Flexible nonlinear blind signal separation in the complex domain

This paper introduces an Independent Component Analysis (ICA) approach to the separation of nonlinear mixtures in the complex domain. Source separation is performed by a complex INFOMAX approach. The neural network which realizes the separation employs the so called "Mirror Model" and is based on adaptive activation functions, whose shape is properly modified during learning. Nonlinear functions involved in the processing of complex signals are realized by pairs of spline neurons called "splitting functions", working on the real and the imaginary part of the signal respectively. Theoretical proof of existence and uniqueness of the solution under proper assumptions is also provided. In particular a simple adaptation algorithm is derived and some experimental results that demonstrate the effectiveness of the proposed solution are shown.     

A semi-parametric Bayesian model for unsupervised differential co-expression analysis

Background  

Differential co-expression analysis is an emerging strategy for characterizing disease related dysregulation of gene expression regulatory networks. Given pre-defined sets of biological samples, such analysis aims at identifying genes that are co-expressed in one, but not in the other set of samples.     

A semi-parametric statistical model for integrating gene expression profiles across different platforms

Determining differentially expressed genes (DEGs) between biological samples is the key to understand how genotype gives rise to phenotype. RNA-seq and microarray are two main technologies for profiling gene expression levels. However, considerable discrepancy has been found between DEGs detected using the two technologies. Integration data across these two platforms has the potential to improve the power and reliability of DEG detection. We propose a rank-based semi-parametric model to determine DEGs using information across different sources and apply it to the integration of RNA-seq and microarray data. By incorporating both the significance of differential expression and the consistency across platforms, our method effectively detects DEGs with moderate but consistent signals. We demonstrate the effectiveness of our method using simulation studies, MAQC/SEQC data and a synthetic microRNA dataset. Our integration method is not only robust to noise and heterogeneity in the data, but also adaptive to the structure of data. In our simulations and real data studies, our approach shows a higher discriminate power and identifies more biologically relevant DEGs than eBayes, DEseq and some commonly used meta-analysis methods.     

Novel two-stage hybrid neural discriminant model for predicting proteins structural classes

In order to establish novel hybrid neural discriminant model, linear discriminant analysis (LDA) was used at the first stage to evaluate the contribution of sequence parameters in determining the protein structural class. An in-house program generated parameters including single amino acid and all dipeptide composition frequencies for 498 proteins came from Zhou [An intriguing controversy over protein structural class prediction, J. Protein Chem. 17(8) (1998) 729-738]. Then, 127 statistically effective parameters were selected by stepwise LDA and were used as inputs of the artificial neural networks (ANNs) to build a two-stage hybrid predictor. In this study, self-consistency and jackknife tests were used to verify the performance of this hybrid model, and were compared with some of prior works. The results showed that our two-stage hybrid neural discriminant model approach is very promising and may play a complementary role to the existing powerful approaches.     

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.     

Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures

In this paper, we review recent advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixing models. After a general introduction to BSS and ICA, we discuss in more detail uniqueness and separability issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they provide non-unique solutions without extra constraints, which are often implemented by using a suitable regularization. In this paper, we explore two possible approaches. The first one is based on structural constraints. Especially, post-nonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. The second approach uses Bayesian inference methods for estimating the best statistical parameters, under almost unconstrained models in which priors can be easily added. In the later part of this paper, various separation techniques proposed for post-nonlinear mixtures and general nonlinear mixtures are reviewed.     

A neural net model for epilepsy

A neural net model based in our previous studies with randomly interconnected neural nets is presented here capable of exhibiting epileptic features. These features can be explained in terms of the structural and dynamical properties of the model. In addition, apart from the fact that this model can imitate epileptic phenomena, it might also help to explain some poorly understood clinical phenomena from which general disturbances can produce focal seizures in the brain.     

A neural model for category learning

We present a general neural model for supervised learning of pattern categories which can resolve pattern classes separated by nonlinear, essentially arbitrary boundaries. The concept of a pattern class develops from storing in memory a limited number of class elements (prototypes). Associated with each prototype is a modifiable scalar weighting factor () which effectively defines the threshold for categorization of an input with the class of the given prototype. Learning involves (1) commitment of prototypes to memory and (2) adjustment of the various factors to eliminate classification errors. In tests, the model ably defined classification boundaries that largely separated complicated pattern regions. We discuss the role which divisive inhibition might play in a possible implementation of the model by a network of neurons.This work was supported in part by the Alfred P. Sloan Foundation and the Ittleson Foundation, Inc.     

A neural network dynamic model reproducing the output signal of the ganglion cell

A functional model of a neural network reproducing the output signal of the ganglion cell is proposed. The model assumes that receptive fields with antagonistic center and periphery are formed.     

A linear framework for time-scale separation in nonlinear biochemical systems

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.     

A hybrid model for reducing ecological bias

A major drawback of epidemiological ecological studies, in which the association between area-level summaries of risk and exposure is used to make inference about individual risk, is the difficulty in characterizing within-area variability in exposure and confounder variables. To avoid ecological bias, samples of individual exposure/confounder data within each area are required. Unfortunately, these may be difficult or expensive to obtain, particularly if large samples are required. In this paper, we propose a new approach suitable for use with small samples. We combine a Bayesian nonparametric Dirichlet process prior with an estimating functions' approach and show that this model gives a compromise between 2 previously described methods. The method is investigated using simulated data, and a practical illustration is provided through an analysis of lung cancer mortality and residential radon exposure in counties of Minnesota. We conclude that we require good quality prior information about the exposure/confounder distributions and a large between- to within-area variability ratio for an ecological study to be feasible using only small samples of individual data.     

A neural model for conditioned avoidance learning

A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared.     

A neural net model for escape learning

An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed. This research was supported in part by the United States Public Health Service Grant RCA GM K6 18,420 and in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Grant No. AF AFOSR 370-64.     

A neural net model for masking phenomena

Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.     

A neural network model for texture discrimination

A model of texture discrimination in visual cortex was built using a feedforward network with lateral interactions among relatively realistic spiking neural elements. The elements have various membrane currents, equilibrium potentials and time constants, with action potentials and synapses. The model is derived from the modified programs of MacGregor (1987). Gabor-like filters are applied to overlapping regions in the original image; the neural network with lateral excitatory and inhibitory interactions then compares and adjusts the Gabor amplitudes in order to produce the actual texture discrimination. Finally, a combination layer selects and groups various representations in the output of the network to form the final transformed image material. We show that both texture segmentation and detection of texture boundaries can be represented in the firing activity of such a network for a wide variety of synthetic to natural images. Performance details depend most strongly on the global balance of strengths of the excitatory and inhibitory lateral interconnections. The spatial distribution of lateral connective strengths has relatively little effect. Detailed temporal firing activities of single elements in the lateral connected network were examined under various stimulus conditions. Results show (as in area 17 of cortex) that a single element's response to image features local to its receptive field can be altered by changes in the global context.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

Optimization for high-density cultivation of heterotrophic Chlorella based on a hybrid neural network model

AIMS: The purpose of this study was to develop a reliable hybrid neural network (HNN) model for heterotrophic growth of Chlorella, based on which optimization for fed-batch (FB) cultivation of Chlorella may be successfully realized. METHODS AND RESULTS: Deterministic kinetic model was preliminarily developed for the optimization of FB cultivation of Chlorella. The highest biomass concentration and the maximum productivity were obtained as: 104.9 g l(-1) dry cell weight and 0.613 g l(-1) h(-1), respectively. After several cultivations had been performed, an HNN model was developed. The efficiency of biomass production was further increased by the optimization using this model. The highest biomass concentration and the maximum productivity attained was: 116.2 g l(-1) dry cell weight and 1.020 g l(-1) h(-1), respectively. CONCLUSION: The HNN model agreed well with experimental results in different cultivations. Comparison between the HNN model and the deterministic model showed that the former had better generalization ability, which made it a reliable tool in modelling and optimization. SIGNIFICANCE AND IMPACT OF THE STUDY: The high cell density and productivity of biomass obtained in this study is of significance for the commercial cultivation of Chlorella. The simple and efficient optimization strategy proposed in this paper may be employed in heterotrophic mass culture of Chlorella as well as other similar organisms.     

A hybrid symbolic-numerical method for determining model structure

In this article, we present a method for determining whether a model is at least locally identifiable and in the case of non-identifiable models whether any of the parameters are individually at least locally identifiable. This method combines symbolic and numeric methods to create an algorithm that is extremely accurate compared to other numeric methods and computationally inexpensive. A series of generic computational steps are developed to create a method that is ideal for practitioners to use. The algorithm is compared to symbolic methods for two capture-recapture models and a compartment model.     

A hybrid computational model for collective cell durotaxis

Collective cell migration is regulated by a complex set of mechanical interactions and cellular mechanisms. Collective migration emerges from mechanisms occurring at single cell level, involving processes like contraction, polymerization and depolymerization, of cell–cell interactions and of cell–substrate adhesion. Here, we present a computational framework which simulates the dynamics of this emergent behavior conditioned by substrates with stiffness gradients. The computational model reproduces the cell’s ability to move toward the stiffer part of the substrate, process known as durotaxis. It combines the continuous formulation of truss elements and a particle-based approach to simulate the dynamics of cell–matrix adhesions and cell–cell interactions. Using this hybrid approach, researchers can quickly create a quantitative model to understand the regulatory role of different mechanical conditions on the dynamics of collective cell migration. Our model shows that durotaxis occurs due to the ability of cells to deform the substrate more in the part of lower stiffness than in the stiffer part. This effect explains why cell collective movement is more effective than single cell movement in stiffness gradient conditions. In addition, we numerically evaluate how gradient stiffness properties, cell monolayer size and force transmission between cells and extracellular matrix are crucial in regulating durotaxis.     

A hybrid process for chiral separation of compound‐forming systems

The resolution of chiral compound‐forming systems using hybrid processes was discussed recently. The concept is of large relevance as these systems form the majority of chiral substances. In this study, a novel hybrid process is presented, which combines pertraction and subsequent preferential crystallization and is applicable for the resolution of such systems. A supported liquid membrane applied in a pertraction process provides enantiomeric enrichment. This membrane contains a solution of a chiral compound acting as a selective carrier for one of the enantiomers. Screening of a large number of liquid membranes and potential carriers using the conductor‐like screening model for realistic solvation method led to the identification of several promising carriers, which were tested experimentally in several pertraction runs aiming to yield enriched (+)‐(S)‐mandelic acid (MA) solutions from racemic feed solutions. The most promising system consisted of tetrahydronaphthalene as liquid membrane and hydroquinine‐4‐methyl‐2‐quinolylether (HMQ) as chiral carrier achieving enantiomeric excesses of 15% in average. The successful production of (+)‐(S)‐MA with a purity above 96% from enriched solutions by subsequent preferential crystallization proved the applicability of the hybrid process. Chirality, 2011. © 2010 Wiley‐Liss, Inc.