Related papers: Kac-Rice fixed point analysis for single- and mult…

We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the…

In this paper, we study the number of real roots of random trigonometric polynomials with iid coefficients. When the coefficients have zero mean, unit variance and some finite high moments, we show that the variance of the number of real…

This manuscript collects three independent works: arXiv:1902.03805, arXiv:1906.04444, with Antonio Lerario and arXiv:2103.10853, together with some additional results, observations, examples and comments, some of which were taken up in the…

The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…

We consider the number of critical points of a stationary planar Gaussian field, restricted to a large domain, whose heights lie in a certain interval. Asymptotics for the mean of this quantity are simple to establish via the Kac-Rice…

A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work…

We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty fixed point set converges geometrically for any starting point. We also show that positivity is crucial for this result to hold, and the concept of…

The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of…

For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elements of G(b,c) whose degree over K is at most some constant B.…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…

Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the…

In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex…

Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…