Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and Autoencoders

We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is a random variable whose components are independent and have a fourth moment strictly less than that of a standard Gaussian random variable and $\eta$ is an $n$-dimensional Gaussian random variable with unknown covariance $\Sigma$: We give an algorithm that provable recovers $A$ and $\Sigma$ up to an additive $\epsilon$ and whose running time and sample complexity are polynomial in $n$ and $1 / \epsilon$. To accomplish this, we introduce a novel "quasi-whitening" step that may be useful in other contexts in which the covariance of Gaussian noise is not known in advance. We also give a general framework for finding all local optima of a function (given an oracle for approximately finding just one) and this is a crucial step in our algorithm, one that has been overlooked in previous attempts, and allows us to control the accumulation of error when we find the columns of $A$ one by one via local search

Structural and compositional properties of 2D CH3NH3PbI3 hybrid halide perovskite: a DFT study

Two-dimensional (2D) hybrid halide perovskites have been scrutinized as candidate materials for solar cells because of their tunable structural and compositional properties. Results based on density functional theory demonstrate its thickness-dependent stability. We have observed that the bandgap decreases from the mono- to quad-layer because of the transformation from 2D towards 3D. Due to the transformation, the carrier mobility is lowered with the corresponding smaller effective mass. On the other hand, the multilayer structures have good optical properties with an absorption coefficient of about 105 cm−1. The calculated absorption spectra lie between 248 nm and 496 nm, leading to optical activity of the 2D multilayer CH3NH3PbI3 systems in the visible and ultraviolet regions. The strength of the optical absorption increases with an increase in thickness. Overall results from this theoretical study suggest that this 2D multilayer CH3NH3PbI3 is a good candidate for photovoltaic and optoelectronic device applications

Biologics for the treatment of pyoderma gangrenosum in ulcerative colitis

Pyoderma gangrenosum (PG) is an uncommon extra-intestinal manifestation of inflammatory bowel disease (IBD). Despite limited published literature, biologics have caused a paradigm shift in the management of this difficult-to-treat skin condition. The clinical data and outcomes of three patients with active ulcerative colitis and concurrent PG treated with biologics (infliximab two and adalimumab one) are reviewed in this report. Biologics were added because of the sub-optimal response of the colonic symptoms and skin lesions to parenteral hydrocortisone therapy. All three patients showed a dramatic response to the addition of the biologics. In view of the rapid healing of the skin lesions, superior response rate, and the additional benefit of improvement in the underlying colonic disease following treatment, anti-tumor necrosis factor blockers should be considered as a first line therapy in the management of PG with underlying IBD

COVID-19 Rapid Antigen Test: Role in Screening Prior to Gastrointestinal Endoscopy

Background/Aims The severe acute respiratory syndrome coronavirus 2 pandemic has affected the gastrointestinal (GI) endoscopy units globally owing to the risk of transmission. We present our data on the use of rapid antigen test (RAT) as a screening tool prior to endoscopy to prevent the transmission of coronavirus disease (COVID-19). Methods This study was a retrospective analysis of patients who underwent any GI endoscopic procedure from July 2020 to October 2020 at a tertiary referral center in New Delhi, India. All patients underwent screening for COVID-19 using RAT, and endoscopy was performed only when the RAT was negative. The data are presented as numbers and percentages. Results A total of 3,002 endoscopic procedures were performed during the study period. Only one endoscopic procedure was performed in a COVID-19 positive patient. A total of 53 healthcare workers were involved in conducting these procedures. Only 2 healthcare workers (3.8%) were diagnosed COVID-19 positive, presumably due to community-acquired infection, during this period. Conclusions The COVID-19 RAT is easily usable as a simple screening tool prior to GI endoscopy during the COVID-19 pandemic

Nations within a nation: variations in epidemiological transition across the states of India, 1990–2016 in the Global Burden of Disease Study

18% of the world's population lives in India, and many states of India have populations similar to those of large countries. Action to effectively improve population health in India requires availability of reliable and comprehensive state-level estimates of disease burden and risk factors over time. Such comprehensive estimates have not been available so far for all major diseases and risk factors. Thus, we aimed to estimate the disease burden and risk factors in every state of India as part of the Global Burden of Disease (GBD) Study 2016

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

Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and Autoencoders

We present a new algorithm for independent component analysis which has provable performance guarantees. In particular, suppose we are given samples of the form y=Ax+η where A is an unknown but non-singular n×n matrix, x is a random variable whose coordinates are independent and have a fourth order moment strictly less than that of a standard Gaussian random variable and η is an n-dimensional Gaussian random variable with unknown covariance Σ: We give an algorithm that provably recovers A and Σ up to an additive ϵϵ and whose running time and sample complexity are polynomial in n and 1/ϵ. To accomplish this, we introduce a novel “quasi-whitening” step that may be useful in other applications where there is additive Gaussian noise whose covariance is unknown. We also give a general framework for finding all local optima of a function (given an oracle for approximately finding just one) and this is a crucial step in our algorithm, one that has been overlooked in previous attempts, and allows us to control the accumulation of error when we find the columns of A one by one via local search

Finding overlapping communities in social networks: Toward a rigorous approach

A community in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social, technological, biological, etc. For many years algorithms for finding communities implicitly assumed communities are nonoverlapping (leading to use of clustering-based approaches) but there is increasing interest in finding overlapping communities. A barrier to finding communities is that the solution concept is often defined in terms of an NP-complete problem such as Clique or Hierarchical Clustering. This paper seeks to initiate a rigorous approach to the problem of finding overlapping communities, where "rigorous" means that we clearly state the following: (a) the object sought by our algorithm (b) the assumptions about the underlying network (c) the (worst-case) running time. The key contribution of this work is the distillation of the prior sociology studies into general assumptions that at once accord well with sociology research and the current understanding of social networks while allowing computationally efficient solutions. Our assumptions about the network lie between worst-case and average-case. An average-case analysis would require a precise probabilistic model of the network, on which there is currently no consensus. However, some plausible assumptions about network parameters can be gleaned from a long body of work in the sociology community spanning five decades focusing on the study of individual communities and ego-centric networks (in graph theoretic terms, this is the subgraph induced on a node's neighborhood). Thus our assumptions are somewhat "local" in nature. Nevertheless they suffice to permit a rigorous analysis of running time of algorithms that recover global structure. Our algorithms use random sampling similar to that in property testing and algorithms for dense graphs. We note however that our networks are not necessarily dense graphs, not even in local neighborhoods. Our algorithms explore a local-global relationship between ego-centric and socio-centric networks that we hope will provide a fruitful framework for future work both in computer science and sociology