Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems

We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs and real edge capacities in $\tilde{O}(\sqrt{t}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}n^{2.843})$ time, where $n$ is the number of vertices, $t$ is the number of distinct edge capacities (flow amounts) and $O(n^{\omega}) < O(n^{2.373})$ is the time taken to multiply two $n$-by-$n$ matrices over a ring. Secondly we extend the problem to graphs with positive integer edge costs and present an algorithm with $\tilde{O}(\sqrt{t}c^{(\omega+5)/4}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}c^{1.843}n^{2.843})$ worst case time complexity, where $c$ is the upper bound on edge costs

Dynamics of Scalar Field in Polymer-like Representation

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are 1-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background independent and diffeomorphism invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism invariant Hilbert space.Comment: 24 pages, accepted for pubilcation in Class. Quant. Gra

Discovery limits for Techni-Omega production in eγe\gamma Collisions

In a strongly-interacting electroweak sector with an isosinglet vector state, such as the techni-omega, $\omega_T$, the direct $\omega_T Z \gamma$ coupling implies that an $\omega_T$ can be produced by $Z \gamma$ fusion in $e \gamma$ collisions. This is a unique feature for high energy $e^+e^-$ or $e^-e^-$ colliders operating in an $e\gamma$ mode. We consider the processes $e^- \gamma \to e^- Z\gamma$ and $e^- \gamma \to e^- W^+ W^- Z$, both of which proceed via an intermediate $\omega_T$. We find that at a 1.5 TeV $e^+e^-$ linear collider operating in an $e\gamma$ mode with an integrated luminosity of 200 fb$^{-1}$, we can discover an $\omega_T$ for a broad range of masses and widths.Comment: To appear in the Proceedings of the 29th International Conference on High Energy Physics, Vancouver, July 1998, 5 pages, Latex, 7 postscript figure

Optimizing Stimulation and Analysis Protocols for Neonatal fMRI

The development of brain function in young infants is poorly understood. The core challenge is that infants have a limited behavioral repertoire through which brain function can be expressed. Neuroimaging with fMRI has great potential as a way of characterizing typical development, and detecting abnormal development early. But, a number of methodological challenges must first be tackled to improve the robustness and sensitivity of neonatal fMRI. A critical one of these, addressed here, is that the hemodynamic response function (HRF) in pre-term and term neonates differs from that in adults, which has a number of implications for fMRI. We created a realistic model of noise in fMRI data, using resting-state fMRI data from infants and adults, and then conducted simulations to assess the effect of HRF of the power of different stimulation protocols and analysis assumptions (HRF modeling). We found that neonatal fMRI is most powerful if block-durations are kept at the lower range of those typically used in adults (full on/off cycle duration 25-30s). Furthermore, we show that it is important to use the age-appropriate HRF during analysis, as mismatches can lead to reduced power or even inverted signal. Where the appropriate HRF is not known (for example due to potential developmental delay), a flexible basis set performs well, and allows accurate post-hoc estimation of the HRF

Induced Magnetic Ordering by Proton Irradiation in Graphite

We provide evidence that proton irradiation of energy 2.25 MeV on highly-oriented pyrolytic graphite samples triggers ferro- or ferrimagnetism. Measurements performed with a superconducting quantum interferometer device (SQUID) and magnetic force microscopy (MFM) reveal that the magnetic ordering is stable at room temperature.Comment: 3 Figure

The Circumstellar Extinction of Planetary Nebulae

We analyze the dependence of circumstellar extinction on core mass for the brightest planetary nebulae (PNe) in the Magellanic Clouds and M31. We show that in all three galaxies, a statistically significant correlation exists between the two quantities, such that high core mass objects have greater extinction. We model this behavior, and show that the relation is a simple consequence of the greater mass loss and faster evolution times of high mass stars. The relation is important because it provides a natural explanation for the invariance of the [O III] 5007 planetary nebula luminosity function (PNLF) with population age: bright Population I PNe are extinguished below the cutoff of the PNLF. It also explains the counter-intuitive observation that intrinsically luminous Population I PNe often appear fainter than PNe from older, low-mass progenitors.Comment: 12 pages, 2 figures, accepted for ApJ, April 10, 199

The triple degenerate star WD1704+481

WD1704+481 is a visual binary in which both components are white dwarfs. We present spectra of the H-alpha line of both stars which show that one component (WD1704+481.2 = Sanduleak B = GR 577) is a close binary with two white dwarf components. Thus, WD1704+481 is the first known triple degenerate star. From radial velocity measurements of the close binary we find an orbital period of 0.1448d, a mass ratio, q=Mbright/Mfaint of q=0.70+-0.03 and a difference in the gravitational redshifts of 11.5+-2.3km/s. The masses of the close pair of white dwarfs predicted by the mass ratio and gravitational redshift difference combined with theoretical cooling curves are 0.39+-0.05 solar mass and 0.56+-0.07 solar masses. WD1704+481 is therefore also likely to be the first example of a double degenerate in which the less massive white dwarf is composed of helium and the other white dwarf is composed of carbon and oxygen.Comment: 5 pages, 4 figure

Population synthesis of accreting white dwarfs: II. X-ray and UV emission

Accreting white dwarfs (WDs) with non-degenerate companions are expected to emit in soft X-rays and the UV, if accreted H-rich material burns stably. They are an important component of the unresolved emission of elliptical galaxies, and their combined ionizing luminosity may significantly influence the optical line emission from warm ISM. In an earlier paper we modeled populations of accreting WDs, first generating WD with main-sequence, Hertzsprung gap and red giant companions with the population synthesis code \textsc{BSE}, and then following their evolution with a grid of evolutionary tracks computed with \textsc{MESA}. Now we use these results to estimate the soft X-ray (0.3-0.7keV), H- and He II-ionizing luminosities of nuclear burning WDs and the number of super-soft X-ray sources for galaxies with different star formation histories. For the starburst case, these quantities peak at $\sim 1$ Gyr and decline by $\sim 1-3$ orders of magnitude by the age of 10 Gyr. For stellar ages of $\sim$~10 Gyr, predictions of our model are consistent with soft X-ray luminosities observed by Chandra in nearby elliptical galaxies and He II 4686$\AA/\rm{H}{\beta}$ line ratio measured in stacked SDSS spectra of retired galaxies, the latter characterising the strength and hardness of the UV radiation field. However, the soft X-ray luminosity and He~II~4686$\AA/\rm{H}{\beta}$ ratio are significantly overpredicted for stellar ages of $\lesssim 4-8$ Gyr. We discuss various possibilities to resolve this discrepancy and tentatively conclude that it may be resolved by a modification of the typically used criteria of dynamically unstable mass loss for giant stars.Comment: 13 pages, 12 figures, MNRAS accepte

Next generation population synthesis of accreting white dwarfs: I. Hybrid calculations using BSE + MESA

Accreting, nuclear-burning white dwarfs have been deemed to be candidate progenitors of type Ia supernovae, and to account for supersoft X-ray sources, novae, etc. depending on their accretion rates. We have carried out a binary population synthesis study of their populations using two algorithms. In the first, we use the binary population synthesis code \textsf{BSE} as a baseline for the "rapid" approach commonly used in such studies. In the second, we employ a "hybrid" approach, in which we use \textsf{BSE} to generate a population of white dwarfs (WD) with non-degenerate companions on the verge of filling their Roche lobes. We then follow their mass transfer phase using the detailed stellar evolution code \textsf{MESA}. We investigate the evolution of the number of rapidly accreting white dwarfs (RAWDs) and stably nuclear-burning white dwarfs (SNBWDs), and estimate the type Ia supernovae (SNe Ia) rate produced by "single-degenerate" systems (SD). We find significant differences between the two algorithms in the predicted numbers of SNBWDs at early times, and also in the delay time distribution (DTD) of SD SNe Ia. Such differences in the treatment of mass transfer may partially account for differences in the SNe Ia rate and DTD found by different groups. Adopting 100\% efficiency for helium burning, the rate of SNe Ia produced by the SD-channel in a Milky-way-like galaxy in our calculations is $2.0\times10^{-4}\rm{yr}^{-1}$, more than an order of magnitude below the observationally inferred value. In agreement with previous studies, our calculated SD DTD is inconsistent with observations.Comment: 13 pages,11 figures, accepted by MNRA