Shortest path routing algorithm for hierarchical interconnection network-on-chip

Interconnection networks play a significant role in efficient on-chip communication for multicore systems. This paper introduces a new interconnection topology called the Hierarchical Cross Connected Recursive network (HCCR) and a shortest path routing algorithm for the HCCR. Proposed topology offers a high degree of regularity, scalability, and symmetry with a reduced number of links and node degree. A unique address encoding scheme is proposed for hierarchical graphical representation of HCCR networks, and based on this scheme a shortest path routing algorithm is devised. The algorithm requires 5(k-1) time where k=logn4-2 and k>0, in worst case to determine the next node along the shortest path

Microscopic activity patterns in the Naming Game

The models of statistical physics used to study collective phenomena in some interdisciplinary contexts, such as social dynamics and opinion spreading, do not consider the effects of the memory on individual decision processes. On the contrary, in the Naming Game, a recently proposed model of Language formation, each agent chooses a particular state, or opinion, by means of a memory-based negotiation process, during which a variable number of states is collected and kept in memory. In this perspective, the statistical features of the number of states collected by the agents becomes a relevant quantity to understand the dynamics of the model, and the influence of topological properties on memory-based models. By means of a master equation approach, we analyze the internal agent dynamics of Naming Game in populations embedded on networks, finding that it strongly depends on very general topological properties of the system (e.g. average and fluctuations of the degree). However, the influence of topological properties on the microscopic individual dynamics is a general phenomenon that should characterize all those social interactions that can be modeled by memory-based negotiation processes.Comment: submitted to J. Phys.

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.This research is supported by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2014- 52291-P, MTM2017-84199-P)

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples --- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Neural Techniques for German Dependency Parsing

Syntactic parsing is the task of analyzing the structure of a sentence based on some predefined formal assumption. It is a key component in many natural language processing (NLP) pipelines and is of great benefit for natural language understanding (NLU) tasks such as information retrieval or sentiment analysis. Despite achieving very high results with neural network techniques, most syntactic parsing research pays attention to only a few prominent languages (such as English or Chinese) or language-agnostic settings. Thus, we still lack studies that focus on just one language and design specific parsing strategies for that language with regards to its linguistic properties. In this thesis, we take German as the language of interest and develop more accurate methods for German dependency parsing by combining state-of-the-art neural network methods with techniques that address the specific challenges posed by the language-specific properties of German. Compared to English, German has richer morphology, semi-free word order, and case syncretism. It is the combination of those characteristics that makes parsing German an interesting and challenging task. Because syntactic parsing is a task that requires many levels of language understanding, we propose to study and improve the knowledge of parsing models at each level in order to improve syntactic parsing for German. These levels are: (sub)word level, syntactic level, semantic level, and sentence level. At the (sub)word level, we look into a surge in out-of-vocabulary words in German data caused by compounding. We propose a new type of embeddings for compounds that is a compositional model of the embeddings of individual components. Our experiments show that character-based embeddings are superior to word and compound embeddings in dependency parsing, and compound embeddings only outperform word embeddings when the part-of-speech (POS) information is unavailable. Thus, we conclude that it is the morpho-syntactic information of unknown compounds, not the semantic one, that is crucial for parsing German. At the syntax level, we investigate challenges for local grammatical function labeler that are caused by case syncretism. In detail, we augment the grammatical function labeling component in a neural dependency parser that labels each head-dependent pair independently with a new labeler that includes a decision history, using Long Short-Term Memory networks (LSTMs). All our proposed models significantly outperformed the baseline on three languages: English, German and Czech. However, the impact of the new models is not the same for all languages: the improvement for English is smaller than for the non-configurational languages (German and Czech). Our analysis suggests that the success of the history-based models is not due to better handling of long dependencies but that they are better in dealing with the uncertainty in head direction. We study the interaction of syntactic parsing with the semantic level via the problem of PP attachment disambiguation. Our motivation is to provide a realistic evaluation of the task where gold information is not available and compare the results of disambiguation systems against the output of a strong neural parser. To our best knowledge, this is the first time that PP attachment disambiguation is evaluated and compared against neural dependency parsing on predicted information. In addition, we present a novel approach for PP attachment disambiguation that uses biaffine attention and utilizes pre-trained contextualized word embeddings as semantic knowledge. Our end-to-end system outperformed the previous pipeline approach on German by a large margin simply by avoiding error propagation caused by predicted information. In the end, we show that parsing systems (with the same semantic knowledge) are in general superior to systems specialized for PP attachment disambiguation. Lastly, we improve dependency parsing at the sentence level using reranking techniques. So far, previous work on neural reranking has been evaluated on English and Chinese only, both languages with a configurational word order and poor morphology. We re-assess the potential of successful neural reranking models from the literature on English and on two morphologically rich(er) languages, German and Czech. In addition, we introduce a new variation of a discriminative reranker based on graph convolutional networks (GCNs). Our proposed reranker not only outperforms previous models on English but is the only model that is able to improve results over the baselines on German and Czech. Our analysis points out that the failure is due to the lower quality of the k-best lists, where the gold tree ratio and the diversity of the list play an important role

Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))