arXiv research

Machine learning reduces wind tunnel testing costs for tall buildings.

New method speeds up inference for tall data models.

Tall wheatgrass outperforms rye in energy and environmental metrics, marginally improving economic viability.

Kernel improves Gaussian process scalability for wide datasets.

Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved met…

Solves area-minimizing surface problem for finite curves in H^2xR.

Kähler complexity one Hamiltonian T-manifolds have trivial paintings.

This paper describes a distributed MapReduce implementation of the minimum Redundancy Maximum Relevance algorithm, a popular feature selection method in bioinformatics and network inference problems. The proposed approach handles both tall/narrow and wide/short datasets. We further provide an open source implementation…

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also known as tall datasets. In scenarios where data are assumed independent, various…

R package spca computes sparse principal components efficiently.

This note provides some new perspectives and calculations regarding an interesting known family of minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$. The surfaces in this family are the catenoids, parabolic catenoids and tall rectangles. Each is foliated by either circles, horocycles or circular arcs in horizontal c…

Light pillars over rippled water appear parallel due to projection geometry.

ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.

The paper proposes methods to estimate MCMC quality with couplings, bounding Wasserstein distance.

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor to this is the increasingly growing size of the datasets available and needed in …

SMI uses mixture models to improve SVGD's performance in Bayesian inference.

New MCMC methods use auxiliary variables to sample from intractable distributions.

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with pr…

Matrix completion, where we wish to recover a low rank matrix by observing a few entries from it, is a widely studied problem in both theory and practice with wide applications. Most of the provable algorithms so far on this problem have been restricted to the offline setting where they provide an estimate of the unkno…

Builds geometric structures for algebraic groups over real closed fields.

Deep learning adapts HVAC models to new buildings.

Study Poisson boundaries of building lattices and generalize rigidity results.

We show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on tw…

We describe some buildings related to complex Kac-Moody groups. First we describe the spherical building of SLn(C) (i.e. the projective geometry PG(Cn)) and its Veronese representation. Next we recall the construction of the affine building associated to a discrete valuation on the rational function field $C(z)$. Then …

Flat subsets in Euclidean buildings are contained within apartments.

The paper studies surface quotients of Fuchsian buildings.

Research proves limits on harmonic map orders into Euclidean buildings.

The n-solvable filtration $\{\mathcal{F}_n\}_{n=0}^\infty$ of the smooth knot concordance group (denoted by $\mathcal{C}$), due to Cochran-Orr-Teichner, has been instrumental in the study of knot concordance in recent years. Part of its significance is due to the fact that certain geometric characterizations of a knot …

In this note, we show that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.

We prove isoperimetric inequalities for quotients of $n$-dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of these buildings.

Harmonic maps to Euclidean buildings have rectifiable singular strata.

Automates building structural design with reduced mass and carbon footprint.

Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual boundary is then a spherical building. When the ambient space is geode…

This paper constructs and proves the uniqueness of pluriharmonic maps to Euclidean buildings.

Machine learning detects building damage in satellite images.

We introduce a construction turning some Coxeter and Davis realizations of buildings into systolic complexes. Consequently groups acting geometrically on buildings of triangle types distinct from $(2,4,4)$, $(2,4,5)$, $(2,5,5)$, and various rank $4$ types are systolic.

A new method reduces the bias in estimating inverse covariance matrices from sketches.

In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex with its additional structure the Torelli building of the surface in question. The…

Deep learning detects building defects from images.

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…

Covering space theory is used to construct new examples of buildings.

Proves unique maps from certain spaces to others.

Future buildings will offer new convenience, comfort, and efficiency possibilities to their residents. Changes will occur to the way people live as technology involves into people's lives and information processing is fully integrated into their daily living activities and objects. The future expectation of smart build…

In this work we study an application of machine learning to the construction industry and we use classical and modern machine learning methods to categorize images of building designs into three classes: Apartment building, Industrial building or Other. No real images are used, but only images extracted from Building I…

Modeling buildings' heat dynamics is a complex process which depends on various factors including weather, building thermal capacity, insulation preservation, and residents' behavior. Gray-box models offer a causal inference of those dynamics expressed in few parameters specific to built environments. These parameters …

In this paper, we give a general group-theoretic construction of affine $\RR$-buildings, and more generally, of affine $Λ$-buildings, associated to semisimple Lie groups over nonarchimedean real closed fields. The construction of Kleiner-Leeb using the asymptotic cone of a Riemannian symmetric space appears as a specia…

Graph2Diff neural network predicts precise code changes for build errors.

Proves regularity of harmonic maps into Euclidean buildings and applies to superrigidity of algebraic groups.