Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]

Rectal and Pouch Recurrences After Surgical Treatment for Familial Adenomatous Polyposis

Familial adenomatous polyposis (FAP) is a genetic disease characterized by multiple adenomatous colorectal polyps and different extracolonic manifestations (ECM). The present work is aimed to analyze the outcome after surgical treatment regarding complications and cancer recurrence. Charts from patients treated between 1977 and 2006 were retrospectively analyzed. Clinical and endoscopic data, results of treatment, pathological reports and information about recurrence were collected. Eighty-eight patients (41 men [46.6%] and 47 women [53.4%]) were assisted. At diagnosis, associated colorectal cancer (CRC) was detected in 53 patients (60.2%), whose average age was higher than those without CRC (40.0 vs. 29.5 years). At colonoscopy, polyposis was classified as attenuated in 12 patients (14.3%). Surgical treatment consisted in total proctocolectomy with ileostomy (PCI, 15 [17.4%]), restorative proctocolectomy (RPC, 27 [31.4%]), total colectomy with ileal-rectum anastomosis (IRA, 42 [48.8%]), palliative segmental resection (1 [1.2%]) and internal bypass (1 [1.2%]). Two patients were not operated on due to religious reasons and advanced disease. Complications occurred in 25 patients (29.0%), more commonly after RPC (48.1%). There was no operative mortality. Local or distant metastases were detected in six (11.3%) patients with CRC treated to cure. During the follow-up of 36 IRA, cancer developed in the rectal cuff in six patients (16.6%), whose average age was higher than in patients without rectal recurrence (45.8 vs. 36.6 years). Five of them have had colonic cancer in the resected specimen. Among the 26 patients followed after RPC, cancer in the ileal pouch developed in 1 (3.8%). (1) Within the present series, FAP patients presented a high incidence of associated CRC and diagnosis was generally established after the third decade of life; (2) operative complications occurred in about one third of the patients, being more frequent after the confection of an ileal reservoir; (3) rectal cancer after IRA was detected in 16.6% of patients and it was associated with greater age and previous colonic carcinoma; (4) both continuous and long-term surveillance of the rectal stump and ileal pouch are necessary during follow-up.

Multiple recurrences of cardiac myxomas with acute tumoral pulmonary embolism

We report the case of a 42-year-old female with a second recurrence of cardiac myxoma. Her first diagnosis was at the age of 24 years, when cardiac tumors were withdrawn from her right ventricle and left atrium. Her first recurrence was at the age of 36 years, when tumors were removed from the left and right atria, and the right ventricle. Six years later, the patient was admitted to the Hospital das Clínicas de Porto Alegre complaining of sudden dyspnea, dry cough, and pain in the right hypochondrium, which bore no relation to breathing. The transesophageal echocardiography showed a small tumor in the interatrial septum, close to the superior vena cava, and 2 larger tumors in the right ventricle, 1 close to the outflow tract and the other almost completely obstructing the right branch of the pulmonary artery. The patient was referred to surgery, in which myxomas were removed from the right atrium and ventricle with extension to the right pulmonary artery. The postoperative period was uneventful.

Effects of flecainide on exercise-induced ventricular arrhythmias and recurrences in genotype-negative patients with catecholaminergic polymorphic ventricular tachycardia.

BACKGROUND: Conventional therapy with beta-blockers is incompletely effective in preventing arrhythmic events in patients with catecholaminergic polymorphic ventricular tachycardia (CPVT). We have previously discovered that flecainide in addition to conventional drug therapy prevents ventricular arrhythmias in patients with genotype-positive CPVT. OBJECTIVE: To study the efficacy of flecainide in patients with genotype-negative CPVT. METHODS: We studied the efficacy of flecainide for reducing ventricular arrhythmias during exercise testing and preventing arrhythmia events during long-term follow-up. RESULTS: Twelve patients with genotype-negative CPVT were treated with flecainide. Conventional therapy failed to control ventricular arrhythmias in all patients. Flecainide was initiated because of significant ventricular arrhythmias (n = 8), syncope (n = 3), or cardiac arrest (n = 1). At the baseline exercise test before flecainide, 6 patients had ventricular tachycardia and 5 patients had bigeminal or frequent ventricular premature beats. Flecainide reduced ventricular arrhythmias at the exercise test in 8 patients compared to conventional therapy, similar to that in patients with genotype-positive CPVT in our previous report. Notably, flecainide completely prevented ventricular arrhythmias in 7 patients. Flecainide was continued in all patients except for one who had ventricular tachycardia at the exercise test on flecainide. During a follow-up of 48±94 months, arrhythmia events (sudden cardiac death and aborted cardiac arrest) associated with noncompliance occurred in 2 patients. Flecainide was not discontinued owing to side effects in any of the patients. CONCLUSIONS: Flecainide was effective in patients with genotype-negative CPVT, suggesting that spontaneous Ca(2+) release from ryanodine channels plays a role in arrhythmia susceptibility, similar to that in patients with genotype-positive CPVT.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Do patients benefit from routine follow-up to detect recurrences after radical cystectomy and ileal orthotopic bladder substitution?

The need for and intensity of follow-up to detect disease recurrence after radical cystectomy (RC) for transitional cell carcinoma (TCC) remains a matter for debate.

Elective neck dissection for carcinomas of the oral cavity: occult metastases, neck recurrences, and adjuvant treatment of pathologically positive necks

BACKGROUND: Supraomohyoid neck dissection (SOHND) is currently performed in patients with carcinoma of the oral cavity with clinically negative neck. Most investigators consider SOHND as a staging procedure. METHODS: Records of 100 patients with cancer of the oral cavity and clinically negative neck undergoing SOHND were reviewed. The rate and significance of occult metastases are evaluated, the neck recurrences are analyzed and the indication of adjuvant radiation of pN+ necks is discussed. RESULTS: In 34 of 1814 of analyzed lymph nodes, metastatic disease was detected as follows: 30 macrometastases and 4 micrometastases. In 13 of 34 metastases (38%), extracapsular spread was observed. Twenty of 100 patients (20%) had to be upstaged. In 9 of 87 (10%) patients without local recurrence and with a minimal follow-up of 24 months, 5 ipsilateral (4 within the dissection field) and 5 contralateral neck recurrences were observed. Regional recurrence developed in 4% and 35% of patients with pN0 and pN+ necks, respectively. CONCLUSIONS: In 20% of patients with oral cavity tumors and pN0 neck, occult metastases were disclosed. Neck recurrences developed significantly more often in patients with pN+ than in those with pN0 necks. To evaluate the exact indication for an adjuvant treatment of patients with cN0/pN+ necks, prospective studies should be performed.

Progress on BIG 1-02/IBCSG 27-02/NSABP B-37, a prospective randomized trial evaluating chemotherapy after local therapy for isolated locoregional recurrences of breast cancer

BACKGROUND: The utility of chemotherapy for women who experience a locoregional recurrence after primary treatment of early breast cancer remains an open question. An international collaborative trial is being conducted by the Breast International Group (BIG), the International Breast Cancer Study Group (IBCSG), and the National Surgical Adjuvant Breast and Bowel Project (NSABP) to determine the effectiveness of cytotoxic therapy for these patients, either alone or in addition to selective use of hormonal therapy and trastuzumab. METHODS: The trial population includes women who have had a previous diagnosis of invasive breast cancer treated by mastectomy or breast-conserving surgery, but subsequently develop an isolated local and/or regional ipsilateral invasive recurrence. Excision of all macroscopic tumor without evidence of systemic disease is required for study entry. Patients are randomized to receive chemotherapy or no chemotherapy; type of chemotherapy is not protocol-specified. Radiation, hormonal therapy, and trastuzumab are given as appropriate. The primary endpoint is disease-free survival (DFS). Quality-of-life measurements are collected at baseline, and then at 9 and 12 months. The accrual goal is 977 patients. RESULTS: This report describes the characteristics of the first 99 patients. Sites of recurrence at study entry were: breast (56%), mastectomy scar/chest wall (35%), and regional lymph nodes (9%). Two-thirds of patients have estrogen-receptor-positive recurrences. CONCLUSION: This is the only trial actively investigating the question of "adjuvant" chemotherapy in locally recurrent breast cancer. The case mix of accrual to date indicates a broad representation of this patient population.

A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Acute, posterior multifocal placoid pigment epitheliopathy: a case of 11 recurrences over 15 years

PURPOSE: To report the case of a patient with recurrent, acute posterior multifocal placoid pigment epitheliopathy. To the best of our knowledge, this is the longest documented course with the greatest number of recurrences reported. METHODS: Observational case report of one patient. A 27-year-old otherwise healthy male patient presented with recurrence of new scotomata over 15 years. Fundus photography, fluorescein angiography, indocyanine green angiography, fundus autofluorescence, and optical coherence tomography documented his clinical course. RESULTS: Over the course of 15 years, the patient developed 11 symptomatic (5 imaging-documented) recurrences of acute, posterior multifocal placoid pigment epitheliopathy affecting both eyes. Each episode manifested with new subjective scotomata and new lesions noted on imaging. Symptoms mostly resolved after each episode, and visual outcome remained excellent (20/20 in the right eye and 20/25 left eye at the last follow-up). CONCLUSION: Although typically monophasic, acute posterior multifocal placoid pigment epitheliopathy can rarely present with a recurrent course over a prolonged period of time and should be considered as a diagnosis in patients presenting with recurrent visual symptoms and new placoid lesions on imaging. In recurrent cases, visual recovery may still remain excellent.