Drift and Diffusion in Periodically Driven Renewal Processes

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process. The first two coefficients, which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail. They may be used to quantify stochastic synchronization.Comment: 29 pages, 6 figures, submitted to Journal of Statistical Physic

Single cell mechanics: stress stiffening and kinematic hardening

Cell mechanical properties are fundamental to the organism but remain poorly understood. We report a comprehensive phenomenological framework for the nonlinear rheology of single fibroblast cells: a superposition of elastic stiffening and viscoplastic kinematic hardening. Our results show, that in spite of cell complexity its mechanical properties can be cast into simple, well-defined rules, which provide mechanical cell strength and robustness via control of crosslink slippage.Comment: 4 pages, 6 figure

Variation in the methods leads to variation in the interpretation of biodiversity–ecosystem multifunctionality relationships

Aims Biodiversity is often positively related to the capacity of an ecosystem to provide multiple functions simultaneously (i.e. multifunctionality). However, there is some controversy over whether biodiversity–multifunctionality relationships depend on the number of functions considered. Particularly, investigators have documented contrasting findings that the effects of biodiversity on ecosystem multifunctionality do not change or increase with the number of ecosystem functions. Here, we provide some clarity on this issue by examining the statistical underpinnings of different multifunctionality metrics. Methods We used simulations and data from a variety of empirical studies conducted across spatial scales (from local to global) and biomes (temperate and alpine grasslands, forests and drylands). We revisited three methods to quantify multifunctionality including the averaging approach, summing approach and threshold-based approach. Important Findings Biodiversity–multifunctionality relationships either did not change or increased as more functions were considered. These results were best explained by the statistical underpinnings of the averaging and summing multifunctionality metrics. Specifically, by averaging the individual ecosystem functions, the biodiversity–multifunctionality relationships equal the population mean of biodiversity-single function relationships, and thus will not change with the number of functions. Likewise, by summing the individual ecosystem functions, the strength of biodiversity–multifunctionality relationships increases as the number of functions increased. We proposed a scaling standardization method by converting the averaging or summing metrics into a scaling metric, which would make comparisons among different biodiversity studies. In addition, we showed that the range-relevant standardization can be applied to the threshold-based approach by solving for the mathematical artefact of the approach (i.e. the effects of biodiversity may artificially increase with the number of functions considered). Our study highlights different approaches yield different results and that it is essential to develop an understanding of the statistical underpinnings of different approaches. The standardization methods provide a prospective way of comparing biodiversity–multifunctionality relationships across studies.This work was supported by the National Natural Science Foundation of China (31600428) to X.J. and a Semper Ardens grant from Carlsberg Foundation to N.J.S. F.T.M. and the global drylands dataset were supported by the European Research Council (ERC Grant Agreements 242658 [BIOCOM] and 647038 [BIODESERT])

A Multielectrode Nerve Cuff for Chronic Velocity Selective Recording in a sheep model

Supra-sacral spinal cord injury (SCI) causes loss of bladder fullness sensation and bladder over-activity, leading to retention and incontinence respectively. Velocity selective recording (VSR) of nerve roots innervating the bladder might enable identification of bladder activity. A 10-electrode nerve cuff for sacral nerve root VSR was developed and tested in a sheep model during acute surgeries and chronic implantation for 6 months. The cuff performed well, with 5.90±1.90 kΩ electrode, and <~800 Ω tissue impedance after 189 days implantation with a stable device and tissues. This is important information for assessing the feasibility of chronic VSR.Clinical Relevance-This demonstrates the manufacturing and performance of a neural interface for chronic monitoring of bladder nerve afferents with applications in urinary incontinence and retention management following SCI

Stochastic resonance in a non Markovian discrete state model for excitable systems

We study a non Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable systems with periodical driving. In the limit of a small amplitude of the external signal we derive expressions for the spectral power amplification and the signal to noise ratio as well as for the inter-spike interval distribution.Comment: 5 pages, 3 figure