Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

OWL-based acquisition and editing of computer-interpretable guidelines with the CompGuide editor

Computer-Interpretable Guidelines (CIGs) are the dominant medium for the delivery of clinical decision support, given the evidence-based nature of their source material. Therefore, these machine-readable versions have the ability to improve practitioner performance and conformance to standards, with availability at the point and time of care. The formalisation of Clinical Practice Guideline knowledge in a machine-readable format is a crucial task to make it suitable for the integration in Clinical Decision Support Systems. However, the current tools for this purpose reveal shortcomings with respect to their ease of use and the support offered during CIG acquisition and editing. In this work, we characterise the current landscape of CIG acquisition tools based on the properties of guideline visualisation, organisation, simplicity, automation, manipulation of knowledge elements, and guideline storage and dissemination. Additionally, we describe the CompGuide Editor, a tool for the acquisition of CIGs in the CompGuide model for Clinical Practice Guidelines that also allows the editing of previously encoded guidelines. The Editor guides the users throughout the process of guideline encoding and does not require proficiency in any programming language. The features of the CIG encoding process are revealed through a comparison with already established tools for CIG acquisition.COMPETE, Grant/Award Number: POCI-01-0145-FEDER-007043; FCT - Fundacao para a Ciencia e Tecnologia, Grant/Award Number: UID/CEC/00319/201

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Quaternion Analysis for Generalized Electromagnetic Fields of Dyons in Isotropic Medium

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple and consistent manner

Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Favorable outcome of early treatment of new onset child and adolescent migraine-implications for disease modification.

There is evidence that the prevalence of migraine in children and adolescents may be increasing. Current theories of migraine pathophysiology in adults suggest activation of central cortical and brainstem pathways in conjunction with the peripheral trigeminovascular system, which ultimately results in release of neuropeptides, facilitation of central pain pathways, neurogenic inflammation surrounding peripheral vessels, and vasodilatation. Although several risk factors for frequent episodic, chronic, and refractory migraine have been identified, the causes of migraine progression are not known. Migraine pathophysiology has not been fully evaluated in children. In this review, we will first discuss the evidence that early therapeutic interventions in the child or adolescent new onset migraineur, may halt or limit progression and disability. We will then review the evidence suggesting that many adults with chronic or refractory migraine developed their migraine as children or adolescents and may not have been treated adequately with migraine-specific therapy. Finally, we will show that early, appropriate and optimal treatment of migraine during childhood and adolescence may result in disease modification and prevent progression of this disease

Chalcogen Impact on Covalency within Molecular [Cu\u3csub\u3e3\u3c/sub\u3e(μ\u3csub\u3e3\u3c/sub\u3e-E)]\u3csup\u3e3+\u3c/sup\u3e Clusters (E = O, S, Se): A Synthetic, Spectroscopic, and Computational Study

Reaction of the tricopper(I)-dinitrogen tris(β-diketiminate) cyclophane, Cu3(N2)L, with O-atom-transfer reagents or elemental Se affords the oxido-bridged tricopper complex Cu3(μ3-O)L (2) or the corresponding Cu3(μ3-Se)L (4), respectively. For 2 and 4, incorporation of the bridging chalcogen donor was supported by electrospray ionization mass spectrometry and K-edge X-ray absorption spectroscopy (XAS) data. Cu L2,3-edge X-ray absorption data quantify 49.5% Cu 3d character in the lowest unoccupied molecular orbital of 2, with Cu 3d participation decreasing to 33.0% in 4 and 40.8% in the related sulfide cluster Cu3(μ3-S)L (3). Multiedge XAS and UV/visible/near-IR spectra are employed to benchmark density functional theory calculations, which describe the copper-chalcogen interactions as highly covalent across the series of [Cu3(μ-E)]3+ clusters. This result highlights that the metal-ligand covalency is not reserved for more formally oxidized metal centers (i.e., CuIII + O2- vs CuII + O-) but rather is a significant contributor even at more typical ligand-field cases (i.e., Cu3II/II/I + E2-). This bonding is reminiscent of that observed in p-block elements rather than in early-transition-metal complexes

Notions of Infinity in Quantum Physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.Comment: 11 page

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio