Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.      

An adaptive human–machine control system based on multiple fuzzy predictive models of operator functional state

Under the framework of adaptive Human–Machine (HM) systems, it has been proposed that human operators’ task level should be dynamically adjusted according to his/her functional state. The construction of models that can reliably predict the operator functional state (OFS) becomes critical to accomplish such adjustments. However, most of the existing models that evaluate the current OFS by using operators’ current physiological data are static and are of no real predictive capability. Thus, when they are used in adaptive HM systems, the resultant task allocation between operators and machines would be time-delayed. To overcome this problem, a one-step-ahead predictive model concept for OFS computation is proposed. Meanwhile, multiple fuzzy models are developed by using the Wang–Mendel method. These models are able to increase the accuracy of the OFS breakdown prediction, as well as to reduce the model training time. In addition, an adaptive task allocation strategy is designed to validate the proposed models. The results demonstrate that, compared to the conventional HM systems, a 6.7% OFS increment and a 57.1% OFS breakdown decrement can be obtained in the multiple models based adaptive HM systems. The multiple predictive models and the adaptive task allocation strategy would pave the way for future implementations of real-time adaptive HM systems.     

The effectiveness of mutation operation in the case of Estimation of Distribution Algorithms

The Estimation of Distribution Algorithms are a class of evolutionary algorithms which adopt probabilistic models to reproduce individuals in the next generation, instead of conventional crossover and mutation operators. In this paper, mutation operators are incorporated into Estimation of Distribution Algorithms in order to maintain the diversities in EDA populations. Two kinds of mutation operators are examined: a bitwise mutation operator and a mutation operator taking account into the probabilistic model. In experiments, we do not only compare the proposed methods with conventional EDAs on a few fitness functions but also analyze sampled probabilistic models by using KL-divergence. The experimental results shown in this paper elucidate that the mutation operator taking account into the probabilistic model improve the search ability of EDAs.     

Towards more biological mutation operators in gene regulation studies

Genetic regulation is often viewed as a complex system whose properties emerge from the interaction of regulatory genes. One major paradigm for studying the complex dynamics of gene regulation uses directed graphs to explore structure, behaviour and evolvability. Mutation operators used in such studies typically involve the insertion and deletion of nodes, and the insertion, deletion and rewiring of links at the network level. These network-level mutational operators are sufficient to allow the statistical analysis of network structure, but impose limitations on the way networks are evolved. There are a wide variety of mutations in DNA sequences that have yet to be analysed for their network-level effects. By modelling an artificial genome at the level of nucleotide sequences and mapping it to a regulatory network, biologically grounded mutation operators can be mapped to network-level mutations. This paper analyses five such sequence level mutations (single-point mutation, transposition, inversion, deletion and gene duplication) for their effects at the network level. Using analytic and simulation techniques, we show that it is rarely the case that nodes and links are cleanly added or deleted, with even the simplest point mutation causing a wide variety of network-level modifications. As expected, the vast majority of simple (single-point) mutations are neutral, resulting in a neutral plateau from which a range of functional behaviours can be reached. By analysing the effects of sequence-level mutations at the network level of gene regulation, we aim to stimulate more careful consideration of mutation operators in gene regulation models than has previously been given.     

A multi-differential neuromorphic approach to motion detection

This paper presents a multi-differential neuromorphic approach to motion detection. The model is based evidence for a differential operators interpretation of the properties of the cortical motion pathway. We discuss how this strategy, which provides a robust measure of speed for a range of types of image motion using a single computational mechanism, forms a useful framework in which to develop future neuromorphic motion systems. We also discuss both our approaches to developing computational motion models, and constraints in the design strategy for transferring motion models to other domains of early visual processing.     

Automatic Combination of Operators in a Genetic Algorithm to Solve the Traveling Salesman Problem

Genetic algorithms are powerful search methods inspired by Darwinian evolution. To date, they have been applied to the solution of many optimization problems because of the easy use of their properties and their robustness in finding good solutions to difficult problems. The good operation of genetic algorithms is due in part to its two main variation operators, namely, crossover and mutation operators. Typically, in the literature, we find the use of a single crossover and mutation operator. However, there are studies that have shown that using multi-operators produces synergy and that the operators are mutually complementary. Using multi-operators is not a simple task because which operators to use and how to combine them must be determined, which in itself is an optimization problem. In this paper, it is proposed that the task of exploring the different combinations of the crossover and mutation operators can be carried out by evolutionary computing. The crossover and mutation operators used are those typically used for solving the traveling salesman problem. The process of searching for good combinations was effective, yielding appropriate and synergic combinations of the crossover and mutation operators. The numerical results show that the use of the combination of operators obtained by evolutionary computing is better than the use of a single operator and the use of multi-operators combined in the standard way. The results were also better than those of the last operators reported in the literature.     

Generation model of positional values as cell operation during the development of multicellular organisms

Many conventional models have used the positional information hypothesis to explain each elementary process of morphogenesis during the development of multicellular organisms. Their models assume that the steady concentration patterns of morphogens formed in an extracellular environment have an important property of positional information, so-called “robustness”. However, recent experiments reported that a steady morphogen pattern, the concentration gradient of the Bicoid protein, during early Drosophila embryonic development is not robust for embryo-to-embryo variability. These reports encourage a reconsideration of a long-standing problem in systematic cell differentiation: what is the entity of positional information for cells? And, what is the origin of the robust boundary of gene expression? To address these problems at a cellular level, in this article we pay attention to the re-generative phenomena that show another important property of positional information, “size invariance”. In view of regenerative phenomena, we propose a new mathematical model to describe the generation mechanism of a spatial pattern of positional values. In this model, the positional values are defined as the values into which differentiable cells transform a spatial pattern providing positional information. The model is mathematically described as an associative algebra composed of various terms, each of which is the multiplication of some fundamental operators under the assumption that the operators are derived from the remarkable properties of cell differentiation on an amputation surface in regenerative phenomena. We apply this model to the concentration pattern of the Bicoid protein during the anterior-posterior axis formation in Drosophila, and consider the conditions needed to establish the robust boundary of the expression of the hunchback gene.     

The mathematical theory of lateral impedance of visual activity and an application of Markov processes

The mathematical relationship describing recurrent lateral inhibition is expressed as a linear operator equation. Under quite general conditions, the operator equation is shown to have a unique nonnegative solution. It is also shown that the linear operator for recurrent impedance is representable as an integral operator and that, when in application to physiological models it is interpreted as recurrent inhibition, the corresponding linear equation assumes a form more general than the well known Hartline-Ratliff equation. Finally, we introduce a class of impedance operators based on the probabilistic theory of Markov processes, solve the corresponding linear integral equation, and apply the theoretical properties of the solution to the analysis of physiological and psychophysical phenomena.     

Modelling the biological invasion of Carcinus maenas (the European green crab)

This paper proposes a system of integro-difference equations to model the spread of Carcinus maenas, commonly called the European green crab, that causes severe damage to coastal ecosystems. A model with juvenile and adult classes is first studied. Here, standard theory of monotone operators for integro-difference equations can be applied and yields explicit formulas for the asymptotic spreading speeds of the juvenile and adult crabs. A second model including an infected class is considered by introducing a castrating parasite Sacculina carcini as a biological control agent. The dynamics are complicated and simulations reveal the occurrence of periodic solutions and stacked fronts. In this case, only conjectures can be made for the asymptotic spreading speeds because of the lack of mathematical theory for non-monotone operators. This paper also emphasizes the need for mathematical studies of non-monotone operators in heterogeneous environments and the existence of stacked front solutions in biological invasion models.     

On the representation of multi-input systems: Computational properties of polynomial algorithms

This paper introduces a theoretical framework for characterizing and classifying simple parallel algorithms and systems with many inputs, for example an array of photoreceptors. The polynomial representation (Taylor series development) of a large class of operators is introduced and its range of validity discussed. The problems involved in the polynomial approximation of systems are also briefly reviewed. Symmetry properties of the input-output map and their implications for the system structure (i.e. its kernels) are studied. Finally, the computational properties of polynomial mappings are characterized.     

On the formulation and analysis of general deterministic structured population models I. Linear Theory

—We define a linear physiologically structured population model by two rules, one for reproduction and one for “movement” and survival. We use these ingredients to give a constructive definition of next-population-state operators. For the autonomous case we define the basic reproduction ratio R ₀ and the Malthusian parameter r and we compute the resolvent in terms of the Laplace transform of the ingredients. A key feature of our approach is that unbounded operators are avoided throughout. This will facilitate the treatment of nonlinear models as a next step. Received 26 July 1996; received in revised form 3 September 1997     

Plant mimicry: evolutionary constraints

Because plants are sessile and their flowers and fruits are aggregated, plant mimics are less likely to be mistaken for their models than animal mimics which are mobile and dispersed among their models. Therefore, operator species are more likely to be deceived by animal mimics than plant mimics. In addition, the autonomy of plant appendages implies that warning mimicry provides less advantage to plants than to animals because plants suffer less from sampling by naive operators. Therefore, the advantage of warning mimicry is much greater for animals than plants. These reasons may explain why plant mimicry is less common than animal mimicry, based on attraction of rather than avoidance by operator species, and limited to the class of aggressive mimicry.     

Plant mimicry: evolutionary constraints

Because plants are sessile and their flowers and fruits are aggregated, plant mimics are less likely to be mistaken for their models than animal mimics which are mobile and dispersed among their models. Therefore, operator species are more likely to be deceived by animal mimics than plant mimics. In addition, the autonomy of plant appendages implies that warning mimicry provides less advantage to plants than to animals because plants suffer less from sampling by naive operators. Therefore, the advantage of warning mimicry is much greater for animals than plants. These reasons may explain why plant mimicry is less common than animal mimicry, based on attraction of rather than avoidance by operator species, and limited to the class of aggressive mimicry.     

On selection criteria in spatially distributed models of competition

Discrete models of competitors (initial population and mutants) are considered in which reproduction is set by an increasing and concave function, and migration in the space consisting of a set of areas is described by a Markov matrix. This allows using the theory of monotonic operators to study problems of selection, coexistence and stability. It is shown that the higher is the number of areas, the more severe are the requirements of selective advantage to the initial population.     

Basic properties of populations generated in the frame of one-parameter discrete model of genetic diversity

Previously, when discussing the properties of one parameter discrete model of genetic diversity (M.Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887-894 (1998)), we took into account Hamming distance distribution only between precursor and arbitrary descendant sequences. However, really there are sets of sequence populations produced during amplification process. In the presented work we have investigated Hamming distance distributions between sequences from different descendant sets produced in the frame of one parameter discrete model. Two basic descendant generation operators (so called amplifiers) are introduced: 1) the last generation amplifier, L, which produces descendants with precursor elimination; 2) all generations amplifier, G, which produces descendants without precursor elimination. Generalization of one-parameter discrete model for the case when precursor sequences do not coincide are carried out. Using this generalization we investigate the distribution of Hamming distances between L- and G-generated sequences. Basic properties of L and G operators, L/G-choice alternative problem have been discussed. Obtained results have common theoretical significance, but they are more suitable for high level genetic diversity process (for example, HIV diversity).     

Frameshift mutations in the bacteriophage Mu repressor gene can confer a trans-dominant virulent phenotype to the phage.

Virulent mutations in the bacteriophage Mu repressor gene were isolated and characterized. Recombination and DNA sequence analysis have revealed that virulence is due to unusual frameshift mutations which change several C-terminal amino acids. The vir mutations are in the same repressor region as the sts amber mutations which, by eliminating several C-terminal amino acids, suppress thermosensitivity of repressor binding to the operators by its N-terminal domain (J. L. Vogel, N. P. Higgins, L. Desmet, V. Geuskens, and A. Toussaint, unpublished data). Vir repressors bind Mu operators very poorly. Thus the Mu repressor C terminus, either by itself or in conjunction with other phage or host proteins, tunes the DNA-binding properties at the repressor N terminus.