32,214 research outputs found
Permutation Classes of Polynomial Growth
A pattern class is a set of permutations closed under the formation of
subpermutations. Such classes can be characterised as those permutations not
involving a particular set of forbidden permutations. A simple collection of
necessary and sufficient conditions on sets of forbidden permutations which
ensure that the associated pattern class is of polynomial growth is determined.
A catalogue of all such sets of forbidden permutations having three or fewer
elements is provided together with bounds on the degrees of the associated
enumerating polynomials.Comment: 17 pages, 4 figure
Validity of the Adiabatic Approximation
We analyze the validity of the adiabatic approximation, and in particular the
reliability of what has been called the "standard criterion" for validity of
this approximation. Recently, this criterion has been found to be insufficient.
We will argue that the criterion is sufficient only when it agrees with the
intuitive notion of slowness of evolution of the Hamiltonian. However, it can
be insufficient in cases where the Hamiltonian varies rapidly but only by a
small amount. We also emphasize the distinction between the adiabatic {\em
theorem} and the adiabatic {\em approximation}, two quite different although
closely related ideas.Comment: 4 pages, 1 figur
Percolation in Directed Scale-Free Networks
Many complex networks in nature have directed links, a property that affects
the network's navigability and large-scale topology. Here we study the
percolation properties of such directed scale-free networks with correlated in-
and out-degree distributions. We derive a phase diagram that indicates the
existence of three regimes, determined by the values of the degree exponents.
In the first regime we regain the known directed percolation mean field
exponents. In contrast, the second and third regimes are characterized by
anomalous exponents, which we calculate analytically. In the third regime the
network is resilient to random dilution, i.e., the percolation threshold is
p_c->1.Comment: Latex, 5 pages, 2 fig
Developmental gene regulatory network architecture across 500 million years of echinoderm evolution
Evolutionary change in morphological features must depend on architectural reorganization of developmental gene regulatory networks (GRNs), just as true conservation of morphological features must imply retention of ancestral developmental GRN features. Key elements of the provisional GRN for embryonic endomesoderm development in the sea urchin are here compared with those operating in embryos of a distantly related echinoderm, a starfish. These animals diverged from their common ancestor 520-480 million years ago. Their endomesodermal fate maps are similar, except that sea urchins generate a skeletogenic cell lineage that produces a prominent skeleton lacking entirely in starfish larvae. A relevant set of regulatory genes was isolated from the starfish Asterina miniata, their expression patterns determined, and effects on the other genes of perturbing the expression of each were demonstrated. A three-gene feedback loop that is a fundamental feature of the sea urchin GRN for endoderm specification is found in almost identical form in the starfish: a detailed element of GRN architecture has been retained since the Cambrian Period in both echinoderm lineages. The significance of this retention is highlighted by the observation of numerous specific differences in the GRN connections as well. A regulatory gene used to drive skeletogenesis in the sea urchin is used entirely differently in the starfish, where it responds to endomesodermal inputs that do not affect it in the sea urchin embryo. Evolutionary changes in the GRNs since divergence are limited sharply to certain cis-regulatory elements, whereas others have persisted unaltered
Epidemic dynamics in finite size scale-free networks
Many real networks present a bounded scale-free behavior with a connectivity
cut-off due to physical constraints or a finite network size. We study epidemic
dynamics in bounded scale-free networks with soft and hard connectivity
cut-offs. The finite size effects introduced by the cut-off induce an epidemic
threshold that approaches zero at increasing sizes. The induced epidemic
threshold is very small even at a relatively small cut-off, showing that the
neglection of connectivity fluctuations in bounded scale-free networks leads to
a strong over-estimation of the epidemic threshold. We provide the expression
for the infection prevalence and discuss its finite size corrections. The
present work shows that the highly heterogeneous nature of scale-free networks
does not allow the use of homogeneous approximations even for systems of a
relatively small number of nodes.Comment: 4 pages, 2 eps figure
Monetary policy and economic activity: a postwar review
Monetary policy ; Financial markets ; Economic conditions
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