28,821 research outputs found
Matrices coupled in a chain. I. Eigenvalue correlations
The general correlation function for the eigenvalues of complex hermitian
matrices coupled in a chain is given as a single determinant. For this we use a
slight generalization of a theorem of Dyson.Comment: ftex eynmeh.tex, 2 files, 8 pages Submitted to: J. Phys.
Moments of the characteristic polynomial in the three ensembles of random matrices
Moments of the characteristic polynomial of a random matrix taken from any of
the three ensembles, orthogonal, unitary or symplectic, are given either as a
determinant or a pfaffian or as a sum of determinants. For gaussian ensembles
comparing the two expressions of the same moment one gets two remarkable
identities, one between an determinant and an
determinant and another between the pfaffian of a anti-symmetric
matrix and a sum of determinants.Comment: tex, 1 file, 15 pages [SPhT-T01/016], published J. Phys. A: Math.
Gen. 34 (2001) 1-1
A column of grains in the jamming limit: glassy dynamics in the compaction process
We investigate a stochastic model describing a column of grains in the
jamming limit, in the presence of a low vibrational intensity. The key control
parameter of the model, , is a representation of granular shape,
related to the reduced void space. Regularity and irregularity in grain shapes,
respectively corresponding to rational and irrational values of , are
shown to be centrally important in determining the statics and dynamics of the
compaction process.Comment: 29 pages, 14 figures, 1 table. Various minor changes and updates. To
appear in EPJ
Universality in survivor distributions: Characterising the winners of competitive dynamics
We investigate the survivor distributions of a spatially extended model of
competitive dynamics in different geometries. The model consists of a
deterministic dynamical system of individual agents at specified nodes, which
might or might not survive the predatory dynamics: all stochasticity is brought
in by the initial state. Every such initial state leads to a unique and
extended pattern of survivors and non-survivors, which is known as an attractor
of the dynamics. We show that the number of such attractors grows exponentially
with system size, so that their exact characterisation is limited to only very
small systems. Given this, we construct an analytical approach based on
inhomogeneous mean-field theory to calculate survival probabilities for
arbitrary networks. This powerful (albeit approximate) approach shows how
universality arises in survivor distributions via a key concept -- the {\it
dynamical fugacity}. Remarkably, in the large-mass limit, the survival
probability of a node becomes independent of network geometry, and assumes a
simple form which depends only on its mass and degree.Comment: 12 pages, 6 figures, 2 table
Slow synaptic dynamics in a network: from exponential to power-law forgetting
We investigate a mean-field model of interacting synapses on a directed
neural network. Our interest lies in the slow adaptive dynamics of synapses,
which are driven by the fast dynamics of the neurons they connect. Cooperation
is modelled from the usual Hebbian perspective, while competition is modelled
by an original polarity-driven rule. The emergence of a critical manifold
culminating in a tricritical point is crucially dependent on the presence of
synaptic competition. This leads to a universal power-law relaxation of
the mean synaptic strength along the critical manifold and an equally universal
relaxation at the tricritical point, to be contrasted with the
exponential relaxation that is otherwise generic. In turn, this leads to the
natural emergence of long- and short-term memory from different parts of
parameter space in a synaptic network, which is the most novel and important
result of our present investigations.Comment: 12 pages, 8 figures. Phys. Rev. E (2014) to appea
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
Building self-evaluation skills through criterion-referenced assessment in public relations
Although technical skills in public relations are essential to practice, skills in self-evaluation, critical thinking, and problem solving are required when new practitioners move to management roles (Van Leuven, 1999). Public relations courses integrate specialist subject knowledge with graduate skill sets and capabilities in non-technical areas (Butcher & Stefani, 1995). Given that autonomy in learning is a skill valued by employers (Clifford, 1999) and advocated by accrediting professional bodies (Anderson, 1999), this study explores how public relations students build skills in and perceive the practice of self-evaluation. Currently, the public relations education literature presents a limited treatment of self-evaluation. Therefore, this study is guided mostly by the education literature and uses criterion-referenced assessment to determine how more than 150 students understand assessment requirements, assess their strengths and weaknesses, and interpret the differences between their self and their tutor's judgement of performance. The results indicate strong support for student understanding of assessment requirements and self-evaluation techniques but lower than expected support for understanding the differences between their self and tutor judgements. These findings are significant to educators, practitioners and professional bodies as they have implications for lifelong learning for public relations professionals
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