Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Filter for Car Tracking Based on Acceleration and Steering Angle

The motion of a car is described using a stochastic model in which the driving processes are the steering angle and the tangential acceleration. The model incorporates exactly the kinematic constraint that the wheels do not slip sideways. Two filters based on this model have been implemented, namely the standard EKF, and a new filter (the CUF) in which the expectation and the covariance of the system state are propagated accurately. Experiments show that i) the CUF is better than the EKF at predicting future positions of the car; and ii) the filter outputs can be used to control the measurement process, leading to improved ability to recover from errors in predictive tracking.

Current deflection at cracks: some insights from modelling

Eddy current testing by current deflection detects surface cracks and geometric features by sensing the re-routing of currents. Currents are diverted by cracks in two ways: down the walls, and along their length at the surface. Current deflection utilises the latter currents, detecting them via their tangential magnetic field. Results from 3-D finite element computer modelling, which show the two forms of deflection, are presented. Further results indicate that the current deflection technique is suitable for the detection of surface cracks in smooth materials with varying material properties.

A further study of the recovery and purification of surfactin from fermentation broth by membrane filtration

Surfactin is a bacterial lipopeptide produced by Bacillus subtilis and is a powerful surfactant, having also antiviral, antibacterial and antitumor properties. The recovery and purification of surfactin from complex fermentation broths is a major obstacle to its commercialization; therefore, a two-step membrane filtration process was developed using a lab scale tangential flow filtration (TFF) unit with 10 kDa MWCO regenerated cellulose (RC) and polyethersulfone (PES)membranes at three different transmembrane pressure (TMP) of 1.5 bar, 2.0 bar and 2.5 bar. Two modes of filtrations were studied, with and without cleaning of membranes prior to UF-2. In a first step of ultrafiltration (UF-1), surfactin was retained effectively by membranes at above its critical micelle concentration (CMC); subsequently in UF-2, the retentate micelles were disrupted by addition of 50% (v/v) methanol solution to allow recovery of surfactin in the permeate. Main protein contaminants were effectively retained by the membrane in UF-2. Flux of permeates, rejection coefficient (R) of surfactin and proteinwere measured during the filtrations. Overall the three different TMPs applied have no significant effect in the filtrations and PES is the more suitable membrane to selectively separate surfactin from fermentation broth, achieving high recovery and level of purity. In addition this two-step UF process is scalable for larger volume of samples without affecting the original functionality of surfactin, although membranes permeability can be affected due to exposure to methanolic solution used in UF-2.

Slicing of soft, flexible solids with industrial applications

Thin slices of soft flexible solids have negligible bending resistance and hence store negligible elastic strain energy; furthermore such offcuts are rarely permanently deformed after slicing. Cutting forces thus depend only on work of separation (toughness work) and friction. These simplifying assumptions are not as restrictive as it might seem, and the mechanics are found to apply to a wide variety of foodstuffs and biological materials. The fracture toughness of such materials may be determined from cutting experiments: the use of scissors instrumented for load and displacement is a popular method where toughness is obtained from the work areas beneath load–displacement plots. Surprisingly, there is no analysis for the variation of forces with scissor blade opening and this paper provides the theory. Comparison is made with experimental results in cutting with scissors. The analysis is generalised to cutting with blades of variable curvature and applied to a commercial food cutting device having a rotating spiral plan form blade. The strong influence of the ‘slice/push ratio’ (blade tangential speed to blade edge normal speed) on the cutting forces is revealed. Small cutting forces are important in food cutting machinery as damage to slices is minimised. How high slice/push ratios may be achieved by choice of blade profile is discussed.

Stress generation in the tension wood of poplar is based on the lateral swelling power of the G-layer

The mechanism of active stress generation in tension wood is still not fully understood. To characterize the functional interdependency between the G-layer and the secondary cell wall, nanostructural characterization and mechanical tests were performed on native tension wood tissues of poplar (Populus nigra x Populus deltoids) and on tissues in which the G-layer was removed by an enzymatic treatment. In addition to the well-known axial orientation of the cellulose fibrils in the G-layer, it was shown that the microfibril angle of the S2-layer was very large (about 36 degrees). The removal of the G-layer resulted in an axial extension and a tangential contraction of the tissues. The tensile stress-strain curves of native tension wood slices showed a jagged appearance after yield that could not be seen in the enzyme-treated samples. The behaviour of the native tissue was modelled by assuming that cells deform elastically up to a critical strain at which the G-layer slips, causing a drop in stress. The results suggest that tensile stresses in poplar are generated in the living plant by a lateral swelling of the G-layer which forces the surrounding secondary cell wall to contract in the axial direction.

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re-U), axial flow Reynolds number (Re-W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers. (c) 2006 Elsevier Ltd. All rights reserved.

Synthesis of isomaltooligosaccharides and oligodextrans in a recycle membrane bioreactor by the combined use of dextransucrase and dextranase

A recycle ultrafiltration membrane reactor was used to develop a continuous synthesis process for the production of isomaltooligosaccharides (IMO) from sucrose, using the enzymes dextransucrase and dextranase. A variety of membranes were tested and the parameters affecting reactor stability, productivity, and product molecular weight distribution were investigated. Enzyme inactivation in the reactor was reduced with the use of a non-ionic surfactant but its use had severe adverse effects on the membrane pore size and porosity. During continuous isomaltooligosaccharide synthesis, dextransucrase inactivation was shown to occur as a result of the dextranase activity and it was dependent mainly on the substrate availability in the reactor and the hydrolytic activity of dextranase. Substrate and dextranase concentrations (50-200 mg/mL(-1) and 10-30 U/mL(-1), respectively) affected permeate fluxes, reactor productivity, and product average molecular weight. The oligodextrans and isomaltooligosaccharides formed had molecular weights lower than in batch synthesis reactions but they largely consisted of oligosaccharides with a degree of polymerization (DP) greater than 5, depending on the synthesis conditions. No significant rejection of the sugars formed was shown by the membranes and permeate flux was dependent on tangential flow velocity. (C) 2004 Wiley Periodicals, Inc.

The role of schizotypy and creativity in a group problem-solving task

The well-studied link between psychotic traits and creativity is a subject of much debate. The present study investigated the extent to which schizotypic personality traits - as measured by O-LIFE (Oxford-Liverpool Inventory of Feelings and Experiences) - equip healthy individuals to engage as groups in everyday tasks. From a sample of 69 students, eight groups of four participants - comprised of high, medium, or low-schizotypy individuals - were assembled to work as a team to complete a creative problem-solving task. Predictably, high scorers on the O-LIFE formulated a greater number of strategies to solve the task, indicative of creative divergent thinking. However, for task success (as measured by time taken to complete the problem) an inverted U shaped pattern emerged, whereby high and low-schizotypy groups were consistently faster than medium schizotypy groups. Intriguing data emerged concerning leadership within the groups, and other tangential findings relating to anxiety, competition and motivation were explored. These findings challenge the traditional cliche that psychotic personality traits are linearly related to creative performance, and suggest that the nature of the problem determines which thinking styles are optimally equipped to solve it. (C) 2009 Elsevier Ltd. All rights reserved.

Liquid flow over a substrate structured by seeded nanoparticles

Recent experiments have demonstrated that nanoparticles which sparsely distributed over a solid substrate can substantially change the flow conditions at the solid surface in the presence of slip. Inspired by these observations, the flow past tiny particles seeded on a solid substrate is investigated theoretically in the framework of an interface formation model. It has been shown, that even a single seeded nanoparticle can reduce significantly the measurable tangential component of hydrodynamic velocity at the substrate and affect the amount of the observed apparent slippage of the liquid. The effect from the particle manifests in a form of a long relaxation tail defined by the characteristic time of the interface formation process. A comparison with experiments has demonstrated a good agreement between theoretically predicted and experimentally observed values of the relaxation tail length scale.

Chain extension in electrospun polystyrene fibres: a SANS study

Small angle neutron scattering techniques were used to quantify the size and shape of the chain conformation in electrospun fibres of atactic polystyrene prepared from solutions in methyl ethyl ketone. Aligned arrays of fibres were collected onto a rotating collector with tangential velocity varying between 0 ms-1 and approximately 15 ms-1. The measured radii of gyration of the polystyrene chains were found to be slightly higher than that expected for samples prepared from solutions in the concentrated regime. The ratio of the radius of gyration parallel and perpendicular to the chain axis was found to be approximately 1.05 in contrast to the substantial macroscopic shape transformation intrinsic to electrospinning. When the tangential velocity of the rotating collector was greater than the flight velocity of the fibres (ca. 4 ms-1), a further extension of the polymer chains was observed with a ratio of the radii of gyration increasing to 1.20 at the highest collector speeds. It is proposed that the heterogeneous processes involved, particularly solvent evaporation and the formation of a polymer skin during electrospinning play a significant role in determining the level of molecular anisotropy in the fibres.

Production of angiotensin converting enzyme inhibitory peptides from β-lactoglobulin and casein derived peptides: an integrative approach

Angiotensin I-converting enzyme (ACE) inhibition is one of the mechanisms by which reduction in blood pressure is exerted. Whey proteins are a rich source of ACE inhibitory peptides and have shown a blood pressure reduction effect i.e. antihypertensive activity. The aim of this work was to develop a simplified process using a combination of adsorption and microfiltration steps for the production of hydrolysates from whey with high ACE inhibitory activity and potency; the latter was measured as the IC50, which is the peptide concentration required to reduce ACE activity by half. This process integrates the selective separation of β-lactoglobulin and casein derived peptides (CDP) from rennet whey and their hydrolysis, which results in partially pure, less complex hydrolysates with high bioactive potency. Hydrolysis was carried out with protease N ‘Amano’ in a thermostatically controlled membrane reactor operated in a batch mode. By applying the integrative approach it was possible to produce from the same feedstock two different hydrolysates that exhibited high ACE inhibition. One hydrolysate was mainly composed of casein-derived peptides with IC50= 285 μg/mL. In this hydrolysate we identified the well known potent ACE-I and anti-hypertensive tri-peptide Ile-Pro-Pro (IPP) and another novel octa-peptide Gln-Asp-Lys-Thr-Glu-Ile-Pro-Thr (QDKTEIPT). The second hydrolysate was mainly composed of β-lactoglobulin derived peptides with IC50=128 µg/mL. This hydrolysate contained a tetra-peptide (Ile-Ile-Ala-Glu) IIAE as one of the two major peptides. A further advantage to this process is that enzyme activity was substantially increased as enzyme product inhibition was reduced.

Chemical characterisation and determination of sensory attributes of hydrolysates produced by enzymatic hydrolysis of whey proteins following a novel integrative process

The overall aim of this work was to characterize the major angiotensin converting enzyme (ACE) inhibitory peptides produced by enzymatic hydrolysis of whey proteins, through the application of a novel integrative process. This process consisted of the combination of adsorption and microfiltration within a stirred cell unit for the selective immobilization of β-lactoglobulin and casein derived peptides (CDP) from whey. The adsorbed proteins were hydrolyzed in-situ which resulted in the separation of peptide products from the substrate and fractionation of peptides. Two different hydrolysates were produced: (i) from CDP (IC50 =287μg/mL) and (ii) from β-lactoglobulin (IC50=128μg/mL). IC50 is the concentration of inhibitor needed to inhibit ACE by half. The well known antihypertensive peptide IPP and several novel peptides that have structural similarities with reported ACE inhibitory peptides were identified and characterized in both hydrolysates. Furthermore, the hydrolysates were assessed for bitterness. No significant difference was found between the control (milk with no hydrolysate) and hydrolysate samples at different concentrations (at, below and above the IC50).

Turbulence dynamics near a turbulent/non-turbulent interface

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (epsilon), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), epsilon decays as z^{-6}, where z is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and epsilon display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness delta of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that delta ~ eta (where eta is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

Dissipation of shear-free turbulence near boundaries

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.