Kernel representation-based nearest neighbor classifier

An improvement to the nearest neighbor classifier (INNC) has shown its excellent classification performance on some classification tasks. However, it is not very clearly known why INNC is able to obtain good performance and what the underlying classification mechanism is. Moreover, INNC cannot classify low-dimensional data well and some high-dimensional data in which sample vectors belonging to different class distribution but have the same vector direction. In order to solve these problems, this paper proposes a novel classification method, named kernel representation-based nearest neighbor classifier (KRNNC), which can not only remedy the drawback of INNC on low-dimensional data, but also obtain competitive classification results on high-dimensional data. We reveal the underlying classification mechanism of KRNNC in details, which can also be regarded as a theoretical supplement of INNC. We first implicitly map all samples into a kernel feature space by using a nonlinear mapping associated with a kernel function. Then, we represent a test sample as a linear combination of all training samples and use the representation ability to perform classification. From the way of classifying test samples, KRNNC can be regarded as the nonlinear extension of INNC. Extensive experimental studies on benchmark datasets and face image databases show the effectiveness of KRNNC.     

Spin-lattice relaxation of nearest neighbor ortho-hydrogen pairs

Specially chosen pulse sequences have been used to isolate the contribution to the nuclear magnetic resonance signal from nearest neighbor oH₂ molecules. Measurements of the rotational diffusion were shown to be consistent with earlier measurements where only oH₂ pairs or only isolated singles could be observed. It was found that the pair magnetization so obtained did not relax exponentially.     

基于最近邻方法的类星体与正常星系光谱分类

随着高质最CCD传感器技术的日渐成熟与广泛应用,以及许多大型巡天计划的相继实施,天体数据量极大,因此天体观测数据的自动识别、分析问题首当其冲.文章在原始测量空间使用最近邻方法(NN)研究了正常星系与类星体光谱的识别问题.正常星系和类星体属于河外天体,一般距离地球较远,其观测光谱会受到许多干扰,所以这两类天体光谱的分类在...     

The statistics of nearest neighbor impurity pair formation in semiconductors2

The equilibrium concentrations of doubly ionized, singly ionized and neutral, nearest neighbor pairs of donor-donor and acceptor-acceptor type of impurity pairs have been studied at the temperature of diffusion. In the calculations, the discrete nature of the host lattice and, the internal energies of the pairs have been taken into account. Further, the effect of degeneracy on pair formations was investigated at high levels of doping densities.     

Spin orderings of the one-dimensional Ising magnet with the nearest and next nearest neighbor interaction

A proof is given of the fact that there exist four possible spin orderings for the one-dimensional Ising magnet with nearest and next-nearest-neighbor interactions.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Improved locality-sensitive hashing method for the approximate nearest neighbor problem

In recent years, the nearest neighbor search(NNS) problem has been widely used in various interesting applications.Locality-sensitive hashing(LSH), a popular algorithm for the approximate nearest neighbor problem, is proved to be an efficient method to solve the NNS problem in the high-dimensional and large-scale databases. Based on the scheme of p-stable LSH, this paper introduces a novel improvement algorithm called randomness-based locality-sensitive hashing(RLSH) based on p-stable LSH. Our proposed algorithm modifies the query strategy that it randomly selects a certain hash table to project the query point instead of mapping the query point into all hash tables in the period of the nearest neighbor query and reconstructs the candidate points for finding the nearest neighbors. This improvement strategy ensures that RLSH spends less time searching for the nearest neighbors than the p-stable LSH algorithm to keep a high recall. Besides, this strategy is proved to promote the diversity of the candidate points even with fewer hash tables. Experiments are executed on the synthetic dataset and open dataset. The results show that our method can cost less time consumption and less space requirements than the p-stable LSH while balancing the same recall.     

Nonlinear diffusion limit for a system with nearest neighbor interactions

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.Work supported by the National Science Foundation under grants no. DMS 8600233 and DMS 8701895     

Phase diagram of a nearest neighbor triangular antiferromagnet in an external field

The order-disorder transition in a nearest neighbor antiferromagnetic triangular lattice in a magnetic field is examined using a Monte Carlo method. Comparisons are made with the Kikuchi approximation of Burely. The phase diagram takes the form conjectured by Domb.     

Ground state spin orderings of the triangular Ising model with the nearest and next nearest neighbor interaction

Low temperature Monte Carlo results are used as an indicator of the size of the repeating unit. An energy minimization is then carried out for a number of configurations. It is proposed that, in the presence of a magnetic field, there are five spin orderings according to the relative sizes of the exchange integrals.     

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.     

Reducing convergence times of self-propelled swarms via modified nearest neighbor rules

Vicsek et al. proposed a biologically inspired model of self-propelled particles, which is now commonly referred to as the Vicsek model. Recently, attention has been directed at modifying the Vicsek model so as to improve convergence properties. In this paper, we propose two modification of the Vicsek model which leads to significant improvements in convergence times. The modifications involve an additional term in the heading update rule which depends only on the current or the past states of the particle’s neighbors. The variation in convergence properties as the parameters of these modified versions are changed are closely investigated. It is found that in both cases, there exists an optimal value of the parameter which reduces convergence times significantly and the system undergoes a phase transition as the value of the parameter is increased beyond this optimal value.     

Multibreather stability in discrete Klein–Gordon equations: Beyond nearest neighbor interactions

We present results on multibreather stability in one-dimensional nonlinear Klein–Gordon chains. Our analysis is based on Aubry?s band theory and perturbation theory. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. Then, we extend our analysis to the case of interactions with up to three neighbors. For next-nearest neighbor and third-nearest neighbor interactions we also extend the theory to study the stability properties of recently found multibreathers that have nonstandard phase shifts (not equal to 0 or π).     

Pairing enhancement in Betts lattices with next nearest neighbor couplings: Exact results

Electron instabilities in the Hubbard model with the next nearest neighbor coupling are calculated by exact diagonalization in finite, two-dimensional Betts cells (lattices). A viable spin and charge coherent pairing, signaled by quantum critical points and a negative charge gap region, is found in 8- and 10-site Betts lattices at small and moderate U regions consistent with our exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008) 075431]. The contour isolines for continuous temperature driven-crossover between the Mott-Hubbard insulating and coherent pairing phases are demonstrated. The criteria for smooth and abrupt phase transitions are found for systematic enhancement of coherent pairing by optimization of the next nearest neighbor coupling parameter.     

以最大原子密度定义合金相中的第一近邻团簇

本文提出利用不同壳层所包含的径向原子密度, 即单位体积内的原子个数随着径向的分布, 来方便而精确地定义团簇, 即具有最大径向原子密度的且表面呈现三角密堆结构的完整壳层为第一近邻团簇. 最后以Al-Ni-Zr合金相为例说明了该方法的合理性与适用性, 及此方法所定义的团簇与非晶形成的关系.     

Determination of fixed points and shift cycles for nearest neighbor cellular automata

One-dimensional nearest neighbor cellular automata defined over Z₂ are characterized in terms of a set of eight nonadditive basis operators which act on the automaton state space. Every evolution rule for such automata can be expressed as an operator which is a direct sum of the basis operators. This approach allows decomposition of automata rules into additive and nonadditive parts. As a result, it is simple to determine fixed points (those states for which the rule reduces to the identity), and shift cycles (sets of states on which the rule reduces to a shift). Sets of states on which any given nearest neighbor automaton reduces to an identity or a shift are characterized. This allows us to obtain some results on the entropic properties of nonadditive automata, although these are not nearly so complete as results obtained for additive automata.     

Recovery of delay time from time series based on the nearest neighbor method

We propose a method for the recovery of delay time from time series of time-delay systems. The method is based on the nearest neighbor analysis. The method allows one to reconstruct delays in various classes of time-delay systems including systems of high order, systems with several coexisting delays, and nonscalar time-delay systems. It can be applied to time series heavily corrupted by additive and dynamical noise.