arXiv research

Efficiently generates high-resolution images with reduced sampling time using LEGO bricks.

Deep RL learns to construct objects from 2D images by avoiding brick overlaps.

This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting and storing objects in an unsupervised way. The toy dataset used to validate suc…

A flexible Bayesian regression package for complex models.

Research examines tiling problems with colored cubes and bricks on a 3D board.

For a smooth oriented surface S, denote by M(S) the set of all ways to represent S as a result of gluing together standard spheres with holes (``the Lego game''). In this paper we give a full set of simple moves and relations which turn M(S) into a connected and simply-connected 2-complex. Results of this kind were fir…

LEGO estimates tangent spaces more robustly than LPCA in noisy data.

New physics models generalize existing brane brick models.

Machine learning refactors knowledge to improve learning efficiency.

In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to $π_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we construct bi-Lipschitz model manifolds for such hyperbolic 3-manifolds, which have a stru…

Unified framework combines trace-induced quantum kernels for improved machine learning models.

We give another proof for a result of Brick stating that the simple connectivity at infinity is a geometric property of finitely presented groups. This allows us to define the rate of vanishing of $\p1i$ for those groups which are simply connected at infinity. Further we show that this rate is linear for cocompact latt…

Game aims to improve social interactions for teenagers with ASD.

Study of braid varieties and their Legendrian isotopy.

Paper calculates ball number of links using Lorentz geometry and circle packing.

For each cardinal $κ$, each natural number $n$ and each simplicial complex $K$ we construct a space $ν^n_κ(K)$ and a map $π\colon ν^n_κ(K) \to K$ such that the following conditions are satisfied. 1. $ν^n_κ(K)$ is a complete metric $n$-dimensional space of weight $κ$. 2. $ν^n_κ(K)$ is an absolute neighborhood extensor i…

This article presents some methods to control the bottom of the spectrum of the Laplacian $λ_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $λ_0$ of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built …

This paper focuses on a new task, i.e., transplanting a category-and-task-specific neural network to a generic, modular network without strong supervision. We design an functionally interpretable structure for the generic network. Like building LEGO blocks, we teach the generic network a new category by directly transp…

This paper focuses on a new task, i.e., transplanting a category-and-task-specific neural network to a generic, modular network without strong supervision. We design a functionally interpretable structure for the generic network. Like building LEGO blocks, we teach the generic network a new category by directly transpl…

Given a smooth, oriented, closed surface $Σ$ of genus zero, possibly with boundary, let $\tildeΣ \longrightarrow Σ$ be a given $G$-cover of $Σ$, where $G$ is a given finite group. Let $S_{n}$ denote the standard sphere with $n$ holes. There are many ways of gluing together several $G$-cover of $S_{n}$ to construct the …

How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group $G$ is said to be properly 3-realizable if there exists a compact 2-polyhedron $K$ with $π_1(K) \cong G$ whose universal cover $\til…

We show that a certain geometric property, the QSF introduced by S. Brick and M. Mihalik, is universally true for {\ibf all} finitely presented groups $Γ$. One way of defining this property is the existence of a smooth compact manifold $M$ with $π_1 M = Γ$, such that $\tilde M$ is geometrically simply-connected ({\it i…

A fundamental question in deep learning concerns the role played by individual layers in a deep neural network (DNN) and the transferable properties of the data representations which they learn. To the extent that layers have clear roles, one should be able to optimize them separately using layer-wise loss functions. S…

We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show that the upper bounds on Matveev's complexity implied by our computations are sharp…

Decomposes ultrametric spaces into scaled simplices.

Robots rely on sensors to provide them with information about their surroundings. However, high-quality sensors can be extremely expensive and cost-prohibitive. Thus many robotic systems must make due with lower-quality sensors. Here we demonstrate via a case study how modeling a sensor can improve its efficacy when em…

Proposed SMO algorithm for OC-SVM+ significantly outperforms non-sequential algorithms.

A finitely presented group is weakly geometrically simply connected (wgsc) if it is the fundamental group of some compact polyhedron whose universal covering is wgsc i.e. it has an exhaustion by compact connected and simply connected sub-polyhedra. We show that this condition is almost-equivalent to Brick's qsf propert…

Online retailers execute a very large number of price updates when compared to brick-and-mortar stores. Even a few mis-priced items can have a significant business impact and result in a loss of customer trust. Early detection of anomalies in an automated real-time fashion is an important part of such a pricing system.…

New mapping class group actions on Hochschild complexes for modular categories.

New kernel interprets 3D anisotropic data with rotations and improved predictions.