2,784 research outputs found
On the localized phase of a copolymer in an emulsion: supercritical percolation regime
In this paper we study a two-dimensional directed self-avoiding walk model of
a random copolymer in a random emulsion. The copolymer is a random
concatenation of monomers of two types, and , each occurring with
density 1/2. The emulsion is a random mixture of liquids of two types, and
, organised in large square blocks occurring with density and ,
respectively, where . The copolymer in the emulsion has an energy
that is minus times the number of -matches minus times the
number of -matches, where without loss of generality the interaction
parameters can be taken from the cone . To make the model mathematically tractable, we assume that the
copolymer is directed and can only enter and exit a pair of neighbouring blocks
at diagonally opposite corners.
In \cite{dHW06}, it was found that in the supercritical percolation regime , with the critical probability for directed bond percolation on
the square lattice, the free energy has a phase transition along a curve in the
cone that is independent of . At this critical curve, there is a transition
from a phase where the copolymer is fully delocalized into the -blocks to a
phase where it is partially localized near the -interface. In the present
paper we prove three theorems that complete the analysis of the phase diagram :
(1) the critical curve is strictly increasing; (2) the phase transition is
second order; (3) the free energy is infinitely differentiable throughout the
partially localized phase.Comment: 43 pages and 10 figure
Measuring degree-degree association in networks
The Pearson correlation coefficient is commonly used for quantifying the
global level of degree-degree association in complex networks. Here, we use a
probabilistic representation of the underlying network structure for assessing
the applicability of different association measures to heavy-tailed degree
distributions. Theoretical arguments together with our numerical study indicate
that Pearson's coefficient often depends on the size of networks with equal
association structure, impeding a systematic comparison of real-world networks.
In contrast, Kendall-Gibbons' is a considerably more robust measure
of the degree-degree association
Copolymer with pinning: variational characterization of the phase diagram
This paper studies a polymer chain in the vicinity of a linear interface
separating two immiscible solvents. The polymer consists of random monomer
types, while the interface carries random charges. Both the monomer types and
the charges are given by i.i.d. sequences of random variables. The
configurations of the polymer are directed paths that can make i.i.d.
excursions of finite length above and below the interface. The Hamiltonian has
two parts: a monomer-solvent interaction ("copolymer") and a monomer-interface
interaction ("pinning"). The quenched and the annealed version of the model
each undergo a transition from a localized phase (where the polymer stays close
to the interface) to a delocalized phase (where the polymer wanders away from
the interface). We exploit the approach developed in [5] and [3] to derive
variational formulas for the quenched and the annealed free energy per monomer.
These variational formulas are analyzed to obtain detailed information on the
critical curves separating the two phases and on the typical behavior of the
polymer in each of the two phases. Our main results settle a number of open
questions.Comment: 46 pages, 9 figure
Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
The study of systems with multiple (not necessarily degenerate) metastable
states presents subtle difficulties from the mathematical point of view related
to the variational problem that has to be solved in these cases. We introduce
the notion of relaxation height in a general energy landscape and we prove
sufficient conditions which are valid even in presence of multiple metastable
states. We show how these results can be used to approach the problem of
multiple metastable states via the use of the modern theories of metastability.
We finally apply these general results to the Blume--Capel model for a
particular choice of the parameters ensuring the existence of two multiple, and
not degenerate in energy, metastable states
Trapping in complex networks
We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF)
networks. We calculate the evolution of the particle density of
random walkers in the presence of one or multiple traps with concentration .
We show using theory and simulations that in ER networks, while for short times
, for longer times exhibits a more
complex behavior, with explicit dependence on both the number of traps and the
size of the network. In SF networks we reveal the significant impact of the
trap's location: is drastically different when a trap is placed on a
random node compared to the case of the trap being on the node with the maximum
connectivity. For the latter case we find
\rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all
, where is the exponent of the degree distribution
.Comment: Appendix adde
The World-Trade Web: Topological Properties, Dynamics, and Evolution
This paper studies the statistical properties of the web of import-export
relationships among world countries using a weighted-network approach. We
analyze how the distributions of the most important network statistics
measuring connectivity, assortativity, clustering and centrality have
co-evolved over time. We show that all node-statistic distributions and their
correlation structure have remained surprisingly stable in the last 20 years --
and are likely to do so in the future. Conversely, the distribution of
(positive) link weights is slowly moving from a log-normal density towards a
power law. We also characterize the autoregressive properties of
network-statistics dynamics. We find that network-statistics growth rates are
well-proxied by fat-tailed densities like the Laplace or the asymmetric
exponential-power. Finally, we find that all our results are reasonably robust
to a few alternative, economically-meaningful, weighting schemes.Comment: 44 pages, 39 eps figure
Manifesto for a European research network into Problematic Usage of the Internet
Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.The Internet is now all-pervasive across much of the globe. While it has positive uses (e.g. prompt access to information, rapid news dissemination), many individuals develop Problematic Use of the Internet (PUI), an umbrella term incorporating a range of repetitive impairing behaviours. The Internet can act as a conduit for, and may contribute to, functionally impairing behaviours including excessive and compulsive video gaming, compulsive sexual behaviour, buying, gambling, streaming or social networks use. There is growing public and National health authority concern about the health and societal costs of PUI across the lifespan. Gaming Disorder is being considered for inclusion as a mental disorder in diagnostic classification systems, and was listed in the ICD-11 version released for consideration by Member States (http://www.who.int/classifications/icd/revision/timeline/en/). More research is needed into disorder definitions, validation of clinical tools, prevalence, clinical parameters, brain-based biology, socio-health-economic impact, and empirically validated intervention and policy approaches. Potential cultural differences in the magnitudes and natures of types and patterns of PUI need to be better understood, to inform optimal health policy and service development. To this end, the EU under Horizon 2020 has launched a new four-year European Cooperation in Science and Technology (COST) Action Programme (CA 16207), bringing together scientists and clinicians from across the fields of impulsive, compulsive, and addictive disorders, to advance networked interdisciplinary research into PUI across Europe and beyond, ultimately seeking to inform regulatory policies and clinical practice. This paper describes nine critical and achievable research priorities identified by the Network, needed in order to advance understanding of PUI, with a view towards identifying vulnerable individuals for early intervention. The network shall enable collaborative research networks, shared multinational databases, multicentre studies and joint publications.Peer reviewe
The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang
equation with sharp wedge initial conditions. Thereby it is confirmed that the
continuum model belongs to the KPZ universality class, not only as regards to
scaling exponents but also as regards to the full probability distribution of
the height in the long time limit.Comment: Proceedings StatPhys 2
Latanoprost and Dorzolamide for the Treatment of Pediatric Glaucoma: The Glaucoma Italian Pediatric Study (Gipsy), Design and Baseline Characteristics
INTRODUCTION: To investigate the efficacy of a treatment strategy with latanoprost and dorzolamide in primary pediatric glaucoma patients partially responsive to surgery. METHODS: Single arm, prospective, interventional multicenter study. Primary pediatric glaucoma patients younger than 13 years after a single surgical procedure with IOP between 22 and 26 mmHg were considered eligible. At baseline, patients were allocated to latanoprost monotherapy once daily. Depending on intraocular pressure (IOP) reduction at first visit, the patients were allocated to one of three groups: continuation of latanoprost monotherapy, addition of dorzolamide twice daily, or switch to dorzolamide three times daily. The same approach for allocation in medication groups was used in all subsequent visits. Patients in the dorzolamide monotherapy group with IOP reduction <20% from baseline were considered non-responders and withdrawn. Study treatment and patient follow-up will continue for 3 years or until treatment failure. The primary endpoint is the percentage of responders. Secondary endpoints are time to treatment failure and frequency of adverse events. RESULTS: A total of 37 patients (69 eyes) were enrolled. The mean age was 4.0 ± 3.8 years, the female/male ratio was 1/1.7, and the majority of patients were Caucasian. Eighty percent of patients had bilateral glaucoma. Goniotomy was the most frequently performed surgery (38.6%), followed by trabeculotomy (22.8%), trabeculectomy (21.1%), and trabeculectomy plus trabeculotomy (17.5%). The baseline IOP was 23.6 ± 1.5 mmHg. CONCLUSION: The study population is representative of patients frequently encountered after the first surgery for primary pediatric glaucoma. The study will produce evidence on the medium-term efficacy of a defined pharmacological approach
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