Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the {\em vector degree}, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.Comment: 33 page

Discrete logarithms in curves over finite fields

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields

Near-complete external difference families

We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.PostprintPeer reviewe

Reversed Dickson polynomials over finite fields

AbstractReversed Dickson polynomials over finite fields are obtained from Dickson polynomials Dn(x,a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear (APN) functions. We find several families of nontrivial RDPPs over finite fields; some of them arise from known APN functions and others are new. Among RDPPs on Fq with q<200, with only one exception, all belong to the RDPP families established in this paper

The acute transcriptome response of the midbrain/diencephalon to injury in the adult mummichog (\u3cem\u3eFundulus heteroclitus\u3c/em\u3e)

Adult fish produce new cells throughout their central nervous system during the course of their lives and maintain a tremendous capacity to repair damaged neural tissue. Much of the focus on understanding brain repair and regeneration in adult fish has been directed at regions of the brainstem and forebrain; however, the mesencephalon (midbrain) and diencephalon have received little attention. We sought to examine differential gene expression in the midbrain/diencephalon in response to injury in the adult fish using RNA-seq. Using the mummichog (Fundulus heteroclitus), we administered a mechanical lesion to the midbrain/diencephalon and examined differentially expressed genes (DEGs) at an acute recovery time of 1 h post-injury. Comparisons of whole transcriptomes derived from isolated RNA of intact and injured midbrain/diencephalic tissue identified 404 DEGs with the vast majority being upregulated. Using qPCR, we validated the upregulation of DEGs pim-2-like, syndecan-4-like, and cd83. Based on genes both familiar and novel regarding the adult brain response to injury, these data provide an extensive molecular profile giving insight into a range of cellular processes involved in the injury response of a brain regenerative-capable vertebrate

The acute transcriptome response of the midbrain/diencephalon to injury in the adult mummichog (\u3cem\u3eFundulus heteroclitus\u3c/em\u3e)

Adult fish produce new cells throughout their central nervous system during the course of their lives and maintain a tremendous capacity to repair damaged neural tissue. Much of the focus on understanding brain repair and regeneration in adult fish has been directed at regions of the brainstem and forebrain; however, the mesencephalon (midbrain) and diencephalon have received little attention. We sought to examine differential gene expression in the midbrain/diencephalon in response to injury in the adult fish using RNA-seq. Using the mummichog (Fundulus heteroclitus), we administered a mechanical lesion to the midbrain/diencephalon and examined differentially expressed genes (DEGs) at an acute recovery time of 1 h post-injury. Comparisons of whole transcriptomes derived from isolated RNA of intact and injured midbrain/diencephalic tissue identified 404 DEGs with the vast majority being upregulated. Using qPCR, we validated the upregulation of DEGs pim-2-like, syndecan-4-like, and cd83. Based on genes both familiar and novel regarding the adult brain response to injury, these data provide an extensive molecular profile giving insight into a range of cellular processes involved in the injury response of a brain regenerative-capable vertebrate

Methods for Evaluating the Content, Usability, and Efficacy of Commercial Mobile Health Apps

Commercial mobile apps for health behavior change are flourishing in the marketplace, but little evidence exists to support their use. This paper summarizes methods for evaluating the content, usability, and efficacy of commercially available health apps. Content analyses can be used to compare app features with clinical guidelines, evidence-based protocols, and behavior change techniques. Usability testing can establish how well an app functions and serves its intended purpose for a target population. Observational studies can explore the association between use and clinical and behavioral outcomes. Finally, efficacy testing can establish whether a commercial app impacts an outcome of interest via a variety of study designs, including randomized trials, multiphase optimization studies, and N-of-1 studies. Evidence in all these forms would increase adoption of commercial apps in clinical practice, inform the development of the next generation of apps, and ultimately increase the impact of commercial apps. Boudreaux, Rajani S Sadasivam, Sean P Mullen, Jennifer L Carey, Rashelle B Hayes, Eric Y Ding, Gary G Bennett, Sherry L Pagoto. Originally published in JMIR Mhealth and Uhealth (http://mhealth.jmir.org), 18.12.2017