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Price of anarchy for mean field games

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arXiv 2018年

作者： Carmona, René Graves, Christy V. Tan, Zongjun Operations Research and Financial Engineering Princeton University Partially United States Program in Applied and Computational Mathematics Princeton University Partially

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean field game equilibrium to the optimal social cost as computed by a central planner. We illustrate properties of such a price of anarchy on linear quadratic extended mean field games, for which explicit computations are possible. A sufficient and necessary condition to have no price of anarchy is presented. Various asymptotic behaviors of the price of anarchy are proved for limiting behaviors of the coefficients in the model and numerics are *** Codes 60K35 Copyright © 2018, The Authors. All rights reserved.

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Frequency-Resolved Optical Gating Recovery via Smoothing Gradient

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arXiv 2019年

作者： Pinilla, Samuel Bendory, Tamir Eldar, Yonina C. Arguello, Henry Department of Electrical Engineering Universidad Industrial de Santander BucaramangaSantander680002 Colombia Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Weizmann Institute of Science Rehovot7610001 Israel Department of Computer Science Universidad Industrial de Santander BucaramangaSantander680002 Colombia

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://***/samuelpinilla/FROG. Copyright © 2019, The Authors. All rights reserved.

关键词： Ultrashort pulses

Hard convex lens-shaped particles: Characterization of dense disordered packings

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arXiv 2019年

作者： Cinacchi, Giorgio Torquato, Salvatore Instituto de Ciencias de Materiales "Nicolás Cabrera" Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco MadridE-28049 Spain Department of Chemistry Department of Physics Institute for the Science and Technology of Materials Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is ‘optimal’ in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction φMRJ ' 0.73. This value is only a few percent lower than φDKP = 0.76210 . . . , the packing fraction of the corresponding densest-known crystalline (degenerate) packings. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method-based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows one to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of 10 contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve. Copyright © 2019, The Authors. All rights reserved.

关键词： Aspect ratio

Multifunctional Composites for Elastic and Electromagnetic Wave Propagation

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arXiv 2019年

作者： Kim, Jaeuk Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Composites are ideally suited to achieve desirable multifunctional effective properties, since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish the first cross-property relations for two-phase composite media that link effective elastic and electromagnetic wave characteristics to one another, including effective wave speeds and attenuation coefficients. This is achieved by deriving accurate formulas for the effective elastodynamic properties that depend on the microstructure via the spectral density and utilizing previous analogous results for effective electromagnetic properties. Our formulas enable us to explore the wave characteristics of a broad class of disordered microstructures, including exotic disordered "hyperuniform" varieties, that can have advantages over crystalline ones, such as nearly optimal, direction-independent properties and robustness against defects. We specifically show that disordered "stealthy" hyperuniform/nonhyperuniform microstructures exhibit novel elastic wave characteristics that have the potential for future applications, e.g., low-pass or narrow-band-pass (using negative Poisson ratio materials) filters that transmit or absorb elastic waves "isotropically" for a range of wavenumbers. We also demonstrate that two-phase media with engineered disorder and phase properties can exhibit "anomalous dispersion" with resonance-like attenuation. Our cross-property relations for effective wave characteristics can be applied to design multifunctional composites via inverse techniques, including exterior components of spacecraft or building materials that require both excellent stiffness and electromagnetic absorption, and heat-sinks for CPUs that have to efficiently emit thermal radiation and suppress mechanical vibrations, and nondestructive evaluation of the elastic moduli of materials from the effective dielectric response. DR Copyright © 2019, The Authors. All rights res

关键词： Microstructure

New tessellation-based procedure to design perfectly hyperuniform disordered dispersions for materials discovery

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arXiv 2019年

作者： Kim, J. Torquato, S. Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, which endows them with novel physical properties. While such unusual materials have received considerable attention, a stumbling block has been an inability to create large samples that are truly hyperuniform due to current computational and experimental limitations. To overcome such barriers, we introduce a new and simple construction procedure that guarantees perfect hyperuniformity for very large sample sizes. This methodology involves tessellating space into cells and then inserting a particle into each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We analytically prove that such dispersions are perfectly hyperuniform in the infinite-sample-size limit. Our methodology enables a remarkable mapping that converts a very large nonhyperuniform disordered dispersion into a perfectly hyperuniform one, which we numerically demonstrate in two and three dimensions. A similar analysis also establishes the hyperuniformity of the famous Hashin-Shtrikman multiscale dispersions, which possess optimal transport and elastic properties. Our hyperuniform designs can be readily fabricated using modern photolithographic and 3D printing technologies. The exploration of the enormous class of hyperuniform dispersions that can be designed and tuned by our tessellation-based methodology paves the way for accelerating the discovery of novel hyperuniform materials. Copyright © 2019, The Authors. All rights reserved.

关键词： 3D printers

APPLE picker: Automatic particle picking, a low-effort cryo-EM framework

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arXiv 2018年

作者： Heimowitz, Ayelet Andén, Joakim Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Center for Computational Biology Flatiron Institute New YorkNY United States Department of Mathematics Princeton University PrincetonNJ United States

Particle picking is a crucial first step in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM). Selecting particles from the micrographs is difficult especially for small particles with low contrast. As high-resolution reconstruction typically requires hundreds of thousands of particles, manually picking that many particles is often too time-consuming. While semi-automated particle picking is currently a popular approach, it may suffer from introducing manual bias into the selection process. In addition, semi-automated particle picking is still somewhat time-consuming. This paper presents the APPLE (Automatic Particle Picking with Low user Effort) picker, a simple and novel approach for fast, accurate, and fully automatic particle picking. While our approach was inspired by template matching, it is completely template-free. This approach is evaluated on publicly available datasets containing micrographs of β-Galactosidase, T20S proteasome, 70S ribosome and keyhole limpet hemocyanin projections. Copyright © 2018, The Authors. All rights reserved.

关键词： Support vector machines

Methodology to construct large realizations of perfectly hyperuniform disordered packings

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arXiv 2019年

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size in Rd are perfectly hyperuniform in the infinite-sample-size limit and the hyperuniformity of such packings is independent of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that pack

关键词： Cells

The Athena++ adaptive mesh refinement framework: Design and magnetohydrodynamic solvers

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arXiv 2020年

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Earth and Space Science Osaka University Toyonaka Osaka560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93107 United States School of Natural Sciences Institute for Advanced Study PrincetonNJ08544 United States Astronomical Institute Tohoku University Sendai Miyagi980-8578 Japan Argonne National Laboratory LemontIL60439 United States

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

Unsupervised particle sorting for high-resolution single-particle cryo-EM

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arXiv 2019年

作者： Zhou, Ye Moscovich, Amit Bendory, Tamir Bartesaghi, Alberto Department of Computer Science Duke University Durham United States Program in Applied and Computational Mathematics Princeton University United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel Department of Biochemistry Duke University School of Medicine Durham United States Department of Electrical and Computer Engineering Duke University Durham United States

Single-particle cryo-Electron Microscopy (EM) has become a popular technique for determining the structure of challenging biomolecules that are inaccessible to other technologies. Recent advances in automation, both in data collection and data processing, have significantly lowered the barrier for non-expert users to successfully execute the structure determination workflow. Many critical data processing steps, however, still require expert user intervention in order to converge to the correct high-resolution structure. In particular, strategies to identify homogeneous populations of particles rely heavily on subjective criteria that are not always consistent or reproducible among different users. Here, we explore the use of unsupervised strategies for particle sorting that are compatible with the autonomous operation of the image processing pipeline. More specifically, we show that particles can be successfully sorted based on a simple statistical model for the distribution of scores assigned during refinement. This represents an important step towards the development of automated workflows for protein structure determination using single-particle *** Codes 62P10 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems