Bias to CMB lensing from lensed foregrounds

Extragalactic foregrounds are known to constitute a limiting systematic in temperature-based cosmic microwave background (CMB) lensing with AdvACT, SPT-3G, Simons Observatory, and CMB S4. Furthermore, since these foregrounds are emitted at cosmological distances, they are also themselves lensed. The correlation between this foreground lensing and CMB lensing causes an additional bias in CMB lensing estimators. In this paper, we quantify for the first time this "lensed foreground bias" for the standard CMB lensing quadratic estimator, the CMB shear, and the CMB magnification estimators, in the case of Simons Observatory and in the absence of multifrequency component separation. This percent-level bias is highly significant in the cross-correlation of CMB lensing with LSST galaxies and comparable to the statistical uncertainty in the CMB lensing autospectrum. We discuss various mitigation strategies and show that "lensed foreground bias-hardening" methods can reduce this bias at some cost in signal to noise. The code used to generate our theory curves is publicly available.1https://github.com/EmmanuelSchaan/LensedForegroundBias

An Assessment of Knowledge and Practices Regarding Tuberculosis in the Context of RNTCP Among Non Allopathic Practitioners in Gwalior District

Introduction: India has the highest TB burden accounting for one-fifth of the global incidence with an estimated 1.98 million cases. Non- allopathic practitioners are the major service providers especially in rural and peri-urban areas, treating not just patients of diarrhea, respiratory infections and abdominal Pain but also of tuberculosis. Objectives: To assess the knowledge of sign and symptoms of TB and its management as per the RNTCP guidelines and to assess the practicing pattern regarding tuberculosis. Material & Methods: The present was carried out among the registered non allopathic practitioners providing their services in Gwalior District during the study period. A total of 150 non allopathic practitioners of various methods from both government and private sectors were interviewed using a pre-designed, pre-tested semi-structured questionnaire. The information was collected on the General profile of the participant, knowledge about signs and symptoms of TB and its management, practices commonly adopted in the management and their views on involvement of non allopathic practitioners in RNTCP programme. Result: The average score of government practitioners was 7.3 compared to 4.6 by private practitioners. There was a statistically significant difference between the two group on issue related to the management of TB patients as per the RNTCP guidelines. Government practitioners relied mostly on sputum examination for diagnosis and follow up compared to private practitioners who chose other modalities like X-ray, blood examination for this work. Conclusion: There is a gap in knowledge and practices of practitioners of both the sectors. Some serious efforts were required to upgrade the knowledge of non allopathic practitioners if the government is serious about controlling tuberculosis in India

On the Complexity of Making a Distinguished Vertex Minimum or Maximum Degree by Vertex Deletion

In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph $G=(V,E)$ and a specified, or "distinguished" vertex $p \in V$, MDD(min) is the problem of finding a minimum weight vertex set $S \subseteq V\setminus \{p\}$ such that $p$ becomes the minimum degree vertex in $G[V \setminus S]$; and MDD(max) is the problem of finding a minimum weight vertex set $S \subseteq V\setminus \{p\}$ such that $p$ becomes the maximum degree vertex in $G[V \setminus S]$. These are known $NP$-complete problems and have been studied from the parameterized complexity point of view in previous work. Here, we prove that for any $\epsilon > 0$, both the problems cannot be approximated within a factor $(1 - \epsilon)\log n$, unless $NP \subseteq DTIME(n^{\log\log n})$. We also show that for any $\epsilon > 0$, MDD(min) cannot be approximated within a factor $(1 -\epsilon)\log n$ on bipartite graphs, unless $NP \subseteq DTIME(n^{\log\log n})$, and that for any $\epsilon > 0$, MDD(max) cannot be approximated within a factor $(1/2 - \epsilon)\log n$ on bipartite graphs, unless $NP \subseteq DTIME(n^{\log\log n})$. We give an $O(\log n)$ factor approximation algorithm for MDD(max) on general graphs, provided the degree of $p$ is $O(\log n)$. We then show that if the degree of $p$ is $n-O(\log n)$, a similar result holds for MDD(min). We prove that MDD(max) is $APX$-complete on 3-regular unweighted graphs and provide an approximation algorithm with ratio $1.583$ when $G$ is a 3-regular unweighted graph. In addition, we show that MDD(min) can be solved in polynomial time when $G$ is a regular graph of constant degree.Comment: 16 pages, 4 figures, submitted to Elsevier's Journal of Discrete Algorithm