Related papers: Operadic approach to wall-crossing
We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The…
We address here the topological equivalence of knots through the so-called Reidemeister moves. These topology-conserving manipulations are recast into dynamical rules on the crossings of knot diagrams. This is presented in terms of a simple…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an…
The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants under a quadratic field extension. This is applied to…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
In this paper, we present an explicit method to identify equivariant suboperads of coinduced operads that contain only fixed points associated to any desired transfer system. Our method works for a class of operads that we call intersection…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
In this paper we prove a wall-crossing formula, a crucial ingredient needed to prove that the correlation function of gauged linear sigma model is independent of the choice of perturbations.
We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation between the Wall form and some invariants of the induced…
This study seeks a better comprehension of anomalies by exploring (n+1)-point perturbative amplitudes in a 2n-dimensional framework. The involved structures combine axial and vector vertices into odd tensors. This configuration enables…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…