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Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as an increase in the market's collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a "best value" portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better-established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market and to what extent. The results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies. [ABSTRACT FROM AUTHOR]

This paper uses established and recently introduced methods from the applied mathematics and statistics literature to study trends in the end-use sector and the capacity of low-carbon hydrogen projects in recent and upcoming decades. First, we examine distributions in plants over time for various end-use sectors and classify them according to metric discrepancy, observing clear similarity across all industry sectors. Next, we compare the distribution of usage sectors between different continents and examine the changes in sector distribution over time. Finally, we judiciously apply several regression models to analyse the association between various predictors and the capacity of global hydrogen projects. Across our experiments, we see a welcome exponential growth in the capacity of zero-carbon hydrogen plants and significant growth of new and planned hydrogen plants in the 2020's across every sector. [ABSTRACT FROM AUTHOR]

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance. [ABSTRACT FROM AUTHOR]

This paper applies new and recently introduced approaches to study trends in gun violence in the United States. We use techniques in both the time and frequency domain to provide a more complete understanding of gun violence dynamics. We analyze gun violence incidents on a state-by-state basis as recorded by the Gun Violence Archive. We have numerous specific phenomena of focus, including periodicity of incidents, locations in time where behavioral changes occur, and shifts in gun violence patterns since April 2020. First, we implement a recently introduced method of spectral density estimation for nonstationary time series to investigate periodicity on a state-by-state basis, including revealing where periodic behaviors change with time. We can also classify different patterns of behavioral changes among the states. We then aim to understand the most significant shifts in gun violence since numerous key events in 2020, including the COVID-19 pandemic, lockdowns, and periods of civil unrest. Our dual-domain analysis provides a more thorough understanding and challenges numerous widely held conceptions regarding the prevalence of gun violence incidents. [ABSTRACT FROM AUTHOR]

This paper uses established and recently introduced methods from the applied mathematics and statistics literature to study trends in the propagation and capacity of low-carbon hydrogen projects over the past two decades. First, we judiciously apply a regression model to estimate the association between various predictors and the capacity of global hydrogen projects. Next, we turn to the geographic propagation of low-carbon hydrogen projects, where we apply a recently introduced method to explore the geographic variance of hydrogen projects over time. Then, we demonstrate that most geographic regions display linear growth in cumulative plants and apply distance correlation to determine the nonlinear dependence between the two most prolific regions - North America and Europe. Finally, we study relationships between the propagation and capacity of green vs blue hydrogen over time, specifically, the time-varying regional consistency between the contribution of green vs blue plants to the total number and capacity of hydrogen plants. • We study a low-carbon hydrogen project database from the International Energy Agency. • An exponential increase in green hydrogen plant capacity is highlighted. • A dramatic closing between the capacity of green and non-green plants is revealed. • New insights revealing spatio-temporal trends in hydrogen propagation are shown. • Relationships between green and fossil-fuelled hydrogen plants are studied over time. [ABSTRACT FROM AUTHOR]

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 spatiotemporal trends in group composition. [ABSTRACT FROM AUTHOR]

Climate change will impact most, if not all, aspects of law and regulation. Law is a key mechanism of social governance, and it has a key role to play in regulating and addressing the causes and consequences of climate change. In the midst of the unfolding climate crisis law schools have a clear and pressing obligation to contribute to efforts to address climate change and its consequences by ensuring climate change law occupies an appropriate place in the law curriculum. In this article we consider the obligation of universities, and law schools in particular, to respond appropriately to the climate crisis in their program offerings. We begin by reflecting on the obligation of law schools and universities to contribute to the public good, an obligation often downplayed given the contemporary emphasis upon the 'job-readiness' of graduates and other neoliberal priorities. We then focus on the obligation of universities and law schools to respond appropriately to climate change. We examine the landscape of climate change law and identify the essential elements of climate change law for inclusion in the law curriculum. And we conclude by identifying examples of ways in which law schools are already incorporating climate change law into their law programs. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including climate change law, climate change and human rights in legal education, and intersection betweenTort Law and climate change.

This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided. [ABSTRACT FROM AUTHOR]

This paper introduces new methods to analyze the changing progression of COVID-19 cases to deaths in different waves of the pandemic. First, an algorithmic approach partitions each country or state's COVID-19 time series into a first wave and subsequent period. Next, offsets between case and death time series are learned for each country via a normalized inner product. Combining these with additional calculations, we can determine which countries have most substantially reduced the mortality rate of COVID-19. Finally, our paper identifies similarities in the trajectories of cases and deaths for European countries and U.S. states. Our analysis refines the popular conception that the mortality rate has greatly decreased throughout Europe during its second wave of COVID-19; instead, we demonstrate substantial heterogeneity throughout Europe and the U.S. The Netherlands exhibited the largest reduction of mortality, a factor of 16, followed by Denmark, France, Belgium, and other Western European countries, greater than both Eastern European countries and U.S. states. Some structural similarity is observed between Europe and the United States, in which Northeastern states have been the most successful in the country. Such analysis may help European countries learn from each other's experiences and differing successes to develop the best policies to combat COVID-19 as a collective unit. [ABSTRACT FROM AUTHOR]

In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century — the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises. • We test the persistence of market behaviours during four distinct financial crises. • We investigate the existence of "best-value" diversification portfolios. • We introduce a new linear operator to fairly compare sectors and stocks across crises. • We develop a random sampling framework to identify investor behavioural biases. • Remarkable persistence in over/under-performing sectors during crises is observed. [ABSTRACT FROM AUTHOR]

This paper introduces a mathematical framework for determining second surge behavior of COVID-19 cases in the United States. Within this framework, a flexible algorithmic approach selects a set of turning points for each state, computes distances between them, and determines whether each state is in (or over) a first or second surge. Then, appropriate distances between normalized time series are used to further analyze the relationships between case trajectories on a month-by-month basis. Our algorithm shows that 31 states are experiencing second surges, while four of the 10 largest states are still in their first surge, with case counts that have never decreased. This analysis can aid in highlighting the most and least successful state responses to COVID-19. [ABSTRACT FROM AUTHOR]

This paper proposes a cluster-based method to analyze the evolution of multivariate time series and applies this to the COVID-19 pandemic. On each day, we partition countries into clusters according to both their cases and death counts. The total number of clusters and individual countries' cluster memberships are algorithmically determined. We study the change in both quantities over time, demonstrating a close similarity in the evolution of cases and deaths. The changing number of clusters of the case counts precedes that of the death counts by 32 days. On the other hand, there is an optimal offset of 16 days with respect to the greatest consistency between cluster groupings, determined by a new method of comparing affinity matrices. With this offset in mind, we identify anomalous countries in the progression from COVID-19 cases to deaths. This analysis can aid in highlighting the most and least significant public policies in minimizing a country's COVID-19 mortality rate. [ABSTRACT FROM AUTHOR]

This paper introduces a new framework of algebraic equivalence relations between time series and new distance metrics between them, then applies these to investigate the Australian "Black Summer" bushfire season of 2019–2020. First, we introduce a general framework for defining equivalence between time series, heuristically intended to be equivalent if they differ only up to noise. Our first specific implementation is based on using change point algorithms and comparing statistical quantities such as mean or variance in stationary segments. We thus derive the existence of such equivalence relations on the space of time series, such that the quotient spaces can be equipped with a metrizable topology. Next, we illustrate specifically how to define and compute such distances among a collection of time series and perform clustering and additional analysis thereon. Then, we apply these insights to analyze air quality data across New South Wales, Australia, during the 2019–2020 bushfires. There, we investigate structural similarity with respect to this data and identify locations that were impacted anonymously by the fires relative to their location. This may have implications regarding the appropriate management of resources to avoid gaps in the defense against future fires. • A flexible framework of equivalence relations between time series is introduced. • We define and investigate new metrics via theoretical propositions and simulation. • Collections of time series may be analyzed in a cross-contextual setting. • We study air quality data across New South Wales during the 2019–2020 bushfires. • We reveal anomalous locations with respect to pollution data and geographic location. [ABSTRACT FROM AUTHOR]

Objectives: To compare the MRI texture profile of acetabular subchondral bone in normal, asymptomatic cam positive, and symptomatic cam-FAI hips and determine the accuracy of a machine learning model for discriminating between the three hip classes. Methods: A case–control, retrospective study was performed including 68 subjects (19 normal, 26 asymptomatic cam, 23 symptomatic cam-FAI). Acetabular subchondral bone of unilateral hip was contoured on 1.5 T MR images. Nine first-order 3D histogram and 16 s-order texture features were evaluated using specialized texture analysis software. Between-group differences were assessed using Kruskal–Wallis and Mann–Whitney U tests, and differences in proportions compared using chi-square and Fisher's exact tests. Gradient-boosted ensemble methods of decision trees were created and trained to discriminate between the three groups of hips, with percent accuracy calculated. Results: Sixty-eight subjects (median age 32 (28–40), 60 male) were evaluated. Significant differences among all three groups were identified with first-order (4 features, all p ≤ 0.002) and second-order (11 features, all p ≤ 0.002) texture analyses. First-order texture analysis could differentiate between control and cam positive hip groups (4 features, all p ≤ 0.002). Second-order texture analysis could additionally differentiate between asymptomatic cam and symptomatic cam-FAI groups (10 features, all p ≤ 0.02). Machine learning models demonstrated high classification accuracy of 79% (SD 16) for discriminating among all three groups. Conclusion: Normal, asymptomatic cam positive, and cam-FAI hips can be discriminated based on their MRI texture profile of subchondral bone using descriptive statistics and machine learning algorithms. Clinical relevance statement: Texture analysis can be performed on routine MR images of the hip and used to identify early changes in bone architecture, differentiating morphologically abnormal from normal hips, prior to onset of symptoms. Key Points: • MRI texture analysis is a technique for extracting quantitative data from routine MRI images. • MRI texture analysis demonstrates that there are different bone profiles between normal hips and those with femoroacetabular impingement. • Machine learning models can be used in conjunction with MRI texture analysis to accurately differentiate between normal hips and those with femoroacetabular impingement. [ABSTRACT FROM AUTHOR]

The article reports that Distance measures, inconsistency matrices and algorithms for the study of epidemiological and financial crises. Topics include methods for multivariate time series analysis and then applies these methods to understand the behavior of financial crises; and substantial homogeneity between the equity indices of countries during the Covid-19 pandemic.

We introduce new frameworks to study spatio-temporal patterns in carbon dioxide emissions, demographic trends and economic patterns across 50 countries over the past 50 years. Our analysis is broken up into four sections. First, we introduce a new method to classify countries into one of three characteristic emissions classes based on a one, two or three-segment piecewise linear model. We reveal that most countries are best represented by a piecewise linear model with one change point. Next, we perform a decade-by-decade study of carbon dioxide trajectories. There, we demonstrate notable changes in cluster structures in each decade. We then study the spatial propagation of emissions over time, highlighting a peak in spatial dispersion in 2000, beyond which there has been a gradual decline in spatial emissions variance over space. Finally, we use carbon dioxide, GDP, and population data and apply dimensionality reduction and clustering to group countries based on similarity in their real and carbon economies. • We analyse 50 years of CO2 emissions data across the 50 top global emitters. • Piecewise linear models determine three classes of country emissions. • A closer decade-by-decade study is performed. • We introduce a new mathematical measure of the geographic dispersion of emissions. • We investigate similarity among countries with respect to their real and carbon economies. [ABSTRACT FROM AUTHOR]

We study how to assess the potential benefit of diversifying an equity portfolio by investing within and across equity sectors. We analyse 20 years of US stock price data, which includes the global financial crisis (GFC) and the COVID-19 market crash, as well as periods of financial stability, to determine the 'all weather' nature of equity portfolios. We establish that one may use the leading eigenvalue of the cross-correlation matrix of log returns as well as graph-theoretic diagnostics such as modularity to quantify the collective behaviour of the market or a subset of it. We confirm that financial crises are characterised by a high degree of collective behaviour of equities, whereas periods of financial stability exhibit less collective behaviour. We argue that during times of increased collective behaviour, risk reduction via sector-based portfolio diversification is ineffective. Using the degree of collectivity as a proxy for the benefit of diversification, we perform an extensive sampling of equity portfolios to confirm the old financial adage that 30–40 stocks provide sufficient diversification. Using hierarchical clustering, we discover a 'best value' equity portfolio for diversification consisting of 36 equities sampled uniformly from 9 sectors. We further show that it is typically more beneficial to diversify across sectors rather than within. Our findings have implications for cost-conscious retail investors seeking broad diversification across equity markets. • We analyse 20 years of US daily stock price data. • PCA and graph theoretic diagnostics quantify the degree of financial market collectivity. • A new sampling procedure compares diversification within and across equity sectors. • A best-value portfolio consisting of 36 equities from 9 sectors is found. • Our portfolio diversification findings may provide cheap diversification for retail investors. [ABSTRACT FROM AUTHOR]