Agent based simulators for Covid-19: Simulating larger models using smaller ones

Agent-based simulators (ABS) are a popular epidemiological modelling tool to study the impact of various non-pharmaceutical interventions in managing an epidemic in a city. They provide the flexibility to accurately model a heterogeneous population with time and location varying, person-specific interactions. Government policies such as localised lockdowns, case isolation, home quarantine etc. and important pandemic developments including presence of variants as well as vaccines, are easily incorporated in an ABS. Typically, for accuracy, each person is modelled separately. This however may make computational time prohibitive when the city population and the simulated time is large. In this paper, we primarily focus on the COVID-19 pandemic and dig deeper into the underlying probabilistic structure of a generic ABS to arrive at modifications that allow smaller models to give accurate statistics for larger ones. We observe that simply considering a smaller aggregate model and scaling up the output leads to inaccuracies. We exploit the observation that in the initial Covid spread phase, the starting infections create a family tree of infected individuals more-or-less independent of the other trees and are modelled well as a multi-type super-critical branching process. Further, the relative proportions amongst the population types stabilises quickly. Soon after, for large city population, once enough people have been infected, the future evolution of the pandemic is closely approximated by its mean field limit with a random starting state. We build upon these insights to develop a shifted, scaled and restart based algorithm that accurately evaluates the ABS's performance using a much smaller model while carefully reducing the bias that may otherwise arise. We theoretically support the proposed algorithm through an asymptotic analysis where the population size increases to infinity.Comment: 33 pages, 13 figures, 6 table

Electrochemical studies on zirconium phosphoborate based heterogeneous membranes

Electrode potential measurements have been applied to study electrical characteristics like transport numbers, permselectivity & fixed charged density of zirconium phosphoborate ion exchange membranes. The potential measurements were made across the cation exchange membrane maintained at 27±0.1 °C, using halide and nitrate salts of alkali and alkaline earth metals as electrolytes. The membrane potentials, transport numbers and permselectivity values increase with increase in average concentration from 0.0055 M to 0.0495 M for 1:1 and 1:2 electrolytes. With the increase in concentration of the electrolyte, the number of counter ions interacting with the membrane surface increases leading to enhanced Donnan exclusion responsible for the increase of transport numbers. Fixed charge density of the membrane (X) for 1:2 electrolytes is higher in magnitude than for 1:1 electrolytes indicating that the cation exchange is taking place as hydrated species. This hypothesis is supported by higher transport numbers for alkaline earth metal ions than alkali metal ions throughout the range of concentration

Spectrum of Pediatric Malignancies: An Observational Single Center Study from Western India

Cancer is a leading cause of death for children and adolescent worldwide. The cure rates in low middle-income countries are dismal (20%) in comparison to high income countries (80%). The first move is to assemble precise data on epidemiology of pediatric cancer across the country and its region wide variation. This study attempts to provide spectrum of pediatric malignancies from a tertiary care hospital in the state of Rajasthan, India. A total of 140 cases were studied retrospectively over a period of two years (April 2018-March 2020). Patients, 0-18 years of age that are diagnosed as a case of malignancy were included in this study. The records of these patients were retrieved and analyzed. Patients were stratified in 4 groups; 0-4 years, 5-9 years, 10-14 years and 15-18 years. Most of the patients fell in 15-18 year group (35.7%), followed by 5-9 year group (28.5%). Majority of cases, 67.8% were male. The male to female ratio is 2.1:1. Leukemia (40%) was the most common malignancy followed by lymphoma, retinoblastoma and malignant bone tumors. Acute lymphoblastic leukemia comprises majority (35/56) of leukemia. Retinoblastoma was predominant malignancy among <5-year children. In all other groups, leukemia was predominant. This study gauges the trend of pediatric malignancies at one of the largest tertiary care hospitals in Rajasthan, which is important in the planning and evaluation of health strategies. As we lack a dedicated pediatric cancer registry, such epidemiological studies play a significant part for this small but distinguished group of patients

A study on pregnancy outcome following previous one spontaneous abortion

Background: Pregnancy plays a unique role in the transformation of women towards completeness. Pregnancy should be considered a unique normal physiological episode in a woman’s life. However in some cases many twists and turns occur which alter the good outcome of pregnancy into a disaster. For those women who have had a previous unsuccessful outcome, pregnancy may bring a lot of inevitable negative emotions. The main objective of our study was to determine pregnancy outcome following previous one spontaneous abortionMethods: A prospective study was done on 756 patients. There were 252 patients in the case group consisting of pregnant females with the history of previous one spontaneous abortion (group A). There were two control groups - primigravida women (group B) & second gravida with history of previous successful pregnancy outcome (group C) who delivered subsequent to our study group. All the antenatal, post natal complications and modes of delivery were noted and compared between the three groups.Results: Pregnancy complications included: threatened miscarriage, premature rupture of membranes (PROM), preterm delivery, intra uterine growth restriction (IUGR), diabetes mellitus, abruption, placenta praevia, preeclampsia, eclampsia and postpartum hemorrhage (PPH). Statistical analysis was carried out using Statistical Package for Social Scientists (SPSS) version 20. Statistical analysis showed that all the complications except preeclampsia, eclampsia, placenta praevia and diabetes were more in the study group than both the control groups (p<0.05). Risk of preeclampsia was more in primigravidae. Rate of caesarean section and instrumental delivery was also significantly increased in women with previous one spontaneous abortion. Conclusions: Women with a history of previous one spontaneous abortion are at an increased risk of complications in the next pregnancy. So careful surveillance should be provided to such women and not to be restricted only to females with history of recurrent pregnancy loss

A Note on Fuzzy Automorphism and Inner Automorphism of Groups

The fuzzification of classical set theory came into existence when Zadeh [1] laid down the concept of a fuzzy set as a generalization of a crisp set. The objective of this paper is to extend the concept of fuzzy endomorphism to fuzzy automorphism. Notions of fuzzy inner automorphism and fuzzy inner automorphism induced by a fuzzy subgroup are introduced. Finally, we obtain the fuzzy analogues of well-known results of classical group theory.Comment: 13 page

Group ring based public key cryptosystems

In this paper, we propose two cryptosystems based on group rings and existing cryptosystem. First one is Elliptic ElGamal type group ring public key cryptosystem whose security is greater than security of cryptosystems based on elliptic curves discrete logarithmic problem (ECDLP). Second is ElGamal type group ring public key cryptosystem, which is analogous to ElGamal public key cryptosystem but has comparatively greater security. Examples are also given for both the proposed cryptosystems