Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data

Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\Box u + u = P (u,$\partial$\_t u,$\partial$\_x u;$\partial$\_t$\partial$\_x u,$\partial$^2\_x u)$ , where P is a homogeneous polynomial of degree three, and with smooth Cauchy data of size $\epsilon \rightarrow 0$. It is known that, under a suitable condition on the nonlinearity, the solution is global-in-time for compactly supported Cauchy data. We prove in this paper that the result holds even when data are not compactly supported but just decaying as $\langle x \rangle^ {--1}$ at infinity, combining the method of Klainerman vector fields with a semiclassical normal forms method introduced by Delort. Moreover, we get a one term asymptotic expansion for u when $t \rightarrow +\infty$

Joint Bayesian variable and graph selection for regression models with network-structured predictors

In this work, we develop a Bayesian approach to perform selection of predictors that are linked within a network. We achieve this by combining a sparse regression model relating the predictors to a response variable with a graphical model describing conditional dependencies among the predictors. The proposed method is well-suited for genomic applications because it allows the identification of pathways of functionally related genes or proteins that impact an outcome of interest. In contrast to previous approaches for network-guided variable selection, we infer the network among predictors using a Gaussian graphical model and do not assume that network information is availableﾠa priori. We demonstrate that our method outperforms existing methods in identifying network-structured predictors in simulation settings and illustrate our proposed model with an application to inference of proteins relevant to glioblastoma survival.

The global stability of the Kaluza-Klein spacetime

In this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in \m R^{1+4} with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein-Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein-Gordon equations with different masses. The techniques we use are based purely in physical space using the vectorfield method.Comment: 80 page

Effects of semi-domesticated reindeer’s maternal condition on calf survival

Semi-domesticated reindeer (Rangifer tarandus) husbandry in Sweden depends largely on sustainable management and productivity of the herd. Herd productivity is determined by the survival of the herd’s offspring from each year, which is affected by factors such as weather conditions, forage abundancy and predation. Predation of the reindeer calves by brown bears (Ursus arctos) can become a significant limiting factor of the herd’s productivity. Previous studies suggest the reindeer maternal condition to have an effect on calf survival. Data from pregnant reindeer was collected through the years 2010 to 2016 in two Swedish reindeer herding communities with high predation rates (Gällivare and Udtja) as part of a project investigating reindeer calf mortality due to brown bear predation. Among other factors recorded, females were weighed prior to calving and the presence of their calves on the summer and autumn gatherings was recorded individually. Data on reindeer weight at precalving was analysed in relation to calf survival. Ordinal regression was used to describe the effect of weight by year and herding community over the probability of calf mortality. Results showed a positive effect of female reindeer’s weight at late pregnancy on the odds of survival of the calf until the autumn. The magnitude of the effect of weight was lower than the fixed effect of herding community. Differences in brown bear presence and year-to-year variations can be highly influential on calf survival. The year 2011 was predicted to have the lowest odds of survival, while the reindeer calves in Gällivare community had an overall higher survival rate than the reindeer calves in Udtja

Personalized Treatment Selection via Product Partition Models with Covariates

Precision medicine is an approach for disease treatment that defines treatment strategies based on the individual characteristics of the patients. Motivated by an open problem in cancer genomics, we develop a novel model that flexibly clusters patients with similar predictive characteristics and similar treatment responses; this approach identifies, via predictive inference, which one among a set of treatments is better suited for a new patient. The proposed method is fully model-based, avoiding uncertainty underestimation attained when treatment assignment is performed by adopting heuristic clustering procedures, and belongs to the class of product partition models with covariates, here extended to include the cohesion induced by the Normalized Generalized Gamma process. The method performs particularly well in scenarios characterized by considerable heterogeneity of the predictive covariates in simulation studies. A cancer genomics case study illustrates the potential benefits in terms of treatment response yielded by the proposed approach. Finally, being model-based, the approach allows estimating clusters' specific response probabilities and then identifying patients more likely to benefit from personalized treatment.Comment: 31 pages, 7 figure

Bayesian predictive modeling for genomic based personalized treatment selection

Efforts to personalize medicine in oncology have been limited by reductive characterizations of the intrinsically complex underlying biological phenomena. Future advances in personalized medicine will rely on molecular signatures that derive from synthesis of multifarious interdependent molecular quantities requiring robust quantitative methods. However, highly-parameterized statistical models when applied in these settings often require a prohibitively large database and are sensitive to proper characterizations of the treatment-by-covariate interactions, which in practice are difficult to specify and may be limited by generalized linear models. In this paper, we present a Bayesian predictive framework that enables the integration of a high-dimensional set of genomic features with clinical responses and treatment histories of historical patients, providing a probabilistic basis for using the clinical and molecular information to personalize therapy for future patients. Our work represents one of the first attempts to define personalized treatment assignment rules based on large-scale genomic data. We use actual gene expression data acquired from The Cancer Genome Atlas in the settings of leukemia and glioma to explore the statistical properties of our proposed Bayesian approach for personalizing treatment selection. The method is shown to yield considerable improvements in predictive accuracy when compared to penalized regression approaches

Calibration strategies for use of the nanoDot OSLD in CT applications.

Aluminum oxide based optically stimulated luminescent dosimeters (OSLD) have been recognized as a useful dosimeter for measuring CT dose, particularly for patient dose measurements. Despite the increasing use of this dosimeter, appropriate dosimeter calibration techniques have not been established in the literature; while the manufacturer offers a calibration procedure, it is known to have relatively large uncertainties. The purpose of this work was to evaluate two clinical approaches for calibrating these dosimeters for CT applications, and to determine the uncertainty associated with measurements using these techniques. Three unique calibration procedures were used to calculate dose for a range of CT conditions using a commercially available OSLD and reader. The three calibration procedures included calibration (a) using the vendor-provided method, (b) relative to a 120 kVp CT spectrum in air, and (c) relative to a megavoltage beam (implemented with 60 Co). The dose measured using each of these approaches was compared to dose measured using a calibrated farmer-type ion chamber. Finally, the uncertainty in the dose measured using each approach was determined. For the CT and megavoltage calibration methods, the dose measured using the OSLD nanoDot was within 5% of the dose measured using an ion chamber for a wide range of different CT scan parameters (80-140 kVp, and with measurements at a range of positions). When calibrated using the vendor-recommended protocol, the OSLD measured doses were on average 15.5% lower than ion chamber doses. Two clinical calibration techniques have been evaluated and are presented in this work as alternatives to the vendor-provided calibration approach. These techniques provide high precision for OSLD-based measurements in a CT environment