Symmetrization procedures for the isoperimetric problem in symmetric spaces of noncompact type

We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized domain is obtained by solving a nonlinear elliptic equation of mean curvature type. We conclude the paper discussing possible applications to the isoperimetric problem in symmetric spaces of noncompact type.Comment: 28 pages, 1 figur

Game Harmony: A Short Note

Strategic uncertainty in game theory may have two different general sources, either alone or in combination: uncertainty because of the existence of a coordination problem, and uncertainty because of a conflict between one own and the other n players' interests. Game harmony is conceived as a generic game property that describes how harmonious (non-conflictual) or disharmonious (conflictual) the interests of the n players are, as embodied in the game payoffs. Pure coordination games are examples of games with maximal game harmony; zero sum games are examples of games with very low game harmony. This note briefly describes attempts to measure game harmony simply as a real-valued number

Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term

We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT). We study the phase diagram of this model and identify the two phases that are well known from previous work: the branched polymer phase and the collapsed phase. We verify that the order of the phase transition dividing the branched polymer phase from the collapsed phase is almost certainly first-order. The nontrivial measure term enlarges the phase diagram, allowing us to explore a region of the phase diagram that has been dubbed the crinkled region. Although the collapsed and branched polymer phases have been studied extensively in the literature, the crinkled region has not received the same scrutiny. We find that the crinkled region is likely a part of the collapsed phase with particularly large finite-size effects. Intriguingly, the behavior of the spectral dimension in the crinkled region at small volumes is similar to that of CDT, as first reported in arXiv:1104.5505, but for sufficiently large volumes the crinkled region does not appear to have 4-dimensional semiclassical features. Thus, we find that the crinkled region of the EDT formulation does not share the good features of the extended phase of CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent results of arXiv:1307.2270, in which the authors used a somewhat different discretization of EDT from the one presented here.Comment: 36 pages, 27 figures. Typos corrected, improved analysis of phase transition, and clarifications added. Conclusions unchanged. Conforms with version published in JHE

Psychotherapeutic approaches to the elderly: Part Two

It is not easy to come to terms with retirement, failing bodily functions, increased vulnerability, potential institutionalisation and inevitable death. For some this is a stage of life tinged with difficult memories of being cared for when they were younger. It is not uncommon to see some older adults with a past history of childhood trauma and adversity develop new onset relationship problems having lost the containment of a career or a loved one. Older people can derive huge benefit from psychotherapeutic approaches. Personal transformation may enable them to go on to enjoy meaningful and fruitful old and new relationships whether in the community or in a care home

The media equation and team formation: Further evidence for experience as a moderator

This study extends previous media equation research, which showed that interdependence but not identity leads to team affiliation effects with computers. The current study used an identity manipulation that more closely replicated the manipulation used in traditional team and group formation research than the original media equation research in this area. The study also sought further evidence for the relationship between experience with computers and behaviour reflecting a media equation pattern of results. Sixty students from the University of Queensland voluntarily participated in the study. Participants were assigned to one of three conditions: control, human team (a team made of only humans) or human-computer team (a team made of computers and humans). Questionnaire measures assessing participants’ affective experience, attitudes and opinions were taken. Participants of high experience, but not low experience, when assigned to either of the team conditions enjoyed the tasks completed on the computer more than participants who worked on their own. When assigned to a team that involved a computer, participants of high experience, but not low experience, reacted negatively towards the computer (in comparison to high experience participants working on their own or on a team without a computer as a team member) – rating the information provided by the computer lower, rating themselves as less influenced by the computer and changing their own ratings and rankings to be less like those of the computer. These results are interpreted in light of the ‘Black Sheep’ literature and recognized as a media equation pattern of results

Spontaneous emission from a two--level atom tunneling in a double--well potential

We study a two-level atom in a double--well potential coupled to a continuum of electromagnetic modes (black body radiation in three dimensions at zero absolute temperature). Internal and external degrees of the atom couple due to recoil during emission of a photon. We provide a full analysis of the problem in the long wavelengths limit up to the border of the Lamb-Dicke regime, including a study of the internal dynamics of the atom (spontaneous emission), the tunneling motion, and the electric field of the emitted photon. The tunneling process itself may or may not decohere depending on the wavelength corresponding to the internal transition compared to the distance between the two wells of the external potential, as well as on the spontaneous emission rate compared to the tunneling frequency. Interference fringes appear in the emitted light from a tunneling atom, or an atom in a stationary coherent superposition of its center--of--mass motion, if the wavelength is comparable to the well separation, but only if the external state of the atom is post-selected.Comment: 24 pages, 4 figures; improved discussion on the limitations of the theor