arXiv subjects

Lijun Zhang

Publications and source records attributed to Lijun Zhang.

At least 271 records · Page 15Linked to original sources

arXiv2016

Design of ternary alkaline-earth metal Sn(II) oxides with potential good p-type conductivity

Oxides with good p-type conductivity have been long sought after to achieve high performance all-oxide optoelectronic devices. Divalent Sn(II) based oxides are promising candidates because of their rather dispersive upper valence bands caused by the Sn-5s/O-2p anti-bonding hybridization. There are so far few known Sn(II) oxides being p-type conductive suitable for device applications. Here, we present via first-principles global optimization structure searches a material design study for a hitherto unexplored Sn(II)-based system, ternary alkaline-earth metal Sn(II) oxides in the stoichiometry of MSn2O3 (M = Mg, Ca, Sr, Ba). We identify two stable compounds of SrSn2O3 and BaSn2O3, which can be stabilized by Sn-rich conditions in phase stability diagrams. Their structures follow the Zintl behaviour and consist of basic structural motifs of SnO3 tetrahedra. Unexpectedly they show distinct electronic properties with band gaps ranging from 1.90 (BaSn2O3) to 3.15 (SrSn2O3) eV, and hole effective masses ranging from 0.87 (BaSn2O3) to above 6.0 (SrSn2O3) m0. Further exploration of metastable phases indicates a wide tunability of electronic properties controlled by the details of the bonding between the basic structural motifs. This suggests further exploration of alkaline-earth metal Sn(II) oxides for potential applications requiring good p-type conductivity such as transparent conductors and photovoltaic absorbers.

cond-mat.mtrl-sci↗

arXiv2016

Optimal Stochastic Strongly Convex Optimization with a Logarithmic Number of Projections

We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient descent~(SGD) methods. To reduce the computation costs pertaining to the projections, we propose an Epoch-Projection Stochastic Gradient Descent~(Epro-SGD) method. The proposed Epro-SGD method consists of a sequence of epochs; it applies SGD to an augmented objective function at each iteration within the epoch, and then performs a projection at the end of each epoch. Given a strongly convex optimization and for a total number of $T$ iterations, Epro-SGD requires only $\log(T)$ projections, and meanwhile attains an optimal convergence rate of $O(1/T)$, both in expectation and with a high probability. To exploit the structure of the optimization problem, we propose a proximal variant of Epro-SGD, namely Epro-ORDA, based on the optimal regularized dual averaging method. We apply the proposed methods on real-world applications; the empirical results demonstrate the effectiveness of our methods.

cs.LG↗

arXiv2016

Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient

This work focuses on dynamic regret of online convex optimization that compares the performance of online learning to a clairvoyant who knows the sequence of loss functions in advance and hence selects the minimizer of the loss function at each step. By assuming that the clairvoyant moves slowly (i.e., the minimizers change slowly), we present several improved variation-based upper bounds of the dynamic regret under the true and noisy gradient feedback, which are {\it optimal} in light of the presented lower bounds. The key to our analysis is to explore a regularity metric that measures the temporal changes in the clairvoyant's minimizers, to which we refer as {\it path variation}. Firstly, we present a general lower bound in terms of the path variation, and then show that under full information or gradient feedback we are able to achieve an optimal dynamic regret. Secondly, we present a lower bound with noisy gradient feedback and then show that we can achieve optimal dynamic regrets under a stochastic gradient feedback and two-point bandit feedback. Moreover, for a sequence of smooth loss functions that admit a small variation in the gradients, our dynamic regret under the two-point bandit feedback matches what is achieved with full information.

cs.LG↗

arXiv2016

An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT solver. The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula. We provide a prototype and show the efficiency of our approach on a number of benchmarks.

cs.LO↗

arXiv2016

High-pressure Phase Stability and Superconductivity of Pnictogen Hydrides and Chemical Trends for Compressed Hydrides

Binary hydrides formed by the pnictogens of phosphorus, arsenic and antimony are studied at high pressures using first principles methods. Stable structures are predicted and their electronic, vibrational and superconducting properties are investigated. We predict that SbH$_{4}$ and AsH$_{8}$ will be high-temperature superconductors at megabar pressures, with critical temperatures in excess of 100 K. The highly symmetric hexagonal SbH$_{4}$ phase is predicted to be stabilized above about 150 GPa, which is readily achievable in diamond anvil cell experiments. We find that all phosphorus hydrides are metastable with respect to decomposition into the elements within the pressure range studied. Trends based on our results and literature data reveal a connection between the high-pressure behaviors and ambient-pressure chemical quantities which provides insight into understanding which elements may form hydrogen-rich high-temperature superconducting phases at high pressures.

cond-mat.supr-con↗

arXiv2016

Intrinsic ultralow lattice thermal conductivity of the unfilled skutterudite FeSb$_3$

It has been generally accepted that unfilled skutterudites process high lattice thermal conductivity ($κ_{l}$) that can be efficiently reduced upon filling. Here by using first principles Boltzmann-Peierls transport calculations, we find pure skutterudite of FeSb$_3$ with no filler in fact has an intrinsic ultralow $κ_{l}$ smaller than that of CoSb$_3$ by one order of magnitude. The value is even smaller than those of most of the fully filled skutterudites. This finding means that with FeSb$_3$ as a reference, filling does not necessarily lower $κ_{l}$. The ultralow $κ_{l}$ of FeSb$_3$ is a consequence of much softened optical phonon branches associated with the weakly bonded Sb$_4$ rings. They overlap more with heat-carrying acoustic phonons and significantly increase the phase space for three-phonon anharmonic scattering processes. This provides an alternative non-filling related mechanism for lowering the $κ_{l}$ of skutterudites.

cond-mat.mtrl-sci↗

arXiv2016

Inverse Design of Inorganic Electrides

Electrides are ionic solids that consist of cationic frameworks and anionic electrons trapped in the voids of lattices. Organic electrides exist in a large abundance, but the thermal instability at room temperature and sensitivity to moisture are bottlenecks that limit their practical uses. Known inorganic electrides are rare but appear to have high thermal and chemical stability and exhibit promising applications as electron-emitting materials, superior catalysts and strong reducing agents. Here, we report a developed inverse-design method that can be used to search for a large variety of inorganic electrides. Our method utilizes the intrinsic property of interstitial electron localization of electrides as the global variable function being incorporated into the swarm-intelligence based structure searches. Through screening 99 binary ionic compounds, we have designed 89 new inorganic electrides that are classified into three-, two-, and zero-dimensional species according to the way that the interstitial electrons are localized and the conductive properties of the systems. Our work reveals the rich abundance of inorganic electrides by extending them into more general forms and provides new structure types for electrides that are not thought of as before.

cond-mat.mtrl-sci↗

arXiv2015

Distribution-based Bisimulation and Bisimulation Metric in Probabilistic Automata

Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic automata were re-proposed by Segala in 1995 which are more general than Rabin's automata. Bisimulations have been proposed for Segala's automata to characterize the equivalence between them. So far the two notions of equivalences and their characteristics have been studied mostly independently. In this paper, we consider Segala's automata, and propose a novel notion of distribution-based bisimulation by joining the existing equivalence and bisimilarities. We demonstrate the utility of our definition by studying distribution-based bisimulation metrics, which gives rise to a robust notion of equivalence for Rabin's automata. We compare our notions of bisimulation to some existing distribution-based bisimulations and discuss their compositionality and relations to trace equivalence. Finally, we show the decidability and complexity of all relations.

cs.FL↗

arXiv2015

Observability of Boolean control networks: A unified approach based on the theories of finite automata

The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define the concept of weighted pair graphs for BCNs. In the sense of each observability, we use the so-called weighted pair graph to transform a BCN to a finite automaton, and then we use the automaton to determine observability. In particular, the two types of observability that rely on initial states and inputs in the literature are determined. Finally, we show that no pairs of the four types of observability are equivalent, which reveals the essence of nonlinearity of BCNs.

math.OC↗

arXiv2015

Stochastic Proximal Gradient Descent for Nuclear Norm Regularization

In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of the gradient, we propose an iterative algorithm based on stochastic proximal gradient descent (SPGD), and take the last iterate of SPGD as the final solution. The main advantage of the proposed algorithm is that its space complexity is $O(m+n)$, in contrast, most of previous algorithms have a $O(mn)$ space complexity. Theoretical analysis shows that it achieves $O(\log T/\sqrt{T})$ and $O(\log T/T)$ convergence rates for general convex functions and strongly convex functions, respectively.

cs.LG↗

arXiv2015

Online Stochastic Linear Optimization under One-bit Feedback

In this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement and online recommendation. We assume the binary feedback is a random variable generated from the logit model, and aim to minimize the regret defined by the unknown linear function. Although the existing method for generalized linear bandit can be applied to our problem, the high computational cost makes it impractical for real-world problems. To address this challenge, we develop an efficient online learning algorithm by exploiting particular structures of the observation model. Specifically, we adopt online Newton step to estimate the unknown parameter and derive a tight confidence region based on the exponential concavity of the logistic loss. Our analysis shows that the proposed algorithm achieves a regret bound of $O(d\sqrt{T})$, which matches the optimal result of stochastic linear bandits.

cs.LG↗

arXiv2015

Towards Making High Dimensional Distance Metric Learning Practical

In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main shortcoming of this approach is that it may result in a suboptimal solution due to the subspace removed by the dimensionality reduction method. In this work, we present a dual random projection frame for DML with high dimensional data that explicitly addresses the limitation of dimensionality reduction for DML. The key idea is to first project all the data points into a low dimensional space by random projection, and compute the dual variables using the projected vectors. It then reconstructs the distance metric in the original space using the estimated dual variables. The proposed method, on one hand, enjoys the light computation of random projection, and on the other hand, alleviates the limitation of most dimensionality reduction methods. We verify both empirically and theoretically the effectiveness of the proposed algorithm for high dimensional DML.

cs.LG↗

arXiv2015

Extending Hybrid CSP with Probability and Stochasticity

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly intertwining discrete, continuous and stochastic dynamics complicates modelling, analysis and verification of stochastic hybrid systems (SHSs). In the literature, this issue has been extensively investigated, but unfortunately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which is called stochastic HCSP (SHCSP). To this end, ordinary differential equations (ODEs) are generalized by stochastic differential equations (SDEs) and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to specify and reason about SHCSP processes. We demonstrate our approach by an example from real-world.

cs.LO↗

arXiv2015

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments.

cs.SE↗

arXiv2015

ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory

Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler--Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al$_{3}$Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.

physics.comp-ph↗

arXiv2015

Theory of Dual-sparse Regularized Randomized Reduction

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptions about the data, e.g., low rank of the data matrix or a large separable margin of classification, which hinder their applications in broad domains. To address these limitations, we propose dual-sparse regularized randomized reduction methods that introduce a sparse regularizer into the reduced dual problem. Under a mild condition that the original dual solution is a (nearly) sparse vector, we show that the resulting dual solution is close to the original dual solution and concentrates on its support set. In numerical experiments, we present an empirical study to support the analysis and we also present a novel application of the dual-sparse regularized randomized reduction methods to reducing the communication cost of distributed learning from large-scale high-dimensional data.

cs.LG↗

arXiv2015

Fast Sparse Least-Squares Regression with Non-Asymptotic Guarantees

In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a low-dimensional space. In particular, we propose to apply the JL transforms to the data matrix and the target vector and then to solve a sparse least-squares problem on the compressed data with a {\it slightly larger regularization parameter}. Theoretically, we establish the optimization error bound of the learned model for two different sparsity-inducing regularizers, i.e., the elastic net and the $\ell_1$ norm. Compared with previous relevant work, our analysis is {\it non-asymptotic and exhibits more insights} on the bound, the sample complexity and the regularization. As an illustration, we also provide an error bound of the {\it Dantzig selector} under JL transforms.

math.ST↗

arXiv2015

Intrinsic transparent conductors without doping

Transparent conductors (TC's) combine the usually contraindicated properties of electrical conductivity with optical transparency and are generally made by starting with a transparent insulator and making it conductive via heavy doping, an approach that generally faces severe 'doping bottlenecks'. We propose a different idea for TC design-starting with a metallic conductor and designing transparency by control of intrinsic interband transitions and intraband plasmonic frequency. We identify the specific design principles for three such prototypical intrinsic TC classes and then search computationally for materials that satisfy them. Remarkably, one of the intrinsic TC, Ag3Al22O34, is predicted also to be a prototype 3D compounds that manifest natural 2D electron gas (2DEG) regions with very high electron density and conductivity.

cond-mat.mtrl-sci↗