Asymptotic stability in differential equations with unbounded delay

In this paper we consider a functional differential equation of the form $$x'=F(t,x,\int_0^t C(at-s) x(s)\,ds)$$ where $a$ is a constant satisfying $0<a<\infty$. Thus, the integral represents the memory of past positions of the solution $x$. We make the assumption that $\int_0^\infty |C(t)|\, dt<\infty$ so that this is a fading memory problem and we are interested in studying the effects of that memory over all those values of $a$. Very different properties of solutions emerge as we vary $a$ and we are interested in developing an approach which handles them in a unified way

Addendum to asymptotic stability in differential equations with unbounded delay

This addendum concerns the paper of the above title found in EJQTDE No. 13 (1999). Throughout that paper was the tacit assumption that the coefficient functions $h(t)$, $b(t)$, and $C(t)$ are all continuous on their respective domains. Every result, as well as the existence result stated at the end of the first section, depended on those functions being continuous. A search of the paper indicates that we failed to state this. We regret any inconvenience which this may have caused any reader

Positive kernels, fixed points, and integral equations

There is substantial literature going back to 1965 showing boundedness properties of solutions of the integro-differential equation x 0 (t) = − Z t 0 A(t − s)h(s, x(s))ds when A is a positive kernel and h is a continuous function using Z T 0 h(t, x(t)) Z t 0 A(t − s)h(s, x(s))dsdt ≥ 0. In that study there emerges the pair: Integro-differential equation and Supremum norm. In this paper we study qualitative properties of solutions of integral equations using the same inequality and obtain results on L p solutions. That is, there occurs the pair: Integral equations and L p norm. The paper also offers many examples showing how to use the L p idea effectively

Necessary and sufficient conditions for large contractions in fixed point theory

Many problems in integral and differential equations involve an equation in which there is almost a contraction mapping. Through some type of transformation we arrive at an operator of the form H(x) = x − f(x). The paper contains two main parts. First we offer several transformations which yield that operator. We then offer necessary and sufficient conditions to ensure that the operator is a large contraction. These operators yield unique fixed points. A partial answer to a question raised in [D. R. Smart, Fixed point theorems, Cambridge University Press, Cambridge, 1980] is given. The last section contains examples and applications

Reconstructing promoter activity from Lux bioluminescent reporters

The bacterial Lux system is used as a gene expression reporter. It is fast, sensitive and non-destructive, enabling high frequency measurements. Originally developed for bacterial cells, it has also been adapted for eukaryotic cells, and can be used for whole cell biosensors, or in real time with live animals without the need for euthanasia. However, correct interpretation of bioluminescent data is limited: the bioluminescence is different from gene expression because of nonlinear molecular and enzyme dynamics of the Lux system. We have developed a computational approach that, for the first time, allows users of Lux assays to infer gene transcription levels from the light output. This approach is based upon a new mathematical model for Lux activity, that includes the actions of LuxAB, LuxEC and Fre, with improved mechanisms for all reactions, as well as synthesis and turn-over of Lux proteins. The model is calibrated with new experimental data for the LuxAB and Fre reactions from Photorhabdus luminescens --- the source of modern Lux reporters --- while literature data has been used for LuxEC. Importantly, the data show clear evidence for previously unreported product inhibition for the LuxAB reaction. Model simulations show that predicted bioluminescent profiles can be very different from changes in gene expression, with transient peaks of light output, very similar to light output seen in some experimental data sets. By incorporating the calibrated model into a Bayesian inference scheme, we can reverse engineer promoter activity from the bioluminescence. We show examples where a decrease in bioluminescence would be better interpreted as a switching off of the promoter, or where an increase in bioluminescence would be better interpreted as a longer period of gene expression. This approach could benefit all users of Lux technology

Obesity Is Associated with Altered Tumor Metabolism in Metastatic Melanoma

PURPOSE: Overweight/obese (OW/OB) patients with metastatic melanoma unexpectedly have improved outcomes with immune checkpoint inhibitors (ICI) and BRAF-targeted therapies. The mechanism(s) underlying this association remain unclear, thus we assessed the integrated molecular, metabolic, and immune profile of tumors, as well as gut microbiome features, for associations with patient body mass index (BMI). EXPERIMENTAL DESIGN: Associations between BMI [normal (NL \u3c 25) or OW/OB (BMI ≥ 25)] and tumor or microbiome characteristics were examined in specimens from 782 patients with metastatic melanoma across 7 cohorts. DNA associations were evaluated in The Cancer Genome Atlas cohort. RNA sequencing from 4 cohorts (n = 357) was batch corrected and gene set enrichment analysis (GSEA) by BMI category was performed. Metabolic profiling was conducted in a subset of patients (x = 36) by LC/MS, and in flow-sorted melanoma tumor cells (x = 37) and patient-derived melanoma cell lines (x = 17) using the Seahorse XF assay. Gut microbiome features were examined in an independent cohort (n = 371). RESULTS: DNA mutations and copy number variations were not associated with BMI. GSEA demonstrated that tumors from OW/OB patients were metabolically quiescent, with downregulation of oxidative phosphorylation and multiple other metabolic pathways. Direct metabolite analysis and functional metabolic profiling confirmed decreased central carbon metabolism in OW/OB metastatic melanoma tumors and patient-derived cell lines. The overall structure, diversity, and taxonomy of the fecal microbiome did not differ by BMI. CONCLUSIONS: These findings suggest that the host metabolic phenotype influences melanoma metabolism and provide insight into the improved outcomes observed in OW/OB patients with metastatic melanoma treated with ICIs and targeted therapies

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

Adjunctive rifampicin for Staphylococcus aureus bacteraemia (ARREST): a multicentre, randomised, double-blind, placebo-controlled trial.

BACKGROUND: Staphylococcus aureus bacteraemia is a common cause of severe community-acquired and hospital-acquired infection worldwide. We tested the hypothesis that adjunctive rifampicin would reduce bacteriologically confirmed treatment failure or disease recurrence, or death, by enhancing early S aureus killing, sterilising infected foci and blood faster, and reducing risks of dissemination and metastatic infection. METHODS: In this multicentre, randomised, double-blind, placebo-controlled trial, adults (≥18 years) with S aureus bacteraemia who had received ≤96 h of active antibiotic therapy were recruited from 29 UK hospitals. Patients were randomly assigned (1:1) via a computer-generated sequential randomisation list to receive 2 weeks of adjunctive rifampicin (600 mg or 900 mg per day according to weight, oral or intravenous) versus identical placebo, together with standard antibiotic therapy. Randomisation was stratified by centre. Patients, investigators, and those caring for the patients were masked to group allocation. The primary outcome was time to bacteriologically confirmed treatment failure or disease recurrence, or death (all-cause), from randomisation to 12 weeks, adjudicated by an independent review committee masked to the treatment. Analysis was intention to treat. This trial was registered, number ISRCTN37666216, and is closed to new participants. FINDINGS: Between Dec 10, 2012, and Oct 25, 2016, 758 eligible participants were randomly assigned: 370 to rifampicin and 388 to placebo. 485 (64%) participants had community-acquired S aureus infections, and 132 (17%) had nosocomial S aureus infections. 47 (6%) had meticillin-resistant infections. 301 (40%) participants had an initial deep infection focus. Standard antibiotics were given for 29 (IQR 18-45) days; 619 (82%) participants received flucloxacillin. By week 12, 62 (17%) of participants who received rifampicin versus 71 (18%) who received placebo experienced treatment failure or disease recurrence, or died (absolute risk difference -1·4%, 95% CI -7·0 to 4·3; hazard ratio 0·96, 0·68-1·35, p=0·81). From randomisation to 12 weeks, no evidence of differences in serious (p=0·17) or grade 3-4 (p=0·36) adverse events were observed; however, 63 (17%) participants in the rifampicin group versus 39 (10%) in the placebo group had antibiotic or trial drug-modifying adverse events (p=0·004), and 24 (6%) versus six (2%) had drug interactions (p=0·0005). INTERPRETATION: Adjunctive rifampicin provided no overall benefit over standard antibiotic therapy in adults with S aureus bacteraemia. FUNDING: UK National Institute for Health Research Health Technology Assessment

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead