Related papers: Complex Interpolation of Matrices with an applicat…
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an…
We say that a complex analytic space, $X$, is an intersection cohomology manifold if and only if the shifted constant sheaf on $X$ is isomorphic to intersection cohomology; this is quickly seen to be equivalent to $X$ being a homology…
We describe all linear operators which maps $n-1$-dimensional simplex of idempotent measures to itself. Such operators divided to two classes: the first class contains all $n\times n$-matrices with non-negative entries which has at least…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*}…
Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
In this paper, spectral properties of matrices with (complex) zeon entries are investigated. It is shown that when $A$ is an $m\times m$ self-adjoint matrix whose characteristic polynomial $\chi_A(u)$ has $m$ ``spectrally simple'' zeros…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
The complex method of interpolation, going back to Calder\'on and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of…
The spectral properties of a multilevel atomic system interacting with multiple electromagnetic fields, a modified inverted-Y system, have been theoretically investigated. In this study, a numerical matrix propagation method has been…
We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
In this work, we study a class of random matrices which interpolate between the Wigner matrix model and various types of patterned random matrices such as random Toeplitz, Hankel, and circulant matrices. The interpolation mechanism is…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
Machine learning of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few machine learning models targeting directional properties, including permanent and transition…
In this paper we consider Modal Team Logic, a generalization of Classical Modal Logic in which it is possible to describe dependence phenomena between data. We prove that most known fragment of Full Modal Team Logic allow the elimination of…