Fast Consensus under Eventually Stabilizing Message Adversaries

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of $2D+1$ for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter $D$, as well as a simple algorithm that matches this bound. It effectively halves the termination time $4D+1$ achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference

Locality-Preserving Oblivious RAM

Oblivious RAMs, introduced by Goldreich and Ostrovsky [JACM\u2796], compile any RAM program into one that is ``memory oblivious\u27\u27, i.e., the access pattern to the memory is independent of the input. All previous ORAM schemes, however, completely break the locality of data accesses (for instance, by shuffling the data to pseudorandom positions in memory). In this work, we initiate the study of locality-preserving ORAMs --- ORAMs that preserve locality of the accessed memory regions, while leaking only the lengths of contiguous memory regions accessed. Our main results demonstrate the existence of a locality-preserving ORAM with poly-logarithmic overhead both in terms of bandwidth and locality. We also study the tradeoff between locality, bandwidth and leakage, and show that any scheme that preserves locality and does not leak the lengths of the contiguous memory regions accessed, suffers from prohibitive bandwidth. To the best of our knowledge, before our work, the only works combining locality and obliviousness were for symmetric searchable encryption [e.g., Cash and Tessaro (EUROCRYPT\u2714), Asharov et al. (STOC\u2716)]. Symmetric search encryption ensures obliviousness if each keyword is searched only once, whereas ORAM provides obliviousness to any input program. Thus, our work generalizes that line of work to the much more challenging task of preserving locality in ORAMs

Improved Streaming Algorithm for Dyck(s) Recognition

Keeping in mind, that any context free language can be mapped to a subset of Dyck languages and by seeing various database applications of Dyck, mainly verifying the well-formedness of XML file, we study the randomized streaming algorithms for the recognition of Dyck(s) languages, with s different types of parenthesis. The main motivation of this work is well known space bound for any T-pass streaming algorithm is (√n/T). Let x be the input stream of length n with maximum height hmax. Here we present a single-pass randomized streaming algorithms to decide the membership of x in Dyck(s) using Counting Bloomfilter (CBF) with space O (hmax) bits, ploylog(n) time per letter with two-sided error probability. Two-sided error is because of the false negative and false positives of counting bloomfilter. This algorithms denies the necessity of streaming reduction of Dyck(s) into Dyck(2), that reduces the space even further by the factor of O (log s), compared to those uses streaming reduction. We also present an improved single-pass randomized streaming algorithm for recognizing Dyck(2) with space O (√n) bits, which is the proven lower bound. Time bound is same polylog(n), as other existing algorithms and error is one-sided. In this algorithm, we extended the existing approach of periodically compressing stack information. Existing approach uses two stacks and a linear hash function, instead of this we are using three stacks and same linear hash function to achieve space lower bound of O (√n). We also present another single-pass streaming algorithm with O (hmax) space that uses counting bloomfilter and directly acts on Dyck(s

Dynare: Reference Manual Version 4

Dynare is a software platform for handling a wide class of economic models, in particular dynamic stochastic general equilibrium (DSGE) and overlapping generations (OLG) models. The models solved by Dynare include those relying on the rational expectations hypothesis, wherein agents form their expectations about the future in a way consistent with the model. But Dynare is also able to handle models where expectations are formed differently: on one extreme, models where agents perfectly anticipate the future; on the other extreme, models where agents have limited rationality or imperfect knowledge of the state of the economy and, hence, form their expectations through a learning process. Dynare offers a user-friendly and intuitive way of describing these models. It is able to perform simulations of the model given a calibration of the model parameters and is also able to estimate these parameters given a dataset. Dynare is a free software, which means that it can be downloaded free of charge, that its source code is freely available, and that it can be used for both non-profit and for-profit purposes.Dynare; Numerical methods; Perturbation; Rational expectations

Crystal monoids & crystal bases: rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2

The vertices of any (combinatorial) Kashiwara crystal graph carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components of the crystal. Working on a purely combinatorial and monoid-theoretical level, we prove some foundational results for these crystal monoids, including the observation that they have decidable word problem when their weight monoid is a finite rank free abelian group. The problem of constructing finite complete rewriting systems, and biautomatic structures, for crystal monoids is then investigated. In the case of Kashiwara crystals of types An, Bn, Cn, Dn, and G2 (corresponding to the q-analogues of the Lie algebras of these types) these monoids are precisely the generalised plactic monoids investigated in work of Lecouvey. We construct presentations via finite complete rewriting systems for all of these types using a unified proof strategy that depends on Kashiwara's crystal bases and analogies of Young tableaux, and on Lecouvey's presentations for these monoids. As corollaries, we deduce that plactic monoids of these types have finite derivation type and satisfy the homological finiteness properties left and right FP∞. These rewriting systems are then applied to show that plactic monoids of these types are biautomatic and thus have word problem soluble in quadratic time

Integrating the finite element method and genetic algorithms to solve structural damage detection and design optimisation problems

This thesis documents fundamental new research in to a specific application of structural box-section beams, for which weight reduction is highly desirable. It is proposed and demonstrated that the weight of these beams can be significantly reduced by using advanced, laminated fibre-reinforced composites in place of steel. Of the many issues raised during this investigation two, of particular importance, are considered in detail; (a) the detection and quantification of damage in composite structures and (b) the optimisation of laminate design to maximise the performance of loaded composite structuress ubject to given constraints. It is demonstrated that both these issues can be formulated and solved as optimisation problems using the finite element method, in which an appropriate objective function is minimised (or maximised). In case (a) the difference in static response obtained from a loaded structure containing damage and an equivalent mathematical model of the structure is minimised by iteratively updating the model. This reveals the damage within the model and subsequently allows the residual properties of the damaged structure to be quantified. Within the scope of this work is the ability to resolve damage, that consists of either penny-shaped sub-surface flaws or tearing damage of box-section beams from surface experimental data. In case (b) an objective function is formulated in terms of a given structural response, or combination of responses that is optimised in order to return an optimal structure, rather than just a satisfactory structure. For the solution of these optimisation problems a novel software tool, based on the integration of genetic algorithms and a commercially available finite element (FE) package, has been developed. A particular advantage of the described method is its applicability to a wide range of engineering problems. The tool is described and its effectiveness demonstrated with reference to two inverse damage detection and quantification problems and one laminate design optimisation problem. The tool allows the full suite of functions within the FE software to be used to solve non-convex optimisation problems, formulated in terms of both discrete and continuous variables, without explicitly stating the form of the stiffness matrix. Furthermore, a priori knowledge about the problem may be readily incorporated in to the method

Variational methods with dependence structure

It is a common practice among humans to deduce, to explain and to make predictions based on concepts that are not directly observable. In Bayesian statistics, the underlying propositions of the unobserved latent variables are summarized in the posterior distribution. With the increasing complexity of real-world data and statistical models, fast and accurate inference for the posterior becomes essential. Variational methods, by casting the posterior inference problem in the optimization framework, are widely used for their flexibility and computational efficiency. In this thesis, we develop new variational methods, studying their theoretical properties and applications. In the first part of the thesis, we utilize dependence structures towards addressing fundamental problems in variational inference (VI): posterior uncertainty estimation, convergence properties, and discrete optimization. Though it is flexible, variational inference often underestimates the posterior uncertainty. This is a consequence of the over-simplified variational family. Mean-field variational inference (MFVI), for example, uses a product of independent distributions as a coarse approximation to the posterior. As a remedy, we propose a hierarchical variational distribution with flexible parameterization that can model the dependence structure between latent variables. With a newly derived objective, we show that the proposed variational method can achieve accurate and efficient uncertainty estimation. We further theoretically study the structured variational inference in the setting of the Stochastic Blockmodel (SBM). The variational distribution is constructed with a pairwise structure among the nodes of a graph. We prove that, in a broad density regime and for general random initializations, the estimated class labels by structured VI converge to the ground truth with high probability. Empirically, we demonstrate structured VI is more robust compared with MFVI when the graph is sparse and the signal to noise ratio is low. When the latent variables are discrete, gradient descent based VI often suffers from bias and high variance in the gradient estimation. With correlated random samples, we propose a novel unbiased, low-variance gradient estimator. We demonstrate that under certain constraints, such correlated sampling gives an optimal control variates for the variance reduction. The efficient gradient estimation can be applied to solve a wide range of problems such as the variable selection, reinforcement learning, natural language processing, among others. For the second part of the thesis, we apply variational methods to the study of generalization problems in the meta-learning. When trained over multiple-tasks, we identify that a variety of the meta-learning algorithms implicitly require the tasks to have a mutually-exclusive dependence structure. This prevents the task-level overfitting problem and ensures the fast adaptation of the algorithm in the face of a new task. However, such dependence structure may not exist for general tasks. When the tasks are non-mutually exclusive, we develop new meta-learning algorithms with variational regularization to prevent the task-level overfitting. Consequently, we can expand the meta-learning to the domains which it cannot be effective on before.Statistic

Probabilistic Structural Analysis Methods for select space propulsion system components (PSAM). Volume 3: Literature surveys and technical reports

The technical effort and computer code developed during the first year are summarized. Several formulations for Probabilistic Finite Element Analysis (PFEA) are described with emphasis on the selected formulation. The strategies being implemented in the first-version computer code to perform linear, elastic PFEA is described. The results of a series of select Space Shuttle Main Engine (SSME) component surveys are presented. These results identify the critical components and provide the information necessary for probabilistic structural analysis