A methodological basis for description and analysis of systems with complex switch-like interactions

 A wide range of complex systems appear to have switch-like interactions, i.e. below (or above) a certain threshold x has no or little influence on y, while above (or below) this threshold the effect of x on y saturates rapidly to a constant level. Switching functions are frequently described by sigmoid functions or combinations of these. Within the context of ordinary differential equations we present a very general methodological basis for designing and analysing models involving complicated switching functions together with any other non-linearities. A procedure to determine position and stability properties of all stationary points lying close to a threshold for one or several variables, so-called singular stationary points, is developed. Such points may represent homeostatic states in models, and are therefore of considerable interest. The analysis provides a profound insight into the generic effects of steep sigmoid interactions on the dynamics around homeostatic points. It leads to qualitative as well as quantitative predictions without using advanced mathematical methods. Thus, it may have an important heuristic function in connection with numerical simulations aimed at unfolding the predictive potential of realistic models. Received 25 January 1996; received in revised form 29 June 1997     

一个具暂时免疫且总人数可变的传染病动力学模型

建立了一个具常恢复率和接触率依赖于总人数的SIRS传染病动力学模型，讨论了系统平衡点的存在性和稳定性，对双线性传染率的特殊情形，给出了传染病平衡点的全局稳定性结论，推广和改进了已有的相应结果。     

一类潜伏期和染病期均传染且具非线性传染率的流行病模型

研究了一类潜伏期和染病期都传染的具非线性传染率的SEIS流行病模型,确定了各类平衡点存在的条件阈值,讨论了各平衡点的稳定性,揭示了潜伏期传染和染病期传染对流行病发展趋势的共同影响．     

Characterizing coal and mineral mines as a regional source of stress to stream fish assemblages

Mining impacts on stream systems have historically been studied over small spatial scales, yet investigations over large areas may be useful for characterizing mining as a regional source of stress to stream fishes. The associations between co-occurring stream fish assemblages and densities of various “classes” of mining occurring in the same catchments were tested using threshold analysis. Threshold analysis identifies the point at which fish assemblages change substantially from best available habitat conditions with increasing disturbance. As this occurred over large regions, species comprising fish assemblages were represented by various functional traits as well as other measures of interest to management (characterizing reproductive ecology and life history, habitat preferences, trophic ecology, assemblage diversity and evenness, tolerance to anthropogenic disturbance and state-recognized game species). We used two threshold detection methods: change-point analysis with indicator analysis and piecewise linear regression. We accepted only those thresholds that were highly statistically significant (p ≤ 0.01) for both techniques and overlapped within ≤5% error. We found consistent, wedge-shaped declines in multiple fish metrics with increasing levels of mining in catchments, suggesting mines are a regional source of disturbance. Threshold responses were consistent across the three ecoregions occurring at low mine densities. For 47.2% of the significant thresholds, a density of only ≤0.01 mines/km² caused a threshold response. In fact, at least 25% of streams in each of our three study ecoregions have mine densities in their catchments with the potential to affect fish assemblages. Compared to other anthropogenic impacts assessed over large areas (agriculture, impervious surface or urban land use), mining had a more pronounced and consistent impact on fish assemblages.     

具有阶段结构和非线性接触率的SI传染病模型的渐近性态

研究了一类具有阶段结构和非线性接触率的传染病模型的渐近性态,得到了传染病最终消除和成为地方病的阀值．     

No unique effect of intergroup competition on cooperation: non-competitive thresholds are as effective as competitions between groups for increasing human cooperative behavior

Explaining cooperation remains a central topic for evolutionary theorists. Many have argued that group selection provides such an explanation: theoretical models show that intergroup competition could have given rise to cooperation that is costly for the individual. Whether group selection actually did play an important role in the evolution of human cooperation, however, is much debated. Recent experiments have shown that intergroup competitions do increase human cooperation, which has been taken as evidence for group selection as a mechanism for the evolution of cooperation. Here we challenge this standard interpretation. Competitions change the payoff structure by creating a threshold effect whereby the group that contributes more earns an additional prize, which creates some incentive for individuals to cooperate. We present four studies that disentangle competition and thresholds, and strongly suggest that it is thresholds – rather than competitions per se – that increase cooperation. Thus, prior intergroup competition experiments provide no evidence of a unique or special role for intergroup competition in promoting human cooperation, and shed no light on whether group selection shaped human evolution.     

SIR传染病数学模型的隔离控制

本文研究的SIR传染病隔离控制,不仅对染病者进行隔离,而且隔离易感者．对该模型闽值进行分析,探讨隔离率与患病人数最大值之间的关系,旨在消除该传染病．仿真表明此法行之有效．     

Direct protein detection with a nano-interdigitated array gate MOSFET

A new protein sensor is demonstrated by replacing the gate of a metal oxide semiconductor field effect transistor (MOSFET) with a nano-interdigitated array (nIDA). The sensor is able to detect the binding reaction of a typical antibody Ixodes ricinus immunosuppressor (anti-Iris) protein at a concentration lower than 1 ng/ml. The sensor exhibits a high selectivity and reproducible specific detection. We provide a simple model that describes the behavior of the sensor and explains the origin of its high sensitivity. The simulated and experimental results indicate that the drain current of nIDA-gate MOSFET sensor is significantly increased with the successive binding of the thiol layer, Iris and anti-Iris protein layers. It is found that the sensor detection limit can be improved by well optimizing the geometrical parameters of nIDA-gate MOSFET. This nanobiosensor, with real-time and label-free capabilities, can easily be used for the detection of other proteins, DNA, virus and cancer markers. Moreover, an on-chip associated electronics nearby the sensor can be integrated since its fabrication is compatible with complementary metal oxide semiconductor (CMOS) technology.     

Denitrification efficiency for defining critical loads of carbon in shallow coastal ecosystems

Denitrification efficiency [DE; (N₂ − N/(DIN + N₂ − N) × 100%)] as an indicator of change associated with nutrient over-enrichment was evaluated for 22 shallow coastal ecosystems in Australia. The rate of carbon decomposition (which can be considered a proxy for carbon loading) is an important control on the efficiency with which coastal sediments in depositional mud basins with low water column nitrate concentrations recycle nitrogen as N₂. The relationship between DE and carbon loading is due to changes in carbon and nitrate (NO₃) supply associated with sediment biocomplexity. At the DE optimum (500–1,000 μmol m⁻² h⁻¹), there is an overlap of aerobic and anaerobic respiration zones (caused primarily by the existence of anaerobic micro-niches within the oxic zone, and oxidized burrow structures penetrating into the anaerobic zone), which enhances denitrification by improving both the organic carbon and nitrate supply to denitrifiers. On either side of the DE optimum zone, there is a reduction in denitrification sites as the sediment loses its three-dimensional complexity. At low organic carbon loadings, a thick oxic zone with low macrofauna biomass exists, resulting in limited anoxic sites for denitrification, and at high carbon loadings, there is a thick anoxic zone and a resultant lack of oxygen for nitrification and associated NO₃ production. We propose a trophic scheme for defining critical (sustainable) carbon loading rates and possible thresholds for shallow coastal ecosystems based on the relationship between denitrification efficiency and carbon loading for 17 of the 22 Australian coastal ecosystems. The denitrification efficiency “optimum” occurs between carbon loadings of about 50 and 100 g C m⁻² year⁻¹. Coastal managers can use this simple trophic scheme to classify the current state of their shallow coastal ecosystems and for determining what carbon loading rate is necessary to achieve any future state. Guest editors: J. H. Andersen & D. J. Conley Eutrophication in Coastal Ecosystems: Selected papers from the Second International Symposium on Research and Management of Eutrophication in Coastal Ecosystems, 20–23 June 2006, Nyborg, Denmark     

Real-time neuronal homeostasis by coordinating VGSC intrinsic properties

Homeostasis of internal environment and cellular metabolism ensures cells’ functions to be stable in living organisms. Cellular homeostasis is believed to be maintained via feedback or feedforward manners. We report a novel mechanism that maintains neuronal homeostasis through coordinating the intrinsic properties of single molecules concurrently. Spike encoding and sodium channel dynamics at cortical neurons were studied by patch-clamp recording. Voltage-gated sodium channels set refractory period and threshold potential toward different directions to stabilize the energetic barrier for firing sequential action potentials. This neuronal homeostasis is not affected by intracellular Ca²⁺ signals and membrane potentials. Real-time homeostasis maintains precise and reliable neuronal encoding without any destabilization.