56 research outputs found
Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
Kinetically constrained lattice models of glasses introduced by Kob and
Andersen (KA) are analyzed. It is proved that only two behaviors are possible
on hypercubic lattices: either ergodicity at all densities or trivial
non-ergodicity, depending on the constraint parameter and the dimensionality.
But in the ergodic cases, the dynamics is shown to be intrinsically cooperative
at high densities giving rise to glassy dynamics as observed in simulations.
The cooperativity is characterized by two length scales whose behavior controls
finite-size effects: these are essential for interpreting simulations. In
contrast to hypercubic lattices, on Bethe lattices KA models undergo a
dynamical (jamming) phase transition at a critical density: this is
characterized by diverging time and length scales and a discontinuous jump in
the long-time limit of the density autocorrelation function. By analyzing
generalized Bethe lattices (with loops) that interpolate between hypercubic
lattices and standard Bethe lattices, the crossover between the dynamical
transition that exists on these lattices and its absence in the hypercubic
lattice limit is explored. Contact with earlier results are made via analysis
of the related Fredrickson-Andersen models, followed by brief discussions of
universality, of other approaches to glass transitions, and of some issues
relevant for experiments.Comment: 59 page
Topological Properties and Broadcasting Algorithmsof the Generalized-Star Cube
Abstract—In this research, another version of the star cube called the generalized-star cube, GSC(n, k, m), is presented as a three level interconnection topology. GSC(n, k, m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star graph with an m-cube. Because there are three parameters m, n, and k, the network size of GSC(n, k, m) can be changed more flexibly than the star graph, star-cube, and (n, k)-star graph. We first investigate the topological properties of the GSC(n, k, m), such as the node degree, diameter, average distance, and cost. Also, the regularity and node symmetry of the GSC(n, k, m) are derived.Then, we illustrate the broadcasting algorithms for both of the single-port and all-port models. To develop these algorithms, we use the spanning binomial tree, the neighbourhood broadcasting algorithm, and the minimum dominating set. The complexities of the broadcasting algorithms are also examined
Properties and algorithms of the (n, k)-star graphs
The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative
to the n-star topology in parallel computation. The (n, k )-star has significant
advantages over the n-star which itself was proposed as an attractive alternative to
the popular hypercube. The major advantage of the (n, k )-star network is its scalability,
which makes it more flexible than the n-star as an interconnection network. In
this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as
well as developing parallel algorithms that run on this network.
The basic topological properties of the (n, k )-star are first studied. These are
useful since they can be used to develop efficient algorithms on this network. We then
study the (n, k )-star network from algorithmic point of view. Specifically, we will
investigate both fundamental and application algorithms for basic communication,
prefix computation, and sorting, etc.
A literature review of the state-of-the-art in relation to the (n, k )-star network as
well as some open problems in this area are also provided
1-perfect codes over dual-cubes
V magistrskem delu spoznamo kodiranje, kode in popolne kode, njihovo posplošitev na grafe ter povezavo med 1-popolnimi kodami in dominantno množico v grafih. Opišemo hiperkocke in dokažemo nekaj njihovih lastnosti. Spoznamo grafe dualnih kock, ki so sorodni hiperkockam. Pokažemo, katere lastnosti dualna kocka podeduje od ustrezne hiperkocke, in tiste, ki so pomembne za tvorjenje 1-popolne kode. Ugotovimo, da je dualna kocka sestavljena iz induciranih hiperkock. Le-te namreč vsebujejo Hammingove kode, ki so 1-popolne kode in to vzamemo kot osnovo za tvorjenje 1-popolne kode v dualni kocki. Nato Hammingove kode z nadaljnjimi algoritmi preoblikujemo tako, da res nastane 1-popolna koda v dualni kocki. S tem dokažemo izrek, da dualna kocka vsebuje 1-popolno kodo natanko tedaj, ko je za . Dobljeni rezultat uporabimo pri postavljanju meja za dominanto število v dualni kocki s poljubnim parametrom.In this thesis we introduce coding, codes and perfect codes, their generalization to graphs, and a connection between 1-perfect codes and dominating sets in graphs. We describe hypercubes and prove some of their characteristics. Dual-cubes, which are similar to hypercubes, are introduced. We show the characteristics that are inherited from hypercubes and some that are important for generating 1-perfect codes. We prove that the dual-cube consists of induced hypercubes. Hypercubes contain Hamming codes which are 1-perfect codes, and this is taken as a basis of creating 1-perfect codes in dual-cubes. Hamming codes are further transformed with algorithms that eventually lead to 1-perfect codes. With this we show that the dual-cube admits a 1-perfect code if and only if for . This result is used for proving tight bounds on the domination number of dual-cube with an arbitrary parameter
Communication Patterns for Randomized Algorithms
Examples of large scale networks include the Internet, peer-to-peer networks, parallel computing systems, cloud computing systems, sensor networks, and social networks. Efficient dissemination of information in large networks such as these is a funda- mental problem. In many scenarios the gathering of information by a centralised controller can be impractical. When designing and analysing distributed algorithms we must consider the limitations imposed by the heterogeneity of devices in the networks. Devices may have limited computational ability or space. This makes randomised algorithms attractive solutions. Randomised algorithms can often be simpler and easier to implement than their deterministic counterparts. This thesis analyses the effect of communication patterns on the performance of distributed randomised algorithms. We study randomized algorithms with application to three different areas.
Firstly, we study a generalization of the balls-into-bins game. Balls into bins games have been used to analyse randomised load balancing. Under the Greedy[d] allocation scheme each ball queries the load of d random bins and is then allocated to the least loaded of them. We consider an infinite, parallel setting where expectedly λn balls are allocated in parallel according to the Greedy[d] allocation scheme in to n bins and subsequently each non-empty bin removes a ball. Our results show that for d = 1,2, the Greedy[d] allocation scheme is self-stabilizing and that in any round the maximum system load for high arrival rates is exponentially smaller for d = 2 compared to d = 1 (w.h.p).
Secondly, we introduce protocols that solve the plurality consensus problem on arbitrary graphs for arbitrarily small bias. Typically, protocols depend heavily on the employed communication mechanism. Our protocols are based on an interest- ing relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that are both time and space efficient and generalize the state of the art for a large range of problem parameters.
Finally, we investigate the effect of restricting the communication of the classical PULL algorithm for randomised rumour spreading. Rumour spreading (broadcast) is a fundamental task in distributed computing. Under the classical PULL algo- rithm, a node with the rumour that receives multiple requests is able to respond to all of them in a given round. Our model restricts nodes such that they can re- spond to at most one request per round. Our results show that the restricted PULL algorithm is optimal for several graph classes such as complete graphs, expanders, random graphs and several Cayley graphs
Incremental approach to particle swarm assisted function optimization
Ph.DDOCTOR OF PHILOSOPH
Design space exploration of RF-circuit blocks
ii iii Acknowledgments This thesis was written in the framework of an internship at NXP Semiconductors. It describes the results of a six months master project. I was supervised by Prof. Dr. W.H.A. Schilders of NXP Semiconductors and the Technical University Eindhoven and furthermore, by Dr. ir. J. A. Croon of NXP Semiconductors. Herewith, I want to express my deep gratitude to Prof. Schilders, who has guided me during the project and for proofreading of the thesis. Furthermore, I want to thank Dr. Croon sincerely for the helpful discussions, for the detailed corrections of the thesis and furthermore for the interesting introduction to semiconductor device modeling. Additionally, I want to thank Univ.-Prof. Dipl.-Ing. Dr. H. Gfrerer of the Johannes Kepler University Linz for reviewing this work and for his useful suggestions during the project. iv vContent
Adaptive Search and Constraint Optimisation in Engineering Design
The dissertation presents the investigation and development of novel adaptive
computational techniques that provide a high level of performance when searching
complex high-dimensional design spaces characterised by heavy non-linear constraint
requirements. The objective is to develop a set of adaptive search engines that will allow
the successful negotiation of such spaces to provide the design engineer with feasible high
performance solutions.
Constraint optimisation currently presents a major problem to the engineering designer and
many attempts to utilise adaptive search techniques whilst overcoming these problems are
in evidence. The most widely used method (which is also the most general) is to
incorporate the constraints in the objective function and then use methods for
unconstrained search. The engineer must develop and adjust an appropriate penalty
function. There is no general solution to this problem neither in classical numerical
optimisation nor in evolutionary computation. Some recent theoretical evidence suggests
that the problem can only be solved by incorporating a priori knowledge into the search
engine.
Therefore, it becomes obvious that there is a need to classify constrained optimisation
problems according to the degree of available or utilised knowledge and to develop search
techniques applicable at each stage. The contribution of this thesis is to provide such a
view of constrained optimisation, starting from problems that handle the constraints on the
representation level, going through problems that have explicitly defined constraints (i.e.,
an easily computed closed form like a solvable equation), and ending with heavily
constrained problems with implicitly defined constraints (incorporated into a single
simulation model). At each stage we develop applicable adaptive search techniques that
optimally exploit the degree of available a priori knowledge thus providing excellent
quality of results and high performance. The proposed techniques are tested using both well
known test beds and real world engineering design problems provided by industry.British Aerospace,
Rolls Royce and Associate
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