Ducks on the torus: existence and uniqueness

We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.Comment: To appear in Journal of Dynamical and Control Systems, presumably Vol. 16 (2010), No. 2; The final publication is available at www.springerlink.co

Renormalisation scheme for vector fields on T2 with a diophantine frequency

We construct a rigorous renormalisation scheme for analytic vector fields on the 2-torus of Poincare type. We show that iterating this procedure there is convergence to a limit set with a ``Gauss map'' dynamics on it, related to the continued fraction expansion of the slope of the frequencies. This is valid for diophantine frequency vectors.Comment: final versio

Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Novel calmodulin mutations associated with congenital arrhythmia susceptibility.

BACKGROUND: Genetic predisposition to life-threatening cardiac arrhythmias such as congenital long-QT syndrome (LQTS) and catecholaminergic polymorphic ventricular tachycardia (CPVT) represent treatable causes of sudden cardiac death in young adults and children. Recently, mutations in calmodulin (CALM1, CALM2) have been associated with severe forms of LQTS and CPVT, with life-threatening arrhythmias occurring very early in life. Additional mutation-positive cases are needed to discern genotype-phenotype correlations associated with calmodulin mutations. METHODS AND RESULTS: We used conventional and next-generation sequencing approaches, including exome analysis, in genotype-negative LQTS probands. We identified 5 novel de novo missense mutations in CALM2 in 3 subjects with LQTS (p.N98S, p.N98I, p.D134H) and 2 subjects with clinical features of both LQTS and CPVT (p.D132E, p.Q136P). Age of onset of major symptoms (syncope or cardiac arrest) ranged from 1 to 9 years. Three of 5 probands had cardiac arrest and 1 of these subjects did not survive. The clinical severity among subjects in this series was generally less than that originally reported for CALM1 and CALM2 associated with recurrent cardiac arrest during infancy. Four of 5 probands responded to β-blocker therapy, whereas 1 subject with mutation p.Q136P died suddenly during exertion despite this treatment. Mutations affect conserved residues located within Ca(2+)-binding loops III (p.N98S, p.N98I) or IV (p.D132E, p.D134H, p.Q136P) and caused reduced Ca(2+)-binding affinity. CONCLUSIONS: CALM2 mutations can be associated with LQTS and with overlapping features of LQTS and CPVT

Insights into adherence to medication and lifestyle recommendations in an international cohort of patients with catecholaminergic polymorphic ventricular tachycardia.

AIMS: In patients with catecholaminergic polymorphic ventricular tachycardia (CPVT), a rare inherited arrhythmia syndrome, arrhythmic events can be prevented by medication and lifestyle recommendations. In patients who experience breakthrough arrhythmic events, non-adherence plays an essential role. We aimed to investigate the incidence and potential reasons for non-adherence to medication and lifestyle recommendations in a large, international cohort of patients with CPVT. METHODS AND RESULTS: An online multilingual survey was shared with CPVT patients worldwide by their cardiologists, through peer-recruitment, and on social media from November 2022 until July 2023. Self-reported non-adherence was measured using the validated Medication Adherence Rating Scale (MARS) and a newly developed questionnaire about lifestyle. Additionally, validated questionnaires were used to assess potential reasons for medication non-adherence. Two-hundred-and-eighteen patients completed the survey, of whom 200 (92%) were prescribed medication [122 (61%) female; median age 33.5 years (interquartile range: 22-50)]. One-hundred-and-three (52%) were prescribed beta-blocker and flecainide, 85 (43%) beta-blocker, and 11 (6%) flecainide. Thirty-four (17%) patients experienced a syncope, aborted cardiac arrest or appropriate implantable cardioverter defibrillator shock after diagnosis. Nineteen (13.4%) patients were exercising more than recommended. Thirty (15%) patients were non-adherent to medication. Female sex [odds ratio (OR) 3.7, 95% confidence interval (CI) 1.3-12.0, P = 0.019], flecainide monotherapy compared to combination therapy (OR 6.8, 95% CI 1.6-31.0, P = 0.010), and a higher agreement with statements regarding concerns about CPVT medication (OR 1.2, 95% CI 1.1-1.3, P < 0.001) were independently associated with non-adherence. CONCLUSION: The significant rate of non-adherence associated with concerns regarding CPVT-related medication, emphasizes the potential for improving therapy adherence by targeted patient education

Age of First Arrhythmic Event in Brugada Syndrome: Data From the SABRUS (Survey on Arrhythmic Events in Brugada Syndrome) in 678 Patients.

BACKGROUND: Data on the age at first arrhythmic event (AE) in Brugada syndrome are from limited patient cohorts. The aim of this study is 2-fold: (1) to define the age at first AE in a large cohort of patients with Brugada syndrome, and (2) to assess the influence of the mode of AE documentation, sex, and ethnicity on the age at first AE. METHODS AND RESULTS: A survey of 23 centers from 10 Western and 4 Asian countries gathered data from 678 patients with Brugada syndrome (91.3% men) with first AE documented at time of aborted cardiac arrest (group A, n=426) or after prophylactic implantable cardioverter-defibrillator implantation (group B, n=252). The vast majority (94.2%) of the patients were 16 to 70 years old at the time of AE, whereas pediatric (70 years) comprised 4.3% and 1.5%, respectively. Peak AE rate occurred between 38 and 48 years (mean, 41.9±14.8; range, 0.27-84 years). Group A patients were younger than in Group B by a mean of 6.7 years (46.1±13.2 versus 39.4±15.0 years; P<0.001). In adult patients (≥16 years), women experienced AE 6.5 years later than men (P=0.003). Whites and Asians exhibited their AE at the same median age (43 years). CONCLUSIONS: SABRUS (Survey on Arrhythmic Events in Brugada Syndrome) presents the first analysis on the age distribution of AE in Brugada syndrome, suggesting 2 age cutoffs (16 and 70 years) that might be important for decision-making. It also allows gaining insights on the influence of mode of arrhythmia documentation, patient sex, and ethnic origin on the age at AE

Profile of Brugada Syndrome Patients Presenting with Their First Documented Arrhythmic Event. Data from the Survey on Arrhythmic Events in BRUgada Syndrome (SABRUS).

BACKGROUND: Detailed information on the profile of Brugada syndrome (BrS) patients presenting their first arrhythmic event (AE) after prophylactic implantation of a cardioverter defibrillator (ICD) is limited. OBJECTIVES: 1) To compare clinical, electrocardiographic, electrophysiologic and genetic profiles of patients who exhibited their first documented AE as aborted cardiac arrest (CA) (group A) with those in whom the AE was documented after prophylactic ICD implantation (group B); 2) To characterize group B patients' profile using the Class II indications for ICD implantation established by HRS/EHRA/APHRS Expert Consensus Statement in 2013. METHODS: A survey of 23 centers from 10 Western and 4 Asian countries enabled data collection of 678 BrS patients with AE (group A, n=426; group B, n=252). RESULTS: First AE occurred in group B patients 6.7 years later than in group A (46.1+ 13.3 vs. 39.4+15.1, P<0.001). Group B patients had a higher incidence of family history of sudden cardiac death (SCD) and SCN5A mutations. Of the 252 group B patients, 189 (75%) complied with the HRS/EHRA/APHRS indications whereas the remaining 63 (25%) did not. CONCLUSION: BrS patients with first AE documented after prophylactic ICD implantation exhibited their AE at a later age with a higher incidence of positive family history of SCD and SCN5A mutations compared to those presenting with an aborted CA. Only 75% of patients who suffered an AE after receiving a prophylactic ICD complied with the 2013 Class II indications, suggesting efforts are still required for improving risk stratification

Gender Differences in Patients with Brugada Syndrome and Arrhythmic Events: Data from a Survey on Arrhythmic Events in 678 Patients.

BACKGROUND: There is limited information on gender differences in patients with Brugada syndrome (BrS) who experienced arrhythmic events (AEs). OBJECTIVES: To compare clinical, electrocardiographic (ECG), electrophysiologic (EP) and genetic characteristics between males and females in BrS-patients with their first AE. METHODS: The multicenter Survey on AE in BrS (SABRUS) collected data on first AE in 678 BrS-patients including 619 (91.3%) males and 59 (8.7%) females aged 0.27 to 84 (mean 42.5±14.1) years at the time of AE. RESULTS: After excluding pediatric patients, females were older than males (49.5±14.4 vs. 43±12.7 years, respectively, P=0.001). Higher proportions of females were observed in the pediatric and elderly populations. In Asians, male/female ratio of AE was ≈9-fold higher compared to Caucasians. Spontaneous type 1 BrS-ECG was associated with earlier onset of AE in pediatric females. A similar prevalence (≈65%) of spontaneous type 1 BrS-ECG was present in males and females above age of 60 years. Females less frequently showed a spontaneous type-1 BrS-ECG (31% vs. 59%, P<0.001) or arrhythmia-inducibility at EP study (34% vs. 64%, P<0.001). An SCN5A mutation was more frequently found in females (47.6% vs. 27.8% in males, P=0.007). CONCLUSIONS: This study confirms that female BrS-patients are much rarer, display less type 1 Brugada-ECG and exhibit lower inducibility rates than males. It shows for the first time that BrS females with AE have higher SCN5A mutation rates as well as the relationship between gender vs. age at onset of AE and ethnicity