The microglial "activation" continuum: from innate to adaptive responses

Microglia are innate immune cells of myeloid origin that take up residence in the central nervous system (CNS) during embryogenesis. While classically regarded as macrophage-like cells, it is becoming increasingly clear that reactive microglia play more diverse roles in the CNS. Microglial "activation" is often used to refer to a single phenotype; however, in this review we consider that a continuum of microglial activation exists, with phagocytic response (innate activation) at one end and antigen presenting cell function (adaptive activation) at the other. Where activated microglia fall in this spectrum seems to be highly dependent on the type of stimulation provided. We begin by addressing the classical roles of peripheral innate immune cells including macrophages and dendritic cells, which seem to define the edges of this continuum. We then discuss various types of microglial stimulation, including Toll-like receptor engagement by pathogen-associated molecular patterns, microglial challenge with myelin epitopes or Alzheimer's β-amyloid in the presence or absence of CD40L co-stimulation, and Alzheimer disease "immunotherapy". Based on the wide spectrum of stimulus-specific microglial responses, we interpret these cells as immune cells that demonstrate remarkable plasticity following activation. This interpretation has relevance for neurodegenerative/neuroinflammatory diseases where reactive microglia play an etiological role; in particular viral/bacterial encephalitis, multiple sclerosis and Alzheimer disease

Agent-based model with asymmetric trading and herding for complex financial systems

Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However, the microscopic origination of the leverage and anti-leverage effects is still not understood, and how to produce these effects in agent-based modeling remains open. On the other hand, in constructing microscopic models, it is a promising conception to determine model parameters from empirical data rather than from statistical fitting of the results. Methods: To study the microscopic origination of the return-volatility correlation in financial systems, we take into account the individual and collective behaviors of investors in real markets, and construct an agent-based model. The agents are linked with each other and trade in groups, and particularly, two novel microscopic mechanisms, i.e., investors' asymmetric trading and herding in bull and bear markets, are introduced. Further, we propose effective methods to determine the key parameters in our model from historical market data. Results: With the model parameters determined for six representative stock-market indices in the world respectively, we obtain the corresponding leverage or anti-leverage effect from the simulation, and the effect is in agreement with the empirical one on amplitude and duration. At the same time, our model produces other features of the real markets, such as the fat-tail distribution of returns and the long-term correlation of volatilities. Conclusions: We reveal that for the leverage and anti-leverage effects, both the investors' asymmetric trading and herding are essential generation mechanisms. These two microscopic mechanisms and the methods for the determination of the key parameters can be applied to other complex systems with similar asymmetries.Comment: 17 pages, 6 figure

Robustness of Random Graphs Based on Natural Connectivity

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the weighted number of closed walks of all lengths and can be regarded as the average eigenvalue obtained from the graph spectrum. In this article, we explore the natural connectivity of random graphs both analytically and numerically and show that it increases linearly with the average degree. By comparing with regular ring lattices and random regular graphs, we show that random graphs are more robust than random regular graphs; however, the relationship between random graphs and regular ring lattices depends on the average degree and graph size. We derive the critical graph size as a function of the average degree, which can be predicted by our analytical results. When the graph size is less than the critical value, random graphs are more robust than regular ring lattices, whereas regular ring lattices are more robust than random graphs when the graph size is greater than the critical value.Comment: 12 pages, 4 figure

A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations