Evidence for an additive inhibitory component of contrast adaptation

The latency of visual responses generally decreases as contrast increases. Recording in the lateral geniculate nucleus (LGN), we find that response latency increases with increasing contrast in ON cells for some visual stimuli. We propose that this surprising latency trend can be explained if ON cells rest further from threshold at higher contrasts. Indeed, while contrast changes caused a combination of multiplicative gain change and additive shift in LGN cells, the additive shift predominated in ON cells. Modeling results supported this theory: the ON cell latency trend was found when the distance-to-threshold shifted with contrast, but not when distance-to-threshold was fixed across contrasts. In the model, latency also increases as surround-to-center ratios increase, which has been shown to occur at higher contrasts. We propose that higher-contrast full-field stimuli can evoke more surround inhibition, shifting the potential further from spiking threshold and thereby increasing response latency

Using mathematical models to help understand biological pattern formation

One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.To cite this article: P.K. Maini, C. R. Biologies 327 (2004)

Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS

Hysteresis and Post Walrasian Economics

Macroeconomics, hysteresis The “new consensus” dsge (dynamic stochastic general equilibrium) macroeconomic model has microfoundations provided by a single representative agent. In this model shocks to the economic environment do not have any lasting effects. In reality adjustments at the micro level are made by heterogeneous agents, and the aggregation problem cannot be assumed away. In this paper we show that the discontinuous adjustments made by heterogeneous agents at the micro level mean that shocks have lasting effects, aggregate variables containing a selective, erasable memory of the shocks experienced. This hysteresis framework provides foundations for the post-Walrasian analysis of macroeconomic systems