Widespread Presence of Glycolaldehyde and Ethylene Glycol Around Sagittarius B2

We report the detection of widespread CH$_2$OHCHO and HOCH$_2$CH$_2$OH emission in Galactic center giant molecular cloud Sagittarius B2 using the Shanghai Tianma 65m Radio Telescope. Our observations show for the first time that the spatial distribution of these two important prebiotic molecules extends over 15 arc-minutes, corresponding to a linear size of approximately 36 pc. These two molecules are not just distributed in or near the hot cores. The abundance of these two molecules seems to decrease from the cold outer region to the central region associated with star-formation activity. Results present here suggest that these two molecules are likely to form through a low temperature process. Recent theoretical and experimental studies demonstrated that prebiotic molecules can be efficiently formed in icy grain mantles through several pathways. However, these complex ice features cannot be directly observed, and most constraints on the ice compositions come from millimeter observations of desorbed ice chemistry products. These results, combined with laboratory studies, strongly support the existence of abundant prebiotic molecules in ices.Comment: 20 pages, 7 figures, accepted by Ap

Precessing jet nozzle connecting to a spinning black hole in M87

The nearby radio galaxy M87 offers a unique opportunity to explore the connections between the central supermassive black hole and relativistic jets. Previous studies of the inner region of M87 revealed a wide opening angle for the jet originating near the black hole. The Event Horizon Telescope resolved the central radio source and found an asymmetric ring structure consistent with expectations from General Relativity. With a baseline of 17 years of observations, there was a shift in the jet's transverse position, possibly arising from an eight to ten-year quasi-periodicity. However, the origin of this sideways shift remains unclear. Here we report an analysis of radio observations over 22 years that suggests a period of about 11 years in the position angle variation of the jet. We infer that we are seeing a spinning black hole that induces the Lense-Thirring precession of a misaligned accretion disk. Similar jet precession may commonly occur in other active galactic nuclei but has been challenging to detect owing to the small magnitude and long period of the variation.Comment: 41 pages, 7 figures, 7 table

Immunization against the Spread of Rumors in Homogenous Networks

<div><p>Since most rumors are harmful, how to control the spread of such rumors is important. In this paper, we studied the process of "immunization" against rumors by modeling the process of rumor spreading and changing the termination mechanism for the spread of rumors to make the model more realistic. We derived mean-field equations to describe the dynamics of the rumor spread. By carrying out steady-state analysis, we derived the spreading threshold value that must be exceeded for the rumor to spread. We further discuss a possible strategy for immunization against rumors and obtain an immunization threshold value that represents the minimum level required to stop the rumor from spreading. Numerical simulations revealed that the average degree of the network and parameters of transformation probability significantly influence the spread of rumors. More importantly, the simulations revealed that immunizing a higher proportion of individuals is not necessarily better because of the waste of resources and the generation of unnecessary information. So the optimal immunization rate should be the immunization threshold.</p></div

Nodes immunization effects on the prevention and control of rumors-spread.

<p>A) Changes in the density of R1 stiflers over time (<i>t</i>) as a function of the immunization rate <i>p</i>. B) Changes in the density of R2 stiflers over time (<i>t</i>) as a function of the immunization rate <i>p</i>. C) Changes in the final value of the R1 and R2 stiflers, and the final size of the rumor (<i>R</i>) as a function of the proportion of the population that is immunized <i>p</i>. The values of the model parameters are <i>λ</i> = 0.45, <i>β</i> = 0.02, <i>γ</i> = 0.53, <i>α</i> = 0.45, <i>θ</i> = 0.50, <i>δ</i> = 0.35, and <math><mrow><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn></mrow></math>.</p

Densities of the four groups in the rumor model over time(<i>t</i>).

<p>The parameters are <i>λ</i> = 0.85, <i>β</i> = 0.03, <i>γ</i> = 0.12, <i>α</i> = <i>θ</i> = 0.25, <i>δ</i> = 0.35, and <math><mrow><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn></mrow></math>.</p

The effect of labour protection laws on the relationship between leverage and wages

Previous research has shown that leverage has a positive effect on wages. Using US state-level labour protection laws as an exogenous shock, we find that the adoption of the law alleviates the effect of leverage on wages. We show that the mitigating effect on the leverage-wag relationship is more pronounced for firms with strong employee bargaining power. Our study highlights the positive role played by labour protection laws in lowering firms’ labour costs and improving their financial flexibility, which complements the literature and advances our understanding of the broad implications of labour protection laws

Structure of the modified SIR rumor spreading model for the rumor-spread process.

<p>R1 represents the stiflers who do not know the truth or falsehood of the rumor and simply lose interest in spreading the rumor, and R2 represents stiflers who see the falsity of the rumor and oppose its spread. The sub-script line label indicates the interaction partner, the super-script line label indicates the rate of state transition.</p

The relationship between the spread threshold (<i>λ</i>_<i>c</i>) and the immunization threshold (<i>p</i>_<i>c</i>).

<p>The parameters are <i>λ</i> = 0.85, <i>θ</i> = 0.45, <i>α</i> = 0.25.</p

Shape of the function <i>g</i>(<i>R</i>).

<p>The parameters are <math><mrow><mi>β</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>03</mn><mo>,</mo><mi>γ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>15</mn><mo>,</mo><mi>θ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>,</mo><mi>α</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>,</mo><mi>δ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>,</mo><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn><mo>,</mo></mrow></math> and <i>p</i> = 0.2.</p