774 research outputs found
Probabilistic analysis of a differential equation for linear programming
In this paper we address the complexity of solving linear programming
problems with a set of differential equations that converge to a fixed point
that represents the optimal solution. Assuming a probabilistic model, where the
inputs are i.i.d. Gaussian variables, we compute the distribution of the
convergence rate to the attracting fixed point. Using the framework of Random
Matrix Theory, we derive a simple expression for this distribution in the
asymptotic limit of large problem size. In this limit, we find that the
distribution of the convergence rate is a scaling function, namely it is a
function of one variable that is a combination of three parameters: the number
of variables, the number of constraints and the convergence rate, rather than a
function of these parameters separately. We also estimate numerically the
distribution of computation times, namely the time required to reach a vicinity
of the attracting fixed point, and find that it is also a scaling function.
Using the problem size dependence of the distribution functions, we derive high
probability bounds on the convergence rates and on the computation times.Comment: 1+37 pages, latex, 5 eps figures. Version accepted for publication in
the Journal of Complexity. Changes made: Presentation reorganized for
clarity, expanded discussion of measure of complexity in the non-asymptotic
regime (added a new section
Probabilistic analysis of the phase space flow for linear programming
The phase space flow of a dynamical system leading to the solution of Linear
Programming (LP) problems is explored as an example of complexity analysis in
an analog computation framework. An ensemble of LP problems with variables
and constraints (), where all elements of the vectors and matrices are
normally distributed is studied. The convergence time of a flow to the fixed
point representing the optimal solution is computed. The cumulative
distribution of the convergence rate
to this point is calculated analytically, in the asymptotic limit of large
, in the framework of Random Matrix Theory. In this limit is found to be a scaling function, namely it is a function
of one variable that is a combination of , and rather then a
function of these three variables separately. From numerical simulations also
the distribution of the computation times is calculated and found to be a
scaling function as well.Comment: 8 pages, latex, 2 eps figures; final published versio
A two-step learning approach for solving full and almost full cold start problems in dyadic prediction
Dyadic prediction methods operate on pairs of objects (dyads), aiming to
infer labels for out-of-sample dyads. We consider the full and almost full cold
start problem in dyadic prediction, a setting that occurs when both objects in
an out-of-sample dyad have not been observed during training, or if one of them
has been observed, but very few times. A popular approach for addressing this
problem is to train a model that makes predictions based on a pairwise feature
representation of the dyads, or, in case of kernel methods, based on a tensor
product pairwise kernel. As an alternative to such a kernel approach, we
introduce a novel two-step learning algorithm that borrows ideas from the
fields of pairwise learning and spectral filtering. We show theoretically that
the two-step method is very closely related to the tensor product kernel
approach, and experimentally that it yields a slightly better predictive
performance. Moreover, unlike existing tensor product kernel methods, the
two-step method allows closed-form solutions for training and parameter
selection via cross-validation estimates both in the full and almost full cold
start settings, making the approach much more efficient and straightforward to
implement
Dynamically Driven Renormalization Group Applied to Sandpile Models
The general framework for the renormalization group analysis of
self-organized critical sandpile models is formulated. The usual real space
renormalization scheme for lattice models when applied to nonequilibrium
dynamical models must be supplemented by feedback relations coming from the
stationarity conditions. On the basis of these ideas the Dynamically Driven
Renormalization Group is applied to describe the boundary and bulk critical
behavior of sandpile models. A detailed description of the branching nature of
sandpile avalanches is given in terms of the generating functions of the
underlying branching process.Comment: 18 RevTeX pages, 5 figure
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A Bethe lattice representation for sandpiles
Avalanches in sandpiles are represented throughout a process of percolation
in a Bethe lattice with a feedback mechanism. The results indicate that the
frequency spectrum and probability distribution of avalanches resemble more to
experimental results than other models using cellular automata simulations.
Apparent discrepancies between experiments are reconciled. Critical behavior is
here expressed troughout the critical properties of percolation phenomena.Comment: 5 pages, 4 figures, submitted for publicatio
Supervised inference of gene-regulatory networks
<p>Abstract</p> <p>Background</p> <p>Inference of protein interaction networks from various sources of data has become an important topic of both systems and computational biology. Here we present a supervised approach to identification of gene expression regulatory networks.</p> <p>Results</p> <p>The method is based on a kernel approach accompanied with genetic programming. As a data source, the method utilizes gene expression time series for prediction of interactions among regulatory proteins and their target genes. The performance of the method was verified using Saccharomyces cerevisiae cell cycle and DNA/RNA/protein biosynthesis gene expression data. The results were compared with independent data sources. Finally, a prediction of novel interactions within yeast gene expression circuits has been performed.</p> <p>Conclusion</p> <p>Results show that our algorithm gives, in most cases, results identical with the independent experiments, when compared with the YEASTRACT database. In several cases our algorithm gives predictions of novel interactions which have not been reported.</p
Neuroprotective Effect of Transplanted Human Embryonic Stem Cell-Derived Neural Precursors in an Animal Model of Multiple Sclerosis
BACKGROUND: Multiple sclerosis (MS) is an immune mediated demyelinating disease of the central nervous system (CNS). A potential new therapeutic approach for MS is cell transplantation which may promote remyelination and suppress the inflammatory process. METHODS: We transplanted human embryonic stem cells (hESC)-derived early multipotent neural precursors (NPs) into the brain ventricles of mice induced with experimental autoimmune encephalomyelitis (EAE), the animal model of MS. We studied the effect of the transplanted NPs on the functional and pathological manifestations of the disease. RESULTS: Transplanted hESC-derived NPs significantly reduced the clinical signs of EAE. Histological examination showed migration of the transplanted NPs to the host white matter, however, differentiation to mature oligodendrocytes and remyelination were negligible. Time course analysis of the evolution and progression of CNS inflammation and tissue injury showed an attenuation of the inflammatory process in transplanted animals, which was correlated with the reduction of both axonal damage and demyelination. Co-culture experiments showed that hESC-derived NPs inhibited the activation and proliferation of lymph node-derived T cells in response to nonspecific polyclonal stimuli. CONCLUSIONS: The therapeutic effect of transplantation was not related to graft or host remyelination but was mediated by an immunosuppressive neuroprotective mechanism. The attenuation of EAE by hESC-derived NPs, demonstrated here, may serve as the first step towards further developments of hESC for cell therapy in MS
Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
Universality in isotropic, abelian and non-abelian, sandpile models is
examined using extensive numerical simulations. To characterize the critical
behavior we employ an extended set of critical exponents, geometric features of
the avalanches, as well as scaling functions describing the time evolution of
average quantities such as the area and size during the avalanche. Comparing
between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K.
Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models
introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C.
Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each
one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file
Support Vector Machines and Kernels for Computational Biology
ISSN:1553-734XISSN:1553-735
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