Related papers: Topological approach to mathematicalprograms with …
In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of $\mathbb{R}^n$, under compactly supported variations. The critical point solves a fourth order…
We study conservative particle systems on W^S, where S is countable and W = {0, ..., N} or the natural numbers. The rate of a particle moving from site x to site y is given by p(x,y) b(eta_x, eta_y), where eta_z is the number of particles…
It is argued that, for strongly non-linear behaviors, a fully deterministic position can hardly be maintained in the micro-macro transitions. This is due to the lack of information on the relevant boundary conditions, and to the tendency of…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…
The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
We show that the empirical process associated with a system of weakly interacting diffusion processes exhibits a form of noise-induced metastability. The result is based on an analysis of the associated McKean--Vlasov free energy, which,…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is…
Advances in the variational approach to the $n$-body problem have led to significant progress in celestial mechanics, uncovering new types of possible orbits. In this paper, critical points of the Lagrangian action associated with the…
The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…
This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an unperturbed system will survive. Under the assumption for…
Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a…
Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite…
We mainly investigate the continuous dependence on parameters of nontrivial solutions for a generalized poly-Laplacian system on the weighted finite graph $G=(V, E)$. We firstly present an existence result of mountain pass type nontrivial…
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing…
In this brief note, we investigate the topological entropy for linear switched systems. Specifically, we use the Levi-Malcev decomposition of Lie-algebra to establish a connection between the basic properties of the topological entropy and…