Related papers: Interval Rearrangement Ensembles
The integrated extinction (IE) is defined as the integral of the scattering cross-section as a function of wavelength. Sohl et al. [1] derived an IE expression for acoustic scattering that is causal, i.e. the scattered wavefront in the…
Turbulence generally arises in shear flows if velocities and hence inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases,…
We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element differential complex of lowest-order, known as the complex of…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…
The extraction and understanding of temporal events and their relations are major challenges in natural language processing. Processing text on a sentence-by-sentence or expression-by-expression basis often fails, in part due to the…
In this paper the gauge embedding procedure of dualization is reassessed through a deeper analysis of the mutual equivalence of vector field models of more generic forms, explicitly, a general modified massive gauge-breaking extension of…
Large Language Models (LLMs) encode meanings of words in the form of distributed semantics. Distributed semantics capture common statistical patterns among language tokens (words, phrases, and sentences) from large amounts of data. LLMs…
We introduce Inner Ensemble Networks (IENs) which reduce the variance within the neural network itself without an increase in the model complexity. IENs utilize ensemble parameters during the training phase to reduce the network variance.…
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.
We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained…
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…
The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational…
We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations…
We establish a precise connection between discrete wavelet transforms (WTs) and entanglement renormalization (ER), a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle…
This paper proves shrinking target results for IETs. Let {a_1\geq a_2 \geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(T^ix,a_i) has full Lebesgue measure (where B(z, e) is the…
We study a class of renormalization group flows on line defects that can be described by a generalized free field with ordered planar contractions on the line. They are realized, for example, in large $N$ gauge theories with matter in the…