9 research outputs found
A scale-free network hidden in the collapsing polymer
We show that the collapsed globular phase of a polymer accommodates a
scale-free incompatibility graph of its contacts. The degree distribution of
this network is found to decay with the exponent up to a
cut-off degree , where is the loop exponent for dense
polymers ( in two dimensions) and is the length of the polymer. Our
results exemplify how a scale-free network (SFN) can emerge from standard
criticality.Comment: 4 pages, 3 figures, address correcte
Deep Spin-Glass Hysteresis Area Collapse and Scaling in the Ising Model
We investigate the dissipative loss in the Ising spin glass in three
dimensions through the scaling of the hysteresis area, for a maximum magnetic
field that is equal to the saturation field. We perform a systematic analysis
for the whole range of the bond randomness as a function of the sweep rate, by
means of frustration-preserving hard-spin mean field theory. Data collapse
within the entirety of the spin-glass phase driven adiabatically (i.e.,
infinitely-slow field variation) is found, revealing a power-law scaling of the
hysteresis area as a function of the antiferromagnetic bond fraction and the
temperature. Two dynamic regimes separated by a threshold frequency
characterize the dependence on the sweep rate of the oscillating field. For
, the hysteresis area is equal to its value in the adiabatic
limit , while for it increases with the
frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
In view of the recently seen dramatic effect of quenched random bonds on
tricritical systems, we have conducted a renormalization-group study on the
effect of quenched random fields on the tricritical phase diagram of the spin-1
Ising model in . We find that random fields convert first-order phase
transitions into second-order, in fact more effectively than random bonds. The
coexistence region is extremely flat, attesting to an unusually small
tricritical exponent ; moreover, an extreme asymmetry of the phase
diagram is very striking. To accomodate this asymmetry, the second-order
boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR
Multiple timescales in a model for DNA denaturation dynamics
The denaturation dynamics of a long double-stranded DNA is studied by means
of a model of the Poland-Scheraga type. We note that the linking of the two
strands is a locally conserved quantity, hence we introduce local updates that
respect this symmetry. Linking dissipation via untwist is allowed only at the
two ends of the double strand. The result is a slow denaturation characterized
by two time scales that depend on the chain length . In a regime up to a
first characteristic time the chain embodies an
increasing number of small bubbles. Then, in a second regime, bubbles coalesce
and form entropic barriers that effectively trap residual double-stranded
segments within the chain, slowing down the relaxation to fully molten
configurations, which takes place at . This scenario is
different from the picture in which the helical constraints are neglected.Comment: 9 pages, 5 figure
The Information Coded in the Yeast Response Elements Accounts for Most of the Topological Properties of Its Transcriptional Regulation Network
The regulation of gene expression in a cell relies to a major extent on transcription factors, proteins which recognize and bind the DNA at specific binding sites (response elements) within promoter regions associated with each gene. We present an information theoretic approach to modeling transcriptional regulatory networks, in terms of a simple “sequence-matching” rule and the statistics of the occurrence of binding sequences of given specificity in random promoter regions. The crucial biological input is the distribution of the amount of information coded in these cognate response elements and the length distribution of the promoter regions. We provide an analysis of the transcriptional regulatory network of yeast Saccharomyces cerevisiae, which we extract from the available databases, with respect to the degree distributions, clustering coefficient, degree correlations, rich-club coefficient and the k-core structure. We find that these topological features are in remarkable agreement with those predicted by our model, on the basis of the amount of information coded in the interaction between the transcription factors and response elements