A Gale-Shapley View of Unique Stable Marriages

Stable marriage of a two-sided market with unit demand is a classic problem that arises in many real-world scenarios. In addition, a unique stable marriage in this market simplifies a host of downstream desiderata. In this paper, we explore a new set of sufficient conditions for unique stable matching (USM) under this setup. Unlike other approaches that also address this question using the structure of preference profiles, we use an algorithmic viewpoint and investigate if this question can be answered using the lens of the deferred acceptance (DA) algorithm (Gale and Shapley, 1962). Our results yield a set of sufficient conditions for USM (viz., MaxProp and MaxRou) and show that these are disjoint from the previously known sufficiency conditions like sequential preference and no crossing. We also provide a characterization of MaxProp that makes it efficiently verifiable, and shows the gap between MaxProp and the entire USM class. These results give a more detailed view of the sub-structures of the USM class.Comment: 18 pages, 1 figur

Secure Non-Interactive Reducibility is Decidable

Secure Non-Interactive Reductions (SNIR) is a recently introduced, but fundamental cryptographic primitive. The basic question about SNIRs is how to determine if there is an SNIR from one 2-party correlation to another. While prior work provided answers for several pairs of correlations, the possibility that this is an undecidable problem in general was left open. In this work we show that the existence of an SNIR between any pair of correlations can be determined by an algorithm. At a high-level, our proof follows the blueprint of a similar (but restricted) result by Khorasgani et al. But combining the spectral analysis of SNIRs by Agrawal et al. (Eurocrypt 2022) with a new variant of a junta theorem by Kindler and Safra, we obtain a complete resolution of the decidability question for SNIRs. The new junta theorem that we identify and prove may be of independent interest

On the connectivity of circularly distributed nodes in ad hoc wireless networks

Abstract-This paper examines the probability of connectivity of ad hoc wireless networks in which nodes are uniformly distributed on the circumference of a circle. We derive the exact probability that the network is composed of at most C clusters. The probability of connectivity is obtained by considering the case of C equal to unity. We also consider the distribution of nodes over a circular disk. The probability of connectivity for this case is found by fitting a log-logistic function using Minimum Mean Square Error (MMSE) criterion

Biomedical Waste Management: A study of knowledge, attitude and practice among health care personnel at tertiary care hospital in Rajkot

Background: Bio medical waste (BMW) collection and proper disposal has become a significant concern for both the medical and general community. Effective management of biomedical waste is not only a legal necessity but also a social responsibility. Objective: To know the knowledge, attitude and practice among health care personnels working in tertiary care centre. Methods: The study was conducted from January 2013 to June 2013. It was a descriptive observational hospital based cross sectional study. Study participants included the resident doctors intern doctors, nursing staff, laboratory technicians, ward boys and sweepers working in the institute who are dealing with BMW. The study was conducted by using pretested, semi-structured proforma. The data was tabulated and interpretation was done by using percentages through Epi Info 3.5.1 software. Results: It included 123 resident doctors and interns, 92 nurses, 13 laboratory technicians, and 54 sanitary staff. Majority of study participants belongs to 21-30 years (61%) age group. More than two third of study participants working in hospital from 1 to 5 years. Only 44.3% study participants received training for bio medical waste management. HIV (74.47%) and Hepatitis B (56.03%) were the main infectious diseases transmitted by the bio medical waste. Conclusion: The importance of training regarding bio medical waste management cannnot be overemphasized, lack of proper and complete knowledge about bio medical waste management impacts practices of appropriate waste disposal

Eribulin treatment for patients with metastatic breast cancer:The United Kingdom experience - a multicenter retrospective study

Introduction: This study examined real-world data from patients who received eribulin for metastatic breast cancer (MBC) collected from 14 hospitals across the UK. Methods: Anonymized data were collected retrospectively from patients with MBC who had received eribulin. The data included the hormone-receptor status, histological diagnosis, age, prior chemotherapy, response to eribulin, progression-free survival (PFS), and overall survival (OS). Results: Among 577 patients analyzed, the median age was 56 years, and most patients (73%) were estrogen-receptor positive. The median OS was 288 days (95% confidence interval [CI]: 261–315), and the PFS was 117 days (95% CI: 105–129). The median OS was higher among older patients (≥65 vs. p = 0.028). The median OS was also higher in patients who received eribulin after fewer prior lines of chemotherapy (≤2 vs. >2 prior: 328 days [95% CI: 264–385] vs. 264 days [95% CI: 229–298]; p = 0.042). Discussion/Conclusion: These retrospective data suggest that eribulin can be successfully used in older patients with MBC. Eribulin treatment was more effective in earlier-line settings, which, while predictable, supports consideration of eribulin as a second-line treatment option. </p

Th1 and Th17 predominance in the enthesitis-related arthritis form of juvenile idiopathic arthritis

Objective: A Th1 biased immune response in synovial fluid has been reported in children with polyarticular and extended oligoarticular-type juvenile idiopathic arthritis (JIA). We investigated T cell phenotypes including Th1, Th2, Th17, and Treg with emphasis on Th17 and Treg, in order to differentiate cytokines in the enthesitis-related arthritis (ERA) form of JIA. Methods: The frequencies of Th1, Th2, Th17, and Treg cells were determined by flow cytometry in peripheral blood (PB) and synovial fluid from patients with ERA and healthy subjects. Levels of interleukin 1&#946; (IL-1&#946; ), IL-6, IL-21, IL-23, and transforming growth factor &#946; (TGF-&#946; ), cytokines that influence Th17 lineage cells, were measured in paired plasma and synovial fluid (SF) samples by ELISA. Frequencies are expressed as percentages and cytokine levels as pg/ml. Results: There were no differences in blood samples in the frequency of Th1, Th2, Th17, and Treg cells between patients and controls. In paired samples, the median frequency of CD4+IFN-&#947; + (20.49 vs 4.03; p &lt; 0.005) and CD4+IL-17+ (2.27 vs 0.57; p &lt; 0.01) cells was significantly higher in SF compared to PB, respectively; whereas the frequency of CD4+IL-4+ (1.79 vs 2.29; p &lt; 0.04) cells was significantly reduced in the SF compared to PB. There was no difference in the frequency of regulatory T cells. Patients receiving methotrexate had fewer Th2 cells, whereas the Childhood Health Assessment Questionnaire score had a negative association with the frequency of Treg. Median levels of IL-1&#946; (p &#60; 0.008), IL-6 (p &lt; 0.0001), and IL-17 (p &lt; 0.0001) were higher in SF than in plasma and levels of TGF-&#946; were lower (p &lt; 0.001). Levels of IL-21 were similar in SF and plasma, whereas IL-23 was undetectable. Conclusion: In patients with ERA, peripheral blood Th1, Th2, Th17, and Treg cells were unchanged, but Th1 and Th17 cells were increased and Th2 cells were reduced in the SF compared to blood. Elevated IL-1&#946; and IL-6 in SF may be responsible for increased Th17 cells

Palatal mucormycosis masquerading as bacterial and fungal osteomyelitis: A rare case report

Mucormycosis is an acute, fulminating, fungal disease that frequently involves oral, cranial, and facial structures. It is an opportunistic fatal infection which occurs in debilitating and immunosuppressive states. This report documents a rare case of localized maxillary mucormycosis in a patient with uncontrolled diabetes, with emphasis on early and prompt diagnosis of the same