Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.

Frequency-dependent attenuation as a potential indicator of oil saturation

At seismic frequencies, wave-induced fluid flow is a major cause of P-wave attenuation in partially saturated porous rocks. Attenuation is of great importance for the oil industry in the interpretation of seismic field data. Here, the effects on P-wave attenuation resulting from changes in oil saturation are studied for media with coexisting water, oil, and gas. For that, creep experiments are numerically simulated by solving Biot's equations for consolidation of poroelastic media with the finite-element method. The experiments yield time-dependent stress?strain relations that are used to calculate the complex P-wave modulus from which frequency-dependent P-wave attenuation is determined. The models are layered media with periodically alternating triplets of layers. Models consisting of triplets of layers having randomly varying layer thicknesses are also considered. The layers in each triplet are fully saturated with water, oil, and gas. The layer saturated with water has lower porosity and permeability than the layers saturated with oil and gas. These models represent hydrocarbon reservoirs in which water is the wetting fluid preferentially saturating regions of lower porosity. The results from the numerical experiments showed that increasing oil saturation, connected to a decrease in gas saturation, resulted in a significant increase of attenuation at low frequencies (lower than 2 Hz). Furthermore, replacing the oil with water resulted in a distinguishable behavior of the frequency-dependent attenuation. These results imply that, according to the physical mechanism of wave-induced fluid flow, frequency-dependent attenuation in media saturated with water, oil, and gas is a potential indicator of oil saturation.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

The hyperinsulinemia produced by concanavalin A in rats is opioid-dependent and hormonally regulated

The present study examines the effect of concanavalin A (Con A) on the blood insulin and glucose levels of rats. Male and female rats treated with Con A (62.5-500 µg/kg) for three days showed a dose- and time-dependent hyperinsulinemia that lasted more than 48 h. Male rats were more sensitive to Con A. Thus, 6 h after treatment with Con A the circulating insulin levels in male rats had increased by 85% (control: 10.2 ± 0.9 mU/l and Con A-treated: 18.8 ± 1 mU/l) compared to only 38% (control: 7.5 ± 0.2 mU/l; Con A-treated: 10.3 ± 0.9 mU/l) in females. An identical response was seen after 12 h. Con A (250 µg/kg) produced time-dependent hypoglycemia in both sexes but more pronounced in males. There was no correlation between the hypoglycemia and hyperinsulinemia described above. The Con A-induced hyperinsulinemia in rats of both sexes was abolished in gonadectomized animals (intact males: +101 ± 17% vs orchiectomized males: -5 ± 3%; intact females: +86 ± 23% vs ovariectomized females: -18 ± 7.2%). Pretreating intact male and female rats with human chorionic gonadotropin also significantly inhibited the Con A-induced hyperinsulinemia. Estradiol (10 µg/kg, im) significantly blocked the Con A-induced increase in circulating insulin in male rats (101 ± 17% for controls vs 32 ± 5.3% for estradiol-treated animals, P<0.05) while testosterone (10 mg/kg, im) had no similar effect on intact female rats. Pretreating Con A-injected rats with opioid antagonists such as naloxone (1 mg/kg, sc) and naltrexone (5 mg/kg, sc) blocked the hyperinsulinemia produced by the lectin in males (control: +101 ± 17% vs naloxone-treated: +5 ± 14%, or naltrexone-treated: -23 ± 4.5%) and females (control: +86 ± 23% vs naloxone-treated: +21 ± 20%, or naltrexone-treated: -18 ± 11%). These results demonstrate that Con A increases the levels of circulating insulin in rats and that this response is opioid-dependent and hormonally regulated.

Pressure and time dependence of the cardiopulmonary reflex response in patients with hypertensive cardiomyopathy

The first minutes of the time course of cardiopulmonary reflex control evoked by lower body negative pressure (LBNP) in patients with hypertensive cardiomyopathy have not been investigated in detail. We studied 15 hypertensive patients with left ventricular dysfunction (LVD) and 15 matched normal controls to observe the time course response of the forearm vascular resistance (FVR) during 3 min of LBNP at -10, -15, and -40 mmHg in unloading the cardiopulmonary receptors. Analysis of the average of 3-min intervals of FVR showed a blunted response of the LVD patients at -10 mmHg (P = 0.03), but a similar response in both groups at -15 and -40 mmHg. However, using a minute-to-minute analysis of the FVR at -15 and -40 mmHg, we observed a similar response in both groups at the 1st min, but a marked decrease of FVR in the LVD group at the 3rd min of LBNP at -15 mmHg (P = 0.017), and -40 mmHg (P = 0.004). Plasma norepinephrine levels were analyzed as another neurohumoral measurement of cardiopulmonary receptor response to LBNP, and showed a blunted response in the LVD group at -10 (P = 0.013), -15 (P = 0.032) and -40 mmHg (P = 0.004). We concluded that the cardiopulmonary reflex response in patients with hypertensive cardiomyopathy is blunted at lower levels of LBNP. However, at higher levels, the cardiopulmonary reflex has a normal initial response that decreases progressively with time. As a consequence of the time-dependent response, the cardiopulmonary reflex response should be measured over small intervals of time in clinical studies.

The role of Ca2+/calmodulin-dependent protein kinase II and calcineurin in TNF-α-induced myocardial hypertrophy

We investigated whether Ca2+/calmodulin-dependent kinase II (CaMKII) and calcineurin (CaN) are involved in myocardial hypertrophy induced by tumor necrosis factor α (TNF-α). The cardiomyocytes of neonatal Wistar rats (1-2 days old) were cultured and stimulated by TNF-α (100 μg/L), and Ca2+ signal transduction was blocked by several antagonists, including BAPTA (4 µM), KN-93 (0.2 µM) and cyclosporin A (CsA, 0.2 µM). Protein content, protein synthesis, cardiomyocyte volumes, [Ca2+]i transients, CaMKIIδB and CaN were evaluated by the Lowry method, [³H]-leucine incorporation, a computerized image analysis system, a Till imaging system, and Western blot analysis, respectively. TNF-α induced a significant increase in protein content in a dose-dependent manner from 10 µg/L (53.56 µg protein/well) to 100 μg/L (72.18 µg protein/well), and in a time-dependent manner from 12 h (37.42 µg protein/well) to 72 h (42.81 µg protein/well). TNF-α (100 μg/L) significantly increased the amplitude of spontaneous [Ca2+]i transients, the total protein content, cell size, and [³H]-leucine incorporation in cultured cardiomyocytes, which was abolished by 4 µM BAPTA, an intracellular Ca2+ chelator. The increases in protein content, cell size and [³H]-leucine incorporation were abolished by 0.2 µM KN-93 or 0.2 µM CsA. TNF-α increased the expression of CaMKIIδB by 35.21% and that of CaN by 22.22% compared to control. These effects were abolished by 4 µM BAPTA, which itself had no effect. These results suggest that TNF-α induces increases in [Ca2+]i, CaMKIIδB and CaN and promotes cardiac hypertrophy. Therefore, we hypothesize that the Ca2+/CaMKII- and CaN-dependent signaling pathways are involved in myocardial hypertrophy induced by TNF-α.

Esculetin, a coumarin derivative, exerts in vitro and in vivo antiproliferative activity against hepatocellular carcinoma by initiating a mitochondrial-dependent apoptosis pathway

This study investigated the in vitro and in vivo antiproliferative activity of esculetin against hepatocellular carcinoma, and clarified its potential molecular mechanisms. Cell viability was determined by the MTT (tetrazolium) colorimetric assay. In vivoantitumor activity of esculetin was evaluated in a hepatocellular carcinoma mouse model. Seventy-five C57BL/6J mice were implanted with Hepa1-6 cells and randomized into five groups (n=15 each) given daily intraperitoneal injections of vehicle (physiological saline), esculetin (200, 400, or 700 mg·kg-1·day-1), or 5-Fu (200 mg·kg-1·day-1) for 15 days. Esculetin significantly decreased tumor growth in mice bearing Hepa1-6 cells. Tumor weight was decreased by 20.33, 40.37, and 55.42% with increasing doses of esculetin. Esculetin significantly inhibited proliferation of HCC cells in a concentration- and time-dependent manner and with an IC50 value of 2.24 mM. It blocked the cell cycle at S phase and induced apoptosis in SMMC-7721 cells with significant elevation of caspase-3 and caspase-9 activity, but did not affect caspase-8 activity. Moreover, esculetin treatment resulted in the collapse of mitochondrial membrane potential in vitro and in vivo accompanied by increased Bax expression and decreased Bcl-2 expression at both transcriptional and translational levels. Thus, esculetin exerted in vitro and in vivo antiproliferative activity in hepatocellular carcinoma, and its mechanisms involved initiation of a mitochondrial-mediated, caspase-dependent apoptosis pathway.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na_2

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wavepackets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na^+_2 ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecularion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na^+ -transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excitedbound Rydberg state. This conclusion is supported by the theoretical simulation.

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.

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.

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.

Solvent-Dependent Formation of Os(0) Complexes by Electrochemical Reduction of [Os(CO)(2,2′-bipyridine)(L)Cl2]; L = Cl−,PrCN

Cyclic voltammetry and ultraviolet−visible/infrared (UV−vis/IR) spectroelectrochemistry were used to study the cathodic electrochemical behavior of the osmium complexes mer-[OsIII(CO) (bpy)Cl3] (bpy = 2,2′-bipyridine) and trans(Cl)-[OsII(CO) (PrCN)(bpy)Cl2] at variable temperature in different solvents (tetrahydrofuran (THF), butyronitrile (PrCN), acetonitrile (MeCN)) and electrolytes (Bu4NPF6, Bu4NCl). The precursors can be reduced to mer-[OsII(CO) (bpy•−)Cl3]2− and trans(Cl)-[OsII(CO)(PrCN) (bpy•−)Cl2]−, respectively, which react rapidly at room temperature, losing the chloride ligands and forming Os(0) species. mer-[OsIII(CO) (bpy)Cl3] is reduced in THF to give ultimately an Os−Os-bonded polymer, probably [Os0(CO) (THF)-(bpy)]n, whereas in PrCN the well-soluble, probably mononuclear [Os0(CO) (PrCN)(bpy)], species is formed. The same products were observed for the 2 electron reduction of trans(Cl)-[OsII(CO)(PrCN) (bpy)Cl2] in both solvents. In MeCN, similar to THF, the[Os0(CO) (MeCN)(bpy)]n polymer is produced. It is noteworthy that the bpy ligand in mononuclear [Os0(CO) (PrCN)(bpy)] is reduced to the corresponding radical anion at a significantly less negative potential than it is in polymeric [Os0(CO) (THF)(bpy)]n: ΔE1/2 = 0.67 V. Major differences also exist in the IR spectra of the Os(0) species: the polymer shows a broad ν(CO) band at much smaller wavenumbers compared to the soluble Os(0) monomer that exhibits a characteristic ν(Pr-CN) band below 2200 cm−1 in addition to the intense and narrow ν(CO) absorption band. For the first time, in this work the M0-bpy(M = Ru, Os) mono- and dicarbonyl species soluble in PrCN have been formulated as a mononuclear complex. Density functional theory (DFT) and time-dependent-DFT calculations confirm the Os(0) oxidation state and suggest that [Os0(CO)(PrCN)(bpy)] is a square planar moiety. The reversible bpy-based reduction of [Os0(CO) (PrCN)(bpy)] triggers catalytic reduction of CO2 to CO and HCOO−.

A numerical model of the ionospheric signatures of time-varying magneticreconnection: I. ionospheric convection

This paper presents a numerical model for predicting the evolution of the pattern of ionospheric convection in response to general time-dependent magnetic reconnection at the dayside magnetopause and in the cross-tail current sheet of the geomagnetic tail. The model quantifies the concepts of ionospheric flow excitation by Cowley and Lockwood (1992), assuming a uniform spatial distribution of ionospheric conductivity. The model is demonstrated using an example in which travelling reconnection pulses commence near noon and then move across the dayside magnetopause towards both dawn and dusk. Two such pulses, 8 min apart, are used and each causes the reconnection to be active for 1 min at every MLT that they pass over. This example demonstrates how the convection response to a given change in the interplanetary magnetic field (via the reconnection rate) depends on the previous reconnection history. The causes of this effect are explained. The inherent assumptions and the potential applications of the model are discussed.