arXiv subjects

Sheng Zhang

Publications and source records attributed to Sheng Zhang.

At least 271 records · Page 15Linked to original sources

arXiv2017

Formal verification of quantum communication protocols using Petri nets

This paper presents a new formal method for verification of quantum communication protocols. By extending the symbolic system of Petri nets, we can define quantum pure states in Petri-net settings. Therefore, it is possible to emerge a framework from formalizing basic quantum phenomena, which are utilized to achieve communication tasks. We also present an example of applying this framework to the modeling and analyzing quantum communication protocols to show how it works.

quant-ph↗

arXiv2017

A Variation Evolving Method for Optimal Control

A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a virtual dimension, the variation time, a dynamic system that describes the variation motion is deduced from the Optimal Control Problem (OCP), and the optimal solution is its equilibrium point. Through this method, the intractable OCP is transformed to the Initial-value Problem (IVP) and it may be solved with mature Ordinary Differential Equation (ODE) numerical integration methods. Especially, the deduced dynamic system is globally stable, so any initial value will evolve to the extremal solution ultimately.

eess.SY↗

arXiv2016

On the geometry of the countably branching diamond graphs

In this article, the bi-Lipschitz embeddability of the sequence of countably branching diamond graphs $(D_k^ω)_{k\in\mathbb{N}}$ is investigated. In particular it is shown that for every $\varepsilon>0$ and $k\in\mathbb{N}$, $D_k^ω$ embeds bi-Lipschiztly with distortion at most $6(1+\varepsilon)$ into any reflexive Banach space with an unconditional asymptotic structure that does not admit an equivalent asymptotically uniformly convex norm. On the other hand it is shown that the sequence $(D_k^ω)_{k\in\mathbb{N}}$ does not admit an equi-bi-Lipschitz embedding into any Banach space that has an equivalent asymptotically midpoint uniformly convex norm. Combining these two results one obtains a metric characterization in terms of graph preclusion of the class of asymptotically uniformly convexifiable spaces, within the class of separable reflexive Banach spaces with an unconditional asymptotic structure. Applications to bi-Lipschitz embeddability into $L_p$-spaces and to some problems in renorming theory are also discussed.

math.MG↗

arXiv2016

Characterization of switching field distributions in Ising-like magnetic arrays

The switching field distribution within arrays of single-domain ferromagnetic islands incorpo- rates both island-island interactions and quenched disorder in island geometry. Separating these two contributions is important for disentangling the effects of disorder and interactions in the magnetization dynamics of island arrays. Using sub-micron, spatially resolved Kerr imaging in an external magnetic field for islands with perpendicular magnetic anisotropy, we map out the evolution of island arrays during hysteresis loops. Resolving and tracking individual islands across four different lattice types and a range of inter-island spacings, we extract the individual switching fields of every island and thereby determine the relative contributions of interactions and quenched disorder in the arrays. The width of the switching field distribution is well explained by a simple model comprising the sum of an array-independent contribution (interpreted as disorder-induced), and a term proportional to the maximum field the fully polarized array could exert on a single island. We conclude that disorder in these arrays is primarily a single-island property.

cond-mat.mes-hall↗

arXiv2016

Five-Collinear Sierpinski Gasket is Not Self-Similar

A geometrical conclusion: Sierpinski gasket, two Sierpinski gaskets in a line, three Sierpinski gaskets in a line, and four Sierpinski gaskets in a line are self-similar, but five Sierpinski gaskets in a line is not, which is proved in this paper.

math.DS↗

arXiv2016

Discrete Weierstrass Fourier Transform and Experiments

We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this paper. In some examples, this method has a faster convergent speed than Discrete Fourier Transform.

math.NA↗

arXiv2015

Direct Visualization of Memory Effects in Artificial Spin Ice

We experimentally demonstrate that arrays of interacting nanoscale ferromagnetic islands, known as artificial spin ice, develop reproducible microstates upon cycling an applied magnetic field. The onset of this memory effect is determined by the strength of the applied field relative to the array coercivity. Specifically, when the applied field strength is almost exactly equal to the array coercivity, several training cycles are required before the array achieves a nearly completely repeatable microstate, whereas when the applied field strength is stronger or weaker than the array coercivity, a repeatable microstate is achieved after the first minor loop. We show through experiment and simulation that this memory exhibited by artificial spin ice is due to a ratchet effect on interacting, magnetically-charged defects in the island moment configuration and to the complexity of the network of strings of reversed moments that forms during magnetization reversal.

cond-mat.mes-hall↗

arXiv2015

Randomized Structural Sparsity via Constrained Block Subsampling for Improved Sensitivity of Discriminative Voxel Identification

In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered potential biomarkers. The main difficulty in doing this is an extremely high dimensional voxel space and few training samples, resulting in unreliable feature selection. In order to deal with the difficulty, stability selection has received a great deal of attention lately, especially due to its finite sample control of false discoveries and transparent principle for choosing a proper amount of regularization. However, it fails to make explicit use of the correlation property or structural information of these discriminative features and leads to large false negative rates. In other words, many relevant but probably correlated discriminative voxels are missed. Thus, we propose a new variant on stability selection "randomized structural sparsity", which incorporates the idea of structural sparsity. Numerical experiments demonstrate that our method can be superior in controlling for false negatives while also keeping the control of false positives inherited from stability selection.

cs.CV↗

arXiv2015

Randomized Structural Sparsity based Support Identification with Applications to Locating Activated or Discriminative Brain Areas: A Multi-center Reproducibility Study

In this paper, we focus on how to locate the relevant or discriminative brain regions related with external stimulus or certain mental decease, which is also called support identification, based on the neuroimaging data. The main difficulty lies in the extremely high dimensional voxel space and relatively few training samples, easily resulting in an unstable brain region discovery (or called feature selection in context of pattern recognition). When the training samples are from different centers and have betweencenter variations, it will be even harder to obtain a reliable and consistent result. Corresponding, we revisit our recently proposed algorithm based on stability selection and structural sparsity. It is applied to the multi-center MRI data analysis for the first time. A consistent and stable result is achieved across different centers despite the between-center data variation while many other state-of-the-art methods such as two sample t-test fail. Moreover, we have empirically showed that the performance of this algorithm is robust and insensitive to several of its key parameters. In addition, the support identification results on both functional MRI and structural MRI are interpretable and can be the potential biomarkers.

cs.CV↗

arXiv2015

Quantum coin flipping secure against channel noises

So far, most of existed single-shot quantum coin flipping(QCF) protocols failed in a noisy quantum channel. Here, we present a nested-structured framework that makes it possible to achieve partially noise-tolerant QCF, due to that there is a trade-off between the security and the justice correctness. It is showed that noise-tolerant single-shot QCF protocols can be produced by filling the presented framework up with existed or even future protocols. We also proved a lower bound of 0.25, with which a cheating Alice or Bob could bias the outcome.

quant-ph↗

arXiv2015

Improved Direct Counterfactual Quantum Communication

Recently, a novel direct counterfactual quantum communication protocol was proposed using chained quantum Zeno effect. We found that this protocol is far from being widely used in practical channels, due to the side effect of 'chained', which leads to a dramatic increase of the equivalent optical distance between Alice and Bob. Therefore, not only the transmission time of a single bit increases in multiple times, but also the protocol is more sensitive to the noise. Here, we proposed an improved protocol, in which quantum interference is employed to destroy the nested structure induced by 'chained' effect. Moreover, we proved that a better counterfactuality is easier to be achieved, and showed that our protocol outperforms the former in the presence of noises.

quant-ph↗

arXiv2015

$(β)$-distortion of some infinite graphs

A distortion lower bound of $Ω(\log(h)^{1/p})$ is proven for embedding the complete countably branching hyperbolic tree of height $h$ into a Banach space admitting an equivalent norm satisfying property $(β)$ of Rolewicz with modulus of power type $p\in(1,\infty)$ (in short property ($β_p$)). Also it is shown that a distortion lower bound of $Ω(\ell^{1/p})$ is incurred when embedding the parasol graph with $\ell$ levels into a Banach space with an equivalent norm with property ($β_p$). The tightness of the lower bound for trees is shown adjusting a construction of Matoušek to the case of infinite trees. It is also explained how our work unifies and extends a series of results about the stability under nonlinear quotients of the asymptotic structure of infinite-dimensional Banach spaces. Finally two other applications regarding metric characterizations of asymptotic properties of Banach spaces, and the finite determinacy of bi-Lipschitz embeddability problems are discussed.

math.MG↗

arXiv2014

Discrete Korn's inequality for shells

We prove Korn's inequalities for Naghdi and Koiter shell models defined on spaces of discontinuous piecewise functions. They are useful in study of discontinuous finite element methods for shells.

math.NA↗

arXiv2014

A linear finite element procedure for the Naghdi shell model

We prove the accuracy of a mixed finite element method for bending dominated shells in which a major part of the membrane/shear strain is reduced, to free up membrane/shear locking. When no part of the membrane/shear strain is reduced, the method becomes a consistent discontinuous Galerkin method that is proven accurate for membrane/shear dominated shells and intermediate shells. The two methods can be coded in a single program by using a parameter. We propose a procedure of numerically detecting the asymptotic behavior of a shell, choosing the parameter value in the method, and producing accurate approximation for a given shell problem. The method uses piecewise linear functions to approximate all the variables. The analysis is carried out for shells whose middle surfaces have the most general geometries, which shows that the method has the optimal order of accuracy for general shells and the accuracy is robust with respect to the shell thickness. In the particular case that the geometrical coefficients of the shell middle surface are piecewise constants the accuracy is uniform with respect to the shell thickness.

math.NA↗

arXiv2014

A discontinuous Galerkin method for the Naghdi shell model

We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise linear functions, the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the error estimate shows how the accuracy is affected by the shell geometry and thickness. It suggests that to achieve optimal rate of convergence, the triangulation should be properly refined in regions where the shell geometry changes dramatically. These are the results for a balanced method in which the primary displacement components and rotation components are approximated by discontinuous piecewise quadratic polynomials, while components of the scaled membrane stress tensor and shear stress vector are approximated by continuous piecewise linear functions. On elements that have edges on the free boundary of the shell, finite element space for displacement components needs to be enriched slightly, for stability purpose. Results on higher order finite elements are also included.

math.NA↗

arXiv2014

Analysis of a discontinuous Galerkin method for Koiter shell

We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the error estimate shows how the accuracy is affected by the shell geometry and thickness. It suggests that to achieve optimal rate of convergence, the triangulation should be properly refined in regions where the shell geometry changes dramatically. The analysis is carried out for a balanced method in which the normal component of displacement is approximated by discontinuous piecewise cubic polynomials, while the tangential components are approximated by discontinuous piecewise quadratic polynomials, with some enrichment on elements that have edges on the free boundary. Components of the membrane stress are approximated by continuous piecewise linear functions.

math.NA↗

arXiv2014

Coarse Quotient Mappings between Metric Spaces

We give a definition of coarse quotient mapping and show that several results for uniform quotient mapping also hold in the coarse setting. In particular, we prove that any Banach space that is a coarse quotient of $L_p\equiv L_p[0,1]$, $1<p<\infty$, is isomorphic to a linear quotient of $L_p$. It is also proved that $\ell_q$ is not a coarse quotient of $\ell_p$ for $1<p<q<\infty$ using Rolewicz's property ($β$).

math.FA↗

arXiv2013

Oscillation in microRNA Feedback Loop

The dynamic behaviors of microRNA and mRNA under external stress are studied with biological experiments and mathematics models. In this study, we developed a mathematic model to describe the biological phenomenon and for the first time reported that, as responses to external stress, the expression levels of microRNA and mRNA sustained oscillation. And the period of the oscillation is much shorter than several reported transcriptional regulation negative feedback loop.

q-bio.MN↗