Effective short-range interaction for spin-singlet P-wave nucleon-nucleon scattering

Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence that arises can be renormalised using an order-Q^2 counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.Comment: 4 pages, 3 figures (pdf

Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

The convergence of haemodynamics, genomics, and endothelial structure in studies of the focal origin of atherosclerosis

The completion of the Human Genome Project and ongoing sequencing of mouse, rat and other genomes has led to an explosion of genetics-related technologies that are finding their way into all areas of biological research; the field of biorheology is no exception. Here we outline how two disparate modern molecular techniques, microarray analyses of gene expression and real-time spatial imaging of living cell structures, are being utilized in studies of endothelial mechanotransduction associated with controlled shear stress in vitro and haemodynamics in vivo. We emphasize the value of such techniques as components of an integrated understanding of vascular rheology. In mechanotransduction, a systems approach is recommended that encompasses fluid dynamics, cell biomechanics, live cell imaging, and the biochemical, cell biology and molecular biology methods that now encompass genomics. Microarrays are a useful and powerful tool for such integration by identifying simultaneous changes in the expression of many genes associated with interconnecting mechanoresponsive cellular pathways

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

Ritual responses to drought: An examination of ritual expressions in Classic Maya written sources

Planting and rain-beckoning rituals are an extremely common way in which past and present human communities have confronted the risk of drought across a range of environments worldwide. In tropical environments, such ceremonies are particularly salient despite widespread assumptions that water supplies are unproblematic in such regions. We demonstrate for the first time that two common but previously under-appreciated Maya rituals are likely planting and rain-beckoning rituals preferentially performed at certain times of the year in close step with the rainy season and the Maya agricultural cycle. We also argue for considerable historical continuity between these Classic Maya ceremonies and later Maya community rituals still performed in times of uncertain weather conditions up to the present day across Guatemala, Belize, and eastern Mexico. During the Terminal Classic period (AD 800-900), the changing role played by ancient Maya drought-related rituals fits into a wider rhetorical shift observed in Maya texts away from the more characteristic focus on royal births, enthronements, marriages, and wars towards greater emphasis on the correct perpetuation of key ceremonies, and we argue that such changes are consistent with palaeoclimatic evidence for a period of diminished precipitation and recurrent drought

Leukotriene receptor expression in esophageal squamous cell cancer and non-transformed esophageal epithelium: a matched case control study

Study questionnaire. (DOC 21 kb

Eccrine porocarcinoma of the head: An important differential diagnosis in the elderly patient

Background: Eccrine porocarcinoma is a rare malignant tumor of the sweat gland, characterized by a broad spectrum of clinicopathologic presentations. Surprisingly, unlike its benign counterpart eccrine poroma, eccrine porocarcinoma is seldom found in areas with a high density of eccrine sweat glands, like the palms or soles. Instead, eccrine porocarcinoma frequently occurs on the lower extremities, trunk and abdomen, but also on the head, resembling various other skin tumors, as illustrated in the patients described herein. Observations: We report 5 cases of eccrine porocarcinoma of the head. All patients were initially diagnosed as having epidermal or melanocytic skin tumors. Only after histopathologic examination were they classified as eccrine porocarcinoma, showing features of epithelial tumors with abortive ductal differentiation. Characteristic clinical, histopathologic and immunohistochemical findings of eccrine porocarcinomas are illustrated. Conclusion: Eccrine porocarcinomas are potentially fatal adnexal malignancies, in which extensive metastatic dissemination may occur. Porocarcinomas are commonly overlooked, or misinterpreted as squamous or basal cell carcinomas as well as other common malignant and even benign skin tumors. Knowledge of the clinical pattern and histologic findings, therefore, is crucial for an early therapeutic intervention, which can reduce the risk of tumor recurrence and serious complications. Copyright (c) 2008 S. Karger AG, Basel