Related papers: Left and right Bousfield localization on lattices
The paper argues the importance of high-quality translation for spoken language translation systems. It describes an architecture suitable for rapid development of high-quality limited-domain translation systems, which has been implemented…
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…
This paper proposes a hierarchical Bayesian model based on spatial concepts that enables a robot to transfer the knowledge of places from experienced environments to a new environment. The transfer of knowledge based on spatial concepts is…
Exchange bias is a horizontal shift of the hysteresis loop observed for a ferromagnetic layer in contact with an antiferromagnetic layer. Since exchange bias is related to the spin structure of the antiferromagnet, for its fundamental…
We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating…
We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a…
The problem of data augmentation in feature space is considered. A new architecture, denoted the FeATure TransfEr Network (FATTEN), is proposed for the modeling of feature trajectories induced by variations of object pose. This architecture…
This paper is concerned with networks of interacting linear systems at sites of a multidimensional lattice. The systems are governed by linear ODEs with constant coefficients driven by external inputs, and their internal dynamics and…
A poset-stratified space is a pair $(S, S \xrightarrow \pi P)$ of a topological space $S$ and a continuous map $\pi: S \to P$ with a poset $P$ considered as a topological space with its associated Alexandroff topology. In this paper we show…
Left-modularity is a concept that generalizes modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the characteristic polynomial of a lattice with such an element, one…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial…
We study a set of $L$ spatial bosonic modes localized on a graph $\Gamma.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\Gamma.$ We analyze how, in the exact many-body eigenstates of the system…
We study the Hall response of the Bose-Hubbard model subjected to a magnetic field. We show that the Hall conductivity is proportional to the particle density plus an integer. The phase diagram is intersected by topological transitions…
M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying…
We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that…
Local kinetic constraints in quantum many-body systems can generate slow dynamics or complete many-body localisation. Here we focus on a modification of the quantum East model: Inspired by random matrix theory, we randomise the connectivity…
We reveal underlying principles of nonlinear localization of a two-component Bose-Einstein condensate loaded into a one-dimensional optical lattice. Our theory shows that spin-dependent optical lattices can be used to manipulate both the…
Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…