In this paper we characterize those bounded linear transformations Tf carrying L1(R1) into the space of bounded continuous functions on R1 , for which the convolution identity T (f ∗ g) = Tf ·Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

We use the SYK family of models with $N$ Majorana fermions to study complexity time evolution, formulated as shortest geodesic length on unitary group manifold between identity and evolution operator, in free, integrable, chaotic systems. Initially, follows trajectory, hence grows linearly time. how this linear growth is eventually truncated by appearance accumulation conjugate points, which si...

We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by KawahigashiSutherland-Takesaki in automorphism case.

A confidence distribution is a complete tool for making frequentist inference parameter of interest based on an assumed parametric model. Indeed, it provides point estimates, along with intervals, allows to define rejection regions testing unilateral and bilateral hypotheses, assign measures evidence or levels prespecified the space, compare other parameters from studies. The aim discuss robust...

Service time distributions at computer processing units are often nonexponential. Empirical studies show that different programs may have markedly different processing time requirements. When queuing disciplines are first come, first served, preemptive priority or nonpreemptive priority, models reflecting these characteristics are difficult to analyze exactly. Available approximate techniques a...

We analyze algorithms for approximating a function $f(x) = \Phi x$ mapping $\Re^d$ to $\Re^d$ using deep linear neural networks, i.e. that learn a function $h$ parameterized by matrices $\Theta_1,...,\Theta_L$ and defined by $h(x) = \Theta_L \Theta_{L-1} ... \Theta_1 x$. We focus on algorithms that learn through gradient descent on the population quadratic loss in the case that the distribution...

It was recently shown that SVD and matrix inversion can be approximated in quantum log-space [1] for well formed matrices. This can be interpreted as a fully logarithmic quantum approximation scheme for both problems. We show that if prBQL = prBPL then every fully logarithmic quantum approximation scheme can be replaced by a probabilistic one. Hence, if classical algorithms cannot approximate t...

We introduce a new parallel algorithm for approximate breadthfirst ordering of an unweighted graph by using bounded asynchrony to parametrically control both the performance and error of the algorithm. This work is based on the k-level asynchronous (KLA) paradigm that trades expensive global synchronizations in the level-synchronous model for local synchronizations in the asynchronous model, wh...

We introduce a new dimension to the widely studied on-line approximate string matching problem, by introducing an error threshold parameter so that the algorithm is allowed to miss occurrences with probability . This is particularly appropriate for this problem, as approximate searching is used to model many cases where exact answers are not mandatory. We show that the relaxed version of the pr...

M computing systems are designed to prevent errors in computation, memory, and communication. Guarding against errors however requires energy, temporal redundancy, or spatial redundancy and therefore consumes resources. But not all systems need to be free of errors: In some systems, either by explicit design or by the nature of the problems they solve, system output quality degrades gracefully ...