@inproceedings{2330, author = {Hainzl, Christian and Robert Seiringer}, pages = {101 -- 104}, publisher = {American Mathematical Society}, title = {{A linear criterion for solutions of non-linear equations, with application to the BCS gap equation}}, doi = {10.1090/conm/500/09823}, volume = {500}, year = {2009}, } @article{2384, abstract = {We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.}, author = {Giuliani, Alessandro and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5-6}, pages = {915 -- 934}, publisher = {Springer}, title = {{The ground state energy of the weakly interacting Bose gas at high density}}, doi = {10.1007/s10955-009-9718-0}, volume = {135}, year = {2009}, } @article{2385, abstract = {We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity, so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground-state energy of the corresponding N -body Hamiltonian with contact interaction provided the total angular momentum L is much less than N2. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground-state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {6}, publisher = {American Physical Society}, title = {{Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime}}, doi = {10.1103/PhysRevA.79.063626}, volume = {79}, year = {2009}, } @article{2386, abstract = {We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T- Tc (0) Tc (0) >5 a ρ1/3, where Tc (0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.}, author = {Robert Seiringer and Ueltschi, Daniel}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {1}, publisher = {American Physical Society}, title = {{Rigorous upper bound on the critical temperature of dilute Bose gases}}, doi = {10.1103/PhysRevB.80.014502}, volume = {80}, year = {2009}, } @article{2387, abstract = {We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.}, author = {Lewin, Mathieu and Robert Seiringer}, journal = {Journal of Statistical Physics}, number = {5}, pages = {1040 -- 1062}, publisher = {Springer}, title = {{Strongly correlated phases in rapidly rotating Bose gases}}, doi = {10.1007/s10955-009-9833-y}, volume = {137}, year = {2009}, } @article{2388, abstract = {This paper provides self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifies the connection of coherence and proper scoring rules to Bregman divergence.}, author = {Predd, Joel B and Robert Seiringer and Lieb, Élliott H and Osherson, Daniel N and Poor, Harold V and Kulkarni, Sanjeev R}, journal = {IEEE Transactions on Information Theory}, number = {10}, pages = {4786 -- 4792}, publisher = {IEEE}, title = {{Probabilistic coherence and proper scoring rules}}, doi = {10.1109/TIT.2009.2027573}, volume = {55}, year = {2009}, } @inproceedings{2433, abstract = {Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into ℝd? Known results easily imply polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED(d-1)→d are undecidable for each d ≥ 5. Our main result is NP-hardness of EMBED2→4 and, more generally, of EMBEDk→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3.}, author = {Matoušek, Jiří and Martin Tancer and Uli Wagner}, pages = {855 -- 864}, publisher = {SIAM}, title = {{Hardness of embedding simplicial complexes in ℝd}}, year = {2009}, } @article{2434, abstract = {For a planar point set we consider the graph whose vertices are the crossing-free straight-line spanning trees of the point set, and two such spanning trees are adjacent if their union is crossing-free. An upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set. We prove a lower bound of Ω(logn/loglogn) for the diameter of the transformation graph of spanning trees on a set of n points in the plane. This nearly matches the known upper bound of O(logn). If we measure the diameter in terms of the number of convex layers k of the point set, our lower bound construction is tight, i.e., the diameter is in Ω(logk) which matches the known upper bound of O(logk). So far only constant lower bounds were known.}, author = {Buchin, Kevin and Razen, Andreas and Uno, Takeaki and Uli Wagner}, journal = {Computational Geometry: Theory and Applications}, number = {8}, pages = {724 -- 730}, publisher = {Elsevier}, title = {{Transforming spanning trees: A lower bound}}, doi = {10.1016/j.comgeo.2008.03.005}, volume = {42}, year = {2009}, } @article{2498, abstract = {Activation of G protein-gated inwardly-rectifying K+ (GIRK or Kir3) channels by metabotropic gamma-aminobutyric acid (B) (GABAB) receptors is an essential signalling pathway controlling neuronal excitability and synaptic transmission in the brain. To investigate the relationship between GIRK channel subunits and GABAB receptors in cerebellar Purkinje cells at post- and pre-synaptic sites, we used biochemical, functional and immunohistochemical techniques. Co-immunoprecipitation analysis demonstrated that GIRK subunits are co-assembled with GABAB receptors in the cerebellum. Immunoelectron microscopy showed that the subunit composition of GIRK channels in Purkinje cell spines is compartment-dependent. Thus, at extrasynaptic sites GIRK channels are formed by GIRK1/GIRK2/GIRK3, post-synaptic densities contain GIRK2/GIRK3 and dendritic shafts contain GIRK1/GIRK3. The post-synaptic association of GIRK subunits with GABAB receptors in Purkinje cells is supported by the subcellular regulation of the ion channel and the receptor in mutant mice. At pre-synaptic sites, GIRK channels localized to parallel fibre terminals are formed by GIRK1/GIRK2/GIRK3 and co-localize with GABAB receptors. Consistent with this morphological evidence we demonstrate their functional interaction at axon terminals in the cerebellum by showing that GIRK channels play a role in the inhibition of glutamate release by GABAB receptors. The association of GIRK channels and GABA B receptors with excitatory synapses at both post- and pre-synaptic sites indicates their intimate involvement in the modulation of glutamatergic neurotransmission in the cerebellum.}, author = {Fernández-Alacid, Laura and Aguado, Carolina and Ciruela, Francisco and Martín, Ricardo J and Colón, José and Cabañero, María José and Gassmann, Martin and Watanabe, Masahiko and Ryuichi Shigemoto and Wickman, Kevin D and Bettler, Bernhard and Sánchez-Prieto, José and Luján, Rafael}, journal = {Journal of Neurochemistry}, number = {4}, pages = {1363 -- 1376}, publisher = {Wiley-Blackwell}, title = {{ Subcellular compartment-specific molecular diversity of pre- and post-synaptic GABAB-activated GIRK channels in Purkinje cells}}, doi = {10.1111/j.1471-4159.2009.06229.x}, volume = {110}, year = {2009}, } @article{2499, abstract = {G protein-coupled receptors (GPCRs) have critical functions in intercellular communication. Although a wide range of different receptors have been identified in the same cells, the mechanism by which signals are integrated remains elusive. The ability of GPCRs to form dimers or larger hetero-oligomers is thought to generate such signal integration. We examined the molecular mechanisms responsible for the GABAB receptor-mediated potentiation of the mGlu receptor signalling reported in Purkinje neurons. We showed that this effect does not require a physical interaction between both receptors. Instead, it is the result of a more general mechanism in which the βγ subunits produced by the Gi-coupled GABAB receptor enhance the mGlu-mediated Gq response. Most importantly, this mechanism could be generally applied to other pairs of Gi- and Gq-coupled receptors and the signal integration varied depending on the time delay between activation of each receptor. Such a mechanism helps explain specific properties of cells expressing two different Gi- and Gq-coupled receptors activated by a single transmitter, or properties of GPCRs naturally coupled to both types of the G protein.}, author = {Rives, Marie L and Vol, Claire and Fukazawa, Yugo and Tinel, Norbert and Trinquet, Eric and Ayoub, Mohammed A and Ryuichi Shigemoto and Pin, Jean-Philippe and Prezèau, Laurent}, journal = {EMBO Journal}, number = {15}, pages = {2195 -- 2208}, publisher = {Wiley-Blackwell}, title = {{Crosstalk between GABAB and mGlu1a receptors reveals new insight into GPCR signal integration}}, doi = {10.1038/emboj.2009.177}, volume = {28}, year = {2009}, } @article{2500, abstract = {To examine the intrasynaptic arrangement of postsynaptic receptors in relation to the functional role of the synapse,we quantitatively analyzed the two-dimensional distribution of AMPA and NMDA receptors (AMPARs and NMDARs, respectively) using SDS-digested freeze-fracture replica labeling (SDS-FRL) and assessed the implication of distribution differences on the postsynaptic responses by simulation. In the dorsal lateral geniculate nucleus, corticogeniculate (CG) synapses were twice as large as retinogeniculate (RG) synapses but expressed similar numbers of AMPARs. Two-dimensional views of replicas revealed that AMPARs form microclusters in both synapses to a similar extent, resulting in larger AMPAR-lacking areas in the CG synapses. Despite the broad difference in the AMPAR distribution within a synapse, our simulations based on the actual receptor distributions suggested that the AMPAR quantal response at individual RG synapses is only slightly larger in amplitude, less variable, and faster in kinetics than that at CG synapses having a similar number of the receptors. NMDARs at the CG synapses were expressed twice as many as those in the RG synapses. Electrophysiological recordings confirmed a larger contribution of NMDAR relative to AMPAR-mediated responses in CG synapses. We conclude that synapse size and the density and distribution of receptors have minor influences on quantal responses and that the number of receptors acts as a predominant postsynaptic determinant of the synaptic strength mediated by both the AMPARs and NMDARs. }, author = {Tarusawa, Etsuko and Matsui, Ko and Budisantoso, Timotheus and Molnár, Elek and Watanabe, Masahiko and Matsui, Minoru and Fukazawa, Yugo and Ryuichi Shigemoto}, journal = {Journal of Neuroscience}, number = {41}, pages = {12896 -- 12908}, publisher = {Society for Neuroscience}, title = {{Input-specific intrasynaptic arrangements of ionotropic glutamate receptors and their impact on postsynaptic responses}}, doi = {10.1523/JNEUROSCI.6160-08.2009}, volume = {29}, year = {2009}, } @article{2501, abstract = {The brain-specific immediate early gene Arc/Arg3.1 is induced in response to a variety of stimuli, including sensory and behavior-linked neural activity. Here we report the generation of transgenic mice, termed TgArc/Arg3.1-d4EGFP, expressing a 4-h half-life form of enhanced green fluorescent protein (d4EGFP) under the control of the Arc/Arg3.1 promoter. We show that d4EGFP-mediated fluorescence faithfully reports Arc/Arg3.1 induction in response to physiological, pathological and pharmacological stimuli, and that this fluorescence permits electrical recording from activated neurons in the live mouse. Moreover, the fluorescent Arc/Arg3.1 indicator revealed activity changes in circumscribed brain areas in distinct modes of stress and in a mouse model of Alzheimer's disease. These findings identify the TgArc/Arg3.1-d4EGFP mouse as a versatile tool to monitor Arc/Arg3.1 induction in neural circuits, both in vitro and in vivo.}, author = {Grinevich, Valery V and Kolleker, Alexander and Eliava, Marina I and Takada, Naoki and Takuma, Hiroshi and Fukazawa, Yugo and Ryuichi Shigemoto and Kuhl, Dietmar and Waters, Jack and Seeburg, Peter H and Osten, Pavel}, journal = {Journal of Neuroscience Methods}, number = {1}, pages = {25 -- 36}, publisher = {Elsevier}, title = {{Fluorescent Arc/Arg3.1 indicator mice: A versatile tool to study brain activity changes in vitro and in vivo}}, doi = {10.1016/j.jneumeth.2009.07.015}, volume = {184}, year = {2009}, } @article{2502, abstract = {In order to acquire phase-contrast images with adequate contrast, conventional TEM requires large amount of defocus. Increasing the defocus improves the low-frequency components but attenuates the high-frequency ones. On the other hand, Zernike phase-contrast TEM (ZPC-TEM) can recover low-frequency components without losing the high-frequency ones under in-focus conditions. ZPC-TEM however, has another problem, especially in imaging of complex biological specimens such as cells and tissues; strong halos appear around specimen structures, and these halos hinder the interpretation of images. Due to this problem, the application of ZPC-TEM has been restricted to imaging of smaller particles. In order to improve the halo appearance, we fabricated a new quarter-wave thin film phase-plate with a smaller central hole and tested it on vitreous biological specimens. ZPC-TEM with the new plate could successfully visualize, in in-focus images, the intracellular fine features of cultured cells and brain tissues. This result indicates that reduction of the central hole diameter makes ZPC-TEM applicable on size scales ranging from protein particles to tissue sections. The application of ZPC-TEM to vitreous biological specimens will be a powerful method to advance the new field of imaging science for ultrastructures in close-to-physiological state.}, author = {Fukuda, Yoshiyuki and Fukazawa, Yugo and Danev, Radostin S and Ryuichi Shigemoto and Nagayama, Kuniaki}, journal = {Journal of Structural Biology}, number = {3}, pages = {476 -- 484}, publisher = {Academic Press}, title = {{Tuning of the Zernike phase-plate for visualization of detailed ultrastructure in complex biological specimens}}, doi = {10.1016/j.jsb.2009.08.011}, volume = {168}, year = {2009}, } @article{2680, abstract = {GABA B receptor subtypes are based on the subunit isoforms GABA B1a and GABA B1b, which associate with GABA B2 subunits to form pharmacologically indistinguishable GABA B(1a,2) and GABA B(1b,2) receptors. Studies with mice selectively expressing GABA B1a or GABA B1b subunits revealed that GABA B(1a,2) receptors are more abundant than GABA B(1b,2) receptors at glutamatergic terminals. Accordingly, it was found that GABA B(1a,2) receptors are more efficient than GABA B(1b,2) receptors in inhibiting glutamate release when maximally activated by exogenous application of the agonist baclofen. Here, we used a combination of genetic, ultrastructural and electrophysiological approaches to analyze to what extent GABA B(1a,2) and GABA B(1b,2) receptors inhibit glutamate release in response to physiological activation. We first show that at hippocampal mossy fiber (MF)-CA3 pyramidal neuron synapses more GABA B1a than GABA B1b protein is present at presynaptic sites, consistent with the findings at other glutamatergic synapses. In the presence of baclofen at concentrations ≥1 μM, both GABA B(1a,2) and GABA B(1b,2) receptors contribute to presynaptic inhibition of glutamate release. However, at lower concentrations of baclofen, selectively GABA B(1a,2) receptors contribute to presynaptic inhibition. Remarkably, exclusively GABA B(1a,2) receptors inhibit glutamate release in response to synaptically released GABA. Specifically, we demonstrate that selectively GABA B(1a,2) receptors mediate heterosynaptic depression of MF transmission, a physiological phenomenon involving transsynaptic inhibition of glutamate release via presynaptic GABA B receptors. Our data demonstrate that the difference in GABA B1a and GABA B1b protein levels at MF terminals is sufficient to produce a strictly GABA B1a-specific effect under physiological conditions. This consolidates that the differential subcellular localization of the GABA B1a and GABA B1b proteins is of regulatory relevance. }, author = {Guetg, Nicole and Seddik, Riad and Vigot, Réjan and Tureček, Rostislav and Gassmann, Martin and Vogt, Kaspar E and Bräuner-Osborne, Hans and Ryuichi Shigemoto and Kretz, Oliver and Frotscher, Michael and Kulik, Ákos and Bettler, Bernhard}, journal = {Journal of Neuroscience}, number = {5}, pages = {1414 -- 1423}, publisher = {Society for Neuroscience}, title = {{The GABA B1a isoform mediates heterosynaptic depression at hippocampal mossy fiber synapses}}, doi = {10.1523/JNEUROSCI.3697-08.2009}, volume = {29}, year = {2009}, } @article{2682, abstract = {The living cell imaging using a two-photon microscope using gold nanoplates and nanoparticle aggregates was demonstrated. The dimensions of the nanoplates were determined through scanning electron microscopy (SEM) and atomic force microscopy. The height of a 100 nm base-length nanotriangle was around 10 nm, while the height of 300 nm base-length nanotriangle was around 12 nm. A spectrophotometer was also used to determine the extinction spectra of gold nanoparticle colloids. Two-photon-induced photoluminescence (TPIPL) under far-field excitation was tested for gold nanoplates on a glass substrate using two-photon laser scanning microscopy (TPLSM). It was observed that living-cell microscopic imaging can be carried out with TPIPL from gold nanoplates and aggregated nanosphere. This method provided a platform for developing tools for biological and biomedical studies.}, author = {Jiang, Yuqiang and Horimoto, Noriko N and Imura, Kohei and Matsui, Ko and Ryuichi Shigemoto}, journal = {Advanced Materials}, number = {22}, pages = {2309 -- 2313}, publisher = {Wiley-Blackwell}, title = {{Bioimaging with two-photon-induced luminescence from triangular nanoplates and nanoparticle aggregates of gold}}, doi = {10.1002/adma.200802312}, volume = {21}, year = {2009}, } @article{2683, abstract = {GABAb receptor (GABAbR)-mediated suppression of glutamate release is critical for limiting glutamatergic transmission across the central nervous system (CNS). Here we show that, upon tetanic stimulation of afferents to lateral amygdala, presynaptic GABAbR-mediated inhibition only occurs in glutamatergic inputs to principle neurons (PNs), not to interneurons (INs), despite the presence of GABAbR in terminals to both types of neurons. The selectivity is caused by differential local GABA accumulation; it requires GABA reuptake and parallels distinct spatial distributions of presynaptic GABAbR in terminals to PNs and INs. Moreover, GABAbR-mediated suppression of theta-burst-induced long-term potentiation (LTP) occurs only in the inputs to PNs, not to INs. Thus, target-cell-specific control of glutamate release by presynaptic GABAbR orchestrates the inhibitory dominance inside amygdala and might contribute to prevention of nonadaptive defensive behaviors.}, author = {Pan, Bingxing and Dong, Yu-Lin and Ito, Wataru and Yanagawa, Yuchio and Ryuichi Shigemoto and Morozov, Alexei A}, journal = {Neuron}, number = {6}, pages = {917 -- 929}, publisher = {Elsevier}, title = {{Selective gating of glutamatergic inputs to excitatory neurons of amygdala by presynaptic GABAb receptor}}, doi = {10.1016/j.neuron.2009.01.029}, volume = {61}, year = {2009}, } @article{2684, abstract = {Calcium-activated potassium channels have been shown to be critically involved in neuronal function, but an elucidation of their detailed roles awaits identification of the microdomains where they are located. This study was undertaken to unravel the precise subcellular distribution of the large-conductance calcium-activated potassium channels (called BK, KCa1.1, or Slo1) in the somatodendritic compartment of cerebellar Purkinje cells by means of postembedding immunogold cytochemistry and SDS-digested freeze-fracture replica labeling (SDS-FRL). We found BK channels to be unevenly distributed over the Purkinje cell plasma membrane. At distal dendritic compartments, BK channels were scattered over the plasma membrane of dendritic shafts and spines but absent from postsynaptic densities. At the soma and proximal dendrites, BK channels formed two distinct pools. One pool was scattered over the plasma membrane, whereas the other pool was clustered in plasma membrane domains overlying subsurface cisterns. The labeling density ratio of clustered to scattered channels was about 60:1, established in SDS-FRL. Subsurface cisterns, also called hypolemmal cisterns, are subcompartments of the endoplasmic reticulum likely representing calciosomes that unload and refill Ca2+ independently. Purkinje cell subsurface cisterns are enriched in inositol 1,4,5-triphosphate receptors that mediate the effects of several neurotransmitters, hormones, and growth factors by releasing Ca2+ into the cytosol, generating local Ca2+ sparks. Such increases in cytosolic [Ca2+] may be sufficient for BK channel activation. Clustered BK channels in the plasma membrane may thus participate in building a functional unit (plasmerosome) with the underlying calciosome that contributes significantly to local signaling in Purkinje cells.}, author = {Walter Kaufmann and Ferraguti, Francesco and Fukazawa, Yugo and Kasugai, Yu and Ryuichi Shigemoto and Laake, Petter and Sexton, Joseph A and Ruth, Peter and Wietzorrek, Georg and Knaus, Hans G and Storm, Johan F and Ottersen, Ole P}, journal = {Journal of Comparative Neurology}, number = {2}, pages = {215 -- 230}, publisher = {Wiley-Blackwell}, title = {{Large-conductance calcium-activated potassium channels in Purkinje cell plasma membranes are clustered at sites of hypolemmal microdomains}}, doi = {10.1002/cne.22066}, volume = {515}, year = {2009}, } @article{2685, abstract = {Conduction velocity (CV) of myelinated axons has been shown to be regulated by oligodendrocytes even after myelination has been completed. However, how myelinating oligodendrocytes regulate CV, and what the significance of this regulation is for normal brain function remain unknown. To address these questions, we analyzed a transgenic mouse line harboring extra copies of the myelin proteolipid protein 1 (plp1) gene (plp1tg/- mice) at 2 months of age. At this stage, the plp1tg/- mice have an unaffected myelin structure with a normally appearing ion channel distribution, but the CV in all axonal tracts tested in the CNS is greatly reduced. We also found decreased axonal diameters and slightly abnormal paranodal structures, both of which can be a cause for the reduced CV. Interestingly the plp1tg/- mice showed altered anxiety-like behaviors, reduced prepulse inhibitions, spatial learning deficits and working memory deficit, all of which are schizophrenia-related behaviors. Our results implicate that abnormalities in the neuron-glia interactions at the paranodal junctions can result in reduced CV in the CNS, which then induces behavioral abnormalities related to schizophrenia.}, author = {Tanaka, Hisataka and Ma, Jianmei and Tanaka, Kenji F and Takao, Keizo and Komada, Munekazu and Tanda, Koichi and Suzuki, Ayaka and Ishibashi, Tomoko and Baba, Hiroko and Isa, Tadashi and Ryuichi Shigemoto and Ono, Katsuhiko and Miyakawa, Tsuyoshi and Ikenaka, Kazuhiro}, journal = {Journal of Neuroscience}, number = {26}, pages = {8363 -- 8371}, publisher = {Society for Neuroscience}, title = {{Mice with altered myelin proteolipid protein gene expression display cognitive deficits accompanied by abnormal neuron-glia interactions and decreased conduction velocities}}, doi = {10.1523/JNEUROSCI.3216-08.2009}, volume = {29}, year = {2009}, } @article{2686, abstract = {Channelrhodopsin-2 (ChR2), one of the archea-type rhodopsins from green algae, is a potentially useful optogenetic tool for restoring vision in patients with photoreceptor degeneration, such as retinitis pigmentosa. If the ChR2 gene is transferred to retinal ganglion cells (RGCs), which send visual information to the brain, the RGCs may be repurposed to act as photoreceptors. In this study, by using a transgenic rat expressing ChR2 specifically in the RGCs under the regulation of a Thy-1.2 promoter, we tested the possibility that direct photoactivation of RGCs could restore effective vision. Although the contrast sensitivities of the optomotor responses of transgenic rats were similar to those observed in the wild-type rats, they were enhanced for visual stimuli of low-spatial frequency after the degeneration of native photoreceptors. This result suggests that the visual signals derived from the ChR2-expressing RGCs were reinterpreted by the brain to form behavior-related vision.}, author = {Tomita, Hiroshi and Sugano, Eriko and Fukazawa, Yugo and Isago, Hitomi and Sugiyama, Yuka and Hiroi, Teru and Ishizuka, Toru and Mushiake, Hajime and Kato, Megumi and Hirabayashi, Masumi and Ryuichi Shigemoto and Yawo, Hiromu and Tamai, Makoto}, journal = {PLoS One}, number = {11}, publisher = {Public Library of Science}, title = {{Visual properties of transgenic rats harboring the channelrhodopsin-2 gene regulated by the thy-1.2 promoter}}, doi = {10.1371/journal.pone.0007679}, volume = {4}, year = {2009}, } @article{2703, abstract = {We consider N×N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. We study the connection between eigenvalue statistics on microscopic energy scales η≪1 and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of the single matrix elements, we first give an upper bound on the density of states on short energy scales of order η∼log N/N. We then prove that the density of states concentrates around the Wigner semicircle law on energy scales η≫N−2/3. We show that most eigenvectors are fully delocalized in the sense that their ℓp-norms are comparable with N1/p−1/2 for p≥2, and we obtain the weaker bound N2/3(1/p−1/2) for all eigenvectors whose eigenvalues are separated away from the spectral edges. We also prove that, with a probability very close to one, no eigenvector can be localized. Finally, we give an optimal bound on the second moment of the Green function. }, author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer}, journal = {Annals of Probability}, number = {3}, pages = {815 -- 852}, publisher = {Institute of Mathematical Statistics}, title = {{Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices}}, doi = {10.1214/08-AOP421}, volume = {37}, year = {2009}, }