Conjectures for the integral moments and ratios of L-functions over function fields

We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of $L$-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of $L$-functions associated with hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_{q}$ in the limit as $g\rightarrow\infty$. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these $L$-functions.Comment: 40 page

Morphology, biostratigraphy, and evolution of PliocenePleistocene diatoms Proboscia barboi..

Proboscia barboi and Proboscia curvirostris are two important diatom biostratigraphic markers from the high latitudes of the North Pacific and North Atlantic Oceans, dating back to the Pliocene-Pleistocene time. This study analyzes the biostratigraphic events and describes the morphology of P. barboi and P. curvirostris, particularly the morphologic variations of the latter species, based on observations of samples of Core U1340A from the IODP Expedition 323 in the Bering Sea. In Site U1340, the First Occurrence of P. curvirostris is observed at 1.52Ma and its First Common Occurrence at 1.39Ma, where morphologic variations were found abundantly. The Last Occurrence of P. curvirostris was found at 0.33Ma, while P. barboi's Last Occurrence is found at 0.67Ma. Based on the morphological similarity and known biostratigraphic distribution, previous authors have assumed that P. curvirostris descends from P. barboi, although this hypothesis is still in debate. At 1.39Ma P. curvirostris shows an increased size and thickness, which is typical of P. barboi, and some specimens display an incipient structure characteristic of P. curvirostris - the secondary spine. This morphology is intermediate between the two species and suggests an evolutionary transition from P. barboi to P. curvirostris. However, P. curvirostris already existed since 1.9Ma in the subarctic indicating that its speciation happened much earlier than 1.39Ma. Furthermore, since P. barboi co-occurs with P. curvirostris in the North Pacific, this evolutionary process was cladogenetic. Besides being evidence for a phylogenetic relationship, the abundant occurrence of intermediate forms at 1.39Ma may constitute a bioevent for a short time interval in the Bering Sea.info:eu-repo/semantics/publishedVersio

Joint interpretation of AER/FGF and ZPA/SHH over time and space underlies hairy2 expression in the chick limb

Embryo development requires precise orchestration of cell proliferation and differentiation in both time and space. A molecular clock operating through gene expression oscillations was first described in the presomitic mesoderm (PSM) underlying periodic somite formation. Cycles of HES gene expression have been further identified in other progenitor cells, including the chick distal limb mesenchyme, embryonic neural progenitors and both mesenchymal and embryonic stem cells. In the limb, hairy2 is expressed in the distal mesenchyme, adjacent to the FGF source (AER) and along the ZPA-derived SHH gradient, the two major regulators of limb development. Here we report that hairy2 expression depends on joint AER/FGF and ZPA/SHH signaling. FGF plays an instructive role on hairy2, mediated by Erk and Akt pathway activation, while SHH acts by creating a permissive state defined by Gli3-A/Gli3-R>1. Moreover, we show that AER/FGF and ZPA/SHH present distinct temporal and spatial signaling properties in the distal limb mesenchyme: SHH acts at a long-term, long-range on hairy2, while FGF has a shortterm, short-range action. Our work establishes limb hairy2 expression as an output of integrated FGF and SHH signaling in time and space, providing novel clues for understanding the regulatory mechanisms underlying HES oscillations in multiple systems, including embryonic stem cell pluripotency. (C) 2012. Published by The Company of Biologists Ltd.FCT, Portugal [SFRH/BD/33176/2007]; Ciencia2007 Program Contract (Portuguese Government); IBB/CBME, LA; FCT, Portugal (National and FEDER COMPETE Program funds) [PTDC/SAU-OBD/099758/2008, PTDC/SAU-OBD/105111/2008]info:eu-repo/semantics/publishedVersio

Analytical approach to directed sandpile models on the Apollonian network

We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two and three point correlation functions are amenable to exact treatment, leading to analytical results for the avalanche distributions in the limit of an infinite system, for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems, when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.Comment: 7 pages in two-column format, 10 illustrations, 5 figure

Teleparallel Spin Connection

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.Comment: 2 pages, RevTeX, to appear in Phys. Rev D (Brief Report