Related papers: Random Residue Sequences and the Number Theoretic …
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert…
An n-dilation of a contraction T acting on a Hilbert space H is a unitary dilation acting on H \oplus C^n. We show that if both defect numbers of T are equal to n, then the closure of the numerical range of T is the intersection of the…
In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained.
We study derived coinvariants of isotropic subbundles on modules over super Heisenberg algebras and construct certain natural transitive Lie algebroids acting on them.
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
The paper introduces new types of nonlinear correlations between bivariate data sets and derives nonlinear auto-correlations on the same data set. These auto-correlations are of different types to match signals with different types of…
The Hilbert series is a generating function that enumerates gauge invariant chiral operators of a supersymmetric field theory with four supercharges and an R-symmetry. In this article I review how counting dressed 't Hooft monopole…
We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained extend recent results of Tao and Ter\"av\"ainen and results of…
A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…
In Transformer-based neural machine translation (NMT), the positional encoding mechanism helps the self-attention networks to learn the source representation with order dependency, which makes the Transformer-based NMT achieve…
Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…
In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…
Deviations between the form of trajectory assumed in a fit to a set of measurements and the actual form of the trajectory can give rise to sequential correlations in the residuals from the fit. These correlations can provide a more powerful…
Preparation of nonclassical light with special quantum properties is essential for quantum technologies. High-harmonic generation (HHG) is a process which not only enables the creation of attosecond pulses but also has the potential to…
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network…
The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a…