5,030 research outputs found
Flexible construction of hierarchical scale-free networks with general exponent
Extensive studies have been done to understand the principles behind
architectures of real networks. Recently, evidences for hierarchical
organization in many real networks have also been reported. Here, we present a
new hierarchical model which reproduces the main experimental properties
observed in real networks: scale-free of degree distribution (frequency
of the nodes that are connected to other nodes decays as a power-law
) and power-law scaling of the clustering coefficient
. The major novelties of our model can be summarized as
follows: {\it (a)} The model generates networks with scale-free distribution
for the degree of nodes with general exponent , and arbitrarily
close to any specified value, being able to reproduce most of the observed
hierarchical scale-free topologies. In contrast, previous models can not obtain
values of . {\it (b)} Our model has structural flexibility
because {\it (i)} it can incorporate various types of basic building blocks
(e.g., triangles, tetrahedrons and, in general, fully connected clusters of
nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the
model can use more than copies of basic blocks of nodes). The
structural features of our proposed model might lead to a better understanding
of architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure
Extracting the hierarchical organization of complex systems
Extracting understanding from the growing ``sea'' of biological and
socio-economic data is one of the most pressing scientific challenges facing
us. Here, we introduce and validate an unsupervised method that is able to
accurately extract the hierarchical organization of complex biological, social,
and technological networks. We define an ensemble of hierarchically nested
random graphs, which we use to validate the method. We then apply our method to
real-world networks, including the air-transportation network, an electronic
circuit, an email exchange network, and metabolic networks. We find that our
method enables us to obtain an accurate multi-scale descriptions of a complex
system.Comment: Figures in screen resolution. Version with full resolution figures
available at
http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd
Melting Crystal, Quantum Torus and Toda Hierarchy
Searching for the integrable structures of supersymmetric gauge theories and
topological strings, we study melting crystal, which is known as random plane
partition, from the viewpoint of integrable systems. We show that a series of
partition functions of melting crystals gives rise to a tau function of the
one-dimensional Toda hierarchy, where the models are defined by adding suitable
potentials, endowed with a series of coupling constants, to the standard
statistical weight. These potentials can be converted to a commutative
sub-algebra of quantum torus Lie algebra. This perspective reveals a remarkable
connection between random plane partition and quantum torus Lie algebra, and
substantially enables to prove the statement. Based on the result, we briefly
argue the integrable structures of five-dimensional
supersymmetric gauge theories and -model topological strings. The
aforementioned potentials correspond to gauge theory observables analogous to
the Wilson loops, and thereby the partition functions are translated in the
gauge theory to generating functions of their correlators. In topological
strings, we particularly comment on a possibility of topology change caused by
condensation of these observables, giving a simple example.Comment: Final version to be published in Commun. Math. Phys. . A new section
is added and devoted to Conclusion and discussion, where, in particular, a
possible relation with the generating function of the absolute Gromov-Witten
invariants on CP^1 is commented. Two references are added. Typos are
corrected. 32 pages. 4 figure
A statistical mechanics description of environmental variability in metabolic networks
Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction system
-analogue of modified KP hierarchy and its quasi-classical limit
A -analogue of the tau function of the modified KP hierarchy is defined by
a change of independent variables. This tau function satisfies a system of
bilinear -difference equations. These bilinear equations are translated to
the language of wave functions, which turn out to satisfy a system of linear
-difference equations. These linear -difference equations are used to
formulate the Lax formalism and the description of quasi-classical limit. These
results can be generalized to a -analogue of the Toda hierarchy. The results
on the -analogue of the Toda hierarchy might have an application to the
random partition calculus in gauge theories and topological strings.Comment: latex2e, a4 paper 15 pages, no figure; (v2) a few references are
adde
Software that goes with the flow in systems biology
A recent article in BMC Bioinformatics describes new advances in workflow systems for computational modeling in systems biology. Such systems can accelerate, and improve the consistency of, modeling through automation not only at the simulation and results-production stages, but also at the model-generation stage. Their work is a harbinger of the next generation of more powerful software for systems biologists
Thermodynamic limit of random partitions and dispersionless Toda hierarchy
We study the thermodynamic limit of random partition models for the instanton
sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical
observables. The physical observables correspond to external potentials in the
statistical model. The partition function is reformulated in terms of the
density function of Maya diagrams. The thermodynamic limit is governed by a
limit shape of Young diagrams associated with dominant terms in the partition
function. The limit shape is characterized by a variational problem, which is
further converted to a scalar-valued Riemann-Hilbert problem. This
Riemann-Hilbert problem is solved with the aid of a complex curve, which may be
thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This
solution of the Riemann-Hilbert problem is identified with a special solution
of the dispersionless Toda hierarchy that satisfies a pair of generalized
string equations. The generalized string equations for the 5D gauge theory are
shown to be related to hidden symmetries of the statistical model. The
prepotential and the Seiberg-Witten differential are also considered.Comment: latex2e using amsmath,amssymb,amsthm packages, 55 pages, no figure;
(v2) typos correcte
Characteristics of Japanese wrestlers with respect to function and structure of limbs
It is well known that hypertrophy and strength gain of the human skeletal muscle are induced by muscle training. It has also been shown that the training effect on size and strength of the skeletal muscle are altered the different athletic training protocols (1, 4). From these findings, it seems possible that wrestlers possess the hypertrophied muscle and stronger muscle strength by specific training.
In the present study, we assess the functional and structural characteristics of the skeletal muscle in Japanese wrestlers
AAindex: amino acid index database, progress report 2008
AAindex is a database of numerical indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. We have added a collection of protein contact potentials to the AAindex as a new section. Accordingly AAindex consists of three sections now: AAindex1 for the amino acid index of 20 numerical values, AAindex2 for the amino acid substitution matrix and AAindex3 for the statistical protein contact potentials. All data are derived from published literature. The database can be accessed through the DBGET/LinkDB system at GenomeNet (http://www.genome.jp/dbget-bin/www_bfind?aaindex) or downloaded by anonymous FTP (ftp://ftp.genome.jp/pub/db/community/aaindex/)
Complex networks theory for analyzing metabolic networks
One of the main tasks of post-genomic informatics is to systematically
investigate all molecules and their interactions within a living cell so as to
understand how these molecules and the interactions between them relate to the
function of the organism, while networks are appropriate abstract description
of all kinds of interactions. In the past few years, great achievement has been
made in developing theory of complex networks for revealing the organizing
principles that govern the formation and evolution of various complex
biological, technological and social networks. This paper reviews the
accomplishments in constructing genome-based metabolic networks and describes
how the theory of complex networks is applied to analyze metabolic networks.Comment: 13 pages, 2 figure
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