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作者： Bandeira, A.S. Scheinberg, K. Vicente, L.N. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Industrial and Systems Engineering Lehigh University Harold S. Mohler Laboratory 200 West Packer Avenue Bethlehem PA 18015-1582 United States CMUC Department of Mathematics University of Coimbra 3001-501 Coimbra Portugal

Interpolation-based trust-region methods are an important class of algorithms forDerivative-Free Optimizationwhich rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations between variables are negligible, implying, in the smooth case, a sparse structure in the Hessian matrix. To be able to exploit Hessian sparsity, existing optimization approaches require the knowledge of the sparsity structure. The goal of this paper is to develop and analyze a method where the sparse models are constructed automatically. The sparse recovery theory developed recently in the field of compressed sensing characterizes conditions under which a sparse vector can be accurately recovered from few random measurements. Such a recovery is achieved by minimizing the l1-norm of a vector subject to the measurements constraints. We suggest an approach for building sparse quadratic polynomial interpolationmodels byminimizing the l1-norm of the entries of themodel Hessian subject to the interpolation conditions. We show that this procedure recovers accurate models when the function Hessian is sparse, using relatively few randomly selected sample points. Motivated by this result, we developed a practical interpolation-based trust-region method using deterministic sample sets and minimum l1-norm quadratic models. Our computational results show that the new approach exhibits a promising numerical performance both in the general case and in the sparse one. © Springer and Mathematical Optimization Society 2012.

关键词： Interpolation

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Towards optimization of a human-inspired heuristic for solving explore-exploit problems

Towards optimization of a human-inspired heuristic for solvi...

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IEEE Annual Conference on Decision and Control

作者： Paul Reverdy Robert C. Wilson Philip Holmes Naomi E. Leonard Department of Mechanical and Aerospace Engineering Princeton University Department of Psychology and Neuroscience Institute Princeton University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781467320658

Motivated by models of human decision making, we consider a heuristic solution for explore-exploit problems. In a numerical example we show that, with appropriate parameter values, the algorithm performs well. However, the parameters of the algorithm trade off exploration against exploitation in a complicated way so that finding the optimal parameter values is not obvious. We show that the optimal parameter values can be analytically computed in some cases and prove that suboptimal parameter tunings can provide robustness to modeling error. The analytic results suggest a feedback control law for dynamically optimizing parameters.

关键词： optimal parameter Heuristics numerical example control law Solve modeling error Exploration

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Importance of reference Hamiltonians containing exact exchange for accurate one-shot GW calculations of Cu2O

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Physical Review B 2012年第23期85卷 235142-235142页

作者： Leah Y. Isseroff Emily A. Carter Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544-5263 USA Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

We show that a “one-shot” GW approach (denoted G0W0) can accurately calculate the photoemission/inverse-photoemission properties of Cu2O. As the results of any perturbative method are heavily dependent on the reference state, the appropriate reference Hamiltonian for G0W0 is identified by evaluating the performance of density-functional-theory-based input wave functions and eigenvalues generated with selected exchange-correlation functionals. It is shown that a reference Hamiltonian employing the hybrid Heyd-Scuseria-Ernzerhof functional used in conjunction with G0W0 produces an accurate photoemission/inverse-photoemission band gap and photoemission spectrum whose character is then further analyzed. The physical origin of why a hybrid functional is required for the zeroth-order wave function is discussed, giving insight into the unique electronic structure of Cu2O in comparison to other transition-metal oxides.

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Efficient coarse simulation of a growing avascular tumor

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Physical Review E 2012年第3期85卷 031912-031912页

作者： Michail E. Kavousanakis Ping Liu Andreas G. Boudouvis John Lowengrub Ioannis G. Kevrekidis School of Chemical Engineering National Technical University of Athens 9 Heroon Polytechniou St. Zographos Athens GR-15780 Greece Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA Department of Mathematics University of California 103 MSTB Irvine California 92697 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The subject of this work is the development and implementation of algorithms which accelerate the simulation of early stage tumor growth models. Among the different computational approaches used for the simulation of tumor progression, discrete stochastic models (e.g., cellular automata) have been widely used to describe processes occurring at the cell and subcell scales (e.g., cell-cell interactions and signaling processes). To describe macroscopic characteristics (e.g., morphology) of growing tumors, large numbers of interacting cells must be simulated. However, the high computational demands of stochastic models make the simulation of large-scale systems impractical. Alternatively, continuum models, which can describe behavior at the tumor scale, often rely on phenomenological assumptions in place of rigorous upscaling of microscopic models. This limits their predictive power. In this work, we circumvent the derivation of closed macroscopic equations for the growing cancer cell populations; instead, we construct, based on the so-called “equation-free” framework, a computational superstructure, which wraps around the individual-based cell-level simulator and accelerates the computations required for the study of the long-time behavior of systems involving many interacting cells. The microscopic model, e.g., a cellular automaton, which simulates the evolution of cancer cell populations, is executed for relatively short time intervals, at the end of which coarse-scale information is obtained. These coarse variables evolve on slower time scales than each individual cell in the population, enabling the application of forward projection schemes, which extrapolate their values at later times. This technique is referred to as coarse projective integration. Increasing the ratio of projection times to microscopic simulator execution times enhances the computational savings. Crucial accuracy issues arising for growing tumors with radial symmetry are addressed by applying th

关键词： SIMULATION methods & models TUMORS -- Growth MATHEMATICAL models CANCER invasiveness STOCHASTIC models computational biology BIONICS PHENOMENOLOGY

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Density of States for a Specified Correlation Function and the Energy Landscape

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Physical Review Letters 2012年第8期108卷 080601-080601页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège B-4000 Liège Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are explained in terms of the roughness of an energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered structures.

关键词： ENERGY levels (Quantum mechanics) CORRELATION (Statistics) MICROSTRUCTURE GROUND state (Quantum mechanics) MONTE Carlo method CONFIGURATION space QUANTITATIVE research

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Model reduction for agent-based social simulation: Coarse-graining a civil violence model

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Physical Review E 2012年第6期85卷 066106-066106页

作者： Yu Zou Vladimir A. Fonoberov Maria Fonoberova Igor Mezic Ioannis G. Kevrekidis Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Aimdyn Inc. 1919 State Street Suite 207 Santa Barbara California 93101 USA Department of Mechanical Engineering University of California Santa Barbara Santa Barbara California 93106 USA

Agent-based modeling (ABM) constitutes a powerful computational tool for the exploration of phenomena involving emergent dynamic behavior in the social sciences. This paper demonstrates a computer-assisted approach that bridges the significant gap between the single-agent microscopic level and the macroscopic (coarse-grained population) level, where fundamental questions must be rationally answered and policies guiding the emergent dynamics devised. Our approach will be illustrated through an agent-based model of civil violence. This spatiotemporally varying ABM incorporates interactions between a heterogeneous population of citizens [active (insurgent), inactive, or jailed] and a population of police officers. Detailed simulations exhibit an equilibrium punctuated by periods of social upheavals. We show how to effectively reduce the agent-based dynamics to a stochastic model with only two coarse-grained degrees of freedom: the number of jailed citizens and the number of active ones. The coarse-grained model captures the ABM dynamics while drastically reducing the computation time (by a factor of approximately 20).

关键词： VIOLENCE SOCIAL dynamics STOCHASTIC models CITIZENS SOCIAL interaction DEGREES of freedom

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Spectral Dynamics of Spatially Incoherent Modulation Instability

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Physical Review Letters 2012年第26期108卷 263902-263902页

作者： Can Sun Laura Waller Dmitry V. Dylov Jason W. Fleischer Department of Electrical Engineering Princeton University Princeton New Jersey 08544 USA General Electric Global Research Center Niskayuna New York 12309 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light modulator to create spatially incoherent beams with arbitrary spectral distributions. As a specific example of the new dynamics possible, we consider the spatial modulation instability of a partially coherent beam. We show that, for statistical beams of uniform intensity and equal correlation length, the underlying spectral shape determines the threshold and visibility of intensity modulations as well as the spectral profile of the growing sidebands. We demonstrate the behavior using statistical light, but the results will hold for any wave-kinetic system, such as plasma, ultracold gases, and turbulent acoustic waves.

关键词： NONLINEAR optics MODULATION theory SPECTRUM analysis BEAM optics GAUSSIAN processes LIGHT modulators SOUND waves COLD gases

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Multilayer thin film growth on crystalline and quasicrystalline surfaces: A phase-field crystal study

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Physical Review B 2012年第24期85卷 245428-245428页

作者： Srevatsan Muralidharan Raika Khodadad Ethan Sullivan 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 and School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

In this paper, we explore the effects of misfit strain fields on both heterogeneous nucleation behavior and anisotropic growth of islands at submonolayer coverages and compositional patterning at complete monolayer coverage via simulations of a phase-field crystal model. In particular, deposition on top of a herringbone structure and quasicrystalline (QC) substrate are considered, the former representing a system with spatially periodic misfit strain fields arising from the presence of surface dislocations, and the latter representing a system which inherently possesses a wide range of local, aperiodic misfit patterns. In the case of single-component systems, we demonstrate that misfit strain fields lead to heterogeneous nucleation behavior and anisotropic island growth. In the case of QC substrate, a wide range of morphologies, such as coexistence of locally hexagonally ordered atomic clusters within a larger scale arrangement with overall QC symmetry and so-called “starfish” aggregates, is observed in a pure system at submonolayer coverages when the adlayer-substrate interaction strength and lattice mismatch are tuned. In the case of bulk-immiscible binary systems at complete monolayer coverage, strain-stabilized compositional domains emerge at low line tension values for both substrates. Interestingly, the compositional domains on the QC substrate inherit their symmetries at sufficiently low line tension values, while at larger line tension values, the domain structure begins to resemble the classical spinodal microstructure. Such domain structures should be readily observable in colloidal systems in which attractive interparticle and particle-substrate interactions can be tuned.

关键词： THIN films CRYSTALS NUCLEATION DISLOCATIONS in crystals MICROSTRUCTURE

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Density-decomposed orbital-free density functional theory for covalently bonded molecules and materials

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Physical Review B 2012年第23期86卷 235109-235109页

作者： Junchao Xia Emily A. Carter Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544-5263 USA Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

We propose a density decomposition scheme using a Wang-Govind-Carter- (WGC-) based kinetic energy density functional (KEDF) to accurately and efficiently simulate various covalently bonded molecules and materials within orbital-free (OF) density functional theory (DFT). By using a local, density-dependent scale function, the total density is decomposed into a highly localized density within covalent bond regions and a flattened delocalized density, with the former described by semilocal KEDFs and the latter treated by the WGC KEDF. The new model predicts reasonable equilibrium volumes, bulk moduli, and phase-ordering energies for various semiconductors compared to Kohn-Sham (KS) DFT benchmarks. The decomposition formalism greatly improves numerical stability and accuracy, while retaining computational speed compared to simply applying the original WGC KEDF to covalent materials. The surface energy of Si(100) and various diatomic molecule properties can be stably calculated and also agree well with KSDFT benchmarks. This linear-scaled, computationally efficient, density-partitioned, multi-KEDF scheme opens the door to large-scale simulations of molecules, semiconductors, and insulators with OFDFT.

关键词： PHYSICAL sciences research MOLECULES SEMICONDUCTORS BENCHMARKING (Management) CRYSTALS SURFACE energy COVALENT bonds (Chemistry)

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Multiple Magnetic Pole Reversals and M?ssbauer Studies in Molecular-based Mixed Valency Ferrimagnet {[N（nC4H9）4][MⅡFeⅢ（C2O4）3]}n （M=Zn、Fe）

Multiple Magnetic Pole Reversals and M?ssbauer Studies in Mo...

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2012 International Conference on Solid State Devices and Materials Science(SSDMS 2012)

作者： Qing Lin Chenglong Lei Guodong Tang Qingmei Zhang Xinlong Dong Fupei Liang Ruijun Wang Siliang Zeng Yun He College of Physics and Technology Guangxi Normal University Department of Information Technology Hainan Medical College College of Chemistry and Chemical Engineering Guangxi Normal University Institute of Applied Physics and Computational Mathematics

The Molecule magnets Materials {[N(n-C4H9)4][MⅡFe Ⅲ(C2O4)3]}n M=Zn Fe were investigated by magnetic measurements and M?ssbauer *** the complex {[N(n-C4H9)4][Zn Ⅱ0.03 Fe Ⅱ0.97 Fe Ⅲ(C2O4)3]}n detailed investigation of the ferromagnetism behaviour, and a compensation temperature has found with the field being less than 1KOe. And the 57 Fe M?ssbauer measurements had been carried out in {[N(nC4H9)4][Fe ⅡFe Ⅲ(C2O4)3]}n to investigate the mixed valency character and antiferromagnetic coupling. Some ferrimagnets consisting of magnetic anisotropy ions and two or more types of antiferromagnetically ordered magnetic ions exhibit this behavior. As the temperature was lowered to 40 K, the Fe Ⅲ doublet subspectrum almost completely turns into a sextet subspectrum. The hyperfine magnetic field increases as the temperature decreasing.

关键词： Molecule-based magnet M?ssbauer spectroscopy spin glass

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