Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Accurate radiometry from space: an essential tool for climate studies

The Earth's climate is undoubtedly changing; however, the time scale, consequences and causal attribution remain the subject of significant debate and uncertainty. Detection of subtle indicators from a background of natural variability requires measurements over a time base of decades. This places severe demands on the instrumentation used, requiring measurements of sufficient accuracy and sensitivity that can allow reliable judgements to be made decades apart. The International System of Units (SI) and the network of National Metrology Institutes were developed to address such requirements. However, ensuring and maintaining SI traceability of sufficient accuracy in instruments orbiting the Earth presents a significant new challenge to the metrology community. This paper highlights some key measurands and applications driving the uncertainty demand of the climate community in the solar reflective domain, e.g. solar irradiances and reflectances/radiances of the Earth. It discusses how meeting these uncertainties facilitate significant improvement in the forecasting abilities of climate models. After discussing the current state of the art, it describes a new satellite mission, called TRUTHS, which enables, for the first time, high-accuracy SI traceability to be established in orbit. The direct use of a ‘primary standard’ and replication of the terrestrial traceability chain extends the SI into space, in effect realizing a ‘metrology laboratory in space’.

Low cost brain-computer interface: first results

Brain-Computer Interfacing (BCI) has been previously demonstrated to restore patient communication, meeting with varying degrees of success. Due to the nature of the equipment traditionally used in BCI experimentation (the electroencephalograph) it is mostly conned to clinical and research environments. The required medical safety standards, subsequent cost of equipment and its application/training times are all issues that need to be resolved if BCIs are to be taken out of the lab/clinic and delivered to the home market. The results in this paper demonstrate a system developed with a low cost medical grade EEG amplier unit in conjunction with the open source BCI2000 software suite thus constructing the cheapest per electrode system available, meeting rigorous clinical safety standards. Discussion of the future of this technology and future work concerning this platform are also introduced.

Inverting the lives of 'others': retelling the Nazi past in 'Ehe im Schatten' and 'Das Leben der Anderen'

The article compares Florian Henckel von Donnersmarck's film Das Leben der Anderen (2006) with Kurt Maetzig's early post-war film Ehe im Schatten (1947). The comparison is based on significant narrative and thematic elements which the films share: They both have a ‘theatre couple’, representatives of the ‘Bildungsbürgertum’, at the centre of the story; in both cases the couple faces a crisis caused by the first and second German dictatorship respectively and then both try to solve the crisis by relying on the classical ‘bürgerliches Erbe’, particularly the ‘bürgerliches Trauerspiel’. The extensive use of the ‘bürgerliches Erbe’ in the films activates the function this heritage had for the definition of the German nation in the nineteenth century. However, while Maetzig's film shows how the ‘heritage’ and its representatives fail in the face of National Socialism, von Donnersmarck's film claims the effectiveness of this ‘heritage’ in the fight against the East German dictatorship. Von Donnersmarck thus inverts a critical film tradition of which Ehe im Schatten is an example; furthermore, as this tradition emerged from dealing with the Third Reich, von Donnersmarck's film, it will be argued, is more interested in the redemption of the Nazi past than the East German past.

Analysis of protein networks in resting and collagen receptor (GPVI)-stimulated platelet sub-proteomes.

Proteomics approaches have made important contributions to the characterisation of platelet regulatory mechanisms. A common problem encountered with this method, however, is the masking of low-abundance (e.g. signalling) proteins in complex mixtures by highly abundant proteins. In this study, subcellular fractionation of washed human platelets either inactivated or stimulated with the glycoprotein (GP) VI collagen receptor agonist, collagen-related peptide, reduced the complexity of the platelet proteome. The majority of proteins identified by tandem mass spectrometry are involved in signalling. The effect of GPVI stimulation on levels of specific proteins in subcellular compartments was compared and analysed using in silico quantification, and protein associations were predicted using STRING (the search tool for recurring instances of neighbouring genes/proteins). Interestingly, we observed that some proteins that were previously unidentified in platelets including teneurin-1 and Van Gogh-like protein 1, translocated to the membrane upon GPVI stimulation. Newly identified proteins may be involved in GPVI signalling nodes of importance for haemostasis and thrombosis.

Gap junctions and connexin hemichannels underpin hemostasis and thrombosis

BACKGROUND: Connexins are a widespread family of membrane proteins that assemble into hexameric hemichannels, also known as connexons. Connexons regulate membrane permeability in individual cells or couple between adjacent cells to form gap junctions and thereby provide a pathway for regulated intercellular communication. We have now examined the role of connexins in platelets, blood cells that circulate in isolation, but upon tissue injury adhere to each other and the vessel wall to prevent blood loss and facilitate wound repair. METHODS AND RESULTS: We report the presence of connexins in platelets, notably connexin37, and that the formation of gap junctions within platelet thrombi is required for the control of clot retraction. Inhibition of connexin function modulated a range of platelet functional responses prior to platelet-platelet contact, and reduced laser induced thrombosis in vivo in mice. Deletion of the Cx37 gene (Gja4) in transgenic mice reduced platelet aggregation, fibrinogen binding, granule secretion and clot retraction indicating an important role for Cx37 hemichannels and gap junctions in platelet thrombus function. CONCLUSIONS: Together, these data demonstrate that platelet gap junctions and hemichannels underpin the control of haemostasis and thrombosis and represent potential therapeutic targets.

The integration of proteomics and systems approaches to map regulatory mechanisms underpinning platelet function.

Platelets in the circulation are triggered by vascular damage to activate, aggregate and form a thrombus that prevents excessive blood loss. Platelet activation is stringently regulated by intracellular signalling cascades, which when activated inappropriately lead to myocardial infarction and stroke. Strategies to address platelet dysfunction have included proteomics approaches which have lead to the discovery of a number of novel regulatory proteins of potential therapeutic value. Global analysis of platelet proteomes may enhance the outcome of these studies by arranging this information in a contextual manner that recapitulates established signalling complexes and predicts novel regulatory processes. Platelet signalling networks have already begun to be exploited with interrogation of protein datasets using in silico methodologies that locate functionally feasible protein clusters for subsequent biochemical validation. Characterization of these biological systems through analysis of spatial and temporal organization of component proteins is developing alongside advances in the proteomics field. This focused review highlights advances in platelet proteomics data mining approaches that complement the emerging systems biology field. We have also highlighted nucleated cell types as key examples that can inform platelet research. Therapeutic translation of these modern approaches to understanding platelet regulatory mechanisms will enable the development of novel anti-thrombotic strategies.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

GSHMC: an efficient method for molecular simulation

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society

A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.