Hopf Bifurcation and Chaos in Tabu Learning Neuron Models

In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. We give a numerical example to verify the theoretical analysis. Then, we demonstrate the chaotic behavior in such a neuron with sinusoidal external input, via computer simulations. Finally, we study the chaotic behaviors in tabu learning two-neuron models, with linear and quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of Bifurcation and Chao

Calculating the cost of work-related stress and psychosocial risks

Work-related stress is expensive. Tackling stress and psychosocial risks can be viewed as too costly, but the reality is that it costs more to ignore them. Stress affects performance and leads to absence from work. If prolonged it may result in serious health problems such as cardiovascular or musculoskeletal diseases. All this comes at a cost. This report summarises the studies focusing on calculating costs of work-related stress and psychosocial risks. The main costs for individuals relate to health impairment, lower income and reduced quality of life. Organisations are affected by costs related to absenteeism, presenteeism, reduced productivity or high staff turnover. Health care costs and poorer business outcomes ultimately affect national economies and society

Nitrogen oxidation consortia dynamics influence the performance of full-scale rotating biological contactors.

Ammonia oxidising microorganisms (AOM) play an important role in ammonia removal in wastewater treatment works (WWTW) including rotating biological contactors (RBCs). Environmental factors within RBCs are known to impact the performance of key AOM, such that only some operational RBCs have shown ability for elevated ammonia removal. In this work, long-term treatment performance of seven full-scale RBC systems along with the structure and abundance of the ammonia oxidising bacteria (AOB) and archaea (AOA) communities within microbial biofilms were examined. Long term data showed the dominance of AOB in most RBCs, although two RBCs had demonstrable shift toward an AOA dominated AOM community. Next Generation Sequencing of the 16S rRNA gene revealed diverse evolutionary ancestry of AOB from RBC biofilms while nitrite-oxidising bacteria (NOBs) were similar to reference databases. AOA were more abundant in the biofilms subject to lower organic loading and higher oxygen concentration found at the distal end of RBC systems. Modelling revealed a distinct nitrogen cycling community present within high performing RBCs, linked to efficient control of RBC process variables (retention time, organic loading and oxygen concentration). We present a novel template for enhancing the resilience of RBC systems through microbial community analysis which can guide future strategies for more effective ammonia removal. To best of the author's knowledge, this is the first comparative study reporting the use of next generation sequencing data on microbial biofilms from RBCs to inform effluent quality of small WWTW

Hopf Bifurcations in a Watt Governor With a Spring

This paper pursues the study carried out by the authors in "Stability and Hopf bifurcation in a hexagonal governor system", focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor differential system. Here are studied the codimension two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.Comment: 30 pages and 7 figure

Noise induced oscillations in non-equilibrium steady state systems

We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle at certain relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.Comment: 11 pages, 4 figures. Submitted to Physica Script

Hopf bifurcation in a gene regulatory network model:Molecular movement causes oscillations

Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Green's functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-$\kappa$B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer

Monitoring occurrence of SARS-CoV-2 in school populations: A wastewater-based approach

Clinical testing of children in schools is challenging, with economic implications limiting its frequent use as a monitoring tool of the risks assumed by children and staff during the COVID-19 pandemic. Here, a wastewater-based epidemiology approach has been used to monitor 16 schools (10 primary, 5 secondary and 1 post-16 and further education) in England. A total of 296 samples over 9 weeks have been analysed for N1 and E genes using qPCR methods. Of the samples returned, 47.3% were positive for one or both genes with a detection frequency in line with the respective local community. WBE offers a low cost, non-invasive approach for supplementing clinical testing and can provide longitudinal insights that are impractical with traditional clinical testing

Recent advances in symmetric and network dynamics

We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as “catastrophe theory.” We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette–Taylor flow, flames, the Belousov–Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network

Wastewater monitoring for detection of public health markers during the COVID-19 pandemic: Near-source monitoring of schools in England over an academic year

Background Schools are high-risk settings for infectious disease transmission. Wastewater monitoring for infectious diseases has been used to identify and mitigate outbreaks in many near-source settings during the COVID-19 pandemic, including universities and hospitals but less is known about the technology when applied for school health protection. This study aimed to implement a wastewater surveillance system to detect SARS-CoV-2 and other public health markers from wastewater in schools in England. Methods A total of 855 wastewater samples were collected from 16 schools (10 primary, 5 secondary and 1 post-16 and further education) over 10 months of school term time. Wastewater was analysed for SARS-CoV-2 genomic copies of N1 and E genes by RT-qPCR. A subset of wastewater samples was sent for genomic sequencing, enabling determination of the presence of SARS-CoV-2 and emergence of variant(s) contributing to COVID-19 infections within schools. In total, >280 microbial pathogens and >1200 AMR genes were screened using RT-qPCR and metagenomics to consider the utility of these additional targets to further inform on health threats within the schools. Results We report on wastewater-based surveillance for COVID-19 within English primary, secondary and further education schools over a full academic year (October 2020 to July 2021). The highest positivity rate (80.4%) was observed in the week commencing 30th November 2020 during the emergence of the Alpha variant, indicating most schools contained people who were shedding the virus. There was high SARS-CoV-2 amplicon concentration (up to 9.2x106 GC/L) detected over the summer term (8th June - 6th July 2021) during Delta variant prevalence. The summer increase of SARS-CoV-2 in school wastewater was reflected in age-specific clinical COVID-19 cases. Alpha variant and Delta variant were identified in the wastewater by sequencing of samples collected from December to March and June to July, respectively. Lead/lag analysis between SARS-CoV-2 concentrations in school and WWTP data sets show a maximum correlation between the two-time series when school data are lagged by two weeks. Furthermore, wastewater sample enrichment coupled with metagenomic sequencing and rapid informatics enabled the detection of other clinically relevant viral and bacterial pathogens and AMR. Conclusions Passive wastewater monitoring surveillance in schools can identify cases of COVID-19. Samples can be sequenced to monitor for emerging and current variants of concern at the resolution of school catchments. Wastewater based monitoring for SARS-CoV-2 is a useful tool for SARS-CoV-2 passive surveillance and could be applied for case identification and containment, and mitigation in schools and other congregate settings with high risks of transmission. Wastewater monitoring enables public health authorities to develop targeted prevention and education programmes for hygiene measures within undertested communities across a broad range of use cases