Decentralized finance (DeFi) protocols use blockchain-based tools to mimic banking, investment and trading solutions provide a viable framework that creates incentives conditions for the development of an alternative financial services market. In this respect, they can be seen as vehicles mitigate portfolio risk, which is particularly important at time increasing uncertainty in markets. particu...

Using the Thermodynamic Formalism, we introduce a Gibbsian model for the identiication of regular grammars based only on positive evidence. This model mimics the natural language acquisition procedure driven by prosody which is here represented by the thermodynamical potential. The statistical question we face is how to estimate the incidence matrix of a subshift of nite type from a sample prod...

We study deterministic parallel computation of the characteristic polynomial of an nn matrix A over an arbitrary eld F of a positive characteristic c n. Our new NC algorithms run in polylogarithmic time and simultaneously enable us to decrease the known upper bounds on processor complexity by order of magnitude except for matrices A forming an algebraic variety of codimension d c ? 1 in the spa...

We derive time-asymptotic decay rates in L for large disturbances to some important classes of solutions of the Cauchy problem for a number of uniformly parabolic equations, provided only that the disturbances belong to appropriate L spaces at initial time. Examples considered include the scalar nonlinear advection–di usion equation ut + f(u)x =(b(u)ux)x and the parabolic system ut + (u’(|u|))x...

We present a multi-threaded solver for symmetric positive de nite linear systems where the coe cient matrix of the problem features a bordered-band non-zero pattern. The algorithms that implement this approach heavily rely on a compact storage format, tailored for this type of matrices, that reduces the memory requirements, produces a regular data access pattern, and allows to cast the bulk of ...

Csisz ar's f -divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semide nite matrices are in the place of probability distributions and the quantum generalization is called quasi-entropy which is related to some other important concepts as covariance, quadratic costs, Fisher information, Cram er-Rao inequality and ...

This paper gives perturbation analyses for the Cholesky factorization A = R T R of a real symmetric positive deenite matrix A, with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations on nite precision oating point computers. First-order and rigorous perturbation bounds are are obtained. The analyses more accurately re...

It seems that there has not been yet any numerically e cient and robust method designed to test whether a general transfer function H(s) = D + C (sE A) B is positive real, where A;E 2 R n and possibly singular, B;C 2 R , and D 2 R . This short paper presents a numerical procedure to ll this void. The procedure combines the technique of Van Dooren to rst extract out the in nite eigenvalues of th...

We study the problems of eeciently learning innnite branches for nite state trees and winninig strategies for closed nite-state games using membership, and branch or strategy queries, respectively. We show that generally no eecient branch learning algorithm exists but we provide such algorithms for several natural cases, in particular for deadend free nite-state trees, the class of trees such t...

A set of matrices over the integers is said to be length k mortal with k positive integer if the zero matrix can be expressed as a product of length k of matrices in the set The set is said to be mortal if it is length k mortal for some nite k We show that the problem of deciding whether a pair of integer matrices is mortal is undecidable and that the problem of deciding for a given k whether a...