相关论文: A Schur transform for spatial stochastic processes

We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over ${\mathbb Z}_p$ can…

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…

In this article, we consider a set of trial wave-functions denoted by $| Q \right>$ and an associated set of operators $A_\alpha$ which generate transformations connecting those trial states. Using variational principles, we show that we…

The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing…

Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…

We develop a formalism for performing real space renormalization group transformations of the "decimation type" using low temperature perturbation theory. This type of transformations beyond $d=1$ is highly nontrivial even for free…

Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

In this paper, the connections are investigated between two different approaches towards the parametrization of multivariable stable all-pass systems in discrete-time. The first approach involves the tangential Schur algorithm, which…

The usefulness of time-frequency analysis methods in the study of quasicrystals was pointed out in a previous paper, where we proved that a tempered distribution $\mu$ on ${\mathbb R}^d$ whose Wigner transform is a measure supported on the…

In this paper we define the shifted Schur process as a measure on sequences of strict partitions. This process is a generalization of the shifted Schur measure introduced in [TW] and [Mat] and is a shifted version of the Schur process…

Motivation: We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix $Q$ which depends on a parameter $\theta$. Computing the probability distribution over states at…

Schur--Weyl--Jones duality establishes the connection between the commuting actions of the symmetric group $S_{n}$ and the partition algebra $P_{k}(n)$ on the tensor space $\left(\mathbb{C}^n\right)^{\otimes k}.$ We give a refinement of…

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…

We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the…

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to…

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…

We present a semiclassical approach for time delay statistics in quantum chaotic systems, in the presence of absorption, for broken time-reversal symmetry. We derive three kinds of expressions for Schur-moments of the time delay operator:…

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting…

The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of…