Related papers: A family of formulas with reversal of arbitrarily …
This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We consider a family of higher-order Boussinesq equations with an arbitrary nonlinearity. We determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. In case of a quadratic nonlinearity…
In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar…
An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a…
We exhibit a three parameter infinite family of quadratic recurrence relations inspired by the well known Somos sequences. For one infinite subfamily we prove that the recurrence generates an infinite sequence of integers by showing that…
We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…
In this article, intended for the Handbook of Recursion Theory, we survey recursion theory on the ordinal numbers, with sections devoted to $\alpha$-recursion theory, $\beta$-recursion theory and the study of the admissibility spectrum.
We show that there exists an uniformly recurrent infinite word whose set of factors is closed under reversal and which has only finitely many palindromic factors.
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
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…
Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…
This paper gives the recursion formula for mixed multiplicities of maximal degrees with respect to joint reductions of ideals, which is one of important results in the mixed multiplicity theory. Using this result, we give consequences on…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.
We will give a simple proof of the ambiguous class number formula.