Mircea Andrecut

Parallel GPU Implementation of Iterative PCA Algorithms

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets, the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from loss of orthogonality, and therefore its applicability is usually limited to the estimation of the first few components. Here we present an algorithm based on Gram-Schmidt orthogonalization (called GS-PCA), which eliminates this shortcoming of NIPALS-PCA. Also, we discuss the GPU (Graphics Processing Unit) parallel implementation of both NIPALS-PCA and GS-PCA algorithms. The numerical results show that the GPU parallel optimized versions, based on CUBLAS (NVIDIA), are substantially faster (up to 12 times) than the CPU optimized versions based on CBLAS (GNU Scientific Library).

A General Model for Binary Cell Fate Decision Gene Circuits with Degeneracy: Indeterminacy and Switch Behavior in the Absence of Cooperativity

Background The gene regulatory circuit motif in which two opposing fate-determining transcription factors inhibit each other but activate themselves has been used in mathematical models of binary cell fate decisions in multipotent stem or progenitor cells. This simple circuit can generate multistability and explains the symmetric “poised” precursor state in which both factors are present in the cell at equal amounts as well as the resolution of this indeterminate state as the cell commits to either cell fate characterized by an asymmetric expression pattern of the two factors. This establishes the two alternative stable attractors that represent the two fate options. It has been debated whether cooperativity of molecular interactions is necessary to produce such multistability. Principal Findings Here we take a general modeling approach and argue that this question is not relevant. We show that non-linearity can arise in two distinct models in which no explicit interaction between the two factors is assumed and that distinct chemical reaction kinetic formalisms can lead to the same (generic) dynamical system form. Moreover, we describe a novel type of bifurcation that produces a degenerate steady state that can explain the metastable state of indeterminacy prior to cell fate decision-making and is consistent with biological observations. Conclusion The general model presented here thus offers a novel principle for linking regulatory circuits with the state of indeterminacy characteristic of multipotent (stem) cells.

Heuristic approach to sparse approximation of gene regulatory networks.

Determining the structure of the gene regulatory network using the information in genomewide profiles of mRNA abundance, such as microarray data, poses several challenges. Typically, static rather than dynamical profile measurements, such as those taken from steady state tissues in various conditions, are the starting point. This makes the inference of causal relationships between genes difficult. Moreover, the paucity of samples relative to the gene number leads to problems such as overfitting and underconstrained regression analysis. Here we present a novel method for the sparse approximation of gene regulatory networks that addresses these issues. It is formulated as a sparse combinatorial optimization problem which has a globally optimal solution in terms of l(0) norm error. In order to seek an approximate solution of the l(0) optimization problem, we consider a heuristic approach based on iterative greedy algorithms. We apply our method to a set of gene expression profiles comprising of 24,102 genes measured over 79 human tissues. The inferred network is a signed directed graph, hence predicts causal relationships. It exhibits typical characteristics of regulatory networks organism with partially known network topology, such as the average number of inputs per gene as well as the in-degree and out-degree distribution.

On the Sparse Reconstruction of Gene Networks

We discuss a heuristic method for the sparse reconstruction of gene networks. The method is based on iterative greedy algorithms, and uses gene expression data from microarray experiments. Also, we show numerically that the greedy algorithms are able to give good approximative solutions to the sparse reconstruction problem even in the presence of significant levels of noise.

Efficient Heuristic Approach to the Weapon-Target Assignment Problem

The weapon‐target assignment problem is a fundamental defense application of operations research. The problem consists of optimally assigning a given number of weapons to a set of targets, so that the post-engagement total expected survival value of the targets is minimized. Since the weapon‐target assignment problem is known to be nondeterministic polynomial time-complete, there are no exact methods to solve it. This paper presents two innovative heuristic algorithms based on simulated annealing and threshold accepting methodstosolvethegeneralweapon‐targetassignmentproblem.Ourcomputationalresultsshow that by using these algorithms, relatively large instances of the weapon‐target assignment problem can be solved near-optimally in a few seconds on a standard personal computer.

Maximal Information Transfer and Behavior Diversity in Random Threshold Networks

Random Threshold Networks (RTNs) are an idealized model of diluted, non-symmetric spin glasses, neural networks or gene regulatory networks. RTNs also serve as an interesting general example of any coordinated causal system. Here we study the conditions for maximal information transfer and behavior diversity in RTNs. These conditions are likely to play a major role in physical and biological systems, perhaps serving as important selective traits in biological systems. We show that the pairwise mutual information is maximized in dynamically critical networks. Also, we show that the correlated behavior diversity is maximized for slightly chaotic networks, close to the critical region. Importantly, critical networks maximize coordinated, diverse dynamical behavior across the network and across time: the information transmission between source and receiver nodes and the diversity of dynamical behaviors, when measured with a time delay between the source and receiver, are maximized for critical networks.

Noise in Genetic Toggle Switch Models

Summary In this paper we study the intrinsic noise effect on the switching behavior of a simple genetic circuit corresponding to the genetic toggle switch model. The numerical results obtained from a noisy mean-field model are compared to those obtained from the stochastic Gillespie simulation of the corresponding system of chemical reactions. Our results show that by using a two step reaction approach for modeling the transcription and translation processes one can make the system to lock in one of the steady states for exponentially long times.

Evidence Of Scale-Free Topology In Gene Regulatory Network Of Human Tissues

We report the reconstruction of the topology of gene regulatory network in human tissues. The results show that the connectivity of the regulatory gene network is characterized by a scale-free distribution. This result supports the hypothesis that scale-free networks may represent the common blueprint for gene regulatory networks.

Competitive optimization of compressed sensing

The compressed sensing framework enables the recovery of a sparse signal from a small number of projections onto random vectors. Here, we propose a new extension method of compressed sensing, applied to signals sparse in the time domain. The method consists, in a competitive ensemble, of compressed sensing devices. We show that this approach leads to a substantial improvement in performance. Also, we propose a simplified version of compressed sensing, in which the random projections are replaced by cyclic correlations with a single random vector. Encouraged by the results obtained with the competitive ensemble approach, we show that the performance can be even more improved by employing a simulated annealing algorithm.

Exact Fourier spectrum recovery

Abstract Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to the sampling grid. Here, we present an exact Fourier spectrum recovery method and we provide an implementation algorithm. Also, we show numerically that the proposed method is robust to noise perturbations.