In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigen-pairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by LS . Then the best approximation problem for the inverse eigen...

We study an interacting particle system on the simple cubic lattice satisfying the nearest neighbor exclusion (NNE) which forbids any two nearest sites to be simultaneously occupied. Under the constraint, we develop an edge-to-site reduction of the Bethe-Peierls entropy approximation of the cluster variation method. The resulting NNE-corrected Bragg-Williams approximation is applied to statisti...

We study the phase diagram, ground state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e. a spin-Peierls chain with both nearest neighbor exchange J1 and next nearest neighbor exchange J2. The phase diagram is calculated using a bosonization Renormalization-Group (RG) method. We propose a (bosonic) bond-operator mean field approximation to calculate the ground state prop...

Multi-Output Dependence (MOD) learning is a generalization of standard classification problems that allows for multiple outputs that are dependent on each other. A primary issue that arises in the context of MOD learning is that for any given input pattern there can be multiple correct output patterns. This changes the learning task from function approximation to relation approximation. Previou...

This article describes a Hopfield-Tank model of the Euclidean traveling salesman problem (using Aiyer’s subspace approach) that incorporates a “fuzzy” interpretation of the rows of the activation array. This fuzzy approach is used to explain the network’s behavior. The fuzzy interpretation consists of computing the center of mass of the positive activations in each row. This produces real numbe...

While the problem of approximate nearest neighbor search has been well-studied for Eu-clidean space and ℓ 1 , few non-trivial algorithms are known for ℓ p when 2 < p < ∞. In this paper, we revisit this fundamental problem and present approximate nearest-neighbor search algorithms which give the first non-trivial approximation factor guarantees in this setting.

K-nearest-neighbor query is an important query in uncertain network, which is finding the k close nodes to a specific node. We first put forward the concept of the credible nearest neighbor query in uncertain network, and give credible k-nearest-neighbor query algorithm. Credible distance is used to describe the distance between nodes in uncertain network. Fuzzy simulation is adopted to decreas...

Given a query object q, reverse k-nearest neighbor (RkNN) search aims to locate those objects of the database that have q among their k-nearest neighbors. In this paper, we propose an approximation method for solving RkNN queries, where the pruning operations and termination tests are guided by a characterization of the intrinsic dimensionality of the data. The method can accommodate any index ...