Reorganization of columnar architecture in the growing visual cortex

Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal circuits. Here, in acute and chronic experiments, we study the layout of ocular dominance (OD) columns in cat primary visual cortex (V1) during a period of substantial postnatal growth. We find that despite a considerable size increase of V1, the spacing between columns is largely preserved. In contrast, their spatial arrangement changes systematically over this period. While in young animals columns are more band-like, layouts become more isotropic in mature animals. We propose a novel mechanism of growth-induced reorganization that is based on the `zigzag instability', a dynamical instability observed in several inanimate pattern forming systems. We argue that this mechanism is inherent to a wide class of models for the activity-dependent formation of OD columns. Analyzing one member of this class, the Elastic Network model, we show that this mechanism can account for the preservation of column spacing and the specific mode of reorganization of OD columns that we observe. We conclude that neurons systematically shift their selectivities during normal development and that this reorganization is induced by the cortical expansion during growth. Our work suggests that cortical circuits remain plastic for an extended period in development in order to facilitate the modification of neuronal circuits to adjust for cortical growth.Comment: 8+13 pages, 4+8 figures, paper + supplementary materia

Magnetization orientation dependence of the quasiparticle spectrum and hysteresis in ferromagnetic metal nanoparticles

We use a microscopic Slater-Koster tight-binding model with short-range exchange and atomic spin-orbit interactions that realistically captures generic features of ferromagnetic metal nanoparticles to address the mesoscopic physics of magnetocrystalline anisotropy and hysteresis in nanoparticle quasiparticle excitation spectra. Our analysis is based on qualitative arguments supported by self-consistent Hartree-Fock calculations for nanoparticles containing up to 260 atoms. Calculations of the total energy as a function of magnetization direction demonstrate that the magnetic anisotropy per atom fluctuates by several percents when the number of electrons in the particle changes by one, even for the largest particles we consider. Contributions of individual orbitals to the magnetic anisotropy are characterized by a broad distribution with a mean more than two orders of magnitude smaller than its variance and with no detectable correlations between anisotropy contribution and quasiparticle energy. We find that the discrete quasiparticle excitation spectrum of a nanoparticle displays a complex non-monotonic dependence on an external magnetic field, with abrupt jumps when the magnetization direction is reversed by the field, explaining recent spectroscopic studies of magnetic nanoparticles. Our results suggests the existence of a broad cross-over from a weak spin-orbit coupling to a strong spin-orbit coupling regime, occurring over the range from approximately 200- to 1000-atom nanoparticles.Comment: 39 pages, 18 figures, to be published in Physical Review

Elementary Excitations of Ferromagnetic Metal Nanoparticles

We present a theory of the elementary spin excitations in transition metal ferromagnet nanoparticles which achieves a unified and consistent quantum description of both collective and quasiparticle physics. The theory starts by recognizing the essential role played by spin-orbit interactions in determining the energies of ferromagnetic resonances in the collective excitation spectrum and the strength of their coupling to low-energy particle-hole excitations. We argue that a crossover between Landau-damped ferromagnetic resonance and pure-state collective magnetic excitations occurs as the number of atoms in typical transition metal ferromagnet nanoparticles drops below approximately $10^4$, approximately where the single-particle level spacing, $\delta$, becomes larger than, $\sqrt{\alpha} E_{\rm res}$, where $E_{\rm res}$ is the ferromagnetic resonance frequency and $\alpha$ is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semi-realistic model Hamiltonians, which we solve numerically for nanoparticles containing several hundred atoms. For small nanoparticles, we find one isolated ferromagnetic resonance collective mode below the lowest particle-hole excitation energy, at $E_{\rm res} \approx 0.1$ meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As $\delta$ approaches $\sqrt{\alpha} E_{\rm res}$, the ferromagnetic collective excitation is more likely to couple strongly with discrete particle-hole excitations. In this regime the distinction between the two types of excitations blurs. We discuss the significance of this picture for the interpretation of recent single-electron tunneling experiments.Comment: 19 pages, 13 figure

A theory for the alignment of cortical feature maps during\ud development

We present a developmental model of ocular dominance column formation that takes into account the existence of an array of intrinsically specified cytochrome oxidase blobs. We assume that there is some molecular substrate for the blobs early in development, which generates a spatially periodic modulation of experience–dependent plasticity. We determine the effects of such a modulation on a competitive Hebbian mechanism for the modification of the feedforward afferents from the left and right eyes. We show how alternating left and right eye dominated columns can develop, in which the blobs are aligned with the centers of the ocular dominance columns and receive a greater density of feedforward connections, thus becoming defined extrinsically. More generally, our results suggest that the presence of periodically distributed anatomical markers early in development could provide a mechanism for the alignment of cortical feature maps

Symmetric Diblock Copolymers in Thin Films (I): Phase stability in Self-Consistent Field Calculations and Monte Carlo Simulations

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M.W. Matsen, J.Chem.Phys. {\bf 106}, 7781 (1997)], we study the ordered phases as a function of incompatibility $\chi$ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from $\chi N=0$ to $\chi N=30$ and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.Comment: to appear in J.Chem.Phy

Transport in magnetically ordered Pt nanocontacts

Pt nanocontacts, like those formed in mechanically controlled break junctions, are shown to develop spontaneous local magnetic order. Our density functional calculations predict that a robust local magnetic order exists in the atoms presenting low coordination, i. e., those forming the atom-sized neck. In contrast to previous work, we thus find that the electronic transport can be spin-polarized, although the net value of the conductance still agrees with available experimental information. Experimental implications of the formation of this new type of nanomagnet are discussed.Comment: 4 pages, 3 figure

Can retinal ganglion cell dipoles seed iso-orientation domains in the visual cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics. While this Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.Comment: 9 figures + 1 Supplementary figure and 1 Supplementary tabl

Zeeman energy and anomalous spin splitting in lateral GaAs quantum dots

The level splittings induced by a horizontal magnetic field in a parabolic two-dimensional quantum dot with spin-orbit interaction are obtained. Characteristic features induced by the spin-orbit coupling are the appearance of zero-field gaps as well as energy splittings that depend on the electronic state and the orientation of the magnetic field in the quantum-dot plane. It is suggested that these quantum-dot properties could be used to determine the Rashba and Dresselhaus spin-orbit intensitiesComment: 6 pages, 6 figures. To be published in Eur. Phys. J. B (2004