Dimension Reduction via Colour Refinement

Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all vertices in the same colour class have the same number of neighbours in every colour class. Tinhofer (Disc. App. Math., 1991), Ramana, Scheinerman, and Ullman (Disc. Math., 1994) and Godsil (Lin. Alg. and its App., 1997) established a tight correspondence between colour refinement and fractional isomorphisms of graphs, which are solutions to the LP relaxation of a natural ILP formulation of graph isomorphism. We introduce a version of colour refinement for matrices and extend existing quasilinear algorithms for computing the colour classes. Then we generalise the correspondence between colour refinement and fractional automorphisms and develop a theory of fractional automorphisms and isomorphisms of matrices. We apply our results to reduce the dimensions of systems of linear equations and linear programs. Specifically, we show that any given LP L can efficiently be transformed into a (potentially) smaller LP L' whose number of variables and constraints is the number of colour classes of the colour refinement algorithm, applied to a matrix associated with the LP. The transformation is such that we can easily (by a linear mapping) map both feasible and optimal solutions back and forth between the two LPs. We demonstrate empirically that colour refinement can indeed greatly reduce the cost of solving linear programs

Climate drives the geography of marine consumption by changing predator communities

The global distribution of primary production and consumption by humans (fisheries) is well-documented, but we have no map linking the central ecological process of consumption within food webs to temperature and other ecological drivers. Using standardized assays that span 105° of latitude on four continents, we show that rates of bait consumption by generalist predators in shallow marine ecosystems are tightly linked to both temperature and the composition of consumer assemblages. Unexpectedly, rates of consumption peaked at midlatitudes (25 to 35°) in both Northern and Southern Hemispheres across both seagrass and unvegetated sediment habitats. This pattern contrasts with terrestrial systems, where biotic interactions reportedly weaken away from the equator, but it parallels an emerging pattern of a subtropical peak in marine biodiversity. The higher consumption at midlatitudes was closely related to the type of consumers present, which explained rates of consumption better than consumer density, biomass, species diversity, or habitat. Indeed, the apparent effect of temperature on consumption was mostly driven by temperature-associated turnover in consumer community composition. Our findings reinforce the key influence of climate warming on altered species composition and highlight its implications for the functioning of Earth’s ecosystems

Algebraic invariants of five qubits

The Hilbert series of the algebra of polynomial invariants of pure states of five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include

Observations of the martian atmosphere with the mars climate sounder

The Mars Climate Sounder (MCS) has obtained measurements of the Martian atmosphere for one Mars year. Onboard the Mars Reconnaissance Orbiter (MRO), MCS continues to acquire high vertical resolution profiles of temperature, dust, condensates of CO2 and H2O, and water vapor by observing the limb of the atmosphere from the surface to 80 km in the spectral intervals 0.3 – 3 ?m and 11.5 – 45 ?m [1]. This paper describes the investigation and introduces some of the observations being studied by the MCS science team. Other presentations by the team at this workshop will describe in greater detail results of ongoing research using MCS data

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Lunar Flashlight: Illuminating the Lunar South Pole

Recent reflectance data from LRO instruments suggest water ice and other volatiles may be present on the surface in lunar permanentlyshadowed regions, though the detection is not yet definitive. Understanding the composition, quantity, distribution, and form of water and other volatiles associated with lunar permanently shadowed regions (PSRs) is identified as a NASA Strategic Knowledge Gap (SKG) for Human Exploration. These polar volatile deposits are also scientifically interesting, having the potential to reveal important information about the delivery of water to the Earth- Moon system

Lunar Flashlight: Illuminating the Moon's South Pole

Recent reflectance data from LRO instruments suggest water ice and other volatiles may be present on the surface in lunar permanently shadowed regions, though the detection is not yet definitive. Understanding the composition, quantity, distribution, and form of water and other volatiles associated with lunar permanently shadowed regions (PSRs) is identified as a NASA Strategic Knowledge Gap (SKG) for Human Exploration. These polar volatile deposits are also scientifically interesting, having the potential to reveal important information about the delivery of water to the Earth-Moon system

Multiple photon effects in fermion-(anti)fermion scattering at SSC energies

We use the theory of Yennie, Frautschi and Suura to realize, via Monte Carlo methods, the process f\,\bbbarf\to f'\,\bbbarf'+n\gamma at SSC and LHC energies, where $f$ and $f'$ are quarks or leptons. QED infrared divergences are canceled to all orders in perturbation theory. The resulting Monte Carlo event generator, SSC-YFS2, is used to study the effects of initial-state photon radiation on these processes in the SSC environment. Sample Monte Carlo data are presented and discussed. We find that the respective multiple-photon effects must be taken into account in discussing precise predictions for SSC physics processes.Comment: 14 pages + 8 figures + 1 tabl

Mesocorticolimbic monoamine correlates of methamphetamine sensitization and motivation.

Methamphetamine (MA) is a highly addictive psychomotor stimulant, with life-time prevalence rates of abuse ranging from 5-10% world-wide. Yet, a paucity of research exists regarding MA addiction vulnerability/resiliency and neurobiological mediators of the transition to addiction that might occur upon repeated low-dose MA exposure, more characteristic of early drug use. As stimulant-elicited neuroplasticity within dopamine neurons innervating the nucleus accumbens (NAC) and prefrontal cortex (PFC) is theorized as central for addiction-related behavioral anomalies, we used a multi-disciplinary research approach in mice to examine the interactions between sub-toxic MA dosing, motivation for MA and mesocorticolimbic monoamines. Biochemical studies of C57BL/6J (B6) mice revealed short- (1 day), as well as longer-term (21 days), changes in extracellular dopamine, DAT and/or D2 receptors during withdrawal from 10, once daily, 2 mg/kg MA injections. Follow-up biochemical studies conducted in mice selectively bred for high vs. low MA drinking (respectively, MAHDR vs. MALDR mice), provided novel support for anomalies in mesocorticolimbic dopamine as a correlate of genetic vulnerability to high MA intake. Finally, neuropharmacological targeting of NAC dopamine in MA-treated B6 mice demonstrated a bi-directional regulation of MA-induced place-conditioning. These results extend extant literature for MA neurotoxicity by demonstrating that even subchronic exposure to relatively low MA doses are sufficient to elicit relatively long-lasting changes in mesocorticolimbic dopamine and that drug-induced or idiopathic anomalies in mesocorticolimbic dopamine may underpin vulnerability/resiliency to MA addiction