On Some Properties of Quadratic APN Functions of a Special Form

In a recent paper, it is shown that functions of the form $L_1(x^3)+L_2(x^9)$, where $L_1$ and $L_2$ are linear, are a good source for construction of new infinite families of APN functions. In the present work we study necessary and sufficient conditions for such functions to be APN

A note on mean volume and surface densities for a class of birth-and-growth stochastic processes

Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as well as the so called mean \emph{extended} volume and surface densities, may be studied in terms of relevant quantities characterizing the process. We extend here known results in the Poissonian case to a wider class of birth-and-growth stochastic processes, proving in particular the absolute continuity of the random time of capture of a point $x\in\R^d$ by processes of this class.Comment: 11 pages; revised version for publication: proof simplified, added new resul

A cautionary note on using the scale prior for the parameter N of a binomial distribution

Statistical analysis of ecological data may require the estimation of the size of a population, or of the number of species with a certain population. This task frequently reduces to estimating the discrete parameter N representing the number of trials in a binomial distribution. In Bayesian methods, there has been a substantial amount of discussion on how to select the prior for N. We propose a prior for N based on an objective measure of the worth that each value of N has in being included in the model space. This prior is compared (through the analysis of the popular snowshoe hare dataset) with the scale prior which, in our opinion, cannot be understood from solid objective considerations

Science and Theology: A Working Synthesis

Theologians and scientists, working independently, have provided worldviews that lead to questions about the meaning of existence and human life. When these disciplines interact, opportunity exists for more profound insight. Two individuals, Johannes Kepler in the sixteenth century and Pierre Teilhard de Chardin in the twentieth, attempted theological reconstructions based on revolutionary theories of their eras. Informed by a fierce faith in God and a rigorous pursuit of truth derived from the scientific method, their attempts at synthesizing these fields led to results that were unexpected, even unwanted. Yet they provide lessons in the present age for interpretations of the new discoveries and the responsibility of humankind to play an active role in the modern creation story

Truthiness or Evidence-Based Reasoning? A Critical Thinking Exercise for the First Year Experience

Barriers to Critical Thinking Biases Emotional reasoning (truthiness) Overuse of personal experience Small case studieshttps://digitalscholarship.unlv.edu/btp_expo/1045/thumbnail.jp