Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing

We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and $d$ nonnegative weights $v_1(i), v_2(i), \ldots, v_{d}(i)$. Our goal is to get an axis-parallel non-overlapping packing of the items into square bins so that for all $j \in [d]$, the sum of the $j^{\textrm{th}}$ weight of items in each bin is at most 1. This is a natural problem arising in logistics, resource allocation, and scheduling. Despite being well studied in practice, surprisingly, approximation algorithms for this problem have rarely been explored. We first obtain two simple algorithms for GVBP having asymptotic approximation ratios $6(d+1)$ and $3(1 + \ln(d+1) + \varepsilon)$. We then extend the Round-and-Approx (R&A) framework [Bansal-Khan, SODA'14] to wider classes of algorithms, and show how it can be adapted to GVBP. Using more sophisticated techniques, we obtain better approximation algorithms for GVBP, and we get further improvement by combining them with the R&A framework. This gives us an asymptotic approximation ratio of $2(1+\ln((d+4)/2))+\varepsilon$ for GVBP, which improves to $2.919+\varepsilon$ for the special case of $d=1$. We obtain further improvement when the items are allowed to be rotated. We also present algorithms for a generalization of GVBP where the items are high dimensional cuboids

Guaranteeing Envy-Freeness under Generalized Assignment Constraints

We study fair division of goods under the broad class of generalized assignment constraints. In this constraint framework, the sizes and values of the goods are agent-specific, and one needs to allocate the goods among the agents fairly while further ensuring that each agent receives a bundle of total size at most the corresponding budget of the agent. Since, in such a constraint setting, it may not always be feasible to partition all the goods among the agents, we conform -- as in recent works -- to the construct of charity to designate the set of unassigned goods. For this allocation framework, we obtain existential and computational guarantees for envy-free (appropriately defined) allocation of divisible and indivisible goods, respectively, among agents with individual, additive valuations for the goods. We deem allocations to be fair by evaluating envy only with respect to feasible subsets. In particular, an allocation is said to be feasibly envy-free (FEF) iff each agent prefers its bundle over every (budget) feasible subset within any other agent's bundle (and within the charity). The current work establishes that, for divisible goods, FEF allocations are guaranteed to exist and can be computed efficiently under generalized assignment constraints. In the context of indivisible goods, FEF allocations do not necessarily exist, and hence, we consider the fairness notion of feasible envy-freeness up to any good (FEFx). We show that, under generalized assignment constraints, an FEFx allocation of indivisible goods always exists. In fact, our FEFx result resolves open problems posed in prior works. Further, for indivisible goods and under generalized assignment constraints, we provide a pseudo-polynomial time algorithm for computing FEFx allocations, and a fully polynomial-time approximation scheme (FPTAS) for computing approximate FEFx allocations.Comment: 29 page

Proton magnetic resonance spectroscopy of brain in obstructive sleep apnoea in North Indian Asian subjects

Background & Objectives: Repeated apnoeic/hypoapnoeic episodes during sleep may produce cerebral damage in patients with obstructive sleep apnoea (OSA). The aim of this study was to determine the absolute concentration of cerebral metabolites in apnoeic and non-apnoeic subjects from different regions of the brain to monitor the regional variation of cerebral metabolites. Methods: Absolute concentration of cerebral metabolites was determined by using early morning proton magnetic resonance spectroscopy (1H MRS) in 18 apnoeic patients with OSA (apnoeics) having apnoea/hypopnoea index (AHI) > 5/h, while 32 were non-apnoeic subjects with AHI < 5/h. Results: The absolute concentration of tNAA [(N-acetylaspartate (NAA)+N-acetylaspartylglutamate (NAAG)] was observed to be statistically significantly lower (P<0.05) in apnoeics in the left temporal and left frontal gray regions compared to non-apnoeics. The Glx (glutamine, Gln + glutamate, Glu) resonance showed higher concentration (but not statistically significant) in the left temporal and left frontal regions of the brain in apnoeics compared to non-apnoeics. The absolute concentration of myo-inositol (mI) was significantly high (P<0.03) in apnoeics in the occipital region compared to non-apnoeics. Interpretation & Conclusions: Reduction in the absolute concentration of tNAA in apnoeics is suggestive of neuronal damage, probably caused by repeated apnoeic episodes in these patients. NAA showed negative correlation with AHI in the left frontal region, while Cho and mI were positively correlated in the occipital region and Glx showed positive correlation in the left temporal region of the brain. Overall, our results demonstrate that the variation in metabolites concentrations is not uniform across various regions of the brain studied in patients with OSA. Further studies with a large cohort of patients to substantiate these observations are required

Fulminant hepatitis in a tropical population: clinical course, cause, and early predictors of outcome

The profiles of patients with fulminant hepatic failure (FHF) from developing countries have not been reported earlier. The current study was conducted prospectively, at a single tertiary care center in India, to document the demographic and clinical characteristics, natural course, and causative profile of patients with FHF as well as to define simple prognostic markers in these patients. Four hundred twenty-three consecutive patients with FHF admitted from January 1987 to June 1993 were included in the study. Each patient's serum was tested for various hepatotropic viruses. Univariate Cox's regression for 28 variables, multivariate Cox's proportional hazard regression, stepwise logistic regression, and Kaplan-Meier survival analysis were done to identify independent predictors of outcome at admission. All patients presented with encephalopathy within 4 weeks of onset of symptoms. Hepatotropic viruses were the likely cause in most of these patients. Hepatitis A (HAV), hepatitis B (HBV), hepatitis D (HDV) viruses, and antitubercular drugs could be implicated as the cause of FHF in 1.7% (n = 7), 28% (n = 117), 3.8% (n = 16), and 4.5% (n = 19) patients, respectively. In the remaining 62% (n = 264) of patients the serological evidence of HAV, HBV, or HDV infection was lacking, and none of them had ingested hepatotoxins. FHF was presumed to be caused by non-A, non-B virus(es) infection. Sera of 50 patients from the latter group were tested for hepatitis E virus (HEV) RNA and HCV RNA. In 31 (62%), HEV could be implicated as the causative agent, and isolated HCV RNA could be detected in 7 (19%). Two hundred eighty eight (66%) patients died. Approximately 75% of those who died did so within 72 hours of hospitalisation. One quarter of the female patients with FHF were pregnant. Mortality among pregnant females, nonpregnant females, and male patients with FHF was similar (P > .1). Univariate analysis showed that age, size of the liver assessed by percussion, grade of coma, presence of clinical features of cerebral edema, presence of infection, serum bilirubin, and prothrombin time prolongation over controls at admission were related to survival (P < .01). The rapidity of onset of encephalopathy and cause of FHF did not influence the outcome. Cox's proportional hazard regression showed age ≥ 40 years, presence of cerebral edema, serum bilirubin ≥ 15 mg/dL, and prothrombin time prolongation of 25 seconds or more over controls were independent predictors of outcome. Ninety-three percent of the patients with three or more of the above prognostic markers died. The sensitivity, specificity, positive predictive value, and the negative predictive value of the presence of three or more of these prognostic factors for mortality was 93%, 80%, 86%, and 89.5%, respectively, with a diagnostic accuracy of 87.3%. We conclude that most of our patients with FHF might have been caused by hepatotropic viral infection, and non-A, non-B virus(es) seems to be the dominant hepatotropic viral infection among these patients. They presented with encephalopathy within 4 weeks of the onset of symptoms. Pregnancy, cause, and rapidity of onset of encephalopathy did not influence survival. The prognostic model developed in the current study is simple and can be performed at admission

Development of eAgromet Prototype to Improve the Performance of Integrated Agromet Advisory Service

In several countries, the systems for forecasting weather are being operated to deal with weather and its related factors affecting agricultural production. India meteorological department (IMD) is providing several types of weather forecasts. One of the forecast service is medium range forecast (MRF). As a part of MRF, the expected values of rain fall, temperature, cloud cover, humidity, wind speed and wind direction for next five days are forecasted twice a week by considering district as a unit. Agriculture is markedly affected by weather condition during crop season. IMD in collaboration with Indian Council of Agriculture Research (ICAR) and State Agriculture Universities (SAUs) has set-up about 130 Agro-meteorological Field Units (AMFUs) and each AMFU covers about five districts. Based on MRF, IMD is rendering Integrated Agromet Advisory Service to the farming community of the country in the form of agromet advisory bulletin. The agromet advisory bulletins contain possible risk mitigation measures for the major crops and livestock. Based on the weather forecast, a group of interdisciplinary scientists and agromet scientists at AMFU prepare district-level agromet advisory bulletins. These bulletins are sent to the farmers and other stakeholders of the corresponding district. To ease the process of preparing agromet bulletins, an effort has started to build IT-based agrometeorological advisory system called, eAgromet. In this paper, we explain the concepts of eAgromet and its operation

Prevalence, Distribution and Functional Significance of the −237C to T Polymorphism in the IL-12Rβ2 Promoter in Indian Tuberculosis Patients

Cytokine/cytokine receptor gene polymorphisms related to structure/expression could impact immune response. Hence, the −237 polymorphic site in the 5′ promoter region of the IL-12Rβ2 (SNP ID: rs11810249) gene associated with the AP-4 transcription motif GAGCTG, was examined. Amplicons encompassing the polymorphism were generated from 46 pulmonary tuberculosis patients, 35 family contacts and 28 miscellaneous volunteers and sequenced. The C allele predominated among patients, (93.4%, 43/46), and in all volunteers and contacts screened, but the T allele was exclusively limited to patients, (6.5%, 3/46). The functional impact of this polymorphism on transcriptional activity was assessed by Luciferase-reporter and electrophoretic mobility shift assays (EMSA). Luciferase-reporter assays showed a significant reduction in transcriptional efficiency with T compared to C allele. The reduction in transcriptional efficiency with the T allele construct (pGIL-12Rb2-T), in U-87MG, THP-1 and Jurkat cell lines, were 53, 37.6, and 49.8% respectively, compared to the C allele construct (pGIL-12Rb2-C). Similarly, densitometric analysis of the EMSA assay showed reduced binding of the AP-4 transcription factor, to T compared to the C nucleotide probe. Reduced mRNA expression in all patients (3/3) harboring the T allele was seen, whereas individuals with the C allele exhibited high mRNA expression (17/25; 68%, p = 0.05). These observations were in agreement with the in vitro assessment of the promoter activity by Luciferase-reporter and EMSA assays. The reduced expression of IL-12Rβ2 transcripts in 8 patients despite having the C allele was attributed to the predominant over expression of the suppressors (IL-4 and GATA-3) and reduced expression of enhancers (IFN-α) of IL-12Rβ2 transcripts. The 17 high IL-12Rβ2 mRNA expressers had significantly elevated IFN-α mRNA levels compared to low expressers and volunteers. Notwithstanding the presence of high levels of IL-12Rβ2 mRNA in these patients elevated IFN-α expression could modulate their immune responses to Mycobacterium tuberculosis

Piloting Upfront Xpert MTB/RIF Testing on Various Specimens under Programmatic Conditions for Diagnosis of TB & DR-TB in Paediatric Population

India accounts for one-fifth of the global TB incidence. While the exact burden of childhood TB is not known, TB remains one of the leading causes of childhood mortality in India. Bacteriological confirmation of TB in children is challenging due to difficulty in obtaining quality specimens, in the absence of which diagnosis is largely based on clinical judgement. While testing multiple specimens can potentially contribute to higher proportion of laboratory confirmed paediatric TB cases, lack of high sensitivity tests adds to the diagnostic challenge. We describe here our experiences in piloting upfront Xpert MTB/RIF testing, for diagnosis of TB in paediatric population in respiratory and extra pulmonary specimens, as recently recommended by WHO.Xpert MTB/RIF testing was offered to all paediatric (0-14 years) presumptive TB cases (both pulmonary and extra-pulmonary) seeking care at public and private health facilities in the project areas covering 4 cities of India.Under this pilot project, 8,370 paediatric presumptive TB & presumptive DR-TB cases were tested between April and-November 2014. Overall, 9,149 specimens were tested, of which 4,445 (48.6%) were non-sputum specimens. Xpert MTB/RIF gave 9,083 (99.2%, CI 99.0-99.4) valid results. Of the 8,143 presumptive TB cases enrolled, 517 (6.3%, CI 5.8-6.9) were bacteriologically confirmed. TB detection rates were two fold higher with Xpert MTB/RIF as compared to smear microscopy. Further, a total of 60 rifampicin resistant TB cases were detected, of which 38 were detected among 512 presumptive TB cases while 22 were detected amongst 227 presumptive DR-TB cases tested under the project.Xpert MTB/RIF with advantages of quick turnaround testing-time, high proportion of interpretable results and feasibility of rapid rollout, substantially improved the diagnosis of bacteriologically confirmed TB in children, while simultaneously detecting rifampicin resistance

Nations within a nation: variations in epidemiological transition across the states of India, 1990–2016 in the Global Burden of Disease Study

18% of the world's population lives in India, and many states of India have populations similar to those of large countries. Action to effectively improve population health in India requires availability of reliable and comprehensive state-level estimates of disease burden and risk factors over time. Such comprehensive estimates have not been available so far for all major diseases and risk factors. Thus, we aimed to estimate the disease burden and risk factors in every state of India as part of the Global Burden of Disease (GBD) Study 2016