检索结果-内蒙古大学图书馆

Recovering Signals from their FROG Trace

学校读者我要写书评

暂无评论

Recovering Signals from their FROG Trace

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Tamir Bendory Dan Edidin Yonina C. Eldar The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics University of Missouri Columbia Missouri USA The Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

ISBN: (纸本)9781538646595

The problem of recovering a signal from its power spectrum is called phase retrieval. This problem appears in a variety of scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. However, the problem for one-dimensional signals is ill-posed as there is no one-to-one mapping between a one-dimensional signal and its power spectrum. In the field of ultra-short laser pulse characterization, it is common to overcome this ill-posedness by using a technique called Frequency-Resolved Optical Gating (FROG). In FROG, the measured data, referred to as FROG trace, is the Fourier magnitude of the product of the underlying signal with several translated versions of itself. Therefore, in order to recover a signal from its FROG trace, one needs to invert a system of phaseless quartic equations. In this paper, we explore the symmetries and uniqueness of the FROG mapping. Our main result states that a signal bandlimited to B is determined uniquely, up to symmetries, by only 3B FROG measurements.

关键词： phase retrieval phaseless quartic system of equations ultra-short laser pulse characterization FROG signals Ultrashort laser pulses power spectra frogs Amphibians RECOVERING Trace One dimensional quartic equations

Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Ma, Chao Bendory, Tamir Boumal, Nicolas Sigworth, Fred Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States Department of Cellular and Molecular Physiology Yale University School of Medicine New HavenCT United States

Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data. Copyright © 2018, The Authors. All rights reserved.

关键词： Alignment

Rational design of stealthy hyperuniform two-phase media with tunable order

学校读者我要写书评

暂无评论

Physical Review E 2018年第2期97卷 023311-023311页

作者： Robert A. DiStasio, Jr. Ge Zhang Frank H. Stillinger Salvatore Torquato Department of Chemistry and Chemical Biology Cornell University Ithaca New York 14853 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA 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

Disordered stealthy hyperuniform materials are exotic amorphous states of matter that have attracted recent attention because of their novel structural characteristics (hidden order at large length scales) and physical properties, including desirable photonic and transport properties. It is therefore useful to devise algorithms that enable one to design a wide class of such amorphous configurations at will. In this paper, we present several algorithms enabling the systematic identification and generation of discrete (digitized) stealthy hyperuniform patterns with a tunable degree of order, paving the way towards the rational design of disordered materials endowed with novel thermodynamic and physical properties. To quantify the degree of order or disorder of the stealthy systems, we utilize the discrete version of the τ order metric, which accounts for the underlying spatial correlations that exist across all relevant length scales in a given digitized two-phase (or, equivalently, a two-spin state) system of interest. Our results impinge on a myriad of fields, ranging from physics, materials science and engineering, visual perception, and information theory to modern data science.

关键词： Pattern formation

Manifold learning for organizing unstructured sets of process observations

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Dietrich, Felix Kooshkbaghi, Mahdi Bollt, Erik M. Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Department of Electrical and Computer Engineering Clarkson Center for Complex Systems Science Clarkson University PotsdamNY13699-5815 United States

Data mining is routinely used to organize ensembles of short temporal observations so as to reconstruct useful, low-dimensional realizations of an underlying dynamical system. In this paper, we use manifold learning to organize unstructured ensembles of observations ("trials") of a system's response surface. We have no control over where every trial starts;and during each trial operating conditions are varied by turning "agnostic" knobs, which change system parameters in a systematic but unknown way. As one (or more) knobs "turn" we record (possibly partial) observations of the system response. We demonstrate how such partial and disorganized observation ensembles can be integrated into coherent response surfaces whose dimension and parametrization can be systematically recovered in a data-driven fashion. The approach can be justified through the Whitney and Takens embedding theorems, allowing reconstruction of manifolds/attractors through different types of observations. We demonstrate our approach by organizing unstructured observations of response surfaces, including the reconstruction of a cusp bifurcation surface for Hydrogen combustion in a Continuous Stirred Tank Reactor. Finally, we demonstrate how this observation-based reconstruction naturally leads to informative transport maps between input parameter space and output/state variable *** codes 37M20 Copyright © 2018, The Authors. All rights reserved.

关键词： Dynamical systems

Using natural travel paths to infer and compare primate cognition in the wild

学校读者我要写书评

暂无评论

iScience 2021年第4期24卷 102343页

作者： Janmaat, Karline R.L. de Guinea, Miguel Collet, Julien Byrne, Richard W. Robira, Benjamin van Loon, Emiel Jang, Haneul Biro, Dora Ramos-Fernández, Gabriel Ross, Cody Presotto, Andrea Allritz, Matthias Alavi, Shauhin Van Belle, Sarie Evolutionary and Population Biology Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam Netherlands Department of Cognitive Psychology Faculty of Social Sciences Leiden University Leiden Netherlands ARTIS Amsterdam Royal zoo Amsterdam Netherlands Department of Social Sciences Oxford Brookes University Oxford United Kingdom Oxford Navigation Group Department of Zoology Oxford University Oxford United Kingdom Centre for Social Learning and Cognitive Evolution School of Psychology and Neuroscience University of St Andrews St Andrew United Kingdom Scottish Primate Research Group Scotland United Kingdom Centre d’Écologie Fonctionnelle et Évolutive Université de Montpellier Montpellier France Eco-anthropologie Muséum National d'Histoire Naturelle CNRS Université de Paris Paris France Theoretical and Computational Ecology Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam Netherlands Department of Human Behavior Ecology and Culture Max Planck Institute for Evolutionary Anthropology Leipzig Germany Department of Brain and Cognitive Sciences University of Rochester Rochester United States Department of Mathematical Modelling of Social Systems Institute for Research on Applied Mathematics and Systems Universidad Nacional Autónoma de México Mexico City Mexico Center for Complexity Sciences Universidad Nacional Autónoma de México Mexico City Mexico Department of Geography and Geosciences Salisbury University Salisbury MA United States School of Psychology and Neuroscience University of St Andrews Scotland United Kingdom Department for the Ecology of Animal Societies Max Planck Institute of Animal Behaviour Konstanz Germany Centre for the Advanced Study of Collective Behaviour University of Konstanz Konstanz Germany Department of Biology University of Konstanz Konstanz Germany Department of Anthropology University of Austin at Texas Austin TX United States

Within comparative psychology, the evolution of animal cognition is typically studied either by comparing indirect measures of cognitive abilities (e.g., relative brain size) across many species or by conducting batteries of decision-making experiments among (typically) a few captive species. Here, we propose a third, complementary approach: inferring and comparing cognitive abilities through observational field records of natural information gradients and the associated variation in decision-making outcomes, using the ranging behavior of wild animals. To demonstrate the feasibility of our proposal, we present the results of a global survey assessing the availability of long-term ranging data sets from wild primates and the willingness of primatologists to share such data. We explore three ways in which such ranging data, with or without the associated behavioral and ecological data often collected by primatologists, might be used to infer and compare spatial cognition. Finally, we suggest how ecological complexity may be best incorporated into comparative analyses. © 2021 The Authors

关键词： Biological Sciences Cognitive Neuroscience Neuroscience

Blind phaseless short-time fourier transform recovery

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Bendory, Tamir Edidin, Dan Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics University of Missouri ColumbiaMO United States Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that in order to determine a pair of generic signals uniquely, up to trivial ambiguities, the number of phaseless measurements one needs to collect is, at most, five times the number of parameters required to describe the signals. This result improves significantly upon previous papers, which required the number of measurements to be quadratic in the number of parameters rather than linear. In addition, we consider the simpler problem of recovering a pair of generic signals from their blind short-time Fourier transform, when the phases are known. In this setting, which can be understood as a special case of the blind deconvolution problem, we show that the number of measurements required to determine the two signals, up to trivial ambiguities, equals exactly the number of parameters to be recovered. As a side result, we study the classical phase retrieval problem-that is, recovering a signal from its Fourier magnitudes-when some entries of the signal are known a priori. We derive a bound on the number of required measurements as a function of the size of the set of known entries. Specifically, we show that if most of the signal's entries are known, then only a few Fourier magnitudes are necessary to determine a signal uniquely. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

Multifunctional Hyperuniform Cellular Networks: Optimality, Anisotropy and Disorder

学校读者我要写书评

暂无评论

arXiv 2018年

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

Disordered hyperuniform heterogeneous materials are new, exotic amorphous states of matter that behave like crystals in the manner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional cellular network solids possess complete photonic band gaps comparable in size to photonic crystals, while at the same time maintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various two-dimensional ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and elastic moduli. We establish the multifunctionality of a class of such low-density networks by demonstrating that they maximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using the machinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical mechanics. We rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the low-density limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks, we show that when short-range and long-range order increases, there is an increase in both the effective conductivity and elastic moduli of the network. Moreover, we demonstrate that the effective conductivity and elastic moduli of various disordered networks derived from disordered "stealthy" hyperuniform point patterns possess virtually optimal values. We note that the optimal networks for conductivity are also optimal for the fluid permeability associated with slow viscous flow through the channels as well as the mean survival time associated with diffusion-controlled reactions in the channels. In summary, we have

关键词： Elastic moduli

Uncovering multiscale order in the prime numbers via scattering

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Torquato, .S. Zhang, .G. De Courcy-Ireland, M. Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Mathematics Princeton University PrincetonNJ08544 United States

The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in physics and materials science, we show that the prime numbers in certain large intervals possess unanticipated order across length scales and represent the first example of a new class of many-particle systems with pure point diffraction patterns, which we call effectively limit-periodic. In particular, the primes in this regime are hyperuniform. This is shown analytically using the structure factor S(k), proportional to the scattering intensity from a many-particle system. Remarkably, the structure factor for primes is characterized by dense Bragg peaks, like a quasicrystal, but positioned at certain rational wavenumbers, like a limit-periodic point pattern. We identify a transition between ordered and disordered prime regimes that depends on the intervals studied. Our analysis leads to an algorithm that enables one to predict primes with high accuracy. Effective limit-periodicity deserves future investigation in physics, independent of its link to the primes. Copyright © 2018, The Authors. All rights reserved.

关键词：

HIDDEN MULTISCALE ORDER IN THE PRIMES

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Torquato, Salvatore Zhang, Ge Courcy-Ireland, Matthew De Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Mathematics Princeton University PrincetonNJ08544 United States

We study the pair correlations between prime numbers in an interval M ≤ p ≤ M + L with M → ∞, L/M → β > 0. By analyzing the structure factor, we prove, conditionally on the Hardy-Littlewood conjecture on prime pairs, that the primes are characterized by unanticipated multiscale order. Specifically, their limiting structure factor is that of a union of an infinite number of periodic systems and is characterized by dense set of Dirac delta functions. Primes in dyadic intervals are the first examples of what we call effectively limit-periodic point configurations. This behavior implies anomalously suppressed density fluctuations compared to uncorrelated (Poisson) systems at large length scales, which is now known as hyperuniformity. Using a scalar order metric τ calculated from the structure factor, we identify a transition between the order exhibited when L is comparable to M and the uncorrelated behavior when L is only logarithmic in M. Our analysis for the structure factor leads to an algorithm to reconstruct primes in a dyadic interval with high accuracy. Copyright © 2018, The Authors. All rights reserved.

关键词： Delta functions