MAD Dispersion Measure Makes Extremal Queue Analysis Simple

A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival- and service-time distributions. We address this extremal queue problem by measuring dispersion in terms of mean absolute deviation (MAD) instead of the more conventional variance, making available methods for distribution-free analysis. Combined with random walk theory, we obtain explicit expressions for the extremal interarrival- and service-time distributions and, hence, the best possible upper bounds for all moments of the waiting time. We also obtain tight lower bounds that, together with the upper bounds, provide robust performance intervals. We show that all bounds are computationally tractable and remain sharp also when the mean and MAD are not known precisely but are estimated based on available data instead. Summary of Contribution: Queueing theory is a classic OR topic with a central role for the GI/G/1 queue. Although this queueing system is conceptually simple, it is notoriously hard to determine the worst-case expected waiting time when only knowing the first two moments of the interarrival- and service-time distributions. In this setting, the exact form of the extremal distribution can only be determined numerically as the solution to a nonconvex nonlinear optimization problem. Our paper demonstrates that using mean absolute deviation (MAD) instead of variance alleviates the computational intractability of the extremal GI/G/1 queue problem, enabling us to state the worst-case distributions explicitly.

The CHIME Fast Radio Burst Population Does Not Track the Star Formation History of the Universe

The redshift distribution of fast radio bursts (FRBs) is not well constrained. The association of the Galactic FRB 200428 with the young magnetar SGR 1935+2154 raises the working hypothesis that FRB sources track the star formation history of the universe. The discovery of FRB 20200120E in association with a globular cluster in the nearby galaxy M81, however, casts doubts on such an assumption. We apply the Monte Carlo method developed in a previous work to test different FRB redshift distribution models against the recently released first CHIME FRB catalog in terms of their distributions in specific fluence, external dispersion measure (DME), and inferred isotropic energy. Our results clearly rule out the hypothesis that all FRBs track the star formation history of the universe. The hypothesis that all FRBs track the accumulated stars throughout history describes the data better but still cannot meet both the DME and the energy criteria. The data seem to be better modeled with either a redshift distribution model invoking a significant delay with respect to star formation or a hybrid model invoking both a dominant delayed population and a subdominant star formation population. We discuss the implications of this finding for FRB source models.

Relationship between Motor Development and the Nutritional Status of Schools in a City of Vale dos Sinos Region, RS, Brazil

This descriptive, quantitative, and cross-sectional study aimed at the relationship between motor development and the nutritional status of schoolchildren aged eight to ten years from the city of Novo Hamburgo. One hundred forty-five students (80 boys and 65 girls) participated in the study, duly enrolled in the municipal school system, and belonged to different schools and regions of the same municipality. The study instruments used were Ulrich's Test of Gross Motor Development - Second Edition (TGMD-2) (2001), the Ministry of Health's food frequency questionnaire, and anthropometric assessments of weight, height, and body mass index (BMI). For data analysis, mean, dispersion measure, frequency and percentage were used. To compare the data, Student's t test was used with tabulation of primary data in the program SPSS 26.0. The results showed that there was no relationship between the nutritional status and motor development of those investigated. However, it was observed that there is a statistically significant difference regarding the time that students spend watching television. Thus, it is understood that the nutritional status is related to the prolonged use of screens, which leads to overweight and obesity and keeps students away from physical activities. Keywords: Motor Skills. Nutritional Status. Child. ResumoO presente estudo descritivo, de caráter quantitativo e transversal, buscou a relação entre o desenvolvimento motor e o estado nutricional de escolares de oito a dez anos de idade, da cidade de Novo Hamburgo. Participaram do estudo 145 escolares (80 meninos e 65 meninas) matriculados na Rede Municipal de ensino que pertenciam a diferentes escolas e regiões do mesmo município. Como instrumentos de estudo foram utilizados o Test of Gross Motor Development – Second Edition (TGMD-2) de Ulrich (2001), o questionário de frequência alimentar do Ministério da Saúde e avaliações antropométricas de peso, estatura e o índice de massa corporal (IMC). Para análise dos dados, utilizou-se média, medida de dispersão, frequência e percentual. Para a comparação dos dados utilizou-se o teste estatístico t de Student com tabulação dos dados primários no programa SPSS 26.0. Os resultados apontaram que não houve relação entre o estado nutricional e o desenvolvimento motor dos investigados. Entretanto, observou-se que há diferença estatística significativa quanto ao tempo em que os escolares permanecem assistindo televisão. Desse modo, entende-se que o estado nutricional pode estar relacionado ao uso prolongado de tela, o que conduz ao sobrepeso e obesidade e afasta os escolares de atividades físicas. Palavras-chave: Destreza Motora. Estado Nutricional. Criança.

FRB 190520B Embedded in a Magnetar Wind Nebula and Supernova Remnant: A Luminous Persistent Radio Source, Decreasing Dispersion Measure, and Large Rotation Measure

Recently, FRB 190520B, which has the largest extragalactic dispersion measure (DM), was discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The DM excess over the intergalactic medium and Galactic contributions is estimated as ∼900 pc cm−3, which is nearly ten times higher than that of other fast-radio-burst (FRB) host galaxies. The DM decreases with the rate ∼0.1 pc cm−3 per day. It is the second FRB associated with a compact persistent radio source (PRS). The rotation measure (RM) is found to be larger than 1.8 × 105rad m−2. In this Letter, we argue that FRB 190520B is powered by a young magentar formed by core collapse of massive stars, embedded in a composite of a magnetar wind nebula (MWN) and supernova remnant (SNR). The energy injection of the magnetar drives the MWN and SN ejecta to evolve together and the PRS is generated by the synchrotron radiation of the MWN. The magnetar has an interior magnetic field B int ∼ (2–4) × 1016 G and an age t age ∼ 14–22 yr. The dense SN ejecta and the shocked shell contribute a large fraction of the observed DM and RM. Our model can naturally and simultaneously explain the luminous PRS, decreasing DM, and extreme RM of FRB 190520B.

What do (most of) our dispersion measures measure (most)? Dispersion?

This paper discusses the degree to which most of the most widely-used measures of dispersion in corpus linguistics are not particularly valid in the sense of actually measuring dispersion rather than some amalgam of a lot of frequency and a little dispersion. The paper demonstrates these issues on the basis of data from a variety of corpora. I then outline how to design a dispersion measure that only measures dispersion and show that (i) it indeed measures information that is different from frequency in an intuitive way and (ii) has a higher degree of predictive power of lexical decision times from the MALD database than nearly all other measures in nearly all corpora tested.

Dissecting the Local Environment of FRB 190608 in the Spiral Arm of its Host Galaxy

We present a high-resolution analysis of the host galaxy of fast radio burst (FRB) 190608, an SB(r)c galaxy at z = 0.11778 (hereafter HG 190608), to dissect its local environment and its contributions to the FRB properties. Our Hubble Space Telescope Wide Field Camera 3 ultraviolet and visible light image reveals that the subarcsecond localization of FRB 190608 is coincident with a knot of star formation (ΣSFR = 1.5 × 10−2 M ⊙ yr−1 kpc−2) in the northwest spiral arm of HG 190608. Using Hβ emission present in our Keck Cosmic Web Imager integral field spectrum of the galaxy with a surface brightness of μ H β = ( 3.36 ± 0.21 ) × 10 − 17 erg s − 1 cm − 2 arcsec − 2 , we infer an extinction-corrected Hα surface brightness and compute a dispersion measure (DM) from the interstellar medium of HG 190608 of DMHost,ISM = 94 ± 38 pc cm−3. The galaxy rotates with a circular velocity v circ = 141 ± 8 km s−1 at an inclination i gas = 37° ± 3°, giving a dynamical mass M halo dyn ≈ 10 11.96 ± 0.08 M ⊙ . This implies a halo contribution to the DM of DMHost,Halo = 55 ± 25 pc cm−3 subject to assumptions on the density profile and fraction of baryons retained. From the galaxy rotation curve, we infer a bar-induced pattern speed of Ω p = 34 ± 6 km s−1 kpc−1 using linear resonance theory. We then calculate the maximum time since star formation for a progenitor using the furthest distance to the arm’s leading edge within the localization, and find t enc = 21 − 6 + 25 Myr. Unlike previous high-resolution studies of FRB environments, we find no evidence of disturbed morphology, emission, or kinematics for FRB 190608.

Statistical Measurements of Dispersion Measure Fluctuations of FRBs

Extragalactic fast radio bursts (FRBs) have large dispersion measures (DMs) and are unique probes of intergalactic electron density fluctuations. By using the recently released First CHIME/FRB Catalog, we reexamined the structure function (SF) of DM fluctuations. It shows a large DM fluctuation similar to that previously reported in Xu & Zhang, but no clear correlation hinting toward large-scale turbulence is reproduced with this larger sample. To suppress the distortion effect from FRB distances and their host DMs, we focus on a subset of CHIME catalog with DM < 500 pc cm−3. A trend of nonconstant SF and nonzero correlation function (CF) at angular separations θ less than 10° is seen, but with large statistical uncertainties. The difference found between SF and that derived from CF at θ ≲ 10° can be ascribed to the large statistical uncertainties or the density inhomogeneities on scales on the order of 100 Mpc. The possible correlation of electron density fluctuations and inhomogeneities of density distribution should be tested when several thousands of FRBs are available.

Unusual Emission Variations Near the Eclipse of Black Widow Pulsar PSR J1720−0533

We report on an unusually bright observation of PSR J1720−0533 using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulsar is in a black widow system that was discovered by the Commensal Radio Astronomy FAST Survey (CRAFTS). By coincidence, a bright scintillation maximum was simultaneous with the eclipse in our observation, which allowed for precise measurements of flux density variations, as well as dispersion measure (DM) and polarization. We found that there are quasi-periodic pulse emission variations with a modulation period of ∼22 s during the ingress of the eclipse, which could be caused by plasma lensing. No such periodic modulation was found during the egress of the eclipse. The linear polarization of the pulsar disappears before the eclipse, even before there is a visually obvious change in DM. We also found that the pulse scattering may play an important role in the eclipse of PSR J1720−0533.

CHIME/FRB Catalog 1 Results: Statistical Cross-correlations with Large-scale Structure

The CHIME/FRB Project has recently released its first catalog of fast radio bursts (FRBs), containing 492 unique sources. We present results from angular cross-correlations of CHIME/FRB sources with galaxy catalogs. We find a statistically significant (p-value ∼ 10−4, accounting for look-elsewhere factors) cross-correlation between CHIME FRBs and galaxies in the redshift range 0.3 ≲ z ≲ 0.5, in three photometric galaxy surveys: WISE × SCOS, DESI-BGS, and DESI-LRG. The level of cross-correlation is consistent with an order-one fraction of the CHIME FRBs being in the same dark matter halos as survey galaxies in this redshift range. We find statistical evidence for a population of FRBs with large host dispersion measure (∼400 pc cm−3) and show that this can plausibly arise from gas in large halos (M ∼ 1014 M ⊙), for FRBs near the halo center (r ≲ 100 kpc). These results will improve in future CHIME/FRB catalogs, with more FRBs and better angular resolution.