BackgroundThe 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 FindingsHere 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.ConclusionThe general model presented here thus offers a novel principle for linking regulatory circuits with the state of indeterminacy characteristic of multipotent (stem) cells.

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 it's 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).

We present a numerical investigation of the minority game model, where the dynamics of the agents is described by the Q-learning algorithm. The numerical results show that the Q-learning dynamics is suppressing the "crowd effect," which is characteristic of the minority game with standard inductive dynamics, and it converges to a stationary state that is close to the optimal Nash equilibrium of the game.

For the largest value of the control parameter, the logistic map is able to generate an infinite chaotic sequence of numbers. Here we describe a simple method for obtaining a random number generator based on this property of the logistic map. Comparing to usual congruential random generators, which are periodic, the logistic random number generator is infinite, aperiodic and not correlated. An aperiodic random number generator is a valuable tool for computer simulation methods.

Faraday rotation measure synthesis is a method for analyzing multichannel polarized radio emissions, and it has emerged as an important tool in the study of galactic and extra-galactic magnetic fields. The method requires the recovery of the Faraday dispersion function from measurements restricted to limited wavelength ranges, which is an ill-conditioned deconvolution problem. Here, we discuss a recovery method, which assumes a sparse approximation of the Faraday dispersion function in an over-complete dictionary of functions. We discuss the general case, when both thin and thick components are included in the model, and we present the implementation of a greedy deconvolution algorithm. We illustrate the method with several numerical simulations that emphasize the effect of the covered range and sampling resolution in the Faraday depth space, and the effect of noise on the observed data.