Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation

TFM-Explorer: mining cis-regulatory regions in genomes

DNA-binding transcription factors (TFs) play a central role in transcription regulation, and computational approaches that help in elucidating complex mechanisms governing this basic biological process are of great use. In this perspective, we present the TFM-Explorer web server that is a toolbox to identify putative TF binding sites within a set of upstream regulatory sequences of genes sharing some regulatory mechanisms. TFM-Explorer finds local regions showing overrepresentation of binding sites. Accepted organisms are human, mouse, rat, chicken and drosophila. The server employs a number of features to help users to analyze their data: visualization of selected binding sites on genomic sequences, and selection of cis-regulatory modules. TFM-Explorer is available at http://bioinfo.lifl.fr/TFM

Non-Pharmacological Treatments in Lewy Body Disease: A Systematic Review

Introduction: Lewy body disease (LBD) is the second most common neurodegenerative disorder in patients older than 65 years. LBD is characterized by heterogeneous symptoms like fluctuation in attention, visual hallucinations, Parkinsonism, and REM sleep behaviour disorders. Considering the relevant social impact of the disease, identifying effective non-pharmacological treatments is becoming a priority. The aim of this systematic review was to provide an up-to-date literature review of the most effective non-pharmacological treatments in patients with LBD, focussing on evidence-based interventions. Methods: Following PRISMA criteria, we carried out a systematic search through three databases (PubMed, Cochrane Libraries, and PEDro) including physical therapy (PT), cognitive rehabilitation (CR), light therapy (LT), transcranial direct current stimulation (tDCS), transcranial magnetic stimulation (TMS), electroconvulsive therapy (ECT), deep brain stimulation (DBS). All studies were qualitatively assessed using standardized tools (CARE and EPHPP). Results: We obtained a total of 1,220 studies of which 23 original articles met eligibility criteria for inclusion. The total number of LBD patients included was 231; mean age was 69.98, predominantly men (68%). Some PT studies highlighted improvements in motor deficits. CR produced significant improvements in mood, cognition, and patient's quality of life and satisfaction. LT outlined a partial trend of improvements in mood and sleep quality. DBS, ECT, and TMS showed some partial improvements mainly on neuropsychiatric symptoms, whereas tDCS provided partial improvements in attention. Conclusion: This review highlights the efficacy of some evidence-based rehabilitation studies in LBD; however, further randomized controlled trials with larger samples are needed to provide definitive recommendations

Norine, the knowledgebase dedicated to nonribosomal peptides, is now open to crowdsourcing

International audienceSince its creation in 2006, Norine remains the unique knowledgebase dedicated to non-ribosomal pep-tides (NRPs). These secondary metabolites, produced by bacteria and fungi, harbor diverse interesting biological activities (such as antibiotic, anti-tumor, siderophore or surfactant) directly related to the diversity of their structures. The Norine team goal is to collect the NRPs and provide tools to analyze them efficiently. We have developed a user-friendly interface and dedicated tools to provide a complete bioinformatics platform. The knowledgebase gathers abundant and valuable annotations on more than 1100 NRPs. To increase the quantity of described NRPs and improve the quality of associated annotations , we are now opening Norine to crowdsourc-ing. We believe that contributors from the scientific community are the best experts to annotate the NRPs they work on. We have developed MyNorine to facilitate the submission of new NRPs or modifications of stored ones. This article presents MyNorine and other novelties of Norine interface released since the first publication. Norine is freely accessible from the following URL: http://bioinfo.lifl.fr/NRP