We give a forbidden pattern characterization for the class of 5 generalized definite languages, show that the corresponding problem is 6 NL-complete and can be solved in quadratic time. We also show that 7 their syntactic complexity coincides with that of the definite languages 8 and give an upper bound of n! for this measure. 9

We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.

Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper we develop a set-theoretic interpretation of the Earth Mover’s Distance (EMD) that naturally yields metric and kernel forms of EMD as generalizations of elementary set operations. In parti...

Chronic diarrhea is a major problem in pediatric patients because it induces malnutrition, general developmental defects, and an extremely death. Thus, important to make accurate diagnosis, find definite etiologies, apply proper treatments.

In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse nonHermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove th...

In this paper we consider minimizing the spectral condition number of a positive semidefinite matrix over a nonempty closed convex set Ω. We show that it can be solved as a convex programming problem, and moreover, the optimal value of the latter problem is achievable. As a consequence, when Ω is positive semidefinite representable, it can be cast into a semidefinite programming problem. We the...

Due to correlation coefficient matrix of initialized samples are not always positive definite, this paper presents the improved Latin Hypercube Sampling (LHS) methods with Evolutionary Algorithm (EA) to control correlation and handle power system probability analysis problem. To deal with the non-positive definite correlation matrix, an improved median Latin hypercube sampling with evolutionary...

We observe that the decision problem for the ∃ theory of real closed fields (RCF) is simply reducible to the decision problem for RCF over a connective-free ∀ language in which the only relation symbol is a strict inequality. In particular, every ∃ RCF sentence φ can be settled by deciding a proposition of the form “polynomial p (which is a sum of squares) takes on strictly positive values over...