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

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

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

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

Hardware Acceleration of Beamforming in a UWB Imaging Unit for Breast Cancer Detection

The Ultrawideband (UWB) imaging technique for breast cancer detection is based on the fact that cancerous cells have different dielectric characteristics than healthy tissues.When a UWB pulse in the microwave range strikes a cancerous region, the reflected signal is more intense than the backscatter originating from the surrounding fat tissue. A UWB imaging system consists of transmitters, receivers, and antennas for the RF part, and of a digital back-end for processing the received signals. In this paper we focus on the imaging unit, which elaborates the acquired data and produces 2D or 3D maps of reflected energies.We show that one of the processing tasks, Beamforming, is the most timing critical and cannot be executed in software by a standard microprocessor in a reasonable time.We thus propose a specialized hardware accelerator for it.We design the accelerator in VHDL and test it in an FPGA-based prototype. We also evaluate its performance when implemented on a CMOS 45nm ASIC technology. The speed-up with respect to a software implementation is on the order of tens to hundreds, depending on the degree of parallelism permitted by the target technology

Interacting Modified Variable Chaplygin Gas in Non-flat Universe

A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.Comment: 9 pages; Accepted for publication in European Physical Journal

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

Phase-space analysis of interacting phantom cosmology

We perform a detailed phase-space analysis of various phantom cosmological models, where the dark energy sector interacts with the dark matter one. We examine whether there exist late-time scaling attractors, corresponding to an accelerating universe and possessing dark energy and dark matter densities of the same order. We find that all the examined models, although accepting stable late-time accelerated solutions, cannot alleviate the coincidence problem, unless one imposes a form of fine-tuning in the model parameters. It seems that interacting phantom cosmology cannot fulfill the basic requirement that led to its construction.Comment: 6 figures, use revtex, v2: minor corrections, references added, accepted for publication in JCA

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

Predicted Infrared and Raman Spectra for Neutral Ti_8C_12 Isomers

Using a density-functional based algorithm, the full IR and Raman spectra are calculated for the neutral Ti_8C_12 cluster assuming geometries of Th, Td, D2d and C3v symmetry. The Th pentagonal dodecahedron is found to be dynamically unstable. The calculated properties of the relaxed structure having C3v symmetry are found to be in excellent agreement with experimental gas phase infrared results, ionization potential and electron affinity measurements. Consequently, the results presented may be used as a reference for further experimental characterization using vibrational spectroscopy.Comment: 6 pages, 5 figures. Physical Review A, 2002 (in press