Sufficient Criteria for Total Differentiability of a Real Valued Function of a Complex Variable in Rn an Extension of H. Rademacher's Result for R²

This thesis provides sufficient conditions for total differentiability almost everywhere of a real-valued function of a complex variable defined on a bounded region in IRn. This thesis extends H. Rademacher's 1918 results in IR2 which culminated in total differentiability, to IR

On the Potential of the Excluded Volume and Auto-Correlation as Neuromorphometric Descriptors

This work investigates at what degree two neuromorphometric measurements, namely the autocorrelation and the excluded volume of a neuronal cell can influence the characterization and classification of such a type of cells. While the autocorrelation function presents good potential for quantifying the dendrite-dendrite connectivity of cells in mosaic tilings, the excluded volume, i.e. the amount of the surround space which is geometrically not accessible to an axon or dendrite, provides a complementary characterization of the cell connectivity. The potential of such approaches is illustrated with respect to real neuronal cells.Comment: 15 pages, 6 figure

Irregular S-cone mosaics in felid retinas: spatial interaction with axonless horizontal revealed by cross-correlation

In most mammals short-wavelength-sensitive (S) cones are arranged in irregular patterns with widely variable intercell distances. Consequently, mosaics of connected interneurons either may show some type of correlation to photoreceptor placement or may establish an independent lattice with compensatory dendritic organization. Since axonless horizontal cells (A-HC’s) are supposed to direct all dendrites to overlying cones, we studied their spatial interaction with chromatic cone subclasses. In the cheetah, the bobcat, and the leopard, anti-S-opsin antibodies have consistently colabeled the A-HC’s in addition to the S cones. We investigated the interaction between the two cell mosaics, using autocorrelation and cross-correlation procedures, including a Voronoi-based density probe. Comparisons with simulations of random mosaics show significantly lower densities of S cones above the cell bodies and primary dendrites of A-HC’s. The pattern results in different long-wavelength-sensitive-L- and S-cone ratios in the central versus the peripheral zones of A-HC dendritic fields. The existence of a related pattern at the synaptic level and its potential significance for color processing may be investigated in further studies

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

Communications Biophysics

Contains reports on five research projects.National Science Foundation (Grant G-16526)National Institutes of Health (Grant MH-04737-02)

V-Proportion: a method based on the Voronoi diagram to study spatial relations in neuronal mosaics of the retina

The visual system plays a predominant role in the human perception. Although all components of the eye are important to perceive visual information, the retina is a fundamental part of the visual system. In this work we study the spatial relations between neuronal mosaics in the retina. These relations have shown its importance to investigate possible constraints or connectivities between different spatially colocalized populations of neurons, and to explain how visual information spreads along the layers before being sent to the brain. We introduce the V-Proportion, a method based on the Voronoi diagram to study possible spatial interactions between two neuronal mosaics. Results in simulations as well as in real data demonstrate the effectiveness of this method to detect spatial relations between neurons in different layers

Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.Comment: 52 pages, 12 figure

Ultrasound-guided in utero injections allow studies of the development and function of the eye

Ultrasound-guided in utero injections into the brain of murine embryos has been shown to facilitate gene delivery. We investigated whether these methods would allow gene transfer into ocular structures. Gene transfer using retroviral vectors or electroporation was found to be quite effective. We determined the window of time, as well as compared several strains of mice, that yield a high degree of survival and successful gene transfer. Several retroviral constructs were tested for expression and coexpresssion of two genes in retinal cell types. In addition, a retroviral vector was engineered to give cone photoreceptor-enriched expression, and a retroviral vector was demonstrated to provide RNAi-mediated loss-of-function. These methods enable access to early ocular structures and provide a more rapid method of assessment of gene and promoter function than possible using genetically engineered mice

Information transmission in oscillatory neural activity

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase relative to the stimulus. We propose a model to reproduce characteristic features of oscillatory spike trains, such as histograms of inter-spike intervals and phase locking of spikes to an oscillatory influence. The proposed model is based on an inhomogeneous Gamma process governed by a density function that is a product of the usual stimulus-dependent rate and a quasi-periodic function. Further, we present an analysis method generalizing the direct method (Rieke et al, 1999; Brenner et al, 2000) to assess the information content in such data. We demonstrate these tools on recordings from relay cells in the lateral geniculate nucleus of the cat.Comment: 18 pages, 8 figures, to appear in Biological Cybernetic

Growth of the adult goldfish eye. II. Increase in retinal cell number

The retinas of adult goldfish, one to four years of age, 4–23 cm in length, were examined with standard paraffin histology to determine if new cells were being added with growth. Retinal cell nuclei were counted and the area of the retina was measured. An analysis of cell densities in various regions throughout the retina showed that the cells are distributed nearly homogeneously. The density (No./mm 2 of retinal surface) of ganglion cells, inner nuclear layer cells and cones decreases with growth, but the density of rods remains constant. Thus the rods account for a larger proportion of the cells in larger retinas. The total number of cells per retina increases: the ganglion cells from 60,000 to 350,000; the inner nuclear layer cells from 1,500,000 to 4,000,000; the cones from 250,000 to 1,400,000; the rods from 1,500,000 to 15,000,000. This increase in the number of retinal neurons implies the formation of even more new synapses, and suggests the adult goldfish retina as a model for both neuro- and synaptogenesis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50001/1/901760303_ftp.pd