arXiv subjects

Howard Bondell

Publications and source records attributed to Howard Bondell.

24 records · Page 2Linked to original sources

arXiv2022

In search of peak human athletic potential: A mathematical investigation

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect", where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics, that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatio-temporal trends in group composition.

physics.soc-ph↗

arXiv2022

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

physics.soc-ph↗

arXiv2021

Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States

This paper introduces a novel approach to spatio-temporal data analysis using metric geometry to study the propagation of COVID-19 across the United States. Using a geodesic Wasserstein metric, we analyse discrepancies between the density functions of new case counts on any given day, incorporating the geographic spread of cases. First, we apply this to identify the periods during which the changes in the geographic distribution of COVID-19 were most profound. The greatest shift occurred between May and June of 2020, when COVID-19 shifted from mostly dominating the Northeastern states to a wider distribution across the country. We support our findings with a new measure of the extent of geodesic variance of a distribution, demonstrating that the geographic imprint of COVID-19 was most concentrated in May 2020. Next, we investigate whether the epidemic exhibited meaningful patterns of spatial reversion, where similar geographic distributions return later. We identify broad similarity between the spread of COVID-19 across the US between the second and third waves, and to a lesser extent, the reemergence of the first wave's Northeastern dominance closer to the present day. This methodology could provide new insights for analysts to monitor the dynamical spread of epidemics and enable regional policymakers to protect their localities. More broadly, the framework we introduce could be applied to a variety of problems evolving over space and time.

physics.soc-ph↗

arXiv2021

On local intrinsic dimensionality of deformation in complex materials

We propose a new metric called s-LID based on the concept of Local Intrinsic Dimensionality to identify and quantify hierarchies of kinematic patterns in heterogeneous media. s-LID measures how outlying a grain's motion is relative to its s nearest neighbors in displacement state space. To demonstrate the merits of s-LID over the conventional measure of strain, we apply it to data on individual grain motions in a set of deforming granular materials. Several new insights into the evolution of failure are uncovered. First, s-LID reveals a hierarchy of concurrent deformation bands that prevails throughout loading history. These structures vary not only in relative dominance but also spatial and kinematic scales. Second, in the nascent stages of the pre-failure regime, s-LID uncovers a set of system-spanning, criss-crossing bands: microbands for small s and embryonic-shearbands at large s, with the former being dominant. At the opposite extreme, in the failure regime, fully formed shearbands at large s dominate over the microbands. The novel patterns uncovered from s-LID contradict the common belief of a causal sequence where a subset of microbands coalesce and/or grow to form shearbands. Instead, s-LID suggests that the deformation of the sample in the lead-up to failure is governed by a complex symbiosis among these different coexisting structures, which amplifies and promotes the progressive dominance of the embryonic-shearbands over microbands. Third, we probed this transition from the microband-dominated regime to the shearband-dominated regime by systematically suppressing grain rotations. We found particle rotation to be an essential enabler of the transition to the shearband-dominated regime. When grain rotations are completely suppressed, this transition is prevented: microbands and shearbands coexist in relative parity.

cond-mat.mtrl-sci↗

arXiv2019

Variational approximations using Fisher divergence

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte Carlo, but these can be expensive when the data set is large and/or the model is complex, so more efficient variational approximations have recently received considerable attention. The traditional variational methods, that seek to minimize the Kullback--Leibler divergence between the posterior and a relatively simple parametric family, provide accurate and efficient estimation of the posterior mean, but often does not capture other moments, and have limitations in terms of the models to which they can be applied. Here we propose the construction of variational approximations based on minimizing the Fisher divergence, and develop an efficient computational algorithm that can be applied to a wide range of models without conjugacy or potentially unrealistic mean-field assumptions. We demonstrate the superior performance of the proposed method for the benchmark case of logistic regression.

stat.ML↗

arXiv2018

Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining if parameters associated with correlated predictors should be shrunk together or kept apart. Under suitable conditions, we prove that this empirical Bayes posterior concentrates around the true sparse parameter at the optimal rate asymptotically. A simplified version of a shotgun stochastic search algorithm is employed to implement the variable selection procedure, and we show, via simulation experiments across different settings and a real-data application, the favorable performance of the proposed method compared to existing methods.

stat.ME↗