In this paper we present a new software tool for dealing with the problem of segmentation in Digital Imagery. The implementation is inspired in the design of a tissue-like P system which solves the problem in constant...
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We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by F. Hache, D. Ricard, and C. Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat c...
We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by F. Hache, D. Ricard, and C. Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by S. G. Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they cannot be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian’s approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian’s approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable to or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespective of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. Lett. 100, 47402 (2008)].
We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role...
We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used.
We investigate numerically the propagation of steady-state monochromatic surface plasmon polaritons (SPPs) in curved chains of metal nanoparticles of various spheroidal shapes. We discuss the SPP propagation (decay of...
We investigate numerically the propagation of steady-state monochromatic surface plasmon polaritons (SPPs) in curved chains of metal nanoparticles of various spheroidal shapes. We discuss the SPP propagation (decay of the amplitude), the polarization conversion due to coupling of orthogonally polarized SPPs, and the electromagnetic field localization in the near-field vicinity of a chain.
Datasets containing sensitive information are often sequentially analyzed by many algorithms. This raises a fundamental question in differential privacy regarding how the overall privacy bound degrades under compositi...
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In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with Dirichlet boundary *** revisit the scattering result below ground state i...
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In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with Dirichlet boundary *** revisit the scattering result below ground state in Killip-Visan-Zhang[The focusing cubic NLS on exterior domains in three ***,1,146-180(2016)]by utilizing the method of Dodson and Murphy[A new proof of scattering below the ground state for the 3d radial focusing cubic ***.,145,4859-4867(2017)]and the dispersive estimate in Ivanovici and Lebeau[Dispersion for the wave and the Schr?dinger equations outside strictly convex obstacles and ***.,355,774-779(2017)],which avoids using the concentration *** conquer the difficulty of the boundary in the focusing case by establishing a local smoothing effect of the *** on this effect and the interaction Morawetz estimates,we prove that the solution decays at a large time interval,which meets the scattering criterion.
This paper shows that the standing, backward- and forward-accelerated large amplitude relativistic electromagnetic solitons induced by intense laser pulse in long underdense collisionless homogeneous plasmas can be ob...
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This paper shows that the standing, backward- and forward-accelerated large amplitude relativistic electromagnetic solitons induced by intense laser pulse in long underdense collisionless homogeneous plasmas can be observed by particle simulations. In addition to the inhomogeneity of the plasma density, the acceleration of the solitons also depends upon not only the laser amplitude but also the plasma length. The electromagnetic frequency of the solitons is between about half and one of the unperturbed electron plasma frequency. The electrostatic field inside the soliton has a one-cycle structure in space, while the transverse electric and magnetic fields have half-cycle and one-cycle structure respectively. Analytical estimates for the existence of the solitons and their electromagnetic frequencies qualitatively coincide with our simulation results.
We propose the utilization of divergences as dissimilarity measure in the Fuzzy c-Means algorithm for the clustering of functional data. Further we adapt the relevance parameter to improve the data representation and ...
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In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here...
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In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high-dimensional random-effects model where each predictor has a small effect, we discover several new ***-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call "infinite-worker limit".Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are *** also propose a new Weighted ONe-shot DistributEd Ridge regression algorithm (WONDER). We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.
In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does n...
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In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).
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