A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

The influence of cutting tool geometry upon aspects of chip flow and tool wear:a theoretical, three dimensional examination of the cutting geometry and the shape of the twist drill

This work is undertaken in the attempt to understand the processes at work at the cutting edge of the twist drill. Extensive drill life testing performed by the University has reinforced a survey of previously published information. This work demonstrated that there are two specific aspects of drilling which have not previously been explained comprehensively. The first concerns the interrelating of process data between differing drilling situations, There is no method currently available which allows the cutting geometry of drilling to be defined numerically so that such comparisons, where made, are purely subjective. Section one examines this problem by taking as an example a 4.5mm drill suitable for use with aluminium. This drill is examined using a prototype solid modelling program to explore how the required numerical information may be generated. The second aspect is the analysis of drill stiffness. What aspects of drill stiffness provide the very great difference in performance between short flute length, medium flute length and long flute length drills? These differences exist between drills of identical point geometry and the practical superiority of short drills has been known to shop floor drilling operatives since drilling was first introduced. This problem has been dismissed repeatedly as over complicated but section two provides a first approximation and shows that at least for smaller drills of 4. 5mm the effects are highly significant. Once the cutting action of the twist drill is defined geometrically there is a huge body of machinability data that becomes applicable to the drilling process. Work remains to interpret the very high inclination angles of the drill cutting process in terms of cutting forces and tool wear but aspects of drill design may already be looked at in new ways with the prospect of a more analytical approach rather than the present mix of experience and trial and error. Other problems are specific to the twist drill, such as the behaviour of the chips in the flute. It is now possible to predict the initial direction of chip flow leaving the drill cutting edge. For the future the parameters of further chip behaviour may also be explored within this geometric model.

An accurate and scalable analytical model for IEEE 802.15.4 slotted CSMA/CA networks

In this paper a Markov chain based analytical model is proposed to evaluate the slotted CSMA/CA algorithm specified in the MAC layer of IEEE 802.15.4 standard. The analytical model consists of two two-dimensional Markov chains, used to model the state transition of an 802.15.4 device, during the periods of a transmission and between two consecutive frame transmissions, respectively. By introducing the two Markov chains a small number of Markov states are required and the scalability of the analytical model is improved. The analytical model is used to investigate the impact of the CSMA/CA parameters, the number of contending devices, and the data frame size on the network performance in terms of throughput and energy efficiency. It is shown by simulations that the proposed analytical model can accurately predict the performance of slotted CSMA/CA algorithm for uplink, downlink and bi-direction traffic, with both acknowledgement and non-acknowledgement modes.

Three-dimensional fluid pressure mapping in porous media using magnetic resonance imaging with gas-filled liposomes

This paper presents and demonstrates a method for using magnetic resonance imaging to measure local pressure of a fluid saturating a porous medium. The method is tested both in a static system of packed silica gel and in saturated sintered glass cylinders experiencing fluid flow. The fluid used contains 3% gas in the form of 3-μm average diameter gas filled 1,2-distearoyl-sn-glycero-3-phosphocholine (C18:0, MW: 790.16) liposomes suspended in 5% glycerol and 0.5% Methyl cellulose with water. Preliminary studies at 2.35 T demonstrate relative magnetic resonance signal changes of 20% per bar in bulk fluid for an echo time TE=40 ms, and 6-10% in consolidated porous media for TE=10 ms, over the range 0.8-1.8 bar for a spatial resolution of 0.1 mm3 and a temporal resolution of 30 s. The stability of this solution with relation to applied pressure and methods for improving sensitivity are discussed. © 2007 Elsevier Inc. All rights reserved.

The structure and dynamics of 2-dimensional fluids in swelling clays

The interlayer pores of swelling 2:1 clays provide an ideal 2-dimensional environment in which to study confined fluids. In this paper we discuss our understanding of the structure and dynamics of interlayer fluid species in expanded clays, based primarily on the outcome of recent molecular modelling and neutron scattering studies. Counterion solvation is compared with that measured in bulk solutions, and at a local level the cation-oxygen coordination is found to be remarkably similar in these two environments. However, for the monovalent ions the contribution to the first coordination shell from the clay surfaces increases with counterion radius. This gives rise to inner-sphere (surface) complexes in the case of potassium and caesium. In this context, the location of the negative clay surface charge (i.e. arising from octahedral or tetrahedral substitution) is also found to be of major importance. Divalent cations, such as calcium, eagerly solvate to form outer-sphere complexes. These complexes are able to pin adjacent clay layers together, and thereby prevent colloidal swelling. Confined water molecules form hydrogen bonds to each other and to the clays' surfaces. In this way their local environment relaxes to close to the bulk water structure within two molecular layers of the clay surface. Finally, we discuss the way in which the simple organic molecules methane, methanol and ethylene glycol behave in the interlayer region of hydrated clays. Quasi-elastic neutron scattering of isotopically labelled interlayer CH 3OD and (CH2OD)2 in deuterated clay allows us to measure the diffusion of the CH3- and CH2-groups in both clay and liquid environments. We find that in both the one-layer methanol solvates and the two-layer glycol solvates the diffusion of the most mobile organic molecules is close to that in the bulk solution.

Characterisation of electrospun polystyrene scaffolds for three-dimensional in vitro biological studies

The purpose of this study was to produce a well-characterised electrospun polystyrene scaffold which could be used routinely for three-dimensional (3D) cell culture experimentation. A linear relationship (p<0.01p<0.01) between three principal process variables (applied voltage, working distance and polymer concentration) and fibre diameter was reliably established enabling a mathematical model to be developed to standardise the electrospinning process. Surface chemistry and bulk architecture were manipulated to increase wetting and handling characteristics, respectively. X-ray photoelectron spectroscopy (XPS) confirmed the presence of oxygen-containing groups after argon plasma treatment, resulting in a similar surface chemistry to treated tissue culture plastic. The bulk architecture of the scaffolds was characterised by scanning electron microscopy (SEM) to assess the alignment of both random and aligned electrospun fibres, which were calculated to be 0.15 and 0.66, respectively. This compared to 0.51 for collagen fibres associated with native tissue. Tensile strength and strain of approximately of 0.15 MPa and 2.5%, respectively, allowed the scaffolds to be routinely handled for tissue culture purposes. The efficiency of attachment of smooth muscle cells to electrospun scaffolds was assessed using a modified 3-[4,5-dimethyl(thiazol-2yl)-3,5-diphery] tetrazolium bromide assay and cell morphology was assessed by phalloidin-FITC staining of F-actin. Argon plasma treatment of electrospun polystyrene scaffold resulted in significantly increased cell attachment (p<0.05p<0.05). The alignment factors of the actin filaments were 0.19 and 0.74 for the random and aligned scaffold respectively, compared to 0.51 for the native tissue. The data suggests that electrospinning of polystyrene generates 3D scaffolds which complement polystyrene used in 2D cell culture systems.

Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Resonance properties of domain boundaries in quasi-two dimensional antiferromagnets

The so-called "internal modes" localized near the domain boundaries in quasi-two dimensional antiferromagnets are investigated. The possible localized states are classified and their frequency dependences on the system discreteness parameter λ=J/β, which describes the ratio of the magnitudes of the exchange interplane interaction and the magnetic anisotropy, are found. A sudden change in the spectrum of the local internal modes is observed at a critical value of this parameter, λ=λb=3/4, where the domain wall shifts from a collinear to a canted shape. When λ<λb there are one symmetric and two antisymmetric local modes, and when λ>λb the modes are two symmetric, one antisymmetric, and one shear. For discreteness parameters close to the critical value, the frequencies of some of the local modes lie deep inside the gap for the linear AFM magnon spectrum and can be observed experimentally. © 2010 American Institute of Physics.