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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Onur Özyeşil Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics Princeton University Princeton NJ USA

3D structure recovery from a collection of 2D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating n locations t 1 , t 2 , ..., tn in ℝ 3 from noisy measurements of a subset of the pairwise directions t i -t j /∥t i -t j ∥, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.

关键词： Estimation Cameras Robustness Noise measurement Three-dimensional displays Accuracy Minimization

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Reliability and Precision Are Optimal for Non-Uniform Distributions of Presynaptic Release Probability

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Journal of Biomedical Science and Engineering 2015年第3期8卷 170-183页

作者： Jean-Marc Fellous Nadia S. Corral-Frías Graduate Interdisciplinary Program in Neuroscience University of Arizona Tucson USA Department of Psychology and Applied Mathematics University of Arizona Tucson USA

Most conceptual and computational models assume that synaptic transmission is reliable, a simplification rarely substantiated by data. The functional consequences of the recruitment of high and low initial release probability synapses on the reliability and precision of their postsynaptic targets are studied in a multi-compartmental model of a hippocampal CA1 pyramidal cell. We show that changes in the firing rate of CA3 afferent inputs (rate remapping) are not reflected in the firing rate of the CA1 cell but in the reliability and precise timing of some of its action potentials, suggesting that a signature of remapping may be found in the precise spike timing of CA1. Our results suggest that about half of the action potentials produced by a CA1 cell can potentially carry reliable information in their precise timing with about 25 ms precision, a time scale on the order of the gamma cycle. We show further that reliable events were primarily elicited by CA3 synapses in a state of low probability of release. Overall, our results suggest that the non-uniform distribution of initial release probabilities observed experimentally achieves an optimum yielding simultaneously high precision and high reliability, and allows large populations of CA3 synapses to contribute to the production of reliable CA1 spiking events.

关键词： Spike Timing Hippocampus Computational Model Synapses

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Digital Microfluidics: Paper-Based Digital Microfluidic Chip for Multiple Electrochemical Assay Operated by a Wireless Portable Control System (Adv. Mater. Technol. 3/2017)

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Advanced Materials Technologies 2017年第3期2卷

作者： Nipapan Ruecha Jumi Lee Heedo Chae Haena Cheong Veasna Soum Pattarachaya Preechakasedkit Orawon Chailapakul Georgi Tanev Jan Madsen Nadnudda Rodthongkum Oh-Sun Kwon Kwanwoo Shin Program in Macromolecular Science Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Chemistry and Institute of Biological Interfaces Sogang University Seoul 04107 Republic of Korea Program in Biotechnology Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Electrochemistry and Optical Spectroscopy Research Unit (EOSRU) Department of Chemistry Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby 2800 Denmark Metallurgy and Materials Science Research Institute Chulalongkorn University Bangkok 10330 Thailand

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Confined disordered strictly jammed binary sphere packings

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Physical Review E 2015年第6期92卷 062207-062207页

作者： D. Chen S. 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

Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H, small to large sphere radius ratio α, and small sphere relative concentration x. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term “confinement frustration.” Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H, though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call “size-disparity” frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance στ2(R) to characterize confined packings and find that these packings possess essentially the same level of

关键词： RESEARCH Combinatorial packing & covering Linear programming Density Powders Sphere packings

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Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

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Physical Review E 2015年第2期92卷 022120-022120页

作者： G. Zhang F. H. Stillinger S. 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

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space Rd. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

关键词： GROUND state (Quantum mechanics) ENERGY levels (Quantum mechanics) EUCLIDEAN domains MOLECULAR dynamics QUANTUM entropy

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Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

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Physical Review E 2015年第2期92卷 022119-022119页

Systems of particles interacting with “stealthy” pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like “pseudo” disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperatur

关键词： THERMODYNAMIC equilibrium PROBABILITY theory QUANTUM spin models MOLECULAR dynamics QUANTUM entropy

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Dispersive optical solitons with Schrödinger-hirota equation using undetermined coefficients

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Journal of Computational and Theoretical Nanoscience 2016年第8期13卷 5288-5293页

作者： Bernstein, Ida Melikechi, Noureddine Zerrad, Essaid Biswas, Anjan Belic, Milivoj Department of Physics and Engineering Delaware State University DoverDE19901-2277 United States Optical Science Center and Applied Research Delaware State University DoverDE19901-2277 United States Department of Mathematical Sciences Delaware State University DoverDE19901-2277 United States Department of Mathematics Faculty of Science King Abdulaziz University Jeddah21589 Saudi Arabia Science Program Texas a and M University at Qatar P. O. Box 23874 Doha Qatar

This paper reports dispersive optical soliton solutions that are modeled by Schrödinger-Hirota equation with spatio-Temporal dispersion in addition to group velocity dispersion. There are two types of nonlinear media studied in this paper. These are Kerr law and power law. Bright, dark and singular soliton solutions are secured along with their respective existence criteria. The method of undetermined coefficients is applied to retrieve these soliton solutions. © Copyright 2016 American Scientific Publishers All rights reserved.

关键词： Group velocity dispersion

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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Usability of VGI for validation of land cover maps (vol 29, pg 1269, 2015)

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2015年第7期29卷 1269-1291页

作者： Fonte, C. C. Lupia, Flavio [a] Department of Mathematics University of Coimbra Coimbra Portugal[b] Institute for Systems Engineering and Computers at Coimbra (INESC Coimbra) Coimbra Portugal[c] School of Engineering and Applied Science Aston University Birmingham UK[d] Ecosystems Services and Management Program International Institute for Applied Systems Analysis (IIASA) Laxenburg Austria[e] School of Geography University of Nottingham Nottingham UK[f] National Institute of Agricultural Economics (INEA) Rome Italy

Volunteered Geographic Information (VGI) represents a growing source of potentially valuable data for many applications, including land cover map validation. It is still an emerging field and many different approaches can be used to take value from VGI, but also many pros and cons are related to its use. Therefore, since it is timely to get an overview of the subject, the aim of this article is to review the use of VGI as reference data for land cover map validation. The main platforms and types of VGI that are used and that are potentially useful are analysed. Since quality is a fundamental issue in map validation, the quality procedures used by the platforms that collect VGI to increase and control data quality are reviewed and a framework for addressing VGI quality assessment is proposed. A review of cases where VGI was used as an additional data source to assist in map validation is made, as well as cases where only VGI was used, indicating the procedures used to assess VGI quality and fitness for use. A discussion and some conclusions are drawn on best practices, future potential and the challenges of the use of VGI for land cover map validation.

关键词： VGI land cover/land use quality validation crowdsourcing

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Covariance estimation using conjugate gradient for 3D classification in CRYO-EM

Covariance estimation using conjugate gradient for 3D classi...

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IEEE International Symposium on Biomedical Imaging

作者： Joakim Andén Eugene Katsevich Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ Department of Statistics Stanford University Stanford CA

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

关键词： Covariance matrices Eigenvalues and eigenfunctions Microscopy Image reconstruction Biology Image resolution

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