Programming of Finite Element Methods in MATLAB

We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. We pay special attention to an efficient programming style using sparse matrices in MATLAB

A prescription for projectors to compute helicity amplitudes in D dimensions

This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.Comment: Matched to the version to be published in Eur. Phys. J.

Obsessive-compulsive disorder : novel insights on executive functions, gut microbiome, and genetics

Background: Obsessive-compulsive disorder (OCD) is characterized by intrusive thoughts and images, and repetitive, time-consuming compulsions. It causes disability and impaired quality of life. The neurobiological model of OCD revolves around dysfunctional brain circuits, referred to as the cortico-striato-thalamocortical (CSTC) loop. Aim: This thesis sought to elucidate neurobiological factors associated with OCD. Methods: In study I, we compared executive functions of patients with OCD (n=29), body dysmorphic disorder (BDD) (n=27), and healthy controls (n=28), using computerized and standardized neuropsychological tasks (CANTAB) for response inhibition (stop-signal task, SST), cognitive flexibility (intra-extra dimensional shift task, IED), and working memory (spatial working memory task, SWM). Correlation between task performance and symptom severity was assessed using linear regression models and effect sizes were measured with Pearson’s r. In study II, we systematically reviewed gut microbiota studies of participants with psychiatric disorders, published up to February 2020, following the PRISMA guidelines and the pre-registered study-protocol at PROSPERO. In study III, we compared gut microbiome of patients with OCD (n=32) with healthy controls (n=32) using whole genome sequencing of stool samples. Moreover, we followed a subset of participants longitudinally to compare changes in gut microbiome within patients with OCD before and after exposure- and response prevention (ERP) therapy (n=15). In study IV, we used whole exome sequencing to explore presence of gene-disruptive rare variants (GDRVs) in patients with severe and treatment-resistant OCD (n=5) who have received deep brain stimulation (DBS). Results: In study I we found no significant differences in test performance between individuals with OCD, BDD, and healthy controls. In study II, 69 studies were included in the systematic review. The majority of studies did not report any significant differences in gut microbiota -diversity indices (44%), but different composition measured by -diversity indices (67%) between patients with psychiatric disorders and healthy controls. However, the results were inconsistent regarding which genera are differentially abundant, except for some studies that reporter lower abundance of butyrate-producing microbes Faecalibacterium prausnitzii and Roseburia species. In study III we found no significant differences in -diversity, -diversity, or taxonomic dissimilarity at the species-level between patients with OCD and healthy controls, or within patients with OCD before and after ERP. Furthermore, functional analysis, based on gut-brain modules that are relevant for metabolizing neuroactive compounds, did not reveal any significant differences between patients with OCD and healthy controls, or within patients with OCD before and after ERP. In study IV, we found three GDRVs, one of which was a missense variant in the ion transporter domain of KCNB1 (hg19 20-47991077-C-T). The patient with that missense variant was a responder to DBS treatment. Conclusions: Study I. Performance on neuropsychological tests suggest that patients with OCD have comparable executive functions with a related group of patients and healthy controls. Study II and III. Despite the suggested importance of the microbiome-gut-brain axis in psychiatric disorders, evidence for altered gut microbiome in psychiatric disorders including OCD is inconclusive. Improved and consistent study design and methodology are crucial for future studies in this research field. Study IV. Patients with severe and treatment-resistant OCD is a cohort fit for whole exome sequencing studies. Despite the small sample size, we found three GDRVs. More samples are required to evaluate if the frequency of GDRVs is higher in this cohort and if GDRVs could predict treatment outcome from DBS. Patients with OCD represent a heterogeneous group, and individual biological factors cannot explain the pathophysiological underpinning of this disorder. Nevertheless, next-generation sequencing opens new opportunities to study complex psychiatric conditions. Genomic analysis of severe and treatment-resistant patients with OCD could increase our understanding of this complex disorder

Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence

In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering of Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=12J$ and temperatures $T_L=\frac{(r_++r_-)-Q^2/M}{4\pi a}, T_R=\frac{r_+-r_-}{4\pi a}$. Using the Minkowski prescription, we compute the real-time correlators of charged scalar and find perfect match with CFT prediction. We further discuss the low-frequency scattering of photons and gravitons by Kerr black hole and find that their retarded Green's functions are in good agreement with CFT prediction. Our study supports the idea that the hidden conformal symmetry in the solution space is essential to Kerr/CFT correspondence.Comment: 15 pages, Latex; typos corrected, references updated; minor correction, published versio