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In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the ``wave function" $\Psi$ living in a Lie group $G$, which satisfies some…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
The study of amplitudes and cross sections in the soft and collinear limits allows for an understanding of their all orders behavior, and the identification of universal structures. At leading power soft emissions are eikonal, and described…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
The paper investigates the general case of incompressible non-classical elasticity with small deformations and rotations. It is shown that the internal spin rotations are important only when a specific Born term is presented in the free…
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…
It is well-known that the Eulerian polynomials, which count permutations in $S_n$ by their number of descents, give the $h$-polynomial/$h$-vector of the simple polytopes known as permutohedra, the convex hull of the $S_n$-orbit for a…
This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {x_a, y_a}_{a=1,... N} arising in coupled matrix models, valid for a broad class of two-variable measures. The result is…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…
We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a generalized Freud weight \[w(x;t)=|x|^{2\lambda+1}\exp\left(-x^4+tx^2\right),\qquad x\in\mathbb{R},\] with parameters $\lambda>-1$…
Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of…
A boolean function $f(x_1,...,x_n)$ is \textit{weakly symmetric} if it is invariant under a transitive permutation group on its variables. A boolean function $f(x_1,...,x_n)$ is \textit{elusive} if we have to check all $x_1$,..., $x_n$ to…
We consider the problem to determine the optimal rotations $R \in {\rm SO}(n)$ which minimize $$W: {\rm SO}(n) \to \mathbb{R}^+_0,\quad W(R\,;D) := ||{\rm sym}(RD - 1)||^2$$ for a given diagonal matrix $D := {\rm diag}(d_1, ..., d_n) \in…