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Lijun Zhang

Publications and source records attributed to Lijun Zhang.

At least 307 records · Page 17Linked to original sources
arXiv2013

Polsat: A Portfolio LTL Satisfiability Solver

In this paper we present a portfolio LTL-satisfiability solver, called Polsat. To achieve fast satisfiability checking for LTL formulas, the tool integrates four representative LTL solvers: pltl, TRP++, NuSMV, and Aalta. The idea of Polsat is to run the component solvers in parallel to get best overall performance; once one of the solvers terminates, it stops all other solvers. Remarkably, the Polsat solver utilizes the power of modern multi-core compute clusters. The empirical experiments show that Polsat takes advantages of it. Further, Polsat is also a testing plat- form for all LTL solvers.

cs.LO↗
arXiv2013

Bisimulations Meet PCTL Equivalences for Probabilistic Automata

Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on probabilistic computation tree logic (PCTL) and its extension PCTL^*. Various behavioral equivalences are proposed, as a powerful tool for abstraction and compositional minimization for PAs. Unfortunately, the equivalences are well-known to be sound, but not complete with respect to the logical equivalences induced by PCTL or PCTL*. The desire of a both sound and complete behavioral equivalence has been pointed out by Segala in 1995, but remains open throughout the years. In this paper we introduce novel notions of strong bisimulation relations, which characterize PCTL and PCTL* exactly. We extend weak bisimulations that characterize PCTL and PCTL* without next operator, respectively. Further, we also extend the framework to simulation preorders. Thus, our paper bridges the gap between logical and behavioral equivalences and preorders in this setting.

cs.LO↗
arXiv2013

Efficient Distance Metric Learning by Adaptive Sampling and Mini-Batch Stochastic Gradient Descent (SGD)

Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to be a positive semi-definite (PSD) matrix. Although stochastic gradient descent (SGD) has been successfully applied to improve the efficiency of DML, it can still be computationally expensive because in order to ensure that the solution is a PSD matrix, it has to, at every iteration, project the updated distance metric onto the PSD cone, an expensive operation. We address this challenge by developing two strategies within SGD, i.e. mini-batch and adaptive sampling, to effectively reduce the number of updates (i.e., projections onto the PSD cone) in SGD. We also develop hybrid approaches that combine the strength of adaptive sampling with that of mini-batch online learning techniques to further improve the computational efficiency of SGD for DML. We prove the theoretical guarantees for both adaptive sampling and mini-batch based approaches for DML. We also conduct an extensive empirical study to verify the effectiveness of the proposed algorithms for DML.

cs.LG↗
arXiv2013

O(logT) Projections for Stochastic Optimization of Smooth and Strongly Convex Functions

Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation can be expensive, leading to a high computational cost per iteration. In this paper, we present a novel algorithm that aims to reduce the number of projections for stochastic optimization. The proposed algorithm combines the strength of several recent developments in stochastic optimization, including mini-batch, extra-gradient, and epoch gradient descent, in order to effectively explore the smoothness and strong convexity. We show, both in expectation and with a high probability, that when the objective function is both smooth and strongly convex, the proposed algorithm achieves the optimal $O(1/T)$ rate of convergence with only $O(\log T)$ projections. Our empirical study verifies the theoretical result.

cs.LG↗
arXiv2013

Genetic Design of Enhanced Valley Splitting towards a Spin Qubit in Silicon

Electronic spins in Silicon (Si) are rising contenders for qubits -- the logical unit of quantum computation-- owing to its outstanding spin coherence properties and compatibility to standard electronics. A remarkable limitation for spin quantum computing in Si hosts is the orbital degeneracy of this material's conduction band, preventing the spin-1/2 states from being an isolated two-level system. So far available samples of Si quantum wells cladded by Ge-Si alloy barriers provide relatively small valley splitting (VS), with the order of 1 meV or less, degrading the fidelity of qubits encoded in spin "up" and "down" states in Si. Here, based on an atomically resolved pseudopotential theory, we demonstrate that ordered Ge-Si layered barriers confining a Si slab can be harnessed to enhance the VS in the active Si region by up to one order of magnitude compared to the random alloy barriers adopted so far. A biologically inspired genetic-algorithm search is employed to identify magic Ge/Si layer sequences of the superlattice barriers that isolate the electron ground state in a single valley composition with VS as large as ~9 meV. The enhanced VS is preserved with the reasonable inter-layer mixing between different species, and is interestingly "protected" even if some larger mixing occurs. Implementation of the optimized layer sequences of barriers, within reach of modern superlattice growth techniques, overcomes in a practical systematic way the main current limitations related to the orbital degeneracy, thus providing a roadmap for reliable spin-only quantum computing in Si.

cond-mat.mes-hall↗
arXiv2012

Roadmap Document on Stochastic Analysis

This document was prepared as part of the MT-LAB research centre. The research centre studies the Modelling of Information Technology and is a VKR Centre of Excellence funded for five years by the VILLUM Foundation. You can read more about MT-LAB at its webpage www.MT-LAB.dk. The goal of the document is to serve as an introduction to new PhD students addressing the research goals of MT-LAB. As such it aims to provide an overview of a number of selected approaches to the modelling of stochastic systems. It should be readable not only by computers scientists with a background in formal methods but also by PhD students in stochastics that are interested in understanding the computer science approach to stochastic model checking. We have no intention of being encyclopedic in our treatment of the approaches or the literature. Rather we have made the selection of material based on the competences of the groups involved in or closely affiliated to MT-LAB, so as to ease the task of the PhD students in navigating an otherwise vast amount of literature. We have decided to publish the document in case other young researchers may find it helpful. The list of authors reflect those that have at times played a significant role in the production of the document.

cs.LO↗
arXiv2012

On the Relationship between LTL Normal Forms and Buechi Automata

In this paper, we consider the problem of translating LTL formulas to Buechi automata. We first translate the given LTL formula into a special disjuctive-normal form (DNF). The formula will be part of the state, and its DNF normal form specifies the atomic properties that should hold immediately (labels of the transitions) and the formula that should hold afterwards (the corresponding successor state). Surprisingly, if the given formula is Until-free or Release-free, the Buechi automaton can be obtained directly in this manner. For a general formula, the construction is slightly involved: an additional component will be needed for each formula that helps us to identify the set of accepting states. Notably, our construction is an on-the-fly construction, and the resulting Buechi automaton has in worst case 2^{2n+1} states where n denotes the number of subformulas. Moreover, it has a better bound 2^{n+1} when the formula is Until- (or Release-) free.

cs.FL↗
arXiv2012

Efficient CSL Model Checking Using Stratification

For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.

cs.LO↗
arXiv2012

Multiple Kernel Learning from Noisy Labels by Stochastic Programming

We study the problem of multiple kernel learning from noisy labels. This is in contrast to most of the previous studies on multiple kernel learning that mainly focus on developing efficient algorithms and assume perfectly labeled training examples. Directly applying the existing multiple kernel learning algorithms to noisily labeled examples often leads to suboptimal performance due to the incorrect class assignments. We address this challenge by casting multiple kernel learning from noisy labels into a stochastic programming problem, and presenting a minimax formulation. We develop an efficient algorithm for solving the related convex-concave optimization problem with a fast convergence rate of $O(1/T)$ where $T$ is the number of iterations. Empirical studies on UCI data sets verify both the effectiveness of the proposed framework and the efficiency of the proposed optimization algorithm.

cs.LG↗
arXiv2011

Efficient Approximation of Optimal Control for Markov Games

We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately. Current techniques provide an accuracy of O(ε^2) on each interval, which leads to an infeasibly large number of intervals. We propose a sequence of approximations that achieve accuracies of O(ε^3), O(ε^4), and O(ε^5), that allow us to drastically reduce the number of intervals that are considered. For CTMDPs, the performance of the resulting algorithms is comparable to the heuristic approach given by Buckholz and Schulz, while also being theoretically justified. All of our results generalise to CTMGs, where our results yield the first practically implementable algorithms for this problem. We also provide positional strategies for both players that achieve similar error bounds.

cs.GT↗
arXiv2011

On Stabilization in Herman's Algorithm

Herman's algorithm is a synchronous randomized protocol for achieving self-stabilization in a token ring consisting of N processes. The interaction of tokens makes the dynamics of the protocol very difficult to analyze. In this paper we study the expected time to stabilization in terms of the initial configuration. It is straightforward that the algorithm achieves stabilization almost surely from any initial configuration, and it is known that the worst-case expected time to stabilization (with respect to the initial configuration) is Theta(N^2). Our first contribution is to give an upper bound of 0.64 N^2 on the expected stabilization time, improving on previous upper bounds and reducing the gap with the best existing lower bound. We also introduce an asynchronous version of the protocol, showing a similar O(N^2) convergence bound in this case. Assuming that errors arise from the corruption of some number k of bits, where k is fixed independently of the size of the ring, we show that the expected time to stabilization is O(N). This reveals a hitherto unknown and highly desirable property of Herman's algorithm: it recovers quickly from bounded errors. We also show that if the initial configuration arises by resetting each bit independently and uniformly at random, then stabilization is significantly faster than in the worst case.

cs.DS↗
arXiv2010

Quantum Interference of Stored Coherent Spin-wave Excitations in a Two-channel Memory

Quantum memories are essential elements in long-distance quantum networks and quantum computation. Significant advances have been achieved in demonstrating relative long-lived single-channel memory at single-photon level in cold atomic media. However, the qubit memory corresponding to store two-channel spin-wave excitations (SWEs) still faces challenges, including the limitations resulting from Larmor procession, fluctuating ambient magnetic field, and manipulation/measurement of the relative phase between the two channels. Here, we demonstrate a two-channel memory scheme in an ideal tripod atomic system, in which the total readout signal exhibits either constructive or destructive interference when the two-channel SWEs are retrieved by two reading beams with a controllable relative phase. Experimental result indicates quantum coherence between the stored SWEs. Based on such phase-sensitive storage/retrieval scheme, measurements of the relative phase between the two SWEs and Rabi oscillation, as well as elimination of the collapse and revival of the readout signal, are experimentally demonstrated.

quant-ph↗
arXiv2009

Electronic correlations in the iron pnictides

In correlated metals derived from Mott insulators, the motion of an electron is impeded by Coulomb repulsion due to other electrons. This phenomenon causes a substantial reduction in the electron's kinetic energy leading to remarkable experimental manifestations in optical spectroscopy. The high-Tc superconducting cuprates are perhaps the most studied examples of such correlated metals. The occurrence of high-Tc superconductivity in the iron pnictides puts a spotlight on the relevance of correlation effects in these materials. Here we present an infrared and optical study on single crystals of the iron pnictide superconductor LaFePO. We find clear evidence of electronic correlations in metallic LaFePO with the kinetic energy of the electrons reduced to half of that predicted by band theory of nearly free electrons. Hallmarks of strong electronic many-body effects reported here are important because the iron pnictides expose a new pathway towards a correlated electron state that does not explicitly involve the Mott transition.

cond-mat.str-el↗
arXiv2009

Electronic structure of Ba(Fe,Ru)2As2 and Sr(Fe,Ir)2As2 alloys

The electronic structures of Ba(Fe,Ru)$_2$As$_2$ and Sr(Fe,Ir)$_2$As$_2$ are investigated using density functional calculations. We find that these systems behave as coherent alloys from the electronic structure point of view. In particular, the isoelectronic substitution of Fe by Ru does not provide doping, but rather suppresses the spin density wave characteristic of the pure Fe compound by a reduction in the Stoner enhancement and an increase in the band width due hybridization involving Ru. The electronic structure near the Fermi level otherwise remains quite similar to that of BaFe$_{2}$As$_{2}$. The behavior of the Ir alloy is similar, except that in this case there is additional electron doping.

cond-mat.supr-con↗
arXiv2009

Density Functional Study of the Over-Doped Iron Chalcogenide: TlFe$_{2}$Se$_{2}$ with ThCr$_{2}$Si$_{2}$ structure

We report density functional calculations of electronic structure and magnetic properties of ternary iron chalcogenide TlFe$_{2}$Se$_{2}$, which occurs in the ThCr$_{2}$Si$_{2}$ structure and discuss the results in relation to the iron-based superconductors. The ground state is antiferromagnetic with checkerboard order and Fe moment $\sim$ 1.90 $μ$B. There is strong magnetoelastic coupling similar to the Fe-based superconductors, reflected in a sensitivity of the Se position to magnetism. Tl is monovalent in this compound, providing heavy electron-doping of 0.5 additional carriers per Fe relative to the parent compounds of the Fe-based superconductors. Other than the change in electron count, the electronic structure is rather similar to those materials. In particular, the Fermi surface is closely related to those of the Fe-based superconductors, except that the electron cylinders are larger, and the hole sections are suppressed. This removes the tendency towards a spin density wave.

cond-mat.supr-con↗
arXiv2008

Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations

Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak simulation over Markov chains, and for strong simulation over probabilistic automata are not efficient, which makes it as yet unclear whether they can be used as effectively as their non-probabilistic counterparts. This paper presents drastically improved algorithms to decide whether some (discrete- or continuous-time) Markov chain strongly or weakly simulates another, or whether a probabilistic automaton strongly simulates another. The key innovation is the use of parametric maximum flow techniques to amortize computations. We also present a novel algorithm for deciding strong probabilistic simulation preorders on probabilistic automata, which has polynomial complexity via a reduction to an LP problem. When extending the algorithms for probabilistic automata to their continuous-time counterpart, we retain the same complexity for both strong and strong probabilistic simulations.

cs.LO↗
arXiv2008

Possible Superconductivity in Fe-Sb Based Materials: Density Functional Study of LiFeSb

We investigate the electronic and other properties of the hypothetical compound LiFeSb in relation to superconducting LiFeAs and FeSe using density functional calculations. The results show that LiFeSb in the LiFeAs structure would be dynamically stable in the sense of having no unstable phonon modes, and would have very similar electronic and magnetic properties to the layered Fe based superconductors. Importantly, a very similar structure for the Fermi surface and a spin density wave related to but stronger than that in the corresponding As compound is found. These results are indicative of possible superconductivity analogous to the Fe-As based compounds if the spin density wave can be suppressed by doping or other means. Prospects for synthesizing this material in pure form or in solid solution with FeTe are discussed.

cond-mat.supr-con↗