arXiv research

Abstract framework for no-arbitrage concepts in topological vector lattices.

New method models negative correlations in knowledge graphs.

L-CNNs preserve gauge symmetry in neural networks.

FCA2VEC embeds formal concept analysis data for large datasets.

Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are visually seducing and conceptually rich for experts. However they present important…

Homotopy classes of gauge fields defined on a manifold using lattice structures.

Markov random field (MRF) learning is intractable, and its approximation algorithms are computationally expensive. We target a small subset of MRF that is used frequently in computer vision. We characterize this subset with three concepts: Lattice, Homogeneity, and Inertia; and design a non-markov model as an alternati…

The paper proposes a unified taxonomy for biclustering methods.

This tutorial explains FCA and its applications in data analysis.

The study examines eigenfunctions on lens spaces using harmonic-counting measures.

This paper uses group theory to create data-free, feature-free clustering.

Concept Relation Discovery and Innovation Enabling Technology (CORDIET), is a toolbox for gaining new knowledge from unstructured text data. At the core of CORDIET is the C-K theory which captures the essential elements of innovation. The tool uses Formal Concept Analysis (FCA), Emergent Self Organizing Maps (ESOM) and…

We develop a method to learn abstract causal graphs from interventional data.

Hybrid subgroups found in non-arithmetic PU(2,1) lattices.

New non-arithmetic lattice found in PU(3,1)

New property identifies arithmetic lattices from nonuniform lattices.

New lattice stick knot condition identified.

Simplified proof for lattice link projections.

This work compares lattice-free and lattice-based training criteria for LVCSR.

Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.

We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…

New lattices from 4-manifolds show manifold properties.

Course on arithmetic lattices at EPFL.

Upper bound for lattice stick number of spatial graphs.

This article classifies reflective hyperbolic lattices of rank 4.

New thin subgroups found in special linear groups via bending techniques.

New rigidity theorem for product of lattices.

We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of immersions: continuous maps between subsets of translation surfaces that respect the b…

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…

The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.

Proves a lattice version of the Atiyah-Singer index theorem.

Vertex distortion measures how far lattice knots deviate from straight lines.

Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm i…

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

Proves properties of arithmetic lattices and hyperbolic manifolds.

A celebrated theorem of Hadwiger states that the Euler-Poincaré characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty such polyhedron. This paper provides an analogue of Hadwiger's result for finitely p…

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…

New method finds lattice polygons that can be dissected into triangles with integer areas.

Study lattices in specific Lie groups for geometric structures.

Study on entanglement complexity of confined ring polymers in lattice tubes.

L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.

Hybrid lattices produce subgroups of PU(n,1) from PU(n-1,1) lattices.

The paper refines transformations of lattice diagrams and introduces dotted diagrams.

Classifies knots by lattice size, finding unknot ratios and crossing numbers.

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev…

Proves effective slope gaps for lattice surfaces.

Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.

Proves actions of higher rank lattices on hyperbolic spaces are elementary.