Interacting new agegraphic Phantom model of dark energy in non-flat universe

In this paper we consider the new agegraphic model of interacting dark energy in non-flat universe. We show that the interacting agegraphic dark energy can be described by a phantom scalar field. Then we show this phantomic description of the agegraphic dark energy and reconstruct the potential of the phantom scalar field.Comment: 8 pages, no figur

Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

Cosmological Evolution Across Phantom Crossing and the Nature of the Horizon

In standard cosmology, with the evolution of the universe, the matter density and thermodynamic pressure gradually decreases. Also in course of evolution, the matter in the universe obeys (or violates) some restrictions or energy conditions. If the matter distribution obeys strong energy condition (SEC), the universe is in a decelerating phase while violation of SEC indicates an accelerated expansion of the universe. In the period of accelerated expansion the matter may be either of quintessence nature or of phantom nature depending on the fulfilment of the weak energy condition (WEC) or violation of it. As recent observational evidences demand that the universe is going through an accelerated expansion so mater should be either quintessence or phantom in nature. In the present work we study the evolution of the universe through the phantom barrier (i.e. the dividing line between the quintessence and phantom era) and examine how apparent and event horizon change across the barrier. Finally, we investigate the possibility of occurrence of any singularity in phantom era.Comment: 7 pages and 4 figure

Interacting Three Fluid System and Thermodynamics of the Universe Bounded by the Event Horizon

The work deals with the thermodynamics of the universe bounded by the event horizon. The matter in the universe has three constituents namely dark energy, dark matter and radiation in nature and interaction between then is assumed. The variation of entropy of the surface of the horizon is obtained from unified first law while matter entropy variation is calculated from the Gibbss' law. Finally, validity of the generalized second law of thermodynamics is examined and conclusions are written point wise.Comment: 7 page

Association between active commuting and incident cardiovascular disease, cancer, and mortality: prospective cohort study

Objective: To investigate the association between active commuting and incident cardiovascular disease (CVD), cancer, and all cause mortality. Design: Prospective population based study. Setting: UK Biobank. Participants: 263 450 participants (106 674 (52%) women; mean age 52.6), recruited from 22 sites across the UK. The exposure variable was the mode of transport used (walking, cycling, mixed mode v non-active (car or public transport)) to commute to and from work on a typical day. Main outcome measures: Incident (fatal and non-fatal) CVD and cancer, and deaths from CVD, cancer, or any causes. Results: 2430 participants died (496 were related to CVD and 1126 to cancer) over a median of 5.0 years (interquartile range 4.3-5.5) follow-up. There were 3748 cancer and 1110 CVD events. In maximally adjusted models, commuting by cycle and by mixed mode including cycling were associated with lower risk of all cause mortality (cycling hazard ratio 0.59, 95% confidence interval 0.42 to 0.83, P=0.002; mixed mode cycling 0.76, 0.58 to 1.00, P<0.05), cancer incidence (cycling 0.55, 0.44 to 0.69, P<0.001; mixed mode cycling 0.64, 0.45 to 0.91, P=0.01), and cancer mortality (cycling 0.60, 0.40 to 0.90, P=0.01; mixed mode cycling 0.68, 0.57 to 0.81, P<0.001). Commuting by cycling and walking were associated with a lower risk of CVD incidence (cycling 0.54, 0.33 to 0.88, P=0.01; walking 0.73, 0.54 to 0.99, P=0.04) and CVD mortality (cycling 0.48, 0.25 to 0.92, P=0.03; walking 0.64, 0.45 to 0.91, P=0.01). No statistically significant associations were observed for walking commuting and all cause mortality or cancer outcomes. Mixed mode commuting including walking was not noticeably associated with any of the measured outcomes. Conclusions: Cycle commuting was associated with a lower risk of CVD, cancer, and all cause mortality. Walking commuting was associated with a lower risk of CVD independent of major measured confounding factors. Initiatives to encourage and support active commuting could reduce risk of death and the burden of important chronic conditions

Sleep characteristics modify the association between genetic predisposition to obesity and anthropometric measurements in 119,679 UK Biobank participants

Background - Obesity is a multifactorial condition influenced by genetics, lifestyle and environment. Objective - To investigate whether the association between a validated genetic profile risk score for obesity (GPRS-obesity) with body mass index (BMI) and waist circumference (WC) was modified by sleep characteristics. Design - This study included cross-sectional data from 119,859 white European adults, aged 37-73 years, participating on the UK Biobank. Interactions between GPRS-obesity, and sleep characteristics (sleep duration, chronotype, day napping, and shift work) in their effects on BMI and WC were investigated. Results - The GPRS-obesity was associated with BMI (β:0.57 kg.m-2 per standard deviation (SD) increase in GPRS, [95%CI:0.55, 0.60]; P=6.3x10-207) and WC (β:1.21 cm, [1.15, 1.28]; P=4.2x10-289). There were significant interactions between GPRS-obesity and a variety of sleep characteristics in their relationship with BMI (P-interaction <0.05). In participants who slept <7 hrs or >9 hrs daily, the effect of GPRS-obesity on BMI was stronger (β:0.60 [0.54, 0.65] and 0.73 [0.49, 0.97] kg.m-2 per SD increase in GPRS, respectively) than in normal length sleepers (7-9 hours; β:0.52 [0.49, 0.55] kg.m-2 per SD). A similar pattern was observed for shiftworkers (β:0.68 [0.59, 0.77] versus 0.54 [0.51, 0.58] kg.m-2 for non-shiftworkers) and for night-shiftworkers (β:0.69 [0.56, 0.82] versus 0.55 [0.51, 0.58] kg.m-2 for non-night- shiftworkers), for those taking naps during the day (β:0.65 [0.52, 0.78] versus 0.51 [0.48, 0.55] kg.m-2 for those who never/rarely had naps) and for those with a self-reported evening chronotype (β:0.72 [0.61, 0.82] versus β:0.52 [0.47, 0.57] kg.m-2 for morning chronotype). Similar findings were obtained using WC as the outcome. Conclusions – This study shows that the association between genetic risk for obesity and phenotypic adiposity measures is exacerbated by adverse sleeping characteristics

Phantom phase power-law solution in f(G)f(G) gravity

Power-law solutions for $f(G)$ gravity coupled with perfect fluid have been studied for spatially flat universe. It is shown that despite the matter dominated and accelerating power-law solutions, the power-law solution exists for an special form of $f(G)$ when this universe enters a Phantom phase.Comment: 10 pages, Published online in Astrophysics and Space Scienc

Interacting new agegraphic viscous dark energy with varying GG

We consider the new agegraphic model of dark energy with a varying gravitational constant, $G$, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.Comment: 12 pages, accepted for publication in IJTP (2010

Statefinder diagnostic and stability of modified gravity consistent with holographic and new agegraphic dark energy

Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in [M. R. Setare, Int. J. Mod. Phys. D 17 (2008) 2219; M. R. Setare, Astrophys. Space Sci. 326 (2010) 27]. We also calculate the statefinder parameters which classify our dark energy model.Comment: 12 pages, 2 figures, accepted by Gen. Relativ. Gravi

Tight Kernel Bounds for Problems on Graphs with Small Degeneracy

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, e.g. planar graphs, H-minor free graphs, and H-topological-minor free graphs. We show that for several natural problems on d-degenerate graphs the best known kernelization upper bounds are essentially tight.Comment: Full version of ESA 201