FASTER ALGORITHMS FOR STABLE ALLOCATION PROBLEMS

We consider a high-multiplicity generalization of the classical stable matching problem known as the stable allocation problem, introduced by Baiou and Balinski in 2002. By leveraging new structural properties and sophisticated data structures, we show how to solve this problem in O(mlog n) time on an bipartite instance with n nodes and m edges, improving the best known running time of O(mn). Our approach simplifies the algorithmic landscape for this problem by providing a common generalization of two different approaches from the literature -- the classical Gale-Shapley algorithm, and a recent algorithm of Baiou and Balinski. Building on this algorithm, we provide an O(m log n) algorithm for the non-bipartite stable allocation problem that introduces a new and useful transformation from non-bipartite to bipartite instances. We also give a polynomial-time algorithm for solving the \u27optimal\u27 variant of the bipartite stable allocation problem, as well as a 2-approximation algorithm for the NP-hard \u27optimal\u27 variant of the non-bipartite stable allocation problem. Finally, we highlight some important connections between the stable allocation problem and the maximum flow problem

Morbidity Patterns in Oncology Patients at FMRI, Gurgaon:A Hospital Based Study at a New Tertiary Care Institute

Objective: This study aims to analyze the patterns of morbidity amongst cancer patients attending a tertiary care hospital.Materials and Methods: Data were collected from various departments dealing in cancer care. Patient’s data were categorized according to diagnosis and place of residence.Results: A total of 1490 new cancer patients were registered. Out of these 1140 were Indians from 22 different states {males= 609 (53.4%) and females= 531 (46.6%)} and remaining 350 patients were from 27 different countries {males= 223 (63.7%) and females=127 (36.3%)}. The five most common cancer site groups amongst all males (n=832) were digestive organs (18.6%) followed by lymphoid, hematopoietic and related tissue (16.8%);  respiratory intrathoracic organs (14.1%); then eye, brain and other parts of central nervous system (11.4%) and lip, oral cavity and  pharynx (9.5%)  and in all females (n=658) the most common cancer site were breast (31.5%) followed by  genital organs (17.3%); digestive organs (11.2%); lymphoid, hematopoietic and related tissue (9.3%) and eye, brain and other parts of nervous system (9.0%).Conclusions:  The present study highlights the pattern of cancer among patients in a corporate tertiary health care institute. There is therefore an inherent bias, the leading sites of malignancies amongst Indian males and females varied from that in the Western population; this could be attributed to various cultural, environmental factors, life style, genetic factors etc. in different regions of India and different nations of the world.

Report of the Topical Group on Cosmic Probes of Dark Matter for Snowmass 2021

Cosmological and astrophysical observations currently provide the only robust, positive evidence for dark matter. Cosmic probes of dark matter, which seek to determine the fundamental properties of dark matter through observations of the cosmos, have emerged as a promising means to reveal the nature of dark matter. This report summarizes the current status and future potential of cosmic probes to inform our understanding of the fundamental nature of dark matter in the coming decade.Comment: Report of the CF3 Topical Group for Snowmass 2021; 35 pages, 10 figures, many references. V3 updates Fig 3-2 and the author lis