Elementary Set Theory

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics. The source files for the text can be found at https://github.com/RPMillspaugh/SetTheoryhttps://commons.und.edu/oers/1006/thumbnail.jp

Contingent Kernel Density Estimation

Kernel density estimation is a widely used method for estimating a distribution based on a sample of points drawn from that distribution. Generally, in practice some form of error contaminates the sample of observed points. Such error can be the result of imprecise measurements or observation bias. Often this error is negligible and may be disregarded in analysis. In cases where the error is non-negligible, estimation methods should be adjusted to reduce resulting bias. Several modifications of kernel density estimation have been developed to address specific forms of errors. One form of error that has not yet been addressed is the case where observations are nominally placed at the centers of areas from which the points are assumed to have been drawn, where these areas are of varying sizes. In this scenario, the bias arises because the size of the error can vary among points and some subset of points can be known to have smaller error than another subset or the form of the error may change among points. This paper proposes a “contingent kernel density estimation” technique to address this form of error. This new technique adjusts the standard kernel on a point-by-point basis in an adaptive response to changing structure and magnitude of error. In this paper, equations for our contingent kernel technique are derived, the technique is validated using numerical simulations, and an example using the geographic locations of social networking users is worked to demonstrate the utility of the method

SNAPSHOT USA 2019 : a coordinated national camera trap survey of the United States

This article is protected by copyright. All rights reserved.With the accelerating pace of global change, it is imperative that we obtain rapid inventories of the status and distribution of wildlife for ecological inferences and conservation planning. To address this challenge, we launched the SNAPSHOT USA project, a collaborative survey of terrestrial wildlife populations using camera traps across the United States. For our first annual survey, we compiled data across all 50 states during a 14-week period (17 August - 24 November of 2019). We sampled wildlife at 1509 camera trap sites from 110 camera trap arrays covering 12 different ecoregions across four development zones. This effort resulted in 166,036 unique detections of 83 species of mammals and 17 species of birds. All images were processed through the Smithsonian's eMammal camera trap data repository and included an expert review phase to ensure taxonomic accuracy of data, resulting in each picture being reviewed at least twice. The results represent a timely and standardized camera trap survey of the USA. All of the 2019 survey data are made available herein. We are currently repeating surveys in fall 2020, opening up the opportunity to other institutions and cooperators to expand coverage of all the urban-wild gradients and ecophysiographic regions of the country. Future data will be available as the database is updated at eMammal.si.edu/snapshot-usa, as well as future data paper submissions. These data will be useful for local and macroecological research including the examination of community assembly, effects of environmental and anthropogenic landscape variables, effects of fragmentation and extinction debt dynamics, as well as species-specific population dynamics and conservation action plans. There are no copyright restrictions; please cite this paper when using the data for publication.Publisher PDFPeer reviewe

Mammal responses to global changes in human activity vary by trophic group and landscape

Wildlife must adapt to human presence to survive in the Anthropocene, so it is critical to understand species responses to humans in different contexts. We used camera trapping as a lens to view mammal responses to changes in human activity during the COVID-19 pandemic. Across 163 species sampled in 102 projects around the world, changes in the amount and timing of animal activity varied widely. Under higher human activity, mammals were less active in undeveloped areas but unexpectedly more active in developed areas while exhibiting greater nocturnality. Carnivores were most sensitive, showing the strongest decreases in activity and greatest increases in nocturnality. Wildlife managers must consider how habituation and uneven sensitivity across species may cause fundamental differences in human–wildlife interactions along gradients of human influence.Peer reviewe

Inter-individual variability of stone marten behavioral responses to a highway

Efforts to reduce the negative impacts of roads on wildlife may be hindered if individuals within the population vary widely in their responses to roads and mitigation strategies ignore this variability. This knowledge is particularly important for medium-sized carnivores as they are vulnerable to road mortality, while also known to use available road passages (e.g., drainage culverts) for safely crossing highways. Our goal in this study was to assess whether this apparently contradictory pattern of high road-kill numbers associated with a regular use of road passages is attributable to the variation in behavioral responses toward the highway between individuals. We investigated the responses of seven radio-tracked stone martens (Martes foina) to a highway by measuring their utilization distribution, response turning angles and highway crossing patterns. We compared the observed responses to simulated movement parameterized by the observed space use and movement characteristics of each individual, but naı¨ve to the presence of the highway. Our results suggested that martens demonstrate a diversity of responses to the highway, including attraction, indifference, or avoidance. Martens also varied in their highway crossing patterns, with some crossing repeatedly at the same location (often coincident with highway passages). We suspect that the response variability derives from the individual’s familiarity of the landscape, including their awareness of highway passage locations. Because of these variable yet potentially attributable responses, we support the use of exclusionary fencing to guide transient (e.g., dispersers) individuals to existing passages to reduce the road-kill risk

Changes in fire regimes since the last glacial maximum: an assessment based on a global synthesis and analysis of charcoal data

Fire activity has varied globally and continuously since the last glacial maximum (LGM) in response to long-term changes in global climate and shorter-term regional changes in climate, vegetation, and human land use. We have synthesized sedimentary charcoal records of biomass burning since the LGM and present global maps showing changes in fire activity for time slices during the past 21,000 years (as differences in charcoal accumulation values compared to pre-industrial). There is strong broad-scale coherence in fire activity after the LGM, but spatial heterogeneity in the signals increases thereafter. In North America, Europe and southern South America, charcoal records indicate less-than-present fire activity during the deglacial period, from 21,000 to ?11,000 cal yr BP. In contrast, the tropical latitudes of South America and Africa show greater-than-present fire activity from ?19,000 to ?17,000 cal yr BP and most sites from Indochina and Australia show greater-than-present fire activity from 16,000 to ?13,000 cal yr BP. Many sites indicate greater-than-present or near-present activity during the Holocene with the exception of eastern North America and eastern Asia from 8,000 to ?3,000 cal yr BP, Indonesia and Australia from 11,000 to 4,000 cal yr BP, and southern South America from 6,000 to 3,000 cal yr BP where fire activity was less than present. Regional coherence in the patterns of change in fire activity was evident throughout the post-glacial period. These complex patterns can largely be explained in terms of large-scale climate controls modulated by local changes in vegetation and fuel load