Interval total colorings of graphs

A total coloring of a graph $G$ is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex $v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where $d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate some properties of interval total colorings. We also determine exact values of the least and the greatest possible number of colors in such colorings for some classes of graphs.Comment: 23 pages, 1 figur

A close examination of double filtering with fold change and t test in microarray analysis

<p>Abstract</p> <p>Background</p> <p>Many researchers use the double filtering procedure with fold change and <it>t </it>test to identify differentially expressed genes, in the hope that the double filtering will provide extra confidence in the results. Due to its simplicity, the double filtering procedure has been popular with applied researchers despite the development of more sophisticated methods.</p> <p>Results</p> <p>This paper, for the first time to our knowledge, provides theoretical insight on the drawback of the double filtering procedure. We show that fold change assumes all genes to have a common variance while <it>t </it>statistic assumes gene-specific variances. The two statistics are based on contradicting assumptions. Under the assumption that gene variances arise from a mixture of a common variance and gene-specific variances, we develop the theoretically most powerful likelihood ratio test statistic. We further demonstrate that the posterior inference based on a Bayesian mixture model and the widely used significance analysis of microarrays (SAM) statistic are better approximations to the likelihood ratio test than the double filtering procedure.</p> <p>Conclusion</p> <p>We demonstrate through hypothesis testing theory, simulation studies and real data examples, that well constructed shrinkage testing methods, which can be united under the mixture gene variance assumption, can considerably outperform the double filtering procedure.</p

Multiwavelength Observations of Pulsar Wind Nebulae

The extended nebulae formed as pulsar winds expand into their surroundings provide information about the composition of the winds, the injection history from the host pulsar, and the material into which the nebulae are expanding. Observations from across the electromagnetic spectrum provide constraints on the evolution of the nebulae, the density and composition of the surrounding ejecta, the geometry of the central engines, and the long-term fate of the energetic particles produced in these systems. Such observations reveal the presence of jets and wind termination shocks, time-varying compact emission structures, shocked supernova ejecta, and newly formed dust. Here I provide a broad overview of the structure of pulsar wind nebulae, with specific examples from observations extending from the radio band to very-high-energy gamma-rays that demonstrate our ability to constrain the history and ultimate fate of the energy released in the spin-down of young pulsars.Comment: 20 pages, 11 figures. Invited review to appear in Proc. of the inaugural ICREA Workshop on "The High-Energy Emission from Pulsars and their Systems" (2010), eds. N. Rea and D. Torres, (Springer Astrophysics and Space Science series

A variable absorption feature in the X-ray spectrum of a magnetar

Soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are slowly rotating, isolated neutron stars that sporadically undergo episodes of long-term flux enhancement (outbursts) generally accompanied by the emission of short bursts of hard X-rays. This behaviour can be understood in the magnetar model, according to which these sources are mainly powered by their own magnetic energy. This is supported by the fact that the magnetic fields inferred from several observed properties of AXPs and SGRs are greater than - or at the high end of the range of - those of radio pulsars. In the peculiar case of SGR 0418+5729, a weak dipole magnetic moment is derived from its timing parameters, whereas a strong field has been proposed to reside in the stellar interior and in multipole components on the surface. Here we show that the X-ray spectrum of SGR 0418+5729 has an absorption line, the properties of which depend strongly on the star's rotational phase. This line is interpreted as a proton cyclotron feature and its energy implies a magnetic field ranging from 2E14 gauss to more than 1E15 gauss.Comment: Nature, 500, 312 (including Supplementary Information

The Precursors and Products of Justice Climates: Group Leader Antecedents and Employee Attitudinal Consequences

Drawing on the organizational justice, organizational climate, leadership and personality, and social comparison theory literatures, we develop hypotheses about the effects of leader personality on the development of three types of justice climates (e.g., procedural, interpersonal, and informational), and the moderating effects of these climates on individual level justice- attitude relationships. Largely consistent with the theoretically-derived hypotheses, the results showed that leader (a) agreeableness was positively related to procedural, interpersonal and informational justice climates, (b) conscientiousness was positively related to a procedural justice climate, and (c) neuroticism was negatively related to all three types of justice climates. Further, consistent with social comparison theory, multilevel data analyses revealed that the relationship between individual justice perceptions and job attitudes (e.g., job satisfaction, commitment) was moderated by justice climate such that the relationships were stronger when justice climate was high

Complex-Distance Potential Theory and Hyperbolic Equations

An extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n is the delta function. This provides a natural model for extended particles in physics. In C^n, interpreted as complex spacetime, D(z) acts as a propagator generating solutions of the wave equation from their initial values. This gives a new connection between elliptic and hyperbolic equations that does not assume analyticity of the Cauchy data. Generalized to Clifford analysis, it induces a similar connection between solutions of elliptic and hyperbolic Dirac equations. There is a natural application to the time-dependent, inhomogeneous Dirac and Maxwell equations, and the `electromagnetic wavelets' introduced previously are an example.Comment: 25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford Algebras, Ixtapa, June 24 - July 4, 199

A primary care, multi-disciplinary disease management program for opioid-treated patients with chronic non-cancer pain and a high burden of psychiatric comorbidity

BACKGROUND: Chronic non-cancer pain is a common problem that is often accompanied by psychiatric comorbidity and disability. The effectiveness of a multi-disciplinary pain management program was tested in a 3 month before and after trial. METHODS: Providers in an academic general medicine clinic referred patients with chronic non-cancer pain for participation in a program that combined the skills of internists, clinical pharmacists, and a psychiatrist. Patients were either receiving opioids or being considered for opioid therapy. The intervention consisted of structured clinical assessments, monthly follow-up, pain contracts, medication titration, and psychiatric consultation. Pain, mood, and function were assessed at baseline and 3 months using the Brief Pain Inventory (BPI), the Center for Epidemiological Studies-Depression Scale scale (CESD) and the Pain Disability Index (PDI). Patients were monitored for substance misuse. RESULTS: Eighty-five patients were enrolled. Mean age was 51 years, 60% were male, 78% were Caucasian, and 93% were receiving opioids. Baseline average pain was 6.5 on an 11 point scale. The average CESD score was 24.0, and the mean PDI score was 47.0. Sixty-three patients (73%) completed 3 month follow-up. Fifteen withdrew from the program after identification of substance misuse. Among those completing 3 month follow-up, the average pain score improved to 5.5 (p = 0.003). The mean PDI score improved to 39.3 (p < 0.001). Mean CESD score was reduced to 18.0 (p < 0.001), and the proportion of depressed patients fell from 79% to 54% (p = 0.003). Substance misuse was identified in 27 patients (32%). CONCLUSIONS: A primary care disease management program improved pain, depression, and disability scores over three months in a cohort of opioid-treated patients with chronic non-cancer pain. Substance misuse and depression were common, and many patients who had substance misuse identified left the program when they were no longer prescribed opioids. Effective care of patients with chronic pain should include rigorous assessment and treatment of these comorbid disorders and intensive efforts to insure follow up

SDSS-IV MaNGA: A serendipitous observation of a potential gas accretion event

The nature of warm, ionized gas outside of galaxies may illuminate several key galaxy evolutionary processes. A serendipitous observation by the MaNGA survey has revealed a large, asymmetric H$\alpha$ complex with no optical counterpart that extends ≈8″ (≈6.3 kpc) beyond the effective radius of a dusty, starbursting galaxy. This H$\alpha$ extension is approximately three times the effective radius of the host galaxy and displays a tail-like morphology. We analyze its gas-phase metallicities, gaseous kinematics, and emission-line ratios and discuss whether this H$\alpha$ extension could be diffuse ionized gas, a gas accretion event, or something else. We find that this warm, ionized gas structure is most consistent with gas accretion through recycled wind material, which could be an important process that regulates the low-mass end of the galaxy stellar mass function.Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration. D.B. is supported by grant RSCF-14-22-00041. A.W. acknowledges support from a Leverhulme Early Career Fellowship. J.H.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under grant number AYA2013-41243-P and thanks the Astrophysics Research Institute of Liverpool John Moores University for their hospitality, and the Spanish Ministry of Education, Culture and Sports for financial support of his visit there, through grant number PR2015-00512

MHD models of Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical modeling of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.Comment: 18 pages, 5 figures, Invited Review, Proceedings of the "ICREA Workshop on The High-Energy Emission from Pulsars and their Systems", Sant Cugat, Spain, April 12-16, 201