Embedding Function Research Articles

Vibrational properties of vacancy in bcc Nb using embedded atom method

Embedded atom method (EAM) with universal form of embedding function along with Morse form of pair potential have been employed to determine the potential for Nb by fitting to Cauchy pressure, shear constants, cohesive energy and vacancy formation energy. Obtained potential is used to calculate the phonon dispersion spectra of this metal. On comparing with experimental phonons, the results using EAM show large discrepancies. In order to overcome this inadequacy of EAM model, we have further employed a modified embedded atom method (MEAM) in which a modified term along with pair potential and embedding function are added in the total energy. Calculated phonon dispersions using the potential obtained from MEAM are found to be closer to experimental results compared to those obtained from EAM. With application of MEAM potential, we have computed local vibrational density of states of atoms in ideal lattice and neighbouring atoms for vacancy. Vacancy formation entropy and mean square thermal displacements of the neighbouring atoms of vacancy are obtained using Green’s function method.

On the Mathematical Analysis of Black-Hole Information Loss Paradox

A Black-hole is an astronomical entity which possesses infinite density at its gravitational singularity or singular point. The capacity of a black-hole to completely rip-off an entire solar system without leaving any evidence is to be noted. A debate has been going on over the past few decades regarding the information storage in black-holes. The discovery of Hawking radiation, which predicts complete evaporation of mass violates unitarity ie. Conservation of probability and energy fails. Recent discoveries suggest that regular remnant of black-hole survives evaporation , as a result information of the object devoured can be contained. These remnants are grouped into embedded sub-manifolds. These manifolds are the result of a five-dimensional constant curvature bulk in space-time. Five-dimensional gravity can be recovered from brane-world resulting from equations of bulk geometry. Gravity can be explained by space-time theory and also quantum theory in the form of Gravitons. On observing the manifold, the gravitons show deformations in dimensions, rather than being constant. The perturbations in geometry can be related to embedding functions which should remain differentiable and regular. Regularity is related to the inverse functions theorem. Manifold observations followed by a mathematical approach can possibly retain information about objects devoured by the black-hole.

The Achievement of Web Server in the Development of ARM Embedded System

Based on open source embedded operating system uClinux, embedded applications system taking ARM microprocessor as the core was connected with Internet. Through embedding Web server to the ARM embedded system functions and adding embedded Gateway Interface CGI program, the interactive delivery with the long-distance customers Web browser order and response information come true.

Atomistic modelling of charge-induced deformation of gold nanowires

Experimental studies have shown that electrolyte-emerged nanoporous metals with nano-wire-resembling ligaments as building blocks can undergo considerable dimensional changes when a potential difference is applied. The primary actuation mechanism is the electric double-layer charging of the internal surface. To study the fundamental physical mechanism, we explore the charge-induced deformation of a gold nanowire using atomistic simulations. The excess charge is taken into account by modifying the embedding function of the surface embedded atom method as informed by density functional theory calculations. Our atomistic simulations indicate that the charge-induced deformation increases considerably for reduced cross-sectional dimensions of the wire, and depends sensitively on the crystallographic orientation. We found that anisotropy-driven surface distortions play an important role in transducing the atomistic charge-induced forces into dimensional changes. To capture the fundamental mechanisms, we present a simple analytical model for the charge-induced strain of gold nanowires that is found to be in excellent agreement with the atomistic simulations.

Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C 12 − C 44)/2, shear constants \(G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5\) and C 44, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.

Born–Infeld extension of Lovelock brane gravity

We present a Born–Infeld-type theory to describe the evolution of p-branes propagating in an N = (p + 2)-dimensional Minkowski spacetime. The expansion of the BI-type volume element gives rise to the (p + 1) Lovelock brane invariants associated with the worldvolume swept out by the brane. Contrary to the Lovelock theory in gravity, the number of Lovelock brane Lagrangians differs in this case, depending on the dimension of the worldvolume as a consequence that we consider the embedding functions, instead of the metric, as the field variables. This model depends on the intrinsic and the extrinsic geometries of the worldvolume and in consequence is a second-order theory as shown in the main text. A classically equivalent action is discussed and we comment on its Weyl invariance in any dimension which naturally requires the introduction of some auxiliary fields.

Secure Modulus Data Hiding Scheme

In 2006, Zhang and Wang proposed a data hiding scheme based on Exploiting Modification Direction (EMD) to increase data hiding capacity. The major benefit of EMD is providing embedding capacity greater than 1 bit per pixel. Since then, many EMD-type data hiding schemes have been proposed. However, a serious disadvantage common to these approaches is that the embedded data is compromised when the embedding function is disclosed. Our proposed secure data hiding scheme remedies this disclosure shortcoming by employing an additional modulus function. The provided security analysis of our scheme demonstrates that attackers cannot get the secret information from the stegoimage even if the embedding function is made public. Furthermore, our proposed scheme also gives a simple solution to the overflow/underflow problem and maintains high embedding capacity and good stegoimage quality.

Effect of Cover Quantization on Steganographic Fisher Information

This article presents an extension of the square root law of imperfect steganography to consider the effects of quantization on the steganographic Fisher information. We make the assumption that the cover elements are quantized i.i.d. samples drawn from an underlying continuous-valued ‘precover’ distribution. In the fine quantization limit, the Fisher information exhibits power scaling with an exponent determined jointly by the smoothness of the precover distribution and the properties of the embedding function. This extension is relevant for understanding the effects of pixel color depth and JPEG quality factor on secure payload of imperfect steganography realized using a mutually independent embedding operation.

Multiple Kernel Spectral Regression for Dimensionality Reduction

Traditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR) solves the problem of learning an embedding function by establishing a regression framework, which can avoid eigen-decomposition of dense matrices. Motivated by the effectiveness of SR, we incorporate multiple kernel learning (MKL) into SR for dimensionality reduction. The proposed approach (termed MKL-SR) seeks an embedding function in the Reproducing Kernel Hilbert Space (RKHS) induced by the multiple base kernels. An MKL-SR algorithm is proposed to improve the performance of kernel-based SR (KSR) further. Furthermore, the proposed MKL-SR algorithm can be performed in the supervised, unsupervised, and semi-supervised situation. Experimental results on supervised classification and semi-supervised classification demonstrate the effectiveness and efficiency of our algorithm.

Nano-mechanical compliance of Müller cells investigated by atomic force microscopy.

It has been known that a single Müller cell displays a large variation in the cytoskeletal compositions along its cell body, suggesting different mechanical properties in different segments. Müller cells are thought to be involved in many retinal diseases such as retinoschisis, which can be facilitated by a mechanical stress. Thus, mapping of mechanical properties on localized nano-domains of Müller cells could provide essential information for understanding their structural functions in the retina and roles in their pathological progresses. Using Atomic Force Microscopy (AFM) - based bio-nano-mechanics, we have investigated the local variations of the mechanical properties of Müller cells in vitro. We have a particular interest in identifying elastic moduli in regions closer to three distinctive segments of the cells - process, endfoot, and soma. Using the modified spherical AFM probes, we were able to accurately determine mechanical properties, i.e., elastic moduli from the obtained force-distance curves. We found that the regions closer to soma were mechanically more compliant than regions closer to endfoot and process of Müller cells. We found that this lateral heterogeneity of the mechanical compliance within a single Müller cell is consistent with reports from other cell types. The local variation in mechanical compliances along a single Müller cell may support their diverse mechanical functions in the retina such as a soft mechanical embedding, mechanosensing, and neurotrophic functions for neurons.

SPECTRAL REGRESSION DISCRIMINANT ANALYSIS FOR HYPERSPECTRAL IMAGE CLASSIFICATION

Abstract. Dimensionality reduction algorithms, which aim to select a small set of efficient and discriminant features, have attracted great attention for Hyperspectral Image Classification. The manifold learning methods are popular for dimensionality reduction, such as Locally Linear Embedding, Isomap, and Laplacian Eigenmap. However, a disadvantage of many manifold learning methods is that their computations usually involve eigen-decomposition of dense matrices which is expensive in both time and memory. In this paper, we introduce a new dimensionality reduction method, called Spectral Regression Discriminant Analysis (SRDA). SRDA casts the problem of learning an embedding function into a regression framework, which avoids eigen-decomposition of dense matrices. Also, with the regression based framework, different kinds of regularizes can be naturally incorporated into our algorithm which makes it more flexible. It can make efficient use of data points to discover the intrinsic discriminant structure in the data. Experimental results on Washington DC Mall and AVIRIS Indian Pines hyperspectral data sets demonstrate the effectiveness of the proposed method.

FROM THE EMBEDDING THEORY TO GENERAL RELATIVITY IN A RESULT OF INFLATION

We study the embedding theory being a formulation of the gravitation theory where the independent variable is the embedding function for the four-dimensional spacetime in a flat ambient space. We do not impose additional constraints which are usually used to remove from the theory the extra solutions not being the solutions of Einstein equations. In order to show the possibility of automatic removal of these extra solutions we analyze the equations of the theory, assuming an inflation period during the expansion of the universe. In the framework of Friedmann–Robertson–Walker (FRW) symmetry we study the initial conditions for the inflation, and we show that after its termination the Einstein equations begin to satisfy with a very high precision. The properties of the theory equations allow us to suppose with confidence that the Einstein equations will satisfy with enough precision out of the framework of FRW symmetry as well. Thus the embedding theory can be considered as a theory of gravity which explains observed facts without any additional modification of it and we can use this theory in a flat space when we try to develop a quantum theory of gravity.

PWP3D: Real-Time Segmentation and Tracking of 3D Objects

We formulate a probabilistic framework for simultaneous region-based 2D segmentation and 2D to 3D pose tracking, using a known 3D model. Given such a model, we aim to maximise the discrimination between statistical foreground and background appearance models, via direct optimisation of the 3D pose parameters. The foreground region is delineated by the zero-level-set of a signed distance embedding function, and we define an energy over this region and its immediate background surroundings based on pixel-wise posterior membership probabilities (as opposed to likelihoods). We derive the differentials of this energy with respect to the pose parameters of the 3D object, meaning we can conduct a search for the correct pose using standard gradient-based non-linear minimisation techniques. We propose novel enhancements at the pixel level based on temporal consistency and improved online appearance model adaptation. Furthermore, straightforward extensions of our method lead to multi-camera and multi-object tracking as part of the same framework. The parallel nature of much of the processing in our algorithm means it is amenable to GPU acceleration, and we give details of our real-time implementation, which we use to generate experimental results on both real and artificial video sequences, with a number of 3D models. These experiments demonstrate the benefit of using pixel-wise posteriors rather than likelihoods, and showcase the qualities, such as robustness to occlusions and motion blur (and also some failure modes), of our tracker.

Models of Mixed Metal-Oxide Interfaces for Atomistic Materials Simulations

ABSTRACTNuclear fuels and materials present special problems to atomistic-scale modeling. At a metal-metal-oxide interface, the metal centers are charged on the oxide side, but neutral on the metallic side. The intimate contact necessitates that atomistic models for these materials be both compatible and consistent with one another at some level. A new "fragment’’ Hamiltonian (FH) model, at the atomistic level, is presented that reduces qualitatively to existing, successful models for metals, such as the embedded atom method, and ceramics, such as the charge equilibration models. Moreover, the FH model possesses both electron hopping and fundamental gaps that appear as separate terms in a generalized embedding function. The electron hopping contributions come from both one-electron and two-electron sources. These contributions appear as a result of the FH point of view, rather than being postulated. The model obeys certain wellknown theoretical limits that come from the nonlinearity of electron hopping processes as the volume of a crystal is changed. The generalized notion of embedding entails two variables instead of one. The ability to account for multiple charge states in the cations leads to the capability within the model to distinguish the qualitative differences among metallic, ionic, and covalent bonding environments. The details of all of these energies, among with fragmentfragment interactions, combine to determine the state of the atom in the material.

Surface reconstruction with higher-order smoothness

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero-level set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased toward the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose a higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multiscale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multiview stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts, and very coarse orientation information.

Efficient many-to-many feature matching under the l1 norm

Matching configurations of image features, represented as attributed graphs, to configurations of model features is an important component in many object recognition algorithms. Noisy segmentation of images and imprecise feature detection may lead to graphs that represent visually similar configurations that do not admit an injective matching. In previous work, we presented a framework which computed an explicit many-to-many vertex correspondence between attributed graphs of features configurations. The framework utilized a low distortion embedding function to map the nodes of the graphs into point sets in a vector space. The Earth Movers Distance (EMD) algorithm was then used to match the resulting points, with the computed flows specifying the many-to-many vertex correspondences between the input graphs. In this paper, we will present a distortion-free embedding, which represents input graphs as metric trees and then embeds them isometrically in the geometric space under the l 1 norm. This not only improves the representational power of graphs in the geometric space, it also reduces the complexity of the previous work using recent developments in computing EMD under l 1. Empirical evaluation of the algorithm on a set of recognition trials, including a comparison with previous approaches, demonstrates the effectiveness and robustness of the proposed framework.

An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model

The quasi-nonlocal quasicontinuum method (QNL) is a consistent hybrid coupling method for atomistic and continuum models. Embedded atom models are empirical many-body potentials that are widely used for FCC metals such as copper and aluminum. In this paper, we consider the QNL method for EAM potentials, and we give a stability and error analysis for a chain with next-nearest neighbor interactions. We identify conditions for the pair potential, electron density function, and embedding function so that the lattice stability of the atomistic and the EAM-QNL models are asymptotically equal.

Introdução ao teorema de Nash e às Branas-mundo

Apesar dos modelos de Branas-mundo terem recebido atenção considerável nos últimos anos por fornecerem várias opções à física contemporânea, seus mecanismos não são completamente entendidos ou apropriadamente justificados. Tendo em vista tal dificuldade, neste trabalho fornecemos uma contribuição pedagógica dirigida especialmente aos alunos de pós-graduação em física, fazendo uma abordagem introdutória a um dos temas importantes em física e geometria no que diz respeito aos fundamentos da teoria de imersão de variedades. Apresentamos uma descrição do teorema de imersão de Nash de 1956 que mostra como fazer uma imersão local entre variedades Riemaniannas mantendo a regularidade e diferenciabilidade das funções de imersão, e de como isso é aplicado à física sob o ponto de vista das Branas-mundo.

DSPs, BRAMs, and a Pinch of Logic

We present three lookup-table-based AES implementations that efficiently use the BlockRAM and DSP units embedded within Xilinx Virtex-5 FPGAs. An iterative module outputs a 32-bit AES round column every clock cycle, with a throughput of 1.67 Gbit/s when processing two 128-bit inputs. This construct is then replicated four times to provide a complete AES round per cycle with 6.7 Gbit/s throughput when processing eight input streams. This, in turn, is replicated ten times for a fully unrolled design providing over 52 Gbit/s of throughput. We also present implementations of a BRAM-based AES key-expansion, CMAC, and CTR modes of operation. Results for designs where DSPs are replaced by regular logic are also presented. The combination and arrangement of the specialized embedded functions available in the FPGA allows us to implement our designs using very few traditional user logic elements such as flip-flops and lookup tables, yet still achieve these high throughputs. HDL source code, simulation testbenches, and software tool commands to reproduce reported results for the three AES variants and CMAC mode are made publicly available. Our contribution concludes with a discussion on comparing cipher implementations in the literature, and why these comparisons can be meaningless without a common reporting methodology, or within the context of a constrained target application.

On the origins of the Finnis–Sinclair potentials

I trace back the origins of the famous Finnis–Sinclair potentials. These potentials mimic the results of tight binding theory through their use of the square root embedding function. From the tentative beginnings of tight binding in the 1930s to 1984 or so, Bloch, Seitz, Montroll, Friedel, Cyrot-Lackmann and Ducastelle are some of the famous names involved, to name just a few. The application of the method of moments to the description of densities of states and its connection to the physics of closed paths linking nearest neighbours interacting atoms helped to formalise Friedel's rectangular band model for the d electrons in transition metals. Extension from perfectly periodic to defective structures could not be but a slow process due to the change of paradigm for solid state scientists and to the necessary caution to be paid to self-consistency. British scientists also contributed significantly in the 1980s. Computer progress and pragmatism helped to go from mainly analytical developments to numerical experiments (another change of paradigm). I also digress on various not so well-known historical points of interest to this story.