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17th European Signal Processing Conference, EUSIPCO 2009

作者： Jafarpour, Sina Polatkan, Güngör Brevdo, Eugene Hughes, Shannon Brasoveanu, Andrei Daubechies, Ingrid Princeton University Departments of Electrical Engineering Computer Science and Mathematics Program in Applied and Computational Mathematics Princeton NJ 08544 United States

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features". © EURASIP, 2009.

关键词： Decision trees

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Multidimensional Hyperbolic Problems and Computations 1

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丛书名： The IMA Volumes in mathematics and its Applications

1000年

作者： James Glimm Andrew J. Majda

ISBN: (数字)9781461391210

ISBN: (纸本)9781461391234

This IMA Volume in mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

关键词： Analysis

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A NUMERICAL STUDY OF THE GAUSSIAN BEAM METHODS FOR SCHR(O|¨)DINGER-POISSON EQUATIONS

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Journal of computational mathematics 2010年第2期28卷 261-272页

作者： Shi Jin Hao Wu Xu Yang Department of Mathematics University of Wisconsin Madison W1 53706 USA Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics University of Wisconsin Madison WI 53706 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544USA

As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

关键词： Schrodinger-Poisson equations Gaussian beam methods Vlasov-Poisson equations

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Overview of the Head and Neck Tumor Segmentation for Magnetic Resonance Guided Applications (HNTS-MRG) 2024 Challenge 1st

Overview of the Head and Neck Tumor Segmentation for Magneti...

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1st Challenge on Head and Neck Tumor Segmentation for MRI-Guided Applications, HNTS-MRG 2024, Held in Conjunction with 27th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2024

作者： Wahid, Kareem A. Dede, Cem El-Habashy, Dina M. Kamel, Serageldin Rooney, Michael K. Khamis, Yomna Abdelaal, Moamen R. A. Ahmed, Sara Corrigan, Kelsey L. Chang, Enoch Dudzinski, Stephanie O. Salzillo, Travis C. McDonald, Brigid A. Mulder, Samuel L. McCullum, Lucas Alakayleh, Qusai Sjogreen, Carlos He, Renjie Mohamed, Abdallah S. R. Lai, Stephen Y. Christodouleas, John P. Schaefer, Andrew J. Naser, Mohamed A. Fuller, Clifton D. Department of Radiation Oncology The University of Texas MD Anderson Cancer HoustonTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer HoustonTX United States Transitional Year Program Corewell Health Wiliam Beaumont Royal OakMI United States Department of Radiation Oncology University of Maryland School of Medicine BaltimoreMD United States Department of Clinical Oncology and Nuclear Medicine Faculty of Medicine Alexandria University Alexandria Egypt UT MD Anderson Cancer CenterUTHealth Houston Graduate School of Biomedical Sciences Houston United States Department of Radiation Oncology Baylor College of Medicine HoustonTX United States Department of Head and Neck Surgery The University of Texas MD Anderson Cancer HoustonTX United States Elekta AtlantaGA United States Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States

ISBN: (纸本)9783031832734

Magnetic resonance (MR)-guided radiation therapy (RT) is enhanc- ing head and neck cancer (HNC) treatment through superior soft tissue con- trast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)- driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto- segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2- weighted scans. The challenge provided 150 HNC cases for training and 50 for final testing hosted on *** using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Simi- larity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver vari- ability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC. © The Author(s) 2025.

关键词： Deep learning

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Ultradense Sphere Packings Derived From Disordered Stealthy Hyperuniform Ground States

arXiv

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arXiv 2025年

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

Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel optical, transport, and mechanical properties. Such packings of identical spheres have been created from SHU ground-state point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, besides the standard "stealthy" pair potential. To explore maximal ranges of the packing fraction , we investigate the distributions of minimum pair distances as well as nearest-neighbor distances of ensembles of SHU point patterns without and with soft-core repulsions in the first three space dimensions as a function of the stealthiness parameter χ and number of particles N within a hypercubic simulation box under periodic boundary conditions. Within the disordered regime (χ max(χ, d), decrease to zero on average as N increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large max(χ, d) independent of N, reaching up to max(χ, d) = 1.0, 0.86, 0.63 in the zero-χ limit and decreasing to max(χ, d) = 1.0, 0.67, 0.47 at χ = 0.45 for d = 1, 2, 3, respectively. We obtain explicit formulas for max(χ, d) as functions of χ and N for a given value of d in both cases with and without soft-core repulsions. In two and three dimensions, our soft-core SHU ground-state packings for small χ become configurationally very close to the corresponding jammed hard-particle packings created by fast compression algorithms, as measured by their pair statistics. As χ increases beyond 0.20, the packings form fewer contacts and linear polymer-like chains as χ tends to 1/2. The resulting structure factors S(k) and pair correlation functions g2(r) reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We show that the degree of large-scale order of the soft-core SHU ground states increases as χ increases from 0 to

关键词： Digital arithmetic

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PARSING NEURAL DYNAMICS WITH INFINITE RECURRENT SWITCHING LINEAR DYNAMICAL SYSTEMS 12

PARSING NEURAL DYNAMICS WITH INFINITE RECURRENT SWITCHING LI...

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12th International Conference on Learning Representations, ICLR 2024

作者： Geadah, Victor Pillow, Jonathan W. Program in Applied and Computational Mathematics Princeton University United States Princeton Neuroscience Institute Princeton University United States

Unsupervised methods for dimensionality reduction of neural activity and behavior have provided unprecedented insights into the underpinnings of neural information processing. One popular approach involves the recurrent switching linear dynamical system (rSLDS) model, which describes the latent dynamics of neural spike train data using discrete switches between a finite number of low-dimensional linear dynamical systems. However, a few properties of rSLDS model limit its deployability on trial varying data, such as a fixed number of states over trials, and no latent structure nor organization of states. Here we overcome these limitations by endowing the rSLDS model with a semi-Markov discrete state process, with latent geometry, that captures key properties of stochastic processes over partitions with flexible state cardinality. We leverage partial differential equations (PDE) theory to derive an efficient, semi-parametric formulation for dynamical sufficient statistics to the discrete states. This process, combined with switching dynamics, defines our infinite recurrent switching linear dynamical system (irSLDS) model class. We first validate and demonstrate the capabilities of our model on synthetic data. Next, we turn to the analysis of mice electrophysiological data during decision-making, and uncover strong non-stationary processes underlying both within-trial and trial-averaged neural activity. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Stochastic systems

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Fat Arcs for Implicitly Defined Curves

Fat Arcs for Implicitly Defined Curves

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7th International Conference on Mathematical Methods for Curves and Surfaces

作者： Bela, Szilvia Juettler, Bert Doctoral Program in Computational Mathematics Austria Institute of Applied Geometry Johannes Kepler University Linz 4040 Altenberger Str. 69 Austria

ISBN: (纸本)9783642116193

We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein-Bezier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.

关键词： Polynomial approximation

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ISING-MODEL SIMULATIONS ON THE MANIFOLDS OF 2-DIMENSIONAL QUANTUM-GRAVITY

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MODERN PHYSICS LETTERS A 1991年第17期6卷 1615-1628页

作者： AGISHTEIN, ME BAILLIE, CF Program in Applied and Computational Mathematics Princeton University Fine Hall Princeton NJ 08544-1000 USA Physics Department University of Colorado Boulder CO 80309 USA

The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.

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Factor Analysis for Spectral Estimation

Factor Analysis for Spectral Estimation

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International Conference on Sampling Theory and Applications

作者： Joakim Anden Amit Singer Program in Applied and Computational Mathematics Princeton University Department of Mathematics and Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781538615669

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.

关键词： Spectrum Analysis power spectra Subspace STATIONARY SOURCES Factor analysis Cryoelectron Microscopy Linear Combination statistical models (nuclear) signals Individual Power simulating

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4D seismic monitoring of CO2 sequestration based upon spectral-element and adjoint methods: Comparison of acoustic, elastic and poroelastic theories 80

4D seismic monitoring of CO2 sequestration based upon spectr...

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Society of Exploration Geophysicists International Exposition and 80th Annual Meeting 2010, SEG 2010

作者： Morency, Christina Luo, Yang Tromp, Jeroen Department of Geosciences Princeton University United States Department of Geosciences and Program in Applied and Computational Mathematics Princeton University United States

ISBN: (纸本)9781617389801

The key issues in CO2 sequestration monitoring involve accurate monitoring, from the injection stage to prediction & verification, of CO2 movement over time for environmental considerations. A natural non-intrusive monitoring technique is referred to as "4D seismics", which involves 3D time-lapse seismic surveys. The success of monitoring the CO2 movement is subject to a proper description of the physical properties of the structure. We realize time-lapse migrations comparing acoustic, elastic, and poroelastic simulations of 4D seismic imaging to characterize the storage zone, based solely upon the first arrival traveltime anomaly arising from the injection of CO2. This approach highlights the influence of using different physical theories on interpreting seismic data, and, more importantly, on extracting the CO2 signature from the seismic wave field. Simulations are performed using a spectral-element method, which allows for highly accurate results. Biot? Equations are implemented to account for poroelastic effects. The sensitivity of observables to the model parameters is quantified based upon finite-frequency sensitivity kernels calculated using an adjoint method. © 2010 SEG.

关键词： Carbon dioxide

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