Related papers: A non commutative sewing lemma

The recent tremendous success of unsupervised word embeddings in a multitude of applications raises the obvious question if similar methods could be derived to improve embeddings (i.e. semantic representations) of word sequences as well. We…

Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise,…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

A criterion for comonadicity of the extension-of- scalars functor associated to an extension of (not necessarily commutative) rings is given. As an application of this criterion, some known results on the comonadicity of such functors are…

In this paper we discuss the results recently published in~[1] about algebraic signal models (ASMs) based on non commutative algebras and their use in convolutional neural networks. Relying on the general tools from algebraic signal…

We prove that the statement "there is a $k$ such that for every $f$ there is a $k$-bounded diagonally non-recursive function relative to $f$" does not imply weak K\"onig's lemma over $\mathrm{RCA}_0 + \mathrm{B}\Sigma^0_2$. This answers a…

We establish a sequential Hopf's Lemma for higher order differential inequalities in one variable and give some applications of this result.

The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.

These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild…

In the preceding Comment it is alleged that a "hidden loophole" in the proof of Hara's theorem has been found, which purportedly invalidates the conclusions of the paper commented upon. I show that there is no such loophole in the…

The main purpose of this paper is to study non-commutative ternary Nambu-Poisson algebras and their Hom-type version. We provide construction results dealing with tensor product and direct sums of two (non-commutative) ternary…

We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.

In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…

We consider the class of smooth convex functions defined over an open convex set. We show that this class is essentially different than the class of smooth convex functions defined over the entire linear space by exhibiting a function that…

We study noncommutative versions of holomorphic and harmonic functions on the unit disk.

Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We…

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…

We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…

We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the…

We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative theory of representing measures of characters of a function algebra. Our main cycle of…