@article{2374, abstract = {A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.}, author = {Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {595 -- 636}, publisher = {Springer}, title = {{Free energy of a dilute Bose gas: Lower bound}}, doi = {10.1007/s00220-008-0428-2}, volume = {279}, year = {2008}, } @article{2376, abstract = {We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {18}, publisher = {American Physical Society}, title = {{Critical temperature and energy gap for the BCS equation}}, doi = {10.1103/PhysRevB.77.184517}, volume = {77}, year = {2008}, } @article{2377, abstract = {We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.}, author = {Hainzl, Christian and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2-3}, pages = {99 -- 107}, publisher = {Springer}, title = {{The BCS critical temperature for potentials with negative scattering length}}, doi = {10.1007/s11005-008-0242-y}, volume = {84}, year = {2008}, } @article{2378, abstract = {We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.}, author = {Robert Seiringer and Yin, Jun}, journal = {Journal of Statistical Physics}, number = {6}, pages = {1139 -- 1154}, publisher = {Springer}, title = {{Ground state energy of the low density hubbard model}}, doi = {10.1007/s10955-008-9527-x}, volume = {131}, year = {2008}, } @article{2379, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Journal of the American Mathematical Society}, number = {4}, pages = {925 -- 950}, publisher = {American Mathematical Society}, title = {{Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators}}, doi = {10.1090/S0894-0347-07-00582-6}, volume = {21}, year = {2008}, } @article{2380, abstract = {The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.}, author = {Hainzl, Christian and Hamza, Eman and Robert Seiringer and Solovej, Jan P}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {349 -- 367}, publisher = {Springer}, title = {{The BCS functional for general pair interactions}}, doi = {10.1007/s00220-008-0489-2}, volume = {281}, year = {2008}, } @article{2381, abstract = {We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.}, author = {Frank, Rupert L and Robert Seiringer}, journal = {Journal of Functional Analysis}, number = {12}, pages = {3407 -- 3430}, publisher = {Academic Press}, title = {{Non-linear ground state representations and sharp Hardy inequalities}}, doi = {10.1016/j.jfa.2008.05.015}, volume = {255}, year = {2008}, } @article{2382, abstract = {We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.}, author = {Robert Seiringer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {459 -- 479}, publisher = {Springer}, title = {{The Lieb-Liniger model as a limit of dilute bosons in three dimensions}}, doi = {10.1007/s00220-008-0521-6}, volume = {284}, year = {2008}, } @article{2383, abstract = {We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.}, author = {Hainzl, Christian and Lewin, Mathieu and Robert Seiringer}, journal = {Reviews in Mathematical Physics}, number = {10}, pages = {1283 -- 1307}, publisher = {World Scientific Publishing}, title = {{A nonlinear model for relativistic electrons at positive temperature}}, doi = {10.1142/S0129055X08003547}, volume = {20}, year = {2008}, } @inbook{2415, author = {Uli Wagner}, booktitle = {Surveys on Discrete and Computational Geometry: Twenty Years Later}, editor = {Goodman, Jacob E and Pach, János and Pollack, Richard}, pages = {443 -- 514}, publisher = {American Mathematical Society}, title = {{k-Sets and k-facets}}, doi = {10.1090/conm/453}, volume = {453}, year = {2008}, } @inproceedings{2432, abstract = {We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.}, author = {Smorodinsky, Shakhar and Sulovský, Marek and Uli Wagner}, pages = {363 -- 373}, publisher = {Springer}, title = {{On center regions and balls containing many points}}, doi = {10.1007/978-3-540-69733-6_36}, volume = {5092}, year = {2008}, } @article{2497, abstract = {Cyclic nucleotide phosphodiesterase 10A (PDE10A) is a member of phosphodiesterase families that degrade cAMP and/or cGMP in distinct intracellular sites. PDE10A has a dual activity on hydrolysis of both cAMP and cGMP, and is prominently expressed in the striatum and the testis. Previous studies suggested that PDE10A is involved in regulation of locomotor activity and potentially related to psychosis, but concrete physiological roles of PDE10A remains elusive yet. In this study, we genetically inactivated PDE10A2, a prominent isoform of PDE10A in the brain, in mice, and demonstrate that PDE10A2 deficiency results in increased social interaction without any major influence on different other behaviors, along with increased levels of striatal cAMP. We also demonstrate that PDE10A2 is selectively distributed in medium spiny neurons, but not interneurons, of the striatal complex. Thus, our results establish a physiological role for PDE10A2 in regulating cAMP pathway and social interaction, and suggest that cAMP signaling cascade in striatal medium spiny neurons might be involved in regulating social interaction behavior in mice.}, author = {Sano, Hiromi and Nagai, Yumiko and Miyakawa, Tsuyoshi and Ryuichi Shigemoto and Yokoi, Mineto}, journal = {Journal of Neurochemistry}, number = {2}, pages = {546 -- 556}, publisher = {Wiley-Blackwell}, title = {{Increased social interaction in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase 10A2}}, doi = {10.1111/j.1471-4159.2007.05152.x}, volume = {105}, year = {2008}, } @misc{2674, author = {Fukazawa, Yugo and Tarusawa, Etsuko and Matsui, Ko and Ryuichi Shigemoto}, booktitle = {Tanpakushitsu kakusan koso Protein nucleic acid enzyme}, number = {4 Suppl}, pages = {436 -- 441}, publisher = {Kyoritsu Shuppan}, title = {{ Ultrastructural insights of postsynaptic glutamate receptor organization }}, volume = {53}, year = {2008}, } @article{2675, abstract = {Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels that generate Ih currents are widely distributed in the brain and have been shown to contribute to various neuronal functions. In the present study, we investigated the functions of Ih in the motion-sensitive projection neurons [wide field vertical (WFV) cells] of the superior colliculus, a pivotal visual center for detection of and orientating to salient objects. Combination of whole cell recordings and immunohistochemical investigations suggested that HCN1 channels dominantly contribute to the Ih in WFV cells among HCN isoforms expressed in the superficial superior colliculus and mainly located on their expansive dendritic trees. We found that blocking Ih suppressed the initiation of short- and fixed-latency dendritic spike responses and led instead to long- and fluctuating-latency somatic spike responses to optic fiber stimulations. These results suggest that the dendritic Ih facilitates the dendritic initiation and/or propagation of action potentials and ensures that WFV cells generate spike responses to distal synaptic inputs in a sensitive and robustly time-locked manner, probably by acting as continuous depolarizing drive and fixing dendritic membrane potentials close to the spike threshold. These functions are different from known functions of dendritic Ih revealed in hippocampal and neocortical pyramidal cells, where they spatiotemporally limit the propagations of synaptic inputs along the apical dendrites by reducing dendritic membrane resistance. Thus we have revealed new functional aspects of Ih, and these dendritic properties are likely critical for visual motion processing in these neurons.}, author = {Endo, Toshiaki and Tarusawa, Etsuko and Notomi, Takuya and Kaneda, Katsuyuki and Hirabayashi, Masumi and Ryuichi Shigemoto and Isa, Tadashi}, journal = {Journal of Neurophysiology}, number = {5}, pages = {2066 -- 2076}, publisher = {American Physiological Society}, title = {{Dendritic Ih ensures high-fidelity dendritic spike responses of motion-sensitive neurons in rat superior colliculus}}, doi = {10.1152/jn.00556.2007}, volume = {99}, year = {2008}, } @article{2676, abstract = {Left-right (L-R) asymmetry is a fundamental feature of higher-order neural function. However, the molecular basis of brain asymmetry remains unclear. We recently reported L-R asymmetry of hippocampal circuitry caused by differential allocation of N-methyl-O-aspartate receptor (NMDAR) subunit GluRε2 (NR2B) in hippocambal synapses. Using electrophysiology and immunocytochemistry, here we analyzed the hippocampal circuitry of the inversus viscerum (iv) mouse that has a randomized laterality of internal organs. The iv mouse hippocampus lacks L-R asymmetry, it exhibits right isomerism in the synaptic distribution of the ε2 subunit, irrespective of the laterality of visceral organs. This independent right isomerism of the hippocampus is the first evidence that a distinct mechanism downstream of the iv mutation generates brain asymmetry.}, author = {Kawakami, Ryosuke and Dobi, Alice and Ryuichi Shigemoto and Ito, Isao}, journal = {PLoS One}, number = {4}, publisher = {Public Library of Science}, title = {{Right isomerism of the brain in inversus viscerum mutant mice}}, doi = {10.1371/journal.pone.0001945}, volume = {3}, year = {2008}, } @article{2677, abstract = {The medial septum (MS) is an indispensable component of the subcortical network which synchronizes the hippocampus at theta frequency during specific stages of information processing. GABAergic neurons exhibiting highly regular firing coupled to the hippocampal theta rhythm are thought to form the core of the MS rhythm-generating network. In recent studies the hyperpolarization-activated, cyclic nucleotide-gated non-selective cation (HCN) channel was shown to participate in theta synchronization of the medial septum. Here, we tested the hypothesis that HCN channel expression correlates with theta modulated firing behaviour of MS neurons by a combined anatomical and electrophysiological approach. HCN-expressing neurons represented a subpopulation of GABAergic cells in the MS partly overlapping with parvalbumin (PV)-containing neurons. Rhythmic firing in the theta frequency range was characteristic of all HCN-expressing neurons. In contrast, only a minority of HCN-negative cells displayed theta related activity. All HCN cells had tight phase coupling to hippocampal theta waves. As a group, PV-expressing HCN neurons had a marked bimodal phase distribution, whereas PV-immunonegative HCN neurons did not show group-level phase preference despite significant individual phase coupling. Microiontophoretic blockade of HCN channels resulted in the reduction of discharge frequency, but theta rhythmic firing was perturbed only in a few cases. Our data imply that HCN-expressing GABAergic neurons provide rhythmic drive in all phases of the hippocampal theta activity. In most MS theta cells rhythm genesis is apparently determined by interactions at the level of the network rather than by the pacemaking property of HCN channels alone.}, author = {Varga, Viktor and Hangya, Balázs and Kránitz, Kinga and Ludányi, Anikó and Zemankovics, Rita and Katona, István and Ryuichi Shigemoto and Freund, Tamás F and Borhegyi, Zsolt}, journal = {Journal of Physiology}, number = {16}, pages = {3893 -- 3915}, publisher = {Wiley-Blackwell}, title = {{The presence of pacemaker HCN channels identifies theta rhythmic GABAergic neurons in the medial septum}}, doi = {10.1113/jphysiol.2008.155242}, volume = {586}, year = {2008}, } @article{2678, abstract = {Mammalian retinas contain abundant neuronal gap junctions, particularly in the inner plexiform layer (IPL), where the two principal neuronal connexin proteins are Cx36 and Cx45. Currently undetermined are coupling relationships between these connexins and whether both are expressed together or separately in a neuronal subtype-specific manner. Although Cx45-expressing neurons strongly couple with Cx36-expressing neurons, possibly via heterotypic gap junctions, Cx45 and Cx36 failed to form functional heterotypic channels in vitro. We now show that Cx36 and Cx45 coexpressed in HeLa cells were colocalized in immunofluorescent puncta between contacting cells, demonstrating targeting/scaffolding competence for both connexins in vitro. However, Cx36 and Cx45 expressed separately did not form immunofluorescent puncta containing both connexins, supporting lack of heterotypic coupling competence. In IPL, 87% of Cx45-immunofluorescent puncta were colocalized with Cx36, supporting either widespread heterotypic coupling or bihomotypic coupling. Ultrastructurally, Cx45 was detected in 9% of IPL gap junction hemiplaques, 90-100% of which also contained Cx36, demonstrating connexin coexpression and cotargeting in virtually all IPL neurons that express Cx45. Moreover, double replicas revealed both connexins in separate domains mirrored on both sides of matched hemiplaques. With previous evidence that Cx36 interacts with PDZ1 domain of zonula occludens-1 (ZO-1), we show that Cx45 interacts with PDZ2 domain of ZO-1, and that Cx36, Cx45, and ZO-1 coimmunoprecipitate, suggesting that ZO-1 provides for coscaffolding of Cx45 with Cx36. These data document that in Cx45-expressing neurons of IPL, Cx45 is almost always accompanied by Cx36, forming "bihomotypic" gap junctions, with Cx45 structurally coupling to Cx45 and Cx36 coupling to Cx36.}, author = {Li, Xinbo and Kamasawa, Naomi and Ciolofan, Cristina and Olson, Carl O and Lu, Shijun and Davidson, Kimberly G and Yasumura, Thomas and Ryuichi Shigemoto and Rash, John E and Nagy, James I}, journal = {Journal of Neuroscience}, number = {39}, pages = {9769 -- 9789}, publisher = {Society for Neuroscience}, title = {{Connexin45-containing neuronal gap junctions in rodent retina also contain connexin36 in both apposing hemiplaques, forming bihomotypic gap junctions, with scaffolding contributed by zonula occludens-1}}, doi = {10.1523/JNEUROSCI.2137-08.2008}, volume = {28}, year = {2008}, } @article{2679, abstract = {Ionotropic glutamate receptors play important roles in spinal processing of nociceptive sensory signals and induction of central sensitization in chronic pain. Here we applied highly sensitive freeze-fracture replica labeling to laminae I-II of the spinal dorsal horn of rats and investigated the numbers, densities, and colocalization of AMPA- and NMDA-type glutamate receptors at individual postsynaptic membrane specializations with a high resolution. All glutamatergic postsynaptic membranes in laminae I-II expressed AMPA receptors, and most of them (96%) were also immunoreactive for the NR1 subunit of NMDA receptors. The numbers of gold particles for AMPA and NMDA receptors at individual postsynaptic membranes showed a linear correlation with the size of postsynaptic membrane specializations and varied in the range of 8-214 and 5-232 with median values of 37 and 28, whereas their densities varied in the range of 325-3365/μm 2 and 102-2263/μm 2 with median values of 1115/μm 2 and 777/μm 2, respectively. Virtually all (99%) glutamatergic postsynaptic membranes expressed GluR2, and most of them (87%) were also immunoreactive for GluR1. The numbers of gold particles for pan-AMPA, NR1, and GluR2 subunits showed a linear correlation with the size of postsynaptic surface areas. Concerning GluR1, there may be two populations of synapses with high and low GluR1 densities. In synapses larger than 0.1 μm 2, GluR1 subunits were recovered in very low numbers. Differential expression of GluR1 and GluR2 subunits suggests regulation of AMPA receptor subunit composition by presynaptic mechanism.}, author = {Antal, Miklós and Fukazawa, Yugo and Eördögh, Mária and Muszil, Dóra and Molnár, Elek and Itakura, Makoto and Takahashi, Masami and Ryuichi Shigemoto}, journal = {Journal of Neuroscience}, number = {39}, pages = {9692 -- 9701}, publisher = {Society for Neuroscience}, title = {{Numbers, densities, and colocalization of AMPA- and NMDA-type glutamate receptors at individual synapses in the superficial spinal dorsal horn of rats}}, doi = {10.1523/JNEUROSCI.1551-08.2008}, volume = {28}, year = {2008}, } @article{2681, abstract = {Left-right asymmetry of the brain has been studied mostly through psychological examination and functional imaging in primates, leaving its molecular and synaptic aspects largely unaddressed. Here, we show that hippocampal CA1 pyramidal cell synapses differ in size, shape, and glutamate receptor expression depending on the laterality of presynaptic origin. CA1 synapses receiving neuronal input from the right CA3 pyramidal cells are larger and have more perforated PSD and a GluR1 expression level twice as high as those receiving input from the left CA3. The synaptic density of GluR1 increases as the size of a synapse increases, whereas that of NR2B decreases because of the relatively constant NR2B expression in CA1 regardless of synapse size. Densities of other major glutamate receptor subunits show no correlation with synapse size, thus resulting in higher net expression in synapses having right input. Our study demonstrates universal left-right asymmetry of hippocampal synapses with a fundamental relationship between synaptic area and the expression of glutamate receptor subunits.}, author = {Shinohara, Yoshiaki and Hirase, Hajime and Watanabe, Masahiko and Itakura, Makoto and Takahashi, Masami and Ryuichi Shigemoto}, journal = {PNAS}, number = {49}, pages = {19498 -- 19503}, publisher = {National Academy of Sciences}, title = {{Left-right asymmetry of the hippocampal synapses with differential subunit allocation of glutamate receptors}}, doi = {10.1073/pnas.0807461105}, volume = {105}, year = {2008}, } @inproceedings{2702, abstract = {We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization. }, author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer}, pages = {167 -- 182}, publisher = {World Scientific Publishing}, title = {{Feynman graphs and renormalization in quantum diffusion}}, doi = {10.1142/9789812833556_0011}, year = {2008}, }