Wolstenholme and Morley, Primes and Pseudoprimes

In this note, we prove $p^2$ is a Morley pseudoprime (of order 2) iff $p^2$ is a Wolstenholme pseudoprime (of order 2) iff $p$ is a Wolstenholme prime iff $p$ is a Morley prime. Concerning pseudoprimes of order 1 that are not powers of primes, only 3 are known of Wolstenholme's type and absolutely none have yet been identified of Morley's type

A Large Deviation Approach to the Measurement of Mobility

We propose an approach to measure the mobility immanent in regular Markov processes. For this purpose, we distinguish between mobility in equilibrium and mobility associated with convergence towards equilibrium. The former aspect is measured as the expectation of a functional, defined on the Cartesian square product of the state space, with respect to the invariant distribution. Based on large deviations techniques, we show how the two aspects of mobility are related and how the second one can be characterized by a certain relative entropy. Finally, we show that some prominent mobility indices can be considered as special cases.mobility index; large deviations; relative entropy

Evaluating Theories of Income Dynamics: A Probabilistic Approach

The paper proposes an approach to evaluate hypotheses about transition dynamics when only the distributions at two points in time are observed. Using principles of statistical mechanics, we show how to adjust in the "most probable" way a hypothesis such that it becomes compatible with the observed distributions. This adjustment procedure also allows to test hypotheses in a statistical sense. The test is based on the relative entropy and is equivalent to a likelihood ratio test. We apply our approach to compare the dynamics of the income distribution between men and women in the U.S. using PSID data.income dynamics; large deviation; relative entropy; misspecification

Equilibrium Mobility

This paper proposes to measure the mobility of a stochastic process as the expected value of a "mobility functional" with respect to its stationary distribution. The mobility functional thereby measures the valuation of movements between states. We not only highlight the conceptual advantages of our approach, but also show how this so-called "equilibrium mobility index" relates to the axiomatic approach by Fields and Ok (7) and the approach based on monotone transition matrices by Conlisk (4) and Dardanoni (5))Mobility indices; mobility functional; equilibrium mobility

A narrative exploration of the lived experience of being born, raised in, and leaving a cultic group: the case of the Exclusive Brethren

There is considerable evidence that experiences in cultic groups can be harmful. Most studies have been on First Generation former members. Second Generation former cultic group members (SGA) are an under-researched population. Multi-Generational former members (MGA), i.e. those born into families whose membership of the cultic group goes back more than two generations appear never to have been researched. This thesis underpinned by social constructionism, explores the experiences of being born and raised in The Exclusive Brethren, an exemplar of a cultic group, and subsequently leaving. As a counselling psychologist and a former member of the Brethren, this thesis is of professional and personal interest. Unstructured interviews were conducted with three male and three female participants in their mid 30s to mid 70s, who left at various times over the last 50 years. Two participants are ‘true SGA’ –their parents were the first generation to join the Brethren. The other four are MGA coming from families with a long generational history in the Brethren. A qualitative narrative inquiry methodology was used, informed by critical and dialogical narrative analysis. Each story’s interview was represented in collaboration with the storytellers using their words as far as possible. At the heart of every story lay their experience in the Brethren; the doctrines and practices forming the bedrock. The stories told how storytellers came to leave and how, in leaving, they renegotiated their identities. A cross-story view led to a continuum model of families’ degree of enmeshment with the Brethren system. The representations were viewed through the lenses of disorganised attachment and identity theory. The implications for therapy were discussed stressing the importance of therapists’ knowledge of cultic groups. Approaches need to facilitate the telling of stories focussing on attachment, identity, trauma, bereavement as well as life and relationships skills

Theory for the Doping Dependence of Spin Fluctuation Induced Shadow States in High-Tc_{c} Superconductors

We analyze the doping dependence of the intensity and energetical position of shadow states in high -T$_{c}$ superconductors within the 2D Hubbard model and using our recently developed numerical method for the self consistent summation of bubble and ladder diagrams. It is shown that shadow states resulting from short range antiferromagnetic correlations occur for small but finite excitation energies which decrease for decreasing doping, reflecting a dynamically broken symmetry with increasing lifetime. Simultanously, the intensity of these new states increases, the quasiparticle dispersion is strongly flattened, and a pseudogap in the density of states occurs. Finally, we discuss the importance of flat bands at the Fermi level and nesting of the Fermi surface as general prerequisites for the observability of shadow states.Comment: 9 pages (TeX) with 3 figures (Postscript