The TAP approach to intensive and extensive connectivity systems

The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.

Contrast integration over area is extensive: a three-stage model of spatial summation

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1–16 c/deg) and raised plaid modulator frequencies (0.25–32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (~4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

Nonlinear non-extensive approach for identification of structured information

The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant subspaces are well separated the problem is readily solvable by a linear technique. Otherwise, the linear approach fails to correctly discriminate the required information. Hence, a non-extensive approach is proposed. The resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one.

Spatially extensive summation of contrast-energy is revealed by contrast detection of micro-pattern textures

Vision must analyze the retinal image over both small and large areas to represent fine-scale spatial details and extensive textures. The long-range neuronal convergence that this implies might lead us to expect that contrast sensitivity should improve markedly with the contrast area of the image. But this is at odds with the orthodox view that contrast sensitivity is determined merely by probability summation over local independent detectors. To address this puzzle, I aimed to assess the summation of luminance contrast without the confounding influence of area-dependent internal noise. I measured contrast detection thresholds for novel Battenberg stimuli that had identical overall dimensions (to clamp the aggregation of noise) but were constructed from either dense or sparse arrays of micro-patterns. The results unveiled a three-stage visual hierarchy of contrast summation involving (i) spatial filtering, (ii) long-range summation of coherent textures, and (iii) pooling across orthogonal textures. Linear summation over local energy detectors was spatially extensive (as much as 16 cycles) at Stage 2, but the resulting model is also consistent with earlier classical results of contrast summation (J. G. Robson & N. Graham, 1981), where co-aggregation of internal noise has obscured these long-range interactions.

An extensive laboratory investigation of the use of bio-oil modified bitumen in road construction

Several roads in Iceland with bio-oil modified surface dressings exhibited severe distresses such as bleeding, binder drain down, and eventually as surface dressing sticking to tires. Samples from six road sections were evaluated in the laboratory to determine the causes of the failure. Binders with and without bio-oil, rapeseed oil and fish oil, were evaluated through a comprehensive rheological and chemical characterization. Both oils, exhibited solubility issues with the bitumen; consequently, the oils covered the aggregates, preventing bonding between binder and stones. It appears that fish oil worked a little better than rapeseed oil for binder modification.

Overweight status is associated with extensive signs of microvascular dysfunction and cardiovascular risk

The aim of this present study was to investigate if overweight individuals exhibit signs of vascular dysfunction associated with a high risk for cardiovascular disease (CVD). One hundred lean and 100 overweight participants were recruited for the present study. Retinal microvascular function was assessed using the Dynamic Retinal Vessel Analyser (DVA), and systemic macrovascular function by means of flow-mediated dilation (FMD). Investigations also included body composition, carotid intimal-media thickness (c-IMT), ambulatory blood pressure monitoring (BP), fasting plasma glucose, triglycerides (TG), cholesterol levels (HDL-C and LDL-C), and plasma von Willebrand factor (vWF). Overweight individuals presented with higher right and left c-IMT (p = 0.005 and p = 0.002, respectively), average 24-h BP values (all p <0.001), plasma glucose (p = 0.008), TG (p = 0.003), TG: HDL-C ratio (p = 0.010), and vWF levels (p = 0.004). Moreover, overweight individuals showed lower retinal arterial microvascular dilation (p = 0.039) and baseline-corrected flicker (bFR) responses (p = 0.022), as well as, prolonged dilation reaction time (RT, p = 0.047). These observations emphasise the importance of vascular screening and consideration of preventive interventions to decrease vascular risk in all individuals with adiposity above normal range.