TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2333
TI - Ground-state energy of a dilute Fermi gas
VL - 412
ER -
TY - CONF
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Yngvason, Jakob
ED - Zambrini, Jean-Claude
ID - 2334
TI - One-dimensional behavior of dilute, trapped Bose gases in traps
ER -
TY - GEN
AB - We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2363
IS - 2
T2 - Communications in Mathematical Physics
TI - Derivation of the Gross-Pitaevskii equation for rotating Bose gases
VL - 264
ER -
TY - JOUR
AB - We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.
AU - Robert Seiringer
ID - 2364
IS - 3
JF - Reviews in Mathematical Physics
TI - A correlation estimate for quantum many-body systems at positive temperature
VL - 18
ER -
TY - JOUR
AB - We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.
AU - Robert Seiringer
ID - 2365
IS - 3
JF - Communications in Mathematical Physics
TI - The thermodynamic pressure of a dilute fermi gas
VL - 261
ER -
TY - JOUR
AB - Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2366
IS - 3
JF - Letters in Mathematical Physics
TI - Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
VL - 77
ER -
TY - CHAP
AB - The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.
AU - Robert Seiringer
ED - Dereziński, Jan
ED - Siedentop, Heinz
ID - 2368
T2 - Large Coulomb Systems
TI - Dilute, trapped Bose gases and Bose-Einstein condensation
VL - 695
ER -
TY - CHAP
AB - One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.
AU - Aizenman, Michael
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Asch, Joachim
ED - Joye, Alain
ID - 2369
T2 - Mathematical Physics of Quantum Mechanics
TI - Bose-Einstein condensation as a quantum phase transition in an optical lattice
VL - 690
ER -
TY - CHAP
AU - Bang-Jensen, Jørgen
AU - Reed, Bruce
AU - Schacht, Bruce
AU - Šámal, Robert
AU - Toft, Bjarne
AU - Uli Wagner
ID - 2416
T2 - Topics in Discrete Mathematics
TI - On six problems posed by Jarik Nešetřil
VL - 26
ER -
TY - JOUR
AB - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.
AU - Matoušek, Jiří
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
ID - 2429
IS - 2
JF - Discrete & Computational Geometry
TI - K-sets in four dimensions
VL - 35
ER -
TY - JOUR
AB - We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√̃) colors in the worst case. We then derive two efficient variants of this simple algorithm. The first is deterministic and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors with high probability. We also show that the O(log 2 n) bound on the number of colors used by our deterministic algorithm is tight on the worst case. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case.
AU - Chent, Ke
AU - Fiat, Amos
AU - Kaplan, Haim
AU - Levy, Meital B
AU - Matoušek, Jiří
AU - Mossel, Elchanan
AU - Pach, János
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
AU - Welzl, Emo
ID - 2430
IS - 5
JF - SIAM Journal on Computing
TI - Online conflict-free coloring for intervals
VL - 36
ER -
TY - CONF
AB - We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most t in an arrangement of n halfspaces in R , for arbitrary n and d (in particular, the dimension d is not considered constant). This partially settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based on the h-matrix of the arrangement (a generalization, introduced by Mulmuley, of the h-vector of a convex polytope). We show that bounding appropriate sums of entries of this matrix reduces to a lemma about quadrupels of sets with certain intersection properties, and we prove this lemma, up to a factor of 2, using tools from multilinear algebra. This extends an approach of Alon and Kalai, who used linear algebra methods for an alternative proof of the classical Upper Bound Theorem. The bounds for the entries of the h-matrix also imply bounds for the number of i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection with crossing numbers of graphs that was one of the main motivations for investigating exact bounds that are valid for arbitrary dimensions.
AU - Uli Wagner
ID - 2431
TI - On a geometric generalization of the Upper Bound Theorem
ER -
TY - JOUR
AB - The highest densities of the two metabotropic GABA subunits, GABA B1 and GABAB2, have been reported as occurring around the glutamatergic synapses between Purkinje cell spines and parallel fibre varicosities. In order to determine how this distribution is achieved during development, we investigated the expression pattern and the cellular and subcellular localization of the GABAB1 and GABAB2 subunits in the rat cerebellum during postnatal development. At the light microscopic level, immunoreactivity for the GABAB1 and GABAB2 subunits was very prominent in the developing molecular layer, especially in Purkinje cells. Using double immunofluorescence, we demonstrated that GABAB1 was transiently expressed in glial cells. At the electron microscopic level, immunoreactivity for GABAB receptors was always detected both pre- and postsynaptically. Presynaptically, GABAB1 and GABAB2 were localized in the extrasynaptic membrane of parallel fibres at all ages, and only rarely in GABAergic axons. Postsynaptically, GABAB receptors were localized to the extrasynaptic and perisynaptic plasma membrane of Purkinje cell dendrites and spines throughout development. Quantitative analysis and three-dimensional reconstructions further revealed a progressive developmental movement of the GABAB1 subunit on the surface of Purkinje cells from dendritic shafts to its final destination, the dendritic spines. Together, these results indicate that GABAB receptors undergo dynamic regulation during cerebellar development in association with the establishment and maturation of glutamatergic synapses to Purkinje cells.
AU - Luján, Rafael
AU - Ryuichi Shigemoto
ID - 2657
IS - 6
JF - European Journal of Neuroscience
TI - Localization of metabotropic GABA receptor subunits GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum
VL - 23
ER -
TY - JOUR
AB - Transmembrane AMPA receptor regulatory proteins (TARPs), including stargazin/γ-2, are associated with AMPA receptors and participate in their surface delivery and anchoring at the postsynaptic membrane. TARPs may also act as a positive modulator of the AMPA receptor ion channel function; however, little is known about other TARP members except for stargazin/γ-2. We examined the synaptic localization of stargazin/γ-2 and γ-8 by immunoelectron microscopy and biochemical analysis. The analysis of sodium dodecyl sulfate-digested freeze-fracture replica labeling revealed that stargazin/γ-2 was concentrated in the postsynaptic area, whereas γ-8 was distributed both in synaptic and extra-synaptic plasma membranes of the hippocampal neuron. When a synaptic plasma membrane-enriched brain fraction was treated with Triton X-100 and separated by sucrose density gradient ultracentrifugation, a large proportion of NMDA receptor and stargazin/γ-2 was accumulated in raft-enriched fractions, whereas AMPA receptor and γ-8 were distributed in both the raft-enriched fractions and other Triton-insoluble fractions. Phosphorylation of stargazin/γ-2 and γ-8 was regulated by different sets of kinases and phosphatases in cultured cortical neurons. These results suggested that stargazin/γ-2 and γ-8 have distinct roles in postsynaptic membranes under the regulation of different intracellular signaling pathways.
AU - Inamura, Mihoko
AU - Itakura, Makoto
AU - Okamoto, Hirotsugu
AU - Hoka, Sumio
AU - Mizoguchi, Akira
AU - Fukazawa, Yugo
AU - Ryuichi Shigemoto
AU - Yamamori, Saori
AU - Takahashi, Masami
ID - 2659
IS - 1
JF - Neuroscience Research
TI - Differential localization and regulation of stargazin-like protein, γ-8 and stargazin in the plasma membrane of hippocampal and cortical neurons
VL - 55
ER -
TY - JOUR
AB - Pavlovian fear conditioning, a simple form of associative learning, is thought to involve the induction of associative, NMDA receptor-dependent long-term potentiation (LTP) in the lateral amygdala. Using a combined genetic and electrophysiological approach, we show here that lack of a specific GABAB receptor subtype, GABAB(1a,2), unmasks a nonassociative, NMDA receptor-independent form of presynaptic LTP at cortico-amygdala afferents. Moreover, the level of presynaptic GABA B(1a,2) receptor activation, and hence the balance between associative and nonassociative forms of LTP, can be dynamically modulated by local inhibitory activity. At the behavioral level, genetic loss of GABA B(1a) results in a generalization of conditioned fear to nonconditioned stimuli. Our findings indicate that presynaptic inhibition through GABAB(1a,2) receptors serves as an activity-dependent constraint on the induction of homosynaptic plasticity, which may be important to prevent the generalization of conditioned fear.
AU - Shaban, Hamdy
AU - Humeau, Yann
AU - Herry, Cyril
AU - Cassasus, Guillaume
AU - Ryuichi Shigemoto
AU - Ciocchi, Stéphane
AU - Barbieri, Samuel
AU - Van Der Putten, Herman V
AU - Kaupmann, Klemens
AU - Bettler, Bernhard
AU - Lüthi, Andreas
ID - 2660
IS - 8
JF - Nature Neuroscience
TI - Generalization of amygdala LTP and conditioned fear in the absence of presynaptic inhibition
VL - 9
ER -
TY - JOUR
AB - GABAB receptors are the G protein-coupled receptors for the main inhibitory neurotransmitter in the brain, γ-aminobutyric acid (GABA). Molecular diversity in the GABAB system arises from the GABAB1a and GABAB1b subunit isoforms that solely differ in their ectodomains by a pair of sushi repeats that is unique to GABAB1a. Using a combined genetic, physiological, and morphological approach, we now demonstrate that GABAB1 isoforms localize to distinct synaptic sites and convey separate functions in vivo. At hippocampal CA3-to-CA1 synapses, GABAB1a assembles heteroreceptors inhibiting glutamate release, while predominantly GABAB1b mediates postsynaptic inhibition. Electron microscopy reveals a synaptic distribution of GABAB1 isoforms that agrees with the observed functional differences. Transfected CA3 neurons selectively express GABAB1a in distal axons, suggesting that the sushi repeats, a conserved protein interaction motif, specify heteroreceptor localization. The constitutive absence of GABAB1a but not GABAB1b results in impaired synaptic plasticity and hippocampus-dependent memory, emphasizing molecular differences in synaptic GABAB functions.
AU - Vigot, Réjan
AU - Barbieri, Samuel
AU - Bräuner-Osborne, Hans
AU - Tureček, Rostislav
AU - Ryuichi Shigemoto
AU - Zhang, Yan Ping
AU - Luján, Rafael
AU - Jacobson, Laura H
AU - Biermann, Barbara
AU - Fritschy, Jean-Marc
AU - Vacher, Claire-Marie
AU - Müller, Matthias P
AU - Sansig, Gilles
AU - Guetg, Nicole
AU - Cryan, John F
AU - Kaupmann, Klemens
AU - Gassmann, Martin
AU - Oertner, Thomas G
AU - Bettler, Bernhard
ID - 2661
IS - 4
JF - Neuron
TI - Differential Compartmentalization and Distinct Functions of GABAB Receptor Variants
VL - 50
ER -
TY - JOUR
AB - G-protein-coupled inwardly rectifying K+ channels (Kir3 channels) coupled to metabotropic GABAB receptors are essential for the control of neuronal excitation. To determine the distribution of Kir3 channels and their spatial relationship to GABAB receptors on hippocampal pyramidal cells, we used a high-resolution immunocytochemical approach. Immunoreactivity for the Kir3.2 subunit was most abundant postsynaptically and localized to the extrasynaptic plasma membrane of dendritic shafts and spines of principal cells. Quantitative analysis of immunogold particles for Kir3.2 revealed an enrichment of the protein around putative glutamatergic synapses on dendritic spines, similar to that of GABA B1. Consistent with this observation, a high degree of coclustering of Kir3.2 and GABAB1 was revealed around excitatory synapses by the highly sensitive SDS-digested freeze-fracture replica immunolabeling. In contrast, in dendritic shafts receptors and channels were found to be mainly segregated. These results suggest that Kir3.2-containing K+ channels on dendritic spines preferentially mediate the effect of GABA, whereas channels on dendritic shafts are likely to be activated by other neurotransmitters as well. Thus, Kir3 channels, localized to different subcellular compartments of hippocampal principal cells, appear to be differentially involved in synaptic integration in pyramidal cell dendrites.
AU - Kulik, Ákos
AU - Vida, Imre
AU - Fukazawa, Yugo
AU - Guetg, Nicole
AU - Kasugai, Yu
AU - Marker, Cheryl L
AU - Rigato, Franck
AU - Bettler, Bernhard
AU - Wickman, Kevin D
AU - Frotscher, Michael
AU - Ryuichi Shigemoto
ID - 2662
IS - 16
JF - Journal of Neuroscience
TI - Compartment-dependent colocalization of Kir3.2-containing K+ channels and GABAB receptors in hippocampal pyramidal cells
VL - 26
ER -
TY - JOUR
AB - The rocker mice are hereditary ataxic mutants that carry a point mutation in the gene encoding the CaV2.1 (P/Q-type) Ca2+ channel α1 subunit, and show the mildest symptoms among the reported CaV2.1 mutant mice. We studied the basic characteristics of the rocker mutant Ca2+ channel and their impacts on excitatory synaptic transmission in cerebellar Purkinje cells (PCs). In acutely dissociated PC somas, the rocker mutant channel showed a moderate reduction in Ca2+ channel current density, whereas its kinetics and voltage dependency of gating remained nearly normal. Despite the small changes in channel function, synaptic transmission in the parallel fiber (PF)-PC synapses was severely impaired. The climbing fiber inputs onto PCs showed a moderate impairment but could elicit normal complex spikes. Presynaptic function of the PF-PC synapses, however, was unexpectedly almost normal in terms of paired-pulse facilitation, sensitivity to extracellular Ca2+ concentration and glutamate concentration in synaptic clefts. Electron microscopic analyses including freeze-fracture replica labeling revealed that both the number and density of postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors substantially decreased without gross structural changes of the PF-PC synapses. We also observed an abnormal arborization of PC dendrites in young adult rocker mice (∼ 1 month old). These lines of evidence suggest that even a moderate dysfunction of CaV2.1 Ca2+ channel can cause substantial changes in postsynaptic molecular composition of the PF-PC synapses and dendritic structure of PCs.
AU - Kodama, Takashi
AU - Itsukaichi-Nishida, Yuko
AU - Fukazawa, Yugo
AU - Wakamori, Minoru
AU - Miyata, Mariko
AU - Molnár, Elek
AU - Mori, Yasuo
AU - Ryuichi Shigemoto
AU - Imoto, Keiji
ID - 2663
IS - 11
JF - European Journal of Neuroscience
TI - A CaV2.1 calcium channel mutation rocker reduces the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses
VL - 24
ER -
TY - GEN
AB - Metabotropic glutamate receptors (mGlus) are a family of G-protein-coupled receptors activated by the neurotransmitter glutamate. Molecular cloning has revealed eight different subtypes (mGlu1-8) with distinct molecular and pharmacological properties. Multiplicity in this receptor family is further generated through alternative splicing. mGlus activate a multitude of signalling pathways important for modulating neuronal excitability, synaptic plasticity and feedback regulation of neurotransmitter release. In this review, we summarize anatomical findings (from our work and that of other laboratories) describing their distribution in the central nervous system. Recent evidence regarding the localization of these receptors in peripheral tissues will also be examined. The distinct regional, cellular and subcellular distribution of mGlus in the brain will be discussed in view of their relationship to neurotransmitter release sites and of possible functional implications.
AU - Ferraguti, Francesco
AU - Ryuichi Shigemoto
ID - 2664
IS - 2
T2 - Cell and Tissue Research
TI - Metabotropic glutamate receptors
VL - 326
ER -
TY - JOUR
AB - We consider the dynamics of N boson systems interacting through a pair potential N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices [InlineMediaObject not available: see fulltext.] solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5, we prove that as N→∞ the limit points of the k-particle density matrices of Ψ N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of this hierarchy remains an open question.
AU - Elgart, Alexander
AU - László Erdös
AU - Schlein, Benjamin
AU - Yau, Horng-Tzer
ID - 2745
IS - 2
JF - Archive for Rational Mechanics and Analysis
TI - Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
VL - 179
ER -