We study the description of Schwarzschild black holes, of entropy S, within matrix theory in the regime N > ∼ S ≫ 1. We obtain the most general matrix theory equation of state by requiring that black holes admit a description within this theory. It has a recognisable form in various cases. In some cases a D dimensional black hole can plausibly be thought of as a D̃ = D + 1 dimensional black hole...

Active fault diagnosis (AFD) of parametric faults is considered in connection with closed loop feedback systems. AFD involves auxiliary signals applied on the closed loop system. A fault signature matrix is introduced in connection with AFD and it is shown that if a limited number of faults can occur in the system, a fault separation in the fault signature matrix can be obtained. Then the singl...

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can estimate the partition function like any other parameter in the model. The est...

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been cha...

Online shopping has become increasingly popular in recent years. More and more people are willing to buy products through Internet instead of physical stores. For promotional purposes, almost all online merchants provide product recommendations to their returning customers. Some of them ask professional recommendation service providers to help develop and maintain recommender systems while othe...

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players’ strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any co...

Data sparsity is a major problem for collaborative filtering (CF) techniques in recommender systems, especially for new users and items. We observe that, while our target data are sparse for CF systems, related and relatively dense auxiliary data may already exist in some other more mature application domains. In this paper, we address the data sparsity problem in a target domain by transferrin...

Improvements to the optimal control Newton-Raphson GRAPE method for exact Hessian calculations are shown with examples of auxiliary matrix and ESCALADE methods. For an ensemble two-level systems realistic MRI conditions, new accelerated between 200 600 times faster ESCALADE, respectively.

Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-...

Linear least-squares regression with a “design” matrix A approximates a given matrix B via minimization of the spectralor Frobenius-norm discrepancy ‖AX − B‖ over every conformingly sized matrix X. Another popular approximation is low-rank approximation via principal component analysis (PCA) — which is essentially singular value decomposition (SVD) — or interpolative decomposition (ID). Classic...