Normal form and exact feedback linearisation of nonlinear stochastic systems: the ideal case

This paper introduces the concepts of stochastic relative degree, normal form and exact feedback linearisation for single-input single-output nonlinear stochastic systems. The systems are defined by stochastic differential equations in which both the drift and the diffusion terms are nonlinear functions of the states and the control input. First, we define new differential operators and the concept of stochastic relative degree. Then we introduce a suitable coordinate change and we show that the dynamics of the transformed state has a simplified structure, which we name normal form. Finally, we show that a condition on the stochastic relative degree of the system is sufficient for it to be rendered linear via a coordinate change and a nonlinear feedback. We provide an analytical example to illustrate the theory

The time is out of joint. Teacher subjectivity during COVID‑19

In this study, we address the issue of mathematics teachers' personal and professional responsiveness to changing circumstances, such as the shift in external demands made on teacher practice due to the COVID-19 pandemic. For investigating a such delicate issue, we take a theoretical approach, which is quite novel in the field of mathematics education: Lacan's psychoanalytical lens. Specifically, we will use this psychoanalytical lens to analyze a case study focusing on a primary school teacher during the first lockdown in Italy, during which school was organized exclusively in the form of distance education. The analysis of the teacher’s crisis and the strategies she adopted to overcome this crisis give some suggestions about possible directions and issues to consider for future mathematics teacher training proposals

Collective discussions for the development of Interpretative Knowledge in Mathematics Teacher Education

We start from the assumption that teachers need a deep and broad mathematical knowledge —called Interpretative Knowledge (IK)—that allows them to support students in building their mathematical knowledge from their own reasoning and productions. In the present study, we aimed to ascertain how collective discussions focusing on the interpretation of students’ productions engage Prospective Teachers (PTs) and impact their IK development. In particular, we observe how this form of collaborative work among PTs allows for the emergence of novel insights into the mathematical aspects of students’ productions that were not considered during previous individual work, and produce changes in PTs’ attitudes towards students’ productions

The quality of turning in Parkinson's disease: a compensatory strategy to prevent postural instability?

The ability to turn while walking is essential for daily living activities. Turning is slower and more steps are required to complete a turn in people with Parkinson's disease (PD) compared to control subjects but it is unclear whether this altered strategy is pathological or compensatory. The aim of our study is to characterize the dynamics of postural stability during continuous series of turns while walking at various speeds in subjects with PD compared to control subjects. We hypothesize that people with PD slow their turns to compensate for impaired postural stability

Ecological specialization to fluctuating resources prevents long-distance migratory raptors from becoming sedentary on islands.

Background The adaptive transition between behavioral strategies, such as the shift from migratoriness to sedentariness, remains an outstanding question in evolutionary ecology. Density-dependent variation in the age of first breeding has been proposed as a feasible mechanism through which long-lived migratory birds with deferred sexual maturity should become sedentary to persist on islands. Although this pattern seems to hold for most raptors and herons, a few exceptions have been identified. One of these exceptions is the Eleonora's falcon, a long-distance migratory bird, which shows one of the most peculiar adaptations in the timing of reproduction and food requirements among raptors. Methodology/Principal Findings Here, we compiled data concerning demography, banding recoveries and satellite tracking of Eleonora's falcons to discuss likely explanations for the exceptional behavior of this insular long-distance migratory species. Conclusions/Significance New data reveal that Eleonora's falcons do return to the natal colonies in their first year and young birds are able to breed. However, in contrast to previous hypothesis, the highly specialized strategy of this and other ecologically similar species, as well as the virtual lack of food during winter at breeding areas prevent them from becoming sedentary on islands. Although the ultimate mechanisms underlying the process of sedentarization remain poorly understood, the evidence provided reveal the existence of important trade-offs associated with ecological specialization that may become particularly relevant in the present context of global change

Li 1s core exciton in LiH studied by x-ray Raman scattering spectroscopy

The Li 1s core excitation spectra in LiH was studied by means of x-ray Raman scattering (XRS) spectroscopy in a wide range of momentum transfers q. The analysis of the near-edge region of the measured spectra in combination with q-dependent ab initio calculations of XRS spectra based on the Bethe-Salpeter equation (BSE) reveals that the prominent peak at the excitation onset arises from two main contributions, namely a pre-edge peak associated to a p-type core exciton and strong transitions to empty states near the bottom of the conduction band, which is in contrast to previous experimental studies that attributed that feature to a single excitonic peak. The p-like angular symmetry of the core exciton is supported by BSE calculations of the relative contributions to the XRS spectra from monopole and dipole transitions and by the observed decrease of its normalised intensity for increasing momentum transfers. Higher energy spectral features in the measured XRS spectra are well reproduced by BSE, as well as by real-space multiple-scattering calculations.Peer reviewe

Copy number variations residing outside the SHOX enhancer region are involved in Short Stature and Léri-Weill dyschondrosteosis

Background: SHOX enhancer CNVs, affecting one or more of the seven recognized evolutionary conserved non-coding elements (CNEs) represent one of the most frequent cause of SHOX-haploinsufficiency. During the diagnostic workflow deletions/duplications have been identified downstream SHOX not including any of the these CNEs. Methods: Fine tiling aCGH and breakpoint PCR were used to characterize the critical interval and to search for novel alterations in a cohort of selected patients. Results: Screening of 252 controls provided evidence that duplications in this area represent likely benign variants whereas none of the deletions were detected. These findings suggested that other alterations relevant for SHOX-haploinsufficiency might be missed by the standard diagnostic methods. To identify such undisclosed elements, the aCGH was used to reanalyze 52 unresolved cases with clinical features strongly suggestive of SHOX-haploinsufficiency. This analysis followed by the screening of 210 patients detected two partially overlapping small deletions of ~12 and ~8 kb in four unrelated individuals, approximately 15 kb downstream SHOX, that were absent in 720 normal stature individuals. Conclusion: Our results strengthen the hypothesis that alterations of yet unidentified cis-regulatory elements residing outside those investigated through conventional methods, might explain the phenotype in ISS/LWD patients thus enlarging the spectrum of variants contributing to SHOX-haploinsufficiency

Variation in genome content and predatory phenotypes between \u3cem\u3eBdellovibrio\u3c/em\u3e sp. NC01 isolated from soil and \u3cem\u3eB. bacteriovorus\u3c/em\u3e type strain HD100

Defining phenotypic and associated genotypic variation among Bdellovibrio may further our understanding of how this genus attacks and kills different Gram-negative bacteria. We isolated Bdellovibrio sp. NC01 from soil. Analysis of 16S rRNA gene sequences and average amino acid identity showed that NC01 belongs to a different species than the type species bacteriovorus. By clustering amino acid sequences from completely sequenced Bdellovibrio and comparing the resulting orthologue groups to a previously published analysis, we defined a ‘core genome’ of 778 protein-coding genes and identified four protein-coding genes that appeared to be missing only in NC01. To determine how horizontal gene transfer (HGT) may have impacted NC01 genome evolution, we performed genome-wide comparisons of Bdellovibrio nucleotide sequences, which indicated that eight NC01 genomic regions were likely acquired by HGT. To investigate how genome variation may impact predation, we compared protein-coding gene content between NC01 and the B. bacteriovorus type strain HD100, focusing on genes implicated as important in successful killing of prey. Of these, NC01 is missing ten genes that may play roles in lytic activity during predation. Compared to HD100, NC01 kills fewer tested prey strains and kills Escherichia coli ML35 less efficiently. NC01 causes a smaller log reduction in ML35, after which the prey population recovers and the NC01 population decreases. In addition, NC01 forms turbid plaques on lawns of E. coli ML35, in contrast to clear plaques formed by HD100. Linking phenotypic variation in interactions between Bdellovibrio and Gram-negative bacteria with underlying Bdellovibrio genome variation is valuable for understanding the ecological significance of predatory bacteria and evaluating their effectiveness in clinical applications

Variation in genome content and predatory phenotypes between Bdellovibrio sp. NC01 isolated from soil and B. bacteriovorus type strain HD100

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Williams, L. E., Cullen, N., DeGiorgis, J. A., Martinez, K. J., Mellone, J., Oser, M., Wang, J., & Zhang, Y. Variation in genome content and predatory phenotypes between Bdellovibrio sp. NC01 isolated from soil and B. bacteriovorus type strain HD100. Microbiology, 165(12), (2019): 1315-1330, doi: 10.1099/mic.0.000861.Defining phenotypic and associated genotypic variation among Bdellovibrio may further our understanding of how this genus attacks and kills different Gram-negative bacteria. We isolated Bdellovibrio sp. NC01 from soil. Analysis of 16S rRNA gene sequences and average amino acid identity showed that NC01 belongs to a different species than the type species bacteriovorus. By clustering amino acid sequences from completely sequenced Bdellovibrio and comparing the resulting orthologue groups to a previously published analysis, we defined a ‘core genome’ of 778 protein-coding genes and identified four protein-coding genes that appeared to be missing only in NC01. To determine how horizontal gene transfer (HGT) may have impacted NC01 genome evolution, we performed genome-wide comparisons of Bdellovibrio nucleotide sequences, which indicated that eight NC01 genomic regions were likely acquired by HGT. To investigate how genome variation may impact predation, we compared protein-coding gene content between NC01 and the B. bacteriovorus type strain HD100, focusing on genes implicated as important in successful killing of prey. Of these, NC01 is missing ten genes that may play roles in lytic activity during predation. Compared to HD100, NC01 kills fewer tested prey strains and kills Escherichia coli ML35 less efficiently. NC01 causes a smaller log reduction in ML35, after which the prey population recovers and the NC01 population decreases. In addition, NC01 forms turbid plaques on lawns of E. coli ML35, in contrast to clear plaques formed by HD100. Linking phenotypic variation in interactions between Bdellovibrio and Gram-negative bacteria with underlying Bdellovibrio genome variation is valuable for understanding the ecological significance of predatory bacteria and evaluating their effectiveness in clinical applications.This research was supported by an Institutional Development Award (IDeA) from the National Institute of General Medical Sciences of the National Institutes of Health under grant no. P20GM103430 and by funding to LEW from Providence College. This material is based upon work conducted at a Rhode Island NSF EPSCoR research facility, the Genomics and Sequencing Center, supported in part by the National Science Foundation EPSCoR Cooperative Agreement #EPS-1004057. This material is based upon work supported in part by the National Science Foundation under EPSCoR Cooperative Agreement #OIA-1655221. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication

Can smartphone technology be used to support an effective home exercise intervention to prevent falls amongst community dwelling older adults?: The TOGETHER feasibility RCT study protocol

INTRODUCTION: Falls have major implications for quality of life, independence and cost to the health service. Strength and balance training has been found to be effective in reducing the rate/risk of falls, as long as there is adequate fidelity to the evidence-based programme. Health services are often unable to deliver the evidence-based dose of exercise and older adults do not always sufficiently adhere to their programme to gain full outcomes. Smartphone technology based on behaviour-change theory has been used to support healthy lifestyles, but not falls prevention exercise. This feasibility trial will explore whether smartphone technology can support patients to better adhere to an evidence-based rehabilitation programme and test study procedures/outcome measures. METHODS AND ANALYSIS: A two-arm, pragmatic feasibility randomised controlled trial will be conducted with health services in Manchester, UK. Seventy-two patients aged 50+years eligible for a falls rehabilitation exercise programme from two community services will receive: (1) standard service with a smartphone for outcome measurement only or (2) standard service plus a smartphone including the motivational smartphone app. The primary outcome is feasibility of the intervention, study design and procedures. The secondary outcome is to compare standard outcome measures for falls, function and adherence to instrumented versions collected using smartphone. Outcome measures collected include balance, function, falls, strength, fear of falling, health-related quality of life, resource use and adherence. Outcomes are measured at baseline, 3 and 6-month post-randomisation. Interviews/focus groups with health professionals and participants further explore feasibility of the technology and trial procedures. Primarily analyses will be descriptive. ETHICS AND DISSEMINATION: The study protocol is approved by North West Greater Manchester East Research Ethics Committee (Rec ref:18/NW/0457, 9/07/2018). User groups and patient representatives were consulted to inform trial design, and are involved in study recruitment. Results will be reported at conferences and in peer-reviewed publications. A dissemination event will be held in Manchester to present the results of the trial. The protocol adheres to the recommended Standard Protocol Items: Recommendations for Interventional Trials (SPIRIT) checklist