We present vector-valued concentration inequalities for the biased measure on the discrete hypercube {−1, 1}n with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These ...
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We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this ab...
In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types,...
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ISBN:
(数字)9798350385144
ISBN:
(纸本)9798350385151
In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types, specific delivery times, multiple warehouses, vehicle fuel constraints, and pick-up from one location and delivery to another. This work proposes and demonstrates a flexible algorithm for solving the VRP via ant colony optimization (ACO) that can address many of the variants discussed above. ACO algorithms mimic the behavior of ants, learning optimal paths to a food source and back to the nest based on stigmergic behavior. This work compares a proposed, more flexible ACO algorithm to a traditional optimization algorithm that is implemented in the Google VRP solver. Readily available data were used to test and demonstrate results. Several VRP variants were implemented in both the (proposed) flexible ACO algorithm and the Google VRP solver. The flexible ACO algorithm performed better in terms of distance traveled versus the Google VRP solver for two variants and worse for three other cases. However, the Google VRP solver was not able to solve some of the VRP variant combinations considered here and failed when solving some backhaul datasets. Because the flexible ACO algorithm was able to better handle many case variations, it may be an attractive alternative optimization tool.
In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical r...
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In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm.
We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show conver...
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The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capaci...
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A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...
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A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different...
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We present a simpler proof of the existence of equilibria for a class of mean field games with common noise, where players interact through the conditional law given the current value of the common noise rather than i...
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