Numerical Analysis of Target Enumeration via Euler Characteristic Integrals: 2 Dimensional Disk Supports

In this paper, we look at the types of errors that are introduced when using the Euler characteristic integral approach to count the number of targets in a discrete sensor field. In contrast to other theoretical analyses, this paper examines discrete sensor fields rather than continuous ones. The probabilities of first and second order errors are worked out combinatorially, and a general formula is found which is discovered to be proportional to much higher order errors. Asymptotic results are also derived. Thus, this work gives us the bias of the Euler characteristic integral as a point estimator for the number of targets in a sensor field, and a general understanding of how the Euler characteristic integral fails, or more often succeeds.Comment: 20 pages, 12 figures, 2 table

Sharp a-contraction estimates for small extremal shocks

In this paper, we study the $a$-contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected to large perturbations. We show that the weight coefficient $a$ can be chosen with amplitude proportional to the size of the shock. The main result of this paper is a key building block in the companion paper, [{arXiv:2010.04761}, 2020], in which uniqueness and BV-weak stability results for $2\times 2$ systems of hyperbolic conservation laws are proved.Comment: 41 pages, 2 figures, minor correction to lemma 4.2 and corresponding changes to section

Uniqueness and weak-BV stability for 2×22\times 2 conservation laws

Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small $BV$ functions which are global solutions of this equation. For any small $BV$ initial data, such global solutions are known to exist. Moreover, they are known to be unique among $BV$ solutions verifying either the so-called Tame Oscillation Condition, or the Bounded Variation Condition on space-like curves. In this paper, we show that these solutions are stable in a larger class of weak (and possibly not even $BV$) solutions of the system. This result extends the classical weak-strong uniqueness results which allow comparison to a smooth solution. Indeed our result extends these results to a weak-$BV$ uniqueness result, where only one of the solutions is supposed to be small $BV$, and the other solution can come from a large class. As a consequence of our result, the Tame Oscillation Condition, and the Bounded Variation Condition on space-like curves are not necessary for the uniqueness of solutions in the $BV$ theory, in the case of systems with 2 unknowns. The method is $L^2$ based. It builds up from the theory of a-contraction with shifts, where suitable weight functions $a$ are generated via the front tracking method.Comment: 25 pages, 1 figur

Urinary MicroRNA Profiling in the Nephropathy of Type 1 Diabetes

Background: Patients with Type 1 Diabetes (T1D) are particularly vulnerable to development of Diabetic nephropathy (DN) leading to End Stage Renal Disease. Hence a better understanding of the factors affecting kidney disease progression in T1D is urgently needed. In recent years microRNAs have emerged as important post-transcriptional regulators of gene expression in many different health conditions. We hypothesized that urinary microRNA profile of patients will differ in the different stages of diabetic renal disease. Methods and Findings: We studied urine microRNA profiles with qPCR in 40 T1D with >20 year follow up 10 who never developed renal disease (N) matched against 10 patients who went on to develop overt nephropathy (DN), 10 patients with intermittent microalbuminuria (IMA) matched against 10 patients with persistent (PMA) microalbuminuria. A Bayesian procedure was used to normalize and convert raw signals to expression ratios. We applied formal statistical techniques to translate fold changes to profiles of microRNA targets which were then used to make inferences about biological pathways in the Gene Ontology and REACTOME structured vocabularies. A total of 27 microRNAs were found to be present at significantly different levels in different stages of untreated nephropathy. These microRNAs mapped to overlapping pathways pertaining to growth factor signaling and renal fibrosis known to be targeted in diabetic kidney disease. Conclusions: Urinary microRNA profiles differ across the different stages of diabetic nephropathy. Previous work using experimental, clinical chemistry or biopsy samples has demonstrated differential expression of many of these microRNAs in a variety of chronic renal conditions and diabetes. Combining expression ratios of microRNAs with formal inferences about their predicted mRNA targets and associated biological pathways may yield useful markers for early diagnosis and risk stratification of DN in T1D by inferring the alteration of renal molecular processes. © 2013 Argyropoulos et al

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Measurement of prompt open-charm production cross sections in proton-proton collisions at root s=13 TeV

The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb(-1). The differential production cross sections of the D*(+/-), D-+/-, and D-0 ((D) over bar (0)) mesons are presented in ranges of transverse momentum and pseudorapidity 4 < p(T) < 100 GeV and vertical bar eta vertical bar < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.Peer reviewe