Unique Translation between Hamiltonian Operators and Functional Integrals

A careful treatment of the discretization errors in the path integral formulation of quantum mechanics leads to a unique prescription for the translation from the Hamiltonian to the action in the functional integral. An example is given by an interaction quadratic in the occupation number, characteristic for manybody bosonic systems. As a result, the term linear in the occupation number (chemical potential) receives a correction as compared to the usual formulation based on coherent states. A perturbative calculation supports the relevance of this correction.Comment: 4 pages, 0 figures, RevTex, added reference

Sensitivity to image recurrence across eye-movement-like image transitions through local serial inhibition in the retina

Standard models of stimulus encoding in the retina postulate that image presentations activate neurons according to the increase of preferred contrast inside the receptive field. During natural vision, however, images do not arrive in isolation, but follow each other rapidly, separated by sudden gaze shifts. We here report that, contrary to standard models, specific ganglion cells in mouse retina are suppressed after a rapid image transition by changes in visual patterns across the transition, but respond with a distinct spike burst when the same pattern reappears. This sensitivity to image recurrence depends on opposing effects of glycinergic and GABAergic inhibition and can be explained by a circuit of local serial inhibition. Rapid image transitions thus trigger a mode of operation that differs from the processing of simpler stimuli and allows the retina to tag particular image parts or to detect transition types that lead to recurring stimulus patterns

Equation of State for Helium-4 from Microphysics

We compute the free energy of helium-4 near the lambda transition based on an exact renormalization-group equation. An approximate solution permits the determination of universal and nonuniversal thermodynamic properties starting from the microphysics of the two-particle interactions. The method does not suffer from infrared divergences. The critical chemical potential agrees with experiment. This supports a specific formulation of the functional integral that we have proposed recently. Our results for the equation of state reproduce the observed qualitative behavior. Despite certain quantitative shortcomings of our approximation, this demonstrates that ab initio calculations for collective phenomena become possible by modern renormalization-group methods.Comment: 9 pages, 6 figures, revtex updated version, journal referenc

A bio-inspired image coder with temporal scalability

We present a novel bio-inspired and dynamic coding scheme for static images. Our coder aims at reproducing the main steps of the visual stimulus processing in the mammalian retina taking into account its time behavior. The main novelty of this work is to show how to exploit the time behavior of the retina cells to ensure, in a simple way, scalability and bit allocation. To do so, our main source of inspiration will be the biologically plausible retina model called Virtual Retina. Following a similar structure, our model has two stages. The first stage is an image transform which is performed by the outer layers in the retina. Here it is modelled by filtering the image with a bank of difference of Gaussians with time-delays. The second stage is a time-dependent analog-to-digital conversion which is performed by the inner layers in the retina. Thanks to its conception, our coder enables scalability and bit allocation across time. Also, our decoded images do not show annoying artefacts such as ringing and block effects. As a whole, this article shows how to capture the main properties of a biological system, here the retina, in order to design a new efficient coder.Comment: 12 pages; Advanced Concepts for Intelligent Vision Systems (ACIVS 2011

Loss of Neuroligin3 specifically downregulates retinal GABAAα2 receptors without abolishing direction selectivity.

The postsynaptic adhesion proteins Neuroligins (NLs) are essential for proper synapse function, and their alterations are associated with a variety of neurodevelopmental disorders. It is increasingly clear that each NL isoform occupies specific subsets of synapses and is able to regulate the function of discrete networks. Studies of NL2 and NL4 in the retina in particular have contributed towards uncovering their role in inhibitory synapse function. In this study we show that NL3 is also predominantly expressed at inhibitory postsynapses in the retinal inner plexiform layer (IPL), where it colocalizes with both GABAA- and glycinergic receptor clusters in a 3:2 ratio. In the NL3 deletion-mutant (knockout or KO) mouse, we uncovered a dramatic reduction of the number of GABAAα2-subunit containing GABAA receptor clusters at the IPL. Retinal activity was thereafter assessed in KO and wild-type (WT) littermates by multi-electrode-array recordings of the output cells of retina, the retinal ganglion cells (RGCs). RGCs in the NL3 KO showed reduced spontaneous activity and an altered response to white noise stimulation. Moreover, upon application of light flashes, the proportion of cells firing at light offset (OFF RGCs) was significantly lower in the NL3 KO compared to WT littermates, whereas the relative number of cells firing at light onset (ON RGCs) increased. Interestingly, although GABAAα2-bearing receptors have been related to direction-selective circuits of the retina, features of direction selective-retinal ganglion cells recorded remained unperturbed in the NL3 KO. Together our data underscore the importance of NL3 for the integrity of specific GABAAergic retinal circuits and identifies NL3 as an important regulator of retinal activity

Coding “What” and “When” in the Archer Fish Retina

Traditionally, the information content of the neural response is quantified using statistics of the responses relative to stimulus onset time with the assumption that the brain uses onset time to infer stimulus identity. However, stimulus onset time must also be estimated by the brain, making the utility of such an approach questionable. How can stimulus onset be estimated from the neural responses with sufficient accuracy to ensure reliable stimulus identification? We address this question using the framework of colour coding by the archer fish retinal ganglion cell. We found that stimulus identity, “what”, can be estimated from the responses of best single cells with an accuracy comparable to that of the animal's psychophysical estimation. However, to extract this information, an accurate estimation of stimulus onset is essential. We show that stimulus onset time, “when”, can be estimated using a linear-nonlinear readout mechanism that requires the response of a population of 100 cells. Thus, stimulus onset time can be estimated using a relatively simple readout. However, large nerve cell populations are required to achieve sufficient accuracy

Unified Treatment of Asymptotic van der Waals Forces

In a framework for long-range density-functional theory we present a unified full-field treatment of the asymptotic van der Waals interaction for atoms, molecules, surfaces, and other objects. The only input needed consists of the electron densities of the interacting fragments and the static polarizability or the static image plane, which can be easily evaluated in a ground-state density-functional calculation for each fragment. Results for separated atoms, molecules, and for atoms/molecules outside surfaces are in agreement with those of other, more elaborate, calculations.Comment: 6 pages, 5 figure

Modeling convergent ON and OFF pathways in the early visual system

For understanding the computation and function of single neurons in sensory systems, one needs to investigate how sensory stimuli are related to a neuron’s response and which biological mechanisms underlie this relationship. Mathematical models of the stimulus–response relationship have proved very useful in approaching these issues in a systematic, quantitative way. A starting point for many such analyses has been provided by phenomenological “linear–nonlinear” (LN) models, which comprise a linear filter followed by a static nonlinear transformation. The linear filter is often associated with the neuron’s receptive field. However, the structure of the receptive field is generally a result of inputs from many presynaptic neurons, which may form parallel signal processing pathways. In the retina, for example, certain ganglion cells receive excitatory inputs from ON-type as well as OFF-type bipolar cells. Recent experiments have shown that the convergence of these pathways leads to intriguing response characteristics that cannot be captured by a single linear filter. One approach to adjust the LN model to the biological circuit structure is to use multiple parallel filters that capture ON and OFF bipolar inputs. Here, we review these new developments in modeling neuronal responses in the early visual system and provide details about one particular technique for obtaining the required sets of parallel filters from experimental data