First-Order Concatenation Theory with Bounded Quantifiers

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.Comment: arXiv admin note: text overlap with arXiv:1804.0636

A Friendly Introduction to Mathematical Logic

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition’s treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel’s First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises. Available on Lulu.com, IndiBound.com, and Amazon.com, as well as wholesale through Ingram Content Group.https://knightscholar.geneseo.edu/geneseo-authors/1005/thumbnail.jp

Reproductive strategy and singing activity: blue tit and great tit compared

The costs and benefits of bird song are likely to vary among species, and different singing patterns may reflect differences in reproductive strategies. We compared temporal patterns of singing activity in two songbird species, the blue tit (Cyanistes caeruleus) and the great tit (Parus major). The two species live side by side year round, and they have similar breeding ecology and similar rates of extra-pair paternity. However, they differ in two aspects of reproductive strategy that may have an influence on song output: blue tits are facultatively polygynous and have a fairly short breeding season with almost no second broods, whereas great tits are socially monogamous but more commonly raise second broods. We found that great tit males continued singing at high levels during the egg-laying and incubation periods, while monogamously paired blue tit males strongly reduced singing activity after the first days of egg-laying by their female. Since males of both species sang much more intensely shortly before sunrise than after sunrise, at midday or in the evening, this difference was most conspicuous at dawn. No differences in singing activity were found within species when testing for male age. We suggest that in contrast to blue tits, great tit males continued singing after egg-laying to defend the territory and to encourage the female for a possible second broo

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1α,25-Dihydroxyvitamin D3 Stimulates Activator Protein 1 DNA-Binding Activity by a Phosphatidylinositol 3-Kinase/Ras/MEK/Extracellular Signal Regulated Kinase 1/2 and c-Jun N-Terminal Kinase 1-Dependent Increase in c-Fos, Fra1, and c-Jun Expression in Human Keratinocytes

1α,25-Dihydroxyvitamin D3 added to human keratinocytes increases differentiation through an activation of the transcription factor activator protein 1. We have previously reported that the 1α,25-dihydroxyvitamin D3-induced increase of activator protein 1 DNA binding activity is mediated by a protein kinase C-independent mechanism. The purpose of this study was to investigate further the mechanisms by which 1α,25-dihydroxyvitamin D3 modulates activator protein 1 DNA binding activity in cultured normal human keratinocytes. Western blotting experiments revealed that 1α,25-dihydroxyvitamin D3 caused a rapid and transient activation of the mitogen-activated protein kinases, extracellular signal regulated kinase 1/2 and c-Jun N-terminal kinase 1. 1α,25-Dihydroxyvitamin D3 also enhanced the expression of the activator protein 1 subunits, c-Fos, Fra1, and c-Jun as determined by northern and western blotting. The 1α,25-dihydroxyvitamin D3-induced activator protein 1 DNA binding activity was completely blocked by the MEK inhibitor PD 98059 indicating that the MEK/extracellular signal regulated kinase pathway is involved in the activation of activator protein 1. Transfection experiments showed that 1α,25-dihydroxyvitamin D3 also increased the activator protein 1-dependent transactivation, which was completely blocked by expression of a dominant negative Ras, suggesting that the 1α,25-dihydroxyvitamin D3-induced activator protein 1 activity involves Ras-dependent signaling. Furthermore, preincubation of the keratinocytes with the specific phosphatidylinositol 3-kinase inhibitors, Wortmannin and LY294002, demonstrated that the 1α,25-dihydroxyvitamin D3-induced activation of extracellular signal regulated kinase 1/2 and c-Jun N-terminal kinase 1 required phosphatidylinositol 3-kinase activity. Finally, preincubation of keratinocytes with a polyclonal antibody against the membrane receptor annexin II, blocked the 1α,25-dihydroxyvitamin D3-induced activation of extracellular signal regulated kinase 1/2 and c-Jun N-terminal kinase 1. Taken together, our results indicate that 1α,25-dihydroxyvitamin D3, via binding to the membrane receptor annexin II, induces activation of the phos-phatidylinositol 3-kinase/Ras/MEK/extracellular signal regulated kinase 1/2 and c-Jun N-terminal kinase 1 signal transduction pathway resulting in increased expression of c-Fos, Fra1, and c-Jun, and subsequently increased activator protein 1 DNA binding activity and gene transcription