Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

The link between land-use management and fluvial flood risk : a chaotic conception?

There is much policy interest in the possible linkages that might exist between land use and downstream fluvial flood risk. On the one hand, this position is sustained by observations from plot- and field-scale studies that suggest land management does affect runoff. On the other, upscaling these effects to show that land-management activities impact upon flood risk at larger catchment scales has proved to be elusive. This review considers the reasons for why this upscaling is problematic. We argue that, rather than it reflecting methodological challenges associated with the difficulties of modelling hydrological processes over very large areas and during extreme runoff events, it reflects the fact that any linkage between land management and flood risk cannot be generalized and taken out of its specific spatial (catchment) and temporal (flood event) context. We use Sayer's (1992) notion of a `chaotic conception' to describe the belief that there is a simple and general association between land management and downstream flood risk rather than the impacts of land management being spatially and temporally contingent in relation to the particular geographical location, time period and scale being considered. Our argument has important practical consequences because it implies that land-management activities to reduce downstream flood risk will be different to traditional flood-reduction interventions such as levees. The purpose of demonstration projects then needs careful consideration such that conclusions made for one project are not transferred uncritically to other scales of analysis or geographical locations.

J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Chaotic dynamics and team effectiveness: evidence from professional basketball

Considering teams as complex adaptive systems (CAS) this study deals with changes in team effectiveness over time in a specific context: professional basketball. The sample comprised 23 basketball teams whose outcomes were analysed over a 12-year period according to two objective measures. The results reveal that all the teams showed chaotic dynamics, one of the key characteristics of CAS. A relationship was also found between teams showing low-dimensional chaotic dynamics and better outcomes, supporting the idea of healthy variability in organizational behaviour. The stability of the squad was likewise found to influence team outcomes, although it was not associated with the chaotic dynamics in team effectiveness. It is concluded that studying teams as CAS enables fluctuations in team effectiveness to be explained, and that the techniques derived from nonlinear dynamical systems, developed specifically for the study of CAS, are useful for this purpose.

Report on the Status of Findings and Recommendations from the City of Cambridge’s Periodic Examination Report dated September 5, 2014 for the period June 1, 2015 through November 30, 2015

Report on the Status of Findings and Recommendations from the City of Cambridge’s Periodic Examination Report dated September 5, 2014 for the period June 1, 2015 through November 30, 2015

Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving

Chaotic systems, when used to drive copies of themselves (or parts of themselves) may induce interesting behaviors in the driven system. In case the later exhibits invariance under amplification or translation, they may show amplification (reduction), or displacement of the attractor. It is shown how the behavior to be obtained is implied by the symmetries involved. Two explicit examples are studied to show how these phenomena manifest themselves under perfect and imperfect coupling.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Dissemination of periodic mammography and patterns of use, by birth cohort, in Catalonia (Spain)

Background: In Catalonia (Spain) breast cancer mortality has declined since the beginning of the 1990s. The dissemination of early detection by mammography and the introduction of adjuvant treatments are among the possible causes of this decrease, and both were almost coincident in time. Thus, understanding how these procedures were incorporated into use in the general population and in women diagnosed with breast cancer is very important for assessing their contribution to the reduction in breast cancer mortality. In this work we have modeled the dissemination of periodic mammography and described repeat mammography behavior in Catalonia from 1975 to 2006. Methods: Cross-sectional data from three Catalan Health Surveys for the calendar years 1994, 2002 and 2006 was used. The dissemination of mammography by birth cohort was modeled using a mixed effects model and repeat mammography behavior was described by age and survey year. Results: For women born from 1938 to 1952, mammography clearly had a period effect, meaning that they started to have periodic mammograms at the same calendar years but at different ages. The age at which approximately 50% of the women were receiving periodic mammograms went from 57.8 years of age for women born in 1938–1942 to 37.3 years of age for women born in 1963–1967. Women in all age groups experienced an increase in periodic mammography use over time, although women in the 50–69 age group have experienced the highest increase. Currently, the target population of the Catalan Breast Cancer Screening Program, 50–69 years of age, is the group that self-reports the highest utilization of periodic mammograms, followed by the 40–49 age group. A higher proportion of women of all age groups have annual mammograms rather than biennial or irregular ones. Conclusion: Mammography in Catalonia became more widely implemented during the 1990s. We estimated when cohorts initiated periodic mammograms and how frequently women are receiving them. These two pieces of information will be entered into a cost-effectiveness model of early detection in Catalonia.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Analysis of the genetic basis of periodic fever with aphthous stomatitis, pharyngitis, and cervical adenitis (PFAPA) syndrome.

PFAPA syndrome is the most common autoinflammatory syndrome in children from Western countries. In spite of its strong familial clustering, its genetic basis and inheritance pattern are still unknown. We performed a comprehensive genetic study on 68 individuals from 14 families. Linkage analysis suggested a susceptibility locus on chromosome 8, but direct molecular sequencing did not support this initial statistical finding. Exome sequencing revealed the absence of any gene that was mutated in all patients. Exhaustive screening of genes involved in other autoinflammatory syndromes or encoding components of the human inflammasome showed no DNA variants that could be linked to PFAPA molecular pathology. Among these, the previously-reported missense mutation V198M in the NLRP3 gene was clearly shown not to co-segregate with PFAPA. Our results on this relatively large cohort indicate that PFAPA syndrome is unlikely to be a monogenic condition. Moreover, none of the several genes known to be involved in inflammation or in autoinflammatory disorders seem to be relevant, alone, to its etiology, suggesting that PFAPA results from oligogenic or complex inheritance of variants in multiple disease genes and/or non-genetic factors.

Phenotypic and genotypic characteristics of cryopyrin-associated periodic syndrome: a series of 136 patients from the Eurofever Registry.

OBJECTIVE: To evaluate genetic, demographic and clinical features in patients with cryopyrin-associated periodic syndrome (CAPS) from the Eurofever Registry, with a focus on genotype-phenotype correlations and predictive disease severity markers. METHODS: A web-based registry retrospectively collected data on patients with CAPS. Experts in the disease independently validated all cases. Patients carrying NLRP3 variants and germline-mutation-negative patients were included. RESULTS: 136 patients were analysed. The median age at disease onset was 9 months, and the median duration of follow-up was 15 years. Skin rash, musculoskeletal involvement and fever were the most prevalent features. Neurological involvement (including severe complications) was noted in 40% and 12% of the patients, respectively, with ophthalmological involvement in 71%, and neurosensory hearing loss in 42%. 133 patients carried a heterozygous, germline mutation, and 3 patients were mutation-negative (despite complete NLRP3 gene screening). Thirty-one different NLRP3 mutations were recorded; 7 accounted for 78% of the patients, whereas 24 rare variants were found in 27 cases. The latter were significantly associated with early disease onset, neurological complications (including severe complications) and severe musculoskeletal involvement. The T348M variant was associated with early disease onset, chronic course and hearing loss. Neurological involvement was less strongly associated with V198M, E311 K and A439 V alleles. Early onset was predictive of severe neurological complications and hearing loss. CONCLUSIONS: Patients carrying rare NLRP3 variants are at risk of severe CAPS; onset before the age of 6 months is associated with more severe neurological involvement and hearing loss. These findings may have an impact on treatment decisions.

Prevalence and determinants of periodic limb movements in the general population.

OBJECTIVE: Periodic limb movements during sleep (PLMS) are sleep phenomena characterized by periodic episodes of repetitive stereotyped limb movements. The aim of this study was to describe the prevalence and determinants of PLMS in a middle to older aged general population. METHODS: Data from 2,162 subjects (51.2% women, mean age = 58.4 ± 11.1 years) participating in a population-based study (HypnoLaus, Lausanne, Switzerland) were collected. Assessments included laboratory tests, sociodemographic data, personal and treatment history, and full polysomnography at home. PLMS index (PLMSI) was determined, and PLMSI > 15/h was considered as significant. RESULTS: Prevalence of PLMSI > 15/h was 28.6% (31.3% in men, 26% in women). Compared to subjects with PLMSI ≤ 15/h, subjects with PLMSI > 15/h were older (p < 0.001), were predominantly males (p = 0.007), had a higher proportion of restless legs syndrome (RLS; p < 0.001), had a higher body mass index (p = 0.001), and had a lower mean glomerular filtration rate (p < 0.001). Subjects with PLMSI > 15/h also had a higher prevalence of diabetes, hypertension, and beta-blocker or hypnotic treatments. The prevalence of antidepressant use was higher, but not statistically significant (p = 0.07). Single nucleotide polymorphisms (SNPs) within BTBD9 (rs3923809), TOX3 (rs3104788), and MEIS1 (rs2300478) genes were significantly associated with PLSMI > 15/h. Conversely, mean hemoglobin and ferritin levels were similar in both groups. In the multivariate analysis, age, male gender, antidepressant intake, RLS, and rs3923809, rs3104788, and rs2300478 SNPs were independently associated with PLMSI > 15/h. INTERPRETATION: PLMS are highly prevalent in our middle-aged European population. Age, male gender, RLS, antidepressant treatment, and specific BTBD9, TOX3, and MEIS1 SNP distribution are independent predictors of PLMSI > 15/h. ANN NEUROL 2016;79:464-474.

Periodic Fever, Aphthous Stomatitis, Pharyngitis, and Cervical Adenitis (PFAPA) Syndrome: a Review of the Pathogenesis.

PFAPA syndrome represents the most common cause of recurrent fever in children in European populations, and it is characterized by recurrent episodes of high fever, pharyngitis, cervical adenitis, and aphthous stomatitis. Many possible causative factors have been explored so far, including infectious agents, immunologic mechanisms and genetic predisposition, but the exact etiology remains unclear. Recent findings demonstrate a dysregulation of different components of innate immunity during PFAPA flares, such as monocytes, neutrophils, complement, and pro-inflammatory cytokines, especially IL-1β, suggesting an inflammasome-mediated innate immune system activation and supporting the hypothesis of an autoinflammatory disease. Moreover, in contrast with previous considerations, the strong familial clustering suggests a potential genetic origin rather than a sporadic disease. In addition, the presence of variants in inflammasome-related genes, mostly in NLRP3 and MEFV, suggests a possible role of inflammasome-composing genes in PFAPA pathogenesis. However, none of these variants seem to be relevant, alone, to its etiology, indicating a high genetic heterogeneity as well as an oligogenic or polygenic genetic background.