ECENT advances in photometric technologies have facilitated the proliferation of extensive astronomical surveys such as MACHO [1], OGLE [2], and recently Pan-STARRS [3]. A light curve is a time series in which the measured phenomenon corresponds to the brightness (magnitude or flux) of a stellar object. Light curves are the basic tool for the analysis of variable stars [4], whose brightness varies through time due to internal physical processes, or to external factors such as interactions with other astronomical objects. Some variable stars, such as eclipsing binaries (EB), cepheids, and RR Lyrae, exhibit periodic behaviors that are reflected on their corresponding light curves. For example, EB stars are systems composed of two stars, whose brightness shows periodic variations due to the mutual eclipses between them. The period of a light curve is a key parameter for classifying variable stars [5], [6], and estimating other parameters such as mass and distance to Earth [7]. Light curves are unevenly sampled due to constraints on the observation schedules: the day-night cycle, weather conditions, cali-Manuscript received February 02, 2011; revised March 28, 2011; accepted March 30, 2011.

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities. The stochastic blockmodel [Social Networks 5 (1983) 109--137] is a social network model with well-defined communities; each node is a member of one community. For a network generated from the Stochastic Blockmodel, we bound the number of nodes "misclustered" by spectral clustering. The asymptotic results in this paper are the first clustering results that allow the number of clusters in the model to grow with the number of nodes, hence the name high-dimensional. In order to study spectral clustering under the stochastic blockmodel, we first show that under the more general latent space model, the eigenvectors of the normalized graph Laplacian asymptotically converge to the eigenvectors of a "population" normalized graph Laplacian. Aside from the implication for spectral clustering, this provides insight into a graph visualization technique. Our method of studying the eigenvectors of random matrices is original.

Many of the conditions in which technology is required to adapt cannot be anticipated during its design stage, creating a significant challenge for the designer. Inspired by the study of a range of biological systems, we propose that degeneracy - the realization of multiple, functionally versatile components with contextually overlapping functional redundancy - will support adaptation in technologies because it effects pervasive flexibility, evolutionary innovation, and homeostatic robustness. We provide examples of degeneracy in a number of rudimentary living technologies from military socio-technical systems to swarm robotics and we present design principles - including protocols, loose regulatory coupling, and functional versatility - that allow degeneracy to arise in both biological and man-made systems. Keywords: pervasive adaptation, degeneracy, living technologies, distributed robustness 1. Introduction Unanticipated requirements can arise throughout a technology's life and are a notoriously difficult engineering problem and a challenging research topic because past routines and contingency plans will be of limited utility. Dealing with new challenges requires exploration, diversity, and bethedging: principles that are common to any discipline in which responses to novelty determine competitive success.

Adaptation to changing environments is a hallmark of biological systems. Diversity in traits is necessary for adaptation and can influence the survival of a population faced with novelty. In habitats that remain stable over many generations, stabilizing selection reduces trait differences within populations, thereby appearing to remove the diversity needed for heritable adaptive responses in new environments. Paradoxically, field studies have documented numerous populations under long periods of stabilizing selection and evolutionary stasis that have rapidly evolved under changed environmental conditions. In this article, we review how cryptic genetic variation (CGV) resolves this diversity paradox by allowing populations in a stable environment to gradually accumulate hidden genetic diversity that is revealed as trait differences when environments change. Instead of being in conflict, environmental stasis supports CGV accumulation and thus appears to facilitate rapid adaptation in new environments as suggested by recent CGV studies. Similarly, degeneracy has been found to support both genetic and non-genetic adaptation at many levels of biological organization. Degenerate, as opposed to diverse or redundant, ensembles appear functionally redundant in certain environmental contexts but functionally diverse in others. CGV and degeneracy paradigms for adaptation are integrated in this review, revealing a common set of principles that support adaptation at multiple levels of biological organization. Though a discussion of simulation studies, molecular-based experimental systems, principles from population genetics, and field experiments, we demonstrate that CGV and degeneracy reflect complementary top-down and bottom-up, respectively, conceptualizations of the same basic phenomenon and arguably capture a universal feature of biological adaptive processes.

The importance of algorithm portfolio techniques for SAT has long been noted, and a number of very successful systems have been devised, including the most successful one --- SATzilla. However, all these systems are quite complex (to understand, reimplement, or modify). In this paper we propose a new algorithm portfolio for SAT that is extremely simple, but in the same time so efficient that it outperforms SATzilla. For a new SAT instance to be solved, our portfolio finds its k-nearest neighbors from the training set and invokes a solver that performs the best at those instances. The main distinguishing feature of our algorithm portfolio is the locality of the selection procedure --- the selection of a SAT solver is based only on few instances similar to the input one.

The sparsity is controlled by the values of k and can be viewed as a design parameter. In machine learning applications, e.g., principal component analysis, this problem is motivated from the following perturbation formulation of matrix A: A Ā E, (1.2) where A is the empirical covariance matrix, Ā is the true covariance matrix, and E is a random perturbation due to having only a finite number of empirical samples. If we assume that the largest eigenvector x of Ā is sparse, then a natural question is to recover x from the noisy observation A when the error E is "small". In this context, the problem (1.1) is also referred to as sparse principal component analysis (sparse PCA). 1 In general, problem (1.1) is non-convex. In fact, it is also NPhard because it can be reduced to the subset selection problem for ordinary least squares regression (Moghaddam et al., 2006), which is known to be NP hard.

It is now well known that decentralised optimisation can be formulated as a potential game, and game-theoretical learning algorithms can be used to find an optimum. One of the most common learning techniques in game theory is fictitious play. However fictitious play is founded on an implicit assumption that opponents' strategies are stationary. We present a novel variation of fictitious play that allows the use of a more realistic model of opponent strategy. It uses a heuristic approach, from the online streaming data literature, to adaptively update the weights assigned to recently observed actions. We compare the results of the proposed algorithm with those of stochastic and geometric fictitious play in a simple strategic form game, a vehicle target assignment game and a disaster management problem. In all the tests the rate of convergence of the proposed algorithm was similar or better than the variations of fictitious play we compared it with. The new algorithm therefore improves the performance of game-theoretical learning in decentralised optimisation.

Unbalanced data arises in many learning tasks such as clustering of multi-class data, hierarchical divisive clustering and semisupervised learning. Graph-based approaches are popular tools for these problems. Graph construction is an important aspect of graph-based learning. We show that graph-based algorithms can fail for unbalanced data for many popular graphs such as k-NN, \epsilon-neighborhood and full-RBF graphs. We propose a novel graph construction technique that encodes global statistical information into node degrees through a ranking scheme. The rank of a data sample is an estimate of its p-value and is proportional to the total number of data samples with smaller density. This ranking scheme serves as a surrogate for density; can be reliably estimated; and indicates whether a data sample is close to valleys/modes. This rank-modulated degree(RMD) scheme is able to significantly sparsify the graph near valleys and provides an adaptive way to cope with unbalanced data. We then theoretically justify our method through limit cut analysis. Unsupervised and semi-supervised experiments on synthetic and real data sets demonstrate the superiority of our method.

Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in this model when the size of the training set is very small. As an alternative, we propose a provably convergent EP algorithm (PC-EP). PC-EP is proved to minimize an energy function which, under some constraints, is bounded from below and whose stationary points coincide with the solution of R-EP. Experiments with synthetic data indicate that when R-EP does not converge, the approximation generated by PC-EP is often better. By contrast, when R-EP converges, both methods perform similarly.

This work presents Drake, a dynamic executive for temporal plans with choice. Dynamic plan execution strategies allow an autonomous agent to react quickly to unfolding events, improving the robustness of the agent. Prior work developed methods for dynamically dispatching Simple Temporal Networks, and further research enriched the expressiveness of the plans executives could handle, including discrete choices, which are the focus of this work. However, in some approaches to date, these additional choices induce significant storage or latency requirements to make flexible execution possible. Drake is designed to leverage the low latency made possible by a preprocessing step called compilation, while avoiding high memory costs through a compact representation. We leverage the concepts of labels and environments, taken from prior work in Assumption-based Truth Maintenance Systems (ATMS), to concisely record the implications of the discrete choices, exploiting the structure of the plan to avoid redundant reasoning or storage. Our labeling and maintenance scheme, called the Labeled Value Set Maintenance System, is distinguished by its focus on properties fundamental to temporal problems, and, more generally, weighted graph algorithms. In particular, the maintenance system focuses on maintaining a minimal representation of non-dominated constraints. We benchmark Drake's performance on random structured problems, and find that Drake reduces the size of the compiled representation by a factor of over 500 for large problems, while incurring only a modest increase in run-time latency, compared to prior work in compiled executives for temporal plans with discrete choices.