Approximation Schemes for Partitioning: Convex Decomposition and Surface Approximation

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved approximation guarantees.Comment: 21 pages, 6 figure

A Constant-Factor Approximation for Multi-Covering with Disks

We consider variants of the following multi-covering problem with disks. We are given two point sets $Y$ (servers) and $X$ (clients) in the plane, a coverage function $\kappa :X \rightarrow \mathcal{N}$, and a constant $\alpha \geq 1$. Centered at each server is a single disk whose radius we are free to set. The requirement is that each client $x \in X$ be covered by at least $\kappa(x)$ of the server disks. The objective function we wish to minimize is the sum of the $\alpha$-th powers of the disk radii. We present a polynomial time algorithm for this problem achieving an $O(1)$ approximation

Capacitated Covering Problems in Geometric Spaces

In this article, we consider the following capacitated covering problem. We are given a set P of n points and a set B of balls from some metric space, and a positive integer U that represents the capacity of each of the balls in B. We would like to compute a subset B\u27 subseteq B of balls and assign each point in P to some ball in B\u27 that contains it, such that the number of points assigned to any ball is at most U. The objective function that we would like to minimize is the cardinality of B\u27. We consider this problem in arbitrary metric spaces as well as Euclidean spaces of constant dimension. In the metric setting, even the uncapacitated version of the problem is hard to approximate to within a logarithmic factor. In the Euclidean setting, the best known approximation guarantee in dimensions 3 and higher is logarithmic in the number of points. Thus we focus on obtaining "bi-criteria" approximations. In particular, we are allowed to expand the balls in our solution by some factor, but optimal solutions do not have that flexibility. Our main result is that allowing constant factor expansion of the input balls suffices to obtain constant approximations for this problem. In fact, in the Euclidean setting, only (1+epsilon) factor expansion is sufficient for any epsilon > 0, with the approximation factor being a polynomial in 1/epsilon. We obtain these results using a unified scheme for rounding the natural LP relaxation; this scheme may be useful for other capacitated covering problems. We also complement these bi-criteria approximations by obtaining hardness of approximation results that shed light on our understanding of these problems

Influence of Nanogels on Mechanical, Dynamic Mechanical, and Thermal Properties of Elastomers

Abstract Use of sulfur crosslinked nanogels to improve various properties of virgin elastomers was investigated for the first time. Natural rubber (NR) and styrene butadiene rubber (SBR) nanogels were prepared by prevulcanization of the respective rubber lattices. These nanogels were characterized by dynamic light scattering, atomic force microscopy (AFM), solvent swelling, mechanical, and dynamic mechanical property measurements. Intermixing of gel and matrix at various ratios was carried out. Addition of NR gels greatly improved the green strength of SBR, whereas presence of SBR nanogels induced greater thermal stability in NR. For example, addition of 16 phr of NR gel increased the maximum tensile stress value of neat SBR by more than 48%. Noticeable increase in glass transition temperature of the gel filled systems was also observed. Morphology of these gel filled elastomers was studied by a combination of energy dispersive X-ray mapping, transmission electron microscopy, and AFM techniques. Particulate filler composite reinforcement models were used to understand the reinforcement mechanism of these nanogels.</p

Petro-tectonic imprints in the sapphirine granulites from Anantagiri, Eastern Ghats mobile belt, India

Sapphirine granulite occurring as lenses in charnockite at Anantagiri, Eastern Ghat, India, displays an array of minerals which developed under different P-T-X conditions. Reaction textures in conjunction with mineral chemical data attest to several Fe-Mg continuous reactions, such as spinel+rutile+quartz+MgFe&#8722;1=sapphirine+ilmenite cordierite=sapphirine+quartz+MgFe&#8722;1 sapphirine+quartz=orthopyroxene+sillimanite+MgFe&#8722;1 orthopyroxene+sapphirine+quartz=garnet+MgFe&#8722;1 orthopyroxene+sillimanite=garnet+quartz+MgFe&#8722;1 orthopyroxene+sillimanite+quartz+MgFe&#8722;1=cordierite. Calculated positions of the reaction curves in P-T space, together with discrete P-T points obtained through geothermobarometry in sapphirine granulite and the closely associated charnockite and mafic granulite, define an anticlockwise P-T trajectory. This comprises a high-T/P prograde metamorphic path which culminated in a pressure regime of 8.3 kb above 950&#176;C, a nearly isobaric cooling (IBC) path (from 950&#176;C, 8.3 kb, to 675&#176;C, 7.5kb) and a terminal decompressive path (from 7.5 to 4.5 kb). Spinel, quartz, high-Mg cordierite, and sapphirine were stabilized during the prograde high-T/P metamorphism, followed by the development of orthopyroxene, sillimanite, and garnet during the IBC. Retrograde low-Mg cordierite appeared as a consequence of decompression in the sapphirine granulite. Deformational structures, reported from the Eastern Ghat granulites, and the available geochronological data indicate that prograde metamorphism could have occurred at 3000&#177;100 and 2500&#177;100 Ma during a compressive orogeny that was associated with high heat influx through mafic magmatism. IBC ensued from Pmax and was thus a direct consequence of prograde metamorphism. However, in the absence of sufficient study on the spatial variation in P-T paths and the strain histories in relation to time, the linkage between IBC and isothermal decompression (ITD) has remained obscure. A prolonged IBC followed by ITD could be the consequence of one extensional mechanism which had an insufficient acceleration at the early stage, or ITD separately could be caused by an unrelated extensional tectonism. The complex cooled nearly isobarically from 2500 Ma. It suffered rapid decompression accompanied by anorthosite and alkaline magmatism at ~1400-1000 Ma

Association of gut microbial dysbiosis with disease severity, response to therapy and disease outcomes in Indian patients with COVID-19

Abstract Background Severe coronavirus disease 2019 (COVID-19) is associated with systemic hyper-inflammation. An adaptive interaction between gut microbiota and host immune systems is important for intestinal homeostasis and systemic immune regulation. The association of gut microbial composition and functions with COVID-19 disease severity is sparse, especially in India. We analysed faecal microbial diversity and abundances in a cohort of Indian COVID-19 patients to identify key signatures in the gut microbial ecology in patients with severe COVID-19 disease as well as in response to different therapies. The composition of the gut microbiome was characterized using 16Sr RNA gene sequences of genomic DNA extracted from faecal samples of 52 COVID-19 patients. Metabolic pathways across the groups were predicted using PICRUSt2. All statistical analyses were done using Vegan in the R environment. Plasma cytokine abundance at recruitment was measured in a multiplex assay. Results The gut microbiome composition of mild and severe patients was found to be significantly different. Immunomodulatory commensals, viz. Lachnospiraceae family members and Bifidobacteria producing butyrate and short-chain fatty acids (SCFAs), were under represented in patients with severe COVID-19, with an increased abundance of opportunistic pathogens like Eggerthella. The higher abundance of Lachnoclostridium in severe disease was reduced in response to convalescent plasma therapy. Specific microbial genera showed distinctive trends in enriched metabolic pathways, strong correlations with blood plasma cytokine levels, and associative link to disease outcomes. Conclusion Our study indicates that, along with SARS-CoV-2, a dysbiotic gut microbial community may also play an important role in COVID-19 severity through modulation of host immune responses

Arsenic mobilization in the aquifers of three physiographic settings of West Bengal, India: understanding geogenic and anthropogenic influences

A comparative hydrogeochemical study was carried out in West Bengal, India covering three physiographic regions, Debagram and Chakdaha located in the Bhagirathi-Hooghly alluvial plain and Baruipur in the delta front, to demonstrate the control of geogenic and anthropogenic influences on groundwater arsenic (As) mobilization. Groundwater samples (n = 90) from tube wells were analyzed for different physico-chemical parameters. The low redox potential (Eh = -185 to -86 mV) and dominant As(III) and Fe(II) concentrations are indicative of anoxic nature of the aquifer. The shallow (100 m) aquifers of Bhagirathi-Hooghly alluvial plains as well as shallow aquifers of delta front are characterized by Ca 2+ {single bond}HCO 3 - type water, whereas Na + and Cl - enrichment is found in the deeper aquifer of delta front. The equilibrium of groundwater with respect to carbonate minerals and their precipitation/dissolution seems to be controlling the overall groundwater chemistry. The low SO 4 2- and high DOC, PO 4 3- and HCO 3 concentrations in groundwater signify ongoing microbial mediated redox processes favoring As mobilization in the aquifer. The As release is influenced by both geogenic (i.e. geomorphology) and anthropogenic (i.e. unsewered sanitation) processes. Multiple geochemical processes, e.g., Fe-oxyhydroxides reduction and carbonate dissolution, are responsible for high As occurrence in groundwaters

Assessment of arsenic exposure from groundwater and rice in Bengal Delta Region, West Bengal, India

(As) induced identifiable health outcomes are now spreading across Indian subcontinent with continuous discovery of high As concentrations in groundwater. This study deals with groundwater hydrochemistry vis-à-vis As exposure assessment among rural population in Chakdaha block, West Bengal, India. The water quality survey reveals that 96% of the tubewells exceed WHO guideline value (10 μg/L of As). The groundwaters are generally anoxic (−283 to −22 mV) with circum-neutral pH (6.3 to 7.8). The hydrochemistry is dominated by HCO3− (208 to 440 mg/L), Ca2+ (79 to 178 mg/L) and Mg2+ (17 to 45 mg/L) ions along with high concentrations of AsT (As total, below detection limit to 0.29 mg/L), FeT (Fe total, 1.2 to 16 mg/L), and Fe(II) (0.74 to 16 mg/L). The result demonstrates that Fe(II)–Fe(III) cycling is the dominant process for the release of As from aquifer sediments to groundwater (and vice versa), which is mainly controlled by the local biogeochemical conditions. The exposure scenario reveals that the consumption of groundwater and rice are the major pathways of As accumulation in human body, which is explained by the dietary habit of the surveyed population. Finally, regular awareness campaign is essential as part of the management and prevention of health outcomes