Related papers: Monotonic Simplification and Recognizing Exchange …
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
A large number of problems in computer vision can be modelled as energy minimization problems in a Markov Random Field (MRF) or Conditional Random Field (CRF) framework. Graph-cuts based $\alpha$-expansion is a standard move-making method…
Our main result has topological, combinatorial and computational flavor. It is motivated by a fundamental conjecture stating that computing Khovanov homology of a closed braid of fixed number of strands has polynomial time complexity. We…
General solutions of the $\hat{R}TT$ equation with a maximal number of free parameters in the specrtal decomposition of vector $SO_q (3)$ $\hat{R}$ matrices are implemented to construct modified braid equations (MBE). These matrices…
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the…
Periodic orbits (POs) play a central role in the circular restricted three-body problem (CRTBP). This paper introduces a method to search for POs by identifying single- and multiple-revolution fixed points in chosen Poincare maps that…
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…
The reachability problem in multi-pushdown automata (MPDA) has many applications in static analysis of recursive programs. An example is safety verification of multi-threaded recursive programs with shared memory. Since these problems are…
In this survey paper we present the $L$--moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot…
We formulate spin magnetohydrodynamics (MHD) by including the magnetic-flux and total angular momentum conservation laws in the hydrodynamic framework. To specify the local angular momentum conservation, we choose the totally antisymmetric…
Existing MWP solvers employ sequence or binary tree to present the solution expression and decode it from given problem description. However, such structures fail to handle the variants that can be derived via mathematical manipulation,…
We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary,…
In classical knot theory, Markov's theorem gives a way of describing all braids with isotopic closures as links in $\mathbb{R}^3$. We present a version of Markov's theorem for extended loop braids with closure in $B^3 \times S^1$, as a…
Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite…
A significant challenge in molecular dynamics (MD) simulations is ensuring that sampled configurations converge to the equilibrium or nonequilibrium stationary distribution of interest. Lack of convergence constrains the estimation of free…
Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property.…
The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the…
We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.
The L-move for classical braids extends naturally to trivalent braids. We follow the L-move approach to the Markov Theorem, to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this L-Move Markov theorem and…
We study point-line configurations, their minimal matroids, and their associated circuit varieties. We present an algorithm for identifying the minimal matroids of these configurations with respect to dependency order, or equivalently, the…