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

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

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

The Post-Festo World of Equivalents, 2 J. Marshall Rev. Intell. Prop. L. 182 (2003)

The Supreme Court again began to delve into substantial patent issues by addressing the interplay between prosecution history estoppel and the doctrine of equivalents. An analysis of the opinions in the Federal Circuit’s en banc ruling, together with the Supreme Court’s own decision may help to clarify some of the unanswered questions still lingering regarding what equivalents are available and when. The prosecution history will take a more prominent place in the minds of both patent prosecutors and litigators as courts attempt to determine the appropriate relationship between prosecution history estoppel and the doctrine of equivalents

On the zeroes of the Pearcey integral

AbstractZeroes for real values of the arguments of the Pearcey integral are numerically evaluated and plotted. From this numerical examination, it is apparent that these zeroes display a high degree of structure, the character of which is revealed through asymptotic analysis. Refinements to the resulting approximations are supplied near the paper's end

Early Cretaceous biogeographic and oceanographic synthesis of Leg 123 (off Northwestern Australia)

Biogeographic observations made by Leg 123 shipboard paleontologists for Lower Cretaceous nannofossils, foraminifers, radiolarians, belemnites, and inoceramids are combined in this chapter to evaluate the paleoceanographic history of the northwestern Australian margin and adjacent basins. Each fossil group is characterized at specific intervals of Cretaceous time and compared with data from Tethyan and Southern Hemisphere high-latitude localities. Special attention is given to the biogeographic observations made for the Falkland Plateau (DSDP Legs 36 and 71) and the Weddell Sea (ODP Leg 113). Both areas have yielded valuable Lower Cretaceous fossil records of the circumantarctic high latitudes. In general, the Neocomian fossil record from DSDP and ODP sites off northwestern Australia has important southern high-latitude affinities and weak Tethyan influence. The same is true for the pelagic lithofacies: radiolarian chert and/or nannofossil limestone, dominant in the Tethyan Lower Cretaceous, are minor lithologies in the Exmouth-Argo sites. These observations, together with the young age of the Argo crust and plate tectonic considerations, suggest that the Argo Basin was not part of the Tethys Realm. The biogeography of the Neocomian radiolarian and nannofossil assemblages suggests opening of a seaway during the Berriasian that connected the circumantarctic area with the Argo Basin, which resulted in the influx of southern high-latitude waters. This conclusion constrains the initial fit and break-up history of Gondwana. Our results favor the loose fit of the western Australian margin with southeast India by Ricou et al. (1990), which accounts for a deeper water connection with the Weddell-Mozambique basins via drowned marginal plateaus as early as the Berriasian. In fits of the du Toit-type (1937), India would remain attached to Antarctica, at least until the late Valanginian, making such a connection impossible. After the Barremian, increasing Tethyan influence is evident in all fossil groups, although southern high-latitude taxa are still present. Biogeographic domains, such as the southern extension of Nannoconus and Ticinella suggest paleolatitudes of about 50°S for the Exmouth-Argo area. Alternatively, if paleolatitudes of about 35° are accepted, these biogeographic limits were displaced northward at least 15° along Australia in comparison to the southern Atlantic. In this case, the proto-circumantarctic current was deflected northward into an eastern boundary current off Australia and carried circumantarctic cold water into the middle latitudes. Late Aptian/early Albian time is characterized by mixing of Tethyan and southern faunal elements and a significant gradient in Albian surface-water temperatures over 10° latitude along the Australian margin, as indicated by planktonic foraminifers. Both phenomena may be indicative of convergence of temperate and antarctic waters near the Australian margin. High fertility conditions, reflected by radiolarian cherts, are suggestive of coastal upwelling during that time

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