A study of pattern recovery in recurrent correlation associative memories

In this paper, we analyze the recurrent correlation associative memory (RCAM) model of Chiueh and Goodman. This is an associative memory in which stored binary memory patterns are recalled via an iterative update rule. The update of the individual pattern-bits is controlled by an excitation function, which takes as its arguement the inner product between the stored memory patterns and the input patterns. Our contribution is to analyze the dynamics of pattern recall when the input patterns are corrupted by noise of a relatively unrestricted class. We make three contributions. First, we show how to identify the excitation function which maximizes the separation (the Fisher discriminant) between the uncorrupted realization of the noisy input pattern and the remaining patterns residing in the memory. Moreover, we show that the excitation function which gives maximum separation is exponential when the input bit-errors follow a binomial distribution. Our second contribution is to develop an expression for the expectation value of bit-error probability on the input pattern after one iteration. We show how to identify the excitation function which minimizes the bit-error probability. However, there is no closed-form solution and the excitation function must be recovered numerically. The relationship between the excitation functions which result from the two different approaches is examined for a binomial distribution of bit-errors. The final contribution is to develop a semiempirical approach to the modeling of the dynamics of the RCAM. This provides us with a numerical means of predicting the recall error rate of the memory. It also allows us to develop an expression for the storage capacity for a given recall error rate

Bayesian graph edit distance

This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

Best practice for collar deployment of tri-axial accelerometers on a terrestrial quadruped to provide accurate measurement of body acceleration

Background: Tri-axial accelerometers are frequently deployed on terrestrial quadrupedal mammals using collars, because they are easy to fit and are thought to have minimal impact on the subject. Collar-attached devices are not fixed to the body and can move independently of the body. This may result in inaccurate measures of acceleration, reducing the accuracy of measured body movement. We determined the effect of collar size and collar weight on acceleration measured by a collar-mounted accelerometer on a quadruped mammal. The aim was to suggest best practice for sizes and weights of collars on which to deploy tri-axial accelerometers. Using pygmy goats, Capra aegagrus hircus, which were trained to walk at different speeds (0.8–3.0 km/h) on a treadmill, we measured body acceleration using a collar-mounted tri-axial accelerometer, with different collar sizes (individual neck circumference + 1 cm to + 9 cm) and collar weight (0.4% to 1.2% of individual weight). Results: There was a significant effect of collar size, collar weight and walking speed on measured acceleration. Measured acceleration was less accurate and more variable when collars were looser and heavier. To measure body acceleration more accurately, we found that collar size should be within 5 cm or 16% of an individual’s neck circumference when it was heavy (up to 1.2% of animal’s body weight) or within 7 cm (33%) of neck circumference if the collar was light (up to 0.6% of animal body weight). Conclusion: We suggest that not only reporting collar size and weight for welfare purposes, but it is also important to consider these aspects for scientific rigour, to ensure data are collected as accurately as possible. We provide guidelines for researchers fitting collar-attached devices to ensure a higher degree of accuracy of recorded body acceleration

Calculation of the emission power distribution of microstructured OLEDs using the reciprocity theorem

S. Zhang, E.R. Martins, G.A. Turnbull and I.D.W. Samuel are grateful to the Scottish Universities Physics Alliance (SUPA) and the Engineering and Physical Sciences Research Council (EPSRC) for financial support.Integrating photonic microstructures into organic light-emitting diodes (OLEDs) has been a widely used strategy to improve their light out-coupling efficiency. However, there is still a need for optical modelling methods which quantitatively characterise the spatial emission pattern of microstructured OLEDs. In this paper, we demonstrate such rigorous calculation using the reciprocity theorem. The calculation of the emission intensity at each direction in the far field can be simplified into only two simple calculations of an incident plane wave propagating from the far field into a single cell of the periodic structure. The emission from microstructured OLED devices with three different grating periods was calculated as a test of the approach, and the calculated results were in good agreement with experiment. This optical modelling method is a useful calculation tool to investigate and control the spatial emission pattern of microstructured OLEDs.PostprintPeer reviewe

Investigation of the magnetic anisotropy in a series of trigonal bipyramidal Mn(II) complexes

Understanding how the magnetic anisotropy in simple coordination complexes can be manipulated is instrumental to the development of single-molecule magnets (SMMs). Clear strategies can then be designed to control both the axial and transverse contributions to the magnetic anisotropy in such compounds, and allow them to reach their full potential. Here we show a strategy for boosting the magnetic anisotropy in a series of trigonal bipyramidal Mn(II) complexes – [MnCl3(HDABCO)(DABCO)] (1), [MnCl3(MDABCO)2]·[ClO4] (2), and [MnCl3(H2O)(MDABCO)] (3). These have been successfully synthesised using the monodentate [DABCO] and [MDABCO]+ ligands. Through static (DC) magnetic measurements and detailed theoretical investigation using ab initio methods, the magnetic anisotropy of each system has been studied. The calculations reveal that the rhombic zero-field splitting (ZFS) term (E) can be tuned as the symmetry around the Mn(II) ion is changed. Furthermore, an in silico investigation reveals a strategy to increase the axial ZFS parameter (D) of trigonal bipyramidal Mn(II) by an order of magnitude

A large axial magnetic anisotropy in trigonal bipyramidal Fe(II)

The first trigonal bipyramidal Fe(II) complex to display slow relaxation of magnetisation has been isolated, with this behaviour found to arise through a combination of a large magnetic anisotropy (D = -27.5 cm-1) and a pseudo-D3h symmetry at the Fe(II) centre, as investigated through ab initio and magnetic studies

Dynamical model of sequential spatial memory: winnerless competition of patterns

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns.Comment: 4 pages, submitted to PR

Renormalization of the mass gap

The full gluon propagator relevant for the description of the truly non-perturbative QCD dynamics, the so-called intrinsically non-perturbative gluon propagator has been derived in our previous work. It explicitly depends on the regularized mass gap, which dominates its structure at small gluon momentum. It is automatically transversal in a gauge invariant way. It is characterized by the presence of severe infrared singularities at small gluon momentum, so the gluons remain massless, and this does not depend on the gauge choice. In this paper we have shown how precisely the renormalization program for the regularized mass gap should be performed. We have also shown how precisely severe infrared singularities should be correctly treated. This allowed to analytically formulate the exact and gauge-invariant criteria of gluon and quark confinement. After the renormalization program is completed, one can derive the gluon propagator applicable for the calculation of physical observables processes, etc., in low-energy QCD from first principles.Comment: 16 pages, no figures, no tables, some minor changes are introduce

Evolution of arboreality and fossoriality in squirrels and aplodontid rodents: Insights from the semicircular canals of fossil rodents

Reconstructing locomotor behaviour for fossil animals is typically done with postcranial elements. However, for species only known from cranial material, locomotor behaviour is difficult to reconstruct. The semicircular canals (SCCs) in the inner ear provide insight into an animal's locomotor agility. A relationship exists between the size of the SCCs relative to body mass and the jerkiness of an animal's locomotion. Additionally, studies have also demonstrated a relationship between SCC orthogonality and angular head velocity. Here, we employ two metrics for reconstructing locomotor agility, radius of curvature dimensions and SCC orthogonality, in a sample of twelve fossil rodents from the families Ischyromyidae, Sciuridae and Aplodontidae. The method utilizing radius of curvature dimensions provided a reconstruction of fossil rodent locomotor behaviour that is more consistent with previous studies assessing fossil rodent locomotor behaviour compared to the method based on SCC orthogonality. Previous work on ischyromyids suggests that this group displayed a variety of locomotor modes. Members of Paramyinae and Ischyromyinae have relatively smaller SCCs and are reconstructed to be relatively slower compared to members of Reithroparamyinae. Early members of the Sciuroidea clade including the sciurid Cedromus wilsoni and the aplodontid Prosciurus relictus are reconstructed to be more agile than ischyromyids, in the range of extant arboreal squirrels. This reconstruction supports previous inferences that arboreality was likely an ancestral trait for this group. Derived members of Sciuridae and Aplodontidae vary in agility scores. The fossil squirrel Protosciurus cf. rachelae is inferred from postcranial material as arboreal, which is in agreement with its high agility, in the range of extant arboreal squirrels. In contrast, the fossil aplodontid Mesogaulus paniensis has a relatively low agility score, similar to the fossorial Aplodontia rufa, the only living aplodontid rodent. This result is in agreement with its postcranial reconstruction as fossorial and with previous indications that early aplodontids were more arboreal than their burrowing descendants

Fermions in three-dimensional spinfoam quantum gravity

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER