Related papers: Combined Algebraic Properties in Gaussian and Quat…
We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result…
Jespers and Sun conjectured that if a finite group $G$ has the property ND, i.e. for every nilpotent element $n$ in the integral group ring $\mathbb{Z}G$ and every primitive central idempotent $e \in \mathbb{Q}G$ one still has $ne \in…
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
In this paper we provide some properties of k-potent elements in algebras obtained by the Cayley-Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt…
Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to…
A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that…
In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be B{\'e}zout is also studied,…
Let $R$ be a commutative ring with a collection of ideals $\{ N_1, N_2, \dots, N_{k-1}\}$ satisfying certain conditions, properties of the set of invertible quadratic residues of the ring $R$ are described in terms of properties of the set…
The content of a polynomial over a ring $R$ is a well understood notion. Ohm and Rush generalized this concept of a content map to an arbitrary ring extension of $R$, although it can behave quite badly. We examine five properties an algebra…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
By combining the findings of two recent, seminal papers by Nualart, Peccati and Tudor, we get that the convergence in law of any sequence of vector-valued multiple integrals $F_n$ towards a centered Gaussian random vector $N$, with given…
This letter generalizes the Graph Signal Recovery (GSR) problem in Graph Signal Processing (GSP) to the Quaternion domain. It extends the Quaternion Least Mean Square (QLMS) in adaptive filtering literature, and Graph LMS (GLMS) algorithm…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…