Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including correlated attractors was reported in the cases of finite and infinite loading. In this paper, by means of a statistical mechanical method, we study the statics and dynamics of the model in both finite and extensive loading, mainly focusing on the retrieval properties of the Hopfield and correlated attractors. In the extensive loading case, we derive the evolution equations by the dynamical replica theory. We found several characteristic temporal behaviours, both in the finite and extensive loading cases. The theoretical results were confirmed by numerical simulations.Comment: 12 pages, 7 figure

A longitudinal study of accommodative changes in biometry during incipient presbyopia

PURPOSE: To profile accommodative biometric changes longitudinally and to determine the influence of age-related ocular structural changes on the accommodative response prior to the onset of presbyopia. METHODS: Twenty participants (aged 34-41 years) were reviewed at six-monthly intervals over two and a half years. At each visit, ocular biometry was measured with the LenStar biometer (www.Haag-Streit.com) in response to 0.00, 3.00 and 4.50 D stimuli. Accommodative responses were measured by the WAM 5500 Auto Ref/Keratometer (www.grandseiko.com). RESULTS: During accommodation, anterior chamber depth reduced (F = 29, p < 0.001), whereas crystalline lens thickness (F = 39, p < 0.001) and axial length (F = 5.4, p = 0.009) increased. The accommodative response (F = 5.5, p = 0.001) and the change in anterior chamber depth (F = 3.1, p = 0.039), crystalline lens thickness (F = 3.0, p = 0.042) and axial length (F = 2.5, p = 0.038) in response to the 4.50 D accommodative target reduced after 2.5 years. However, the change in anterior chamber depth (F = 2.2, p = 0.097), crystalline lens thickness (F = 1.7, p = 0.18) and axial length (F = 1.0, p = 0.40) per dioptre of accommodation exerted remained invariant after 2.5 years. The increase in disaccommodated crystalline lens thickness with age was not significantly associated with the reduction in accommodative response (R = 0.32, p = 0.17). CONCLUSION: Despite significant age-related structural changes in disaccommodated biometry, the change in biometry per dioptre of accommodation exerted remained invariant with age. The present study supports the Helmholtz theory of accommodation and suggests an increase in lenticular stiffness is primarily responsible for the onset of presbyopia

A program to analyse optical coherence tomography images of the ciliary muscle

Purpose: To describe and validate bespoke software designed to extract morphometric data from ciliary muscle Visante Anterior Segment Optical Coherence Tomography (AS-OCT) images. Method: Initially, to ensure the software was capable of appropriately applying tiered refractive index corrections and accurately measuring orthogonal and oblique parameters, 5 sets of custom-made rigid gas-permeable lenses aligned to simulate the sclera and ciliary muscle were imaged by the Visante AS-OCT and were analysed by the software. Human temporal ciliary muscle data from 50 participants extracted via the internal Visante AS-OCT caliper method and the software were compared. The repeatability of the software was also investigated by imaging the temporal ciliary muscle of 10 participants on 2 occasions. Results: The mean difference between the software and the absolute thickness measurements of the rigid gas-permeable lenses were not statistically significantly different from 0 (t = -1.458, p = 0.151). Good correspondence was observed between human ciliary muscle measurements obtained by the software and the internal Visante AS-OCT calipers (maximum thickness t = -0.864, p = 0.392, total length t = 0.860, p = 0.394). The software extracted highly repeatable ciliary muscle measurements (variability ≤6% of mean value). Conclusion: The bespoke software is capable of extracting accurate and repeatable ciliary muscle measurements and is suitable for analysing large data sets

Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilised by synaptic noise and well separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretica

Dynamical replica theoretic analysis of CDMA detection dynamics

We investigate the detection dynamics of the Gibbs sampler for code-division multiple access (CDMA) multiuser detection. Our approach is based upon dynamical replica theory which allows an analytic approximation to the dynamics. We use this tool to investigate the basins of attraction when phase coexistence occurs and examine its efficacy via comparison with Monte Carlo simulations.Comment: 18 pages, 2 figure

Finite Size Effects in Separable Recurrent Neural Networks

We perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics, away from saturation. We find two types of finite size effects: thermal fluctuations, and disorder-induced `frozen' corrections to the mean-field laws. The finite size effects are described by equations that correspond to a time-dependent Ornstein-Uhlenbeck process. We show how the theory can be used to understand and quantify various finite size phenomena in recurrent neural networks, with and without detailed balance.Comment: 24 pages LaTex, with 4 postscript figures include

Does rebound tonometry probe misalignment modify intraocular pressure measurements in human eyes?

Purpose. To examine the influence of positional misalignments on intraocular pressure (IOP) measurement with a rebound tonometer. Methods. Using the iCare rebound tonometer, IOP readings were taken from the right eye of 36 healthy subjects at the central corneal apex (CC) and compared to IOP measures using the Goldmann applanation tonometer (GAT). Using a bespoke rig, iCare IOP readings were also taken 2 mm laterally from CC, both nasally and temporally, along with angular deviations of 5 and 10 degrees, both nasally and temporally to the visual axis. Results. Mean IOP ± SD, as measured by GAT, was 14.7±2.5 mmHg versus iCare tonometer readings of 17.4±3.6 mmHg at CC, representing an iCare IOP overestimation of 2.7±2.8 mmHg (P<0.001), which increased at higher average IOPs. IOP at CC using the iCare tonometer was not significantly different to values at lateral displacements. IOP was marginally underestimated with angular deviation of the probe but only reaching significance at 10 degrees nasally. Conclusions. As shown previously, the iCare tonometer overestimates IOP compared to GAT. However, IOP measurement in normal, healthy subjects using the iCare rebound tonometer appears insensitive to misalignments. An IOP underestimation of <1 mmHg with the probe deviated 10 degrees nasally reached statistical but not clinical significance levels. © 2013 Ian G. Beasley et al

Order-Parameter Flow in the SK Spin-Glass II: Inclusion of Microscopic Memory Effects

We develop further a recent dynamical replica theory to describe the dynamics of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution equations for macroscopic order parameters. We show how microscopic memory effects can be included in the formalism through the introduction of a dynamic order parameter function: the joint spin-field distribution. The resulting formalism describes very accurately the relaxation phenomena observed in numerical simulations, including the typical overall slowing down of the flow that was missed by the previous simple two-parameter theory. The advanced dynamical replica theory is either exact or a very good approximation.Comment: same as original, but this one is TeXabl

Development of fluorescent peptide G protein-coupled receptor activation biosensors for NanoBRET characterization of intracellular allosteric modulators

G protein-coupled receptors (GPCRs) are widely therapeutically targeted, and recent advances in allosteric modulator development at these receptors offer further potential for exploitation. Intracellular allosteric modulators (IAM) represent a class of ligands that bind to the receptor–effector interface (e.g., G protein) and inhibit agonist responses noncompetitively. This potentially offers greater selectivity between receptor subtypes compared to classical orthosteric ligands. However, while examples of IAM ligands are well described, a more general methodology for assessing compound interactions at the IAM site is lacking. Here, fluorescent labeled peptides based on the Gα peptide C terminus are developed as novel binding and activation biosensors for the GPCR-IAM site. In TR-FRET binding studies, unlabeled peptides derived from the Gαs subunit were first characterized for their ability to positively modulate agonist affinity at the β2-adrenoceptor. On this basis, a tetramethylrhodamine (TMR) labeled tracer was synthesized based on the 19 amino acid Gαs peptide (TMR-Gαs19cha18, where cha = cyclohexylalanine). Using NanoBRET technology to detect binding, TMR-Gαs19cha18 was recruited to Gs coupled β2-adrenoceptor and EP2 receptors in an agonist-dependent manner, but not the Gi-coupled CXCR2 receptor. Moreover, NanoBRET competition binding assays using TMR-Gαs19cha18 enabled direct assessment of the affinity of unlabeled ligands for β2-adrenoceptor IAM site. Thus, the NanoBRET platform using fluorescent-labeled G protein peptide mimetics offers novel potential for medium-throughput screens to identify IAMs, applicable across GPCRs coupled to a G protein class. Using the same platform, Gs peptide biosensors also represent useful tools to probe orthosteric agonist efficacy and the dynamics of receptor activation