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arXiv 2020年

作者： Nardini, John T. Lagergren, John H. Hawkins-Daarud, Andrea Curtin, Lee Morris, Bethan Rutter, Erica M. Swanson, Kristin R. Flores, Kevin B. Department of Mathematics North Carolina State University RaleighNC United States Statistical and Applied Mathematical Sciences Insitute DurhamNC United States Mathematical NeuroOncology Laboratory Precision Neurotherapeutics Innovation Program Mayo Clinic PhoenixAZ United States Centre for Mathematical Medicine and Biology University of Nottingham Nottingham United Kingdom Department of Applied Mathematics University of California Merced MercedCA United States

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data is sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions. Copyright © 2020, The Authors. All rights reserved.

关键词： Learning systems

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Editorial Expression of Concern: Altered neuregulin 1-erbB4 signaling contributes to NMDA> receptor hypofunction in schizophrenia

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Nature medicine 2024年第3期30卷 911页

作者： Chang-Gyu Hahn Hoau-Yan Wang Dan-Sung Cho Konrad Talbot Raquel E Gur Wade H Berrettini Kalindi Bakshi Joshua Kamins Karin E Borgmann-Winter Steven J Siegel Robert J Gallop Steven E Arnold Department of Psychiatry Cellular and Molecular Neuropathology Program Center for Neurobiology and Behavior University of Pennsylvania Philadelphia 19104 Pennsylvania USA. hahnc@mail.med.upenn.edu. Department of Physiology and Pharmacology City University of New York Medical School 160 Convent Avenue New York 10031 New York USA. Department of Psychiatry Cellular and Molecular Neuropathology Program Center for Neurobiology and Behavior University of Pennsylvania Philadelphia 19104 Pennsylvania USA. Department of Mathematics Applied Statistics Program West Chester University 323 Anderson Hall West Chester 19380 Pennsylvania USA.

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Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

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Physical Review E 2020年第3期101卷 032124-032124页

作者： Ge Zhang Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g2(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the two-dimensional one-component plas

关键词： Classical statistical mechanics

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Exponential acceleration of macroscopic quantum tunneling in a Floquet Ising model

arXiv

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arXiv 2023年

作者： Grattan, George Barton, Brandon A. Feeney, Sean Mossi, Gianni Patnaik, Pratik Sagal, Jacob C. Carr, Lincoln D. Oganesyan, Vadim Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St CO Golden80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Physics Colorado School of Mines 1523 Illinois St CO Golden80401 United States KBR Inc. 601 Jefferson St. HoustonTX77002 United States NASA Ames Research Center Moffett FieldCA94035 United States Department of Physics and Astronomy College of Staten Island CUNY Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center CUNY New YorkNY10016 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States

The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. Slow MQT is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate the possibility to accelerate MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three qualitatively distinct regimes as a function of drive strength: (i) for weak drive, the system exhibits exponentially slow MQT alongside robust magnetic order, as expected;(ii) at intermediate drive strength, we find polynomial decay of rates alongside vanishing magnetic order consistent with critical or paramagnetic state;(iii) at very strong drive strengths both the tunnelling rate and time-averaged magnetic order remain finite with increasing system size. We support these claims with extensive full wavefunction and matrix-product state numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers. © 2023, CC BY.

关键词： Ising model

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Identifying Quantum Correlations Using Explicit SO(3) to SU(2) Maps

arXiv

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arXiv 2022年

作者： Dilley, Daniel Gonzales, Alvin Byrd, Mark School of Physics and Applied Physics Southern Illinois University Carbondale 1245 Lincoln Drive CarbondaleIL62901 United States School of Computing Southern Illinois University Carbondale 1230 Lincoln Drive CarbondaleIL62901 United States Intelligence Community Postdoctoral Research Fellowship Program Argonne National Laboratory 9700 S. Cass Avenue LemontIL60439 United States Mathematics Department University of Arkansas-Fort Smith 5210 Grand Avenue Fort SmithAR72913 United States

Quantum state manipulation of two-qubits on the local systems by special unitaries induces special orthogonal rotations on the Bloch spheres. An exact formula is given for determining the local unitaries for some given rotation on the Bloch sphere. The solution allows for easy manipulation of two-qubit quantum states with a single definition that is programmable. With this explicit formula, modifications to the correlation matrix are made simple. Using our solution, it is possible to diagonalize the correlation matrix without solving for the parameters in SU(2) that define the local unitary that induces the special orthogonal rotation in SO(3). Since diagonalization of the correlation matrix is equivalent to diagonalization of the interaction Hamiltonian, manipulating the correlation matrix is important in time-optimal control of a two-qubit state. The relationship between orthogonality conditions on SU(2) and SO(3) are given and manipulating the correlation matrix when only one qubit can be accessed is discussed. Copyright © 2022, The Authors. All rights reserved.

关键词： Hamiltonians

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Hyperuniformity of generalized random organization models

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Physical Review E 2019年第2期99卷 022115-022115页

作者： Zheng Ma Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Studies of random organization models of monodisperse (i.e., identical) spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent hyperuniformity is preserved when the model is generalized to particles with a size distribution and/or nonspherical shapes. We begin by examining binary disks in two dimensions and demonstrate that their critical states are hyperuniform as two-phase media, but not hyperuniform nor multihyperuniform as point patterns formed by the particle centroids. We further confirm the generality of our findings by studying particles with a continuous size distribution. Finally, to study the effect of rotational degrees of freedom, we extend our model to noncircular particles, namely, hard rectangles with various aspect ratios, including the hard-needle limit. Although these systems exhibit only short-range orientational order, hyperuniformity is still preserved. Our analysis reveals that the redistribution of the “mass” of the particles rather than the particle centroids is central to this dynamical process. The consideration of the “active volume fraction” of generalized random organization models may help to resolve which universality class they belong to and hence may lead to a deeper theoretical understanding of absorbing-state models. Our results suggest that general particle systems subject to random organization can be a robust way to fabricate a wide class of hyperuniform states of matter by tuning the structures via different particle-size and -shape distributions. This in turn potentially enables the creation of multifunctional hyperuniform materials with desirable optical, transport, and mechanical properties.

关键词： Classical statistical mechanics

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End-to-end quantum machine learning implemented with controlled quantum dynamics

arXiv

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arXiv 2020年

作者： Wu, Re-Bing Cao, Xi Xie, Pinchen Liu, Yu-Xi Department of Automation Tsinghua University Beijing100084 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Micro-Nano Electronics Tsinghua University Beijing100084 China

This work presents a hardware-friendly end-to-end quantum machine learning scheme that can be implemented with imperfect near-term intermediate-scale quantum processors. The proposal transforms the machine learning task to the optimization of a quantum control system, which parameterize the learning model by experimentally tunable control variables. Our design also enables automated feature selection by encoding the raw input data to quantum states through agent control variables. Comparing with the gate-based parameterized quantum circuits, the resulting end-to-end quantum learning models is easy to implement as there are only few ad-hoc parameters to be determined by the designer. Numerical simulations on the benchmarking MNIST dataset without down-sampling the images demonstrate that the proposed scheme can achieve comparable high performance with only 3-5 qubits than known quantum machine learning models. The scheme is promising for efficiently performing large-scale real-world learning tasks using intermediate-scale quantum processors. Copyright © 2020, The Authors. All rights reserved.

关键词： Benchmarking

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Unified approach to secondary effects on the CMB B-mode polarization

arXiv

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arXiv 2021年

作者： Namikawa, Toshiya Naruko, Atsushi Saito, Ryo Taruya, Atsushi Yamauchi, Daisuke Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Center for Gravitational Physics Yukawa Institute for Theoretical Physics Kyoto University Kyoto606-8502 Japan Frontier Research Institute for Interdisciplinary Sciences Department of Physics Tohoku University Sendai980-8578 Japan Graduate School of Science and Engineering Yamaguchi University Yamaguchi753-8512 Japan Kavli Institute for the Physics and Mathematics of the Universe Todai Institute for Advanced Study The University of Tokyo Chiba277-8583 Japan Faculty of Engineering Kanagawa University Kanagawa221-8686 Japan

We develop a systematic and unified approach to estimate all possible secondary (i.e. non-primordial) nonlinear effects to the cosmic microwave background (CMB) polarization, named curve-of-sight integration approach. In this approach, the Boltzmann equation for polarized photons is rewritten in a line-of-sight integral along an exact geodesic in the perturbed universe, rather than a geodesic in the background universe used in the linear-order CMB calculation. This approach resolves the difficulty to solve the Boltzmann hierarchy with the nonlinear gravitational effects in the photon free-streaming regime and thus unifies the standard remapping approach for CMB lensing into the direct approach solving the Boltzmann equation for the nonlinear collisional effects. In this paper, we derive formulae that: (i) include all the nonlinear effects;(ii) can treat extended sources such as the contributions after the reionization. It offers a solid framework to discuss possible systematics in the standard estimation of CMB lensing by the remapping approach. As an explicit demonstration, we estimate the secondary B-mode power spectrum induced by all foreground gravitational effects: lensing, redshift, time-delay, emission-angle, and polarization-rotation effects. We define these effects properly so that they do not have any overlap, also without overlooking any effect. Then, we show that these effects only give corrections of the order of 0.001- − 0.01% to the standard lensing-induced B-mode power spectrum in the concordance Λ cold dark matter model. Our result confirms the reliability of using the remapping approach in upcoming CMB experiments aiming to detect the primordial gravitational waves with the tensor-to-scalar ratio of r ∼ 10−3 © 2021, CC BY.

关键词： Boltzmann equation

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Uncertainty quantification by random measures and fields

arXiv

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arXiv 2020年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Massive Dynamics PrincetonNJ08542 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk functionals of input-output maps. These are the ANOVA decomposition of the intensity measure and the decomposition of the random measure variance, each into subspaces. Orthogonal random measures furnish sensitivity distributions. We show that the random counting measure may be used to construct positive random fields, which admit decompositions of covariance and sensitivity indices and may be used to represent interacting particle systems. The first and second order global sensitivity analyses conveyed through random counting measures elucidate and integrate different notions of uncertainty quantification, and the global sensitivity analysis of random fields conveys the proportionate functional contributions to covariance. This framework complements others when used in conjunction with for instance algorithmic uncertainty and model selection uncertainty *** Codes 60G57, 60G60, 60G55 © 2020, CC-BY-NC-ND.

关键词： Uncertainty analysis

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Chiral quasi-bound states in the continuum

arXiv

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arXiv 2020年

作者： Overvig, Adam Yu, Nanfang Alù, Andrea Photonics Initiative Advanced Science Research Center The Graduate Center The City University of New York United States Department of Applied Physics and Applied Mathematics Columbia University United States Physics Program Graduate Center City University of New York United States

Quasi-bound states in the continuum (q-BICs) are resonant states of suitably tailored nanostructures with long optical lifetimes controlled by symmetry-breaking perturbations. While in planarized ultrathin devices the resulting Fano resonance is limited to linear polarization, we show here that chiral perturbations extend q-BIC concepts to arbitrary elliptical polarizations. Using geometric phase engineering, we realize metasurfaces with ultrasharp Fano spectral features that can shape the impinging wavefront with near-unity efficiency, while at the same time precisely filtering their spectral content. Copyright © 2020, The Authors. All rights reserved.

关键词： Polarization

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