Related papers: Computation of invariant densities for continued f…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…
We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the first n digits of its continued fraction expansion performs in the order of n^4 mathematical operations. The…
The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids at thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when…
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differential equations have invariants, and numerical schemes for…
Computing the permanent of a $(0,1)$-matrix is a well-known $\#P$-complete problem. In this paper, we present an expression for the permanent of a bipartite graph in terms of the determinant of the graph and its subgraphs, obtained by…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We show that the additive-slow-Farey version of the traditional continued fractions algorithm has a natural interpretation as a method for producing integer partitions of a positive number $n$ into two smaller numbers, with multiplicity. We…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.
We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al.…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…
In the present paper, we introduce the concept of universal graph series. We then present four invariants of graphs and discuss some of their properties. In particular, one of these invariants is a generalization of the chromatic symmetric…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
We study the existence of invariant quadrics for a class of systems of difference equations in ${\mathbb R}^n$ defined by linear fractionals sharing denominator. Such systems can be described in terms of some square matrix $A$ and we prove…