Self-Organization on Social Media: Endo-Exo Bursts and Baseline Fluctuations

A salient dynamic property of social media is bursting behavior. In this paper, we study bursting behavior in terms of the temporal relation between a preceding baseline fluctuation and the successive burst response using a frequency time series of 3,000 keywords on Twitter. We found that there is a fluctuation threshold up to which the burst size increases as the fluctuation increases and that above the threshold, there appears a variety of burst sizes. We call this threshold the critical threshold. Investigating this threshold in relation to endogenous bursts and exogenous bursts based on peak ratio and burst size reveals that the bursts below this threshold are endogenously caused and above this threshold, exogenous bursts emerge. Analysis of the 3,000 keywords shows that all the nouns have both endogenous and exogenous origins of bursts and that each keyword has a critical threshold in the baseline fluctuation value to distinguish between the two. Having a threshold for an input value for activating the system implies that Twitter is an excitable medium. These findings are useful for characterizing how excitable a keyword is on Twitter and could be used, for example, to predict the response to particular information on social media.     

Detection of a lactate threshold during incremental exercise?

An important question in the study of the exercise response is the real or imaginary nature of the anaerobic threshold, and mathematical modeling techniques have been invoked to assist in resolving this issue. Two opposing views with competing data models recently published in this journal are criticized. One view suggests a segmented model with a discontinuous first derivative at the threshold. The other suggests a continuous model over the whole work load range, implying the anaerobic threshold to be imaginary. However, neither group of authors has devoted proper rigorous attention to the models they use. Had this been done, some of the divergence of opinion may have been avoided. Ideal data from an alternate segmented model that has a continuous first derivative at the threshold are considered for comparative purposes. This suggests that the log-log transformation method may well lead to improved detection of a threshold when one exists, although the estimates of the threshold value obtained are unreliable. Modeling methodology is a useful approach to the resolution of scientific issues, but there exist fundamental implications and alternatives that must be fully recognized.     

A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.     

A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.     

The concept of threshold and its potential application to landscape planning

The concept of threshold can potentially be applied to conservation planning of species, habitats, and ecosystems. It also has significance in managing social–ecological systems for resilience. However, our understanding and use of threshold has been scattered among various disciplines, and the link to conservation planning and social–ecological system management has not been strongly established. The review of the use of threshold in various disciplines reveals that the term is used in a similar manner in both natural and social sciences: a threshold is a point or a zone on an independent variable, and if it is crossed, a sudden, large change in the state of a dependent variable occurs. Even a small change in the independent variable brings this drastic change; nonlinear relationship characterizes the threshold response. Thresholds also separate alternative regimes in a social–ecological system. The discussion of the application of threshold concept to watershed planning concludes that although using one threshold value of impervious surfaces in a watershed to regulate new developments and retrofit old ones is a cost-effective method, a more integrated approach is needed. The use of habitat amount threshold to conserve species promotes proactive planning that would prioritize areas for protection before the threshold is reached and would restore habitat based on the threshold target. However, species-specific data to decide on the threshold is often lacking, and the identification of thresholds is not straightforward. Nonetheless, the concept of threshold is appealing for proactive planning and significant in managing social–ecological systems for resilience.     

Threshold fatigue and information transfer

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin–Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies. Action Editor: David Golomb     

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.     

The reinfection threshold

Thresholds in transmission are responsible for critical changes in infectious disease epidemiology. The epidemic threshold indicates whether infection invades a totally susceptible population. The reinfection threshold indicates whether self-sustained transmission occurs in a population that has developed a degree of partial immunity to the pathogen (by previous infection or vaccination). In models that combine susceptible and partially immune individuals, the reinfection threshold is technically not a bifurcation of equilibria as correctly pointed out by Breban and Blower. However, we show that a branch of equilibria to a reinfection submodel bifurcates from the disease-free equilibrium as transmission crosses this threshold. Consequently, the full model indicates that levels of infection increase by two orders of magnitude and the effect of mass vaccination becomes negligible as transmission increases across the reinfection threshold.     

Tolerance and threshold in the extrinsic coagulation system

This paper focus on the quest for mechanisms that are able to create tolerance and an activation threshold in the extrinsic coagulation cascade. We propose that the interplay of coagulation inhibitor and blood flow creates threshold behavior. First we test this hypothesis in a minimal, four dimensional model. This model can be analysed by means of time scale analysis. We find indeed that only the interplay of blood flow and inhibition together are able to produce threshold behavior. The mechanism relays on a combination of raw substance supply and wash-out effect by the blood flow and a stabilization of the resting state by the inhibition. We use the insight into this minimal model to interpret the simulation results of a large model. Here, we find that the initiating steps (TF that produces together with fVII(a) factor Xa) does not exhibit threshold behavior, but the overall system does. Hence, the threshold behavior appears via the feedback loop (in that fIIa produces indirectly fXa that in turn produces fIIa again) inhibited by ATIII and blood flow.     

A curve of thresholds governs plague epizootics in Central Asia

A core concept of infectious disease epidemiology is the abundance threshold, below which an infection is unable to invade or persist. There have been contrasting theoretical predictions regarding the nature of this threshold for vector-borne diseases, but for infections with an invertebrate vector, it is common to assume a threshold defined by the ratio of vector and host abundances. Here, we show in contrast, both from field data and model simulations, that for plague (Yersinia pestis) in Kazakhstan, the invasion threshold quantity is based on the product of its host (Rhombomys opimus) and vector (mainly Xenopsylla spp.) abundances, resulting in a combined threshold curve with hyperbolic shape. This shape implies compensation between host and vector abundances in permitting infection, which has important implications for disease control. Realistic joint thresholds, supported by data, should promote improved understanding, prediction and management of disease occurrence in this and other vector-borne disease systems.     

Selection of Statistical Thresholds in Graphical Models

Reconstruction of gene regulatory networks based on experimental data usually relies on statistical evidence, necessitating the choice of a statistical threshold which defines a significant biological effect. Approaches to this problem found in the literature range from rigorous multiple testing procedures to ad hoc P-value cut-off points. However, when the data implies graphical structure, it should be possible to exploit this feature in the threshold selection process. In this article we propose a procedure based on this principle. Using coding theory we devise a measure of graphical structure, for example, highly connected nodes or chain structure. The measure for a particular graph can be compared to that of a random graph and structure inferred on that basis. By varying the statistical threshold the maximum deviation from random structure can be estimated, and the threshold is then chosen on that basis. A global test for graph structure follows naturally.     

Threshold criteria for conversion of probability of species presence to either–or presence–absence

For many applications the continuous prediction afforded by species distribution modeling must be converted to a map of presence or absence, so a threshold probability indicative of species presence must be fixed. Because of the bias in probability outputs due to frequency of presences (prevalence), a fixed threshold value, such as 0.5, does not usually correspond to the threshold above which the species is more likely to be present. In this paper four threshold criteria are compared for a wide range of sample sizes and prevalences, modeling a virtual species in order to avoid the omnipresent error sources that the use of real species data implies. In general, sensitivity–specificity difference minimizer and sensitivity–specificity sum maximizer criteria produced the most accurate predictions. The widely-used 0.5 fixed threshold and Kappa-maximizer criteria are the worst ones in almost all situations. Nevertheless, whatever the criteria used, the threshold value chosen and the research goals that determined its choice must be stated.     

Influence of surface anesthesia on the pressure pain threshold measured with different-sized probes

Transcutaneous pressure with pressure probes of arbitrary diameters have been commonly used for measuring the threshold and magnitude of muscle pain, yet this procedure lacks scientific validation. To examine the valid probe dimensions, we conducted physiological experiments using 34 human subjects. Pin-prick pain, pressure pain threshold (PPT) to pressure probes of various diameters, heat pain threshold, and electrical pain threshold of deep tissues were measured before and after application of surface lidocaine anesthesia to the skin surface over the brachioradial muscle in a double-blinded manner. The anesthesia neither affected PPT with larger probes (diameters: 1.6 and 15?mm) nor increased electric pain threshold of deep structures, whereas it diminished pain count in pin-prick test and PPT with a 1.0?mm diameter probe, suggesting that mechanical pain thresholds measured with 1.6 and 15?mm probes reflect the pain threshold of deep tissues, possibly muscle. Pain thresholds to heat did not change after application of the anesthesia. These results suggest that larger pressure probes can give a better estimation of muscular pain threshold.     

Is a T-test value > 10 really reliable in identifying wood from the same tree trunk?

Being able to determine with certainty whether two wood samples derive from the same tree is important in many disciplines, especially in dendroarchaeology. In the past, a t-test threshold > 10 based on oak (Quercus sp,) was proposed for this purpose, and ever since this value has also been applied to other species. However, the effectiveness of the threshold is continually being questioned. The purpose of this paper is to determine whether this threshold is correct and to verify the possibility of identifying wood samples belonging to the same tree.     

Time threshold for second positive phototropism is decreased by a preirradiation with red light

A second positive phototropic response is exhibited by a plant after the time of irradiation has exceeded a time threshold. The time threshold of dark-grown seedlings is about 15 minutes for Arabidopsis thaliana. This threshold is decreased to about 4 minutes by a 669-nanometer preirradiation. Tobacco (Nicotiana tabacum) seedlings show a similar response. The time threshold of dark-grown seedlings is about 60 minutes for tobacco, and is decreased to about 15 minutes after a preirradiation with either 450- or 669- nanometer light. The existence of a time threshold for second positive phototropism and the dependence of this threshold on the irradiation history of the seedling contribute to the complexity of the fluence response relationship for phototropism.     

Susceptibility differences in chemical carcinogenesis linearize the dose-response relationship: threshold doses can be defined only for individuals

The debate on thresholds in dose-response relationships for chemical carcinogenesis concentrates on the question of mechanisms of action that come into play only at dose levels that overwhelm compensatory control mechanism, such as DNA repair or regulation of cell proliferation and death. In this article, individual susceptibility differences are introduced. It is postulated that one single threshold dose cannot be defined for a heterogeneous population because both the background rate of carcinogenesis and specific exposure-related effects differ between individuals. A threshold dose can therefore be defined only on an individual basis and for a given organ. Expressed as a time-to-tumor, the threshold dose results in tumor manifestation at exactly the end of the specified observation period. For those individuals who do not have cancer by the end of this period, the dose was below their individual threshold dose, for those who do have cancer, the dose was above their threshold dose. Based on this concept, a distinction between genotoxic and non-genotoxic carcinogens is no longer required; both types modulate time-to-tumor. Although the present analysis does not allow to define a threshold dose for a population, the setting of a "limit value" for regulatory purposes can be considered if regulators are aware of the fact that this splits a population at some percentile into a group for which the chosen standard is protective and a group for which it might not be. Investigation of factors that confer particular susceptibility to individuals is the key to an understanding of the dose-response relationship at low dose.     

神经元放电阈值的可变性及其意义

神经元能够将不同时空模式的突触输入转化为时序精确的动作电位输出，这种灵活、可靠的信息编码方式是神经集群在动态环境或特定任务下产生所需活动模式的重要基础。动作电位的产生遵循全或无规律，只有当细胞膜电压达到放电阈值时，神经元才产生动作电位。放电阈值在细胞内和细胞间具有高度可变性，具体动态依赖于刺激输入和放电历史。特别是，放电阈值对动作电位起始前的膜电压变化十分敏感，这种状态依赖性产生的生物物理根源包括Na⁺失活和K⁺激活。在绝大多数神经元中，动作电位的触发位置是轴突起始端，这个位置处的阈值可变性是决定神经元对时空输入转化规律的关键因素。但是，电生理实验中动作电位的记录位置却通常是胞体或近端树突，此处的阈值可变性高于轴突起始端，而其产生的重要根源是轴突动作电位的反向传播。基于胞体测量的相关研究显示，放电阈值动态能够增强神经元的时间编码、特征选择、增益调控和同时侦测能力。本文首先介绍放电阈值的概念及量化方法，然后详细梳理近年来国内外关于放电阈值可变性及产生根源的研究进展，在此基础上归纳总结放电阈值可变性对神经元编码的重要性，最后对未来放电阈值的研究方向进行展望。     

A systems model approach to the ventilatory anaerobic threshold

An analogue systems model of whole-body human bioenergetics predicts a change in kinetics of VO2 time series values as a result of exercise levels above an anaerobic threshold. Plotted VO2 results from exercising subjects appear to confirm this change. The purpose of this study is to describe the background to the systems model analogue of the anaerobic threshold and a test procedure devised to estimate this threshold. The estimate so obtained has the dual advantages of being based on model theory and of not being subject to the sort of ambient variations inherent in a single-test determination. A non-homogeneous group of eight subjects comprising a full replicate of a 2(3) factorial experimental design, with factors age, sex and training status, took part in the study. On one hand the results indicate acceptance of the systems model theory. On the other, the analogue threshold measure possesses corresponding properties to the conventional anaerobic threshold. It is higher for trained (155-214 W) than for untrained subjects (108-158 W), higher for males (149-214 W) than for females (108-170 W), and displays no evident interaction effects. Results for the VO2 time constant and for the work efficiency, display similar effects except for an interaction in the latter between age and training status. These experimental findings are regarded as confirmatory of the nature of the analogue threshold measure.     

Anti-activator QslA defines the quorum sensing threshold and response in Pseudomonas aeruginosa

Quorum sensing (QS) in a bacterial population is activated when extracellular concentration of QS signal reaches a threshold, but how this threshold is determined remains largely unknown. In this study, we report the identification and characterization of a novel anti-activator encoded by qslA in Pseudomonas aeruginosa. The null mutation of qslA elevated AHL-dependent QS and PQS signalling, increased the expression of QS-dependent genes, and enhanced the virulence factor production and pathogenicity. We further present evidence that modulation of QS by QslA is due to protein-protein interaction with LasR, which prevents LasR from binding to its target promoter. QslA also influences the threshold concentration of QS signal needed for QS activation; in the absence of qslA, QS is activated by nine times less N-3-oxo-dodecanoyl-homoserine lactone (3-oxo-C12-HSL) than that in wild type. The findings from this study depict a new mechanism that governs the QS threshold in P. aeruginosa.     

Influence of surface anesthesia on the pressure pain threshold measured with different-sized probes

Transcutaneous pressure with pressure probes of arbitrary diameters have been commonly used for measuring the threshold and magnitude of muscle pain, yet this procedure lacks scientific validation. To examine the valid probe dimensions, we conducted physiological experiments using 34 human subjects. Pin-prick pain, pressure pain threshold (PPT) to pressure probes of various diameters, heat pain threshold, and electrical pain threshold of deep tissues were measured before and after application of surface lidocaine anesthesia to the skin surface over the brachioradial muscle in a double-blinded manner. The anesthesia neither affected PPT with larger probes (diameters: 1.6 and 15 mm) nor increased electric pain threshold of deep structures, whereas it diminished pain count in pin-prick test and PPT with a 1.0 mm diameter probe, suggesting that mechanical pain thresholds measured with 1.6 and 15 mm probes reflect the pain threshold of deep tissues, possibly muscle. Pain thresholds to heat did not change after application of the anesthesia. These results suggest that larger pressure probes can give a better estimation of muscular pain threshold.