Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and computational biology (e.g., protein folding), just to name a few application areas. We propose a linear-time randomized algorithm for approximating the trac...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

In seismic exploration, dense and evenly spatial sampled traces are crucial for successful implementation of most data processing interpretation algorithms. Recently, numerous reconstruction approaches based on deep learning have been presented. High dimension-based methods the benefit making full use signal at different perspectives. However, with transformation dimension from low to high, par...

In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important new ingredient ...

Trace driven simulations are too slow for use in solvers. Analytic models require work from a person to understand the array enough to model it. Table based models offer the possibility of automatically measuring the performance of an array for use in a solver. We explain a simplistic way of generating the input points in the table. We then explore three different ways of performing the interpo...

Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...

The theory of cyclic linear codes in its ring-theoretic formulation is a core topic of classical coding theory. A simplified approach is in my textbook [1]. The language of ring theory is not needed. We will present a self-contained description of the more general theory of cyclic additive codes using the same method. This includes cyclic quantum stabilizer codes as a special case. The basic in...

I study various properties of the critical limits of correlators containing insertions of conserved and anomalous currents. In particular, I show that the improvement term of the stress tensor can be fixed unambiguously, studying the RG interpolation between the UV and IR limits. The removal of the improvement ambiguity is encoded in a variational principle, which makes use of sum rules for the...

This thesis aims to address a number of program reasoning problems faced every day by programmers, using the technique of symbolic execution. Symbolic execution has the advantage of avoiding "infeasible" paths in the program (paths that cannot be exercised for any input), exploring which could provide spurious information about the program and mislead the programmer. However, as symbolic execut...

The accuracy of Finite Element approximation depends on the size and shape of elements. The proposed theory clarifies the source of shape related errors. A new general accuracy condition based on the maximum eigenvalue of the element stiffness matrix (or, alternatively, its trace) is presented. Several new and several familiar geometric criteria follow directly from the eigenvalue condition as ...