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Rui Shi

Publications and source records attributed to Rui Shi.

106 records · Page 6Linked to original sources
arXiv2019

Constraints on Superconducting Cosmic Strings from the Global $21$-cm Signal before Reionization

Electromagnetic radiation from the cusp region of superconducting cosmic strings leads to a radio excess in the photon spectrum in the early universe and can produce a deep absorption feature in the global 21cm signal before the epoch of reionization. We study the constraints on the parameter space of superconducting strings which can be derived by demanding that the absorption feature is not larger in amplitude than what has recently been reported by the EDGES collaboration.

astro-ph.CO↗
arXiv2018

A Stochastic Trust Region Algorithm Based on Careful Step Normalization

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within a specified interval. The complete algorithm---which dynamically chooses whether or not to employ normalized steps---is proved to have convergence guarantees that are similar to those possessed by a traditional stochastic gradient approach under various sets of conditions related to the accuracy of the stochastic gradient estimates and choice of stepsize sequence. The results of numerical experiments are presented when the method is employed to minimize convex and nonconvex machine learning test problems. These results illustrate that the method can outperform a traditional stochastic gradient approach.

math.OC↗
arXiv2018

On irreducible operators in factor von Neumann algebras

Let $\mathcal M$ be a factor von Neumann algebra with separable predual and let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to $\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(T)'\cap \mathcal M={\mathbb C} I$. In this note, we show that the set of irreducible operators in $\mathcal M$ is a dense $G_δ$ subset of $\mathcal M$ in the operator norm. This is a natural generalization of a theorem of Halmos.

math.OA↗
arXiv2018

A note on the Voiculescu's theorem for commutative C$^*$-algebras in semifinite von Neumann algebras

In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a semifinite von Neumann algebra. A result of D. Hadwin for approximate summands of representations into a finite von Neumann factor $\mathcal{R}$ is also extended.

math.OA↗
arXiv2017

Large Margin Learning in Set to Set Similarity Comparison for Person Re-identification

Person re-identification (Re-ID) aims at matching images of the same person across disjoint camera views, which is a challenging problem in multimedia analysis, multimedia editing and content-based media retrieval communities. The major challenge lies in how to preserve similarity of the same person across video footages with large appearance variations, while discriminating different individuals. To address this problem, conventional methods usually consider the pairwise similarity between persons by only measuring the point to point (P2P) distance. In this paper, we propose to use deep learning technique to model a novel set to set (S2S) distance, in which the underline objective focuses on preserving the compactness of intra-class samples for each camera view, while maximizing the margin between the intra-class set and inter-class set. The S2S distance metric is consisted of three terms, namely the class-identity term, the relative distance term and the regularization term. The class-identity term keeps the intra-class samples within each camera view gathering together, the relative distance term maximizes the distance between the intra-class class set and inter-class set across different camera views, and the regularization term smoothness the parameters of deep convolutional neural network (CNN). As a result, the final learned deep model can effectively find out the matched target to the probe object among various candidates in the video gallery by learning discriminative and stable feature representations. Using the CUHK01, CUHK03, PRID2011 and Market1501 benchmark datasets, we extensively conducted comparative evaluations to demonstrate the advantages of our method over the state-of-the-art approaches.

cs.CV↗
arXiv2017

A generalization of the Voiculescu theorem for normal operators in semifinite von Neumann algebras

In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful normal semifinite tracial weight $τ$, a normal operator is an arbitrarily small $(\max\{\|\cdot\|, \Vert\cdot\Vert_{2}\})$-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each self-adjoint operator can be diagonalized modulo norm ideals satisfying a natural condition.

math.OA↗
arXiv2017

Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$ and let $τ$ be a faithful normal semifinite tracial weight of $\mathcal M$. Suppose that $H$ and $H_1$ are self-adjoint operators affiliated with $\mathcal{M}$. We show that if $H-H_1$ is in $\mathcal{M}\cap L^{1}\left(\mathcal{M},τ\right)$, then the ${norm}$ absolutely continuous parts of $H$ and $H_1$ are unitarily equivalent. This implies that the real part of a non-normal hyponormal operator in $\mathcal M$ is not a perturbation by $\mathcal{M}\cap L^{1}\left(\mathcal{M},τ\right)$ of a diagonal operator. Meanwhile, for $n\ge 2$ and $1\leq p<n$, by modifying Voiculescu's invariant we give examples of commuting $n$-tuples of self-adjoint operators in $\mathcal{M}$ that are not arbitrarily small perturbations of commuting diagonal operators modulo $\mathcal{M}\cap L^{p}\left(\mathcal{M},τ\right)$.

math.OA↗
arXiv2016

Registration of Volumetric Prostate Scans using Curvature Flow

Radiological imaging of the prostate is becoming more popular among researchers and clinicians in searching for diseases, primarily cancer. Scans might be acquired with different equipment or at different times for prognosis monitoring, with patient movement between scans, resulting in multiple datasets that need to be registered. For these cases, we introduce a method for volumetric registration using curvature flow. Multiple prostate datasets are mapped to canonical solid spheres, which are in turn aligned and registered through the use of identified landmarks on or within the gland. Theoretical proof and experimental results show that our method produces homeomorphisms with feature constraints. We provide thorough validation of our method by registering prostate scans of the same patient in different orientations, from different days and using different modes of MRI. Our method also provides the foundation for a general group-wise registration using a standard reference, defined on the complex plane, for any input. In the present context, this can be used for registering as many scans as needed for a single patient or different patients on the basis of age, weight or even malignant and non-malignant attributes to study the differences in general population. Though we present this technique with a specific application to the prostate, it is generally applicable for volumetric registration problems.

cs.GR↗
arXiv2014

On a class of operators in the hyperfinite ${\rm II}_1$ factor

Let $R$ be the hyperfinite ${\rm II}_1$ factor and let $u,v$ be two generators of $R$ such that $u^*u=v^*v=1$ and $vu=e^{2πiθ} uv$ for an irrational number $θ$. In this paper we study the class of operators $uf(v)$, where $f$ is a bounded Lebesgue measurable function on the unit circle $S^1$. We calculate the spectrum and Brown spectrum of operators $uf(v)$, and study the invariant subspace problem of such operators relative to $R$. We show that under general assumptions the von Neumann algebra generated by $uf(v)$ is an irreducible subfactor of $R$ with index $n$ for some natural number $n$, and the $C^*$-algebra generated by $uf(v)$ and the identity operator is a generalized universal irrational rotation $C^*$-algebra.

math.OA↗
arXiv2014

One-dimensional steady transport by molecular dynamics simulation: Non-Boltzmann position distribution and non-Arrhenius dynamical behavior

A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged in the intense thermal diffusion. In this article, we employ an accurate method in molecular dynamics simulation to determine the drift velocity of a particle driven by a weak external force in a one-dimensional periodic potential. With the calculated drift velocity, we found that the mobility and diffusion of the particle obey the Einstein relation, whereas their temperature dependences deviate from the Arrhenius law. A microscopic hopping mechanism was proposed to explain the non-Arrhenius behavior. Moreover, the position distribution of the particle in the potential well was found to deviate from the Boltzmann equation in a non-equilibrium steady state. The non-Boltzmann behavior may be attributed to the thermostat which introduces and effective "viscous" drag opposite to the drift direction of the particle.

cond-mat.stat-mech↗
arXiv2013

A reduction theory for operators in type $\rm{I}_{n}$ von Neumann algebras

In this paper, we study the structure of operators in a type $\mathrm{I}_{n}$ von Neumann algebra $\mathscr{A}$. Inspired by the Jordan canonical form theorem, our main motivation is to figure out the relation between the structure of an operator $A$ in $\mathscr{A}$ and the property that a bounded maximal abelian set of idempotents contained in the relative commutant $\{A\}^{\prime} \cap\mathscr{A}$ is unique up to similarity. Furthermore, we classify this class of operators with the property by $K$-theory for Banach algebras. Some views and techniques are from von Neumann's reduction theory.

math.OA↗
arXiv2013

Unitary operators in the orthogonal complement of a type $\mathrm{I}$ von Neumann algebra in a type $\mathrm{II}^{}_{1}$ factor

It is well-known that the equality $$L^{}_{G}\ominus L^{}_{H}=\bar{\mathrm{span}\{L_{g}:g\in G-H\}^{\mathrm{SOT}}}$$ holds for $G$ an i.c.c. group and $H$ a subgroup in $G$, where $L^{}_{G}$ and $L^{}_{H}$ are the corresponding group von Neumann algebras and $L^{}_{G}\ominus L^{}_{H}$ is the set $\{x\in L^{}_{G}:E^{}_{L^{}_{H}}(x)=0\}$ with $E^{}_{L^{}_{H}}$ the conditional expectation defined from $L^{}_{G}$ onto $L^{}_{H}$. Inspired by this, it is natural to ask whether the equality $$N\ominus A=\bar{\mathrm{span}\{u: u\mbox{is unitary in}N\ominus A\}^{\mathrm{SOT}}}$$ holds for $N$ a type $\mbox{II}^{}_{1}$ factor and $A$ a von Neumann subalgebra of $N$. In this paper, we give an affirmative answer to this question for the case $A$ a type I von Neumann algebra.

math.OA↗
arXiv2012

Direct integrals of strongly irreducible operators

Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible operators. In this paper, we show that a bounded linear operator A is similar to a direct integral of strongly irreducible operators if its commutant contains a bounded maximal abelian set of idempotents. We find that bounded linear operators which are similar to direct integrals of strongly irreducible operators form a dense subset of L(H) in the operator norm.

math.FA↗
arXiv2012

A similarity invariant of a class of n-normal operators in terms of K-theory

In this paper, we prove an analogue of the Jordan canonical form theorem for a class of $n$-normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction theory. This is a continuation of our study of bounded linear operators, the commutants of which contain bounded maximal abelian set of idempotents. Furthermore, we give a complete similarity invariant for this class of operators by $K$-theory for Banach algebras.

math.FA↗