MDR Codes: A New Class of RAID-6 Codes with Optimal Rebuilding and Encoding

As storage systems grow in size, device failures happen more frequently than ever before. Given the commodity nature of hard drives employed, a storage system needs to tolerate a certain number of disk failures while maintaining data integrity, and to recover lost data with minimal interference to normal disk I/O operations. RAID-6, which can tolerate up to two disk failures with the minimum redundancy, is becoming widespread. However, traditional RAID-6 codes suffer from high disk I/O overhead during recovery. In this paper, we propose a new family of RAID-6 codes, the Minimum Disk I/O Repairable (MDR) codes, which achieve the optimal disk I/O overhead for single failure recoveries. Moreover, we show that MDR codes can be encoded with the minimum number of bit-wise XOR operations. Simulation results show that MDR codes help to save about half of disk read operations than traditional RAID-6 codes, and thus can reduce the recovery time by up to 40%.Comment: Accepted version. Please refer to http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6804945 for the published version. 0733-8716/14/$31.00 \c{opyright} 2014 IEE

Escape dynamics based on bounded rationality

The bounded rationality plays a vital role in the collective behavior of the evacuation process. Also investigating human behavior in such an extreme situation is a continuing concern within social psychology. In this paper, we construct a cellular automaton (CA) model for the escape dynamics, and the bounded rational behavior induced by heterogeneous information is introduced. The non-trivial behavior shows in the replicator dynamics method with mean field approximation, where people's perception of the distribution of population and velocity is reduced to an average value in a certain direction. Analyzing the escape efficiency shows that under the premise of rationality, the bounded rational strategy can get higher performance. Interestingly, a quantifiable meta-stable state appears in the escape process, and the escape time is power-law dependent on system size.Comment: 11 pages, 10 figures. Some corrections in the text were made. Submitted to Physica

Estimating Net Effects of Treatments in Treatment Sequence without the Assumption of Strongly Ignorable Treatment Assignment

In sequential causal inference, one estimates the causal net effect of treatment in treatment sequence on an outcome after last treatment in the presence of time-dependent covariates between treatments, improves the estimation by the untestable assumption of strongly ignorable treatment assignment, and obtains consistent but non-genuine likelihood-based estimate. In this article, we introduce the net effect of treatment as parameter for the conditional distribution of outcome given all treatments and time-dependent covariates and show that it is equal to the causal net effect of treatment under the assumption of strongly ignorable treatment assignment. As a result, we can estimate the net effect of treatment and evaluate its causal interpretation in two separate steps. The first step is fucus of this article while the second step can be accomplished by usual sensitivity analyses. We construct point parametrization for the conditional outcome distribution in which the parameters of interest are the point effects of single-point treatments. With point parametrization and without the untestable assumption, we estimate the net effect of treatment by maximum likelihood, improve the estimation by testable pattern of the net effect of treatment, and obtain unbiased consistent maximum-likelihood estimate for the net effect of treatment with finite-dimensional pattern.Comment: arXiv admin note: substantial text overlap with arXiv:1411.119

Agent-based opinion formation modeling in social network: a perspective of social psychology

Most previous works on opinion modeling lack the simultaneous study of individual mental activity and group behavior. This paper is motivated to propose an agent-based online opinion formation model based on attitude change theory, group behavior theory and evolutionary game theory in the perspective of sociology and psychology. In this model, there are three factors influencing the persuasion process, including credibility of the leaders, characteristic of the recipient, and group environment. The proposed model is applied to Twitter to analyze the influence of topic type, parameter changing, and opinion leaders on opinion formation. Experimental results show that the opinion evolution of controversial topic shows greater uncertainty and sustainability. The ratio of benefit to cost has a significant impact on opinion formation and a moderate ratio will result in the longest relaxation time or most unified global opinions. Furthermore, celebrities with a large number of followers are more capable of influencing public opinion than experts. This paper enriches the researches on opinion formation modeling, and the results provide managerial insights for business on public relations and market prediction.Comment: 29 pages,7 figures and 4 tables, accepted by Informs Annual Meeting 201

The equivalent classical metrics on the Cartan-Hartogs Domains

In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, we prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau's Schwarz lemma we prove that the Bergman metric is equivalent to the Einstein-K\"ahler metric. That means the Yau's conjecture is true on Cartan-Hartogs domain.Comment: 19 page

A novel algorithm to get the Fourier power spectra of a real sequence

For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative sequence. Based on the relation of discrete Fourier transforms between the two sequences, the features of Fourier power spectra of the integer and fractional periods for a real sequence have been investigated. It has proved mathematically that after calculating the Fourier power spectrum at an integer period, the Fourier power spectra of the fractional periods associated this integer period can be easily represented by the computational result of the Fourier power spectrum at the integer period for the sequence. A computational experience using a protein sequence shows that some of the computed results are a kind of Fourier power spectra corresponding to new frequencies which can't be obtained from the traditional discrete Fourier transform. Therefore, the algorithm would be a new realization method for discrete Fourier transform of the real sequence

Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories

We construct higher derivative supervertices in an effective theory of maximal supergravity in various dimensions, in the super spinor helicity formalism, and derive non-renormalization conditions on up to 14-derivative order couplings from supersymmetry. These non-renormalization conditions include Laplace type equations on the coefficients of $R^4$, $D^4R^4$, and $D^6R^4$ couplings. We also find additional constraining equations, which are consistent with previously known results in the effective action of toroidally compactified type II string theory, and elucidate many features thereof.Comment: 52 pages, 6 figures, reference added, section 3 expanded and section 5 restructure

Constraining Higher Derivative Supergravity with Scattering Amplitudes

We study supersymmetry constraints on higher derivative deformations of type IIB supergravity by consideration of superamplitudes. Combining constraints of on-shell supervertices and basic results from string perturbation theory, we give a simple argument for the non-renormalization theorem of Green and Sethi, and some of its generalizations.Comment: 9 pages, 2 figures; references ad

The Time Dimension of Science: Connecting the Past to the Future

A central question in science of science concerns how time affects citations. Despite the long-standing interests and its broad impact, we lack systematic answers to this simple yet fundamental question. By reviewing and classifying prior studies for the past 50 years, we find a significant lack of consensus in the literature, primarily due to the coexistence of retrospective and prospective approaches to measuring citation age distributions. These two approaches have been pursued in parallel, lacking any known connections between the two. Here we developed a new theoretical framework that not only allows us to connect the two approaches through precise mathematical relationships, it also helps us reconcile the interplay between temporal decay of citations and the growth of science, helping us uncover new functional forms characterizing citation age distributions. We find retrospective distribution follows a lognormal distribution with exponential cutoff, while prospective distribution is governed by the interplay between a lognormal distribution and the growth in the number of references. Most interestingly, the two approaches can be connected once rescaled by the growth of publications and citations. We further validate our framework using both large-scale citation datasets and analytical models capturing citation dynamics. Together this paper presents a comprehensive analysis of the time dimension of science, representing a new empirical and theoretical basis for all future studies in this area.Comment: To appear in Journal of Informetric

Life Span of Solutions for a Semilinear Heat Equation with Initial Data Non-Rarefied at ∞\infty

We study the Cauchy problem for a semilinear heat equation with initial data non-rarefied at $\infty$. Our interest lies in the discussion of the effect of the non-rarefied factors on the life span of solutions, and some sharp estimates on the life span is established.Comment: 15 page