Neural coding in the visual system of Drosophila melanogaster: how do small neural populations support visually guided behaviours?

All organisms wishing to survive and reproduce must be able to respond adaptively to a complex, changing world. Yet the computational power available is constrained by biology and evolution, favouring mechanisms that are parsimonious yet robust. Here we investigate the information carried in small populations of visually responsive neurons in Drosophila melanogaster. These so-called ‘ring neurons’, projecting to the ellipsoid body of the central complex, are reported to be necessary for complex visual tasks such as pattern recognition and visual navigation. Recently the receptive fields of these neurons have been mapped, allowing us to investigate how well they can support such behaviours. For instance, in a simulation of classic pattern discrimination experiments, we show that the pattern of output from the ring neurons matches observed fly behaviour. However, performance of the neurons (as with flies) is not perfect and can be easily improved with the addition of extra neurons, suggesting the neurons’ receptive fields are not optimised for recognising abstract shapes, a conclusion which casts doubt on cognitive explanations of fly behaviour in pattern recognition assays. Using artificial neural networks, we then assess how easy it is to decode more general information about stimulus shape from the ring neuron population codes. We show that these neurons are well suited for encoding information about size, position and orientation, which are more relevant behavioural parameters for a fly than abstract pattern properties. This leads us to suggest that in order to understand the properties of neural systems, one must consider how perceptual circuits put information at the service of behaviour

Radiative Corrections to W and Quark Propagators in the Resonance Region

We discuss radiative corrections to W and quark propagators in the resonance region, |s-M^2| \lsim M*Gamma. We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to [M*Gamma/(s-M^2)]^n, (n=1,2...), i.e. to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the Pinch Technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the Z case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.Comment: 19 pages, 7 figures, LaTeX (uses epsfig). Slight rewording of the abstract and one of the sentences of the text. Minor misprints corrected. To appear in Phys. Rev.

Insect-inspired visual navigation on-board an autonomous robot: real-world routes encoded in a single layer network

Insect-Inspired models of visual navigation, that operate by scanning for familiar views of the world, have been shown to be capable of robust route navigation in simulation. These familiarity-based navigation algorithms operate by training an artificial neural network (ANN) with views from a training route, so that it can then output a familiarity score for any new view. In this paper we show that such an algorithm – with all computation performed on a small low-power robot – is capable of delivering reliable direction information along real-world outdoor routes, even when scenes contain few local landmarks and have high-levels of noise (from variable lighting and terrain). Indeed, routes can be precisely recapitulated and we show that the required computation and storage does not increase with the number of training views. Thus the ANN provides a compact representation of the knowledge needed to traverse a route. In fact, rather than losing information, there are instances where the use of an ANN ameliorates the problems of sub optimal paths caused by tortuous training routes. Our results suggest the feasibility of familiarity-based navigation for long-range autonomous visual homing

Sleep and the heart: interoceptive differences linked to poor experiential sleep quality in anxiety and depression

Interoception is the sense through which internal bodily changes are signalled and perceived. Individual differences in interoception are linked to emotional style and vulnerability to affective disorders. Here we test how experiential sleep quality relates to dimensions of interoceptive ability. 180 adults (42 ‘non-clinical’ individuals, 138 patients accessing mental health services) rated their quality of sleep before performing tests of cardiac interoception. Poor sleep quality was associated with lower measures of interoceptive performance accuracy, and higher self-report measures of interoceptive sensibility in individuals with diagnoses of depression and/or anxiety. Additionally, poor sleep quality was associated with impaired metacognitive interoceptive awareness in patients with diagnoses of depression (alone or with anxiety). Thus, poor sleep quality, a common early expression of psychological disorder, impacts cardiac interoceptive ability and experience across diagnoses. Sleep disruption can contribute to the expression of affective psychopathology through effects on perceptual and interpretative dimensions of bodily awareness

The gauge invariant effective potential: equilibrium and non-equilibrium aspects

We propose a gauge invariant formulation of the effective potential in terms of a gauge invariant order parameter, for the Abelian Higgs model. The one-loop contribution at zero and finite temperature is computed explicitly, and the leading terms in the high temperature expansion are obtained. The result is contrasted to the effective potential obtained in several covariant gauge-fixing schemes, and the gauge invariant quantities that can be reliably extracted from these are identified. It is pointed out that the gauge invariant effective potential in the one-loop approximation is complex for {\em all values} of the order parameter between the maximum and the minimum of the tree level potential, both at zero and non-zero temperature. The imaginary part is related to long-wavelength instabilities towards phase separation. We study the real-time dynamics of initial states in the spinodal region, and relate the imaginary part of the effective potential to the growth rate of equal-time gauge invariant correlation functions in these states. We conjecture that the spinodal instabilities may play a role in non-equilibrium processes {\em inside} the nucleating bubbles if the transition is first order.Comment: 27 pages revtex 3.0, no figures; one reference adde

Asymptotic properties of Born-improved amplitudes with gauge bosons in the final state

For processes with gauge bosons in the final state we show how to continuously connect with a single Born-improved amplitude the resonant region, where resummation effects are important, with the asymptotic region far away from the resonance, where the amplitude must reduce to its tree-level form. While doing so all known field-theoretical constraints are respected, most notably gauge-invariance, unitarity and the equivalence theorem. The calculations presented are based on the process $f\bar{f}\to ZZ$, mediated by a possibly resonant Higgs boson; this process captures all the essential features, and can serve as a prototype for a variety of similar calculations. By virtue of massive cancellations the resulting closed expressions for the differential and total cross-sections are particularly compact.Comment: 23 pages, Latex, 4 Figures, uses axodra

The pinch technique at two-loops: The case of mass-less Yang-Mills theories

The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quite interestingly, the well-known one-loop correspondence between the pinch technique and the background field method in the Feynman gauge persists also at two-loops. The renormalization is discussed in detail, and is shown to respect the aforementioned correspondence. Second, we present an absorptive derivation, exploiting the unitarity of the $S$-matrix and the underlying BRS symmetry; at this stage we deal only with tree-level and one-loop physical amplitudes. The gauge-invariant sub-amplitudes defined by means of this absorptive construction correspond precisely to the imaginary parts of the $n$-point functions defined in the full two-loop derivation, thus furnishing a highly non-trivial self-consistency check for the entire method. Various future applications are briefly discussed.Comment: 29 pages, uses Revtex, 22 Figures in a separate ps fil

Gauge Invariant Higgs mass bounds from the Physical Effective Potential

We study a simplified version of the Standard Electroweak Model and introduce the concept of the physical gauge invariant effective potential in terms of matrix elements of the Hamiltonian in physical states. This procedure allows an unambiguous identification of the symmetry breaking order parameter and the resulting effective potential as the energy in a constrained state. We explicitly compute the physical effective potential at one loop order and improve it using the RG. This construction allows us to extract a reliable, gauge invariant bound on the Higgs mass by unambiguously obtaining the scale at which new physics should emerge to preclude vacuum instability. Comparison is made with popular gauge fixing procedures and an ``error'' estimate is provided between the Landau gauge fixed and the gauge invariant results.Comment: 23 pages, 2 figures, REVTE

A multiloop improvement of non-singlet QCD evolution equations

An approach is elaborated for calculation of "all loop" contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the "nonforward" ER-BL equation from these diagrams that dominate for a large value of $b_0$, the first $\beta$-function coefficient. Calculations are performed in the covariant $\xi$-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter $\xi=-3$ generalizes the standard "naive nonabelianization" approximation. The solutions are obtained to the ER-BL evolution equation (taken at the "all loop" improved kernel), which are in form similar to one-loop solutions. A consequence for QCD descriptions of hard processes and the benefits and incompleteness of the approach are briefly discussed.Comment: 13 pages, revtex, 2 figures are enclosed as eps-file, the text style and figures are corrected following version, accepted for publication to Phys. Rev.