On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type

We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability

Averting Robot Eyes

Home robots will cause privacy harms. At the same time, they can provide beneficial services—as long as consumers trust them. This Essay evaluates potential technological solutions that could help home robots keep their promises, avert their eyes, and otherwise mitigate privacy harms. Our goals are to inform regulators of robot-related privacy harms and the available technological tools for mitigating them, and to spur technologists to employ existing tools and develop new ones by articulating principles for avoiding privacy harms. We posit that home robots will raise privacy problems of three basic types: (1) data privacy problems; (2) boundary management problems; and (3) social/relational problems. Technological design can ward off, if not fully prevent, a number of these harms. We propose five principles for home robots and privacy design: data minimization, purpose specifications, use limitations, honest anthropomorphism, and dynamic feedback and participation. We review current research into privacy-sensitive robotics, evaluating what technological solutions are feasible and where the harder problems lie. We close by contemplating legal frameworks that might encourage the implementation of such design, while also recognizing the potential costs of regulation at these early stages of the technology

Forbidden induced subgraphs and the price of connectivity for feedback vertex set.

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined as the maximum ratio cfvs(G)/fvs(G) over all connected graphs G in G. It is known that the poc-fvs for general graphs is unbounded. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for H-free graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H|=1

The Marmara Sea Gateway since ~16 ky BP: non-catastrophic causes of paleoceanographic events in the Black Sea at 8.4 and 7.15 ky BP

The Late Quaternary history of connection of the Black Sea to the Eastern Mediterranean has been intensely debated. Ryan, Pitman and coworkers advocate two pulses of outflow from the Black Sea to the world ocean at ~16–14.7 ky BP and ~11–10 ky BP. From ~14.7–11 ky BP and from ~10–8.4 ky BP, they suggest that the level of the Black Sea fell to ~ -100 m. At 8.4 ky BP, they further claim that a catastrophic flood occurred in a geological instant, refilling the Black Sea with saline waters from the Mediterranean. In contrast, we continue to gather evidence from seismic profiles and dated cores in the Marmara Sea which demonstrate conclusively that the proposed flood did not occur. Instead, the Black Sea has been at or above the Bosphorus sill depth and flowing into the world ocean unabated since ~10.5 ky BP. This conclusion is based on continuous Holocene water-column stratification (leading to sapropel deposition in the Marmara Sea and the Aegean Sea), proxy indicators of sea-surface salinity, and migration of endemic species across the Bosphorus in both directions whenever appropriate hydrographic conditions existed in the strait. The two pulses of outflow documented by Ryan, Pitman and coworkers find support in our data, and we have modified our earlier interpretations so that these pulses now coincide with the development of mid-shelf deltas: \Delta 2 (16–14.7 ky BP) and \Delta 1 (10.5–9 ky BP) at the southern end of the Bosphorus Strait. However, continued Black Sea outflow after 9 ky BP prevented the northward advection of Mediterranean water and the entry of open-marine species into the Black Sea for more than 1000 years. Sufficient Mediterranean water to change the Sr-isotopic composition of slope and shelf water masses was not available until ~8.4 ky BP (along with the first arrival of many varieties of marine fauna and flora), whereas euryhaline molluscs did not successfully populate the Black Sea shelves until ~7.15 ky BP. Instead of relying on catastrophic events, we recognize a slow, progressive reconnection of the Black Sea to the world ocean, accompanied by significant time lags

Reassessing Political Explanations for Murders of Police

Author's manuscript made available in accordance with the publisher's policy.The article discusses how Jacobs and Carmichael, drawing on the racial threat thesis, argue that the overrepresentation of Blacks among felons who murder police is in part explained by Blacks' conscious or unconscious responses to political subordination by the State. In testing this argument, Jacobs and Carmichael find that their key theoretical variable—the presence of a Black mayor—is inversely related to police homicides and injurious assaults across many model specifications. This article describes a limited reanalysis of Jacobs and Carmichael's homicide data and additional analyses with a larger sample of cities. The findings suggest that the significance of the Black mayor variable may have been an artifact of model specification. Instead, there is evidence that Black city council representation may be associated with reduced homicides of police by Blacks. Further research is needed, however, because of the limited explanatory power of the key factors highlighted in past research

Physical Properties of Metallic Antiferromagnetic CaCo{1.86}As2 Single Crystals

We report studies of CaCo{1.86}As2 single crystals. The electronic structure is probed by angle-resolved photoemission spectroscopy (ARPES) measurements of CaCo{1.86}As2 and by full-potential linearized augmented-plane-wave calculations for the supercell Ca8Co15As16 (CaCo{1.88}As2). Our XRD crystal structure refinement is consistent with the previous combined refinement of x-ray and neutron powder diffraction data showing a collapsed-tetragonal ThCr2Si2-type structure with 7(1)% vacancies on the Co sites corresponding to the composition CaCo{1.86}As2 [D. G. Quirinale et al., Phys. Rev. B 88, 174420 (2013)]. The anisotropic magnetic susceptibility chi(T) data are consistent with the magnetic neutron diffraction data of Quirianale et al. that demonstrate the presence of A-type collinear antiferromagnetic order below the Neel temperature TN = 52(1) K with the easy axis being the tetragonal c axis. However, no clear evidence from the resistivity rho(T) and heat capacity Cp(T) data for a magnetic transition at TN is observed. A metallic ground state is demonstrated from band calculations and the rho(T), Cp(T) and ARPES data, and spin-polarized calculations indicate a competition between the A-type AFM and FM ground states. The Cp(T) data exhibit a large Sommerfield electronic coefficient reflecting a large density of states at the Fermi energy D(EF), consistent with the band structure calculations which also indicate a large D(EF) arising from Co 3d bands. At 1.8 K the M(H) data for H|| c exhibit a well-defined first-order spin-flop transition at an applied field of 3.5 T. The small ordered moment of 0.3 muB/Co obtained from the M(H) data at low T, the large exchange enhancement of chi and the lack of a self-consistent interpretation of the chi(T) and M(H,T) data in terms of a local moment Heisenberg model together indicate that the magnetism of CaCo{1.86}As2 is itinerant.Comment: 18 pages, 15 figures, 4 tables, 61 references; v2: extended the fits of experimental data by additional electronic structure calculations; published versio

Further Tests of the Influence of Black Mayors on Murders of Police: A Response to Jacobs

Author's manuscript made available in accordance with the publisher's policy.In response to our reanalysis and extension of Jacobs and Carmichael (2002) in which we found no evidence of a Black mayor effect, Jacobs (this issue) critiques our article on theoretical and methodological grounds. Theoretically, Jacobs argues that we did not provide sufficient justification for the inclusion of the percentage of the city council that was Black. Methodological criticisms include failure to include a nonlinear specification of percent divorced, improper temporal ordering, and the inclusion of only a single regional dummy variable. In our rejoinder we clarify the theoretical importance of the percentage of the city council that was Black and we address each of Jacobs’ methodological concerns. In additional analyses, we again find that the effect of the Black mayor variable is not robust to model specification or data employed, which was the point of our original article