We give a new proof of the singular continuity of Minkowski’s $?$-function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of $3\times 3$ nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than $\log 2$.

Vowel deletion is frequent in the Chichicastenango dialect of K’iche’ (Maya). Whereas deletion in content words is reportedly predictable based on vowel quality, syllable structure and stress, deletion in function words is much more variable. This article investigates vowel deletion in a corpus of spontaneous, monologic speech. The results show that deletion in content words is highly regular, occurring to lax vowels in unstressed, CV syllables adjacent to the stressed syllable. A difference can be observed between vowels belonging to stress domain internal morphemes and extrametrical morphemes. Deletion in extrametrical morphemes is somewhat less regular, and does not occur in word-final syllables. In function words, vowel deletion is sensitive to similar conditions to those that affect content words, but is highly variable and is influenced by the phrase-level context.

This paper analyzes individual behavior in multi-armed bandit problems. We use a between-subjects experiment to implement four bandit problems that vary based on the horizon (indefinite or finite) and the number of bandit arms (two or three). We analyze commonly suggested strategies and find that an overwhelming majority of subjects are best fit by either a probabilistic “win-stay lose-shift” strategy or reinforcement learning. However, we show that subjects violate the assumptions of the probabilistic win-stay lose-shift strategy as switching depends on more than the previous outcome. We design two new “biased” strategies that adapt either reinforcement learning or myopic quantal response by incorporating a bias toward choosing the previous arm. We find that a majority of subjects are best fit by one of these two strategies but also find heterogeneity in subjects’ best-fitting strategies. We show that the performance of our biased strategies is robust to adapting popular strategies from other literatures (e.g., EWA and I-SAW) and using different selection criteria. Additionally, we find that our biased strategies best fit a majority of subjects when analyzing a new treatment with a new set of subjects.

Mammalian species richness is commonly highest at mid- to high elevations, but the accumulation of sediment that might bury and preserve skeletal remains generally occurs at lower elevations, leading to concerns that fossil assemblages are biased toward low-elevation taxa. Here, I use extant mammals as an analogue to test the basin-scale spatial overlap between species ranges and sediment sinks where burial and fossilization would be possible. Sediment sinks are estimated within five topographically complex regions in western North America by identifying areas with both a low slope and a high contributing area of runoff and are compared with point occurrences of mammals compiled from the Global Biodiversity Information Facility (GBIF). I find that, among the test areas, 82–96% of all species have occurrences that overlap with a sediment sink, despite common offsets in the elevations of maximum sink area and maximum species richness: summed across all test areas, 83% of species and 87% of total sediment sink area are found in the lowest 1000 m of the test areas. Although many other factors can act against the fossilization of terrestrial mammals, these results indicate that the spatial distribution of mammal species with respect to sediment sinks should not in itself impose a major bias at the basin scale.

This paper presents a comprehensive analysis of the frequency and severity of accidents involving electric vehicles (EVs) in comparison to internal combustion engine vehicles (ICEVs). It draws on extensive data from Norway from 2020 to 2023, a period characterised by significant EV adoption. We examine over two million registered EVs that collectively account for 28 billion kilometres of travel. In total we have analysed 139 billion kilometres of travel and close to 14,0000 accidents across all fuel types. We supplement this data with data from the Highway Loss Data Institute in the US and Association of British Insurers data in the UK as well as information from the Guy Carpenter large loss motor database.

A thorough analysis comparing accident frequency and severity of EVs with ICEVs in the literature to date has yet to be conducted, which this paper aims to address. This research will assist actuaries and analysts across various domains, including pricing, reserving and reinsurance considerations.

Our findings reveal a notable reduction in the frequency of accidents across all fuel types over time. Specifically, EVs demonstrate a lower accident frequency compared to ICEVs, a trend that may be attributed more to advancements in technology rather than the inherent characteristics of the fuel type, even when adjusted for COVID. Furthermore, our analysis indicates that EVs experience fewer accidents involving single units relative to non-EV and suggests a decrease in driver error and superior performance on regular road types.

Reduction in EV accident frequency of 17% and a change in the distribution of average severity with higher damage costs and lower injury costs leading to an overall reduction of 11%

However, it is important to note that when accidents do occur, the number of units involved as a proxy for severity involving EVs is marginally higher than those involving ICEVs. The average claim cost profile for EVs changes significantly with property damage claims being more expensive and bodily injury claims being less expensive for EVs.

Overall, our research concludes that EVs present a lower risk profile compared to their ICEV counterparts, highlighting the evolving landscape of vehicle safety in the context of increasing EV utilisation.