On Convergence Properties of the EM Algorithm for Gaussian Mixtures

"Expectation-Maximization'' (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models.

Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.

Alterations in receptor binding properties of recent human influenza H3N2 viruses are associated with reduced natural killer cell lysis of infected cells

Natural killer (NK) cell recognition of influenza virus-infected cells involves hemagglutinin (HA) binding to sialic acid (SA) on activating NK receptors. SA also acts as a receptor for the binding of influenza virus to its target host cells. The SA binding properties of H3N2 influenza viruses have been observed to change during circulation in humans: recent isolates are unable to agglutinate chicken red blood cells and show reduced affinity for synthetic glycopolymers representing SA-alpha-2,3-lactose (3'SL-PAA) and SA-alpha-2,6-N-acetyl lactosamine (6'SLN-PAA) carbohydrates. Here, NK lysis of cells infected with human H3N2 influenza viruses isolated between 1969 and 2003 was analyzed. Cells infected with recent isolates (1999 to 2003) were found to be lysed less effectively than cells infected with older isolates (1969 to 1996). This change occurred concurrently with the acquisition of two new potential glycosylation site motifs in RA. Deletion of the potential glycosylation site motif at 133 to 135 in HA1 from a recent isolate partially restored the agglutination phenotype to a recombinant virus, indicating that the HA-SA interaction is inhibited by the glycosylation modification. Deletion of either of the recently acquired potential glycosylation sites from HA led to increased NK lysis of cells infected with recombinant viruses carrying modified HA. These results indicate that alterations in RA glycosylation may affect NK cell recognition of influenza virus-infected cells in addition to virus binding to host cells.

Electrochemical fabrication and electrocatalytic properties of nanostructured mesoporous platinum microelectrodes

Electrodeposition from a lyotropic liquid crystal template medium was used to produce nanostructured platinum microelectrodes with high specific surface area and high mass transport efficiency. Compared to polished and conventional platinized microelectrodes, well-ordered nanostructured platinum microelectrodes exhibited enhanced electrocatalytic properties for oxygen and ascorbic acid, whilst well-ordered nanostructured platinum microelectrodes offered improved electrocatalytic properties for oxygen reduction compared to disordered nanostructured platinum microelectrodes.

Consequences of N,C,N '- and C,N,N '-coordination modes on electronic and photophysical properties of cyclometalated aryl ruthenium(II) complexes

The effects of isoelectronic replacement of a neutral nitrogen donor atom by an anionic carbon atom in terpyridine ruthenium(II) complexes on the electronic and photophysical properties of the resulting N,C,N'- and C,N,N'-cyclometalated aryl ruthenium(II) complexes were investigated. To this end, a series of complexes was prepared either with ligands containing exclusively nitrogen donor atoms, that is, [Ru(R-1-tpy)(R-2-tpy)](2+) (R-1, R-2 = H, CO2Et), or bearing either one N,C,N'- or C,N,N'-cyclometalated ligand and one tpy ligand, that is, [Ru(R-1-(NCN)-C-Lambda-N-Lambda)(R-2-tpy)](+) and [Ru(R-1-(CNN)-N-Lambda-N-Lambda)(R-2-tpy)](+), respectively. Single-crystal X-ray structure determinations showed that cyclometalation does not significantly alter the overall geometry of the complexes but does change the bond lengths around the ruthenium(II) center, especially the nitrogen-to-ruthenium bond length trans to the carbanion. Substitution of either of the ligands with electron-withdrawing ester functionalities fine-tuned the electronic properties and resulted in the presence of an IR probe. Using trends obtained from redox potentials, emission energies, IR spectroelectrochemical responses, and the character of the lowest unoccupied molecular orbitals from DFT studies, it is shown that the first reduction process and luminescence are associated with the ester-substituted C,N,N'-cyclometalated ligand in [Ru(EtO2C-(CNN)-N-Lambda-N-Lambda)(tpy)](+). Cyclometalation in an N,C,N'-bonding motif changed the energetic order of the ruthenium d(zx), d(yz), and d(xy) orbitals. The red-shifted absorption in the N,C,N'-cyclometalated complexes is assigned to MLCT transitions to the tpy ligand. The red shift observed upon introduction of the ester moiety is associated with an increase in intensity of low-energy transitions, rather than a red shift of the main transition. Cyclometalation in the C,N,N'-binding motif also red-shifts the absorption, but the corresponding transition is associated with both ligand types. Luminescence of the cyclometalated complexes is relatively independent of the mode of cyclometalation, obeying the energy gap law within each individual series.

Assessing the frictional and abrasion-resisting properties of hooves and claws

Hoof abrasion and slips on floors are known to have negative effects on animal health and welfare. This paper describes a new design of test rig for use in a universal materials test machine. The rig enables the frictional and abrasion-resisting properties of hoof horn to be investigated under controlled conditions, in vitro. To assess the performance of the rig, pilot experiments were carried out which indicated both test surface roughness and specimen hydration interact to alter frictional coefficient and mechanical work done to lose a unit volume of hoof material by abrasive wear.

Comparison of mechanical properties of tension and opposite wood in Populus

In this paper we focused on the differences of mechanical properties of tension and normal wood of 1-year-old poplar trees, artificially tilted. Elastic and fracture properties have been measured and linked to the anatomy. Tension wood is well known because it prevents good surface finishing and leads to difficulties with sawing. We studied three main mechanical properties: young modulus, energy of cutting and longitudinal residual strain of maturation (with strain gauges) because of their importance in wood technology. Moreover, this work takes place in a larger project of study, the phenomena of axes re-orientation in trees (allowing by the production of reaction wood), where these data are required for biomechanical modelling. The results show that tension wood has a higher young modulus, needs a higher energy to be cut and exhibited a higher level of longitudinal residual strain of maturation than those of normal wood. The results suggest that these differences require deeper analysis of the wood than anatomy: measurement of microfibril orientation in the S2 layer and also the lignin composition in monomeric units.

Effects of high pressure on functional properties of soy protein

Simultaneous measurement of the effects of low soy protein concentration, pH and high pressure treatment at room temperature on solubility, emulsifying properties and rheological properties (loss modulus, G '') of soy protein isolate (SPI) were evaluated. Central composite rotatable designs (2(3)) were employed over two pH ranges (2.66-4.34 and 5.16-6.84) with SPI concentration (0.32-3.68%) and pressure (198-702 MPa) as the other independent variables. The surface responses were obtained for protein solubility, emulsifying activity index (EAI) and G ''. The samples with the highest effect on protein solubility, EAI and G '' values were evaluated, as well, by electrophoresis and free sulphydryl determination. The pH was the main factor that affected protein solubility, with solubility at a maximum at pH < 3 or pH > 6. Increasing SPI concentration and decreasing/increasing the pH away from the isoelectric point both caused a reduction in EAI. Loss modulus (G '') was found to increase with SPI concentration in both pH ranges. (c) 2006 Elsevier Ltd. All rights reserved.

Alterations in receptor binding properties of recent human influenza H3N2 viruses are associated with reduced natural killer cell lysis of infected cells

Natural killer (NK) cell recognition of influenza virus-infected cells involves hemagglutinin (HA) binding to sialic acid (SA) on activating NK receptors. SA also acts as a receptor for the binding of influenza virus to its target host cells. The SA binding properties of H3N2 influenza viruses have been observed to change during circulation in humans: recent isolates are unable to agglutinate chicken red blood cells and show reduced affinity for synthetic glycopolymers representing SA-alpha-2,3-lactose (3'SL-PAA) and SA-alpha-2,6-N-acetyl lactosamine (6'SLN-PAA) carbohydrates. Here, NK lysis of cells infected with human H3N2 influenza viruses isolated between 1969 and 2003 was analyzed. Cells infected with recent isolates (1999 to 2003) were found to be lysed less effectively than cells infected with older isolates (1969 to 1996). This change occurred concurrently with the acquisition of two new potential glycosylation site motifs in RA. Deletion of the potential glycosylation site motif at 133 to 135 in HA1 from a recent isolate partially restored the agglutination phenotype to a recombinant virus, indicating that the HA-SA interaction is inhibited by the glycosylation modification. Deletion of either of the recently acquired potential glycosylation sites from HA led to increased NK lysis of cells infected with recombinant viruses carrying modified HA. These results indicate that alterations in RA glycosylation may affect NK cell recognition of influenza virus-infected cells in addition to virus binding to host cells.

The statistical properties of tropical ice clouds generated by the West-African and Australian monsoons from ground-based radar-lidar observations

In the present paper we characterize the statistical properties of non-precipitating tropical ice clouds (deep ice anvils resulting from deep convection and cirrus clouds) over Niamey, Niger, West Africa, and Darwin, northern Australia, using ground-based radar–lidar observations from the Atmospheric Radiation Measurement (ARM) programme. The ice cloud properties analysed in this paper are the frequency of ice cloud occurrence, cloud fraction, the morphological properties (cloud-top height, base height, and thickness), the microphysical and radiative properties (ice water content, visible extinction, effective radius, terminal fall speed, and concentration), and the internal cloud dynamics (in-cloud vertical air velocity). The main highlight of the paper is that it characterizes for the first time the probability density functions of the tropical ice cloud properties, their vertical variability and their diurnal variability at the same time. This is particularly important over West Africa, since the ARM deployment in Niamey provides the first vertically resolved observations of non-precipitating ice clouds in this crucial area in terms of redistribution of water and energy in the troposphere. The comparison between the two sites also provides an additional observational basis for the evaluation of the parametrization of clouds in large-scale models, which should be able to reproduce both the statistical properties at each site and the differences between the two sites. The frequency of ice cloud occurrence is found to be much larger over Darwin when compared to Niamey, and with a much larger diurnal variability, which is well correlated with the diurnal cycle of deep convective activity. The diurnal cycle of the ice cloud occurrence over Niamey is also much less correlated with that of deep convective activity than over Darwin, probably owing to the fact that Niamey is further away from the deep convective sources of the region. The frequency distributions of cloud fraction are strongly bimodal and broadly similar over the two sites, with a predominance of clouds characterized either by a very small cloud fraction (less than 0.3) or a very large cloud fraction (larger than 0.9). The ice clouds over Darwin are also much thicker (by 1 km or more statistically) and are characterized by a much larger diurnal variability than ice clouds over Niamey. Ice clouds over Niamey are also characterized by smaller particle sizes and fall speeds but in much larger concentrations, thereby carrying more ice water and producing more visible extinction than the ice clouds over Darwin. It is also found that there is a much larger occurrence of downward in-cloud air motions less than 1 m s−1 over Darwin, which together with the larger fall speeds retrieved over Darwin indicates that the life cycle of ice clouds is probably shorter over Darwin than over Niamey.

New results on the thermodynamical properties of the climate system

In this paper the authors exploit two equivalent formulations of the average rate of material entropy production in the climate system to propose an approximate splitting between contributions due to vertical and eminently horizontal processes. This approach is based only on 2D radiative fields at the surface and at the top of atmosphere. Using 2D fields at the top of atmosphere alone, lower bounds to the rate of material entropy production and to the intensity of the Lorenz energy cycle are derived. By introducing a measure of the efficiency of the planetary system with respect to horizontal thermodynamic processes, it is possible to gain insight into a previous intuition on the possibility of defining a baroclinic heat engine extracting work from the meridional heat flux. The approximate formula of the material entropy production is verified and used for studying the global thermodynamic properties of climate models (CMs) included in the Program for Climate Model Diagnosis and Intercomparison (PCMDI)/phase 3 of the Coupled Model Intercomparison Project (CMIP3) dataset in preindustrial climate conditions. It is found that about 90% of the material entropy production is due to vertical processes such as convection, whereas the large-scale meridional heat transport contributes to only about 10% of the total. This suggests that the traditional two-box models used for providing a minimal representation of entropy production in planetary systems are not appropriate, whereas a basic—but conceptually correct—description can be framed in terms of a four-box model. The total material entropy production is typically 55 mW m−2 K−1, with discrepancies on the order of 5%, and CMs’ baroclinic efficiencies are clustered around 0.055. The lower bounds on the intensity of the Lorenz energy cycle featured by CMs are found to be around 1.0–1.5 W m−2, which implies that the derived inequality is rather stringent. When looking at the variability and covariability of the considered thermodynamic quantities, the agreement among CMs is worse, suggesting that the description of feedbacks is more uncertain. The contributions to material entropy production from vertical and horizontal processes are positively correlated, so that no compensation mechanism seems in place. Quite consistently among CMs, the variability of the efficiency of the system is a better proxy for variability of the entropy production due to horizontal processes than that of the large-scale heat flux. The possibility of providing constraints on the 3D dynamics of the fluid envelope based only on 2D observations of radiative fluxes seems promising for the observational study of planets and for testing numerical models.

From BTBPs to BTPhens: the effect of ligand pre-organization on the extraction properties of quadridentate bis-triazine ligands

The synthesis, lanthanide complexation and solvent extraction of An(III) and Ln(III) radiotracers from nitric acid solutions by a pre-organized, phenanthroline-derived bis-triazine ligand CyMe4-BTPhen are described. It was found that the ligand separated Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and faster extraction kinetics compared to its 2,2’-bipyridine counterpart CyMe4-BTBP. The origins of the ligands extraction properties were established by a combination of solvent extraction experiments, X-ray crystallography, kinetics and surface tension measurements and lanthanide NMR spectroscopy.

Structure and magnetic properties of an unprecedented syn-antiμ-nitrito-1κO:2κO′ bridged Mn(iii)-salen complex and its isoelectronic and isostructural formate analogue

The preparation, crystal structures and magnetic properties of two new isoelectronic and isomorphous formate-and nitrite-bridged 1D chains of Mn(III)-salen complexes, [Mn(salen)(HCOO)](n) (1) and [Mn(salen)(NO2)](n) (2), where salen is the dianion of N,N'-bis(salicylidene)-1,2-diaminoethane, are presented. The structures show that the salen ligand coordinates to the four equatorial sites of the metal ion and the formate or nitrite ions coordinate to the axial positions to bridge the Mn(III)-salen units through a syn-anti mu-1 kappa O:2 kappa O' coordination mode. Such a bridging mode is unprecedented in Mn(III) for formate and in any transition metal ion for nitrite. Variable-temperature magnetic susceptibility measurements of complexes 1 and 2 indicate the presence of ferromagnetic exchange interactions with J values of 0.0607 cm(-1) (for 1) and 0.0883 cm(-1) (for 2). The ac measurements indicate negligible frequency dependence for 1 whereas compound 2 exhibits a decrease of chi(ac)' and a concomitant increase of chi(ac)'' on elevating frequency around 2 K. This finding is an indication of slow magnetization reversal characteristic of single-chain magnets or spin-glasses. The mu-nitrito-1 kappa O:2 kappa O' bridge seems to be a potentially superior magnetic coupler to the formate bridge for the construction of single-molecule/-chain magnets as its coupling constant is greater and the chi(ac)' and chi(ac)'' show frequency dependence.

Structure and magnetic properties of a tetranuclear Cu(II) complex containing the 2-(pyridine-2-yliminomethyl)-phenol ligand

A tetranuclear Cu(II) complex [Cu4L4(H2O)4](ClO4)4 has been synthesized using the terdentate Schiff base 2-(pyridine-2-yliminomethyl)-phenol (HL) (the condensation product of salicylaldehyde and 2-aminopyridine) and copper perchlorate. Chemical characterizations such as IR and UV/Vis of the complex have been carried out. A single-crystal diffraction study shows that the complex contains a nearly planar tetranuclear core containing four copper atoms, which occupy four equivalent five-coordinate sites with a square pyramidal environment. Magnetic measurements have been carried out over the temperature range 2–300K and with 100Oe field strengths. Analysis of magnetic susceptibility data indicates a strong antiferromagnetic (J1=−638cm−1) exchange interaction between diphenoxo-bridged Cu(II) centers and a moderate antiferromagnetic (J2=−34cm−1) interaction between N–C–N bridged Cu(II) centers. Magnetic exchange interactions (J’s) are also discussed on the basis of a computational study using DFT methodology. The spin density distribution (singlet ground state) is calculated to visualize the effect of delocalization of spin density through bridging groups.