Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Self-assembly of PEGylated peptide conjugates containing a modified amyloid β-peptide fragment

The self-assembly of PEGylated peptides containing a modified sequence from the amyloid beta peptide, FEK LVFF, has been studied in aqueous solution. PEG molar masses PEG1k, PEG2k, and PEG10k were used in the conjugates. It is shown that the three FFK LVFF-PEG hybrids form fibrils comprising a FFKLVFF core and a PEG corona. The beta-sheet secondary structure of the peptide is retained in the FFK LVFF fibril core. At sufficiently high concentrations, FEK LVFF-PEG1k and FEK LVFF-PEG2k form a nema tic phase, while PEG10k-FEK LVFF exhibits a hexagonal columnar phase. Simultaneous small angle neutron scattering/shear flow experiments were performed to study the shear flow alignment of the nematic and hexagonal liquid crystal phases. On drying, PEG crystallization occurs without disruption of the FFK LVFF beta-sheet structure leading to characteristic peaks in the X-ray diffraction pattern and FTIR spectra. The stability of beta-sheet structures was also studied in blends of FFKLVFF-PEG conjugates with poly(acrylic acid) (PAA). While PEG crystallization is only observed up to 25% PAA content in the blends, the FFK LVFF beta-sheet structure is retained up to 75% PAA.

Polymer − surfactant vesicular complexes in aqueous medium

The introduction of ionic single-tailed surfactants to aqueous solutions of EO18BO10 [EO = poly(ethylene oxide), BO = poly(1,2-butylene oxide), subscripts denote the number of repeating units] leads to the formation of vesicles, as probed by laser scanning confocal microscopy. Dynamic light scattering showed that the dimensions of these aggregates at early stages of development do not depend on the sign of the surfactant head group charge. Small-angle X-ray scattering (SAXS) analysis indicated the coexistence of smaller micelles of different sizes and varying polymer content in solution. In strong contrast to the dramatic increase of size of dispersed particles induced by surfactants in dilute solution, the d-spacing of corresponding mesophases reduces monotonically upon increasing surfactant loading. This effect points to the suppression of vesicles as a consequence of increasing ionic strength in concentrated solutions. Maximum enhancements of storage modulus and thermal stability of hybrid gels take place at different compositions, indicating a delicate balance between the number and size of polymer-poor aggregates (population increases with surfactant loading) and the number and size of polymer−surfactant complexes (number and size decrease in high surfactant concentrations).

Small-angle x-ray scattering study of flow alignment of a thermotropic liquid crystal in the nematic and smectic phases

WThe capillary flow alignment of the thermotropic liquid crystal 4-n-octyl-4′-cyanobiphenyl in the nematic and smectic phases is investigated using time-resolved synchrotron small-angle x-ray scattering. Samples were cooled from the isotropic phase to erase prior orientation. Upon cooling through the nematic phase under Poiseuille flow in a circular capillary, a transition from the alignment of mesogens along the flow direction to the alignment of layers along the flow direction (mesogens perpendicular to flow) appears to occur continuously at the cooling rate applied. The transition is centered on a temperature at which the Leslie viscosity coefficient α3 changes sign. The configuration with layers aligned along the flow direction is also observed in the smectic phase. The transition in the nematic phase on cooling has previously been ascribed to an aligning-nonaligning or tumbling transition. At high flow rates there is evidence for tumbling around an average alignment of layers along the flow direction. At lower flow rates this orientation is more clearly defined. The layer alignment is ascribed to surface-induced ordering propagating into the bulk of the capillary, an observation supported by the parallel alignment of layers observed for a static sample at low temperatures in the nematic phase.

Physical interpretation of the correlation between multi-angle spectral data and canopy height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally.

Comparison of algal and fish sources on the oxidative stability of poultry meat and its enrichment with omega-3 polyunsaturated fatty acids

Human consumption of long-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) is below recommendations, and enriching chicken meat (by incorporating LC n-3 PUFA into broiler diets) is a viable means of increasing consumption. Fish oil is the most common LC n-3 PUFA supplement used but is unsustainable and reduces the oxidative stability of the meat. The objective of this experiment was to compare fresh fish oil (FFO) with fish oil encapsulated (EFO) in a gelatin matrix (to maintain its oxidative stability) and algal biomass at a low (LAG, 11), medium (MAG, 22), or high (HAG, 33 g/kg of diet) level of inclusion. The C22:6n-3 contents of the FFO, EFO, and MAG diets were equal. A control (CON) diet using blended vegetable oil was also made. As-hatched 1-d-old Ross 308 broilers (144) were reared (21 d) on a common starter diet then allocated to treatment pens (4 pens per treatment, 6 birds per pen) and fed treatment diets for 21 d before being slaughtered. Breast and leg meat was analyzed (per pen) for fatty acids, and cooked samples (2 pens per treatment) were analyzed for volatile aldehydes. Concentrations (mg/100 g of meat) of C20:5n-3, C22:5n-3, and C22:6n-3 were (respectively) CON: 4, 15, 24; FFO: 31, 46, 129; EFO: 18, 27, 122; LAG: 9, 19, 111; MAG: 6, 16, 147; and HAG: 9, 14, 187 (SEM: 2.4, 3.6, 13.1) in breast meat and CON: 4, 12, 9; FFO: 58, 56, 132; EFO: 63, 49, 153; LAG: 13, 14, 101; MAG: 11, 15, 102; HAG: 37, 37, 203 (SEM: 7.8, 6.7, 14.4) in leg meat. Cooked EFO and HAG leg meat was more oxidized (5.2 mg of hexanal/kg of meat) than the other meats (mean 2.2 mg/kg, SEM 0.63). It is concluded that algal biomass is as effective as fish oil at enriching broiler diets with C22:6 LC n-3 PUFA, and at equal C22:6n-3 contents, there is no significant difference between these 2 supplements on the oxidative stability of the meat that is produced.

Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Modelling small angle neutron scattering data from electrospun fibres

Electrospinning is a technique employed to produce nanoscale to microscale sized fibres by the application of a high voltage to a spinneret containing a polymer solution. Here we examine how small angle neutron scattering data can be modelled to analyse the polymer chain conformation. We prepared 1:1 blends of deuterated and hydrogenated atactic-polystyrene fibres from solutions in N, N-Dimethylformamide and Methyl Ethyl Ketone. The fibres themselves often contain pores or voiding within the internal structure on the length scales that can interfere with scattering experiments. A model to fit the scattering data in order to obtain values for the radius of gyration of the polymer molecules within the fibres has been developed, that includes in the scattering from the voids. Using this model we find that the radius of gyration is 20% larger than in the bulk state and the chains are slightly extended parallel to the fibre axis.