The sample autocorrelation function and the detection of long-memory processes

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.

'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 .

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Synaptic vesicle glycoprotein 2A modulates vesicular release and calcium channel function at peripheral sympathetic synapses

Synaptic vesicle glycoprotein (SV)2A is a transmembrane protein found in secretory vesicles and is critical for Ca2+-dependent exocytosis in central neurons, although its mechanism of action remains uncertain. Previous studies have proposed, variously, a role of SV2 in the maintenance and formation of the readily releasable pool (RRP) or in the regulation of Ca2+ responsiveness of primed vesicles. Such previous studies have typically used genetic approaches to ablate SV2 levels; here, we used a strategy involving small interference RNA (siRNA) injection to knockdown solely presynaptic SV2A levels in rat superior cervical ganglion (SCG) neuron synapses. Moreover, we investigated the effects of SV2A knockdown on voltage-dependent Ca2+ channel (VDCC) function in SCG neurons. Thus, we extended the studies of SV2A mechanisms by investigating the effects on vesicular transmitter release and VDCC function in peripheral sympathetic neurons. We first demonstrated an siRNA-mediated SV2A knockdown. We showed that this SV2A knockdown markedly affected presynaptic function, causing an attenuated RRP size, increased paired-pulse depression and delayed RRP recovery after stimulus-dependent depletion. We further demonstrated that the SV2A–siRNA-mediated effects on vesicular release were accompanied by a reduction in VDCC current density in isolated SCG neurons. Together, our data showed that SV2A is required for correct transmitter release at sympathetic neurons. Mechanistically, we demonstrated that presynaptic SV2A: (i) acted to direct normal synaptic transmission by maintaining RRP size, (ii) had a facilitatory role in recovery from synaptic depression, and that (iii) SV2A deficits were associated with aberrant Ca2+ current density, which may contribute to the secretory phenotype in sympathetic peripheral neurons.

Symmorphosis through dietary regulation: a combinatorial role for proteolysis, autophagy and protein synthesis in normalising muscle metabolism and function of hypertrophic mice after acute starvation

Animals are imbued with adaptive mechanisms spanning from the tissue/organ to the cellular scale which insure that processes of homeostasis are preserved in the landscape of size change. However we and others have postulated that the degree of adaptation is limited and that once outside the normal levels of size fluctuations, cells and tissues function in an aberant manner. In this study we examine the function of muscle in the myostatin null mouse which is an excellent model for hypertrophy beyond levels of normal growth and consequeces of acute starvation to restore mass. We show that muscle growth is sustained through protein synthesis driven by Serum/Glucocorticoid Kinase 1 (SGK1) rather than Akt1. Furthermore our metabonomic profiling of hypertrophic muscle shows that carbon from nutrient sources is being channelled for the production of biomass rather than ATP production. However the muscle displays elevated levels of autophagy and decreased levels of muscle tension. We demonstrate the myostatin null muscle is acutely sensitive to changes in diet and activates both the proteolytic and autophagy programmes and shutting down protein synthesis more extensively than is the case for wild-types. Poignantly we show that acute starvation which is detrimental to wild-type animals is beneficial in terms of metabolism and muscle function in the myostatin null mice by normalising tension production.

Syncytiotrophoblast extracellular vesicles from pre-eclampsia placentas differentially affect platelet function

Pre-eclampsia (PE) complicates around 3% of all pregnancies and is one of the most common causes of maternal mortality worldwide. The pathophysiology of PE remains unclear however its underlying cause originates from the placenta and manifests as raised blood pressure, proteinuria, vascular or systemic inflammation and hypercoagulation in the mother. Women who develop PE are also at significantly higher risk of subsequently developing cardiovascular (CV) disease. In PE, the failing endoplasmic reticulum, oxidative and inflammatory stressed syncytiotrophoblast layer of the placenta sheds increased numbers of syncytiotrophoblast extracellular vesicles (STBEV) into the maternal circulation. Platelet reactivity, size and concentration are also known to be altered in some women who develop PE, although the underlying reasons for this have not been determined. In this study we show that STBEV from disease free placenta isolated ex vivo by dual placental perfusion associate rapidly with platelets. We provide evidence that STBEV isolated from normal placentas cause platelet activation and that this is increased with STBEV from PE pregnancies. Furthermore, treatment of platelets with aspirin, currently prescribed for women at high risk of PE to reduce platelet aggregation, also inhibits STBEV-induced reversible aggregation of washed platelets. Increased platelet reactivity as a result of exposure to PE placenta derived STBEVs correlates with increased thrombotic risk associated with PE. These observations establish a possible direct link between the clotting disturbances of PE and dysfunction of the placenta, as well as the known increased risk of thromboembolism associated with this condition.

Diel surface temperature range scales with lake size

Ecological and biogeochemical processes in lakes are strongly dependent upon water temperature. Long-term surface warming of many lakes is unequivocal, but little is known about the comparative magnitude of temperature variation at diel timescales, due to a lack of appropriately resolved data. Here we quantify the pattern and magnitude of diel temperature variability of surface waters using high-frequency data from 100 lakes. We show that the near-surface diel temperature range can be substantial in summer relative to long-term change and, for lakes smaller than 3 km2, increases sharply and predictably with decreasing lake area. Most small lakes included in this study experience average summer diel ranges in their near-surface temperatures of between 4 and 7°C. Large diel temperature fluctuations in the majority of lakes undoubtedly influence their structure, function and role in biogeochemical cycles, but the full implications remain largely unexplored.