Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Uniqueness and extinction properties of generalised Markov branching processes

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Casual link and consensual arrangements in estoppel

Analyses the Court of Appeal decision in Powell v Benney on whether in a claim of proprietary estoppel the expectation of a couple that they would receive two properties owned, and promised to them, by a deceased friend was out of proportion to the detriment suffered by them in looking after the friend and improving his properties for their own use. Considers: (1) the approach to be taken to the requirement of a causal link between the assurance given and the conduct constituting the detriment relied on; and (2) consensual arrangements and estoppel equity.

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbol-assisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in medium-rate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.

Making the link: a customised social networking site can foster learning

Thanks to the internet, students today can do things that students of the past could not. They can learn formally or informally by interacting on social networking sites in a way that is not easily accomplished in a lecture theatre or classroom.

Translating Nietzsche, mediating literature: Alexander Tille and the limits of Anglo-German intercultural transfer

Dr. Alexander Tille (1866–1912) was one of the key-figures in Anglo-German intercultural transfer towards the end of the 19th century. As a lecturer in German at Glasgow University he was the first to translate and edit Nietzsche’s work into English. Writers such as W. B. Yeats were influenced by Nietzsche and used Tille’s translations. Tille’s social Darwinist reading of the philosopher’s oeuvre, however, had a narrowing impact on the reception of Nietzsche in the Anglo-Saxon world for decades. Through numerous publications Tille disseminated knowledge about British authors (e.g., Robert Louis Stevenson, William Wordsworth) in Germany and about German authors (e.g., Johann Wolfgang von Goethe) in Britain. His role as mediator also extended into areas such as history, religion, and industry. During the Boer war, however, Tille’s outspoken pro-German nationalism brought him in conflict with his British host society. After being physically attacked by his students he returned to Germany and published a highly anglophobic monograph. Tille personifies the paradox of Anglo-German relations in the pre-war years, which deteriorated despite an increase in intercultural transfer and knowledge about the respective Other. [From the Author]

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

The missing link between information and action: hastenings and delays as universal reactions to performance feedback

This chapter focuses on what the key decision makers in organizations decide after having received information on the current state of the organizational performance. Because of strong attributions to success and failure, it is impossible to predict in advance which concrete actions will occur. We can however find out what kinds of actions are decided upon by means of an organizational learning model that focuses on the hastenings and delays after performance feedback. As an illustration, the responses to performance signals by trainers and club owners in Dutch soccer clubs are analyzed.

Bridging the gap between marine biogeochemical and fisheries sciences; configuring the zooplankton link

Exploring climate and anthropogenic impacts on marine ecosystems requires an understanding of how trophic components interact. However, integrative end-to-end ecosystem studies (experimental and/or modelling) are rare. Experimental investigations often concentrate on a particular group or individual species within a trophic level, while tropho-dynamic field studies typically employ either a bottom-up approach concentrating on the phytoplankton community or a top-down approach concentrating on the fish community. Likewise the emphasis within modelling studies is usually placed upon phytoplankton-dominated biogeochemistry or on aspects of fisheries regulation. In consequence the roles of zooplankton communities (protists and metazoans) linking phytoplankton and fish communities are typically under-represented if not (especially in fisheries models) ignored. Where represented in ecosystem models, zooplankton are usually incorporated in an extremely simplistic fashion, using empirical descriptions merging various interacting physiological functions governing zooplankton growth and development, and thence ignoring physiological feedback mechanisms. Here we demonstrate, within a modelled plankton food-web system, how trophic dynamics are sensitive to small changes in parameter values describing zooplankton vital rates and thus the importance of using appropriate zooplankton descriptors. Through a comprehensive review, we reveal the mismatch between empirical understanding and modelling activities identifying important issues that warrant further experimental and modelling investigation. These include: food selectivity, kinetics of prey consumption and interactions with assimilation and growth, form of voided material, mortality rates at different age-stages relative to prior nutrient history. In particular there is a need for dynamic data series in which predator and prey of known nutrient history are studied interacting under varied pH and temperature regimes.