A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

On Y-Linked Genes and Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Fear memory reactivation after extinction activates plasticity in the lateral amygdala

Little is known about the neuronal changes that occur within the lateral amygdala (LA) following fear extinction. In fear extinction, the repeated presentation of a conditioned stimulus (CS), in the absence of a previously paired aversive unconditioned stimulus (US), reduces fear elicited by the CS. Fear extinction is an active learning process that leads to the formation of a consolidated extinction memory, however it is fragile and prone to spontaneous recovery and renewal under environmental changes such as context. Understanding the neural mechanisms underlying fear extinction is of great clinical relevance, as psychological treatments of several anxiety disorders rely largely on extinction-based procedures and relapse is major clinical problem. This study investigated plasticity in the LA following fear memory reactivation in rats with and without extinction training. Phosphorylated MAPK (p44/42 ERK/MAPK), a protein kinase required in the amygdala for fear learning and its extinction, was used as a marker for neuronal plasticity. Rats (N = 11) underwent a Pavlovian auditory fear conditioning and extinction paradigm, and later received a single conditioned stimulus presentation to reactivate the fear memory. Results showed more pMAPK+ expressing neurons in the LA following extinction-reactivation compared to control rats, with the largest number of pMAPK+ neurons counted in the ventral LA, especially including the ventro-lateral subdivision (LAvl). These findings indicate that LA subdivision specific plasticity occurs to the conditioned fear memory in the LAvl following extinction-reactivation. These findings provide important insight into the organisation of fear memories in the LA, and pave the way for future research in the memory mechanisms of fear extinction and its pathophysiology.

Studies of the star-forming structures in the dense interstellar medium: a view by dust extinction

New stars in galaxies form in dense, molecular clouds of the interstellar medium. Measuring how the mass is distributed in these clouds is of crucial importance for the current theories of star formation. This is because several open issues in them, such as the strength of different mechanism regulating star formation and the origin of stellar masses, can be addressed using detailed information on the cloud structure. Unfortunately, quantifying the mass distribution in molecular clouds accurately over a wide spatial and dynamical range is a fundamental problem in the modern astrophysics. This thesis presents studies examining the structure of dense molecular clouds and the distribution of mass in them, with the emphasis on nearby clouds that are sites of low-mass star formation. In particular, this thesis concentrates on investigating the mass distributions using the near infrared dust extinction mapping technique. In this technique, the gas column densities towards molecular clouds are determined by examining radiation from the stars that shine through the clouds. In addition, the thesis examines the feasibility of using a similar technique to derive the masses of molecular clouds in nearby external galaxies. The papers presented in this thesis demonstrate how the near infrared dust extinction mapping technique can be used to extract detailed information on the mass distribution in nearby molecular clouds. Furthermore, such information is used to examine characteristics crucial for the star formation in the clouds. Regarding the use of extinction mapping technique in nearby galaxies, the papers of this thesis show that deriving the masses of molecular clouds using the technique suffers from strong biases. However, it is shown that some structural properties can still be examined with the technique.

On the ignition and extinction problems in forced convection systems

In this paper the problem of ignition and extinction has been formulated for the flow of a compressible fluid with Prandtl and Schmidt numbers taken as unity. In particular, the problems of (i) a jet impinging on a wall of combustible material and (ii) the opposed jet diffusion flame have been studied. In the wall jet case, three approximations in the momentum equation namely, (i) potential flow, (ii) viscous flow, (ii) viscous incompressible with k = 1 and (iii) Lees' approximation (taking pressure gradient terms zero) are studied. It is shown that the predictions of the mass flow rates at extinction are not very sensitive to the approximations made in the momentum equation. The effects of varying the wall temperature in the case (i) and the jet temperature in the case (ii) on the extinction speeds have been studied. The effects of varying the activation energy and the free stream oxidant concentration in case (ii), have also been investigated.

Vegetational history and geochronology of several sites in South Southwestern Ontario with discussion on mastodon extinction in Southern Ontario /

This study has three purposes: to establish a chronologically controlled vegetational history for a number of sites in south Southwestern Ontario; to utilize the resulting data to support and/or add to the current understanding of Quaternary geology and stratigraphy, and the glacial and postglacial history of the Great Lakes in south Southwestern Ontario; and to attempt to propose a possible explanation for the extinction of the mastodon in Southern Ontario. Palynological and geochronological analyses were conducted on material collected from eleven sites (east to west): Verbeke Mastodon Site, Woloshko Mastodon Site, Walker Pond II, Pond Mills I, Lake Hunger Bog, Bouckaert Site. Mabee Site, Cornell Bog. Colles Lake I, Folden Mastodon Site and Forest Pond. Individual geochronologically controlled (where possible) vegetational histories were reconstructed for each of the sites investigated. The results of the individual studies, when considered in overview. indicated the existance of an established closed boreal forest throughout south Southwestern Ontario by 10,000 years B.P. This evidence for a significant climatic change coincident throughout south Southwestern Ontario supports the proposed age of 10,000 years B.P. for the Pleistocene/Holocene Boundary (Terasmae, 1972). Remnant patches of 'open spruce parkland' persisted in small local 'wet' areas. It was in these areas that the mastodon was restricted during early Holocene time. With continued encroachment by the surrounding boreal forest, possibly speeded up by this browser's destructive feeding habits, the spruce enclaves shrank and the mastodon became extinct in south Southwestern Ontario. The results of this thesis basically support Dreimanis' (1967, 1968) proposed 'Environmental-Climatic' theory for mastodon extinction. It is suggested that increased dryness during the present interglacial compared to the climate of earlier interglacials may be the key to unravelling the problem of mastodon extinction in eastern North America.

Biases in comparative analyses of extinction risk: mind the gap

1. Comparative analyses are used to address the key question of what makes a species more prone to extinction by exploring the links between vulnerability and intrinsic species’ traits and/or extrinsic factors. This approach requires comprehensive species data but information is rarely available for all species of interest. As a result comparative analyses often rely on subsets of relatively few species that are assumed to be representative samples of the overall studied group. 2. Our study challenges this assumption and quantifies the taxonomic, spatial, and data type biases associated with the quantity of data available for 5415 mammalian species using the freely available life-history database PanTHERIA. 3. Moreover, we explore how existing biases influence results of comparative analyses of extinction risk by using subsets of data that attempt to correct for detected biases. In particular, we focus on links between four species’ traits commonly linked to vulnerability (distribution range area, adult body mass, population density and gestation length) and conduct univariate and multivariate analyses to understand how biases affect model predictions. 4. Our results show important biases in data availability with c.22% of mammals completely lacking data. Missing data, which appear to be not missing at random, occur frequently in all traits (14–99% of cases missing). Data availability is explained by intrinsic traits, with larger mammals occupying bigger range areas being the best studied. Importantly, we find that existing biases affect the results of comparative analyses by overestimating the risk of extinction and changing which traits are identified as important predictors. 5. Our results raise concerns over our ability to draw general conclusions regarding what makes a species more prone to extinction. Missing data represent a prevalent problem in comparative analyses, and unfortunately, because data are not missing at random, conventional approaches to fill data gaps, are not valid or present important challenges. These results show the importance of making appropriate inferences from comparative analyses by focusing on the subset of species for which data are available. Ultimately, addressing the data bias problem requires greater investment in data collection and dissemination, as well as the development of methodological approaches to effectively correct existing biases.

An Efficient and Verifiable Solution to the Millionaire Problem

A new solution to the millionaire problem is designed on the base of two new techniques: zero test and batch equation. Zero test is a technique used to test whether one or more ciphertext contains a zero without revealing other information. Batch equation is a technique used to test equality of multiple integers. Combination of these two techniques produces the only known solution to the millionaire problem that is correct, private, publicly verifiable and efficient at the same time.