Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Ribonucleotide reductase genes of Bacillus prophages: a refuge to introns and intein coding sequences.

The ribonucleotide reductase gene tandem bnrdE/bnrdF in SPbeta-related prophages of different Bacillus spp. isolates presents different configurations of intervening sequences, comprising one to three of six non-homologous splicing elements. Insertion sites of group I introns and intein DNA are clustered in three relatively short segments encoding functionally important domains of the ribonucleotide reductase. Comparison of the bnrdE homologs reveals mutual exclusion of a group I intron and an intein coding sequence flanking the codon that specifies a conserved cysteine. In vivo splicing was demonstrated for all introns. However, for two of them a part of the mRNA precursor molecules remains unspliced. Intergenic bnrdE-bnrdF regions are unexpectedly long, comprising between 238 and 541 nt. The longest encodes a putative polypeptide related to HNH homing endonucleases.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Mitotic figure counts are significantly overestimated in resection specimens of invasive breast carcinomas.

Several authors have demonstrated an increased number of mitotic figures in breast cancer resection specimen when compared with biopsy material. This has been ascribed to a sampling artifact where biopsies are (i) either too small to allow formal mitotic figure counting or (ii) not necessarily taken form the proliferating tumor periphery. Herein, we propose a different explanation for this phenomenon. Biopsy and resection material of 52 invasive ductal carcinomas was studied. We counted mitotic figures in 10 representative high power fields and quantified MIB-1 immunohistochemistry by visual estimation, counting and image analysis. We found that mitotic figures were elevated by more than three-fold on average in resection specimen over biopsy material from the same tumors (20±6 vs 6±2 mitoses per 10 high power fields, P=0.008), and that this resulted in a relative diminution of post-metaphase figures (anaphase/telophase), which made up 7% of all mitotic figures in biopsies but only 3% in resection specimen (P<0.005). At the same time, the percentages of MIB-1 immunostained tumor cells among total tumor cells were comparable in biopsy and resection material, irrespective of the mode of MIB-1 quantification. Finally, we found no association between the size of the biopsy material and the relative increase of mitotic figures in resection specimen. We propose that the increase in mitotic figures in resection specimen and the significant shift towards metaphase figures is not due to a sampling artifact, but reflects ongoing cell cycle activity in the resected tumor tissue due to fixation delay. The dwindling energy supply will eventually arrest tumor cells in metaphase, where they are readily identified by the diagnostic pathologist. Taken together, we suggest that the rapidly fixed biopsy material better represents true tumor biology and should be privileged as predictive marker of putative response to cytotoxic chemotherapy.

La régression tumorale n'est pas un facteur de risque d'atteinte du ganglion sentinelle dans les mélanomes fins (indice de Breslow < or = 1 mm) [Tumour regression is not predictive for higher risk of sentinel node involvement in thin melanomas (Breslow thickness < or = 1 mm)]

Background: Thin melanomas (Breslow thickness <= 1 mm) are considered highly curable. The aim of this study was to evaluate the correlation between histological tumour regression and sentinel lymph node (SLN) involvement in thin melanomas. Patients and methods: This was a retrospective single-centre study of 34 patients with thin melanomas undergoing SLN biopsy between April 1998 and January 2005. Results: The study included 14 women and 20 men of mean age 56.3 years. Melanomas were located on the neck (n = 3), soles (n = 4), trunk (n = 13) and extremities (n = 14). Pathological examination showed 25 SSM, four acral lentiginous melanomas, three in situ melanomas, one nodular melanoma and one unclassified melanoma with a mean Breslow thickness of 0.57 mm. Histological tumour regression was observed in 26 over 34 cases and ulceration was found in one case. Clark levels were as follows: I (n = 3), II (n = 20), III (n = 9), IV (n = 2). Growth phase was available in 15 cases (seven radial and eight vertical). Mitotic rates, available in 24 cases, were: 0 (n = 9), 1 (n = 11), 2 (n = 2), 3 (n = 1), 6 (n = 1). One patient with histological tumour regression (2.9% of cases and 3.8% of cases with regressing tumours) had a metastatic SLN. One patient negative for SLN had a lung relapse and died of the disease. Mean follow-up was 26.2 months. Conclusion: The results of the present study and the analysis of the literature show that histological regression of the primary tumour does not seem predictive of higher risk of SLN involvement in thin melanomas. This suggests that screening for SLN is not indicated in thin melanomas, even those with histological regression.

Predictive value of the acid fast smear for detection of Mycobacterium tuberculosis in respiratory specimens in a Reference Center of HIV/Aids in Rio de Janeiro, Brazil

In order to evaluate the predictive value of acid fast bacilii (AFB) smear for the diagnosis of Mycobacterium tuberculosis in respiratory specimens in a setting with a high prevalence of Aids and an unknown prevalence of nontuberculous mycobacteria (NTM), we retrospectively examined specimens cultured for mycobacteria between 1 September 1993 and 30 September 1994 and medical records of patients with positive culture in a General Hospital, Aids reference in Rio de Janeiro, Brazil. Seventy three per cent (1517/2077) of samples were respiratory specimens and mycobacteria were recovered from 20.6% (313/1517) of these. M. tuberculosis was identified in 94.2% (295/313) and NTM in 5.8% (18/313). The yield of positive AFB smear and of positive culture was 6.1% (93/1517) and 20.6% (313/1517), respectively. The positive predictive value (PPV) of AFB for M. tuberculosis was 98.4% in expectorated sputum and 96.4% in bronchoalveolar lavage. Forty four percent (130/295) of specimens with positive culture for M. tuberculosis and 66.7% (12/18) for NTM were from patients HIV positive. The conclusion was that in our study population, the PPV of AFB for M. tuberculosis in respiratory specimens was high and the prevalence of NTM was low despite the high prevalence of HIV positive.

The Body Action and Posture Coding System (BAP): Development and Reliability

Several methods are available for coding body movement in nonverbal behavior research, but there is no consensus on a reliable coding system that can be used for the study of emotion expression. Adopting an integrative approach, we developed a new method, the Body Action and Posture (BAP) coding system, for the time-aligned micro description of body movement on an anatomical level (different articulations of body parts), a form level (direction and orientation of movement), and a functional level (communicative and self-regulatory functions). We applied the system to a new corpus of acted emotion portrayals, examined its comprehensiveness and demonstrated intercoder reliability at three levels: a) occurrence, b) temporal precision and c) segmentation. We discuss issues for further validation and propose some research applications.

Predictive models of syncope causes in an outpatient clinic

The investigation of unexplained syncope remains a challenging clinical problem. In the present study we sought to evaluate the diagnostic value of a standardized work-up focusing on non invasive tests in patients with unexplained syncope referred to a syncope clinic, and whether certain combinations of clinical parameters are characteristic of rhythmic and reflex causes of syncope. METHODS AND RESULTS: 317 consecutive patients underwent a standardized work-up including a 12-lead ECG, physical examination, detailed history with screening for syncope-related symptoms using a structured questionnaire followed by carotid sinus massage (CSM), and head-up tilt test. Invasive testings including an electrophysiological study and implantation of a loop recorder were only performed in those with structural heart disease or traumatic syncope. Our work-up identified an etiology in 81% of the patients. Importantly, three quarters of the causes were established non invasively combining head-up tilt test, CSM and hyperventilation testing. Invasive tests yielded an additional 7% of diagnoses. Logistic analysis identified age and number of significant prodromes as the only predictive factors of rhythmic syncope. The same two factors, in addition to the duration of the ECG P-wave, were also predictive of vasovagal and psychogenic syncope. These factors, optimally combined in predictive models, showed a high negative and a modest positive predictive value. CONCLUSION: A standardized work-up focusing on non invasive tests allows to establish more than three quarters of syncope causes. Predictive models based on simple clinical parameters may help to distinguish between rhythmic and other causes of syncope

Persistence of a Gastrocutaneous Fistula after gastrostomy removal in children: Incidence and predictive factors

Background/Purpose: The aims of this study were to determine the incidence of persistent gastrocutaneous fistulas (GCF) after gastrostomy removal and to identify associated risk factors. Methods: This retrospective study included 75 children from the Centre Hospitalier Universitaire Vaudois, Lausanne, Switzerland who had a gastrostomy performed between 1988 and 2010. The records of the children were reviewed for sex, age at the time of gastrostomy removal, underlying disease, type of gastrostomy placement and length of use, and then analyzed in order to find a correlation between the GCF and these parameters. Results: The gastrostomy orifice did not close spontaneously within the first month in 33 of the patients (44%), and 15 subsequently underwent surgical closure. The mean duration of gastrostomy use was significantly longer in children who developed a persistent GCF (30 vs. 19 months, P = 0.03). The other parameters studied did not show any significant association with the persistence of a GCF. Conclusions: The only predictive factor determining the persistence of a GCF was found to be the timespan between the placement and removal of the gastrostomy appliance. Elective surgical closure of the gastrostomy orifice should be considered after 1 month of persistent GCF.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.