The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated dat...
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An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accuracy beyond density functional theory is often needed to describe the intermolecular i...
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We propose anefficient and robust iterative solutiontothe multi-object matching problem. We first clarify serious limitationsofcurrent methodsaswellasthe inappropriateness of the standard iteratively reweighted least ...
ISBN:
(纸本)9781713829546
We propose anefficient and robust iterative solutiontothe multi-object matching problem. We first clarify serious limitationsofcurrent methodsaswellasthe inappropriateness of the standard iteratively reweighted least squares procedure. Inview ofthese limitations, we suggestanovel and more reliable iterative reweighting strategy that incorporates information from higher-order neighborhoods by exploiting the graph connection Laplacian. We provide partial theoretical guarantees and demonstrate the superior performance of our procedure over state-of-the-art methods using both synthetic and real datasets.
作者：
AGISHTEIN, MEMIGDAL, AADepartment of Physics
University of California at San Diego La Jolla CA 92093 USA1 1 Current address: Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton NY 08544-100 USA.
The dynamics of vortex surfaces in an ideal fluid is considered. The Hamiltonian and the action are constructed and topological conservation laws are discussed. The axially symmetric case is reduced to an effective 2d...
The dynamics of vortex surfaces in an ideal fluid is considered. The Hamiltonian and the action are constructed and topological conservation laws are discussed. The axially symmetric case is reduced to an effective 2d problem and studied numerically. There is qualitative correspondence with the results of Moore and Krasny for the purely 2d problem. The general case is approximated by means of a triangulated surface and a corresponding computer model is constructed, taking into account the topological conservation laws. The axially symmetric motion of the triangulated surface agrees with the 2d model, but there are some angular instabilities, which may lead to new vortex structures. The large-scale asymmetric 3d simulations with fairly developed instabilities are reported. The results agree with the general scenario of hierarchy of vortex structures.
The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient c...
The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient condition for uniform first-order accuracy and, consequently, the elimination of the “ghost force” is formulated in terms of the reconstruction schemes. The quasi-nonlocal approach is discussed as a special case of this condition. Examples of reconstruction schemes that satisfy this condition are presented. Transition between atom-based and element-based summation rules are studied.
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of t...
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of the Clebsch fields is responsible for generation of two energy spectra E(k)∝k−7/3 and E(k)∝k−2 at scales somewhat larger than those corresponding to the -5/3 inertial range. This interaction is also responsible for the experimentally observed Gaussian statistics of the velocity differences at large scales, and the nontrivial scaling behavior of their high-order moments for inertial-range values of the displacement r. The ‘‘anomalous scaling exponents’’ are derived and compared with experimental data.
We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various gen...
We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various generalizations of the classical Cauchy-Born rule. In particular, we discuss a so-called local Cauchy-Born rule which is very general and particularly easy to use. As an application, we use the atomistically derived continuum models to study the elastic deformation of carbon nanotubes.
We propose a method for mapping a spatially discrete problem, stemming from the spatial discretization of a parabolic or hyperbolic partial differential equation of gradient type, to a heterogeneous one with certain c...
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We propose a method for mapping a spatially discrete problem, stemming from the spatial discretization of a parabolic or hyperbolic partial differential equation of gradient type, to a heterogeneous one with certain comparable dynamical features pertaining, in particular, to coherent structures. We focus the analysis on a (1+1)-dimensional φ4 model and confirm the theoretical predictions numerically. We also discuss possible generalizations of the method and the ensuing qualitative analogies between heterogeneous and discrete systems and their dynamics.
By analyzing the momentum distribution obtained from path integral and phonon calculations we find that the protons in hexagonal ice experience an anisotropic quasiharmonic effective potential with three distinct prin...
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By analyzing the momentum distribution obtained from path integral and phonon calculations we find that the protons in hexagonal ice experience an anisotropic quasiharmonic effective potential with three distinct principal frequencies that reflect molecular orientation. Due to the importance of anisotropy, anharmonic features of the environment cannot be extracted from existing experimental distributions that involve the spherical average. The full directional distribution is required, and we give a theoretical prediction for this quantity that could be verified in future experiments. Within the quasiharmonic context, anharmonicity in the ground-state dynamics of the proton is substantial and has quantal origin, a finding that impacts the interpretation of several spectroscopies.
Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (...
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Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (1) it is capable of finding a variable number of communities, (2) it can detect communities of DNA loci either adjacent or distant in the 1D sequence, and (3) it allows us to obtain a principled value of k, the number of communities present. Forcing k = 2, our method recovers earlier findings of Lieberman-Aiden, et al. (2009), but letting k be a parameter, our method obtains as optimal value k* = 6, discovering new candidate communities. In addition to discovering large communities that partition entire chromosomes, we also show that CD can detect small-scale topologically associating domains (TADs) such as those found in Dixon, et al. (2012). CD thus provides a natural and flexible statistical framework for understanding the folding structure of DNA at multiple scales in Hi-C data.
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