Related papers: Random Residue Sequences and the Number Theoretic …
The results of Bergelson-Host-Kra and Leibman say that a multiple polynomial correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a…
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…
We consider sequences of homogeneous sums based on independent random variables and satisfying a central limit theorem (CLT). We address the following question: "In which cases is it not possible to reduce such an asymptotic result to the…
Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic…
We study a special inhomogeneous quantum network consisting of a ring of $M$ pseudo-spins (here $M = 4$) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This…
We point out that the transport properties of non-interacting fermionic chains tunnel-coupled to two reservoirs at their ends can be mapped to those of a single quantum dot that is tunnel-coupled to two transformed reservoirs. The…
Hermite reciprocity refers to a series of natural isomorphisms involving compositions of symmetric, exterior, and divided powers of the standard $SL_2$-representation. We survey several equivalent constructions of these isomorphisms, as…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is…
The authors consider the length, $l_N$, of the length of the longest increasing subsequence of a random permutation of $N$ numbers. The main result in this paper is a proof that the distribution function for $l_N$, suitably centered and…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
We propose a new approach to the resummation of the transverse-momentum distribution of a high-mass colour-singlet system in hadronic collisions. The resummation is performed in momentum space and is free of kinematic singularities at small…
Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of…
The Hanbury-Brown Twiss correlation function for two identical particles is studied for systems with cylindrical symmetry. Its shape for small values of the relative momentum is derived in a model independent way. In addition to the usual…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
A perceptron that learns the opposite of its own output is used to generate a time series. We analyse properties of the weight vector and the generated sequence, like the cycle length and the probability distribution of generated sequences.…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
Neural machine translation (NMT) usually works in a seq2seq learning way by viewing either source or target sentence as a linear sequence of words, which can be regarded as a special case of graph, taking words in the sequence as nodes and…
We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value…