We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors of systems outside the system satisfy Schrödinger equation. A process of collision-type interaction between a microscopic system and a macroscopic system is ...

Logistic regression and matrix factorization specifically SVD are both very popular in application areas of computational advertising and recommender system. This project basically can be divided into two parts. The first part is to test different optimization methods to solve sparse 2-class logistic regression. This is a convex non-smooth problem. Particularly, I’ll try to answer the question ...

We introduce a method for deriving a metric, locally based on the Fisher information matrix, into the data space. A self-organizing map (SOM) is computed in the new metric to explore financial statements of enterprises. The metric measures local distances in terms of changes in the distribution of an auxiliary random variable that reflects what is important in the data. In this paper the variab...

We examine a queueing system with multiple primary servers and a fewer number of auxiliary servers. There are two classes of customers-those who require service from a primary server working alone and those who require service from a primary server who is assisted by an auxiliary server. Though the apparent Markovian state space is fivedimensional, we show that an aggregation results in an exac...

In this note, we explain the implementation detail of multigrid methods. We will use the approach by space decomposition and subspace correction method; see Chapter: Subspace Correction Method and Auxiliary Space Method. The matrix formulation will be obtained naturally, when the functions’ basis representation is inserted. We also include a simplified implementation of multigrid methods using ...

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of ...

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fu...

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of Uq(ŝl2 ) over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator representations used previously. We derive generalized T -Q relations in which 3 of these parameters shift. After a suitable restriction of parameters, we give an ex...

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary nonparametric maximum likelihood density estimators are shown to be asymptotically normal. If the parametric model is correctly specified, it is furthermore shown that the asymptotic variance-covariance matrix equals the inverse of the Fisher-information matrix. T...