Related papers: Combinatorial Morse flows are hard to find
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
We establish new Bonferroni-type lower bounds for the probability of a union of finitely many events where the selection of intersections in the estimates is determined by the clique complex of a chordal graph.
We characterize the rate of convergence of a converging volume-normalized Yamabe flow in terms of Morse theoretic properties of the limiting metric. If the limiting metric is an integrable critical point for the Yamabe functional (for…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple". Here we consider a very simple mixture of two colloidal and one non-adsorbing polymer species which can be…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30,…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
We describe a method to address efficiently problems of two-phase flow in the regime of low particle Reynolds number and negligible Brownian motion. One of the phases is an incompressible continuous fluid and the other a discrete…
Detecting anomalies in link streams that represent various kinds of interactions is an important research topic with crucial applications. Because of the lack of ground truth data, proposed methods are mostly evaluated through their ability…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…
Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.
We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
Given a compact surface $\mathcal{M}$ with a smooth area form $\omega$, we consider an open and dense subset of the set of smooth closed 1-forms on $\mathcal{M}$ with isolated zeros which admit at least one saddle loop homologous to zero…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative…