Related papers: Attouch-Th\'era Duality, Generalized Cycles and Ga…
I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the…
This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to…
We show how to generalize the classical duals found by Gabadadze {\it et al} to a very large class of self-interacting theories. This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory…
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods based on the intersection theory in the space of complete…
A cycle in a graph is called dominating if every edge of the graph is incident with a vertex of the cycle. In this paper, we investigate forbidden pairs guaranteeing the existence of a dominating cycle in 2-connected graphs.
We study bases of the lattice generated by the cycles of an undirected graph, defined as the integer linear combinations of the 0/1-incidence vectors of cycles. We prove structural results for this lattice, including explicit formulas for…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for existence of a grazing family of periodic solutions, is given. The properties of these periodic…
Gale duality is an involution of point configurations in projective spaces. Goppa duality extends this concept to a duality between linear series on a Gorenstein curve passing through prescribed points. We generalize this classical result…
Accurate prediction of road user movement is increasingly required by many applications ranging from advanced driver assistance systems to autonomous driving, and especially crucial for road safety. Even though most traffic accident…
Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems.…
We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
A linear section of a double vector bundle is a parallel pair of sections which form a vector bundle morphism; examples include the complete lifts of vector fields to tangent bundles and the horizontal lifts arising from a connection in a…
Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We use elementary variational arguments to prove, and improve on, gap estimates which arise in simulating quantum circuits by adiabatic evolution.
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…