Resonance bifurcations of robust heteroclinic networks

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a long-period periodic orbit. Resonance bifurcations for heteroclinic networks are more complicated because different subcycles in the network can undergo resonance at different parameter values, but have, until now, not been systematically studied. In this article we present the first investigation of resonance bifurcations in heteroclinic networks. Specifically, we study two heteroclinic networks in $\R^4$ and consider the dynamics that occurs as various subcycles in each network change stability. The two cases are distinguished by whether or not one of the equilibria in the network has real or complex contracting eigenvalues. We construct two-dimensional Poincare return maps and use these to investigate the dynamics of trajectories near the network. At least one equilibrium solution in each network has a two-dimensional unstable manifold, and we use the technique developed in [18] to keep track of all trajectories within these manifolds. In the case with real eigenvalues, we show that the asymptotically stable network loses stability first when one of two distinguished cycles in the network goes through resonance and two or six periodic orbits appear. In the complex case, we show that an infinite number of stable and unstable periodic orbits are created at resonance, and these may coexist with a chaotic attractor. There is a further resonance, for which the eigenvalue combination is a property of the entire network, after which the periodic orbits which originated from the individual resonances may interact. We illustrate some of our results with a numerical example.Comment: 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs.htm

Engaging Government-Industry-University Partnerships to Further Gender Equity in STEM Workforce Education Through Technology and Information System Learning Tools

This paper has two goals: First, to detail processes through which a project funded under a National Science Foundation workforce development program (Innovative Technology Experiences for Students and Teachers, ITEST) leveraged active partnerships among government agencies, industry firms, and universities to develop and study an innovative, out-of-school information system and technology workforce education program. The aim of the program was to improve equity of opportunity for high school girls. The program engaged young women from underrepresented subgroups in data science, analytics, information communication technology, and programming learning activities in an experiential, law enforcement computer forensics context. This description of the research team’s process is intended as inspiration and guidance to others considering developing similar programs targeting workforce development in science and technical fields through an equity lens. Second, this paper shares reflections from senior project personnel on lessons learned while working with cross-sector collaborations, including challenges encountered while implementing components of the program facilitated by the partnership model. The authors adopt a reflective practice orientation, considering implications regarding the most useful—and evolving—roles that cross-sector partnerships might play in developing programs to help students traditionally underrepresented in technical fields be more aware of, interested in, and prepared for careers in science, technology, engineering, and mathematics (STEM) disciplines. In so doing, the authors offer insights about how university partners might address potential tensions involved in such collaborations

Couple relationship quality and the infant home language environment: Gender-specific findings.

Couple relationship quality is known to drop significantly across the transition to parenthood (Ahlborg & Strandmark, 2001; Doss, Rhoades, Stanley, & Markman, 2009), yet individual differences in the amount of parent-to-infant talk have rarely been studied in relation to variation in couple relationship quality. Addressing this gap, the current study of 93 first-time parents with 4-month-old infants included multimeasure reports of couple relationship quality from both mothers and fathers and examined associations between couple relationship quality and the home language environment, assessed via the Language Environment Analysis (LENA), when infants were approximately 7 months old. LENA consists of a wearable talk pedometer that records a full day of naturalistic parent-infant talk and is coupled to software that provides automated analysis. Given the covariation between depression and both couple relationship quality and parental infant-directed talk, both maternal and paternal depression were controlled for in all analyses. Results showed that, for mothers of sons, frequency of infant-directed talk was inversely related to couple relationship quality. Consistent with family systems theory, this finding provides partial support for the compensation hypothesis. However, variation in couple relationship quality was unrelated to infant-directed speech in fathers or in mothers of daughters. Together, these findings demonstrate that the gender composition of the parent-infant dyads plays a moderating role on the association between couple relationship quality and parent-infant talk. (PsycINFO Database Record (c) 2020 APA, all rights reserved)

Honour Watch #012

The twelfth issue of Honour Watch from February of 2018.https://scholarworks.moreheadstate.edu/msu_honors_publications/1040/thumbnail.jp

A Bayesian mixture modelling approach for spatial proteomics.

Analysis of the spatial sub-cellular distribution of proteins is of vital importance to fully understand context specific protein function. Some proteins can be found with a single location within a cell, but up to half of proteins may reside in multiple locations, can dynamically re-localise, or reside within an unknown functional compartment. These considerations lead to uncertainty in associating a protein to a single location. Currently, mass spectrometry (MS) based spatial proteomics relies on supervised machine learning algorithms to assign proteins to sub-cellular locations based on common gradient profiles. However, such methods fail to quantify uncertainty associated with sub-cellular class assignment. Here we reformulate the framework on which we perform statistical analysis. We propose a Bayesian generative classifier based on Gaussian mixture models to assign proteins probabilistically to sub-cellular niches, thus proteins have a probability distribution over sub-cellular locations, with Bayesian computation performed using the expectation-maximisation (EM) algorithm, as well as Markov-chain Monte-Carlo (MCMC). Our methodology allows proteome-wide uncertainty quantification, thus adding a further layer to the analysis of spatial proteomics. Our framework is flexible, allowing many different systems to be analysed and reveals new modelling opportunities for spatial proteomics. We find our methods perform competitively with current state-of-the art machine learning methods, whilst simultaneously providing more information. We highlight several examples where classification based on the support vector machine is unable to make any conclusions, while uncertainty quantification using our approach provides biologically intriguing results. To our knowledge this is the first Bayesian model of MS-based spatial proteomics data.LG was supported by the BBSRC Strategic Longer and Larger grant (Award BB/L002817/1) and the Wellcome Trust Senior Investigator Award 110170/Z/15/Z awarded to KSL. PDWK was supported by the MRC (project reference MC_UP_0801/1). CMM was supported by a Wellcome Trust Technology Development Grant (Grant number 108467/Z/15/Z). OMC is a Wellcome Trust Mathematical Genomics and Medicine student supported financially by the School of Clinical Medicine, University of Cambridge. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Voices from Beyond the School Gates: Students’ and Their Parents’ Lived Experience of School Exclusion

There have been growing concerns in England about increasing numbers of students, many of whom have Special Education Needs and Disabilities (SEND) or come from disadvantaged backgrounds, who experience education disaffection and failure (Farouk 2017; DfE 2017; Perraudin and McIntyre 2018; Edwards 2018). Moreover, there have been increasing calls for research that works collaboratively with students and other stakeholders (ie parents and school leaders) to address these issues (see Edwards and Brown 2020). This article explores students’ and their parents’ experiences in relation to school exclusion. Drawing on participant action research methods three former excluded students and their parents who successfully re-engaged their education were trained to carry out interviews with five recently excluded secondary school students and their parents. Findings from the interviews stand juxtaposed to political discourses that view exclusion as being influenced by poor parenting or student deviance. Rather, our findings illustrate a spiral of disillusionment, educational disengagement, fractured relationships between students, parents and teachers that emerges as our participants encountered a series of life events that coincided with the educational processes in schools. We consider these findings and, in line with Freire (1972; 2005), we propose a dialogic and relational intervention that enables excluded students to collaborate with their parents and school leaders to make meaningful changes to their own and their schools’ practices in order to help them re-engage with their education

An analysis of speed related UK accidents using a human functional failure methodology

Accidents involving either illegal or inappropriate speeding play a part in a large proportion of accidents involving cars. The types of typical failure generating scenarios found in car accidents where illegal speeding or inappropriate speeding is contributory are compared using the detailed human functional failure methodology developed in the European TRACE project (TRaffic Accident Causation in Europe), funded by the European Commission. Using on-scene cases from the UK ‘On The Spot’ database (funded by the UK Department for Transport and Highways Agency), a sample of cases where speed is contributory have been analysed. An overview of speeding cases from the 4,000 in-depth cases available in the dataset is also presented. The results highlight not only the differences between inappropriate and illegal speeding cases, but also the differences in the functional failures experienced by both the ‘at fault’ and ‘not at fault’ road users in both types of speed-related accidents. The results form a unique base of knowledge for future work on the human-related issues associated with speeding of both types, for all crash participants. Also considered is how new technologies can address speeding accidents

An evaluation of the relationship between Gray’s revised RST and Eysenck’s PEN: distinguishing BIS and FFFS in Carver and White’s BIS/BAS scales

Recent revisions of Gray's Reinforcement Sensitivity Theory (RST) have important implications for self-report measures of approach and avoidance behaviours and how Gray's model relates to other personality models. In this paper, we examine the revised RST by comparing Carver and White's (1994) original one-factor solution of the BIS scale with two alternative two-factor solutions separating BIS-Anxiety and FFFS-Fear. We also examine the relationships between Eysenck's PEN and revised RST factors. Two hundred and twelve participants completed Carver and White's BIS/BAS scales and Eysenck's Personality Questionnaire-Revised. Confirmatory factor analyses of the original BIS scale showed that the hypothesized two-factor model of BIS-Anxiety and FFFS-Fear was the best fit to these data. Associations between the revised RST and Eysenck's PEN were examined using path analysis. In line with theoretical predictions, Psychoticism was related to revised BIS-Anxiety and BAS, Neuroticism to revised BIS-Anxiety and FFFS- Fear, and Extraversion to BAS and FFFS-Fear. Distinctions between BAS subscales and their associations to BIS, N and P were made in terms of past, present and future focus. Possible explanations for mixed findings in the literature and implications for future research are discussed

On designing heteroclinic networks from graphs

Copyright © 2013 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Physica D: Nonlinear Phenomena. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D: Nonlinear Phenomena Vol. 265 (2013), DOI: 10.1016/j.physd.2013.09.006Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined to a large extent by the constraints and dimension of the system. As these networks are of great interest as dynamical models of biological and cognitive processes, it is useful to understand how particular graphs can be realised as robust heteroclinic networks that are attracting. This paper presents two methods of realizing arbitrarily complex directed graphs as robust heteroclinic networks for flows generated by ODEs---we say the ODEs {\em realise} the graphs as heteroclinic networks between equilibria that represent the vertices. Suppose we have a directed graph on $n_v$ vertices with $n_e$ edges. The "simplex realisation" embeds the graph as an invariant set of a flow on an $(n_v-1)$-simplex. This method realises the graph as long as it is one- and two-cycle free. The "cylinder realisation" embeds a graph as an invariant set of a flow on a $(n_e+1)$-dimensional space. This method realises the graph as long as it is one-cycle free. In both cases we find the graph as an invariant set within an attractor, and discuss some illustrative examples, including the influence of noise and parameters on the dynamics. In particular we show that the resulting heteroclinic network may or may not display "memory" of the vertices visited.Mathematical Biosciences Institute (MBI), OhioRoyal SocietyUniversity of Aucklan