923 research outputs found
Regional growth, national membership and European structural funds : an empirical appraisal
regional development
Phase diagram of a generalized ABC model on the interval
We study the equilibrium phase diagram of a generalized ABC model on an
interval of the one-dimensional lattice: each site is occupied by a
particle of type \a=A,B,C, with the average density of each particle species
N_\a/N=r_\a fixed. These particles interact via a mean field
non-reflection-symmetric pair interaction. The interaction need not be
invariant under cyclic permutation of the particle species as in the standard
ABC model studied earlier. We prove in some cases and conjecture in others that
the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique
density profile \p_\a(x) except for some special values of the r_\a for
which the system undergoes a second order phase transition from a uniform to a
nonuniform periodic profile at a critical temperature .Comment: 25 pages, 6 figure
On the functions counting walks with small steps in the quarter plane
Models of spatially homogeneous walks in the quarter plane
with steps taken from a subset of the set of jumps to the eight
nearest neighbors are considered. The generating function of the numbers of such walks starting at the origin and
ending at after steps is studied. For all
non-singular models of walks, the functions and are continued as multi-valued functions on having
infinitely many meromorphic branches, of which the set of poles is identified.
The nature of these functions is derived from this result: namely, for all the
51 walks which admit a certain infinite group of birational transformations of
, the interval of variation of splits into
two dense subsets such that the functions and are shown to be holonomic for any from the one of them and
non-holonomic for any from the other. This entails the non-holonomy of
, and therefore proves a conjecture of
Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure
Adaptive System for Collaborative Online Laboratories
International audienceIn the last decade, researchers in the Online Engineering field have attempted to provide hands-on, web-based approaches for Distance Learning. The primary goal of this research is to produce online laboratories that serve as the educational substitute for in situ laboratories. A limitation of existing online laboratories, however, is that they generally only allow a single user to be connected at a time. Since group learning activities, such as peer assistance, peer emulation, and collaborative experimental setup, are core dimensions of the traditional laboratory experience, this shortcoming is a significant pedagogical bottleneck. Recent research has focused on creating Collaborative Online Laboratories (COL) which attempt to address this shortcoming by focusing on the group awareness aspect of the laboratory learning experience. This paper discusses how group awareness can serve as a key component in replicating the collaborative aspect of learning in local laboratories. We discuss strategies for describing group awareness and how these strategies are associated both with a tutor's pedagogical objectives and in the management of the group of collaborating students. We describe an experimental system that we have developed that uses Semantic Web technologies to define a knowledge-driven system that allows researchers to describe and execute a variety of collaborative strategies for online laboratories
On the dynamical behavior of the ABC model
We consider the ABC dynamics, with equal density of the three species, on the
discrete ring with sites. In this case, the process is reversible with
respect to a Gibbs measure with a mean field interaction that undergoes a
second order phase transition. We analyze the relaxation time of the dynamics
and show that at high temperature it grows at most as while it grows at
least as at low temperature
The grand canonical ABC model: a reflection asymmetric mean field Potts model
We investigate the phase diagram of a three-component system of particles on
a one-dimensional filled lattice, or equivalently of a one-dimensional
three-state Potts model, with reflection asymmetric mean field interactions.
The three types of particles are designated as , , and . The system is
described by a grand canonical ensemble with temperature and chemical
potentials , , and . We find that for
the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature . For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that , where is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities .Comment: 24 pages, 3 figure
An approximate analysis of a bernoulli alternating service model
We consider a discrete-time queueing system with one server
and two types of customers, say type-1 and type-2 customers. The server
serves customers of either type alternately according to a Bernoulli pro-
cess. The service times of the customers are deterministically equal to
1 time slot. For this queueing system, we derive a functional equation
for the joint probability generating function of the number of type-1 and
type-2 customers. The functional equation contains two unknown partial
generating functions which complicates the analysis. We investigate the
dominant singularity of these two unknown functions and propose an
approximation for the coefficients of the Maclaurin series expansion of
these functions. This approximation provides a fast method to compute
approximations of various performance measures of interest
Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues
We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for an egalitarian PS queue with customer classes, we show that the marginal queue length distribution for class factorizes over the number of other customer types. The factorizing coefficients equal the queue length probabilities of a PS queue for type in isolation, in which the customers of the other types reside \textit{ permanently} in the system. Similarly, the (conditional) mean sojourn time for class can be obtained by conditioning on the number of permanent customers of the other types. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian processor-sharing models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights. \u
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