Statistical modeling of a nonstationary spatial extremal dependence structure is a challenging problem. In practice, parametric max-stable processes are commonly used for modeling spatially-indexed block maxima data, where the stationarity assumption is often made to make inference easier. However, this assumption is unreliable for data observed over a large or complex domain. In this work, we develop a computationally-efficient method to estimate nonstationary extremal dependence using max-stable processes, which builds upon and extends an approach recently proposed in the classical geostatistical literature. More precisely, we divide the spatial domain into a fine grid of subregions, each having its own set of dependence-related parameters, and then impose LASSO ($L_1$) or Ridge ($L_2$) penalties to obtain spatially-smooth estimates. We then also subsequently merge the subregions sequentially together with a new algorithm to enhance the model's performance. Here we focus on the popular Brown-Resnick process, although extensions to other classes of max-stable processes are also possible. We discuss practical strategies for adequately defining the subregions and merging them back together. To make our method suitable for high-dimensional datasets, we exploit a pairwise likelihood approach and discuss the choice of pairs to achieve reasonable computational and statistical efficiency. We apply our proposed method to a dataset of annual maximum temperature in Nepal and show that our approach fits reasonably and realistically captures the complex non-stationarity in the extremal dependence.

A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs.

A connected graph is total domination stable upon edge removal, if the removal of an arbitrary edge does not change the total domination number. We determine the minimum number of edges required for a total domination stable graph in terms of its order and total domination number.

Despite high taxonomic diversity elsewhere in North America during the Pleistocene, vertebrate faunas are exceedingly rare in the region of northern Mexico. Térapa, a unique fossil site located in the present-day desert of Northcentral Sonora, Mexico (29°41́N, 109°39́W, 605. m elevation), contributes to our understanding of the paleoecology and paleoclimate of the region during the Late Pleistocene, ca. 43,000-40,000. cal.yr BP. At least 60 vertebrate taxa, including amphibians, turtles, a crocodilian, snakes, birds and many mammals, have been recovered from an 11-m thick sequence of fossiliferous sediments. The diversity and tropical affinity of these taxa suggest a more-forested environment than the thornscrub desert habitat present in this region today.Isotopic analyses of tooth enamel carbonate from ancient mammalian herbivores suggest that the Sonoran desert has undergone considerable climate change since the Late Pleistocene. Bulk carbon (́13C) and oxygen (́18O) isotopes from nine mammalian fossils indicate a habitat mosaic with variations in diet that include browsers, mixed feeders and C4 hyper-grazers (́13C range of -10‰ to 2‰). Unique to this site are 13C tooth enamel values of -6.1 and -5.6 ‰ for the deer Odocoileus, which suggest a more variable diet than strict browsing, including possibly feeding on CAM and/or C4 plants. Serial sampling of carbon (δ13C) and oxygen (δ18O) isotopes for ancient mammal teeth with hypsodont dentitions (fossil Equus and Bison,) as well as δ18O meteroric water estimates from well-supported climatic models suggest a cooler and more equable environment at Térapa during the Late Pleistocene. These results also support previous habitat reconstructions inferred from the macrobotanical and packrat midden records of northern Sonora (Mexico). High-resolution stable isotope geochemistry indicates that: 1) ancient Térapa was covered with forest and grassland habitats that extended northward into Mexico by about 350km relative to their present-day northern limits during the Late Pleistocene; and 2) an Amount Effect (AE) is demonstrated in the fossil record at Térapa even though the climate was less seasonal compared to the modern desert habitat.

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination edge critical if the removal of any arbitrary edge increases the total domination number. On the other hand, a graph is total domination edge stable if the removal of any arbitrary edge has no effect on the total domination number. In this paper, we characterize total domination edge critical graphs. We also investigate various properties of total domination edge stable graphs.

Let k be a positive integer and G = (V (G),E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k-1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). A graph G is called βk- -stable if βk(G - e) = βk(G) for every edge e of E(G). First we give a necessary and sufficient condition for βk--stable graphs. Then we establish four equivalent conditions for βk--stable trees.

Kangaroos are the world's most diverse group of herbivorous marsupials. Following late-Miocene intensification of aridity and seasonality, they radiated across Australia, becoming the continent's ecological equivalents of the artiodactyl ungulates elsewhere. Their diversity peaked during the Pleistocene, but by approximately 45,000 years ago, 90% of larger kangaroos were extinct, along with a range of other giant species. Resolving whether climate change or human arrival was the principal extinction cause remains highly contentious. Here we combine craniodental morphology, stable-isotopic, and dental microwear data to reveal that the largest-ever kangaroo, Procoptodon goliah, was a chenopod browse specialist, which may have had a preference for Atriplex (saltbushes), one of a few dicots using the C4 photosynthetic pathway. Furthermore, oxygen isotope signatures of P. goliah tooth enamel show that it drank more in low-rainfall areas than its grazing contemporaries, similar to modern saltbush feeders. Saltbushes and chenopod shrublands in general are poorly flammable, so landscape burning by humans is unlikely to have caused a reduction in fodder driving the species to extinction. Aridity is discounted as a primary cause because P. goliah evolved in response to increased aridity and disappeared during an interval wetter than many it survived earlier. Hunting by humans, who were also bound to water, may have been a more decisive factor in the extinction of this giant marsupial.

Neogene land-mammal localities are very rare in the northeastern U.S.; therefore, the late Miocene/early Pliocene Gray Fossil Site in eastern Tennessee can clarify paleoecological dynamics during a time of dramatic global change. In particular, the identification of ancient forests and past climate regimes will better our understanding of the environmental context of mammalian evolution during the late Cenozoic. Stable isotope analyses of bulk and serial samples of fossil tooth enamel from all ungulates present at the Gray site elucidate paleoecological reconstructions. The herbivorous megafauna include taxa of likely North American and Eurasian ancestry including: the tapir Tapirus polkensis, rhino Teleoceras cf. T. hicksi, camel cf. Megatylopus sp., peccary Tayassuidae, and proboscidean Gomphotheriidae. The tapir, rhino, camel, and peccary yield mean stable carbon isotope (δ13C) tooth enamel values of - 13.0‰, - 13.3‰, - 13.8‰, and - 13.1‰, respectively, suggesting forest-dwelling browsers. This range of δ13C values indicates the presence of a C3 dominated ancient local flora. Because δ13C values decline with increasing canopy density, the ancient temperate forests from the Gray site were moderately dense. The lack of significant C4 plant consumption (i.e., tooth enamel δ13C values < - 9‰) suggests the presence of forests large enough to independently support the continued browsing of sustainable populations of browsers from the Gray site. In contrast, bulk and serial δ13C values ranging from - 0.7‰ to 0.3‰ from a gomphothere tusk support a diet consisting of C4 grasses, suggesting the presence of C4 grasslands within the individuals home range. The rare earth element (REE) analyses of the gomphothere tusk and the teeth of Tapirus and Teleoceras indicates that these individuals shared similar depositional environments; thus, demonstrating the concurrent presence of C3 forests and C4 grasslands in the northeast. Stable carbon and oxygen serial sample variation of the tapir, rhino, peccary, and gomphothere is less than 1.5‰, suggesting minor differences in seasonal temperature and/or precipitation. These data support the possibility of a North American forest refugium in the southern Appalachians during a time typified by more open environments.

Stable isotopes of mammoths and mastodons have the potential to illuminate ecological changes in late Pleistocene landscapes and megafaunal populations as these species approached extinction. The ecological factors at play in this extinction remain unresolved, but isotopes of bone collagen (δ13C, δ15N) and tooth enamel (δ13C, δ18O, 87Sr/86Sr) from midwestern North America are leveraged to examine ecological and behavioral changes that occurred during the last interglacial-glacial cycle. Both species had significant C3 contributions to their diets and experienced increasing levels of niche overlap as they approached extinction. A subset of mastodons after the last glacial maximum exhibit low δ15N values that may represent expansion into a novel ecological niche, perhaps densely occupied by other herbivores. Stable isotopes from serial and microsampled enamel show increasing seasonality and decreasing temperatures as mammoths transitioned from Marine Isotope Stage (MIS) 5e to glacial conditions (MIS 4, MIS 3, MIS 2). Isotopic variability in enamel suggests mobility patterns and life histories have potentially large impacts on the interpretation of their stable isotope ecology. This study further refines the ecology of midwestern mammoths and mastodons demonstrating increasing seasonality and niche overlap as they responded to landscape changes in the final millennia before extinction.

Synthetic biological designers are demanding tools to help with the design and verifica- tion process of new biological models. Some of the most common tools available aggregate multiple simulation results into one “clean” trajectory that hopefully is representative of the system’s behavior. However, for systems exhibiting multiple stable states, these techniques fail to show all the possible trajectories of the system. This work introduces a method capable of detecting the presence of more than one “typical” trajectory in a system, which can also be integrated with other available simulation tools.