Essential Incompleteness of Arithmetic Verified by Coq

A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural numbers, and functions operating on these codes are proved to be primitive recursive. The weak axiom system is proved to be essentially incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the associated Coq source files see the TeX sources, or see <http://r6.ca/Goedel20050512.tar.gz

Flucytosine and cryptococcosis: time to urgently address the worldwide accessibility of a 50-year-old antifungal.

Current, widely accepted guidelines for the management of HIV-associated cryptococcal meningoencephalitis (CM) recommend amphotericin B combined with flucytosine (5-FC) for ≥2 weeks as the initial induction treatment of choice. However, access to flucytosine in Africa and Asia, where disease burden is greatest, is inadequate at present. While research into identifying effective and well-tolerated antifungal combinations that do not contain flucytosine continues, an ever-increasing body of evidence from in vitro, in vivo and clinical studies points to the benefits of flucytosine in the treatment of CM in both intravenous combinations with amphotericin B and oral combinations with high-dose fluconazole. This article provides an up-to-date review of this evidence, and the current issues and challenges regarding increasing access to this key component of combination antifungal therapy for cryptococcosis

Heisenberg exchange in magnetic monoxides

The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.Comment: 21 pages, 1 figure, submitted to Phys. Rev. B 1/19/07. Realized J=4V^2/U applies generally, as opposed to J=2V^2/U from one-electron theory (1/28 revision

Using surveys of Affymetrix GeneChips to study antisense expression.

We have used large surveys of Affymetrix GeneChip data in the public domain to conduct a study of antisense expression across diverse conditions. We derive correlations between groups of probes which map uniquely to the same exon in the antisense direction. When there are no probes assigned to an exon in the sense direction we find that many of the antisense groups fail to detect a coherent block of transcription. We find that only a minority of these groups contain coherent blocks of antisense expression suggesting transcription. We also derive correlations between groups of probes which map uniquely to the same exon in both sense and antisense direction. In some of these cases the locations of sense probes overlap with the antisense probes, and the sense and antisense probe intensities are correlated with each other. This configuration suggests the existence of a Natural Antisense Transcript (NAT) pair. We find the majority of such NAT pairs detected by GeneChips are formed by a transcript of an established gene and either an EST or an mRNA. In order to determine the exact antisense regulatory mechanism indicated by the correlation of sense probes with antisense probes, a further investigation is necessary for every particular case of interest. However, the analysis of microarray data has proved to be a good method to reconfirm known NATs, discover new ones, as well as to notice possible problems in the annotation of antisense transcripts

A new wader, Recurvirostridae (Charadriiformes), from the early Eocene of Portugal

A new wader (Aves, Charadriiformes, Recurvirostridae) from the Early Eocene site of Silveirinha, in Lower Mondego region, Central Portugal, is described. Comparisons have been made with other forms, both extant and fossil; its affmities are discussed. Silveirinha wader is ascribed to Fluviatilavis antunesi, n. gen. n. sp

Photonic band mixing in linear chains of optically coupled micro-spheres

The paper deals with optical excitations arising in a one-dimensional chain of identical spheres due optical coupling of whispering gallery modes (WGM). The band structure of these excitations depends significantly on the inter-mixing between WGMs characterized by different values of angular quantum number, $l$. We develop a general theory of the photonic band structure of these excitations taking these effects into account and applied it to several cases of recent experimental interest. In the case of bands originating from WQMs with the angular quantum number of the same parity, the calculated dispersion laws are in good qualitative agreement with recent experiment results. Bands resulting from hybridization of excitations resulting from whispering gallery modes with different parity of $l$ exhibits anomalous dispersion properties characterized by a gap in the allowed values of \emph{wave numbers} and divergence of group velocity.Comment: RevTex, 28 pages, 7 Figure

Halcyornis toliapicus (aves: Lower Eocene, England) indicates advanced neuromorphology in Mesozoic Neornithes

Our recent X-ray micro computer-tomographic (μCT) investigations of Prophaethon shrubsolei and Odontopteryx toliapica from the Lower Eocene London Clay Formation of England revealed the avian brain to have been essentially modern in form by 55 Ma, but that an important vision-related synapomorphy of living birds, the eminentia sagittalis of the telencephalon, was poorly developed. This evidence suggested that the feature probably appeared close to the end of the Mesozoic. Here we use μCT analysis to describe the endocranium of Halcyornis toliapicus, also from the London Clay Formation. The affinities of Halcyornis have been hotly debated, with the taxon referred to the Charadriiformes (Laridae), Coraciiformes (Alcedinidae, and its own family Halcyornithidae) and most recently that Halcyornithidae may be a possible senior synonym of Pseudasturidae (Pan-Psittaciformes). Unlike Prophaethon and Odontopteryx, the eminentia sagittalis of Halcyornis is strongly developed and comparable to that of living species. Like those London Clay taxa, the eminentia sagittalis occupies a rostral position on the telencephalon. The senses of Halcyornis appear to have been well developed. The length of the cochlear duct of the inner ear indicates a hearing sensitivity within the upper range of living species, and enlarged olfactory lobes suggest a reasonable reliance on sense of smell. The optic nerves were especially well developed which, together with the strong development of the eminentia sagittalis, indicates a high degree of visual specialization in Halcyornis. The advanced development of the eminentia sagittalis further supports a Mesozoic age for the appearance of this structure and associated neural architectural complexity found in extant Aves. The eminentia sagittalis of living Psittaciformes is situated caudally on the telencephalon, making a Pan-Psittaciformes relationship unlikely for Halcyorni

Deficiency of G1 regulators P53, P21Cip1 and/or pRb decreases hepatocyte sensitivity to TGFbeta cell cycle arrest

TGFbeta is critical to control hepatocyte proliferation by inducing G1-growth arrest through multiple pathways leading to inhibition of E2F transcription activity. The retinoblastoma protein pRb is a key controller of E2F activity and G1/S transition which can be inhibited in viral hepatitis. It is not known whether the impairment of pRb would alter the growth inhibitory potential of TGFbeta in disease. We asked how Rb-deficiency would affect responses to TGFbeta-induced cell cycle arrest.Publisher PDFPeer reviewe

TO EXAMINE THE DIFFERENCES IN REARFOOT KINEMATICS DURING TREADMILL AND OVERGROUND RUNNING

This study examined the differences between the kinematics of rearfoot motion in overground (OG) and treadmill (TM) running. Two subjects ran at various speeds under both conditions and a three-dimensional analysis was performed using the Peak Motus Analysis system. TM running produced repeatable and consistent measures of rearfoot motion across all speeds however OG running was more variable. While there are some differences between the two modes, this can be explained by TM mechanics and TM testing cannot be dismissed based on this. Speed was found to influence most variables making speed control critical in obtaining reliable measures of rearfoot motion. The TM easily and accurately provides this, which advocates its use in locomotion studies. It was concluded that speed control is more important than the mode of runnin

Controllable Neural Story Plot Generation via Reinforcement Learning

Language-modeling--based approaches to story plot generation attempt to construct a plot by sampling from a language model (LM) to predict the next character, word, or sentence to add to the story. LM techniques lack the ability to receive guidance from the user to achieve a specific goal, resulting in stories that don't have a clear sense of progression and lack coherence. We present a reward-shaping technique that analyzes a story corpus and produces intermediate rewards that are backpropagated into a pre-trained LM in order to guide the model towards a given goal. Automated evaluations show our technique can create a model that generates story plots which consistently achieve a specified goal. Human-subject studies show that the generated stories have more plausible event ordering than baseline plot generation techniques.Comment: Published in IJCAI 201