Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

On the time-dependent analysis of Gamow decay

Gamow's explanation of the exponential decay law uses complex 'eigenvalues' and exponentially growing 'eigenfunctions'. This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any wavefunction is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover, the presentation can well be used in physics lectures to students.

Time-dependent flows in the coupled solar wind-magnetosphere-ionosphere system

Concepts of time-dependent flow in the coupled solar wind-magnetosphere-ionosphere system are discussed and compared with the frequently-adopted steady-state paradigm. Flows are viewed as resulting from departures of the system from equilibrium excited by dayside and nightside reconnection processes, with the flows then taking the system back towards a new equilibrium configuration. The response of the system to reconnection impulses, continuous but unbalanced reconnection and balanced steady-state reconnection are discussed in these terms. It is emphasized that in the time-dependent case the ionospheric and interplanetary electric fields are generally inductively decoupled from each other; a simple mapping of the interplanetary electric field along equipotential field lines into the ionosphere occurs only in the electrostatic steady-state case.

Time-dependent gel to gel transformation of a peptide based supramolecular gelator

A dipeptide with a long fatty acid chain at its N-terminus gives hydrogels in phosphate buffer in the pH range 7.0–8.5. The hydrogel with a gelator concentration of 0.45% (w/v) at pH 7.46 (physiological pH) provides a very good platform to study dynamic changes within a supramolecular framework as it exhibits remarkable change in its appearance with time. Interestingly, the first formed transparent hydrogel gradually transforms into a turbid gel within 2 days. These two forms of the hydrogel have been thoroughly investigated by using small angle X-ray scattering (SAXS), powder X-ray diffraction (PXRD), field emission scanning electron microscopic (FE-SEM) and high-resolution transmission electron microscopic (HR-TEM) imaging, FT-IR and rheometric analyses. The SAXS and low angle PXRD studies substantiate different packing arrangements for the gelator molecules for these two different gel states (the freshly prepared and the aged hydrogel). Moreover, rheological studies of these two gels reveal that the aged gel is stiffer than the freshly prepared gel.

Assessing macro uncertainty in real-time when data are subject to revision

Model-based estimates of future uncertainty are generally based on the in-sample fit of the model, as when Box-Jenkins prediction intervals are calculated. However, this approach will generate biased uncertainty estimates in real time when there are data revisions. A simple remedy is suggested, and used to generate more accurate prediction intervals for 25 macroeconomic variables, in line with the theory. A simulation study based on an empirically-estimated model of data revisions for US output growth is used to investigate small-sample properties.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

The global response to tropical heating in the Madden-Julian oscillation during the northern winter

A life cycle of the Madden–Julian oscillation (MJO) was constructed, based on 21 years of outgoing long-wave radiation data. Regression maps of NCEP–NCAR reanalysis data for the northern winter show statistically significant upper-tropospheric equatorial wave patterns linked to the tropical convection anomalies, and extratropical wave patterns over the North Pacific, North America, the Atlantic, the Southern Ocean and South America. To assess the cause of the circulation anomalies, a global primitive-equation model was initialized with the observed three-dimensional (3D) winter climatological mean flow and forced with a time-dependent heat source derived from the observed MJO anomalies. A model MJO cycle was constructed from the global response to the heating, and both the tropical and extratropical circulation anomalies generally matched the observations well. The equatorial wave patterns are established in a few days, while it takes approximately two weeks for the extratropical patterns to appear. The model response is robust and insensitive to realistic changes in damping and basic state. The model tropical anomalies are consistent with a forced equatorial Rossby–Kelvin wave response to the tropical MJO heating, although it is shifted westward by approximately 20° longitude relative to observations. This may be due to a lack of damping processes (cumulus friction) in the regions of convective heating. Once this shift is accounted for, the extratropical response is consistent with theories of Rossby wave forcing and dispersion on the climatological flow, and the pattern correlation between the observed and modelled extratropical flow is up to 0.85. The observed tropical and extratropical wave patterns account for a significant fraction of the intraseasonal circulation variance, and this reproducibility as a response to tropical MJO convection has implications for global medium-range weather prediction. Copyright © 2004 Royal Meteorological Society

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Including a time-of-year effect in the analysis of a matched case-control study

Motivated by a matched case-control study to investigate potential risk factors for meningococcal disease amongst adolescents, we consider the analysis of matched case-control studies where disease incidence, and possibly other risk factors, vary with time of year. For the cases, the time of infection may be recorded. For controls, however, the recorded time is simply the time of data collection, which is shortly after the time of infection for the matched case, and so depends on the latter. We show that the effect of risk factors and interactions may be adjusted for the time of year effect in a standard conditional logistic regression analysis without introducing any bias. We also show that, if the time delay between data collection for cases and controls is constant, provided this delay is not very short, estimates of the time of year effect are approximately unbiased. In the case that the length of the delay varies over time, the estimate of the time of year effect is biased. We obtain an approximate expression for the degree of bias in this case. Copyright © 2004 John Wiley & Sons, Ltd.

Transcriptional profiling of the LPS induced NF-kappaB response in macrophages

BACKGROUND: Exposure of macrophages to bacterial products such as lipopolysaccharide (LPS) results in activation of the NF-kappaB transcription factor, which orchestrates a gene expression programme that underpins the macrophage-dependent immune response. These changes include the induction or repression of a wide range of genes that regulate inflammation, cell proliferation, migration and cell survival. This process is tightly regulated and loss of control is associated with conditions such as septic shock, inflammatory diseases and cancer. To study this response, it is important to have in vitro model systems that reflect the behaviour of cells in vivo. In addition, it is necessary to understand the natural differences that can occur between individuals. In this report, we have investigated and compared the LPS response in macrophage derived cell lines and peripheral blood mononuclear cell (PBMC) derived macrophages. RESULTS: Gene expression profiles were determined following LPS treatment of THP-1 cells for 1 and 4 hours. LPS significantly induced or repressed 72 out of 465 genes selected as being known or putative NF-kappaB target genes, which exhibited 4 temporal patterns of expression. Results for 34 of these genes, including several genes not previously identified as LPS target genes, were validated using real time PCR. A high correlation between microarray and real time PCR data was found. Significantly, the LPS induced expression profile of THP-1 cells, as determined using real time PCR, was found to be very similar to that of human PBMC derived macrophages. Interestingly, some differences were observed in the LPS response between the two donor PBMC macrophage populations. Surprisingly, we found that the LPS response in U937 cells was dramatically different to both THP-1 and PBMC derived macrophages. CONCLUSION: This study revealed a dynamic and diverse transcriptional response to LPS in macrophages, involving both the induction and repression of gene expression in a time dependent manner. Moreover, we demonstrated that the LPS induced transcriptional response in the THP-1 cell line is very similar to primary PBMC derived macrophages. Therefore, THP-1 cells represent a good model system for studying the mechanisms of LPS and NF-kappaB dependent gene expression.

Ingestion of onion soup high in quercetin inhibits platelet aggregation and essential components of the collagen-stimulated platelet activation pathway in man: a pilot study

Epidemiological data suggest that those who consume a diet rich in quercetin-containing foods may have a reduced risk of CVD. Furthermore, in vitro and ex vivo studies have observed the inhibition of collagen-induced platelet activation by quercetin. The aim of the present study was to investigate the possible inhibitory effects of quercetin ingestion from a dietary source on collagen-stimulated platelet aggregation and signalling. A double-blind randomised cross-over pilot study was undertaken. Subjects ingested a soup containing either a high or a low amount of quercetin. Plasma quercetin concentrations and platelet aggregation and signalling were assessed after soup ingestion. The high-quercetin soup contained 69 mg total quercetin compared with the low-quercetin soup containing 5 mg total quercetin. Plasma quercetin concentrations were significantly higher after high-quercetin soup ingestion than after low-quercetin soup ingestion and peaked at 2.59 (SEM 0.42) mu mol/l. Collagen-stimulated (0.5 mu g/ml) platelet aggregation was inhibited after ingestion of the high-quercetin soup in a time-dependent manner. Collagen-stimulated tyrosine phosphorylation of a key component of the collagen-signalling pathway via glycoprotein VI, Syk, was significantly inhibited by ingestion of the high-quercetin soup. The inhibition of Syk tyrosine phosphorylation was correlated with the area under the curve for the high-quercetin plasma profile. In conclusion, the ingestion of quercetin from a dietary source of onion soup could inhibit some aspects of collagen-stimulated platelet aggregation and signalling ex vivo. This further substantiates the epidemiological data suggesting that those who preferentially consume high amounts of quercetin-containing foods have a reduced risk of thrombosis and potential CVD risk.

Platelet nitric oxide synthase is activated by tyrosine dephosphorylation: possible role for SHP-1 phosphatase

Background: Endothelial nitric oxide synthase (eNOS) activity in endothelial cells is regulated by post-translational phosphorylation of critical serine, threonine and tyrosine residues in response to a variety of stimuli. However, the post-translational regulation of eNOS in platelets is poorly defined. Objectives: We investigated the role of tyrosine phosphorylation in the regulation of platelet eNOS activity. Methods: Tyrosine phosphorylation of eNOS and interaction with the tyrosine phosphatase SHP-1 were investigated by coimmunoprecipitation and immunoblotting. An in vitro immunoassay was used to determine eNOS activity together with the contribution of protein tyrosine phosphorylation. Results: We found platelet eNOS was tyrosine phosphorylated under basal conditions. Thrombin induced a dose- and time-dependent increase in eNOS activity without altering overall level of tyrosine phosphorylation, although we did observe evidence of minor tyrosine dephosphorylation. In vitro tyrosine dephosphorylation of platelet eNOS using a recombinant protein tyrosine phosphatase enhanced thrombin-induced activity compared to thrombin alone, but had no effect on endothelial eNOS activity either at basal or after stimulation with bradykinin. Having shown that dephosphorylation could modulate platelet eNOS activity we examined the role of potential protein phosphatases important for platelet eNOS activity. We found SHP-1 protein tyrosine phosphatase, co-associated with platelet eNOS in resting platelets, but does not associate with eNOS in endothelial cells. Stimulation of platelets with thrombin increased SHP-1 association with eNOS, while inhibition of SHP-1 abolished the ability of thrombin to induce elevated eNOS activity. Conclusions: Our data suggest a novel role for tyrosine dephosphorylation in platelet eNOS activation, which may be mediated by SHP-1.