107 research outputs found
Distributed finite-time stabilization of entangled quantum states on tree-like hypergraphs
Preparation of pure states on networks of quantum systems by controlled
dissipative dynamics offers important advantages with respect to circuit-based
schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are
considered, dead-beat stabilization becomes possible in principle. Here, we
focus on pure states that can be stabilized by distributed, unsupervised
dynamics in finite time on a network of quantum systems subject to realistic
quasi-locality constraints. In particular, we define a class of quasi-locality
notions, that we name "tree-like hypergraphs," and show that the states that
are robustly stabilizable in finite time are then unique ground states of a
frustration-free, commuting quasi-local Hamiltonian. A structural
characterization of such states is also provided, building on a simple yet
relevant example.Comment: 6 pages, 3 figure
Semigroup approach to diffusion and transport problems on networks
Models describing transport and diffusion processes occurring along the edges
of a graph and interlinked by its vertices have been recently receiving a
considerable attention. In this paper we generalize such models and consider a
network of transport or diffusion operators defined on one dimensional domains
and connected through boundary conditions linking the end-points of these
domains in an arbitrary way (not necessarily as the edges of a graph are
connected). We prove the existence of -semigroups solving such problems
and provide conditions fully characterizing when they are positive
Differential equation approximations for Markov chains
We formulate some simple conditions under which a Markov chain may be
approximated by the solution to a differential equation, with quantifiable
error probabilities. The role of a choice of coordinate functions for the
Markov chain is emphasised. The general theory is illustrated in three
examples: the classical stochastic epidemic, a population process model with
fast and slow variables, and core-finding algorithms for large random
hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups
We study in this paper some connections between the Fraisse theory of
amalgamation classes and ultrahomogeneous structures, Ramsey theory, and
topological dynamics of automorphism groups of countable structures.Comment: 73 pages, LaTeX 2e, to appear in Geom. Funct. Ana
OWA-based fuzzy m-ary adjacency relations in Social Network Analysis.
In this paper we propose an approach to Social Network Analysis (SNA) based on fuzzy m-ary adjacency relations. In particular, we show that the dimension of the analysis can naturally be increased and interesting results can be derived. Therefore, fuzzy m-ary adjacency relations can be computed starting from fuzzy binary relations and introducing OWA-based aggregations. The behavioral assumptions derived from the measure and the exam of individual propensity to connect with other suggest that OWA operators can be considered particularly suitable in characterizing such relationships.reciprocal relation; fuzzy preference relation; priority vector; normalization
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