Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

Elephant Search with Deep Learning for Microarray Data Analysis

Even though there is a plethora of research in Microarray gene expression data analysis, still, it poses challenges for researchers to effectively and efficiently analyze the large yet complex expression of genes. The feature (gene) selection method is of paramount importance for understanding the differences in biological and non-biological variation between samples. In order to address this problem, a novel elephant search (ES) based optimization is proposed to select best gene expressions from the large volume of microarray data. Further, a promising machine learning method is envisioned to leverage such high dimensional and complex microarray dataset for extracting hidden patterns inside to make a meaningful prediction and most accurate classification. In particular, stochastic gradient descent based Deep learning (DL) with softmax activation function is then used on the reduced features (genes) for better classification of different samples according to their gene expression levels. The experiments are carried out on nine most popular Cancer microarray gene selection datasets, obtained from UCI machine learning repository. The empirical results obtained by the proposed elephant search based deep learning (ESDL) approach are compared with most recent published article for its suitability in future Bioinformatics research.Comment: 12 pages, 5 Tabl

Theory of Robustness of Irreversible Differentiation in a Stem Cell System: Chaos hypothesis

Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell systems - stochastic differentiation of stem cells and the robustness of a system due to regulation of this differentiation - are found to be general properties of a system of interacting cells exhibiting chaotic intra-cellular reaction dynamics and cell division, whose presence does not depend on the detail of the model. It is found that stem cells differentiate into other cell types stochastically due to a dynamical instability caused by cell-cell interactions, in a manner described by the Isologous Diversification theory. This developmental process is shown to be stable not only with respect to molecular fluctuations but also with respect to removal of cells. With this developmental process, the irreversible loss of multipotency accompanying the change from a stem cell to a differentiated cell is shown to be characterized by a decrease in the chemical diversity in the cell and of the complexity of the cellular dynamics. The relationship between the division speed and this loss of multipotency is also discussed. Using our model, some predictions that can be tested experimentally are made for a stem cell system.Comment: 31 pages, 10 figures, submitted to Jour. Theor. Bio

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA