Generalizing Boolean Satisfiability II: Theory

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

Magellanic Cloud Structure from Near-IR Surveys II: Star Count Maps and the Intrinsic Elongation of the LMC

I construct a near-IR star count map of the LMC and demonstrate, using the viewing angles derived in Paper I, that the LMC is intrinsically elongated. I argue that this is due to the tidal force from the Milky Way. The near-IR data from the 2MASS and DENIS surveys are used to create a star count map of RGB and AGB stars, which is interpreted through ellipse fitting. The radial number density profile is approximately exponential with a scale-length 1.3-1.5 kpc. However, there is an excess density at large radii that may be due to the tidal effect of the Milky Way. The position angle and ellipticity profile converge to PA_maj = 189.3 +/- 1.4 degrees and epsilon = 0.199 +/- 0.008 for r > 5 deg. At large radii there is a drift of the center of the star count contours towards the near side of the plane, which can be undrestood as due to viewing perspective. The fact that PA_maj differes from the line of nodes position angle Theta = 122.5 +/- 8.3 (cf. Paper I) indicates that the LMC disk is not circular, but has an intrinsic ellipticity of 0.31. The LMC is elongated in the general direction of the Galactic center, and is elongated perpendicular to the Magellanic Stream and the velocity vector of the LMC center of mass. This suggests that the elongation of the LMC has been induced by the tidal force of the Milky Way. The position angle of the line of nodes differs from the position angle Theta_max of the line of maximum line of sight velocity gradient: Theta_max - Theta = 20-60 degrees. This could be due to: (a) streaming along non-circular orbits in the elongated disk; (b) uncertainties in the transverse motion of the LMC center of mass; (c) precession and nutation of the LMC disk as it orbits the Milky Way (expected on theoretical grounds). [Abridged]Comment: Astronomical Journal, in press. 34 pages, LaTeX, with 7 PostScript figures. Contains minor revisions with respect to previously posted version. Check out http://www.stsci.edu/~marel/lmc.html for a large scale (23x21 degree) stellar number-density image of the LMC constructed from RGB and AGB stars in the 2MASS and DENIS surveys. The paper is available with higher resolution color figures from http://www.stsci.edu/~marel/abstracts/abs_R32.htm

Factorisation of analytic representations in the unit disk and number-phase statistics of a quantum harmonic oscillator

The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorisation and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorisation properties of a superposition state.Comment: to appear in J. Phys. A, LaTeX, 13 pages, no figures. More information on http://www.technion.ac.il/~brif/science.htm

T2 FLAIR hyperintensity volume Is associated with cognitive function and quality of life in clinically stable patients with lower grade gliomas

Survival outcomes for patients with lower grade gliomas (LrGG) continue to improve. However, damage caused both by tumor growth and by the consequences of treatment often leads to significantly impaired cognitive function and quality of life (QoL). While neuropsychological testing is not routine, serial clinical MRIs are standard of care for patients with LrGG. Thus, having a greater understanding of MRI indicators of cognitive and QoL impairment risk could be beneficial to patients and clinicians. In this work we sought to test the hypothesis that in clinically stable LrGG patients, T2 FLAIR hyperintensity volumes at the time of cognitive assessment are associated with impairments of cognitive function and QoL and could be used to help identify patients for cognitive and QoL assessments and interventions. We performed anatomical MR imaging, cognitive testing and QoL assessments cross-sectionally in 30 clinically stable grade 2 and 3 glioma patients with subjective cognitive concerns who were 6 or more months post-treatment. Larger post-surgical T2 FLAIR volume at testing was significantly associated with lower cognitive performance, while pre-surgical tumor volume was not. Older patients had lower cognitive performance than younger patients, even after accounting for normal age-related declines in performance. Patients with Astrocytoma, IDH mutant LrGGs were more likely to show lower cognitive performance than patients with Oligodendroglioma, IDH mutant 1p19q co-deleted LrGGs. Previous treatment with combined radiation and chemotherapy was associated with poorer self-reported QoL, including self-reported cognitive function. This study demonstrates the importance of appreciating that LrGG patients may experience impairments in cognitive function and QoL over their disease course, including during periods of otherwise sustained clinical stability. Imaging factors can be helpful in identifying vulnerable patients who would benefit from cognitive assessment and rehabilitation

Milky Way potentials in CDM and MOND. Is the Large Magellanic Cloud on a bound orbit?

We compute the Milky Way potential in different cold dark matter (CDM) based models, and compare these with the modified Newtonian dynamics (MOND) framework. We calculate the axis ratio of the potential in various models, and find that isopotentials are less spherical in MOND than in CDM potentials. As an application of these models, we predict the escape velocity as a function of the position in the Galaxy. This could be useful in comparing with future data from planned or already-underway kinematic surveys (RAVE, SDSS, SEGUE, SIM, GAIA or the hypervelocity stars survey). In addition, the predicted escape velocity is compared with the recently measured high proper motion velocity of the Large Magellanic Cloud (LMC). To bind the LMC to the Galaxy in a MOND model, while still being compatible with the RAVE-measured local escape speed at the Sun's position, we show that an external field modulus of less than $0.03 a_0$ is needed.Comment: Accepted for publication in MNRAS, 13 pages, 7 figures, 3 table

Creating quanta with "annihilation" operator

An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|\psi>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|\psi >$. Moreover, for certain `hyper-Poissonian' states $|\psi>$ the mean number of quanta in the (normalized) state $\hat{a}|\psi>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|\psi >$. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.Comment: 10 pages, LaTex, an extended version with several references added and the text divided into sections; to appear in J. Phys.

A consistent quantum model for continuous photodetection processes

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.Comment: 12 pages, 4 figure

Adult infiltrating gliomas with WHO 2016 integrated diagnosis: additional prognostic roles of ATRX and TERT

The “integrated diagnosis” for infiltrating gliomas in the 2016 revised World Health Organization (WHO) classification of tumors of the central nervous system requires assessment of the tumor for IDH mutations and 1p/19q codeletion. Since TERT promoter mutations and ATRX alterations have been shown to be associated with prognosis, we analyzed whether these tumor markers provide additional prognostic information within each of the five WHO 2016 categories. We used data for 1206 patients from the UCSF Adult Glioma Study, the Mayo Clinic and The Cancer Genome Atlas (TCGA) with infiltrative glioma, grades II-IV for whom tumor status for IDH, 1p/19q codeletion, ATRX, and TERT had been determined. All cases were assigned to one of 5 groups following the WHO 2016 diagnostic criteria based on their morphologic features, and IDH and 1p/19q codeletion status. These groups are: (1) Oligodendroglioma, IDH-mutant and 1p/19q-codeleted; (2) Astrocytoma, IDH-mutant; (3) Glioblastoma, IDH-mutant; (4) Glioblastoma, IDH-wildtype; and (5) Astrocytoma, IDH-wildtype. Within each group, we used univariate and multivariate Cox proportional hazards models to assess associations of overall survival with patient age at diagnosis, grade, and ATRX alteration status and/or TERT promoter mutation status. Among Group 1 IDH-mutant 1p/19q-codeleted oligodendrogliomas, the TERT-WT group had significantly worse overall survival than the TERT-MUT group (HR: 2.72, 95% CI 1.05–7.04, p = 0.04). In both Group 2, IDH-mutant astrocytomas and Group 3, IDH-mutant glioblastomas, neither TERT mutations nor ATRX alterations were significantly associated with survival. Among Group 4, IDH-wildtype glioblastomas, ATRX alterations were associated with favorable outcomes (HR: 0.36, 95% CI 0.17–0.81, p = 0.01). Among Group 5, IDH-wildtype astrocytomas, the TERT-WT group had significantly better overall survival than the TERT-MUT group (HR: 0.48, 95% CI 0.27–0.87), p = 0.02). Thus, we present evidence that in certain WHO 2016 diagnostic groups, testing for TERT promoter mutations or ATRX alterations may provide additional useful prognostic information

The Magellanic Stream, High-Velocity Clouds and the Sculptor Group

The Magellanic Stream is a 100\deg x 10\deg filament of gas which lies within the Galactic halo and contains ~ 2 x 10^8 \Msun of neutral hydrogen. We present data from the HI Parkes All Sky Survey (HIPASS) in the first complete survey of the entire Magellanic Stream and its surroundings. We also present a summary of the reprocessing techniques used to recover large-scale structure in the Stream. The Stream properties revealed include: bifurcation along the main Stream filament; dense, isolated clouds which follow the entire length of the Stream; head-tail structures; and a complex filamentary web at the head where gas is being freshly stripped away from the Small Magellanic Cloud and the Bridge. Debris which appears to be of Magellanic origin extends out to 20\deg from the main Stream filaments. The large number of elongated Stream clouds suggests the presence of shearing motions within the Stream, arising from tidal forces or interaction with the tenuous Galactic halo. Clouds along the sightline to the less distant half of the Sculptor Group, show anomalous properties. We argue that these clouds represent halo material, and are not distant Sculptor Group clouds. This result has significant implications for the hypothesis that there might exist distant, massive HVCs within the Local Group. (abridged