A Newman-Penrose Calculator for Instanton Metrics

We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman-Penrose formalism. Gravitational instantons are exact solutions of Einstein's vacuum field equations with Euclidean signature. The Newman-Penrose formalism, which supplies a toolbox for studying the exact solutions of Einstein's field equations, was adopted to the instanton case and our code translates it for the computational use.Comment: 13 pages. Matches the published version. The web page of the codes is changed as https://github.com/tbirkandan/NPInstanto

On Tractable Exponential Sums

We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}}$, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate polynomial with integer coefficients. We show that the sum can be evaluated in polynomial time in n and log N when f is a quadratic polynomial. This is true even when the factorization of N is unknown. Previously, this was known for a prime modulus N. On the other hand, for very specific families of polynomials of degree \ge 3, we show the problem is #P-hard, even for any fixed prime or prime power modulus. This leads to a complexity dichotomy theorem - a complete classification of each problem to be either computable in polynomial time or #P-hard - for a class of exponential sums. These sums arise in the classifications of graph homomorphisms and some other counting CSP type problems, and these results lead to complexity dichotomy theorems. For the polynomial-time algorithm, Gauss sums form the basic building blocks. For the hardness results, we prove group-theoretic necessary conditions for tractability. These tests imply that the problem is #P-hard for even very restricted families of simple cubic polynomials over fixed modulus N

A Mathematica Notebook for Computing the Homology of Iterated Products of Groups

Let G be a group which admits the structure of an iterated product of central extensions and semidirect products of abelian groups G i (both finite and infinite). We describe a Mathematica 4.0 notebook for computing the homology of G, in terms of some homological models for the factor groups G i and the products involved. Computational results provided by our program have allowed the simplification of some of the formulae involved in the calculation of H n (G). Consequently the efficiency of the method has been improved as well. We include some executions and examples

A genetic algorithm for cocyclic hadamard matrices

A genetic algorithm for finding cocyclic Hadamard matrices is described. Though we focus on the case of dihedral groups, the algorithm may be easily extended to cover any group. Some executions and examples are also included, with aid of Mathematica 4.0

The cohomological reduction method for computing n-dimensional cocyclic matrices

Provided that a cohomological model for $G$ is known, we describe a method for constructing a basis for $n$-cocycles over $G$, from which the whole set of $n$-dimensional $n$-cocyclic matrices over $G$ may be straightforwardly calculated. Focusing in the case $n=2$ (which is of special interest, e.g. for looking for cocyclic Hadamard matrices), this method provides a basis for 2-cocycles in such a way that representative $2$-cocycles are calculated all at once, so that there is no need to distinguish between inflation and transgression 2-cocycles (as it has traditionally been the case until now). When $n>2$, this method provides an uniform way of looking for higher dimensional $n$-cocyclic Hadamard matrices for the first time. We illustrate the method with some examples, for $n=2,3$. In particular, we give some examples of improper 3-dimensional $3$-cocyclic Hadamard matrices.Comment: 17 pages, 0 figure

Integrase Strand Transfer Inhibitor Use and Cancer Incidence in a Large Cohort Setting

Background: Limited data exist examining the association between incident cancer and cumulative integrase inhibitor (INSTI) exposure. Methods: Participants were followed from baseline (latest of local cohort enrollment or January 1, 2012) until the earliest of first cancer, final follow-up, or December 31, 2019. Negative binomial regression was used to assess associations between cancer incidence and time-updated cumulative INSTI exposure, lagged by 6 months. Results: Of 29 340 individuals, 74% were male, 24% were antiretroviral treatment (ART)-naive, and median baseline age was 44 years (interquartile range [IQR], 36-51). Overall, 13 950 (48%) individuals started an INSTI during follow-up. During 160 657 person-years of follow-up ([PYFU] median 6.2; IQR, 3.9-7.5), there were 1078 cancers (incidence rate [IR] 6.7/1000 PYFU; 95% confidence interval [CI], 6.3-7.1). The commonest cancers were non-Hodgkin lymphoma (n=113), lung cancer (112), Kaposi's sarcoma (106), and anal cancer (103). After adjusting for potential confounders, there was no association between cancer risk and INSTI exposure (≤6 months vs no exposure IR ratio: 1.15 [95% CI, 0.89-1.49], >6-12 months; 0.97 [95% CI, 0.71-1.32], >12-24 months; 0.84 [95% CI, 0.64-1.11], >24-36 months; 1.10 [95% CI, 0.82-1.47], >36 months; 0.90 [95% CI, 0.65-1.26] [P=.60]). In ART-naive participants, cancer incidence decreased with increasing INSTI exposure, mainly driven by a decreasing incidence of acquired immune deficiency syndrome cancers; however, there was no association between INSTI exposure and cancer for those ART-experienced (interaction P<.0001). Conclusions: Cancer incidence in each INSTI exposure group was similar, despite relatively wide CIs, providing reassuring early findings that increasing INSTI exposure is unlikely to be associated with an increased cancer risk, although longer follow-up is needed to confirm this finding

Contemporary antiretrovirals and body-mass index: a prospective study of the RESPOND cohort consortium

BACKGROUND: Weight gain effects of individual antiretroviral drugs are not fully understood. We investigated associations between a prespecified clinically significant increase (>7%) in body-mass index (BMI) and contemporary antiretroviral use. METHODS: The International Cohort Consortium of Infectious Diseases (RESPOND) is a prospective, multicohort collaboration, including data from 17 well established cohorts and over 29 000 people living with HIV. People with HIV under prospective follow-up from Jan 1, 2012, and older than 18 years were eligible for inclusion. Each cohort contributed a predefined minimum number of participants related to the size of the specific cohort (with a minimum of 1000 participants). Participants were required to have CD4 cell counts and HIV viral load measurement in the 12 months before or within 3 months after baseline. For all antiretroviral drugs received at or after RESPOND entry, changes from pre-antiretroviral BMI levels (baseline) were considered at each BMI measurement during antiretroviral treatment. We used logistic regression to identify individual antiretrovirals that were associated with first occurrence of a more than 7% increase in BMI from pre-antiretroviral BMI. We adjusted analyses for time on antiretrovirals, pre-antiretroviral BMI, demographics, geographical region, CD4 cell count, viral load, smoking status, and AIDS at baseline. RESULTS: 14 703 people were included in this study, of whom 7863 (53·5%) had a more than 7% increase in BMI. Compared with lamivudine, use of dolutegravir (odds ratio [OR] 1·27, 95% CI 1·17-1·38), raltegravir (1·37, 1·20-1·56), and tenofovir alafenamide (1·38, 1·22-1·35) was significantly associated with a more than 7% BMI increase, as was low pre-antiretroviral BMI (2·10, 1·91-2·31 for underweight vs healthy weight) and Black ethnicity (1·61, 1·47-1·76 vs White ethnicity). Higher CD4 count was associated with a reduced risk of BMI increase (0·97, 0·96-0·98 per 100 cells per μL increase). Relative to lamivudine, dolutegravir without tenofovir alafenamide (OR 1·21, 95% CI 1·19-1·32) and tenofovir alafenamide without dolutegravir (1·33, 1·15-1·53) remained independently associated with a more than 7% increase in BMI; the associations were higher when dolutegravir and tenofovir alafenamide were used concomitantly (1·79, 1·52-2·11, and 1·70, 1·44-2·01, respectively). INTERPRETATION: Clinicians and people with HIV should be aware of associations between weight gain and use of dolutegravir, tenofovir alafenamide, and raltegravir, particularly given the potential consequences of weight gain, such as insulin resistance, dyslipidaemia, and hypertension. FUNDING: The CHU St Pierre Brussels HIV Cohort, The Austrian HIV Cohort Study, The Australian HIV Observational Database, The AIDS Therapy Evaluation in the Netherlands national observational HIV cohort, The EuroSIDA cohort, The Frankfurt HIV Cohort Study, The Georgian National AIDS Health Information System, The Nice HIV Cohort, The ICONA Foundation, The Modena HIV Cohort, The PISCIS Cohort Study, The Swiss HIV Cohort Study, The Swedish InfCare HIV Cohort, The Royal Free HIV Cohort Study, The San Raffaele Scientific Institute, The University Hospital Bonn HIV Cohort and The University of Cologne HIV Cohorts, ViiV Healthcare, and Gilead Sciences

Similar but different: Integrated phylogenetic analysis of Austrian and Swiss HIV-1 sequences reveal differences in transmission patterns of the local HIV-1 epidemics.

OBJECTIVES Phylogenetic analyses of two or more countries allow to detect differences in transmission dynamics of local HIV-1 epidemics beyond differences in demographic characteristics. METHODS A maximum-likelihood phylogenetic tree was built using pol-sequences of the Swiss HIV Cohort Study (SHCS) and the Austrian HIV Cohort Study (AHIVCOS), with international background sequences. Three types of phylogenetic cherries (clusters of size 2) were analyzed further: 1) Domestic cherries, 2) International cherries and 3) SHCS/AHIVCOS-cherries. Transmission group and ethnicities observed within the cherries were compared to the respective distribution expected from a random distribution of patients on the phylogeny. RESULTS The demographic characteristics of the AHIVCOS (included patients: 3'141) and the SHCS (included patients: 12'902) are very similar. In the AHIVCOS, 36.5% of the patients were in domestic cherries, 8.3% in international cherries, and 7.0% in SHCS/AHIVCOS cherries. Similarly, in the SHCS, 43.0% of the patients were in domestic cherries, 8.2% in international cherries, and 1.7% in SHCS/AHIVCOS cherries. While international cherries in the SHCS were dominated by heterosexuals (HET) with MSM being underrepresented, the opposite was the case for the AHIVCOS. In both cohorts, cherries with one patient belonging to the transmission group intravenous drug user (IDU) and the other one non-IDU were underrepresented. CONCLUSION In both cohorts, international HIV transmission plays a major role in the local epidemics, mostly driven by MSM in the AHIVOS, and by HET in the SHCS, highlighting the importance of international collaborations to understand global HIV transmission links on the way to eliminate HIV