Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Menopausal status: A possible predictive factor for recurrence in women with cancer of the uterine cervix without pelvic lymph node metastasis

Objectives: To evaluate risk factors for recurrence of carcinoma of the uterine cervix among women who had undergone radical hysterectomy without pelvic lymph node metastasis, while taking into consideration not only the classical histopathological factors but also sociodemographic, clinical and treatment-related factors. Study design: This was an exploratory analysis on 233 women with carcinoma of the uterine cervix (stages IB and IIA) who were treated by means of radical hysterectomy and pelvic lymphadenectomy, with free surgical margins and without lymph node metastases on conventional histopathological examination. Women with histologically normal lymph nodes but with micrometastases in the immunohistochemical analysis (AE1/AE3) were excluded. Disease-free survival for sociodemographic, clinical and histopathological variables was calculated using the Kaplan-Meier method. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Results: Twenty-seven recurrences were recorded (11.6%), of which 18 were pelvic, four were distant, four were pelvic + distant and one was of unknown location. The five-year disease-free survival rate among the study population was 88.4%. The independent risk factors for recurrence in the multivariate analysis were: postmenopausal status (HR 14.1; 95% CI: 3.7-53.6; P < 0.001), absence of or slight inflammatory reaction (HR 7.9; 95% CI: 1.7-36.5; P = 0.008) and invasion of the deepest third of the cervix (FIR 6.1; 95% CI: 1.3-29.1; P = 0.021). Postoperative radiotherapy was identified as a protective factor against recurrence (HR 0.02; 95% CI: 0.001-0.25; P = 0.003). Conclusion: Postmenopausal status is a possible independent risk factor for recurrence even when adjusted for classical prognostic factors (such as tumour size, depth of turnout invasion, capillary embolisation) and treatment-related factors (period of treatment and postoperative radiotherapy status). (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Recurrence quantification analysis of electrostatic fluctuations in fusion plasmas

We have investigated plasma turbulence at the edge of a tokamak plasma using data from electrostatic potential fluctuations measured in the Brazilian tokamak TCABR. Recurrence quantification analysis has been used to provide diagnostics of the deterministic content of the series. We have focused our analysis on the radial dependence of potential fluctuations and their characterization by recurrence-based diagnostics. Our main result is that the deterministic content of the experimental signals is most pronounced at the external part of the plasma column just before the plasma radius. Since the chaoticity of the signals follows the same trend, we have concluded that the electrostatic plasma turbulence at the tokamak plasma edge can be partially explained by means of a deterministic nonlinear system. (C) 2007 Elsevier B.V. All rights reserved.

A gene signature in histologically normal surgical margins is predictive of oral carcinoma recurrence

Background: Oral Squamous Cell Carcinoma (OSCC) is a major cause of cancer death worldwide, which is mainly due to recurrence leading to treatment failure and patient death. Histological status of surgical margins is a currently available assessment for recurrence risk in OSCC; however histological status does not predict recurrence, even in patients with histologically negative margins. Therefore, molecular analysis of histologically normal resection margins and the corresponding OSCC may aid in identifying a gene signature predictive of recurrence.Methods: We used a meta-analysis of 199 samples (OSCCs and normal oral tissues) from five public microarray datasets, in addition to our microarray analysis of 96 OSCCs and histologically normal margins from 24 patients, to train a gene signature for recurrence. Validation was performed by quantitative real-time PCR using 136 samples from an independent cohort of 30 patients.Results: We identified 138 significantly over-expressed genes (> 2-fold, false discovery rate of 0.01) in OSCC. By penalized likelihood Cox regression, we identified a 4-gene signature with prognostic value for recurrence in our training set. This signature comprised the invasion-related genes MMP1, COL4A1, P4HA2, and THBS2. Overexpression of this 4-gene signature in histologically normal margins was associated with recurrence in our training cohort (p = 0.0003, logrank test) and in our independent validation cohort (p = 0.04, HR = 6.8, logrank test).Conclusion: Gene expression alterations occur in histologically normal margins in OSCC. Over-expression of the 4-gene signature in histologically normal surgical margins was validated and highly predictive of recurrence in an independent patient cohort. Our findings may be applied to develop a molecular test, which would be clinically useful to help predict which patients are at a higher risk of local recurrence.

DNA methylation patterns in bladder cancer and washing cell sediments: a perspective for tumor recurrence detection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Surgical treatment of renal cell carcinoma recurrence at the renal fossa following radical nephrectomy

CONTEXTO: A recorrência local única do carcinoma renal de células claras em seu leito renal após nefrectomia radical é um evento raro. Estima-se que essa situação ocorra em 0,8% a 3,6% do total de procedimentos. Comumente, seu diagnóstico é realizado através de tomografia computadorizada de abdômen ou ultra-som renal usados no acompanhamento desses pacientes. É polêmico qual o melhor tratamento dessa rara condição entre urologistas e oncologistas devido aos poucos relatos em literatura. RELATO DE CASO: Relatamos um caso de recidiva neoplásica única no leito renal após quatro anos e meio da nefrectomia radical por adenocarcinoma de células claras, sem evidência de metástases a distância em outros órgãos. O diagnóstico foi realizado por meio de tomografia abdominal em acompanhamento ambulatorial, observando-se massa retroperitoneal em topografia renal. A massa foi retirada por meio de uma incisão subcostal ampliada, em cirurgia sem intercorrências. O paciente evoluiu bem no pós-operatório. Após um ano e meio do procedimento, foi evidenciada uma metástase no pulmão esquerdo, e seis meses após, outra recorrência metastática na nona costela anterior à direita, mesmo com paciente totalmente assintomático. O tratamento cirúrgico agressivo em recorrência local única é um bom método para controlar essa rara doença. Tomografia computadorizada de abdômen deve ser feita em acompanhamento de carcinoma renal por longos períodos após a nefrectomia radical para o diagnóstico de recorrências tardias e o tratamento deve ser feito como o de uma metástase recorrente única.

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)