Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Ana

Preceding rule induction with instance reduction methods

A new prepruning technique for rule induction is presented which applies instance reduction before rule induction. An empirical evaluation records the predictive accuracy and size of rule-sets generated from 24 datasets from the UCI Machine Learning Repository. Three instance reduction algorithms (Edited Nearest Neighbour, AllKnn and DROP5) are compared. Each one is used to reduce the size of the training set, prior to inducing a set of rules using Clark and Boswell's modification of CN2. A hybrid instance reduction algorithm (comprised of AllKnn and DROP5) is also tested. For most of the datasets, pruning the training set using ENN, AllKnn or the hybrid significantly reduces the number of rules generated by CN2, without adversely affecting the predictive performance. The hybrid achieves the highest average predictive accuracy

A psychoanalytic concept illustrated: Will, must, may, can — revisiting the survival function of primitive omnipotence

The author explores the linear thread connecting the theory of Freud and Klein, in terms of the central significance of the duality of the life and death instinct and the capacity of the ego to tolerate contact with internal and external reality. Theoretical questions raised by later authors, informed by clinical work with children who have suffered deprivation and trauma in infancy, are then considered. Theoretical ideas are illustrated with reference to observational material of a little boy who suffered deprivation and trauma in infancy. He was first observed in the middle of his first year of life while he was living in foster care, and then later at the age of two years and three months, when he had been living with his adoptive parents for more than a year

First-principles Calculation of the Formation Energy in MgO-CaO Solid Solutions

The electronic structure and total energy were calculated for ordered and disordered MgO-CaO solid solutions within the multiple scattering theory in real space and the local density approximation. Based on the dependence of the total energy on the unit cell volume the equilibrium lattice parameter and formation energy were determined for different solution compositions. The formation energy of the solid solutions is found to be positive that is in agreement with the experimental phase diagram, which shows a miscibility gap.Comment: 11 pages, 3 figure

Velocity-selective sublevel resonance of atoms with an array of current-carrying wires

Resonance transitions between the Zeeman sublevels of optically-polarized Rb atoms traveling through a spatially periodic magnetic field are investigated in a radio-frequency (rf) range of sub-MHz. The atomic motion induces the resonance when the Zeeman splitting is equal to the frequency at which the moving atoms feel the magnetic field oscillating. Additional temporal oscillation of the spatially periodic field splits a motion-induced resonance peak into two by an amount of this oscillation frequency. At higher oscillation frequencies, it is more suitable to consider that the resonance is mainly driven by the temporal field oscillation, with its velocity-dependence or Doppler shift caused by the atomic motion through the periodic field. A theoretical description of motion-induced resonance is also given, with emphasis on the translational energy change associated with the internal transition.Comment: 7 pages, 3 figures, final versio

Renal pericytes: regulators of medullary blood flow

Regulation of medullary blood flow (MBF) is essential in maintaining normal kidney function. Blood flow to the medulla is supplied by the descending vasa recta (DVR), which arise from the efferent arterioles of juxtamedullary glomeruli. DVR are composed of a continuous endothelium, intercalated with smooth muscle-like cells called pericytes. Pericytes have been shown to alter the diameter of isolated and in situ DVR in response to vasoactive stimuli that are transmitted via a network of autocrine and paracrine signalling pathways. Vasoactive stimuli can be released by neighbouring tubular epithelial, endothelial, red blood cells and neuronal cells in response to changes in NaCl transport and oxygen tension. The experimentally described sensitivity of pericytes to these stimuli strongly suggests their leading role in the phenomenon of MBF autoregulation. Because the debate on autoregulation of MBF fervently continues, we discuss the evidence favouring a physiological role for pericytes in the regulation of MBF and describe their potential role in tubulo-vascular cross-talk in this region of the kidney. Our review also considers current methods used to explore pericyte activity and function in the renal medulla

Trapping of Single Atoms with Single Photons in Cavity QED

Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000) and Pinkse et al., Nature 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. Firstly, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts. Secondly, we explore the quantitative features of the resulting atomic motion and how these dynamics are mapped onto variations of the intracavity field. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents qualitatively new physics for optical forces at the single-photon level. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the free-space theory and the quantum theory, so it is not clear that description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.Comment: 19 pages, 22 figure files, REVTEX, corrected spelling, LaTeX now produces postscript which includes figures, minor changes to figures. Final version to be published in Physical Review A, expanded summary of results in introduction, minor changes to figures and tex

‘Ethnic group’, the state and the politics of representation

The assertion, even if only by implication, that ‘ethnic group’ categories represent ‘real’ tangible entities, indeed identities, is commonplace not only in the realms of political and policy discourse but also amongst contemporary social scientists. This paper, following Brubaker (2002), questions this position in a number of key respects: of these three issues will dominate the discussion that follows. First, there is an interrogation of the proposition that those to whom the categories/labels refer constitute sociologically meaningful ‘groups’ as distinct from (mere) human collectivities. Secondly, there is the question of how these categories emerge, i.e. exactly what series of events, negotiations and contestations lie behind their construction and social acceptance. Thirdly, and as a corollary to the latter point, we explore the process of reification that leads to these categories being seen to represent ‘real things in the world’ (ibid.)

The Self Model and the Conception of Biological Identity in Immunology

The self/non-self model, first proposed by F.M. Burnet, has dominated immunology for sixty years now. According to this model, any foreign element will trigger an immune reaction in an organism, whereas endogenous elements will not, in normal circumstances, induce an immune reaction. In this paper we show that the self/non-self model is no longer an appropriate explanation of experimental data in immunology, and that this inadequacy may be rooted in an excessively strong metaphysical conception of biological identity. We suggest that another hypothesis, one based on the notion of continuity, gives a better account of immune phenomena. Finally, we underscore the mapping between this metaphysical deflation from self to continuity in immunology and the philosophical debate between substantialism and empiricism about identity