On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<dimensional projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

Composition Space Analysis in the Development of Copper Molybdate Hybrids Decorated by a Bifunctional Pyrazolyl/1,2,4-Triazole Ligand

A bitopic ligand, 4-(3,5-dimethylpyrazol-4-yl)-1,2,4-triazole (Hpz-tr) (1), containing two different heterocyclic moieties was employed for the design of copper(II)–molybdate solids under hydrothermal conditions. In the multicomponent CuII/Hpz-tr/MoVI system, a diverse set of coordination hybrids, [Cu(Hpz-tr)2SO4]·3H2O (2), [Cu(Hpz-tr)Mo3O10] (3), [Cu4(OH)4(Hpz-tr)4Mo8O26]·6H2O (4), [Cu(Hpz-tr)2Mo4O13] (5), and [Mo2O6(Hpz-tr)]·H2O (6), was prepared and characterized. A systematic investigation of these systems in the form of a ternary crystallization diagram approach was utilized to show the influence of the molar ratios of starting reagents, the metal (CuII and MoVI) sources, the temperature, etc., on the reaction products outcome. Complexes 2–4 dominate throughout a wide crystallization range of the composition triangle, while the other two compounds 5 and 6 crystallize as minor phases in a narrow concentration range. In the crystal structures of 2–6, the organic ligand behaves as a short [N–N]-triazole linker between metal centers Cu···Cu in 2–4, Cu···Mo in 5, and Mo···Mo in 6, while the pyrazolyl function remains uncoordinated. This is the reason for the exceptional formation of low-dimensional coordination motifs: 1D for 2, 4, and 6 and 2D for 3 and 5. In all cases, the pyrazolyl group is involved in H bonding (H-donor/H-acceptor) and is responsible for π–π stacking, thus connecting the chain and layer structures in more complicated H-bonding architectures. These compounds possess moderate thermal stability up to 250–300 °C. The magnetic measurements were performed for 2–4, revealing in all three cases antiferromagnetic exchange interactions between neighboring CuII centers and long-range order with a net moment below Tc of 13 K for compound 4.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

Nonlinear three-dimensional noise filter with low-dose CT angiography: effect on the detection of small high-contrast objects in a phantom model

To study the effect of a nonlinear noise filter on the detection of simulated endoleaks in a phantom with 80- and 100-kVp multidetector computed tomographic (CT) angiography.

Surface-acoustic-wave counterflow micropumps for on-chip liquid motion control in two-dimensional microchannel arrays

Fully controlled liquid injection and flow in hydrophobic polydimethylsiloxane (PDMS) two-dimensional microchannel arrays based on on-chip integrated, low-voltage-driven micropumps are demonstrated. Our architecture exploits the surface-acoustic-wave (SAW) induced counterflow mechanism and the effect of nebulization anisotropies at crossing areas owing to lateral propagating SAWs. We show that by selectively exciting single or multiple SAWs, fluids can be drawn from their reservoirs and moved towards selected positions of a microchannel grid. Splitting of the main liquid flow is also demonstrated by exploiting multiple SAW beams. As a demonstrator, we show simultaneous filling of two orthogonal microchannels. The present results show that SAW micropumps are good candidates for truly integrated on-chip fluidic networks allowing liquid control in arbitrarily shaped two-dimensional microchannel arrays.

Full body low radiation radiography using Lodox Statscan

Lodox Statscan provides high-speed, high-quality, low radiation, full body imaging in a single scan, combined with three-dimensional reconstructive and zooming functionality. Several trauma centres have incorporated it into their advanced trauma life support protocol. This review gives a brief overview of the system.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

Low resolution brain electromagnetic tomography (LORETA) functional imaging in acute, neuroleptic-naive, first-episode, productive schizophrenia

Functional imaging of brain electrical activity was performed in nine acute, neuroleptic-naive, first-episode, productive patients with schizophrenia and 36 control subjects. Low-resolution electromagnetic tomography (LORETA, three-dimensional images of cortical current density) was computed from 19-channel of electroencephalographic (EEG) activity obtained under resting conditions, separately for the different EEG frequencies. Three patterns of activity were evident in the patients: (1) an anterior, near-bilateral excess of delta frequency activity; (2) an anterior-inferior deficit of theta frequency activity coupled with an anterior-inferior left-sided deficit of alpha-1 and alpha-2 frequency activity; and (3) a posterior-superior right-sided excess of beta-1, beta-2 and beta-3 frequency activity. Patients showed deviations from normal brain activity as evidenced by LORETA along an anterior-left-to-posterior-right spatial axis. The high temporal resolution of EEG makes it possible to specify the deviations not only as excess or deficit, but also as inhibitory, normal and excitatory. The patients showed a dis-coordinated brain functional state consisting of inhibited prefrontal/frontal areas and simultaneously overexcited right parietal areas, while left anterior, left temporal and left central areas lacked normal routine activity. Since all information processing is brain-state dependent, this dis-coordinated state must result in inadequate treatment of (externally or internally generated) information.

Two-dimensional assembly and local redox-activity of molecular hybrid structures in an electrochemical environment

The self-assembly and redox-properties of two viologen derivatives, N-hexyl-N-(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-H) and N,N-bis(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-SH), immobilized on Au(111)-(1x1) macro-electrodes were investigated by cyclic voltammetry, surface enhanced infrared spectroscopy (SEIRAS) and in situ scanning tunneling microscopy (STM). Depending on the assembly conditions one could distinguish three different types of adlayers for both viologens: a low coverage disordered and an ordered striped phase of flat oriented molecules as well as a high coverage monolayer composed of tilted viologen moieties. Both molecules, HS-6V6-H and HS-6V6-SH, were successfully immobilized on Au(poly) nano-electrodes, which gave a well-defined redox-response in the lower pA–current range. An in situ STM configuration was employed to explore electron transport properties of single molecule junctions Au(T)|HS-6V6-SH(HS-6V6-H)|Au(S). The observed sigmoidal potential dependence, measured at variable substrate potential ES and at constant bias voltage (ET–ES), was attributed to electronic structure changes of the viologen moiety during the one-electron reduction/re-oxidation process V2+ V+. Tunneling experiments in asymmetric, STM-based junctions Au(T)-S-6V6-H|Au(S) revealed current (iT)–voltage (ET) curves with a maximum located at the equilibrium potential of the redox-process V2+ V+. The experimental iT–ET characteristics of the HS-6V6-H–modified tunneling junction were tentatively attributed to a sequential two-step electron transfer mechanism.

Validation of novel 3-dimensional electrocardiographic mapping of atrial tachycardias by invasive mapping and ablation: a multicenter study

OBJECTIVES This study prospectively evaluated the role of a novel 3-dimensional, noninvasive, beat-by-beat mapping system, Electrocardiographic Mapping (ECM), in facilitating the diagnosis of atrial tachycardias (AT). BACKGROUND Conventional 12-lead electrocardiogram, a widely used noninvasive tool in clinical arrhythmia practice, has diagnostic limitations. METHODS Various AT (de novo and post-atrial fibrillation ablation) were mapped using ECM followed by standard-of-care electrophysiological mapping and ablation in 52 patients. The ECM consisted of recording body surface electrograms from a 252-electrode-vest placed on the torso combined with computed tomography-scan-based biatrial anatomy (CardioInsight Inc., Cleveland, Ohio). We evaluated the feasibility of this system in defining the mechanism of AT-macro-re-entrant (perimitral, cavotricuspid isthmus-dependent, and roof-dependent circuits) versus centrifugal (focal-source) activation-and the location of arrhythmia in centrifugal AT. The accuracy of the noninvasive diagnosis and detection of ablation targets was evaluated vis-à-vis subsequent invasive mapping and successful ablation. RESULTS Comparison between ECM and electrophysiological diagnosis could be accomplished in 48 patients (48 AT) but was not possible in 4 patients where the AT mechanism changed to another AT (n = 1), atrial fibrillation (n = 1), or sinus rhythm (n = 2) during the electrophysiological procedure. ECM correctly diagnosed AT mechanisms in 44 of 48 (92%) AT: macro-re-entry in 23 of 27; and focal-onset with centrifugal activation in 21 of 21. The region of interest for focal AT perfectly matched in 21 of 21 (100%) AT. The 2:1 ventricular conduction and low-amplitude P waves challenged the diagnosis of 4 of 27 macro-re-entrant (perimitral) AT that can be overcome by injecting atrioventricular node blockers and signal averaging, respectively. CONCLUSIONS This prospective multicenter series shows a high success rate of ECM in accurately diagnosing the mechanism of AT and the location of focal arrhythmia. Intraprocedural use of the system and its application to atrial fibrillation mapping is under way.

True four-dimensional analysis of thoracic aortic displacement and distension using model-based segmentation of computed tomography angiography.

Previous analyses of aortic displacement and distension using computed tomography angiography (CTA) were performed on double-oblique multi-planar reformations and did not consider through-plane motion. The aim of this study was to overcome this limitation by using a novel computational approach for the assessment of thoracic aortic displacement and distension in their true four-dimensional extent. Vessel segmentation with landmark tracking was executed on CTA of 24 patients without evidence of aortic disease. Distension magnitudes and maximum displacement vectors (MDV) including their direction were analyzed at 5 aortic locations: left coronary artery (COR), mid-ascending aorta (ASC), brachiocephalic trunk (BCT), left subclavian artery (LSA), descending aorta (DES). Distension was highest for COR (2.3 ± 1.2 mm) and BCT (1.7 ± 1.1 mm) compared with ASC, LSA, and DES (p < 0.005). MDV decreased from COR to LSA (p < 0.005) and was highest for COR (6.2 ± 2.0 mm) and ASC (3.8 ± 1.9 mm). Displacement was directed towards left and anterior at COR and ASC. Craniocaudal displacement at COR and ASC was 1.3 ± 0.8 and 0.3 ± 0.3 mm. At BCT, LSA, and DES no predominant displacement direction was observable. Vessel displacement and wall distension are highest in the ascending aorta, and ascending aortic displacement is primarily directed towards left and anterior. Craniocaudal displacement remains low even close to the left cardiac ventricle.

Steady streaming in a two-dimensional box model of a passive cochlea

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencies.