1,779 research outputs found
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
time,
where is the number of vertices, is the number of distinct edge
capacities (flow amounts) and is the time taken
to multiply two -by- matrices over a ring. Secondly we extend the problem
to graphs with positive integer edge costs and present an algorithm with
worst case time complexity, where is
the upper bound on edge costs
Priorities in gravitational waveforms for future space-borne detectors: vacuum accuracy or environment?
In preparation for future space-borne gravitational-wave (GW) detectors,
should the modelling effort focus on high-precision vacuum templates or on the
astrophysical environment of the sources? We perform a systematic comparison of
the phase contributions caused by 1) known environmental effects in both
gaseous and stellar matter backgrounds, or 2) high-order post-Newtonian {(PN)}
terms in the evolution of mHz GW sources {during the inspiral stage of massive
binaries}. We use the accuracy of currently available analytical waveform
models as a benchmark {value, finding} the following trends: the largest
unmodelled phase contributions are likely environmental rather than PN for
binaries lighter than ~M, where is the
redshift. Binaries heavier than ~M do not require
more accurate {inspiral} waveforms due to low signal-to-noise ratios (SNRs).
For high-SNR sources, environmental {phase contributions} are relevant at low
redshift, while high-order vacuum templates are required at . Led by
these findings, we argue that including environmental effects in waveform
models should be prioritised in order to maximize the science yield of future
mHz detectors.Comment: Accepted in MNRA
Optimization of suppression for two-element treatment liners for turbomachinery exhaust ducts
Sound wave propagation in a soft-walled rectangular duct with steady uniform flow was investigated at exhaust conditions, incorporating the solution equations for sound wave propagation in a rectangular duct with multiple longitudinal wall treatment segments. Modal analysis was employed to find the solution equations and to study the effectiveness of a uniform and of a two-sectional liner in attenuating sound power in a treated rectangular duct without flow (M = 0) and with uniform flow of Mach 0.3. Two-segment liners were shown to increase the attenuation of sound as compared to a uniform liner. The predicted sound attenuation was compared with measured laboratory results for an optimized two-segment suppressor. Good correlation was obtained between the measured and predicted suppressions when practical variations in the modal content and impedance were taken into account. Two parametric studies were also completed
Finding the Minimum-Weight k-Path
Given a weighted -vertex graph with integer edge-weights taken from a
range , we show that the minimum-weight simple path visiting
vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k
M). If the weights are reals in , we provide a
-approximation which has a running time of \tilde{O}(2^k
\poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem
of -tree, in which we wish to find a minimum-weight copy of a -node tree
in a given weighted graph , under the same restrictions on edge weights
respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k)
M n^3) and a -approximate solution of running time
\tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above
algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201
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“Pay what you want” as threshold public good provision
Prevailing wisdom on “pay what you want” (PWYW) pricing focuses on the influence of altruism or fairness on consumers’ payments. In this paper, we offer a different perspective by demonstrating that, if the seller and consumers interact repeatedly, and future provision of PWYW depends on whether current revenue under PWYW is sufficient for the seller to achieve financial goals, then paying under PWYW can be likened to paying for a threshold public good. Our model implies that continuous provision of PWYW can be profitable even when all consumers are self-interested. We find in two experiments that if there is pre-payment online chat-room-style communication among consumers, then efficient tacit coordination at the payment stage can be accomplished to achieve continuous PWYW provision. We also show experimentally that pre-payment communication can sustain PWYW provision even when consumers have limited feedback about each other’s payments, or limited information about the market
LNCS
We present the tool Quasy, a quantitative synthesis tool. Quasy takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the most-likely environment behaviors given as a probability distribution on the possible input sequences. Quasy solves these two quantitative synthesis problems by reduction to instances of 2-player games and Markov Decision Processes (MDPs) with quantitative winning objectives. Quasy can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic mean-payoff games with 2 players, MDPs with mean-payoff objectives, and ergodic MDPs with mean-payoff parity objectives
Direct formation of massive black holes via dynamical collapse in metal-enriched merging galaxies at : fully cosmological simulations
We present the results of the first fully cosmological hydrodynamical
simulations studying the merger-driven model for massive black hole (BH) seed
formation via direct collapse. Using the zoom-in technique as well as particle
splitting, we achieve a final spatial resolution of pc. We show that the
major merger of two massive galaxies at redshift results in the
formation of a nuclear supermassive disk (SMD) of only pc in radius, owing
to a prodigious gas inflow sustained at - yr. The
core of the merger remnant is metal-rich, well above solar abundance, and the
SMD reaches a gaseous mass of in less than a
million years after the merger, despite a concurrent prominent nuclear
starburst. Dynamical heating as gas falls into the deepest part of the
potential well, and heating and stirring by supernova blastwaves, generate a
turbulent multi-phase interstellar medium, with a gas velocity dispersion
exceeding 100 km s. As a result, only moderate fragmentation occurs in
the inner - pc despite the temperature falls below K. The SMD is
Jeans-unstable as well as bar-unstable and will collapse further adiabatically,
becoming warm and ionized. We show that the SMD, following inevitable
contraction, will become general relativistic unstable and directly form a
supermassive BH of mass in the range - , essentially
skipping the stage of BH seed formation. These results confirm that mergers
between the most massive galaxies at - can naturally explain the
rapid emergence of bright high-redshift quasars.Comment: 14 pages, 8 figures, submitted to Ap
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