Positive representations of finite groups in Riesz spaces

In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive $G$-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.Comment: 23 pages. To appear in International Journal of Mathematic

Partial order and a T0T_0-topology in a set of finite quantum systems

A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states, density matrices, etc) into their counterparts in the supersystem $\Sigma (n)$ (for $m|n$). The compatibility of these embeddings is studied. The concept of ubiquity is introduced for quantities which fit with this structure. It is shown that various entropic quantities are ubiquitous. The sets of various quantities become $T_0$-topological spaces with the divisor topology, which encapsulates fundamental physical properties. These sets can be converted into directed-complete partial orders (dcpo), by adding `top elements'. The continuity of various maps among these sets is studied

Exploiting Semantic Proximity in Peer-to-Peer Content Searching

A lot of recent work has dealt with improving performance of content searching in peer-to-peer file sharing systems. In this paper we attack this problem by modifying the overlay topology describing the peer relations in the system. More precisely, we create a semantic overlay, linking nodes that are "semantically close", by which we mean that they are interested in similar documents. This semantic overlay provides the primary search mechanism, while the initial peer-to-peer system provides the fail-over search mechanism. We focus on implicit approaches for discovering semantic proximity. We evaluate and compare three candidate methods, and review open questions

Diagnosing students' difficulties in learning mathematics

This study considers the results of a diagnostic test of student difficulty and contrasts the difference in performance between the lower attaining quartile and the higher quartile. It illustrates a difference in qualitative thinking between those who succeed and those who fail in mathematics, illustrating a theory that those who fail are performing a more difficult type of mathematics (coordinating procedures) than those who succeed (manipulating concepts). Students who have to coordinate or reverse processes in time will encounter far greater difficulty than those who can manipulate symbols in a flexible way. The consequences of such a dichotomy and implications for remediation are then considered

Mass Spectrometry-Based Proteomics for Translational Research: A Technical Overview

Mass spectrometry-based investigation of clinical samples enables the high-throughput identification of protein biomarkers. We provide an overview of mass spectrometry-based proteomic techniques that are applicable to the investigation of clinical samples. We address sample collection, protein extraction and fractionation, mass spectrometry modalities, and quantitative proteomics. Finally, we examine the limitations and further potential of such technologies. Liquid chromatography fractionation coupled with tandem mass spectrometry is well suited to handle mixtures of hundreds or thousands of proteins. Mass spectrometry-based proteome elucidation can reveal potential biomarkers and aid in the development of hypotheses for downstream investigation of the molecular mechanisms of disease

Snapping Turtle, Chelydra serpentina, Overland Movements Near the Southeastern Extent of its Range

Terrestrial movements of turtles are of interest due to the conservation implications for this imperiled group and the general lack of information on this topic, particularly in wide-ranging species. The snapping turtle, Chelydra serpentina, is one of the most broadly distributed chelonians in the world; they occur from southeastern Canada westward to Alberta and throughout the eastern half of the United States and into Central America. Most research on this species has been focused on populations in the northern portion of the range. In this study, we radio-tracked five turtles in southwestern Georgia, where published data on spatial ecology and movements are lacking. Turtles exhibited extensive overland movements which we suspect occurred in response to drought