Related papers: Lifting Cocycles: From Heuristic to Theory
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
We construct an explicit Hamiltonian cycle in the state graph of the 5-puzzle on a toroidal 2x 3 grid, a graph with 720 vertices. The cycle is described by a short symbolic sequence of 48 moves over the alphabet {L,R,V}, repeated $15$…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…
This publication serves as an overview of clique topology -- a novel matrix analysis technique used to extract structural features from neural activity data that contains hidden nonlinearities. We highlight work done by Gusti et al. which…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
Many robotics applications require alignment and fusion of observations obtained at multiple views to form a global model of the environment. Multi-way data association methods provide a mechanism to improve alignment accuracy of pairwise…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we…
Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…
In order to have cohomological operations for de Rham p-adic cohomology with coefficients as manageable as possible, the main purpose of this paper is to solve intrinsically and from a cohomological point of view the lifting problem of…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…
The topology method is an algorithm for accurate estimation of instantaneous heartbeat intervals using millimeter-wave radar signals. In this model, feature points are extracted from the skin displacement waveforms generated by heartbeats…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…
We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…
Computation of homology or cohomology is intrinsically a problem of high combinatorial complexity. Recently we proposed a new efficient algorithm for computing cohomologies of Lie algebras and superalgebras. This algorithm is based on…
We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional $U(1)$ gauge theory with and without fermion content. This algorithm includes reversible jumps between…
This letter deals with the problem of clutter edge detection and localization in training data. To this end, the problem is formulated as a binary hypothesis test assuming that the ranks of the clutter covariance matrix are known, and…