5,924 research outputs found
Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
Gorsky et al. presented an explicit construction of Whitham deformations of
the Seiberg-Witten curve for the \calN = 2 SUSY Yang-Mills theory.
We extend their result to all classical gauge groups and some other cases such
as the spectral curve of the affine Toda Toda system. Our
construction, too, uses fractional powers of the superpotential that
characterizes the curve. We also consider the -plane integral of
topologically twisted theories on four-dimensional manifolds with
in the language of these explicitly constructed Whitham
deformations and an integrable hierarchy of the KdV type hidden behind.Comment: latex, 39pp, no figure; some more comments and references on
integrable systems are added, and many typos are correcte
SIMCOMP/SUBCOMP: chemical structure search servers for network analyses
One of the greatest challenges in bioinformatics is to shed light on the relationship between genomic and chemical significances of metabolic pathways. Here, we demonstrate two types of chemical structure search servers: SIMCOMP (http://www.genome.jp/tools/simcomp/) for the chemical similarity search and SUBCOMP (http://www.genome.jp/tools/subcomp/) for the chemical substructure search, where both servers provide links to the KEGG PATHWAY and BRITE databases. The SIMCOMP is a graph-based method for searching the maximal common subgraph isomorphism by finding the maximal cliques in the association graph. In contrast, the SUBCOMP is an extended method for solving the subgraph isomorphism problem. The obtained links to PATHWAY or BRITE databases can be used to interpret as the biological meanings of chemical structures from the viewpoint of the various biological functions including metabolic networks
Symmetries and tau function of higher dimensional dispersionless integrable hierarchies
A higher dimensional analogue of the dispersionless KP hierarchy is
introduced. In addition to the two-dimensional ``phase space'' variables
of the dispersionless KP hierarchy, this hierarchy has extra spatial
dimensions compactified to a two (or any even) dimensional torus. Integrability
of this hierarchy and the existence of an infinite dimensional of ``additional
symmetries'' are ensured by an underlying twistor theoretical structure (or a
nonlinear Riemann-Hilbert problem). An analogue of the tau function, whose
logarithm gives the function (``free energy'' or ``prepotential'' in the
contest of matrix models and topological conformal field theories), is
constructed. The infinite dimensional symmetries can be extended to this tau
(or ) function. The extended symmetries, just like those of the
dispersionless KP hierarchy, obey an anomalous commutation relations.Comment: 50 pages, (Changes: a few references are added; numbering of formulas
are slightly modified
Space-efficient Feature Maps for String Alignment Kernels
String kernels are attractive data analysis tools for analyzing string data.
Among them, alignment kernels are known for their high prediction accuracies in
string classifications when tested in combination with SVM in various
applications. However, alignment kernels have a crucial drawback in that they
scale poorly due to their quadratic computation complexity in the number of
input strings, which limits large-scale applications in practice. We address
this need by presenting the first approximation for string alignment kernels,
which we call space-efficient feature maps for edit distance with moves
(SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP)
and feature maps (FMs) of random Fourier features (RFFs) for large-scale string
analyses. The original FMs for RFFs consume a huge amount of memory
proportional to the dimension d of input vectors and the dimension D of output
vectors, which prohibits its large-scale applications. We present novel
space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of
the original FMs to O(d) of SFMs with a theoretical guarantee with respect to
concentration bounds. We experimentally test SFMEDM on its ability to learn SVM
for large-scale string classifications with various massive string data, and we
demonstrate the superior performance of SFMEDM with respect to prediction
accuracy, scalability and computation efficiency.Comment: Full version for ICDM'19 pape
Non-degenerate solutions of universal Whitham hierarchy
The notion of non-degenerate solutions for the dispersionless Toda hierarchy
is generalized to the universal Whitham hierarchy of genus zero with
marked points. These solutions are characterized by a Riemann-Hilbert problem
(generalized string equations) with respect to two-dimensional canonical
transformations, and may be thought of as a kind of general solutions of the
hierarchy. The Riemann-Hilbert problem contains arbitrary functions
, , which play the role of generating functions of
two-dimensional canonical transformations. The solution of the Riemann-Hilbert
problem is described by period maps on the space of -tuples
of conformal maps from disks of the
Riemann sphere and their complements to the Riemann sphere. The period maps are
defined by an infinite number of contour integrals that generalize the notion
of harmonic moments. The -function (free energy) of these solutions is also
shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no
figur
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
MACiE: a database of enzyme reaction mechanisms.
SUMMARY: MACiE (mechanism, annotation and classification in enzymes) is a publicly available web-based database, held in CMLReact (an XML application), that aims to help our understanding of the evolution of enzyme catalytic mechanisms and also to create a classification system which reflects the actual chemical mechanism (catalytic steps) of an enzyme reaction, not only the overall reaction. AVAILABILITY: http://www-mitchell.ch.cam.ac.uk/macie/.EPSRC (G.L.H. and J.B.O.M.), the BBSRC (G.J.B. and J.M.T.—CASE studentship in association with Roche Products Ltd; N.M.O.B. and J.B.O.M.—grant BB/C51320X/1), the Chilean Government’s Ministerio de Planificacio´n y Cooperacio´n and
Cambridge Overseas Trust (D.E.A.) for funding and Unilever for supporting the Centre for Molecular Science Informatics.application note restricted to 2 printed pages web site: http://www-mitchell.ch.cam.ac.uk/macie
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
E-zyme: predicting potential EC numbers from the chemical transformation pattern of substrate-product pairs
Motivation: The IUBMB's Enzyme Nomenclature system, commonly known as the Enzyme Commission (EC) numbers, plays key roles in classifying enzymatic reactions and in linking the enzyme genes or proteins to reactions in metabolic pathways. There are numerous reactions known to be present in various pathways but without any official EC numbers, most of which have no hope to be given ones because of the lack of the published articles on enzyme assays
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