Recognition of general patterns using neural networks

The Hopfield model of neural network stores memory in its symmetric synaptic connections and can only learn to recognize sets of nearly orthogonal patterns. A new algorithm is put forth to permit the recognition of general (non-orthogonal) patterns. The algorithm specifies the construction of the new network's memory matrix T _ij, which is, in general, asymmetrical and contains the Hopfield neural network (Hopfield 1982) as a special case. We find further that in addition to this new algorithm for general pattern recognition, there exists in fact a large class of T _ij memory matrices which permit the recognition of non-orthogonal patterns. The general form of this class of T _ij memory matrix is presented, and the projection matrix neural network (Personnaz et al. 1985) is found as a special case of this general form. This general form of memory matrix extends the library of memory matrices which allow a neural network to recognize non-orthogonal patterns. A neural network which followed this general form of memory matrix was modeled on a computer and successfully recognized a set of non-orthogonal patterns. The new network also showed a tolerance for altered and incomplete data. Through this new method, general patterns may be taught to the neural network.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Reconstructing an ultrametric galled phylogenetic network from a distance matrix

Given a distance matrix M that specifies the pairwise evolutionary distances between n species, the phylogenetic tree reconstruction problem asks for an edge-weighted phylogenetic tree that satisfies M, if one exists. We study some extensions of this problem to rooted phylogenetic networks. Our main result is an O(n(2) log n)-time algorithm for determining whether there is an ultrametric galled network that satisfies M, and if so, constructing one. In fact, if such an ultrametric galled network exists, our algorithm is guaranteed to construct one containing the minimum possible number of nodes with more than one parent (hybrid nodes). We also prove that finding a largest possible submatrix M' of M such that there exists an ultrametric galled network that satisfies M' is NP-hard. Furthermore, we show that given an incomplete distance matrix (i.e. where some matrix entries are missing), it is also NP-hard to determine whether there exists an ultrametric galled network which satisfies it.     

The evolution of ADHD: a disorder of communication?

Attention deficit hyperactivity disorder (ADHD) is the most commonly diagnosed psychiatric condition. Many believe that the central disability is impaired inhibition, which leads to reduced abilities in social skills, self-control, organization and time management. The behaviors identified by clinicians as problematic--inattention, hyperactivity and impulsivity--have been incorporated into several evolutionary models as selectively adaptive cognitive skills for surviving the challenges of a variable Pleistocene environment. We propose that the "disabilities" exhibited by individuals with ADHD are maladaptive, and we concur with Barkley that there is a central impairment in the behavioral inhibition system. The underlying neural anatomy and physiology support the possibility that neurotransmitter pathology may have an impact on other interlinked systems (including language), and may also account for the frequent comorbidity of aggression, anxiety, depression, and learning disabilities (many of which are language-related). Language skills compete with other cognitive activities for the attentional system, and thus the evolution of language could not in fact be independent of the evolution of attention. If language represents the ultimate expression of the attentional system, and some individuals with ADHD are seriously impaired in the coordination of interlinked neural systems (including language), then ADHD fits Jerome Wakefield's definition of "harmful dysfunction," and communication impairments should be investigated more thoroughly by clinicians.     

A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype

We present a cellular automaton model of clonal evolution in cancer aimed at investigating the emergence of the glycolytic phenotype. In the model each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. This implies that cells might react differently to the environment and when space and nutrients are limited only the fittest cells will survive. With this model we have investigated the impact of the environment on the growth dynamics of the tumour. In particular, we have analysed the influence of the tissue oxygen concentration and extra-cellular matrix density on the dynamics of the model. We found that the environment influences both the growth and the evolutionary dynamics of the tumour. For low oxygen concentration we observe tumours with a fingered morphology, while increasing the matrix density gives rise to more compact tumours with wider fingers. The distribution of phenotypes in the tumour is also affected, and we observe that the glycolytic phenotype is most likely to emerge in a poorly oxygenated tissue with a high matrix density. Our results suggest that it is the combined effect of the oxygen concentration and matrix density that creates an environment where the glycolytic phenotype has a growth advantage and consequently is most likely to appear.     

Computer-assisted pattern recognition model for the identification of slowly growing mycobacteria including Mycobacterium tuberculosis.

We present a computerized pattern recognition model used to speciate mycobacteria based on their restriction fragment length polymorphism (RFLP) banding patterns. DNA fragment migration distances were normalized to minimize lane-to-lane variability of band location both within and among gels through the inclusion of two internal size standards in each sample. The computer model used a library of normalized RFLP patterns derived from samples of known origin to create a probability matrix which was then used to classify the RFLP patterns from samples of unknown origin. The probability matrix contained the proportion of bands that fell within defined migration distance windows for each species in the library of reference samples. These proportions were then used to compute the likelihood that the banding pattern of an unknown sample corresponded to that of each species represented in the probability matrix. As a test of this process, we developed an automated, computer-assisted model for the identification of Mycobacterium species based on their normalized RFLP banding patterns. The probability matrix contained values for the M. tuberculosis complex, M. avium, M. intracellulare, M. kansasii and M. gordonae species. Thirty-nine independent strains of known origin, not included in the probability matrix, were used to test the accuracy of the method in classifying unknowns: 37 of 39 (94.9%) were classified correctly. An additional set of 16 strains of known origin representing species not included in the model were tested to gauge the robustness of the probability matrix. Every sample was correctly identified as an outlier, i.e. a member of a species not included in the original matrix.(ABSTRACT TRUNCATED AT 250 WORDS)     

The construction of a simultaneous functional order in nervous systems

In a previous paper (Part I) we introduced a model that constructs a simultaneous functional order in a set of neuronal elements by monitoring the coincidences in their signal activities (the so-called coincidence-model). The simultaneous signal activity in a neural net will be constrained both by its physical restrictions and by environmental constraints. In this paper we present the results of simulation experiments that were performed to study the influence of environmental constraits on the resulting functional order in a set of neural elements corresponding to a onedimensional detector array. We show that the coincidence-model produces a functional order that encodes the physical constraints of the environment. Moreover, we demonstrate that the signal activity in the neural net (the perceptions) can be related to events in the outer world. We provide some examples to demonstrate that our model may prove useful to gain insight into certain developmental disorders.     

Mathematical modeling of collagen turnover in biological tissue

We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF- $\beta $ and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF- $\beta $ increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.     

Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem

We present an application of the Kohonen algorithm to the traveling salesman problem: Using only this algorithm, without energy function nor any parameter choosen ad hoc, we found good suboptimal tours. We give a neural model version of this algorithm, closer to classical neural networks. This is illustrated with various numerical examples.     

On co-existence,foraging strategy and the biogeography of weasels and stoats (Mustela nivalis and M. erminea) in Britain

Summary Mustela nivalis and M. erminea, two sympatric species of weasels of superficially similar appearance and habits, have different breeding and foraging strategies associated with the difference in their body size. M. nivalis is more efficient in exploiting small rodent prey, and can breed rapidly to take immediate advantage of rodent peaks, but is vulnerable to local extinction during rodent declines. M. erminea has more generalized food habits, and is the larger and probably the dominant species, but is limited by delayed implantation to producing only one litter a year. M. nivalis is therefore superior in exploitation competition, and erminea in interference competition. We offer the hypothesis that the co-existence of the two species is permitted by a balance of these competitive advantages determined, at a given time or place, by the heterogeneity of the environment and the distribution of the prey fauna. We use this hypothesis to explain cases where co-existence has either broken down or is not recorded (the results of simultaneous introductions to New Zealand and Terschelling Island, and of myxomatosis in Britain, and the distribution of nivalis and Erminea on the offshore islands of Britain). We argue that the diversity and size distribution of the prey fauna of an island (which are both related to its area and isolation) are important in deciding the species and size of mustelids surviving there; for example, we suggest that nivalis was present in Ireland in immediate post-glacial times but became extinct with the lemmings.     

Variation Thresholds for Extinction and Their Implications for Conservation Strategies

We examine the degree to which fitting simple dynamic models to time series of population counts can predict extinction probabilities. This is both an active branch of ecological theory and an important practical topic for resource managers. We introduce an approach that is complementary to recently developed techniques for estimating extinction risks (e.g., diffusion approximations) and, like them, requires only count data rather than the detailed ecological information available for traditional population viability analyses. Assuming process error, we use four different models of population growth to generate snapshots of population dynamics via time series of the lengths commonly available to ecologists. We then ask to what extent we can identify which of several broad classes of population dynamics is evident in the time series snapshot. Along the way, we introduce the idea of "variation thresholds," which are the maximum amount of process error that a population may withstand and still have a specified probability of surviving for a given length of time. We then show how these thresholds may be useful to both ecologists and resource managers, particularly when dealing with large numbers of poorly understood species, a common problem faced by those designing biodiversity reserves.     

The natural variation of a neural code

The way information is represented by sequences of action potentials of spiking neurons is determined by the input each neuron receives, but also by its biophysics, and the specifics of the circuit in which it is embedded. Even the "code" of identified neurons can vary considerably from individual to individual. Here we compared the neural codes of the identified H1 neuron in the visual systems of two families of flies, blow flies and flesh flies, and explored the effect of the sensory environment that the flies were exposed to during development on the H1 code. We found that the two families differed considerably in the temporal structure of the code, its content and energetic efficiency, as well as the temporal delay of neural response. The differences in the environmental conditions during the flies' development had no significant effect. Our results may thus reflect an instance of a family-specific design of the neural code. They may also suggest that individual variability in information processing by this specific neuron, in terms of both form and content, is regulated genetically.     

The use of matrices in analyzing the three-dimensional behavior of the vestibulo-ocular reflex

The vestibulo-ocular reflex rotates the eye about the axis of a head rotation at the same speed but in the opposite direction to make the visual axes in space independent of head motion. This reflex works in all three degrees of freedom: roll, pitch, and yaw. The rotations may be described by vectors and the reflex by a transformation in the form of a matrix. The reflex consists of three parts: sensory, central, and motor. The transduction of head rotation into three neural signals, which may also be described by a vector, is described by a canal matrix. The neural, motorcommand vector is transformed to an eye rotation by a muscle matrix. Since these two matrices are known, one can solve for the central matrix which gives the strength of the connections between all the vestibular neurons and all the eye-muscle motoneurons. The role of the metric tensor in these transformations is described. This method of analysis is used in three applications. A lesion may be simulated by altering the elements in any or all of the three component matrices. By matrix multiplication, the resulting abnormal behavior of the reflex can be described quantitatively in all degrees of freedom. The method is also used to directly compare the differences in brain-stem connections between humans and rabbits that accommodate the altered actions of the muscles of the two species. Finally the method allows a quantitative assessment of the changes that take place in the brainstem connections when plastic changes are induced by artificially dissociating head movements from apparent motion of the visual environment.     

Statistical-mechanical measure of stochastic spiking coherence in a population of inhibitory subthreshold neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure M ( s ) by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure M ( s ) is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of M ( s ), we quantitatively characterize the stochastic spiking coherence, and find that M ( s ) reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure M ( s ) may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.     

Spatially structured metapopulation models: global and local assessment of metapopulation capacity

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.     

Matrix heterogeneity affects population size of the harvest mice: Bayesian estimation of matrix resistance and model validation

It has been increasingly recognized that landscape matrices are an important factor determining patch connectivity and hence the population size of organisms living in highly fragmented landscapes. However, most previous studies estimated the effect of matrix heterogeneity using prior information regarding dispersal or habitat preferences of a focal organism. Here we estimated matrix resistance of harvest mice in agricultural landscapes using a novel pattern‐oriented modeling with Bayesian estimation and no prior information, and then conducted model validation using data sets independent from those used for model construction. First, we investigated the distribution patterns of harvest mice for approximately 400 habitat patches, and estimated matrix resistance for different matrix types using statistical models incorporating patch size, patch environment, and patch connectivity. We used Bayesian estimation with a Markov chain Monte Carlo algorithm, and searched for appropriate matrix resistance that best explained the distribution pattern. Patch connectivity as well as patch quality was an important determinant of local population size for the harvest mice. Moreover, matrix resistance was far from uniform, with rice and crop fields exhibiting low resistance and forests, creeks, roads and residential areas showing much higher resistance. The deviance explained by this model (heterogeneous matrix model) was much larger than that obtained by the model with no consideration of matrix heterogeneity (homogeneous matrix model). Second, we obtained distribution data from five additional landscapes that were more fragmented than that used for model construction, and used them for model validation. The heterogeneous matrix model well predicted the population size for four out of five landscapes. In contrast, the homogeneous model considerably overestimated population sizes in all cases. Our approach is widely applicable to species living in fragmented landscapes, especially those for which prior information regarding movement or dispersal is difficult to obtain.     

边缘幸存空间──一个新概念的提出

通过对物种及其生存空间的研究,提出了边缘幸存空间这一新的概念─—物种生存空间之外,居群不能稳定地延续,而生物个体可以存在的空间。还讨论了边缘幸存空间的存在特点及明确了几种在地层中识别边缘幸存空间的方法。最后,以这一概念为基础,讨论了西藏白垩纪赛诺曼期Ｂｉｓｃｕｔｕｍｅｌｌｉｐｔｉｃｕｍ的发现及其意义。     

When should cuckolded males care for extra-pair offspring?

In socially monogamous species with bi-parental care, males suffer reduced reproductive success if their mate engages in extra-pair copulations (EPCs). One might therefore expect that males should refuse to care for a brood if they can detect that an EPC has occurred. Here, we use a game-theory model to study male brood care in the face of EPCs in a cooperatively breeding species in which offspring help to raise their (half-) siblings in their parents' next breeding attempt. We show that under certain conditions males are selected to care even for broods completely unrelated to themselves. This counterintuitive result arises through a form of pseudo-reciprocity, whereby surviving extra-pair offspring, when helping to rear their younger half-siblings, can more than compensate for the cost incurred by the male that raised them. We argue that similar effects may not be limited to cooperative breeders, but may arise in various contexts in which cooperation between (half-) siblings occurs.