Concept

Vector calculus

Related publications (128)

Diversity of radial spin textures in chiral materials

Oleg Yazyev, Daniel Gosalbez Martinez, Alberto Crepaldi

We introduce a classification of the radial spin textures in momentum space that emerge at the high-symmetry points in crystals characterized by nonpolar chiral point groups (D2, D3, D4, D6, T, O). Based on the symmetry constraints imposed by these point g ...

College Pk2023

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Philadelphia2023

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Haoqi Wang, Zhigang Li

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Ieee Computer Soc2023

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

Revisiting the General Identifiability Problem

Negar Kiyavash, Ehsan Mokhtarian, Yaroslav Kivva, Seyed Jalal Etesami

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show t ...

2022

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Tommaso Vanzan

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

2022

The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

Michael Christoph Gastpar, Erixhen Sula

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, ou ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Further results on latent discourse models and word embeddings

Youssef Allouah

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

MICROTOME PUBL2021

Matter matters in Einstein-Cartan gravity

Andrey Shkerin, Georgios Karananas, Sebastian Zell

We study scalar, fermionic and gauge fields coupled nonminimally to gravity in the Einstein-Cartan formulation. We construct a wide class of models with nondynamical torsion whose gravitational spectra comprise only themassless graviton. Eliminating nonpro ...

AMER PHYSICAL SOC2021

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