Multiplication and Modulo are Lattice Linear

In this paper, we analyze lattice linearity of multiplication and modulo operations. We demonstrate that these operations are lattice linear and the parallel processing algorithms that we study for both these operations are able to exploit the lattice linearity of their respective problems. This implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other and are still guaranteed to converge within the same time complexity. These algorithms also exhibit properties similar to snap-stabilization, i.e., starting from an arbitrary state, the system follows the trace strictly according to its specification

Lattice Linear Problems vs Algorithms

Modelling problems using predicates that induce a partial order among global states was introduced as a way to permit asynchronous execution in multiprocessor systems. A key property of such problems is that the predicate induces one lattice in the state space which guarantees that the execution is correct even if nodes execute with old information about their neighbours. Thus, a compiler that is aware of this property can ignore data dependencies and allow the application to continue its execution with the available data rather than waiting for the most recent one. Unfortunately, many interesting problems do not exhibit lattice linearity. This issue was alleviated with the introduction of eventually lattice linear algorithms. Such algorithms induce a partial order in a subset of the state space even though the problem cannot be defined by a predicate under which the states form a partial order. This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It also introduces a new class of algorithms called (fully) lattice linear algorithms. A characteristic of these algorithms is that the entire reachable state space is partitioned into one or more lattices and the initial state locks into one of these lattices. Thus, under a few additional constraints, the initial state can uniquely determine the final state. For demonstration, we present lattice linear self-stabilizing algorithms for minimal dominating set and graph colouring problems, and a parallel processing 2-approximation algorithm for vertex cover. The algorithm for minimal dominating set converges in n moves, and that for graph colouring converges in n+2m moves. The algorithm for vertex cover is the first lattice linear approximation algorithm for an NP-Hard problem; it converges in n moves. Some part is cut due to 1920 character limit. Please see the pdf for full abstract.Comment: arXiv admin note: text overlap with arXiv:2209.1470

Lattice Linearity in Assembling Myopic Robots on an Infinite Triangular Grid

In this paper, we study the problem of gathering distance-1 myopic robots on an infinite triangular grid. We show that the algorithm developed by Goswami et al. (SSS, 2022) is lattice linear. This implies that a distributed scheduler, assumed therein, is not required for this algorithm: it runs correctly in asynchrony. It also implies that the algorithm works correctly even if the robots are equipped with a unidirectional \textit{camera} to see the neighbouring robots (rather than an omnidirectional one, which would be required under a distributed scheduler). Due to lattice linearity, we can predetermine the point of gathering. We also show that this algorithm converges in $2n$ rounds, which is lower than that ($2.5(n+1)$ rounds) shown in Goswami et al.Comment: arXiv admin note: text overlap with arXiv:2302.0720

Technical Report: Using Static Analysis to Compute Benefit of Tolerating Consistency

Synchronization is the Achilles heel of concurrent programs. Synchronization requirement is often used to ensure that the execution of the concurrent program can be serialized. Without synchronization requirement, a program suffers from consistency violations. Recently, it was shown that if programs are designed to tolerate such consistency violation faults (\cvf{s}) then one can obtain substantial performance gain. Previous efforts to analyze the effect of \cvf-tolerance are limited to run-time analysis of the program to determine if tolerating \cvf{s} can improve the performance. Such run-time analysis is very expensive and provides limited insight. In this work, we consider the question, `Can static analysis of the program predict the benefit of \cvf-tolerance?' We find that the answer to this question is affirmative. Specifically, we use static analysis to evaluate the cost of a \cvf and demonstrate that it can be used to predict the benefit of \cvf-tolerance. We also find that when faced with a large state space, partial analysis of the state space (via sampling) also provides the required information to predict the benefit of \cvf-tolerance. Furthermore, we observe that the \cvf-cost distribution is exponential in nature, i.e., the probability that a \cvf has a cost of $c$ is $A.B^{-c}$, where $A$ and $B$ are constants, i.e., most \cvf{s} cause no/low perturbation whereas a small number of \cvf{s} cause a large perturbation. This opens up new aveneus to evaluate the benefit of \cvf-tolerance

App for Resume-Based Job Matching with Speech Interviews and Grammar Analysis: A Review

Through the advancement in natural language processing (NLP), specifically in speech recognition, fully automated complex systems functioning on voice input have started proliferating in areas such as home automation. These systems have been termed Automatic Speech Recognition Systems (ASR). In this review paper, we explore the feasibility of an end-to-end system providing speech and text based natural language processing for job interview preparation as well as recommendation of relevant job postings. We also explore existing recommender-based systems and note their limitations. This literature review would help us identify the approaches and limitations of the various similar use-cases of NLP technology for our upcoming project.Comment: 4 pages, 2 figures, literature revie

The World's Biggest Country: India's Demographic Trajectory and it's Impact on Muslims, the Parliament and the Labour Market

India's dynamic population has undergone significant shifts over the years. Recently, surpassing China's total population presents a unique opportunity for growth and development. While facing the challenges of managing a large population, India also grapples with economic and resource-related complexities. Additionally, there are internal challenges stemming from communal differences among religious communities and representation in governance. These factors necessitate well-informed and effective policymaking. To ensure the smooth functioning of this vibrant democracy, it is crucial to focus on economic progress and enhancing quality of life. Understanding key concepts like demographic shifts, variations in age groups, uneven population growth, skill disparities, and resource requirements is paramount for a comprehensive approach. This paper explores various facets of India's population dynamics and addresses the hurdles in achieving sustainable growth and effective governance

Clinical profile of patients with prosthetic heart valve thrombosis undergoing fibrinolytic therapy and NYHA class as a predictor of outcome

Background: Prosthetic heart valve thrombosis (PHVT) is a potentially fatal complication of heart valve replacement with mechanical prostheses mainly due to thrombosis.Aim: The study aimed to evaluate the clinical profile of the patients presenting with PHVT undergoing fibrinolytic therapy and analyzing patients with respect to New York Heart Association (NYHA) functional class on presentation and its association with outcome of fibrinolytic therapy.Settings & design: This was prospective, observational study conducted from June, 2016 to April, 2017. Total 133 patients with prosthetic heart valve thrombosis were included. Materials and methods: Routine blood investigations included complete hemogram, liver and renal function tests. Prothrombin time with INR was done on admission. The diagnosis of PHVT was assessed by fluoroscopy and/or echocardiography (transthoracic/transesophageal). Follow-up at 6 months was scheduled for all patients.Statistical analysis: Parametric values between two groups were performed using the independent sample t-test or chi-square test, as appropriate. Univariate and multivariate logistic regression was used to find out factors associated with outcome.Results: All patients received fibrinolytic therapy in which 108 (81.2%) were treated with streptokinase and 25 (18.8%) were treated with urokinase. On presentation, 48.9% patients were in NYHA class III, 41.4% in NYHA class IV and 9.77% in NYHA class II. Fibrinolytic therapy was successful in 105 patients (78.9%) and it failed in 28 patients (21.1%). Mortality in NYHA class II was 0%, NYHA class III was 4.6% and in NYHA class IV was 23.6%. During 6 months follow up prosthetic heart valve thrombosis recurred in 12 (11.43%) patients.Conclusion: From our single centre experience, fibrinolytic therapy is fairly effective first line therapy for prosthetic heart valve thrombosis and NYHA functional class on presentation can predict the outcome of fibrinolytic therapy

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation