Related papers: Generalised Modal Analysis with the Pad\'e-Laplace…
Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system…
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…
Euler's formula, an extraordinary mathematical formula, establishes a vital link between complex-valued operations and trigonometric functions, finding widespread application in various fields. With the end of Moore's Law, electronic…
Modality is the linguistic ability to describe events with added information such as how desirable, plausible, or feasible they are. Modality is important for many NLP downstream tasks such as the detection of hedging, uncertainty,…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
Given a complex semisimple Lie algebra ${\mathfrak g}$ and a commutative ${\mathbb C}$-algebra $A$, let ${\mathfrak g}[A] = {\mathfrak g} \otimes A$ be the corresponding generalized current algebra. In this paper we explore questions…
Multiple data types naturally co-occur when describing real-world phenomena and learning from them is a long-standing goal in machine learning research. However, existing self-supervised generative models approximating an ELBO are not able…
We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessarily linear, acting between some measurable rearrangement…
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
We use a probabilistic approach to describe the behavior as $n -> \infty$ of the Laplace transforms of $P^n$, where $P$ a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer in the…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
Termination analysis of C programs is a challenging task. On the one hand, the analysis needs to be precise enough to draw meaningful conclusions. On the other hand, relevant programs in practice are large and require substantial…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(K_R)---a natural extension of propositional modal logic K_R by counting expressions---which plays an important role in the area of knowledge…
Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invariant sets associated to such equations. In this work, we use…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…