Maximally-localized Wannier functions for disordered systems: application to amorphous silicon

We use the maximally-localized Wannier function method to study bonding properties in amorphous silicon. This study represents, to our knowledge, the first application of the Wannier-function analysis to a disordered system. Our results show that, in the presence of disorder, this method is extremely helpful in providing an unambiguous picture of the bond distribution. In particular, defect configurations can be studied and characterized with a novel degree of accuracy that was not available before.Comment: 4 pages, with 3 PostScript figures embedded. Uses RevTex and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_as

Bilateral Symmetry of Visual Function Loss in Cone-Rod Dystrophies.

PURPOSE: To investigate bilateral symmetry of visual impairment in cone-rod dystrophy (CRD) patients and understand the feasibility of clinical trial designs treating one eye and using the untreated eye as an internal control. METHODS: This was a retrospective study of visual function loss measures in 436 CRD patients followed at the Ophthalmology Department of the Catholic University in Rome. Clinical measures considered were best-corrected visual acuity, focal macular cone electroretinogram (fERG), and Ganzfeld cone-mediated and rod-mediated electroretinograms. Interocular agreement in each of these clinical indexes was assessed by t- and Wilcoxon tests for paired samples, structural (Deming) regression analysis, and intraclass correlation. Baseline and follow-up measures were analyzed. A separate analysis was performed on the subset of 61 CRD patients carrying likely disease-causing mutations in the ABCA4 gene. RESULTS: Statistical tests show a very high degree of bilateral symmetry in the extent and progression of visual impairment in the fellow eyes of CRD patients. CONCLUSIONS: These data contribute to a better understanding of CRDs and support the feasibility of clinical trial designs involving unilateral eye treatment with the use of fellow eye as internal control

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

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

Central Retina Functional Damage in Usher Syndrome Type 2: 22 Years of Focal Macular ERG Analysis in a Patient Population From Central and Southern Italy.

PURPOSE: Recent studies show that patients with Usher syndrome type 2 (USH2) have abnormal cone structure and density in the central retina. This occurs in the presence of normal acuity, opening the quest for additional sensitive functional measures of central cone function in USH. We tested here whether focal macular cone electroretinogram (fERG) could be such a tool. METHODS: This retrospective study of central cone function loss was based on data from 47 patients with USH2 from the Ophthalmology Department of the Policlinico Gemelli/Catholic University in Rome. The analysis focused on the decrease of the fERG, obtained in response to a 41-Hz sinusoidal modulation of a uniform field presented to the central 18\ub0, generated by red light-emitting diodes (LEDs) and superimposed on an equiluminant steady adapting background. fERG decrease was compared with the decrease of best-corrected visual acuity and Goldmann kinetic perimetry V4E field. RESULTS: fERG follow-up data document a severe and precocious loss of central cone function in USH2 patients, preceding losses in other measures of cone function. fERG is already reduced to 40% of control at the beginning of the second decade of life, and by 25 years of age, all USH2 patients have fERGs less than 30% of control values. CONCLUSIONS: fERG represents a sensitive tool to evaluate central cone function in USH2, anticipating the decline of other central cone function measures, such as visual acuity and Goldmann perimetry

Maximally-localized generalized Wannier functions for composite energy bands

We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.Comment: 22 pages, two-column style with 4 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_wan

Analysis of spatial relationships in three dimensions: tools for the study of nerve cell patterning

<p>Abstract</p> <p>Background</p> <p>Multiple technologies have been brought to bear on understanding the three-dimensional morphology of individual neurons and glia within the brain, but little progress has been made on understanding the rules controlling cellular patterning. We describe new matlab-based software tools, now available to the scientific community, permitting the calculation of spatial statistics associated with 3D point patterns. The analyses are largely derived from the Delaunay tessellation of the field, including the nearest neighbor and Voronoi domain analyses, and from the spatial autocorrelogram.</p> <p>Results</p> <p>Our tools enable the analysis of the spatial relationship between neurons within the central nervous system in 3D, and permit the modeling of these fields based on lattice-like simulations, and on simulations of minimal-distance spacing rules. Here we demonstrate the utility of our analysis methods to discriminate between two different simulated neuronal populations.</p> <p>Conclusion</p> <p>Together, these tools can be used to reveal the presence of nerve cell patterning and to model its foundation, in turn informing on the potential developmental mechanisms that govern its establishment. Furthermore, in conjunction with analyses of dendritic morphology, they can be used to determine the degree of dendritic coverage within a volume of tissue exhibited by mature nerve cells.</p

Modeling Activity and Target-Dependent Developmental Cell Death of Mouse Retinal Ganglion Cells Ex Vivo

Programmed cell death is widespread during the development of the central nervous system and serves multiple purposes including the establishment of neural connections. In the mouse retina a substantial reduction of retinal ganglion cells (RGCs) occurs during the first postnatal week, coinciding with the formation of retinotopic maps in the superior colliculus (SC). We previously established a retino-collicular culture preparation which recapitulates the progressive topographic ordering of RGC projections during early post-natal life. Here, we questioned whether this model could also be suitable to examine the mechanisms underlying developmental cell death of RGCs. Brn3a was used as a marker of the RGCs. A developmental decline in the number of Brn3a-immunolabelled neurons was found in the retinal explant with a timing that paralleled that observed in vivo. In contrast, the density of photoreceptors or of starburst amacrine cells increased, mimicking the evolution of these cell populations in vivo. Blockade of neural activity with tetrodotoxin increased the number of surviving Brn3a-labelled neurons in the retinal explant, as did the increase in target availability when one retinal explant was confronted with 2 or 4 collicular slices. Thus, this ex vivo model reproduces the developmental reduction of RGCs and recapitulates its regulation by neural activity and target availability. It therefore offers a simple way to analyze developmental cell death in this classic system. Using this model, we show that ephrin-A signaling does not participate to the regulation of the Brn3a population size in the retina, indicating that eprhin-A-mediated elimination of exuberant projections does not involve developmental cell death

Expression of SPIG1 Reveals Development of a Retinal Ganglion Cell Subtype Projecting to the Medial Terminal Nucleus in the Mouse

Visual information is transmitted to the brain by roughly a dozen distinct types of retinal ganglion cells (RGCs) defined by a characteristic morphology, physiology, and central projections. However, our understanding about how these parallel pathways develop is still in its infancy, because few molecular markers corresponding to individual RGC types are available. Previously, we reported a secretory protein, SPIG1 (clone name; D/Bsp120I #1), preferentially expressed in the dorsal region in the developing chick retina. Here, we generated knock-in mice to visualize SPIG1-expressing cells with green fluorescent protein. We found that the mouse retina is subdivided into two distinct domains for SPIG1 expression and SPIG1 effectively marks a unique subtype of the retinal ganglion cells during the neonatal period. SPIG1-positive RGCs in the dorsotemporal domain project to the dorsal lateral geniculate nucleus (dLGN), superior colliculus, and accessory optic system (AOS). In contrast, in the remaining region, here named the pan-ventronasal domain, SPIG1-positive cells form a regular mosaic and project exclusively to the medial terminal nucleus (MTN) of the AOS that mediates the optokinetic nystagmus as early as P1. Their dendrites costratify with ON cholinergic amacrine strata in the inner plexiform layer as early as P3. These findings suggest that these SPIG1-positive cells are the ON direction selective ganglion cells (DSGCs). Moreover, the MTN-projecting cells in the pan-ventronasal domain are apparently composed of two distinct but interdependent regular mosaics depending on the presence or absence of SPIG1, indicating that they comprise two functionally distinct subtypes of the ON DSGCs. The formation of the regular mosaic appears to be commenced at the end of the prenatal stage and completed through the peak period of the cell death at P6. SPIG1 will thus serve as a useful molecular marker for future studies on the development and function of ON DSGCs