For instance, widely applicable non-exponential large deviation upper bounds are derived for empirical distributions and averages of independent and identically distributed samples under minimal integrability assumptions, notably accommodating heavy-tailed distributions. Other interesting manifestations of the abstract results include new results on the rate of convergence of empirical measures in Wasserstein distance, uniform large deviation bounds, and variational problems involving optimal transport costs, as well as an application to error estimates for approximate solutions of stochastic optimization problems. The proofs build on the Dupuis–Ellis weak convergence approach to large deviations as well as the duality theory for convex risk measures.
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Ruchi, Sangeetika, Svetlana Dubinkina, and Jana de Wiljes. "Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation." Nonlinear Processes in Geophysics 28, no. 1 (January 15, 2021): 23–41. http://dx.doi.org/10.5194/npg-28-23-2021.
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Abstract. Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark.
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Ke, Qidi, and Lingfeng Tang. "Performance Optimization of Slotted Blades for Low-Specific Speed Centrifugal Pumps." Advances in Civil Engineering 2023 (January 5, 2023): 1–16. http://dx.doi.org/10.1155/2023/9612947.
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Centrifugal pumps are widely used for the transport of fluids, but low-specific-speed centrifugal pumps widely have problems with serious backflow and low efficiency. In this paper, a low-specific-speed centrifugal pump with a specific speed of 55 is used as a research object. By combining numerical simulation and orthogonal experiment, the pressure distribution and velocity distribution of the flow channel are analyzed, the priority of each geometric factor for slits on pump performance is determined, the geometric parameter structure of the slotted blade is optimized by entropy weight on TOPSIS, the optimal impeller slit solution is obtained. The results show that with a balance of head and efficiency, the order of influence of the factors is: slit center width b > diameter of slit D > shrinkage ratio of slit f > depth of slit h > deflection angle of slit β . The optimal combination of slit geometry parameters is: slit center width is 3 m m , diameter of the slit is 200 m m , shrinkage ratio of the slit is 0.5, depth of the slit is 6 m m , and the deflection angle of the slit is 20°. Through ANSYS FLUENT simulation and experiment of closed pump experiment system, confirmed that hydraulic performance is improved.
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Wang, Sini, Zhongyi Zuo, and Yan Liu. "Study on Location of Bus Stop in Subway Service Area Based on Residents’ Travel Accessibility." Sustainability 15, no. 5 (March 2, 2023): 4517. http://dx.doi.org/10.3390/su15054517.
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This research aims at establishing an integrated urban public transport system with a subway route supplemented by conventional bus lines, in order to enable residents’ “door-to-door” travel. This paper first analyzed the attraction area of the subway, and then used the GIS tools to calculate and analyze residents’ accessibility to adjacent bus stops. Moreover, it created a preliminary layout of bus stops for residential areas with extremely low accessibility using an improved potential model. From the perspective of minimizing residents’ travel costs and bus stop infrastructure deployment costs, a bus stop site selection optimization model was developed. According to the characteristics of the model, the non-dominated sorting genetic algorithm II (NSGA-II) was employed to solve the optimal bus stop locations. In addition, the entropy weight technique for order of preference by similarity to ideal solution (TOPSIS) evaluation model was used to evaluate and sort candidate schemes, accordingly, and thus the optimal site selection scheme was identified. Finally, a before-after comparative analysis on residents’ travel accessibility was conducted. Results show that the proposed method can effectively improve residents’ accessibility to bus stops, which facilitates residents to transfer from conventional bus to subway. Furthermore, it provides a basis for the follow-up optimization of the connection between subway and conventional bus lines.
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Sanchez Torreguitart, Ismael, Tom Verstraete, and Lasse Mueller. "Optimization of the LS89 Axial Turbine Profile Using a CAD and Adjoint Based Approach †." International Journal of Turbomachinery, Propulsion and Power 3, no. 3 (August 9, 2018): 20. http://dx.doi.org/10.3390/ijtpp3030020.
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The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for computational fluid dynamics (CFD) validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents a sound methodology to design and optimize the LS89 using computer-aided design (CAD) at design conditions. The novelty of the study resides in the parametrization of design space, which is done at the CAD level, and the detailed analysis of the aerodynamic performance of the optimized design. Higher level constraints are imposed on the shape, such as the trailing edge thickness, the axial chord length, and G2 geometric continuity between the suction side and pressure side at the leading edge. The gradients used for the optimization are obtained by applying algorithmic differentiation to the CAD kernel and grid generator and the discrete adjoint method to the CFD solver. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced while keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The flow is governed by the Reynolds-averaged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case.
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Zhang, Wenying, Xifu Wang, and Kai Yang. "Incentive Contract Design for the Water-Rail-Road Intermodal Transportation with Travel Time Uncertainty: A Stackelberg Game Approach." Entropy 21, no. 2 (February 9, 2019): 161. http://dx.doi.org/10.3390/e21020161.
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In the management of intermodal transportation, incentive contract design problem has significant impacts on the benefit of a multimodal transport operator (MTO). In this paper, we analyze a typical water-rail-road (WRR) intermodal transportation that is composed of three serial transportation stages: water, rail and road. In particular, the entire transportation process is planned, organized, and funded by an MTO that outsources the transportation task at each stage to independent carriers (subcontracts). Due to the variability of transportation conditions, the travel time of each transportation stage depending on the respective carrier’s effort level is unknown (asymmetric information) and characterized as an uncertain variable via the experts’ estimations. Considering the decentralized decision-making process, we interpret the incentive contract design problem for the WRR intermodal transportation as a Stackelberg game in which the risk-neutral MTO serves as the leader and the risk-averse carriers serve as the followers. Within the framework of uncertainty theory, we formulate an uncertain bi-level programming model for the incentive contract design problem under expectation and entropy decision criteria. Subsequently, we provide the analytical results of the proposed model and analyze the optimal time-based incentive contracts by developing a hybrid solution method which combines a decomposition approach and an iterative algorithm. Finally, we give a simulation example to investigate the impact of asymmetric information on the optimal time-based incentive contracts and to identify the value of information for WRR intermodal transportation.
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El-Rashidy, Rawia Ahmed, and Susan Grant-Muller. "THE EVALUATION OF REDUNDANCY FOR ROAD TRAFFIC NETWORKS." TRANSPORT 31, no. 4 (December 21, 2016): 427–39. http://dx.doi.org/10.3846/16484142.2016.1255913.
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This paper presents two redundancy indices for road traffic network junctions and also an aggregated network redundancy index. The proposed redundancy indices could be implemented to identify optimal design alternatives during the planning stage of the network junctions whereas the aggregated network redundancy index could assess the best control and management policies under disruptive events. Furthermore, effective measures of network redundancy are important to policy makers in understanding the current resilience and future planning to mitigate the impacts of greenhouse gases. The proposed junction indices cover the static aspect of redundancy, i.e. alternative paths, and the dynamic feature of redundancy reflected by the availability of spare capacity under different network loading and service level. The proposed redundancy indices are based on the entropy concept, due to its ability to measure the system configuration in addition to being able to model the inherent uncertainty in road transport network conditions. Various system parameters based on different combinations of link flow, relative link spare capacity and Relative Link Speed (RLS) were examined. However, the two redundancy indices developed from the combined RLS and relative link spare capacity showed strong correlation with junction delay and volume capacity ratio of a synthetic road transport network of Delft city. Furthermore, the developed redundancy indices responded well to demand variation under the same network conditions and supply variations. Another case study on Junction 3A in M42 motorway near Birmingham demonstrated that the developed redundancy index is able to reflect the impact of the Active Traffic Management (ATM) scheme introduced in 2006.
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Galanakis, D., E. Khatami, K. Mikelsons, A. Macridin, J. Moreno, D. A. Browne, and M. Jarrell. "Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1941 (April 28, 2011): 1670–86. http://dx.doi.org/10.1098/rsta.2010.0228.
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Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t ′, we find a classical critical point at temperature T c . This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature T c extrapolates to zero as t ′ vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid–gas transition.
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Altschuler, Jason M., Jonathan Niles-Weed, and Austin J. Stromme. "Asymptotics for Semidiscrete Entropic Optimal Transport." SIAM Journal on Mathematical Analysis 54, no. 2 (March 14, 2022): 1718–41. http://dx.doi.org/10.1137/21m1440165.
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Guo, Yanan, Qiong Tong, Zhengjiao Li, and Yuhao Zhao. "Research on Carbon Emission Quota of Railway in China from the Perspective of Equity and Efficiency." Sustainability 14, no. 21 (October 24, 2022): 13789. http://dx.doi.org/10.3390/su142113789.
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Under the constraint of total carbon emissions, the allocation of carbon emission quotas of 18 railway bureaus in China is conducted to the realization of carbon emission reduction targets of China’s railway transportation industry. This paper proposes a carbon emission quota model for China’s railway industry from the perspective of equity and efficiency and innovatively undertakes research on the allocation of carbon emission quotas for railway administrations. This paper constructs an econometric model to analyze the impact of various influencing factors on China’s railway operation carbon emission and predicts the total carbon emission of China’s railway operation from 2021 to 2030 by scenario analysis method. From the perspective of equity and efficiency, apply the entropy method to give weight to historical responsibility, egalitarianism, and efficiency principle to obtain the initial allocation value of the carbon emission quota of the operator’s 18 regional railway bureau groups; the ZSG-DEA model is used to obtain the optimal allocation. The results show that railway passenger turnover, freight turnover, vehicle structure, and per capita GDP have a promoting effect on railway carbon emission, and the proportion of clean energy has an inhibitory effect on carbon emission. There is a gap between the distribution results under the single principle and the comprehensive distribution results; the combination of both can more effectively promote the development of the railway industry. From the perspective of equity and efficiency, the carbon emission quota of 18 railway bureau groups in China is high in the east and low in the west. Among them, the Shanghai railway bureau obtains the most carbon emission quota, while the Qinghai–Tibet railway bureau obtains the least carbon emission quota. The research results provide a reference for the railway bureau to coordinate emission reduction and the construction of the railway transport carbon emission market.
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Rigollet, Philippe, and Jonathan Weed. "Entropic optimal transport is maximum-likelihood deconvolution." Comptes Rendus Mathematique 356, no. 11-12 (November 2018): 1228–35. http://dx.doi.org/10.1016/j.crma.2018.10.010.
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Clason, Christian, Dirk A. Lorenz, Hinrich Mahler, and Benedikt Wirth. "Entropic regularization of continuous optimal transport problems." Journal of Mathematical Analysis and Applications 494, no. 1 (February 2021): 124432. http://dx.doi.org/10.1016/j.jmaa.2020.124432.
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