Existence and stability criteria for phase-locked modes in ring neural networks based on the spike time resetting curve method

We developed a systematic and consistent mathematical approach to predicting 1:1 phase-locked modes in ring neural networks of spiking neurons based on the open loop spike time resetting curve (STRC) and its almost equivalent counterpart—the phase resetting curve (PRC). The open loop STRCs/PRCs were obtained by injecting into an isolated model neuron a triangular shaped time-dependent stimulus current closely resembling an actual synaptic input. Among other advantages, the STRC eliminates the confusion regarding the undefined phase for stimuli driving the neuron outside of the unperturbed limit cycle. We derived both open loop PRC and STRC-based existence and stability criteria for 1:1 phase-locked modes developed in ring networks of spiking neurons. Our predictions were in good agreement with the closed loop numerical simulations. Intuitive graphical methods for predicting phase-locked modes were also developed both for half-centers and for larger ring networks.     

Notch in the pathway: the roles of Notch signaling in neural crest development

Here, we review recent studies that suggest that Notch signaling has two roles during neural crest development: first in establishing the neural crest domain within the ectoderm via lateral induction and subsequently in diversifying the fates of cells that arise from the neural crest via lateral inhibition. The first of these roles, specification of neural crest via lateral induction, has been explored primarily in the cranial neural folds from which the cranial neural crest arises. Evidence for such a role has thus far only been obtained from chick and frog; results from these two species differ, but share the feature that Notch signaling regulates genes that are expressed by cranial neural crest through effects on expression of Bmp family members. The second of these roles, diversification of neural crest progeny via lateral inhibition, has been identified thus far only in trunk neural crest. Evidence from several species suggests that Notch-mediated lateral inhibition functions in multiple episodes in this context, in each case inhibiting neurogenesis. In the 'standard' mode of lateral inhibition, Notch promotes proliferation and in the 'instructive' mode, it promotes specific secondary fates, including cell death or glial differentiation. We raise the possibility that a single molecular mechanism, inhibition of so-called proneural bHLH genes, underlies both modes of lateral inhibition mediated by Notch signaling.     

Existence and stability of equilibria in age-structured population dynamics

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.     

Margins of stability in young adults with traumatic transtibial amputation walking in destabilizing environments

Understanding how lower-limb amputation affects walking stability, specifically in destabilizing environments, is essential for developing effective interventions to prevent falls. This study quantified mediolateral margins of stability (MOS) and MOS sub-components in young individuals with traumatic unilateral transtibial amputation (TTA) and young able-bodied individuals (AB). Thirteen AB and nine TTA completed five 3-min walking trials in a Computer Assisted Rehabilitation ENvironment (CAREN) system under each of three test conditions: no perturbations, pseudo-random mediolateral translations of the platform, and pseudo-random mediolateral translations of the visual field. Compared to the unperturbed trials, TTA exhibited increased mean MOS and MOS variability during platform and visual field perturbations (p<0.010). AB exhibited increased mean MOS during visual field perturbations and increased MOS variability during both platform and visual field perturbations (p<0.050). During platform perturbations, TTA exhibited significantly greater values than AB for mean MOS (p<0.050) and MOS variability (p<0.050); variability of the lateral distance between the center of mass (COM) and base of support at initial contact (p<0.005); mean and variability of the range of COM motion (p<0.010); and variability of COM peak velocity (p<0.050). As determined by mean MOS and MOS variability, young and otherwise healthy individuals with transtibial amputation achieved lateral stability similar to that of their able-bodied counterparts during unperturbed and visually-perturbed walking. However, based on mean and variability of MOS, unilateral transtibial amputation was shown to have affected lateral walking stability during platform perturbations.     

Parallel morphological/neural processing of hyperspectral images using heterogeneous and homogeneous platforms

The wealth spatial and spectral information available from last-generation Earth observation instruments has introduced extremely high computational requirements in many applications. Most currently available parallel techniques treat remotely sensed data not as images, but as unordered listings of spectral measurements with no spatial arrangement. In thematic classification applications, however, the integration of spatial and spectral information can be greatly beneficial. Although such integrated approaches can be efficiently mapped in homogeneous commodity clusters, low-cost heterogeneous networks of computers (HNOCs) have soon become a standard tool of choice for dealing with the massive amount of image data produced by Earth observation missions. In this paper, we develop a new morphological/neural algorithm for parallel classification of high-dimensional (hyperspectral) remotely sensed image data sets. The algorithm’s accuracy and parallel performance is tested in a variety of homogeneous and heterogeneous computing platforms, using two networks of workstations distributed among different locations, and also a massively parallel Beowulf cluster at NASA’s Goddard Space Flight Center in Maryland.

Learning and coding of concepts in neural networks

Our environment consists of virtually an infinite number of scenarios in which we have to function. In order to respond properly to an incoming stimulus, the brain has first to analyze it, and to find out the basic familiar elements that are part of it. In other words, by using a library which contains a relatively small number of basic concepts, the brain analyzes the multitude of incoming events. Some of those basic concepts are innate, but many of them must be learned, in order to accommodate for the arbitrary environment around us. A classifying box is defined as the neural network that finds out the familiar concepts that are present in an incoming stimulus. Models for classifying boxes are introduced, and possible mechanisms by which they may establish their libraries of concepts are suggested, and then compared and evaluated by computer simulations.     

Enrichment and foodchain stability: the impact of different forms of predator-prey interaction

We propose a simple model of an ecological foodchain of arbitrary length. The model is very general in nature and describes a whole class of foodchains. Using the methods of qualitative analysis the model's stability can be analysed without restricting the predator-prey interaction to any specific functional form. The model can therefore be used to study the effect of different functional forms on the stability of the foodchain. We demonstrate that the stability of steady states may strongly depend on the exact functional form of the interaction function used. It is shown that a class of interaction functions exists, which are similar to the widely used Holling functions but bestow radically different stability properties upon the model. An example is shown in which enrichment has a stabilizing effect on the foodchain. By contrast enrichment destabilizes steady states if Holling functions are used.     

A ferromagnetic model for the action of electric and magnetic fields in cryopreservation

Recent discussions in the literature have questioned the ability of electromagnetic exposure to inhibit ice crystal formation in supercooled water. Here we note that strong electric fields are able to disrupt the surface boundary layer of inert air on the surface of materials, promoting higher rates of heat transport. We also note that most biological tissues contain ferromagnetic materials, both biologically precipitated magnetite (Fe₃O₄) as well as environmental contaminants that get accidentally incorporated into living systems. Although present at trace levels, the number density of these particulates is high, and they have extraordinarily strong interactions with weak, low-frequency magnetic fields of the sort involved in claims of electromagnetic cryopreservation. Magnetically-induced mechanical oscillation of these particles provides a plausible mechanism for the disruption of ice-crystal nucleation in supercooled water.     

Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.     

The emergence of neural activity and its role in the development of the enteric nervous system

The enteric nervous system (ENS) is a vital part of the autonomic nervous system that regulates many gastrointestinal functions, including motility and secretion. All neurons and glia of the ENS arise from neural crest-derived cells that migrate into the gastrointestinal tract during embryonic development. It has been known for many years that a subpopulation of the enteric neural crest-derived cells expresses pan-neuronal markers at early stages of ENS development. Recent studies have demonstrated that some enteric neurons exhibit electrical activity from as early as E11.5 in the mouse, with further maturation of activity during embryonic and postnatal development. This article discusses the maturation of electrophysiological and morphological properties of enteric neurons, the formation of synapses and synaptic activity, and the influence of neural activity on ENS development.     

Kinetic measures of restabilisation during volitional stepping reveal age-related alterations in the control of mediolateral dynamic stability

Research examining age-related changes in dynamic stability during stepping has recognised the importance of the restabilisation phase, subsequent to foot-contact. While regulation of the net ground reaction force (GRF_net) line of action is believed to influence dynamic stability during steady-state locomotion, such control during restabilisation remains unknown. This work explored the origins of age-related decline in mediolateral dynamic stability by examining the line of action of GRF_net relative to the centre of mass (COM) during restabilisation following voluntary stepping. Healthy younger and older adults (n=20 per group) performed three single-step tasks (varying speed and step placement), altering the challenge to stability control. Age-related differences in magnitude and intertrial variability of the angle of divergence of GRF_net line of action relative to the COM were quantified, along with the peak mediolateral and vertical GRF_net components. The angle of divergence was further examined at discrete points during restabilisation, to uncover events of potential importance to stability control. Older adults exhibited a reduced angle of divergence throughout restabilisation. Temporal and spatial constraints on stepping increased the magnitude and intertrial variability of the angle of divergence, although not differentially among the older adults. Analysis of the time-varying angle of divergence revealed age-related reductions in magnitude, with increases in timing and intertrial timing variability during the later phase of restabilisation. This work further supports the idea that age-related challenges in lateral stability control emerge during restabilisation. Age-related alterations during the later phase of restabilisation may signify challenges with reactive control.     

Nonlinear stability analyses of vegetative pattern formation in an arid environment

The development of spontaneous stationary vegetative patterns in an arid isotropic homogeneous environment is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a fourth-order partial differential time-evolution logistic equation for the total plant biomass per unit area divided by the carrying capacity of its territory and defined on an unbounded flat spatial domain. Those patterns that consist of parallel stripes, labyrinth-like mazes, rhombic arrays of rectangular patches, and hexagonal distributions of spots or gaps are generated by the balance between the effects of short-range facilitation and long-range competition. Then those theoretical predictions are compared with both relevant observational evidence and existing numerical simulations as well as placed in the context of the results from some recent nonlinear pattern formation studies.     

Effect of homogeneous magnetic fields on responses to toxic stimulation in spirostomum ambiguum

Effects of DC magnetic fields, up to 125,000 G, on the survival of the ciliated protozoan Spirostomum ambiguum exposed to the toxic substance 2,2′-dipyridyldisulfide are reported. The magnetic field diminishes the ability of the organism to survive the drug, and lengthens the extension phase of the contraction cycle. It is proposed that the magnetic field alters the regulation of intracellular (C²⁺) transients.     

Expression of form and pattern in plants — a role for biophysical fields

Coordinated or ‘field’ behaviour of cells of a tissue can be treated as an interaction between signals and a responding system. When the response involves the reaction of similar cells to a gradient, the field properties are thought to reside mainly in the signal. It is not generally recognized that initially uniform properties in the responding tissue can contribute to the specification of geometrical detail. One such feature is that a tissue may have an intrinsic wavelength, e.g. for the diameter of a new-forming organ. Another is tensor properties. Both features can greatly expand the role of signals in the expression of pattern.     

Stability switches,oscillatory multistability,and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.     

Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic

In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.     

Restricted patterns of Hoxd10 and Hoxd11 set segmental differences in motoneuron subtype complement in the lumbosacral spinal cord

During normal vertebrate development, Hoxd10 and Hoxd11 are expressed by differentiating motoneurons in restricted patterns along the rostrocaudal axis of the lumbosacral (LS) spinal cord. To assess the roles of these genes in the attainment of motoneuron subtypes characteristic of LS subdomains, we examined subtype complement after overexpression of Hoxd10 or Hoxd11 in the embryonic chick LS cord and in a Hoxd10 loss-of-function mouse embryo. Data presented here provide evidence that Hoxd10 defines the position of the lateral motor column (LMC) as a whole and, in rostral LS segments, specifically promotes the development of motoneurons of the lateral subdivision of the lateral motor column (LMCl). In contrast, Hoxd11 appears to impart a caudal and medial LMC (LMCm) identity to some motoneurons and molecular profiles suggestive of a suppression of LMC development in others. We also provide evidence that Hoxd11 suppresses the expression of Hoxd10 and the retinoic acid synthetic enzyme, retinaldehyde dehydrogenase 2 (RALDH2). In a normal chick embryo, Hoxd10 and RALDH2 are expressed throughout the LS region at early stages of motoneuron differentiation but their levels decline in Hoxd11-expressing caudal LS segments that ultimately contain few LMCl motoneurons. We hypothesize that one of the roles played by Hoxd11 is to modulate Hoxd10 and local retinoic acid levels and thus, perhaps define the caudal boundaries of the LMC and its subtype complement.     

The activation of a neuralizing factor in the neural plate is correlated with its homoiogenetic-inducing activity

Summary Neural plates which are induced in the dorsal ectoderm of Triturus by the underlying mesoderm acquire, in turn, neural-inducing activity. This process is correlated with the appearance of neural-inducing activity in the microsomal fraction of the neural plate homogenate. The high-speed supernatant also acquires inducing activity after neural induction, but to a lesser extent. The experiments suggest that a masked neuralizing factor, which is already present in the ectoderm, is in part activated and exported from the inducing neural plate cells.