Detecting quantum speedup in closed and open systems

We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the proposed measure to several typical closed and open quantum systems, illustrating that quantum coherence (or entanglement) and the memory effect of the environment together can become resources for longitudinally or transversely accelerating dynamical evolution under specific conditions and assumptions.Comment: 7 pages, 4 figures; Accepted for publication in New Journal of Physic

Distributionally Robust Counterpart in Markov Decision Processes

This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and seeks the strategy which maximizes the expected performance under the most adversarial distribution. In particular, we generalize previous study \cite{xu2012distributionally} which concentrates on distribution sets with very special structure to much more generic class of distribution sets, and show that the optimal strategy can be obtained efficiently under mild technical condition. This significantly extends the applicability of distributionally robust MDP to incorporate probabilistic information of uncertainty in a more flexible way.Comment: Added references. Corrected typos. Modified a mistake in Example 2 (Variance). Provided more details of the simulatio

The magnetospheric activity of bare strange quark stars

In Ruderman & Sutherland (RS75) model, the normal neutron stars as pulsars bear a severe problem, namely the binding energy problem that both ions (e.g., ${}_{26}^{56}$Fe) and electrons on normal neutron star surface can be pulled out freely by the unipolar generator induced electric field so that sparking on polar cap can hardly occur. {\bf This problem could be solved within the Partially Screened Gap (PSG) model in the regime of neutron stars}. However, in this paper we extensively study this problem in a bare strange quark star (BSS) model. We find that the huge potential barrier built by the electric field in the vacuum gap above polar cap could usually prevent electrons from streaming into the magnetosphere unless the electric potential of a pulsar is sufficiently lower than that at infinite interstellar medium. Other processes, such as the diffusion and thermionic emission of electrons have also been included here. Our conclusions are as follows: both positive and negative particles on a BSS's surface would be bound strongly enough to form a vacuum gap above its polar cap as long as the BSS is not charged (or not highly negative charged), and multi-accelerators could occur in a BSS's magnetosphere. Our results would be helpful to distinguish normal neutron stars and bare quark stars through pulsar's magnetospheric activities.Comment: 6 pages, 4 figures, 3 tables; accepted for publication in MNRA

Categorization Axioms for Clustering Results

Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging applications. Therefore, it is very worth establishing an unified axiomatic framework for data clustering. In the literature, it is an open problem and has been proved very challenging. In this paper, clustering results are axiomatized by assuming that an proper clustering result should satisfy categorization axioms. The proposed axioms not only introduce classification of clustering results and inequalities of clustering results, but also are consistent with prototype theory and exemplar theory of categorization models in cognitive science. Moreover, the proposed axioms lead to three principles of designing clustering algorithm and cluster validity index, which follow many popular clustering algorithms and cluster validity indices.Comment: 16 page

A Note on (3,1)-Choosable Toroidal Graphs

An $(L,d)^*$-coloring is a mapping $\phi$ that assigns a color $\phi(v)\in L(v)$ to each vertex $v\in V(G)$ such that at most $d$ neighbors of $v$ receive colore $\phi(v)$. A graph is called $(m,d)^*$-choosable, if $G$ admits an $(L,d)^*$-coloring for every list assignment $L$ with $|L(v)|\geq m$ for all $v\in V(G)$. In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles and $l$-cycles for some $l \in \{5,7\}$, is $(3,1)^*$-choosable.Comment: 7 page

Central-limit approach to risk-aware Markov decision processes

Whereas classical Markov decision processes maximize the expected reward, we consider minimizing the risk. We propose to evaluate the risk associated to a given policy over a long-enough time horizon with the help of a central limit theorem. The proposed approach works whether the transition probabilities are known or not. We also provide a gradient-based policy improvement algorithm that converges to a local optimum of the risk objective.Comment: arXiv admin note: text overlap with arXiv:1403.6530 by other author

An adaptive gradient method for computing generalized tensor eigenpairs

High order tensor arises more and more often in signal processing,data analysis, higher-order statistics, as well as imaging sciences. In this paper, an adaptive gradient (AG) method is presented for generalized tensor eigenpairs. Global convergence and linear convergence rate are established under some suitable conditions. Numerical results are reported to illustrate the efficiency of the proposed method. Comparing with the GEAP method, an adaptive shifted power method proposed by Tamara G. Kolda and Jackson R. Mayo [SIAM J. Matrix Anal. Appl., 35 (2014), pp. 1563-1581], the AG method is much faster and could reach the largest eigenpair with a higher probability

Incentivizing Users of Data Centers Participate in The Demand Response Programs via Time-Varying Monetary Rewards

Demand response is widely employed by today's data centers to reduce energy consumption in response to the increasing of electricity cost. To incentivize users of data centers participate in the demand response programs, i.e., breaking the "split incentive" hurdle, some prior researches propose market-based mechanisms such as dynamic pricing and static monetary rewards. However, these mechanisms are either intrusive or unfair. In this paper, we use time-varying rewards to incentivize users, who have flexible deadlines and are willing to trading performance degradation for monetary rewards, grant time-shifting of their requests. With a game-theoretic framework, we model the game between a single data center and its users. Further, we extend our design via integrating it with two other emerging practical demand response strategies: server shutdown and local renewable energy generation. With real-world data traces, we show that a DC with our design can effectively shed its peak electricity load and overall electricity cost without reducing its profit, when comparing it with the current practice where no incentive mechanism is established

Spectral projected gradient methods for generalized tensor eigenvalue complementarity problem

This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We investigate two monotone ascent spectral projected gradient (SPG) methods for TEiCP. We also present a shifted scaling-and-projection algorithm (SPA), which is a great improvement of the original SPA method proposed by Ling, He and Qi [Comput. Optim. Appl., DOI 10.1007/s10589-015-9767-z]. Numerical comparisons with some existed gradient methods in the literature are reported to illustrate the efficiency of the proposed methods.Comment: arXiv admin note: text overlap with arXiv:1601.0139

Log-Harnack Inequality for Gruschin Type Semigroups

By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups whose generator might be both degenerate and non-Lipschitzian.Comment: 14 page