Related papers: Random Residue Sequences and the Number Theoretic …
We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform…
In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated…
The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and…
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…
Reimann and Slaman initiated the study of sequences that are Martin-L\"of random with respect to a continuous measure, establishing fundamental facts about NCR, the collection of sequences that are not Martin-L\"of random with respect to…
Neural sequence-to-sequence networks with attention have achieved remarkable performance for machine translation. One of the reasons for their effectiveness is their ability to capture relevant source-side contextual information at each…
The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued…
We theoretically study the non-Hermitian systems, the non-Hermiticity of which arises from the unequal hopping amplitude (UHA) dimers. The distinguishing features of these models are that they have full real spectra if all of the…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
We consider the model of random sequential adsorption, with depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…
We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture is equivalent to the conjecture that finite translates of square-integrable functions on the Heisenberg group are linearly independent.
The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of…
The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is extended to dynamical problems. The auto-correlation functions of the Transverse Ising chain are derived by this method. It is shown that the Trotter-directional…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…
This study presents a novel model for invertible sentence embeddings using a residual recurrent network trained on an unsupervised encoding task. Rather than the probabilistic outputs common to neural machine translation models, our…