A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study higher rank inner products and their tilings to describe tori degenerations.
Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadr…
Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.
In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi diagrams and compactifications of configuration spaces. We study moving and colliding p…
A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2*pi/3 but less than 2*pi. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with greatest cone angles. In this paper we use elementary Euclidean geometry to describe…
Proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, wher…
A new method for Bayesian optimization uses Voronoi tessellation candidates to reduce search time.
Constructs an explicit cycle in arithmetic group cohomology.
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrat…
Estimates BV functions from noisy data using Voronoi diagrams.
This note characterizes monohedral tilings of regular polygons with up to three tiles.
Deviance Voronoi residuals improve earthquake insurance risk assessment.
The study of tiling homology on flat surfaces, proving impossibility of certain tilings.
New tiles allow efficient knot mosaics for small knots.
Rep-tiles fill cubes in any dimension.
Study tiling spaces over irrational tori using diffeological classification.
Shellable tilings on simplicial complexes help understand their structure.
In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly constructed highly singular symplectic spaces and we show that they are diffeomorphic…
The study classifies tilings of the sphere by congruent quadrilaterals.
New method constructs tilings of the plane using directed edges and alignments.
New tile types for knots and links reduce complexity.
Study on tilings of the plane with two types of tiles of varying areas.
New spectral sequences derived from shellable tilings.
The main goal of this paper is to define a 1-1 correspondence between between substitution tilings constructed by inflation and the arithmetic of positional representation in the underlying real vector space. It introduces a generalization of inflationary tessellations to equivalence classes of tiles. Two tiles belong …
We study square-tiled tori, that is, tori obtained from a finite collection of unit squares by parallel side identifications. Square-tiled tori can be parametrized in a natural way that allows to count the number of square-tiled tori tiled by a given number of square tiles. There is a natural $\mathrm{SL}(2,\mathbf{Z})…
We determine the topology of the moduli space of periodic tilings of the plane by parallelograms. To each such tiling, we associate combinatorial data via the zone curves of the tiling. We show that all tilings with the same combinatorial data form an open subset in a suitable Euclidean space that is homotopy equivalen…
Softens tilings in 3D space, proving conjectures about polyhedral tilings.
Paper proves corner connection tiles can represent knots with fewer tiles.
This paper classifies all 3D rep-tiles up to homeomorphism.
In this note we prove that any monohedral tiling of the closed circular unit disc with topological discs as tiles has a -fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain t…
Proposes a new adversarial model to avoid accuracy vs. adversarial accuracy tradeoff.
Algorithm finds adversarial examples for k-NN classifiers using Voronoi diagrams.
4-ball can be tiled with knotted surfaces.
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two different viewpoints, one with constructive techniques to enumerate such tiling…
The study explores maps of 2- and 3-uniform tilings on the torus.
In this paper we describe the pentagonal tiling of the plane defined in the article "A regular pentagonal tiling of the plane" by P. L. Bowers and K. Stephenson as a conformal substitution tiling and summarize many of its properties given in the mentioned article. We show furthermore why such tiling is not FLC with res…
Accurate taxi demand-supply forecasting is a challenging application of ITS (Intelligent Transportation Systems), due to the complex spatial and temporal patterns. We investigate the impact of different spatial partitioning techniques on the prediction performance of an LSTM (Long Short-Term Memory) network, in the con…
In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to …
The paper explores different perspectives on rhombile tilings.
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the p…
Shear moves connect square-tiled surfaces in quadratic differentials.
Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-…
The study finds arithmetic groups often in square-tiled surface monodromies.
This note connects tiling billiards dynamics to Novikov's problem via helicoidal construction.
Expanding on prime knots with 6 or less mosaic tiles, this paper analyzes those with 7 tiles.
Extremal length is a conformal invariant that transfers naturally to the discrete setting, giving square tilings as a natural combinatorial analog of conformal mappings. Recent work by S. Hersonsky has explored generalizing these ideas to three-dimensional cube tilings. The connections between discrete extremal length …
Constructs surfaces that can be tiled by a finite set of rigid motion congruence classes of tiles.