On the Optimality of a Class of LP-based Algorithms

In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the simple LP-based rounding algorithm for the \\VC problem is optimal assuming the UGC. Complementing Raghavendra's result, our result generalizes to a class of strict, covering/packing type CSPs

On Quadratic Programming with a Ratio Objective

Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture, semidefinite programming techniques give optimal approximation algorithms. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problems we study are QP-Ratio : \max_{\{-1,0,1\}^n} \frac{\sum_{i \not = j} a_{ij} x_i x_j}{\sum x_i^2}, and Normalized QP-Ratio : \max_{\{-1,0,1\}^n} \frac{\sum_{i \not = j} a_{ij} x_i x_j}{\sum d_i x_i^2}, where d_i = \sum_j |a_{ij}| We consider an SDP relaxation obtained by adding constraints to the natural eigenvalue (or SDP) relaxation for this problem. Using this, we obtain an $\tilde{O}(n^{1/3})$ algorithm for QP-ratio. We also obtain an $\tilde{O}(n^{1/4})$ approximation for bipartite graphs, and better algorithms for special cases. As with other problems with ratio objectives (e.g. uniform sparsest cut), it seems difficult to obtain inapproximability results based on P!=NP. We give two results that indicate that QP-Ratio is hard to approximate to within any constant factor. We also give a natural distribution on instances of QP-Ratio for which an n^\epsilon approximation (for \epsilon roughly 1/10) seems out of reach of current techniques

Improved NP-Inapproximability for 2-Variable Linear Equations

An instance of the 2-Lin(2) problem is a system of equations of the form "x_i + x_j = b (mod 2)". Given such a system in which it\u27s possible to satisfy all but an epsilon fraction of the equations, we show it is NP-hard to satisfy all but a C*epsilon fraction of the equations, for any C < 11/8 = 1.375 (and any 0 < epsilon <= 1/8). The previous best result, standing for over 15 years, had 5/4 in place of 11/8. Our result provides the best known NP-hardness even for the Unique Games problem, and it also holds for the special case of Max-Cut. The precise factor 11/8 is unlikely to be best possible; we also give a conjecture concerning analysis of Boolean functions which, if true, would yield a larger hardness factor of 3/2. Our proof is by a modified gadget reduction from a pairwise-independent predicate. We also show an inherent limitation to this type of gadget reduction. In particular, any such reduction can never establish a hardness factor C greater than 2.54. Previously, no such limitation on gadget reductions was known

Role of magnetic resonance spectroscopy in brain space occupying lesions for detection of malignancy and grading of malignant lesions

Background: Magnetic resonance (MR) spectroscopy is a non-invasive technique that enables tissue characterization on a biochemical level using radio frequency signals emitted by the nuclei in the tissue. Primary aim is at determining the utility of MR spectroscopy to differentiate malignant from benign lesions and to assess its role in grading of gliomas as secondary objectives.Methods: MR system with proton spectroscopic capability using standard head coils and quantum gradients used in a sample size of 50 patients with intracranial space occupying lesions in conventional MRI. The diagnostic accuracy of the spectroscopic data based on the Cho/Naa ratios was used to detect the malignant lesions and distinguish them from the benign lesions.Results: The lesion characterization using the MR spectroscopic data in distinguishing malignant lesions from benign was statistically compared with the histopathological data using chi square tests proved to be significant with p value of less than 0.05. Grading of the malignant space occupying lesion with the available spectroscopic data was done with the corresponding histopathology that proved statistically not significant.Conclusions: Statistical data proves utility of MR spectroscopic data in differentiating malignant occupying lesions from benign. Role of spectroscopic data in grading the malignant lesion to differentiate to low and high grade could not be determined statistically which may be attributed to low sample size in the secondary objective

Development of the Indian Reference Case for undertaking economic evaluation for health technology assessment

Background: Health technology assessment (HTA) is globally recognised as an important tool to guide evidence-based decision-making. However, heterogeneity in methods limits the use of any such evidence. The current research was undertaken to develop a set of standards for conduct of economic evaluations for HTA in India, referred to as the Indian Reference Case. Methods: Development of the reference case comprised of a four-step process: (i) review of existing international HTA guidelines; (ii) systematic review of economic evaluations for three countries to assess adherence with pre-existing country-specific HTA guidelines; (iii) empirical analysis to assess the impact of alternate assumptions for key principles of economic evaluation on the results of cost-effectiveness analysis; (iv) stakeholder consultations to assess appropriateness of the recommendations. Based on the inferences drawn from the first three processes, a preliminary draft of the reference case was developed, which was finalised based on stakeholder consultations. Findings: The Indian Reference Case provides twelve recommendations on eleven key principles of economic evaluation: decision problem, comparator, perspective, source of effectiveness evidence, measure of costs, health outcomes, time-horizon, discounting, heterogeneity, uncertainty analysis and equity analysis, and for presentation of results. The recommendations are user-friendly and have scope to allow for context-specific flexibility. Interpretation: The Indian Reference Case is expected to provide guidance in planning, conducting, and reporting of economic evaluations. It is anticipated that adherence to the Reference Case would increase the quality and policy utilisation of future evaluations. However, with advancement in the field of health economics efforts aimed at refining the Indian Reference Case would be needed. Funding: This research received no specific grant from any funding agency, commercial, or not-for-profit sectors. The research was undertaken as part of doctoral thesis of Sharma D, who received scholarship from the Indian Council of Medical Research (ICMR), New Delhi, India

Impact of India's publicly financed health insurance scheme on public sector district hospitals: a health financing perspective

Background: Districts hospitals in India play a pivotal role in delivering health care services in the public sector and are empanelled under India's national health insurance scheme i.e. Ayushman Bharat Pradhan Mantri Jan Aarogya Yojana (PMJAY). In this paper, we evaluate the extent to which the PMJAY impacts the district hospitals from a financing perspective. Methods: We used cost data from India's nationally representative costing study—‘Costing of Health Services in India’ (CHSI) to determine the incremental cost of treating PMJAY patients, after adjusting for resources that are paid through supply-side government financing route. Second, we used data on number and claim value paid to public district and sub-district hospitals during 2019, to determine the additional revenue generated through PMJAY. The annual net financial gain per district hospital was estimated as the difference between payments under PMJAY, and the incremental cost of delivering the services. Findings: At current levels of utilisation, the district hospitals in India gain a net annual financial benefit of $26.1 (₹ 1839.3) million, which can potentially increase up to$ 41.8 (₹ 2942.9) million with an increase in the share of patient volume. For an average district hospital, we estimate net annual financial gain of $169,607 (₹ 11.9 million), increasing up to$ 271,372 (₹ 19.1 million) per hospital with increased utilisation. Interpretation: Demand-side financing mechanisms can be used to strengthen the public sector. Increasing utilisation of district hospitals, by either gatekeeping or improving availability of services will enhance financial gains for district hospitals and strengthen public sector. Funding: Department of Health Research, Ministry of Health & Family Welfare, Government of India

AR2, a novel automatic muscle artifact reduction software method for ictal EEG interpretation: Validation and comparison of performance with commercially available software.

Objective: To develop a novel software method (AR2) for reducing muscle contamination of ictal scalp electroencephalogram (EEG), and validate this method on the basis of its performance in comparison to a commercially available software method (AR1) to accurately depict seizure-onset location. Methods: A blinded investigation used 23 EEG recordings of seizures from 8 patients. Each recording was uninterpretable with digital filtering because of muscle artifact and processed using AR1 and AR2 and reviewed by 26 EEG specialists. EEG readers assessed seizure-onset time, lateralization, and region, and specified confidence for each determination. The two methods were validated on the basis of the number of readers able to render assignments, confidence, the intra-class correlation (ICC), and agreement with other clinical findings. Results: Among the 23 seizures, two-thirds of the readers were able to delineate seizure-onset time in 10 of 23 using AR1, and 15 of 23 using AR2 (

An economic evaluation of implementing a decentralized dengue screening intervention under the National Vector Borne Disease Control Programme in Tamil Nadu, South India.

BACKGROUND Lack of effective early screening is a major obstacle for reducing the fatality rate and disease burden of dengue. In light of this, the government of Tamil Nadu has adopted a decentralized dengue screening strategy at the primary healthcare (PHC) facilities using blood platelet count. Our objective was to determine the cost-effectiveness of a decentralized screening strategy for dengue at PHC facilities compared with the current strategy at the tertiary health facility (THC) level. METHODS Decision tree analysis followed a hypothetical cohort of 1000 suspected dengue cases entering the model. The cost-effectiveness analysis was performed at a 3% discount rate for the proposed and current strategy. The outcomes are expressed in incremental cost-effectiveness ratios (ICERs) per quality-adjusted life years gained. One-way sensitivity analysis and probabilistic sensitivity analysis were done to check the uncertainty in the outcome. RESULTS The proposed strategy was found to be cost-saving and ICER was estimated to be -41 197. PSA showed that the proposed strategy had a 0.84 probability of being an economically dominant strategy. CONCLUSIONS The proposed strategy is cost-saving, however, it is recommended to consider optimal population coverage, costs to economic human resources and collateral benefits of equipment