arXiv research

Builds geometric structures for algebraic groups over real closed fields.

Study Poisson boundaries of building lattices and generalize rigidity results.

Thermal dynamics modeling has been a critical issue in building heating, ventilation, and air-conditioning (HVAC) systems, which can significantly affect the control and maintenance strategies. Due to the uniqueness of each specific building, traditional thermal dynamics modeling approaches heavily depending on physics…

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.

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.

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.

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…

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…

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

We compute the compactly supported cohomology of the standard realization of any locally finite building.

Transfer learning improves HVAC fault detection with minimal labeled data.

One of the key technologies for future large-scale location-aware services covering a complex of multi-story buildings --- e.g., a big shopping mall and a university campus --- is a scalable indoor localization technique. In this paper, we report the current status of our investigation on the use of deep neural network…

The relationship between minimal algebraic Kac-Moody groups and twin buildings is well known as is the relationship between formal completions in one direction and affine buildings. Nevertheless, as the completion of a Kac-Moody group in one direction destroys the opposite BN-pair, there exists no longer a twin buildin…

In this paper we show how to realize all knot (and link) types as C^{2} smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "building blocks" that are particular segments of helices and circles. We use these building blocks to construct all closed b…

The paper discusses building ETF risk models using a multilevel classification taxonomy.

This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.

Novel probabilistic models forecast residential heating and electricity demand at hourly resolution.

Clients are increasingly looking for fast and effective means to quickly and frequently survey and communicate the condition of their buildings so that essential repairs and maintenance work can be done in a proactive and timely manner before it becomes too dangerous and expensive. Traditional methods for this type of …

Deep learning boosts building energy load forecasting.

We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.

We describe the set of possible vector valued side lengths of n-gons in thick Euclidean buildings of rank 2. This set is determined by a finite set of homogeneous linear inequalities, which we call the generalized triangle inequalities. These inequalities are given in terms of the combinatorics of the spherical Coxeter…

The area of building energy management has received a significant amount of interest in recent years. This area is concerned with combining advancements in sensor technologies, communications and advanced control algorithms to optimize energy utilization. Reinforcement learning is one of the most prominent machine lear…

We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preservin…

This note corrects some omissions in section 2 of the paper "Lipschitz connectivity and filling invariants in solvable groups and buildings."

We generalize the natural cross ratio on the ideal boundary of a rank one symmetric spaces, or even $\mathrm{CAT}(-1)$ space, to higher rank symmetric spaces and (non-locally compact) Euclidean buildings - we obtain vector valued cross ratios defined on simplices of the building at infinity. We show several properties …

In all types of disasters, from earthquakes to armed conflicts, aid workers need accurate and timely data such as damage to buildings and population displacement to mount an effective response. Remote sensing provides this data at an unprecedented scale, but extracting operationalizable information from satellite image…

The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dime…

The paper studies fibering properties of RACGs and random subcomplexes of buildings.

Occupant behavior (OB) and in particular window openings need to be considered in building performance simulation (BPS), in order to realistically model the indoor climate and energy consumption for heating ventilation and air conditioning (HVAC). However, the proposed OB window opening models are often biased towards …

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. Corollary: the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

Study shows visual feedback and monetary incentives reduce plugload energy consumption in commercial buildings.

This paper deals with non-Archimedean representations of punctured surface groups in PGL(3), associated actions on Euclidean buildings (of type A2), and degenerations of real convex projective structures on surfaces. The main result is that, under good conditions on Fock-Goncharov generalized shear parameters, non-Arch…

Parreau compactified the Hitchin component of a closed surface $S$ of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of $π_1(S)$ on an $\mathbb R$-Euclidean building. In this paper, we use the positivity properties of Hitchin representatio…