Stability of an upwind Petrov Galerkin discretization of convection diffusion equations

We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an inf-sup condition, which are uniform in mesh-width and viscosity, up to a logarithm, as long as the viscosity is smaller than the mesh-width or the crosswind diffusion is smaller than the streamline diffusion. The analysis allows for the formation of a boundary layer.Comment: v1: 18 pages. 2 figures. v2: 22 pages. Numerous details added and completely rewritten final proof. 8 pages appendix with old proo

A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills

A simplicial gauge theory

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.Comment: 24 pages. v2: New version includes a longer introduction and a discrete Noether's theorem. v3: Section 4 on Noether's theorem has been expanded with Proposition 8, section 2 has been expanded with a paragraph on standard LGT. v4: Thorough revision with new introduction and more background materia

Charge orderings in the atomic limit of the extended Hubbard model

The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for charge orderings are obtained. The phase diagrams include three types of charge ordered phases and the nonordered phase. The system exhibits very rich structure and shows unusual multicritical behavior. In the limiting case of tij = 0, the EHM is equivalent to the pseudospin model with single-ion anisotropy 1/2U, exchange interaction W in an effective magnetic field (mu-1/2U-zW). This classical spin model is analyzed using the MC method for the canonical ensemble. The phase diagram is compared with the known results for the Blume-Capel model.Comment: 9 pages, 10 figure

Conductivity in a symmetry broken phase: Spinless fermions with 1/d1/d corrections

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.Comment: 23 pages, 19 figures included with psfig, Revtex; Physical Review B15, in press (October/November 1996) depending on the printer/screen driver, it might be necessary to comment out figures 3,4,5,10,11,12,19 and have them printed separatel

Nasjonal utdanning for skoleledere : hvorfor?

Utdanningssektoren i Norge har vært utsatt for flere reformer og endringer de siste tiår. Internasjonale undersøkelser viser at norske elever kommer dårligere ut enn andre sammenlignbare land. Norge har satt fokus på resultater i skolen og ledelsens betydning for elevenes læring. OECD-rapporten Improving School Leadership – Privacy and Practice (2006-2008) pekte på at Norge hadde få sentrale tiltak eller føringer rettet mot skoleledelse sammenlignet med andre land. Høsten 2009 opprettet Utdanningsdirektoratet på oppdrag fra Kunnskapsdepartementet en nasjonal utdanning for skoleledere. Denne satsingen er et nytt fenomen i Norge. Fokuset i vår oppgave er knyttet til hvilken begrunnelse som ligger bak denne satsingen. Den nasjonale utdanningen som tilbys vil kunne si noe om hvilke skoleledere Staten ønsker og hvordan en ser på skolen i nåtid og fremtid. Denne utdanningen vil være ett av myndighetenes verktøy for å styre norsk utdanning. For å finne hva de utdanningspolitiske myndigheter legger til grunn for en nasjonal utdanning, valgte vi en kvalitativ metode. Vi fant at en temaanalytisk tilnærming ville belyse hva som var kommunisert gjennom politiske styringsdokumenter og funn gjennom intervju av sentrale aktører knyttet opp mot skolelederutdanningen. Med utgangspunkt i denne empirien mener vi at vi har funnet noen svar på hva myndighetene vil med denne satsingen. Alle funn viser et behov for en styrking av ledelse, og at det er behov for et kraftfullt og tydelig lederskap i skolen. Skoleledelse som fagfelt må løftes fram for å kunne endre skolen til å bli en lærende organisasjon for å heve skolens kvalitet og elevenes læringsutbytte. Men hvordan dette bør gjøres, og hvem som har ansvaret for det, er det ikke noen tydelig enighet om mellom de politiske og faglige aktørene. Det er heller ikke uttrykt enighet om hva som bør vektlegges av innhold i utdanningen, og om man kan utdannes til å bli en bedre skoleleder. Bør det heller satses på å utvikle framfor å utdanne? Det vi imidlertid ser er at det uttrykkes et behov for en nasjonal styring der politikerne i større grad involverer seg mer direkte i skolen. Det desentraliserte styringssystemet som følge av Kunnskapsløftet ser ut til å svekkes noe i forhold til en sterkere sentralisering

Impairment of Sexual Life in 3,485 Dermatological Outpatients From a Multicentre Study in 13 European Countries

Skin conditions may have a strong impact on patients' sexual life, and thus influence personal relationships. Sexual issues are difficult to discuss directly in clinical practice, and a mediated instrument may be useful to capture such information. In this study item 9 of the Dermatology Life Quality Index was used to collect information on sexual impact of several skin conditions in 13 European countries. Among 3,485 patients, 23.1% reported sexual problems. The impairment was particularly high in patients with hidradenitis suppurativa, prurigo, blistering disorders, psoriasis, urticaria, eczema, infections of the skin, or pruritus. Sexual impact was strongly associated with depression, anxiety, and suicidal ideation. It was generally more frequent in younger patients and was positively correlated with clinical severity and itch. It is important to address the issue of sexual well-being in the evaluation of patients with skin conditions, since it is often linked to anxiety, depression, and even suicidal ideation.Peer reviewedFinal Published versio

Computational study of stratified two phase oil/water flow in horizontal pipes

Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.Stratified oil/water two-phase flow in a horizontal tube is numerically simulated using commercial CFD package FLUENT 6.3. The simulations are based on Volume of Fluid (VOF) model. It solves a single momentum equation shared by the fluids, and the volume fraction of each of the fluid in each computational cell is tracked throughout the domain. The RNG k- model together with standard wall treatment as the nearwall modelling method is used for turbulence modelling. The effects of surface tension along the interface between two fluids are calculated using Continuum Surface Force (CSF) model. The simulation is performed in a time-dependent way so that the numerical stabilization could be achieved. The final solution which corresponds to steady-state flow is analyzed. Results of pressure drop, slip ratio, interface height and the axial velocity profiles are verified by experimental data. The predictions of pressure drop, slip ratio and interface height are observed to compare favourably with experimental measurements, and estimated flow quantities such as axial velocity profiles are also satisfactory.vk201

A Unified Analytic Framework for Prioritization of Non-Coding Variants of Uncertain Significance in Heritable Breast and Ovarian Cancer

Background Sequencing of both healthy and disease singletons yields many novel and low frequency variants of uncertain significance (VUS). Complete gene and genome sequencing by next generation sequencing (NGS) significantly increases the number of VUS detected. While prior studies have emphasized protein coding variants, non-coding sequence variants have also been proven to significantly contribute to high penetrance disorders, such as hereditary breast and ovarian cancer (HBOC). We present a strategy for analyzing different functional classes of non-coding variants based on information theory (IT) and prioritizing patients with large intragenic deletions. Methods We captured and enriched for coding and non-coding variants in genes known to harbor mutations that increase HBOC risk. Custom oligonucleotide baits spanning the complete coding, non-coding, and intergenic regions 10 kb up- and downstream of ATM, BRCA1, BRCA2, CDH1, CHEK2, PALB2, and TP53 were synthesized for solution hybridization enrichment. Unique and divergent repetitive sequences were sequenced in 102 high-risk, anonymized patients without identified mutations in BRCA1/2. Aside from protein coding and copy number changes, IT-based sequence analysis was used to identify and prioritize pathogenic non-coding variants that occurred within sequence elements predicted to be recognized by proteins or protein complexes involved in mRNA splicing, transcription, and untranslated region (UTR) binding and structure. This approach was supplemented by in silico and laboratory analysis of UTR structure. Results 15,311 unique variants were identified, of which 245 occurred in coding regions. With the unified IT-framework, 132 variants were identified and 87 functionally significant VUS were further prioritized. An intragenic 32.1 kb interval in BRCA2 that was likely hemizygous was detected in one patient. We also identified 4 stop-gain variants and 3 reading-frame altering exonic insertions/deletions (indels). Conclusions We have presented a strategy for complete gene sequence analysis followed by a unified framework for interpreting non-coding variants that may affect gene expression. This approach distills large numbers of variants detected by NGS to a limited set of variants prioritized as potential deleterious changes