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.

Local and global consistency properties for student placement

In the context of resource allocation on the basis of priorities, Ergin (2002) identifies a necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a consistency principle. Ergin (2002) formulates consistency as a local property based on a fixed population of agents and fixed resources -- we refer to this condition as local consistency and to his condition on the priority structure as local acyclicity. We identify a related but stronger necessary and sufficient condition (unit acyclicity) on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property. Next, we provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. We identify a necessary and sufficient condition (local shift-freeness) on the priority structure such that the student-optimal stable mechanism satisfies local converse consistency. Interestingly, local acyclicity implies local shift-freeness and hence the student-optimal stable mechanism more frequently satisfies local converse consistency than local consistency. Finally, in order for the student-optimal stable mechanism to be globally conversely consistent, one again has to impose unit acyclicity on the priority structure. Hence, unit acyclicity is a necessary and sufficient condition on the priority structure for the student-optimal stable mechanism to satisfy global consistency or global converse consistency.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Consistency and optimality

Assume that the problem Qo is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T U {ConT} as the minimal extension of T proving for some algorithm that it decides Qo as fast as any algorithm B with the property that T proves that B decides Qo. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.

A logistic regression approach to estimating customer profit loss due to lapses in insurance

This article focuses on business risk management in the insurance industry. A methodology for estimating the profit loss caused by each customer in the portfolio due to policy cancellation is proposed. Using data from a European insurance company, customer behaviour over time is analyzed in order to estimate the probability of policy cancelation and the resulting potential profit loss due to cancellation. Customers may have up to two different lines of business contracts: motor insurance and other diverse insurance (such as, home contents, life or accident insurance). Implications for understanding customer cancellation behaviour as the core of business risk management are outlined.

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.

Pre-Election Positions and Voting Behaviour in Parliament: Consistency among Swiss MPs

This article examines the determinants of positional incongruence between pre-election statements and post-election behaviour in the Swiss parliament between 2003 and 2009. The question is examined at the individual MP level, which is appropriate for dispersion-of-powers systems like Switzerland. While the overall rate of political congruence reaches about 85%, a multilevel logit analysis detects the underlying factors which push or curb a candidate's propensity to change his or her mind once elected. The results show that positional changes are more likely when (1) MPs are freshmen, (2) individual voting behaviour is invisible to the public, (3) the electoral district magnitude is not small, (4) the vote is not about a party's core issue, (5) the MP belongs to a party which is located in the political centre, and (6) if the pre-election statement dissents from the majority position of the legislative party group. Of these factors, the last one is paramount.

Effects of MRI scan acceleration on brain volume measurement consistency.

PURPOSE: To evaluate the effects of recent advances in magnetic resonance imaging (MRI) radiofrequency (RF) coil and parallel imaging technology on brain volume measurement consistency. MATERIALS AND METHODS: In all, 103 whole-brain MRI volumes were acquired at a clinical 3T MRI, equipped with a 12- and 32-channel head coil, using the T1-weighted protocol as employed in the Alzheimer's Disease Neuroimaging Initiative study with parallel imaging accelerations ranging from 1 to 5. An experienced reader performed qualitative ratings of the images. For quantitative analysis, differences in composite width (CW, a measure of image similarity) and boundary shift integral (BSI, a measure of whole-brain atrophy) were calculated. RESULTS: Intra- and intersession comparisons of CW and BSI measures from scans with equal acceleration demonstrated excellent scan-rescan accuracy, even at the highest acceleration applied. Pairs-of-scans acquired with different accelerations exhibited poor scan-rescan consistency only when differences in the acceleration factor were maximized. A change in the coil hardware between compared scans was found to bias the BSI measure. CONCLUSION: The most important findings are that the accelerated acquisitions appear to be compatible with the assessment of high-quality quantitative information and that for highest scan-rescan accuracy in serial scans the acquisition protocol should be kept as consistent as possible over time. J. Magn. Reson. Imaging 2012;36:1234-1240. ©2012 Wiley Periodicals, Inc.

Melan-A-specific cytotoxic T cells are associated with tumor regression and autoimmunity following treatment with anti-CTLA-4.

PURPOSE: Ipilimumab is a monoclonal antibody that blocks the immune-inhibitory interaction between CTL antigen 4 (CTLA-4) and its ligands on T cells. Clinical trials in cancer patients with ipilimumab have shown promising antitumor activity, particularly in patients with advanced melanoma. Often, tumor regressions in these patients are correlated with immune-related side effects such as dermatitis, enterocolitis, and hypophysitis. Although these reactions are believed to be immune-mediated, the antigenic targets for the cellular or humoral immune response are not known. EXPERIMENTAL DESIGN: We enrolled patients with advanced melanoma in a phase II study with ipilimumab. One of these patients experienced a complete remission of his tumor. The specificity and functional properties of CD8-positive T cells in his peripheral blood, in regressing tumor tissue, and at the site of an immune-mediated skin rash were investigated. RESULTS: Regressing tumor tissue was infiltrated with CD8-positive T cells, a high proportion of which were specific for Melan-A. The skin rash was similarly infiltrated with Melan-A-specific CD8-positive T cells, and a dramatic (>30-fold) increase in Melan-A-specific CD8-positive T cells was apparent in peripheral blood. These cells had an effector phenotype and lysed Melan-A-expressing tumor cells. CONCLUSIONS: Our results show that Melan-A may be a major target for both the autoimmune and antitumor reactions in patients treated with anti-CTLA-4, and describe for the first time the antigen specificity of CD8-positive T cells that mediate tumor rejection in a patient undergoing treatment with an anti-CTLA-4 antibody. These findings may allow a better integration of ipilimumab into other forms of immunotherapy.

Alcohol and nonlethal injuries: a Swiss emergency department study on the risk relationship between acute alcohol consumption and type of injury.

BACKGROUND: Acute alcohol consumption has been reported to be an important risk factor for injury, but clear scientific evidence on issues such as injury type is not available. The present study aims to improve the knowledge of the importance of alcohol consumption as an injury determinant with regards to two dimensions of the type of injury, namely the nature and the body region involved. METHODS: Risk relationships between two injury type components and acute alcohol use were estimated through multinomial and logistic regression models based on data from 7,529 patients-among whom 3,682 had injury diagnoses-gathered in a Swiss emergency department. RESULTS: Depending on the type of injury, between 31.1% and 48.7% of casualties report alcohol use before emergency department attendance. The multinomial regression models show that even low alcohol levels are consistently associated with nearly all natures of injury and body regions. A persistent dose-response effect between alcohol levels and risk associations was observed for almost all injury types. CONCLUSIONS: The results highlight the importance and consistency of the risk association between low and moderate levels of acute alcohol consumption and all types of injury. None of the body regions and natures of injury could pride on absence of association between alcohol and injury. Public health, prevention, and care implications are considered.