Lower Bounds for Nonforgetting Restarting Automata and CD-Systems of Restarting Automata

The nonforgetting restarting automaton is a generalization of the restarting automaton that, when executing a restart operation, changes its internal state based on the current state and the actual contents of its read/write window instead of resetting it to the initial state. Another generalization of the restarting automaton is the cooperating distributed system (CD-system) of restarting automata. Here a finite system of restarting automata works together in analyzing a given sentence, where they interact based on a given mode of operation. As it turned out, CD-systems of restarting automata of some type X working in mode =1 are just as expressive as nonforgetting restarting automata of the same type X. Further, various types of determinism have been introduced for CD-systems of restarting automata called strict determinism, global determinism, and local determinism, and it has been shown that globally deterministic CD-systems working in mode =1 correspond to deterministic nonforgetting restarting automata. Here we derive some lower bound results for some types of nonforgetting restarting automata and for some types of CD-systems of restarting automata. In this way we establish separations between the corresponding language classes, thus providing detailed technical proofs for some of the separation results announced in the literature.

Lower Bounds for Achieving Synchronous Early Stopping Consensus with Orderly Crash Failures

In this paper, we discuss the consensus problem for synchronous distributed systems with orderly crash failures. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, first, we present a bivalency argument proof to solve the open problem of proving the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t < n - 1. Then, we extend the system model with orderly crash failures to a new model in which a process is allowed to send multiple messages to the same destination process in a round and the failing processes still respect the order specified by the protocol in sending messages. For this new model, we present a uniform consensus protocol, in which all non-faulty processes always decide and stop immediately by the end of f + 1 rounds. We prove that the lower bound of early stopping protocols for both consensus and uniform consensus are f + 1 rounds under the new model, and our proposed protocol is optimal.

Understanding mathematics for young children : a guide for Foundation Stage and Lower Primary Teachers.

Guía para tener una comprensión más clara de las matemáticas y de los materiales que se utilizan en el aula con niños de tres a ocho años. Muestra cómo ayudarlos en el desarrollo y la comprensión de las matemáticas por sí mismos, en lugar de aprender recetas y rutinas. Al final de cada capítulo se incluyen algunos ejemplos de actividades que pueden ser utilizadas en las distintas edades. Contiene estrategias para el cálculo mental.

The Influence of Body Condition on the Stopover Ecology of Least Sandpipers in the Lower Mississippi Alluvial Valley during Fall Migration

Many shorebirds are long-distance migrants and depend on the energy gained at stopover sites to complete migration. Competing hypotheses have described strategies used by migrating birds; the energy-selection hypothesis predicts that shorebirds attempt to maximize energy gained at stopover sites, whereas the time-selection hypothesis predicts that shorebirds attempt to minimize time spent at stopover sites. The energy- and time-selection hypotheses both predict that birds in better condition will depart sites sooner. However, numerous studies of stopover duration have found little support for this prediction, leading to the suggestion that migrating birds operate under energy and time constraints for only a small portion of the migratory season. During fall migration 2002, we tested the prediction that birds in better condition depart stopover sites sooner by examining the relationship between stopover duration and body condition for migrating Least Sandpipers (Calidris minutilla) at three stopover sites in the Lower Mississippi Alluvial Valley. We also tested the assumption made by the Lower Mississippi Alluvial Valley Migratory Bird Science Team that shorebirds stay in the Mississippi Valley for 10 d. The assumption of 10 d was used to estimate the amount of habitat required by shorebirds in the Mississippi Valley during fall migration; a period longer than 10 d would increase the estimate of the amount habitat required. We used multiple-day constancy models of apparent survival and program MARK to estimate stopover duration for 293 individually color-marked and resighted Least Sandpipers. We found that a four-day constancy interval and a site x quadratic time trend interaction term best modeled apparent survival. We found only weak support for body condition as a factor explaining length of stopover duration, which is consistent with findings from similar work. Stopover duration estimates were 4.1 d (95% CI = 2.8–6.1) for adult Least Sandpipers at Bald Knob National Wildlife Refuge, Arkansas, 6.5 d (95% CI = 4.9–8.7) for adult and 6.1 d (95% CI =4.2–9.1) for juvenile Least Sandpipers at Yazoo National Wildlife Refuge, Mississippi, and 6.9 d (95% CI = 5.5–8.7) for juvenile Least Sandpipers at Morgan Brake National Wildlife Refuge, Mississippi. Based on our estimates of stopover duration and the assumption made by the Lower Mississippi Alluvial Valley Migratory Bird Science Team, there is sufficient habitat in the lower Mississippi Valley to support shorebirds during fall migration.

The response of tropospheric circulation to perturbations in lower-stratospheric temperature

A multiple regression analysis of the NCEP-NCAR reanalysis dataset shows a response to increased solar activity of a weakening and poleward shift of the subtropical jets. This signal is separable from other influences, such as those of El Nino-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO), and is very similar to that seen in previous studies using global circulation models (GCMs) of the effects of an increase in solar spectral irradiance. The response to increased stratospheric (volcanic) aerosol is found in the data to be a weakening and equatorward shift of the jets. The GCM studies of the solar influence also showed an impact on tropospheric mean meridional circulation with a weakening and expansion of the tropical Hadley cells and a poleward shift of the Ferrel cells. To understand the mechanisms whereby the changes in solar irradiance affect tropospheric winds and circulation, experiments have been carried out with a simplified global circulation model. The results show that generic heating of the lower stratosphere tends to weaken the subtropical jets and the tropospheric mean meridional circulations. The positions of the jets, and the extent of the Hadley cells, respond to the distribution of the stratospheric heating, with low-latitude heating forcing them to move poleward, and high-latitude or latitudinally uniform heating forcing them equatorward. The patterns of response are similar to those that are found to be a result of the solar or volcanic influences, respectively, in the data analysis. This demonstrates that perturbations to the heat balance of the lower stratosphere, such as those brought about by solar or volcanic activity, can produce changes in the mean tropospheric circulation, even without any direct forcing below the tropopause.

Is Antarctic climate most sensitive to ozone depletion in the middle or lower stratosphere?

Antarctic stratospheric ozone depletion has been associated with an observed downward trend in tropospheric geopotential height and temperature. Stratospheric ozone depletion peaks in October–November, whereas tropospheric trends are largest in December–January, concurrent with maximum ozone changes close to the tropopause. Surface temperatures are most sensitive to ozone loss near the tropopause, therefore it has been suggested that the observed tropospheric response is forced mainly by ozone depletion in the lower stratosphere. In this study the climate response to ozone depletion exclusively below 164 hPa is simulated using HadSM3-L64, and compared with simulations in which ozone depletion is prescribed exclusively above 164 hPa. Results indicate that the tropospheric response is dominated by ozone changes above 164 hPa, with ozone changes in the lowermost stratosphere playing an insignificant role. A tropospheric response is also seen in fall/winter which agrees well with observations and has not been found in modeling studies previously.