A few more Lonely Runners

Lonely Runner Conjecture, proposed by J\"{o}rg M. Wills and so nomenclatured by Luis Goddyn, has been an object of interest since it was first conceived in 1967 : Given positive integers $k$ and $n_1,n_2,\ldots,n_k$ there exists a positive real number $t$ such that the distance of $t\cdot n_j$ to the nearest integer is at least $\frac{1}{k+1}$, $\forall~~1\leq j\leq k$. In a recent article Beck, Hosten and Schymura described the Lonely Runner polyhedron and provided a polyhedral approach to identifying families of lonely runner instances. We revisit the Lonely Runner polyhedron and highlight some new families of instances satisfying the conjecture. In addition, we relax the sufficiency of existence of an integer point in the Lonely Runner polyhedron to prove the conjecture. Specifically, we propose that it suffices to show the existence of a lattice point of certain superlattices of the integer lattice in the Lonely Runner polyhedron

Online Universal Dirichlet Factor Portfolios

We revisit the online portfolio allocation problem and propose universal portfolios that use factor weighing to produce portfolios that out-perform uniform dirichlet allocation schemes. We show a few analytical results on the lower bounds of portfolio growth when the returns are known to follow a factor model. We also show analytically that factor weighted dirichlet sampled portfolios dominate the wealth generated by uniformly sampled dirichlet portfolios. We corroborate our analytical results with empirical studies on equity markets that are known to be driven by factors

Unsupervised Early Exit in DNNs with Multiple Exits

Deep Neural Networks (DNNs) are generally designed as sequentially cascaded differentiable blocks/layers with a prediction module connected only to its last layer. DNNs can be attached with prediction modules at multiple points along the backbone where inference can stop at an intermediary stage without passing through all the modules. The last exit point may offer a better prediction error but also involves more computational resources and latency. An exit point that is `optimal' in terms of both prediction error and cost is desirable. The optimal exit point may depend on the latent distribution of the tasks and may change from one task type to another. During neural inference, the ground truth of instances may not be available and error rates at each exit point cannot be estimated. Hence one is faced with the problem of selecting the optimal exit in an unsupervised setting. Prior works tackled this problem in an offline supervised setting assuming that enough labeled data is available to estimate the error rate at each exit point and tune the parameters for better accuracy. However, pre-trained DNNs are often deployed in new domains for which a large amount of ground truth may not be available. We model the problem of exit selection as an unsupervised online learning problem and use bandit theory to identify the optimal exit point. Specifically, we focus on Elastic BERT, a pre-trained multi-exit DNN to demonstrate that it `nearly' satisfies the Strong Dominance (SD) property making it possible to learn the optimal exit in an online setup without knowing the ground truth labels. We develop upper confidence bound (UCB) based algorithm named UEE-UCB that provably achieves sub-linear regret under the SD property. Thus our method provides a means to adaptively learn domain-specific optimal exit points in multi-exit DNNs. We empirically validate our algorithm on IMDb and Yelp datasets.Comment: To be presented at International conference on AI-ML system

Melt-Spun SiGe Nano-Alloys: Microstructural Engineering Towards High Thermoelectric Efficiency

Silicon-germanium (SiGe) alloys are prominent high-temperature thermoelectric (TE) materials used as a powering source for deep space applications. In this work, we employed rapid cooling rates for solidification by melt-spinning and rapid heating rates for bulk consolidation employing spark plasma sintering to synthesize high-performance p-type SiGe nano-alloys. The current methodology exhibited a TE figure-of-merit (ZT) approximate to 0.94 at 1123 K for a higher cooling rate of similar to 3.0 x 10(7) K/s. This corresponds to approximate to 88% enhancement in ZT when compared with currently used radioisotope thermoelectric generators (RTGs) in space flight missions, approximate to 45% higher than pressure-sintered p-type alloys, which results in a higher output power density, and TE conversion efficiency (eta) approximate to 8% of synthesized SiGe nano-alloys estimated using a cumulative temperature dependence (CTD) model. The ZT enhancement is driven by selective scattering of phonons rather than of charge carriers by the high density of grain boundaries with random orientations and induced lattice-scale defects, resulting in a substantial reduction of lattice thermal conductivity and high power factor. The TE characteristics of synthesized alloys presented using the constant property model (CPM) and CTD model display their high TE performance in high-temperature regimes along with wide suitability of segmentation with different mid-temperature TE materials

Measuring routine childhood vaccination coverage in 204 countries and territories, 1980-2019 : a systematic analysis for the Global Burden of Disease Study 2020, Release 1

Background Measuring routine childhood vaccination is crucial to inform global vaccine policies and programme implementation, and to track progress towards targets set by the Global Vaccine Action Plan (GVAP) and Immunization Agenda 2030. Robust estimates of routine vaccine coverage are needed to identify past successes and persistent vulnerabilities. Drawing from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2020, Release 1, we did a systematic analysis of global, regional, and national vaccine coverage trends using a statistical framework, by vaccine and over time. Methods For this analysis we collated 55 326 country-specific, cohort-specific, year-specific, vaccine-specific, and dosespecific observations of routine childhood vaccination coverage between 1980 and 2019. Using spatiotemporal Gaussian process regression, we produced location-specific and year-specific estimates of 11 routine childhood vaccine coverage indicators for 204 countries and territories from 1980 to 2019, adjusting for biases in countryreported data and reflecting reported stockouts and supply disruptions. We analysed global and regional trends in coverage and numbers of zero-dose children (defined as those who never received a diphtheria-tetanus-pertussis [DTP] vaccine dose), progress towards GVAP targets, and the relationship between vaccine coverage and sociodemographic development. Findings By 2019, global coverage of third-dose DTP (DTP3; 81.6% [95% uncertainty interval 80.4-82 .7]) more than doubled from levels estimated in 1980 (39.9% [37.5-42.1]), as did global coverage of the first-dose measles-containing vaccine (MCV1; from 38.5% [35.4-41.3] in 1980 to 83.6% [82.3-84.8] in 2019). Third- dose polio vaccine (Pol3) coverage also increased, from 42.6% (41.4-44.1) in 1980 to 79.8% (78.4-81.1) in 2019, and global coverage of newer vaccines increased rapidly between 2000 and 2019. The global number of zero-dose children fell by nearly 75% between 1980 and 2019, from 56.8 million (52.6-60. 9) to 14.5 million (13.4-15.9). However, over the past decade, global vaccine coverage broadly plateaued; 94 countries and territories recorded decreasing DTP3 coverage since 2010. Only 11 countries and territories were estimated to have reached the national GVAP target of at least 90% coverage for all assessed vaccines in 2019. Interpretation After achieving large gains in childhood vaccine coverage worldwide, in much of the world this progress was stalled or reversed from 2010 to 2019. These findings underscore the importance of revisiting routine immunisation strategies and programmatic approaches, recentring service delivery around equity and underserved populations. Strengthening vaccine data and monitoring systems is crucial to these pursuits, now and through to 2030, to ensure that all children have access to, and can benefit from, lifesaving vaccines. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

The global burden of adolescent and young adult cancer in 2019 : a systematic analysis for the Global Burden of Disease Study 2019

Background In estimating the global burden of cancer, adolescents and young adults with cancer are often overlooked, despite being a distinct subgroup with unique epidemiology, clinical care needs, and societal impact. Comprehensive estimates of the global cancer burden in adolescents and young adults (aged 15-39 years) are lacking. To address this gap, we analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, with a focus on the outcome of disability-adjusted life-years (DALYs), to inform global cancer control measures in adolescents and young adults. Methods Using the GBD 2019 methodology, international mortality data were collected from vital registration systems, verbal autopsies, and population-based cancer registry inputs modelled with mortality-to-incidence ratios (MIRs). Incidence was computed with mortality estimates and corresponding MIRs. Prevalence estimates were calculated using modelled survival and multiplied by disability weights to obtain years lived with disability (YLDs). Years of life lost (YLLs) were calculated as age-specific cancer deaths multiplied by the standard life expectancy at the age of death. The main outcome was DALYs (the sum of YLLs and YLDs). Estimates were presented globally and by Socio-demographic Index (SDI) quintiles (countries ranked and divided into five equal SDI groups), and all estimates were presented with corresponding 95% uncertainty intervals (UIs). For this analysis, we used the age range of 15-39 years to define adolescents and young adults. Findings There were 1.19 million (95% UI 1.11-1.28) incident cancer cases and 396 000 (370 000-425 000) deaths due to cancer among people aged 15-39 years worldwide in 2019. The highest age-standardised incidence rates occurred in high SDI (59.6 [54.5-65.7] per 100 000 person-years) and high-middle SDI countries (53.2 [48.8-57.9] per 100 000 person-years), while the highest age-standardised mortality rates were in low-middle SDI (14.2 [12.9-15.6] per 100 000 person-years) and middle SDI (13.6 [12.6-14.8] per 100 000 person-years) countries. In 2019, adolescent and young adult cancers contributed 23.5 million (21.9-25.2) DALYs to the global burden of disease, of which 2.7% (1.9-3.6) came from YLDs and 97.3% (96.4-98.1) from YLLs. Cancer was the fourth leading cause of death and tenth leading cause of DALYs in adolescents and young adults globally. Interpretation Adolescent and young adult cancers contributed substantially to the overall adolescent and young adult disease burden globally in 2019. These results provide new insights into the distribution and magnitude of the adolescent and young adult cancer burden around the world. With notable differences observed across SDI settings, these estimates can inform global and country-level cancer control efforts. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

The global burden of cancer attributable to risk factors, 2010-19 : a systematic analysis for the Global Burden of Disease Study 2019

Background Understanding the magnitude of cancer burden attributable to potentially modifiable risk factors is crucial for development of effective prevention and mitigation strategies. We analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 to inform cancer control planning efforts globally. Methods The GBD 2019 comparative risk assessment framework was used to estimate cancer burden attributable to behavioural, environmental and occupational, and metabolic risk factors. A total of 82 risk-outcome pairs were included on the basis of the World Cancer Research Fund criteria. Estimated cancer deaths and disability-adjusted life-years (DALYs) in 2019 and change in these measures between 2010 and 2019 are presented. Findings Globally, in 2019, the risk factors included in this analysis accounted for 4.45 million (95% uncertainty interval 4.01-4.94) deaths and 105 million (95.0-116) DALYs for both sexes combined, representing 44.4% (41.3-48.4) of all cancer deaths and 42.0% (39.1-45.6) of all DALYs. There were 2.88 million (2.60-3.18) risk-attributable cancer deaths in males (50.6% [47.8-54.1] of all male cancer deaths) and 1.58 million (1.36-1.84) risk-attributable cancer deaths in females (36.3% [32.5-41.3] of all female cancer deaths). The leading risk factors at the most detailed level globally for risk-attributable cancer deaths and DALYs in 2019 for both sexes combined were smoking, followed by alcohol use and high BMI. Risk-attributable cancer burden varied by world region and Socio-demographic Index (SDI), with smoking, unsafe sex, and alcohol use being the three leading risk factors for risk-attributable cancer DALYs in low SDI locations in 2019, whereas DALYs in high SDI locations mirrored the top three global risk factor rankings. From 2010 to 2019, global risk-attributable cancer deaths increased by 20.4% (12.6-28.4) and DALYs by 16.8% (8.8-25.0), with the greatest percentage increase in metabolic risks (34.7% [27.9-42.8] and 33.3% [25.8-42.0]). Interpretation The leading risk factors contributing to global cancer burden in 2019 were behavioural, whereas metabolic risk factors saw the largest increases between 2010 and 2019. Reducing exposure to these modifiable risk factors would decrease cancer mortality and DALY rates worldwide, and policies should be tailored appropriately to local cancer risk factor burden. Copyright (C) 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe

Global, regional, and national sex differences in the global burden of tuberculosis by HIV status, 1990–2019: results from the Global Burden of Disease Study 2019

Background Tuberculosis is a major contributor to the global burden of disease, causing more than a million deaths annually. Given an emphasis on equity in access to diagnosis and treatment of tuberculosis in global health targets, evaluations of differences in tuberculosis burden by sex are crucial. We aimed to assess the levels and trends of the global burden of tuberculosis, with an emphasis on investigating differences in sex by HIV status for 204 countries and territories from 1990 to 2019. Methods We used a Bayesian hierarchical Cause of Death Ensemble model (CODEm) platform to analyse 21 505 site-years of vital registration data, 705 site-years of verbal autopsy data, 825 site-years of sample-based vital registration data, and 680 site-years of mortality surveillance data to estimate mortality due to tuberculosis among HIV-negative individuals. We used a population attributable fraction approach to estimate mortality related to HIV and tuberculosis coinfection. A compartmental meta-regression tool (DisMod-MR 2.1) was then used to synthesise all available data sources, including prevalence surveys, annual case notifications, population-based tuberculin surveys, and tuberculosis cause-specific mortality, to produce estimates of incidence, prevalence, and mortality that were internally consistent. We further estimated the fraction of tuberculosis mortality that is attributable to independent effects of risk factors, including smoking, alcohol use, and diabetes, for HIV-negative individuals. For individuals with HIV and tuberculosis coinfection, we assessed mortality attributable to HIV risk factors including unsafe sex, intimate partner violence (only estimated among females), and injection drug use. We present 95% uncertainty intervals for all estimates. Findings Globally, in 2019, among HIV-negative individuals, there were 1.18 million (95% uncertainty interval 1.08-1.29) deaths due to tuberculosis and 8.50 million (7.45-9.73) incident cases of tuberculosis. Among HIV-positive individuals, there were 217 000 (153 000-279 000) deaths due to tuberculosis and 1.15 million (1.01-1.32) incident cases in 2019. More deaths and incident cases occurred in males than in females among HIV-negative individuals globally in 2019, with 342 000 (234 000-425 000) more deaths and 1.01 million (0.82-1.23) more incident cases in males than in females. Among HIV-positive individuals, 6250 (1820-11 400) more deaths and 81 100 (63 300-100 000) more incident cases occurred among females than among males in 2019. Age-standardised mortality rates among HIV-negative males were more than two times greater in 105 countries and age-standardised incidence rates were more than 1.5 times greater in 74 countries than among HIV-negative females in 2019. The fraction of global tuberculosis deaths among HIV-negative individuals attributable to alcohol use, smoking, and diabetes was 4.27 (3.69-5.02), 6.17 (5.48-7.02), and 1.17 (1.07-1.28) times higher, respectively, among males than among females in 2019. Among individuals with HIV and tuberculosis coinfection, the fraction of mortality attributable to injection drug use was 2.23 (2.03-2.44) times greater among males than females, whereas the fraction due to unsafe sex was 1.06 (1.05-1.08) times greater among females than males. Interpretation As countries refine national tuberculosis programmes and strategies to end the tuberculosis epidemic, the excess burden experienced by males is important. Interventions are needed to actively communicate, especially to men, the importance of early diagnosis and treatment. These interventions should occur in parallel with efforts to minimise excess HIV burden among women in the highest HIV burden countries that are contributing to excess HIV and tuberculosis coinfection burden for females. Placing a focus on tuberculosis burden among HIV-negative males and HIV and tuberculosis coinfection among females might help to diminish the overall burden of tuberculosis. This strategy will be crucial in reaching both equity and burden targets outlined by global health milestone