arXiv research

The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.

Novel theory combines combinatorial and topological elements.

New combinatorial structure for hierarchically hyperbolic spaces.

The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.

Fractional combinatorial flow improves surface conformal structures.

New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.

Study explores properties of bipartite knots.

Study on deforming discrete conformal structures on surfaces with boundaries.

The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evaluations pose challenges for current techniques in discrete optimization and machine …

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity…

SRL embeds combinatorial optimization into RL for better decision-making.

We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker than the existence of the corresponding foliation, is sufficient to guarantee t…

The paper applies combinatorial Ricci flows to prove hyperbolic structures on 3-manifolds.

Combinatorial definition of bordered Floer theory for torus-boundary manifolds.

Polynomial-time method solves complex combinatorial semi-bandits.

We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study hyperbolic structures on three-dimensional manifolds

In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold that are analogues of objects in differential geometry. We study a cochain product and prove several statements about its convergence to the wedge product on differential forms. Also, for cochains with an inner p…

Unified framework for gradient estimation in combinatorial spaces.

The study generalizes origamis to flat surfaces, exploring their combinatorial and geometric properties.

The paper proves a combinatorial Ricci flow converges to hyperbolic structures on certain 3-manifolds.

This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary…

New combinatorial structures for Teichmüller spaces with Thurston's metric are explored.

Study inert and ambiguous classes in modular group using combinatorial methods.

Combinatorial Ricci flow finds hyperbolic metrics on 3-manifolds.

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a number of known results. New results include a combinatorial characterization of c…

Neural framework learns one solution from multiple for combinatorial problems.

VCSMC improves efficiency in Bayesian phylogenetic inference.

Study introduces combinatorial criterion for quasi-isometry groups of Euclidean spaces.

Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.

Computing uniformization maps for surfaces has been a challenging problem and has many practical applications. In this paper, we provide a theoretically rigorous algorithm to compute such maps via combinatorial Calabi flow for vertex scaling of polyhedral metrics on surfaces, which is an analogue of the combinatorial Y…

Algorithm constructs and classifies weaving diagrams using combinatorial methods.

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of 3-manifolds with transitive cyclic symmetry can be generalised to an infinite fami…

A new deep learning framework for topological data.

The paper studies the combinatorial p-th Calabi flow for finite and infinite circle patterns.

Bayesian optimization for high-dimensional combinatorial spaces using embeddings.

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinatorial envelope of a set-function along with new necessary conditi…

New algorithm reduces regret in combinatorial causal bandits without graph structure.

The hyperbolic structure of equilateral pentagons is mapped to a tiling of the hyperbolic plane.

Surveying machine learning for solving graph optimization problems.

Researchers compute spin structures on hyperelliptic curves using braid groups.

We extend to a scheme-theoretic context the notion of a combinatorial differential form, due to A.Kock in the framework of synthetic differential geometry. We show that group-valued combinatorial forms on a scheme may be identified, under very general hypotheses, with traditional Lie algebra-valued differential forms, …

In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner prop…

Detects right-veering properties in open books using combinatorial methods.

New algorithm finds high-reward combinatorial sets with fewest pulls.

Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.

A new algorithm tackles delayed combinatorial semi-bandit with causal relations.

Constructs combinatorial 2D topological field theories from cyclic A-infinity algebras.

We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…