On quantifying uncertainties for the linearized BGK kinetic equation

We consider the linearized BGK equation and want to quantify uncertainties in the case of modelling errors. More specifically, we want to quantify the error produced if the pre-determined equilibrium function is chosen inaccurately. In this paper we consider perturbations in the velocity and in the temperature of the equilibrium function and consider how much the error is amplified in the solution

Updates and Debate Concerning Margin Adequacy and Management following Breast-Conserving Surgery

Objective: Breast-conserving surgery (BCS) experienced a significant surge during the last decades due to the increase of early breast cancer detection. Central to the discussion is margin adequacy which represents one of the most significant predictive factors for local relapse. This paper aims to shed light on the problem of margins in breast surgery. Mechanism: We performed a systematic narrative review of the literature by conducting a search using Medline/PubMed, Scopus, and Embase. The following keywords were considered: "breast-conserving surgery"AND "margins"/"margin". Findings in Brief: In the case of invasive breast cancer, "no ink on tumor"can be considered an adequate margin, while for ductal carcinoma in situ (DCIS), a distance of 2 mm from tumor should be obtained. Many novel tools have been developed based both on the latest radiological imaging techniques and on the tissue expression of certain markers, with the aim of precise navigation of tumor excision and intraoperative evaluation of cavity excision margins. Oncoplastic surgery can be considered oncologically safe while improving the cosmetic outcome and patients' quality of life. The appropriate use of adjuvant treatments in the context of a multidisciplinary and personalized management of breast cancer is the only means to omit a second intervention in some carefully selected cases. Conclusions: Debate still exists concerning the definition of adequate clear margin following BCS for DCIS. Further studies are required to better assess multimodal treatment approaches in this condition

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Gait Analysis of Autistic Children with Echo State Networks

Poster presented at the NIPS'06 Worshop on Echo State Networks and Liquid State Machine

Portrait of Candida albicans Adherence Regulators

Cell-substrate adherence is a fundamental property of microorganisms that enables them to exist in biofilms. Our study focuses on adherence of the fungal pathogen Candida albicans to one substrate, silicone, that is relevant to device-associated infection. We conducted a mutant screen with a quantitative flow-cell assay to identify thirty transcription factors that are required for adherence. We then combined nanoString gene expression profiling with functional analysis to elucidate relationships among these transcription factors, with two major goals: to extend our understanding of transcription factors previously known to govern adherence or biofilm formation, and to gain insight into the many transcription factors we identified that were relatively uncharacterized, particularly in the context of adherence or cell surface biogenesis. With regard to the first goal, we have discovered a role for biofilm regulator Bcr1 in adherence, and found that biofilm regulator Ace2 is a major functional target of chromatin remodeling factor Snf5. In addition, Bcr1 and Ace2 share several target genes, pointing to a new connection between them. With regard to the second goal, our findings reveal existence of a large regulatory network that connects eleven adherence regulators, the zinc-response regulator Zap1, and approximately one quarter of the predicted cell surface protein genes in this organism. This limited yet sensitive glimpse of mutant gene expression changes had thus defined one of the broadest cell surface regulatory networks in C. albicans

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

We analyze Nf=2 nucleon mass data with respect to their dependence on the pion mass down to mpi = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon sigma-term. Our lattice data below mpi = 435 MeV is well described by O(p^4) BChPT and we find sigma=37(8)(6) MeV for the sigma-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r_0=0.501(10)(11) fm.Comment: 26 pages, 11 figures, 5 tables. Version to appear in NPB with a few more details on the fit parameter

International Guillain-Barré Syndrome Outcome Study (IGOS): protocol of a prospective observational cohort study on clinical and biological predictors of disease course and outcome in Guillain-Barré syndrome

Guillain-Barré syndrome (GBS) is an acute polyradiculoneuropathy with a highly variable clinical presentation, course, and outcome. The factors that determine the clinical variation of GBS are poorly understood which complicates the care and treatment of individual patients. The protocol of the ongoing International GBS Outcome Study (IGOS), a prospective, observational, multi-centre cohort study that aims to identify the clinical and biological determinants and predictors of disease onset, subtype, course and outcome of GBS is presented here. Patients fulfilling the diagnostic criteria for GBS, regardless of age, disease severity, variant forms, or treatment, can participate if included within two weeks after onset of weakness. Information about demography, preceding infections, clinical features, diagnostic findings, treatment, course and outcome is collected. In addition, cerebrospinal fluid and serial blood samples for serum and DNA is collected at standard time points. The original aim was to include at least 1000 patients with a follow-up of 1-3 years. Data are collected via a web-based data entry system and stored anonymously. IGOS started in May 2012 and by January 2017 included more than 1400 participants from 143 active centres in 19 countries across 5 continents. The IGOS data/biobank is available for research projects conducted by expertise groups focusing on specific topics including epidemiology, diagnostic criteria, clinimetrics, electrophysiology, antecedent events, antibodies, genetics, prognostic modelling, treatment effects and long-term outcome of GBS. The IGOS will help to standardize the international collection of data and biosamples for future research of GBS. ClinicalTrials.gov Identifier: NCT01582763

Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs

The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis for the space of such polynomials, i.e. finite element hat functions, that are centered at the bin nodes rather than at the samples, as is the case for the standard kernel density estimation approach. This feature naturally provides an approximation that is scalable with respect to the sample size. On the other hand, unlike other strategies that use a finite element approach, the proposed approximation does not require the solution of a linear system. In addition, a simple rule that relates the bin size to the sample size eliminates the need for bandwidth selection procedures. The proposed density estimator has unitary integral, does not require a constraint to enforce positivity, and is consistent. The proposed approach is validated through numerical examples in which samples are drawn from known PDFs. The approach is also used to determine approximations of (unknown) PDFs associated with outputs of interest that depend on the solution of a stochastic partial differential equation

Colored Resonant Signals at the LHC: Largest Rate and Simplest Topology

We study the colored resonance production at the LHC in a most general approach. We classify the possible colored resonances based on group theory decomposition, and construct their effective interactions with light partons. The production cross section from annihilation of valence quarks or gluons may be on the order of 400 - 1000 pb at LHC energies for a mass of 1 TeV with nominal couplings, leading to the largest production rates for new physics at the TeV scale, and simplest event topology with dijet final states. We apply the new dijet data from the LHC experiments to put bounds on various possible colored resonant states. The current bounds range from 0.9 to 2.7 TeV. The formulation is readily applicable for future searches including other decay modes.Comment: 29 pages, 9 figures. References updated and additional K-factors include