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4th International Symposium on Communications, Control, and Signal Processing, ISCCSP-2010

作者： Beltrani, Vincent Dominy, Jason Ho, Tak-San Rabitz, Herschel Department of Chemistry Princeton University NJ 08544 United States Program in Applied and Computational Mathematics Princeton University NJ 08544 United States

ISBN: (纸本)9781424462858

A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i→f. For transition probabilities 0 i→fi→f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse ftuence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members. ©2010 IEEE.

关键词： Quantum optics

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Why Gabor frames? Two fundamental measures of coherence and their role in model selection

Why Gabor frames? Two fundamental measures of coherence and ...

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作者： Bajwa, Waheed U. Calderbank, Robert Jafarpour, Sina Department of Electrical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Computer Science Princeton University Princeton NJ 08544 United States

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carr

关键词： Recovery

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Hydrogen in tungsten: Absorption, diffusion, vacancy trapping, and decohesion

Hydrogen in tungsten: Absorption, diffusion, vacancy trappin...

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作者： Johnson, Donald F. Carter, Emily A. Department of Chemistry Princeton University Princeton NJ 08544 United States Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

Understanding the interaction between atomic hydrogen and solid tungsten is important for the development of fusion reactors in which proposed tungsten walls would be bombarded with high energy particles including hydrogen isotopes. Here, we report results from periodic density-functional theory calculations for three crucial aspects of this interaction: surface-to-subsurface diffusion of H into W, trapping of H at vacancies, and H-enhanced decohesion, with a view to assess the likely extent of hydrogen isotope incorporation into tungsten reactor walls. We find energy barriers of (at least) 2.08 eV and 1.77 eV for H uptake (inward diffusion) into W(001) and W(110) surfaces, respectively, along with very small barriers for the reverse process (outward diffusion). Although H dissolution in defect-free bulk W is predicted to be endothermic, vacancies in bulk W are predicted to exothermically trap multiple H atoms. Furthermore, adsorbed hydrogen is predicted to greatly stabilize W surfaces such that decohesion (fracture) may result from high local H concentrations. © 2010 Materials Research Society.

关键词： Tungsten

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Nonlocal orbital-free kinetic energy density functional for semiconductors

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Physical Review B 2010年第4期81卷 045206-045206页

作者： Chen Huang Emily A. Carter Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and the reduced density gradient, with an internal parameter formally related to the material’s static dielectric constant. We determine the accuracy of the KEDF within orbital-free density functional theory (DFT) by applying it to a variety of common semiconductors. With only two adjustable parameters, the KEDF reproduces quite well the exact noninteracting KEDF (i.e., Kohn-Sham DFT) predictions of bulk moduli, equilibrium volumes, and equilibrium energies. The two parameters in our KEDF are sensitive primarily to changes in the local crystal structure (such as atomic coordination number) and exhibit good transferability between different tetrahedrally-bonded phases. This local crystal structure dependence is rationalized by considering Thomas-Fermi dielectric screening theory.

关键词： .Phases orbital-free KEDF bulk moduli

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Level sets of quantum control landscapes

Level sets of quantum control landscapes

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International Symposium on Communications Control and Signal Processing (ISCCSP)

作者： Vincent Beltrani Jason Dominy Tak-San Ho Herschel Rabitz Department of Chemistry Princeton University NJ USA Program in Applied and Computational Mathematics Princeton University NJ USA

A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i¿f . For transition probabilities 0 < P i¿f < 1, a first order diffeomorphic modulation observable response preserving homotopy (D-MORPH) algorithm is utilized to investigate level sets. At the top of the control landscape, P i¿f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse fluence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members.

关键词： Level set Communication system control Control systems Optimal control Topology Signal processing algorithms Centralized control Relativistic quantum mechanics Process control Signal processing

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High-dimensional data fusion via joint manifold learning

High-dimensional data fusion via joint manifold learning

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2010 AAAI Fall Symposium

作者： Davenport, Mark A. Hegde, Chinmay Duarte, Marco F. Baraniuk, Richard G. Department of Statistics Stanford University Stanford CA 94305 United States Department of Electrical and Computer Engineering Rice University Houston TX 77005 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

ISBN: (纸本)9781577354888

The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that acquire large amounts of very high-dimensional data. To cope with such a data deluge, manifold models are often developed that provide a powerful theoretical and algorithmic framework for capturing the intrinsic structure of data governed by a low-dimensional set of ***, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that joint manifold structure can lead to improved performance for manifold learning. Additionally, we leverage recent results concerning random projections of manifolds to formulate a universal, network-scalable dimensionality reduction scheme that efficiently fuses the data from all sensors. Copyright © 2010, Association for the Advancement of Artificial Intelligence. All rights reserved.

关键词： Sensor networks

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Influence of nonequilibrium lipid transport, membrane compartmentalization, and membrane proteins on the lateral organization of the plasma membrane

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Physical Review E 2010年第1期81卷 011908-011908页

作者： Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Compositional lipid domains (lipid rafts) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes, lifetimes, and spatial localization of these domains are rather poorly understood at the moment. We propose a robust mechanism for the formation of finite-sized lipid raft domains in plasma membranes, the competition between phase separation in an immiscible lipid system and active cellular lipid transport processes naturally leads to the formation of such domains. Simulations of a continuum model reveal that the raft size distribution is broad and the average raft size is strongly dependent on the rates of cellular and interlayer lipid transport processes. We demonstrate that spatiotemporal variations in the recycling may enable the cell to localize larger raft aggregates at specific parts along the membrane. Moreover, we show that membrane compartmentalization may further facilitate spatial localization of the raft domains. Finally, we demonstrate that local interactions with immobile membrane proteins can spatially localize the rafts and lead to further clustering.

关键词： Cell membranes

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Lipid Microdomains: Structural Correlations, Fluctuations, and Formation Mechanisms

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Physical Review Letters 2010年第11期104卷 118101-118101页

作者： Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Compositional lipid microdomains (“lipid rafts”) in mammalian plasma membranes are believed to facilitate many important cellular processes. While several physically distinct scenarios predicting the presence of finite-sized microdomains in vivo have been proposed in the past, direct experimental verification or falsification of model predictions has remained elusive. Herein, we demonstrate that the combination of the spatial correlation and temporal fluctuation spectra of the lipid domains can be employed to unambiguously differentiate between the existing theoretical scenarios. Furthermore, the differentiation of the raft formation mechanisms using this methodology can be achieved by collecting data at physiologically relevant conditions without the need to tune control parameters.

关键词： Cell membranes

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Nucleation of Ordered Phases in Block Copolymers

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Physical Review Letters 2010年第14期104卷 148301-148301页

作者： Xiuyuan Cheng Ling Lin Weinan E Pingwen Zhang An-Chang Shi School of Mathematical Sciences and The Key Laboratory of Mathematics and Applied Mathematics Peking University Beijing 100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-1000 USA Department of Physics and Astronomy McMaster University Hamilton Ontario L8S 4M1 Canada

Nucleation of various ordered phases in block copolymers is studied by examining the free-energy landscape within the self-consistent field theory. The minimum energy path (MEP) connecting two ordered phases is computed using a recently developed string method. The shape, size, and free-energy barrier of critical nuclei are obtained from the MEP, providing information about the emergence of a stable ordered phase from a metastable phase. In particular, structural evolution of embryonic gyroid nucleus is predicted to follow two possible MEPs, revealing an interesting transition pathway with an intermediate perforated layered structure.

关键词： Nucleation

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Geometrical ambiguity of pair statistics. II. Heterogeneous media

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Physical Review E 2010年第1期82卷 011106-011106页

作者： Yang Jiao Frank H. Stillinger Salvatore Torquato Department of Chemistry and Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics and Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA

In the first part of this series of two papers [Y. Jiao, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 011105 (2010)], we considered the geometrical ambiguity of pair statistics associated with point configurations. Here we focus on the analogous problem for heterogeneous media (materials). Heterogeneous media are ubiquitous in a host of contexts, including composites and granular media, biological tissues, ecological patterns, and astrophysical structures. The complex structures of heterogeneous media are usually characterized via statistical descriptors, such as the n-point correlation function Sn. An intricate inverse problem of practical importance is to what extent a medium can be reconstructed from the two-point correlation function S2 of a target medium. Recently, general claims of the uniqueness of reconstructions using S2 have been made based on numerical studies, which implies that S2 suffices to uniquely determine the structure of a medium within certain numerical accuracy. In this paper, we provide a systematic approach to characterize the geometrical ambiguity of S2 for both continuous two-phase heterogeneous media and their digitized representations in a mathematically precise way. In particular, we derive the exact conditions for the case where two distinct media possess identical S2, i.e., they form a degenerate pair. The degeneracy conditions are given in terms of integral and algebraic equations for continuous media and their digitized representations, respectively. By examining these equations and constructing their rigorous solutions for specific examples, we conclusively show that in general S2 is indeed not sufficient information to uniquely determine the structure of the medium, which is consistent with the results of our recent study on heterogeneous-media reconstruction [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. U.S.A. 106, 17634 (2009)]. The analytical examples include complex patterns composed of building blo

关键词： Inverse problems

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