18,609 research outputs found
Generalized Connectors
An -connector is an acyclic directed graph having inputs and outputs and satisfying the following condition: given any one-to-one correspondence between inputs and distinct outputs, there exists a set of vertex-disjoint paths that join each input to the corresponding output. It is known that the minimum possible number of edges in an -connector lies between lower and upper bounds that are asymptotic to and respectively. A generalized -connector satisfies the following stronger condition: given any one-to-many correspondence between inputs and disjoint sets of outputs, there exists a set of vertex-disjoint trees that join each input to the corresponding set of outputs. It is shown that the minimum number of edges in a generalized -connector is asymptotic to the minimum number in an -connector
Some Graph-Colouring Theorems with Applications to Generalized Connection Networks
With the aid of a new graph-colouring theorem, we give a simple explicit construction for generalized n-connectors with 2k - 1 stages and O( n1 + 1 / k (log n )( k - 1)/ 2 ) edges. This is asymptotically the best explicit construction known for generalized connectors
Practical Wide-Sense Nonblocking Generalized Connectors
In this note, we show that wide-sense nonblocking networks can be obtained by cascading a pair of Cantor networks or a pair of Clos networks. The only constraint placed on the routing algorithms is that branching be restricted to the second network in the cascade. This result yields practical network for multipoint communication with complexities O(N(logN)2 and O(N1+1/r)
A Robust Parsing Algorithm For Link Grammars
In this paper we present a robust parsing algorithm based on the link grammar
formalism for parsing natural languages. Our algorithm is a natural extension
of the original dynamic programming recognition algorithm which recursively
counts the number of linkages between two words in the input sentence. The
modified algorithm uses the notion of a null link in order to allow a
connection between any pair of adjacent words, regardless of their dictionary
definitions. The algorithm proceeds by making three dynamic programming passes.
In the first pass, the input is parsed using the original algorithm which
enforces the constraints on links to ensure grammaticality. In the second pass,
the total cost of each substring of words is computed, where cost is determined
by the number of null links necessary to parse the substring. The final pass
counts the total number of parses with minimal cost. All of the original
pruning techniques have natural counterparts in the robust algorithm. When used
together with memoization, these techniques enable the algorithm to run
efficiently with cubic worst-case complexity. We have implemented these ideas
and tested them by parsing the Switchboard corpus of conversational English.
This corpus is comprised of approximately three million words of text,
corresponding to more than 150 hours of transcribed speech collected from
telephone conversations restricted to 70 different topics. Although only a
small fraction of the sentences in this corpus are "grammatical" by standard
criteria, the robust link grammar parser is able to extract relevant structure
for a large portion of the sentences. We present the results of our experiments
using this system, including the analyses of selected and random sentences from
the corpus.Comment: 17 pages, compressed postscrip
Detection of the elite structure in a virtual multiplex social system by means of a generalized -core
Elites are subgroups of individuals within a society that have the ability
and means to influence, lead, govern, and shape societies. Members of elites
are often well connected individuals, which enables them to impose their
influence to many and to quickly gather, process, and spread information. Here
we argue that elites are not only composed of highly connected individuals, but
also of intermediaries connecting hubs to form a cohesive and structured
elite-subgroup at the core of a social network. For this purpose we present a
generalization of the -core algorithm that allows to identify a social core
that is composed of well-connected hubs together with their `connectors'. We
show the validity of the idea in the framework of a virtual world defined by a
massive multiplayer online game, on which we have complete information of
various social networks. Exploiting this multiplex structure, we find that the
hubs of the generalized -core identify those individuals that are high
social performers in terms of a series of indicators that are available in the
game. In addition, using a combined strategy which involves the generalized
-core and the recently introduced -core, the elites of the different
'nations' present in the game are perfectly identified as modules of the
generalized -core. Interesting sudden shifts in the composition of the elite
cores are observed at deep levels. We show that elite detection with the
traditional -core is not possible in a reliable way. The proposed method
might be useful in a series of more general applications, such as community
detection.Comment: 13 figures, 3 tables, 19 pages. Accepted for publication in PLoS ON
Fluctuation Statistics in Networks: a Stochastic Path Integral Approach
We investigate the statistics of fluctuations in a classical stochastic
network of nodes joined by connectors. The nodes carry generalized charge that
may be randomly transferred from one node to another. Our goal is to find the
time evolution of the probability distribution of charges in the network. The
building blocks of our theoretical approach are (1) known probability
distributions for the connector currents, (2) physical constraints such as
local charge conservation, and (3) a time-scale separation between the slow
charge dynamics of the nodes and the fast current fluctuations of the
connectors. We derive a stochastic path integral representation of the
evolution operator for the slow charges. Once the probability distributions on
the discrete network have been studied, the continuum limit is taken to obtain
a statistical field theory. We find a correspondence between the diffusive
field theory and a Langevin equation with Gaussian noise sources, leading
nevertheless to non-trivial fluctuation statistics. To complete our theory, we
demonstrate that the cascade diagrammatics, recently introduced by Nagaev,
naturally follows from the stochastic path integral. We extend the
diagrammatics to calculate current correlation functions for an arbitrary
network. One primary application of this formalism is that of full counting
statistics (FCS). We stress however, that the formalism is suitable for general
classical stochastic problems as an alternative to the traditional master
equation or Doi-Peliti technique. The formalism is illustrated with several
examples: both instantaneous and time averaged charge fluctuation statistics in
a mesoscopic chaotic cavity, as well as the FCS and new results for a
generalized diffusive wire.Comment: Final version accepted in J. Math. Phys. Discussion of conservation
laws, Refs., 1 Fig., and minor extensions added. 23 pages, 9 figs.,
double-column forma
Modeling and Analyzing Adaptive User-Centric Systems in Real-Time Maude
Pervasive user-centric applications are systems which are meant to sense the
presence, mood, and intentions of users in order to optimize user comfort and
performance. Building such applications requires not only state-of-the art
techniques from artificial intelligence but also sound software engineering
methods for facilitating modular design, runtime adaptation and verification of
critical system requirements.
In this paper we focus on high-level design and analysis, and use the
algebraic rewriting language Real-Time Maude for specifying applications in a
real-time setting. We propose a generic component-based approach for modeling
pervasive user-centric systems and we show how to analyze and prove crucial
properties of the system architecture through model checking and simulation.
For proving time-dependent properties we use Metric Temporal Logic (MTL) and
present analysis algorithms for model checking two subclasses of MTL formulas:
time-bounded response and time-bounded safety MTL formulas. The underlying idea
is to extend the Real-Time Maude model with suitable clocks, to transform the
MTL formulas into LTL formulas over the extended specification, and then to use
the LTL model checker of Maude. It is shown that these analyses are sound and
complete for maximal time sampling. The approach is illustrated by a simple
adaptive advertising scenario in which an adaptive advertisement display can
react to actions of the users in front of the display.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
Non-linear analysis of two-layer timber beams considering interlayer slip and uplift
A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. A modified principle of virtual work is employed in formulating the finite element method. The basic unknowns are strains. The following assumptions are adopted in the mathematical model: materials are taken to be non-linear and can differ from layer to layer; interacting shear and normal contact tractions between layers are derived from the non-linear shear contact traction-slip and the non-linear normal contact traction-uplift characteristics of the connectors; the geometrically linear and materially non-linear Bernoulli's beam theory is assumed for each layer. The formulation is found to be accurate, reliable and computationally effective. The suitability of the theory is validated by the comparison of the numerical solution and the experimental results of full-scale laboratory tests on a simply supported beam. An excellent agreement between measured and calculated results is observed for all load levels. The further objective of the paper is the analysis of the effect of different normal contact traction-uplift constitutive relationships on the kinematic and static quantities in a statically determined and undetermined structure. While the shear contact traction-slip constitutive relationship dictates the deformability of the composite beam and has a substantial influence on most of the static and kinematic quantities of the composite beam, a variable normal contact traction-uplift constitutive relationship is in most cases negligible
- …