1,444 research outputs found
Cavity approach for modeling and fitting polymer stretching
The mechanical properties of molecules are today captured by single molecule
manipulation experiments, so that polymer features are tested at a nanometric
scale. Yet devising mathematical models to get further insight beyond the
commonly studied force--elongation relation is typically hard. Here we draw
from techniques developed in the context of disordered systems to solve models
for single and double--stranded DNA stretching in the limit of a long polymeric
chain. Since we directly derive the marginals for the molecule local
orientation, our approach allows us to readily calculate the experimental
elongation as well as other observables at wish. As an example, we evaluate the
correlation length as a function of the stretching force. Furthermore, we are
able to fit successfully our solution to real experimental data. Although the
model is admittedly phenomenological, our findings are very sound. For
single--stranded DNA our solution yields the correct (monomer) scale and, yet
more importantly, the right persistence length of the molecule. In the
double--stranded case, our model reproduces the well-known overstretching
transition and correctly captures the ratio between native DNA and
overstretched DNA. Also in this case the model yields a persistence length in
good agreement with consensus, and it gives interesting insights into the
bending stiffness of the native and overstretched molecule, respectively.Comment: 12 pages; 3 figures; 1 tabl
The configuration multi-edge model: Assessing the effect of fixing node strengths on weighted network magnitudes
Complex networks grow subject to structural constraints which affect their
measurable properties. Assessing the effect that such constraints impose on
their observables is thus a crucial aspect to be taken into account in their
analysis. To this end,we examine the effect of fixing the strength sequence in
multi-edge networks on several network observables such as degrees, disparity,
average neighbor properties and weight distribution using an ensemble approach.
We provide a general method to calculate any desired weighted network metric
and we show that several features detected in real data could be explained
solely by structural constraints. We thus justify the need of analytical null
models to be used as basis to assess the relevance of features found in real
data represented in weighted network form.Comment: 11 pages. 4 figure
Optimization as a result of the interplay between dynamics and structure
In this work we study the interplay between the dynamics of a model of
diffusion governed by a mechanism of imitation and its underlying structure.
The dynamics of the model can be quantified by a macroscopic observable which
permits the characterization of an optimal regime. We show that dynamics and
underlying network cannot be considered as separated ingredients in order to
achieve an optimal behavior.Comment: 12 pages, 4 figures, to appear in Physica
Synchronization reveals topological scales in complex networks
We study the relationship between topological scales and dynamic time scales
in complex networks. The analysis is based on the full dynamics towards
synchronization of a system of coupled oscillators. In the synchronization
process, modular structures corresponding to well defined communities of nodes
emerge in different time scales, ordered in a hierarchical way. The analysis
also provides a useful connection between synchronization dynamics, complex
networks topology and spectral graph analysis.Comment: 4 pages, 3 figure
Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics
One way to incorporate systematic uncertainties into the calculation of
confidence intervals is by integrating over probability density functions
parametrizing the uncertainties. In this note we present a development of this
method which takes into account uncertainties in the prediction of background
processes, uncertainties in the signal detection efficiency and background
efficiency and allows for a correlation between the signal and background
detection efficiencies. We implement this method with the Feldman & Cousins
unified approach with and without conditioning. We present studies of coverage
for the Feldman & Cousins and Neyman ordering schemes. In particular, we
present two different types of coverage tests for the case where systematic
uncertainties are included. To illustrate the method we show the relative
effect of including systematic uncertainties the case of dark matter search as
performed by modern neutrino tel escopes.Comment: 23 pages, 10 figures, replaced to match published versio
Spectral density of random graphs with topological constraints
The spectral density of random graphs with topological constraints is
analysed using the replica method. We consider graph ensembles featuring
generalised degree-degree correlations, as well as those with a community
structure. In each case an exact solution is found for the spectral density in
the form of consistency equations depending on the statistical properties of
the graph ensemble in question. We highlight the effect of these topological
constraints on the resulting spectral density.Comment: 24 pages, 6 figure
Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators
We introduce two coupled map lattice models with nonconservative interactions
and a continuous nonlinear driving. Depending on both the degree of
conservation and the convexity of the driving we find different behaviors,
ranging from self-organized criticality, in the sense that the distribution of
events (avalanches) obeys a power law, to a macroscopic synchronization of the
population of oscillators, with avalanches of the size of the system.Comment: 4 pages, Revtex 3.0, 3 PostScript figures available upon request to
[email protected]
Synchronization processes in complex networks
We present an extended analysis, based on the dynamics towards
synchronization of a system of coupled oscillators, of the hierarchy of
communities in complex networks. In the synchronization process, different
structures corresponding to well defined communities of nodes appear in a
hierarchical way. The analysis also provides a useful connection between
synchronization dynamics, complex networks topology and spectral graph
analysis.Comment: 16 pages, 4 figures. To appear in Physica D "Special Issue on
dynamics on complex networks
The derived category of quasi-coherent sheaves and axiomatic stable homotopy
We prove in this paper that for a quasi-compact and semi-separated (non
necessarily noetherian) scheme X, the derived category of quasi-coherent
sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of
Hovey, Palmieri and Strickland, answering a question posed by Strickland.
Moreover we show that it is unital and algebraic. We also prove that for a
noetherian semi-separated formal scheme X, its derived category of sheaves of
modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy
category. It is algebraic but if the formal scheme is not a usual scheme, it is
not unital, therefore its abstract nature differs essentially from that of the
derived category of a usual scheme.Comment: v2: 31 pages, some improvements in exposition; v3 updated
bibliography, to appear Adv. Mat
- âŠ