Some Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions

This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of the hook lengths of p, are polynomial functions of n. A similar result is obtained for symmetric functions of the contents and shifted parts of n.Comment: 20 pages. Correction of some inaccuracies, and a new Theorem 4.

Satellite data relay and platform locating in oceanography. Report of the In Situ Ocean Science Working Group

The present and future use of satellites to locate offshore platforms and relay data from in situ sensors to shore was examined. A system of the ARGOS type will satisfy the increasing demand for oceanographic information through data relay and platform location. The improved ship navigation provided by the Global Positioning System (GPS) will allow direct observation of currents from underway ships. Ocean systems are described and demand estimates on satellite systems are determined. The capabilities of the ARGOS system is assessed, including anticipated demand in the next decade

FGF/heparin differentially regulates Schwann cell and olfactory ensheathing cell interactions with astrocytes: a role in astrocytosis

After injury, the CNS undergoes an astrocyte stress response characterized by reactive astrocytosis/proliferation, boundary formation, and increased glial fibrillary acidic protein (GFAP) and chondroitin sulfate proteoglycan (CSPG) expression. Previously, we showed that in vitro astrocytes exhibit this stress response when in contact with Schwann cells but not olfactory ensheathing cells (OECs). In this study, we confirm this finding in vivo by demonstrating that astrocytes mingle with OECs but not Schwann cells after injection into normal spinal cord. We show that Schwann cell-conditioned media (SCM) induces proliferation in monocultures of astrocytes and increases CSPG expression in a fibroblast growth factor receptor 1 (FGFR1)-independent manner. However, SCM added to OEC/astrocyte cocultures induces reactive astrocytosis and boundary formation, which, although sensitive to FGFR1 inhibition, was not induced by FGF2 alone. Addition of heparin to OEC/astrocyte cultures induces boundary formation, whereas heparinase or chlorate treatment of Schwann cell/astrocyte cultures reduces it, suggesting that heparan sulfate proteoglycans (HSPGs) are modulating this activity. In vivo, FGF2 and FGFR1 immunoreactivity was increased over grafted OECs and Schwann cells compared with the surrounding tissue, and HSPG immunoreactivity is increased over reactive astrocytes bordering the Schwann cell graft. These data suggest that components of the astrocyte stress response, including boundary formation, astrocyte hypertrophy, and GFAP expression, are mediated by an FGF family member, whereas proliferation and CSPG expression are not. Furthermore, after cell transplantation, HSPGs may be important for mediating the stress response in astrocytes via FGF2. Identification of factors secreted by Schwann cells that induce this negative response in astrocytes would further our ability to manipulate the inhibitory environment induced after injury to promote regeneration

The cost and income of the farm poultry flock

Cover title

Correction to: “Constraining climate forecasts: The role of prior assumptions”

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The importance of forecasting regional wind power ramping: a case study for the UK

In recent years there has been a significant change in the distribution of wind farms in Great Britain, with a trend towards very large offshore farms clustered together in zones. However, there are concerns these clusters could produce large ramping events on time scales of less than 6 hours as local meteorological phenomena simultaneously impact the production of several farms. This paper presents generation data from the wind farms in the Thames Estuary (the largest cluster in the world) for 2014 and quantifies the high frequency power ramps. Based on a case study of a ramping event which occurred on 3rd November 2014, we show that due to the large capacity of the cluster, a localised ramp can have a significant impact on the cost of balancing the power system on a national level if it is not captured by the forecast of the system operator. The planned construction of larger offshore wind zones will exacerbate this problem. Consequently, there is a need for accurate regional wind power forecasts to minimise the costs of managing the system. This study shows that state-of-the-art high resolution forecast models have capacity to provide valuable information to mitigate this impact

Phosphorylation by Akt within the ST loop of AMPK-α1 down-regulates its activation in tumour cells

The insulin/IGF-1 (insulin-like growth factor 1)-activated protein kinase Akt (also known as protein kinase B) phosphorylates Ser(487) in the ‘ST loop’ (serine/threonine-rich loop) within the C-terminal domain of AMPK-α1 (AMP-activated protein kinase-α1), leading to inhibition of phosphorylation by upstream kinases at the activating site, Thr(172). Surprisingly, the equivalent site on AMPK-α2, Ser(491), is not an Akt target and is modified instead by autophosphorylation. Stimulation of HEK (human embryonic kidney)-293 cells with IGF-1 caused reduced subsequent Thr(172) phosphorylation and activation of AMPK-α1 in response to the activator A769662 and the Ca(2+) ionophore A23187, effects we show to be dependent on Akt activation and Ser(487) phosphorylation. Consistent with this, in three PTEN (phosphatase and tensin homologue deleted on chromosome 10)-null tumour cell lines (in which the lipid phosphatase PTEN that normally restrains the Akt pathway is absent and Akt is thus hyperactivated), AMPK was resistant to activation by A769662. However, full AMPK activation could be restored by pharmacological inhibition of Akt, or by re-expression of active PTEN. We also show that inhibition of Thr(172) phosphorylation is due to interaction of the phosphorylated ST loop with basic side chains within the αC-helix of the kinase domain. Our findings reveal that a previously unrecognized effect of hyperactivation of Akt in tumour cells is to restrain activation of the LKB1 (liver kinase B1)–AMPK pathway, which would otherwise inhibit cell growth and proliferation

The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance

Dynamics of reentry are studied in a one dimensional loop of model cardiac cells with discrete intercellular gap junction resistance ($R$). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasi-periodic ($QP$) at a critical loop length ($L_{crit}$) that decreases with $R$. Quasi-periodic reentry exists from $L_{crit}$ to a minimum length ($L_{min}$) that is also shortening with $R$. The decrease of $L_{crit}(R)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$.Comment: 6 pages, 7 figure

Patente in der europäischen Finanzindustrie: terra incognita?

Die unklare Formulierung des Artikels 52 des Europäischen Patentübereinkommens hat zu einer Unsicherheit bezüglich der Patentierbarkeit von Erfindungen mit finanzwirtschaftlichem Hintergrund am Europäischen Patentamt (EPA) geführt. Der vorliegende Artikel gibt einen Überblick über die geltende Rechtslage in Europa und stellt sie den relevanten Regelungen in den USA gegenüber. In einer empirischen Erhebung werden 1761 Patentanmeldungen am EPA identifiziert, denen eine Erfindung mit finanzwirtschaftlichem Hintergrund zu Grunde liegt. Die Analyse dieser Patente zeigt, dass nur lediglich circa 20 Prozent aller bisher abgeschlossenen Anmeldeverfahren zu einer Patentgewährung geführt haben. Verglichen mit einer durchschnittlichen langfristigen Gewährungsrate von rund 68 Prozent scheint das EPA restriktiv bei der Gewährung von "Finanzpatenten" zu sein. Dieses Ergebnis ist für die Bemühungen um einen neuen regulativen Rahmen zur Vermeidung zukünftiger Finanzmarktkrisen relevant. Eine umfassende Patentierung könnte einer schnellen Verbreitung von aus regulatorischen Gründen gewünschten Methoden im Wege stehen.The imprecise wording of article 52 of the European Patent Convention lead to uncertainty with regard to the patentability of inventions related to financial methods and processes at the European Patent Office (EPO). This article summarizes the relevant legislation in Europe and contrasts it with the legislation in the US. In the empirical part of the paper, 1,761 EPO patent applications based on inventions related to financial methods and processes are identified. The analysis of those patent applications demonstrates that only 20 Prozent of the completed application procedures led to a final patent grant. Compared to an overall grant rate of about 68 Prozent at the EPO this finding highlights that the EPO pursues a restrictive approach towards the award of "financial patents". This finding bears relevance for the future design of a regulatory framework for the financial industry: Widespread patenting could hinder fast diffusion of financial innovation and hamper regulators' efforts to implement them