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 $n$ variables and $m$ constraints ($n>m$), 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 ${\cal F}^{(n,m)}(\Delta)$ of the convergence rate $\Delta_{min}$ to this point is calculated analytically, in the asymptotic limit of large $(n,m)$, in the framework of Random Matrix Theory. In this limit ${\cal F}^{(n,m)}(\Delta)$ is found to be a scaling function, namely it is a function of one variable that is a combination of $n$, $m$ and $\Delta$ 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

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

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

Word correlation matrices for protein sequence analysis and remote homology detection

<p>Abstract</p> <p>Background</p> <p>Classification of protein sequences is a central problem in computational biology. Currently, among computational methods discriminative kernel-based approaches provide the most accurate results. However, kernel-based methods often lack an interpretable model for analysis of discriminative sequence features, and predictions on new sequences usually are computationally expensive.</p> <p>Results</p> <p>In this work we present a novel kernel for protein sequences based on average word similarity between two sequences. We show that this kernel gives rise to a feature space that allows analysis of discriminative features and fast classification of new sequences. We demonstrate the performance of our approach on a widely-used benchmark setup for protein remote homology detection.</p> <p>Conclusion</p> <p>Our word correlation approach provides highly competitive performance as compared with state-of-the-art methods for protein remote homology detection. The learned model is interpretable in terms of biologically meaningful features. In particular, analysis of discriminative words allows the identification of characteristic regions in biological sequences. Because of its high computational efficiency, our method can be applied to ranking of potential homologs in large databases.</p