A threshold result for an epidemiological model

A threshold parameter R ₀ is identified for an SIRS epidemiological model which has nonlinear incidence and a distributed delay for transfer out of the removed class. For R ₀ < 1, the disease free equilibrium is proved to be the global attractor for all solutions.Research supplied in part by NSERC A-8965     

Wave-separation in complex systems. Application to brain-signals

A departure from single-system dynamics, that may arise in characterizing self-organized dynamics of complex systems, is dealt with by using the Karhunen-Loève expansion of the trajectory matrix to decompose an experimental signal in a sum of spectral features. For an electroencephalographic -signal, a separation of waves and extraction of additive sub-signals are achieved, each sub-signal covering a well-bounded and physiologically meaningful frequency range. From the subsignals, an attractor that vanishes on phase-randomizing the data is characterized, under conditions where none was found for the recorded signal.     

The dynamics of experimental arable weed communities under different management practices

Abstract. Weed communities, comprising 12 introduced species at constant starting densities and three species already present in the seed bank, were followed through three years of continuous winter wheat. The wheat and weeds were subjected to two treatments in a split-plot factorial design, organic contrasting with conventional fertilizer, and ploughing plus hand-roguing contrasting with minimum tillage plus herbicide. The minimum tilled plots developed in a uniform manner, and became dominated by very high densities of Anisantha sterilis. Agrostemma githago and Galium aparine also persisted in these plots at lower densities. The ploughed plots had a lower total density but a greater range of species. Stellaria media, Veronica persica and Avena fatua were the most common; other species occurred at lower densities. The major effect of fertilizer treatment was a greater initial increase by G. aparine on the organic, minimum tilled plots compared with the conventionally fertilized, minimum tilled plots. Species associated with minimum tillage were annuals with either no or a short term seed bank and autumn germination and rather predictable dynamics, whereas species that did well under ploughing were either spring germinating or had a persistent seed bank, implying greater annual variation in population size associated with weather conditions. There seemed no clear way to distinguish between those species which were abundant on the ploughed plots and those which were scarce under all conditions using readily accessible data.     

Multi-scale trajectory analysis:powerful conceptual tool for understanding ecological change

The model at the basis of trajectory analysis is conceptually simple.When applied to time series vegetation data,the projectile becomes a surrogate for vegetation state,the trajectory for the evolving vegetation process,and the properties of the trajectory for the true process characteristics.Notwithstanding its simplicity,the model is well-defined under natural circumstances and easily adapted to serial vegetation data,irrespective of source.As a major advantage,compared to other models that isolate the elementary processes and probe vegetation dynamics for informative regularities on the elementary level,the trajectory model allows us to probe for regularities on the level of the highest process integrity.Theories and a data analytical methodology developed around the trajectory model are outlined,including many numerical examples.A rich list of key references and volumes of supplementary information supplied in the Web Only Appendices rounds out the presentation.     

A theoretical account of cue averaging in the rodent head direction system

Head direction (HD) cell responses are thought to be derived from a combination of internal (or idiothetic) and external (or allothetic) sources of information. Recent work from the Jeffery laboratory shows that the relative influence of visual versus vestibular inputs upon the HD cell response depends on the disparity between these sources. In this paper, we present simulation results from a model designed to explain these observations. The model accurately replicates the Knight et al. data. We suggest that cue conflict resolution is critically dependent on plastic remapping of visual information onto the HD cell layer. This remap results in a shift in preferred directions of a subset of HD cells, which is then inherited by the rest of the cells during path integration. Thus, we demonstrate how, over a period of several minutes, a visual landmark may gain cue control. Furthermore, simulation results show that weaker visual landmarks fail to gain cue control as readily. We therefore suggest a second longer term plasticity in visual projections onto HD cell areas, through which landmarks with an inconsistent relationship to idiothetic information are made less salient, significantly hindering their ability to gain cue control. Our results provide a mechanism for reliability-weighted cue averaging that may pertain to other neural systems in addition to the HD system.     

Detailed Analysis of a Nonlinear Prey-Predator Model

A model of competition between populations of two species, describedby a two dimensional map, is analytically and numerically studied. A rich dynamics is observed.     

Computational constraints that may have favoured the lamination of sensory cortex

At the transition from early reptilian ancestors to primordial mammals, the areas of sensory cortex that process topographic modalities acquire the laminar structure of isocortex. A prominent step in lamination is granulation, whereby the formerly unique principal layer of pyramidal cells is split by the insertion of a new layer of excitatory, but intrinsic, granule cells, layer IV. I consider the hypothesis that granulation, and the differentiation between supra- and infra-granular pyramidal layers, may be advantageous to support fine topography in their sensory maps. Fine topography implies a generic distinction between where information, explicitly mapped on the cortical sheet, and what information, represented in a distributed fashion as a distinct firing pattern across neurons. These patterns can be stored on recurrent collaterals in the cortex, and such memory can help substantially in the analysis of current sensory input. The simulation of a simplified network model demonstrates that a non-laminated patch of cortex must compromise between transmitting where information or retrieving what information. The simulation of a modified model including differentiation of a granular layer shows a modest but significant quantitative advantage, expressed as a less severe trade-off between what and where. The further connectivity differentiation between infra-granular and supra-granular pyramidal layers is shown to match the mix of what and where information optimal for their respective target structures.