Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Photodynamic Diagnosis of Non-muscle-invasive Bladder Cancer with Hexaminolevulinate Cystoscopy: A Meta-analysis of Detection and Recurrence Based on Raw Data.

BACKGROUND: Studies on hexaminolevulinate (HAL) cystoscopy report improved detection of bladder tumours. However, recent meta-analyses report conflicting effects on recurrence. OBJECTIVE: To assess available clinical data for blue light (BL) HAL cystoscopy on the detection of Ta/T1 and carcinoma in situ (CIS) tumours, and on tumour recurrence. DESIGN, SETTING, AND PARTICIPANTS: This meta-analysis reviewed raw data from prospective studies on 1345 patients with known or suspected non-muscle-invasive bladder cancer (NMIBC). INTERVENTION: A single application of HAL cystoscopy was used as an adjunct to white light (WL) cystoscopy. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: We studied the detection of NMIBC (intention to treat [ITT]: n=831; six studies) and recurrence (per protocol: n=634; three studies) up to 1 yr. DerSimonian and Laird's random-effects model was used to obtain pooled relative risks (RRs) and associated 95% confidence intervals (CIs) for outcomes for detection. RESULTS AND LIMITATIONS: BL cystoscopy detected significantly more Ta tumours (14.7%; p<0.001; odds ratio [OR]: 4.898; 95% CI, 1.937-12.390) and CIS lesions (40.8%; p<0.001; OR: 12.372; 95% CI, 6.343-24.133) than WL. There were 24.9% patients with at least one additional Ta/T1 tumour seen with BL (p<0.001), significant also in patients with primary (20.7%; p<0.001) and recurrent cancer (27.7%; p<0.001), and in patients at high risk (27.0%; p<0.001) and intermediate risk (35.7%; p=0.004). In 26.7% of patients, CIS was detected only by BL (p<0.001) and was also significant in patients with primary (28.0%; p<0.001) and recurrent cancer (25.0%; p<0.001). Recurrence rates up to 12 mo were significantly lower overall with BL, 34.5% versus 45.4% (p=0.006; RR: 0.761 [0.627-0.924]), and lower in patients with T1 or CIS (p=0.052; RR: 0.696 [0.482-1.003]), Ta (p=0.040; RR: 0.804 [0.653-0.991]), and in high-risk (p=0.050) and low-risk (p=0.029) subgroups. Some subgroups had too few patients to allow statistically meaningful analysis. Heterogeneity was minimised by the statistical analysis method used. CONCLUSIONS: This meta-analysis confirms that HAL BL cystoscopy significantly improves the detection of bladder tumours leading to a reduction of recurrence at 9-12 mo. The benefit is independent of the level of risk and is evident in patients with Ta, T1, CIS, primary, and recurrent cancer.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Human papilloma virus type and recurrence rate after surgical clearance of anal condylomata acuminata

Résumé : Le condylome acuminé anal (CAA), transmis par contact sexuel, résulte d'une infection par Human Papilloma Virus (HPV). Son traitement chirurgical est grevé d'un taux de récidive de 4-29%. Le but de cette étude était d'identifier une éventuelle corrélation entre type d'HPV présent dans les CAA excisés chirurgicalement et taux de récidive de la maladie, Cette étude rétrospective porte sur 140 patients opérés au Centre Hospitalier Universitaire Vaudois de CAA, entre 1990 et 2005. Le diagnostic lésionnel a été confirmé par un examen histomorphologique. Le(s) type(s) d'HPV présent(s) dans ces lésions a été déterminé par Polymerase Chain Reaction (PCR). Les patients ont donné leur accord à cette analyse et complété un questionnaire. Une éventuelle corrélation entre récidive de CAA, type d'HPV et status HIV a été recherchée. HPV 6 et 11 sont les virus les plus fréquemment découverts (51% et 28%, respectivement) chez les 140 patients (123H/17F). Trente-cinq (25%) d'entre eux ont présenté une récidive. HPV 11 était present chez 19 (41%) sujets. Ceci est statistiquement significatif (P<0.05), en comparaison aux autres HPVs. Il n'y a par contre pas de différence significative entre la fréquence de récidive des 33 (24%) patients HIV-positifs et le reste du collectif. HPV 11 est donc associé à un taux de récidive de CAA significativement élevé. Un suivi strict des patients atteints est nécessaire pour identifier une récidive et la traiter sans délai, notamment lorsque HPV 11 est present. Ces résultats innovateurs soulèvent la question de la nécessité de pratiquer une typisation virale systématique sur les lésions excisées. La justification d'une telle attitude demande toutefois encore d'être confirmée.

Residual venous obstruction, alone and in combination with D-dimer, as a risk factor for recurrence after anticoagulation withdrawal following a first idiopathic deep vein thrombosis in the prolong study.

OBJECTIVE: This study aims to assess the predictive value of residual venous obstruction (RVO) for recurrent venous thrombo-embolism (VTE) in a study using D-dimer to predict outcome. DESIGN: This is a multicentre randomised open-label study. METHODS: Patients with a first episode of idiopathic VTE were enrolled on the day of anticoagulation discontinuation when RVO was determined by compression ultrasonography in those with proximal deep vein thrombosis (DVT) of the lower limbs. D-dimer was measured after 1 month. Patients with normal D-dimer did not resume anticoagulation while patients with abnormal D-dimer were randomised to resume anticoagulation or not. The primary outcome measure was recurrent VTE over an 18-month follow-up. RESULTS: A total of 490 DVT patients were analysed (after excluding 19 for different reasons and 118 for isolated pulmonary embolism (PE)). Recurrent DVT occurred in 19% (19/99) of patients with abnormal D-dimer who did not resume anticoagulation and 10% (31/310) in subjects with normal D-dimer (adjusted hazard ratio: 2.1; p = 0.02). Recurrences were similar in subjects either with (11%, 17/151) or without RVO (13%, 32/246). Recurrent DVT rates were also similar for normal D-dimer, with or without RVO, and for abnormal D-dimer, with or without RVO. CONCLUSIONS: Elevated D-dimer at 1 month after anticoagulation withdrawal is a risk factor for recurrence, while RVO at the time of anticoagulation withdrawal is not.

Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

Theta-duality on Prym varieties and a Torelli Theorem

Let $\pi : \widetilde C \to C$ be an unramified double covering of irreducible smooth curves and let $P$ be the attached Prym variety. We prove the scheme-theoretic theta-dual equalities in the Prym variety $T(\widetilde C)=V^2$ and $T(V^2)=\widetilde C$, where $V^2$ is the Brill-Noether locus of $P$ associated to $\pi$ considered by Welters. As an application we prove a Torelli theorem analogous to the fact that the symmetric product $D^{(g)}$ of a curve $D$ of genus $g$ determines the curve.

Risk Prediction Scores for Recurrence and Progression of Non-Muscle Invasive Bladder Cancer: An International Validation in Primary Tumours

Abstract Objective: We aimed to determine the validity of two risk scores for patients with non-muscle invasive bladder cancer in different European settings, in patients with primary tumours. Methods: We included 1,892 patients with primary stage Ta or T1 non-muscle invasive bladder cancer who underwent a transurethral resection in Spain (n = 973), the Netherlands (n = 639), or Denmark (n = 280). We evaluated recurrence-free survival and progression-free survival according to the European Organisation for Research and Treatment of Cancer (EORTC) and the Spanish Urological Club for Oncological Treatment (CUETO) risk scores for each patient and used the concordance index (c-index) to indicate discriminative ability. Results: The 3 cohorts were comparable according to age and sex, but patients from Denmark had a larger proportion of patients with the high stage and grade at diagnosis (p,0.01). At least one recurrence occurred in 839 (44%) patients and 258 (14%) patients had a progression during a median follow-up of 74 months. Patients from Denmark had the highest 10- year recurrence and progression rates (75% and 24%, respectively), whereas patients from Spain had the lowest rates (34% and 10%, respectively). The EORTC and CUETO risk scores both predicted progression better than recurrence with c-indices ranging from 0.72 to 0.82 while for recurrence, those ranged from 0.55 to 0.61. Conclusion: The EORTC and CUETO risk scores can reasonably predict progression, while prediction of recurrence is more difficult. New prognostic markers are needed to better predict recurrence of tumours in primary non-muscle invasive bladder cancer patients.