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We utilize the Monte Carlo radiation transport code, Pandurata, to create images, spectra, polarization maps, and light curves from a set of general relativistic magnetohydrodynamic simulations of tilted, truncated, black hole accretion…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an…
This contribution is motivated by old and recent works on matrix powers and their applications on combinatorial sequences. We give in this paper the $s$-th powers and the inverses for special upper triangular matrices and the $s$-th powers…
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent…
Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…
By using one of the definitions of the Bernoulli numbers, we prove that they solve particular odd and even lower triangular Toeplitz (l.t.T.) systems of equations. In a paper Ramanujan writes down a sparse lower triangular system solved by…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
The tensor-structured parametric analysis (TPA) has been recently developed for simulating and analysing stochastic behaviours of gene regulatory networks [Liao et. al., 2015]. The method employs the Fokker-Planck approximation of the…
We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for…
The Hasegawa-Wakatani models are used in the study of confinement of hot plasmas with externally imposed magnetic fields. The nonlinear terms in the Hasegawa-Wakatani models complicate the analysis of the system as they propagate local…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…