TY - JOUR
AB - We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2397
IS - 2
JF - Letters in Mathematical Physics
TI - Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs
VL - 100
ER -
TY - GEN
AB - We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.
AU - Jakšić, Vojkan
AU - Ogata, Yoshiko
AU - Pillet, Claude A
AU - Robert Seiringer
ID - 2398
IS - 6
T2 - Reviews in Mathematical Physics
TI - Quantum hypothesis testing and non-equilibrium statistical mechanics
VL - 24
ER -
TY - CHAP
AB - Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.
AU - Robert Seiringer
ED - Rivasseau, Vincent
ED - Robert Seiringer
ED - Solovej, Jan P
ED - Spencer, Thomas
ID - 2399
T2 - Quantum Many Body Systems
TI - Cold quantum gases and bose einstein condensation
VL - 2051
ER -
TY - JOUR
AB - We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior.
AU - Timothy Browning
AU - Valckenborgh, K Van
ID - 240
IS - 2
JF - Experimental Mathematics
TI - Sums of three squareful numbers
VL - 21
ER -
TY - JOUR
AB - If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2400
IS - 2
JF - Communications in Mathematical Physics
TI - Binding of polarons and atoms at threshold
VL - 313
ER -
TY - JOUR
AB - We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞].
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2401
IS - 1
JF - Journal of Statistical Physics
TI - Further implications of the Bessis-Moussa-Villani conjecture
VL - 149
ER -
TY - JOUR
AB - We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power.
AU - Frank, Rupert L
AU - Robert Seiringer
ID - 2402
IS - 9
JF - Journal of Mathematical Physics
TI - Lieb-Thirring inequality for a model of particles with point interactions
VL - 53
ER -
TY - JOUR
AB - We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.
AU - Robert Seiringer
AU - Yngvason, Jakob
AU - Zagrebnov, Valentin A
ID - 2403
IS - 11
JF - Journal of Statistical Mechanics Theory and Experiment
TI - Disordered Bose-Einstein condensates with interaction in one dimension
VL - 2012
ER -
TY - JOUR
AB - The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 241
IS - 2
JF - Israel Journal of Mathematics
TI - Binary forms as sums of two squares and Châtelet surfaces
VL - 191
ER -
TY - JOUR
AB - The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.
AU - Ebersberger, Ingo
AU - De Matos Simoes, Ricardo
AU - Kupczok, Anne
AU - Gube, Matthias
AU - Kothe, Erika
AU - Voigt, Kerstin
AU - Von Haeseler, Arndt
ID - 2411
IS - 5
JF - Molecular Biology and Evolution
TI - A consistent phylogenetic backbone for the fungi
VL - 29
ER -
TY - JOUR
AB - We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n).
AU - Baier, Stephan
AU - Timothy Browning
AU - Marasingha, Gihan
AU - Zhao, Liangyi
ID - 242
IS - 3
JF - Proceedings of the Edinburgh Mathematical Society
TI - Averages of shifted convolutions of d3 (n)
VL - 55
ER -
TY - JOUR
AB - Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.
AU - Timothy Browning
AU - Heath-Brown, Roger
ID - 243
IS - 5
JF - Geometric and Functional Analysis
TI - Quadratic polynomials represented by norm forms
VL - 22
ER -
TY - JOUR
AB - The colored Tverberg theorem asserts that for eve;ry d and r there exists t=t(d,r) such that for every set C ⊂ ℝ d of cardinality (d + 1)t, partitioned into t-point subsets C 1, C 2,...,C d+1 (which we think of as color classes; e. g., the points of C 1 are red, the points of C 2 blue, etc.), there exist r disjoint sets R 1, R 2,...,R r⊆C that are rainbow, meaning that {pipe}R i∩C j{pipe}≤1 for every i,j, and whose convex hulls all have a common point. All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojević, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof more concrete and intuitive, and accessible to a wider audience.
AU - Matoušek, Jiří
AU - Martin Tancer
AU - Uli Wagner
ID - 2438
IS - 2
JF - Discrete & Computational Geometry
TI - A geometric proof of the colored Tverberg theorem
VL - 47
ER -
TY - JOUR
AB - A Monte Carlo approximation algorithm for the Tukey depth problem in high dimensions is introduced. The algorithm is a generalization of an algorithm presented by Rousseeuw and Struyf (1998) . The performance of this algorithm is studied both analytically and experimentally.
AU - Chen, Dan
AU - Morin, Pat
AU - Uli Wagner
ID - 2439
IS - 5
JF - Computational Geometry: Theory and Applications
TI - Absolute approximation of Tukey depth: Theory and experiments
VL - 46
ER -
TY - JOUR
AB - We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.
AU - Timothy Browning
AU - Haynes, Alan K
ID - 244
IS - 2
JF - International Journal of Number Theory
TI - Incomplete kloosterman sums and multiplicative inverses in short intervals
VL - 9
ER -
TY - CONF
AB - We present an algorithm for computing [X, Y], i.e., all homotopy classes of continuous maps X → Y, where X, Y are topological spaces given as finite simplicial complexes, Y is (d - 1)-connected for some d ≥ 2 (for example, Y can be the d-dimensional sphere S d), and dim X ≤ 2d - 2. These conditions on X, Y guarantee that [X, Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds generators and relations for it. We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology). We hope that a further extension of the methods developed here will yield an algorithm for computing, in some cases of interest, the ℤ 2-index, which is a quantity playing a prominent role in Borsuk-Ulam style applications of topology in combinatorics and geometry, e.g., in topological lower bounds for the chromatic number of a graph. In a certain range of dimensions, deciding the embeddability of a simplicial complex into ℝ d also amounts to a ℤ 2-index computation. This is the main motivation of our work. We believe that investigating the computational complexity of questions in homotopy theory and similar areas presents a fascinating research area, and we hope that our work may help bridge the cultural gap between algebraic topology and theoretical computer science.
AU - Čadek, Martin
AU - Marek Krcál
AU - Matoušek, Jiří
AU - Sergeraert, Francis
AU - Vokřínek, Lukáš
AU - Uli Wagner
ID - 2440
TI - Computing all maps into a sphere
ER -
TY - CONF
AB - Eigenvalues associated to graphs are a well-studied subject. In particular the spectra of the adjacency matrix and of the Laplacian of random graphs G(n, p) are known quite precisely. We consider generalizations of these matrices to simplicial complexes of higher dimensions and study their eigenvalues for the Linial-Meshulam model X k(n, p) of random k-dimensional simplicial complexes on n vertices. We show that for p = Ω(log n/n), the eigenvalues of both, the higher-dimensional adjacency matrix and the Laplacian, are a.a.s. sharply concentrated around two values. In a second part of the paper, we discuss a possible higherdimensional analogue of the Discrete Cheeger Inequality. This fundamental inequality expresses a close relationship between the eigenvalues of a graph and its combinatorial expansion properties; in particular, spectral expansion (a large eigenvalue gap) implies edge expansion. Recently, a higher-dimensional analogue of edge expansion for simplicial complexes was introduced by Gromov, and independently by Linial, Meshulam and Wallach and by Newman and Rabinovich. It is natural to ask whether there is a higher-dimensional version of Cheeger's inequality. We show that the most straightforward version of a higher-dimensional Cheeger inequality fails: for every k > 1, there is an infinite family of k-dimensional complexes that are spectrally expanding (there is a large eigenvalue gap for the Laplacian) but not combinatorially expanding.
AU - Gundert, Anna
AU - Uli Wagner
ID - 2441
TI - On Laplacians of random complexes
ER -
TY - JOUR
AB - Constitutive endocytic recycling is a crucial mechanism allowing regulation of the activity of proteins at the plasma membrane and for rapid changes in their localization, as demonstrated in plants for PIN-FORMED (PIN) proteins, the auxin transporters. To identify novel molecular components of endocytic recycling, mainly exocytosis, we designed a PIN1-green fluorescent protein fluorescence imaging-based forward genetic screen for Arabidopsis thaliana mutants that showed increased intracellular accumulation of cargos in response to the trafficking inhibitor brefeldin A (BFA). We identified bex5 (for BFA-visualized exocytic trafficking defective), a novel dominant mutant carrying a missense mutation that disrupts a conserved sequence motif of the small GTPase, RAS GENES FROM RAT BRAINA1b. bex5 displays defects such as enhanced protein accumulation in abnormal BFA compartments, aberrant endosomes, and defective exocytosis and transcytosis. BEX5/RabA1b localizes to trans-Golgi network/early endosomes (TGN/EE) and acts on distinct trafficking processes like those regulated by GTP exchange factors on ADP-ribosylation factors GNOM-LIKE1 and HOPM INTERACTOR7/BFA-VISUALIZED ENDOCYTIC TRAFFICKING DEFECTIVE1, which regulate trafficking at the Golgi apparatus and TGN/EE, respectively. All together, this study identifies Arabidopsis BEX5/RabA1b as a novel regulator of protein trafficking from a TGN/EE compartment to the plasma membrane.
AU - Feraru, Elena
AU - Feraru, Mugurel Ioan
AU - Asaoka, Rin
AU - Paciorek, Tomasz
AU - De Rycke, Riet M
AU - Tanaka, Hirokazu
AU - Nakano, Akihiko
AU - Jirí Friml
ID - 2453
IS - 7
JF - Plant Cell
TI - BEX5/RabA1b regulates trans-Golgi network-to-plasma membrane protein trafficking in Arabidopsis
VL - 24
ER -
TY - JOUR
AB - The third EMBO Conference on Plant Molecular Biology, which focused on ‘Plant development and environmental interactions’,was held in May 2012 in Matera, Italy. Here, we review some of the topics and themes that emerged from the various contributions; namely, steering technologies, transcriptional networks and hormonal regulation, small RNAs, cell and tissue polarity, environmental control and natural variation. We intend to provide the reader who might have missed this remarkable event with a glimpse of the recent progress made in this blossoming research field.
AU - Beeckman, Tom
AU - Friml, Jirí
ID - 2456
IS - 20
JF - Development
TI - Plant developmental biologists meet on stairways in Matera
VL - 139
ER -
TY - JOUR
AB - Initiation and successive development of organs induce mechanical stresses at the cellular level. Using the tomato shoot apex, a new study now proposes that mechanical strain regulates the plasma membrane abundance of the PIN1 auxin transporter, thereby reinforcing a positive feed-back loop between growth and auxin accumulation.
AU - Li, Hongjiang
AU - Friml, Jirí
AU - Grunewald, Wim
ID - 2458
IS - 16
JF - Current Biology
TI - Cell polarity: Stretching prevents developmental cramps
VL - 22
ER -
TY - JOUR
AB - Coordinated, subcellular trafficking of proteins is one of the fundamental properties of the multicellular eukaryotic organisms. Trafficking involves a large diversity of compartments, pathways, cargo molecules, and vesicle-sorting events. It is also crucial in regulating the localization and, thus, the activity of various proteins, but the process is still poorly genetically defined in plants. In the past, forward genetics screens had been used to determine the function of genes by searching for a specific morphological phenotype in the organism population in which mutations had been induced chemically or by irradiation. Unfortunately, these straightforward genetic screens turned out to be limited in identifying new regulators of intracellular protein transport, because mutations affecting essential trafficking pathways often lead to lethality. In addition, the use of these approaches has been restricted by functional redundancy among trafficking regulators. Screens for mutants that rely on the observation of changes in the cellular localization or dynamics of fluorescent subcellular markers enable, at least partially, to circumvent these issues. Hence, such image-based screens provide the possibility to identify either alleles with weak effects or components of the subcellular trafficking machinery that have no strong impact on the plant growth.
AU - Zwiewka, Marta
AU - Friml, Jirí
ID - 2459
IS - May
JF - Frontiers in Plant Science
TI - Fluorescence imaging-based forward genetic screens to identify trafficking regulators in plants
VL - 3
ER -
TY - JOUR
AB - Interneurons are critical for neuronal circuit function, but how their dendritic morphologies and membrane properties influence information flow within neuronal circuits is largely unknown. We studied the spatiotemporal profile of synaptic integration and short-term plasticity in dendrites of mature cerebellar stellate cells by combining two-photon guided electrical stimulation, glutamate uncaging, electron microscopy, and modeling. Synaptic activation within thin (0.4 μm) dendrites produced somatic responses that became smaller and slower with increasing distance from the soma, sublinear subthreshold input-output relationships, and a somatodendritic gradient of short-term plasticity. Unlike most studies showing that neurons employ active dendritic mechanisms, we found that passive cable properties of thin dendrites determine the sublinear integration and plasticity gradient, which both result from large dendritic depolarizations that reduce synaptic driving force. These integrative properties allow stellate cells to act as spatiotemporal filters of synaptic input patterns, thereby biasing their output in favor of sparse presynaptic activity. Stellate cells are critical sources of inhibition in the cerebellum, but how their dendrites integrate excitatory synaptic inputs is unknown. Abrahamsson et al. show that thin dendrites and passive membrane properties of SCs promote sublinear synaptic summation and distance-dependent short-term plasticity.
AU - Abrahamsson, Therese
AU - Cathala, Laurence
AU - Matsui, Ko
AU - Ryuichi Shigemoto
AU - DiGregorio, David A
ID - 2474
IS - 6
JF - Neuron
TI - Thin dendrites of cerebellar interneurons confer sublinear synaptic integration and a gradient of short-term plasticity
VL - 73
ER -
TY - JOUR
AB - Background: One of the best-characterized causative factors of Alzheimer's disease (AD) is the generation of amyloid-β peptide (Aβ). AD subjects are at high risk of epileptic seizures accompanied by aberrant neuronal excitability, which in itself enhances Aβ generation. However, the molecular linkage between epileptic seizures and Aβ generation in AD remains unclear. Results: X11 and X11-like (X11L) gene knockout mice suffered from epileptic seizures, along with a malfunction of hyperpolarization-activated cyclic nucleotide gated (HCN) channels. Genetic ablation of HCN1 in mice and HCN1 channel blockage in cultured Neuro2a (N2a) cells enhanced Aβ generation. Interestingly, HCN1 levels dramatically decreased in the temporal lobe of cynomolgus monkeys (Macaca fascicularis) during aging and were significantly diminished in the temporal lobe of sporadic AD patients. Conclusion: Because HCN1 associates with amyloid-β precursor protein (APP) and X11/X11L in the brain, genetic deficiency of X11/X11L may induce aberrant HCN1 distribution along with epilepsy. Moreover, the reduction in HCN1 levels in aged primates may contribute to augmented Aβ generation. Taken together, HCN1 is proposed to play an important role in the molecular linkage between epileptic seizures and Aβ generation, and in the aggravation of sporadic AD.
AU - Saito, Yuhki
AU - Inoue, Tsuyoshi
AU - Zhu, Gang
AU - Kimura, Naoki
AU - Okada, Motohiro
AU - Nishimura, Masaki
AU - Murayama, Shigeo
AU - Kaneko, Sunao
AU - Ryuichi Shigemoto
AU - Imoto, Keiji
AU - Suzuki, Toshiharu
ID - 2475
IS - 1
JF - Molecular Neurodegeneration
TI - Hyperpolarization-activated cyclic nucleotide gated channels: A potential molecular link between epileptic seizures and Aβ generation in Alzheimer's disease
VL - 7
ER -
TY - JOUR
AB - Recently developed pharmacogenetic and optogenetic approaches, with their own advantages and disadvantages, have become indispensable tools in modern neuroscience. Here, we employed a previously described knock-in mouse line (GABA ARγ2 77Ilox) in which the γ2 subunit of the GABA A receptor (GABA AR) was mutated to become zolpidem insensitive (γ2 77I) and used viral vectors to swap γ2 77I with wild-type, zolpidem-sensitive γ2 subunits (γ2 77F). The verification of unaltered density and subcellular distribution of the virally introduced γ2 subunits requires their selective labelling. For this we generated six N- and six C-terminal-tagged γ2 subunits, with which cortical cultures of GABA ARγ2 -/- mice were transduced using lentiviruses. We found that the N-terminal AU1 tag resulted in excellent immunodetection and unimpaired synaptic localization. Unaltered kinetic properties of the AU1-tagged γ2 ( AU1γ2 77F) channels were demonstrated with whole-cell patch-clamp recordings of spontaneous IPSCs from cultured cells. Next, we carried out stereotaxic injections of lenti- and adeno-associated viruses containing Cre-recombinase and the AU1γ2 77F subunit (Cre-2A- AU1γ2 77F) into the neocortex of GABA ARγ2 77Ilox mice. Light microscopic immunofluorescence and electron microscopic freeze-fracture replica immunogold labelling demonstrated the efficient immunodetection of the AU1 tag and the normal enrichment of the AU1γ2 77F subunits in perisomatic GABAergic synapses. In line with this, miniature and action potential-evoked IPSCs whole-cell recorded from transduced cells had unaltered amplitudes, kinetics and restored zolpidem sensitivity. Our results obtained with a wide range of structural and functional verification methods reveal unaltered subcellular distributions and functional properties of γ2 77I and AU1γ2 77F GABA ARs in cortical pyramidal cells. This transgenic-viral pharmacogenetic approach has the advantage that it does not require any extrinsic protein that might endow some unforeseen alterations of the genetically modified cells. In addition, this virus-based approach opens up the possibility of modifying multiple cell types in distinct brain regions and performing alternative recombination-based intersectional genetic manipulations.
AU - Sümegi, Máté
AU - Fukazawa, Yugo
AU - Matsui, Ko
AU - Lörincz, Andrea
AU - Eyre, Mark D
AU - Nusser, Zoltán
AU - Ryuichi Shigemoto
ID - 2476
IS - 7
JF - Journal of Physiology
TI - Virus-mediated swapping of zolpidem-insensitive with zolpidem-sensitive GABA A receptors in cortical pyramidal cells
VL - 590
ER -
TY - JOUR
AB - Dynamic activity of glia has repeatedly been demonstrated, but if such activity is independent from neuronal activity, glia would not have any role in the information processing in the brain or in the generation of animal behavior. Evidence for neurons communicating with glia is solid, but the signaling pathway leading back from glial-to-neuronal activity was often difficult to study. Here, we introduced a transgenic mouse line in which channelrhodopsin-2, a light-gated cation channel, was expressed in astrocytes. Selective photostimulation of these astrocytes in vivo triggered neuronal activation. Using slice preparations, we show that glial photostimulation leads to release of glutamate, which was sufficient to activate AMPA receptors on Purkinje cells and to induce long-term depression of parallel fiber-to-Purkinje cell synapses through activation of metabotropic glutamate receptors. In contrast to neuronal synaptic vesicular release, glial activation likely causes preferential activation of extrasynaptic receptors that appose glial membrane. Finally, we show that neuronal activation by glial stimulation can lead to perturbation of cerebellar modulated motor behavior. These findings demonstrate that glia can modulate the tone of neuronal activity and behavior. This animal model is expected to be a potentially powerful approach to study the role of glia in brain function.
AU - Sasaki, Takuya
AU - Beppu, Kaoru
AU - Tanaka, Kenji F
AU - Fukazawa, Yugo
AU - Ryuichi Shigemoto
AU - Matsui, Ko
ID - 2477
IS - 50
JF - PNAS
TI - Application of an optogenetic byway for perturbing neuronal activity via glial photostimulation
VL - 109
ER -
TY - JOUR
AB - Visual information must be relayed through the lateral geniculate nucleus before it reaches the visual cortex. However, not all spikes created in the retina lead to postsynaptic spikes and properties of the retinogeniculate synapse contribute to this filtering. To understand the mechanisms underlying this filtering process, we conducted electrophysiology to assess the properties of signal transmission in the Long-Evans rat. We also performed SDS-digested freeze-fracture replica labeling to quantify the receptor and transporter distribution, as well as EM reconstruction to describe the 3D structure. To analyze the impact of transmitter diffusion on the activity of the receptors, simulations were integrated. We identified that a large contributor to the filtering is the marked paired-pulse depression at this synapse, which was intensified by the morphological characteristics of the contacts. The broad presynaptic and postsynaptic contact area restricts transmitter diffusion two dimensionally. Additionally, the presence of multiple closely arranged release sites invites intersynaptic spillover, which causes desensitization of AMPA receptors. The presence of AMPA receptors that slowly recover from desensitization along with the high presynaptic release probability and multivesicular release at each synapse also contribute to the depression. These features contrast with many other synapses where spatiotemporal spread of transmitter is limited by rapid transmitter clearance allowing synapses to operate more independently. We propose that the micrometer-order structure can ultimately affect the visual information processing.
AU - Budisantoso, Timotheus
AU - Matsui, Ko
AU - Kamasawa, Naomi
AU - Fukazawa, Yugo
AU - Ryuichi Shigemoto
ID - 2514
IS - 7
JF - Journal of Neuroscience
TI - Mechanisms underlying signal filtering at a multisynapse contact
VL - 32
ER -
TY - JOUR
AB - We investigated the temporal and spatial expression of SK2 in the developing mouse hippocampus using molecular and biochemical techniques, quantitative immunogold electron microscopy, and electrophysiology. The mRNA encoding SK2 was expressed in the developing and adult hippocampus. Western blotting and immunohistochemistry showed that SK2 protein increased with age. This was accompanied by a shift in subcellular localization. Early in development (P5), SK2 was predominantly localized to the endoplasmic reticulum in the pyramidal cell layer. But by P30 SK2 was almost exclusively expressed in the dendrites and spines. The level of SK2 at the postsynaptic density (PSD) also increased during development. In the adult, SK2 expression on the spine plasma membrane showed a proximal-to-distal gradient. Consistent with this redistribution and gradient of SK2, the selective SK channel blocker apamin increased evoked excitatory postsynaptic potentials (EPSPs) only in CA1 pyramidal neurons from mice older than P15. However, the effect of apamin on EPSPs was not different between synapses in proximal or distal stratum radiatum or stratum lacunosum-moleculare in adult. These results show a developmental increase and gradient in SK2-containing channel surface expression that underlie their influence on neurotransmission, and that may contribute to increased memory acquisition during early development.
AU - Ballesteros-Merino, Carmen
AU - Lin, Michael
AU - Wu, Wendy W
AU - Ferrándiz-Huertas, Clotilde
AU - Cabañero, María José
AU - Watanabe, Masahiko
AU - Fukazawa, Yugo
AU - Ryuichi Shigemoto
AU - Maylie, James G
AU - Adelman, John P
AU - Luján, Rafael
ID - 2515
IS - 6
JF - Hippocampus
TI - Developmental profile of SK2 channel expression and function in CA1 neurons
VL - 22
ER -
TY - JOUR
AB - Left-right asymmetry of human brain function has been known for a century, although much of molecular and cellular basis of brain laterality remains to be elusive. Recent studies suggest that hippocampal CA3-CA1 excitatory synapses are asymmetrically arranged, however, the functional implication of the asymmetrical circuitry has not been studied at the behavioral level. In order to address the left-right asymmetry of hippocampal function in behaving mice, we analyzed the performance of "split-brain" mice in the Barnes maze. The "split-brain" mice received ventral hippocampal commissure and corpus callosum transection in addition to deprivation of visual input from one eye. In such mice, the hippocampus in the side of visual deprivation receives sensory-driven input. Better spatial task performance was achieved by the mice which were forced to use the right hippocampus than those which were forced to use the left hippocampus. In two-choice spatial maze, forced usage of left hippocampus resulted in a comparable performance to the right counterpart, suggesting that both hippocampal hemispheres are capable of conducting spatial learning. Therefore, the results obtained from the Barnes maze suggest that the usage of the right hippocampus improves the accuracy of spatial memory. Performance of non-spatial yet hippocampus-dependent tasks (e.g. fear conditioning) was not influenced by the laterality of the hippocampus.
AU - Shinohara, Yoshiaki
AU - Hosoya, Aki
AU - Yamasaki, Nobuyuki
AU - Ahmed, Hassan
AU - Hattori, Satoko
AU - Eguchi, Megumi
AU - Yamaguchi, Shun
AU - Miyakawa, Tsuyoshi
AU - Hirase, Hajime
AU - Ryuichi Shigemoto
ID - 2687
IS - 2
JF - Hippocampus
TI - Right-hemispheric dominance of spatial memory in split-brain mice
VL - 22
ER -
TY - JOUR
AB - To gain insights into structure-function relationship of excitatory synapses, we revisit our quantitative analysis of synaptic AMPAR by highly sensitive freeze-fracture replica labeling in eight different connections. All of these connections showed linear correlation between synapse size and AMPAR number indicating a common intra-synapse-type relationship in CNS synapses. On the contrary, inter-synapse-type relationship is unexpected indicating no correlation between averages of synapse size and AMPAR number. Interestingly, connections with large average synapse size and low AMPAR density showed high variability of AMPAR number and mosaic distribution within the postsynaptic membrane. We propose an idea that these connections may quickly exhibit synaptic plasticity by modifying AMPAR density/number whereas those with high AMPAR density change their efficacy by modifying synapse size.
AU - Fukazawa, Yugo
AU - Ryuichi Shigemoto
ID - 2688
IS - 3
JF - Current Opinion in Neurobiology
TI - Intra-synapse-type and inter-synapse-type relationships between synaptic size and AMPAR expression
VL - 22
ER -
TY - JOUR
AB - R-type calcium channels (RTCCs) are well known for their role in synaptic plasticity, but little is known about their subcellular distribution across various neuronal compartments. Using subtype-specific antibodies, we characterized the regional and subcellular localization of Ca v2.3 in mice and rats at both light and electron microscopic levels. Ca v2.3 immunogold particles were found to be predominantly presynaptic in the interpeduncular nucleus, but postsynaptic in other brain regions. Serial section analysis of electron microscopic images from the hippocampal CA1 revealed a higher density of immunogold particles in the dendritic shaft plasma membrane compared with the pyramidal cell somata. However, the labeling densities were not significantly different among the apical, oblique, or basal dendrites. Immunogold particles were also observed over the plasma membrane of dendritic spines, including both synaptic and extrasynaptic sites. Individual spine heads contained <20 immunogold particles, with an average density of ~260 immunoparticles per μm 3 spine head volume, in accordance with the density of RTCCs estimated using calcium imaging (Sabatini and Svoboda, 2000). The Ca v2.3 density was variable among similar-sized spine heads and did not correlate with the density in the parent dendrite, implying that spines are individual calcium compartments operating autonomously from their parent dendrites.
AU - Parajuli, Laxmi K
AU - Nakajima, Chikako
AU - Kulik, Ákos
AU - Matsui, Ko
AU - Schneider, Toni
AU - Ryuichi Shigemoto
AU - Fukazawa, Yugo
ID - 2689
IS - 39
JF - Journal of Neuroscience
TI - Quantitative regional and ultra structural localization of the Ca v2 3 subunit of R type calcium channel in mouse brain
VL - 32
ER -
TY - GEN
AU - László Erdös
ID - 2696
T2 - ArXiv
TI - Universality for random matrices and log-gases
ER -
TY - CONF
AU - László Erdös
ID - 2700
TI - Lecture notes on quantum Brownian motion
VL - 95
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.
AU - Chatterjee, Krishnendu
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 2715
TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
VL - 18
ER -
TY - JOUR
AB - Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that c ≤ N σ ij 2 ≤ c -1 for some constant c > 0, we prove that, in the limit N → ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M -1.
AU - László Erdös
AU - Yau, Horng-Tzer
AU - Yin, Jun
ID - 2767
IS - 1-2
JF - Probability Theory and Related Fields
TI - Bulk universality for generalized Wigner matrices
VL - 154
ER -
TY - JOUR
AB - We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i. e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum.
AU - László Erdös
AU - Hasler, David G
ID - 2768
IS - 2
JF - Communications in Mathematical Physics
TI - Wegner estimate and Anderson localization for random magnetic fields
VL - 309
ER -
TY - JOUR
AB - We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {X J} N j=1 are close to their classical location {y j} N j=1 determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that E|x j - γ j| 2 ≤ N-1-ε on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for sample covariance matrices.
AU - László Erdös
AU - Schlein, Benjamin
AU - Yau, Horng-Tzer
AU - Yin, Jun
ID - 2769
IS - 1
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
TI - The local relaxation flow approach to universality of the local statistics for random matrices
VL - 48
ER -
TY - JOUR
AB - Consider N×N Hermitian or symmetric random matrices H with independent entries, where the distribution of the (i,j) matrix element is given by the probability measure vij with zero expectation and with variance σ ιj 2. We assume that the variances satisfy the normalization condition Σiσij2=1 for all j and that there is a positive constant c such that c≤Nσ ιj 2 ιc -1. We further assume that the probability distributions νij have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eigenvalue distribution of H is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order (Nη) -1 where η is the imaginary part of the spectral parameter in the Stieltjes transform. There are three corollaries to this strong local semicircle law: (1) Rigidity of eigenvalues: If γj=γj,N denotes the classical location of the j-th eigenvalue under the semicircle law ordered in increasing order, then the j-th eigenvalue λj is close to γj in the sense that for some positive constants C, c P{double-struck}(∃j:|λ j-γ j|≥(logN) CloglogN[min(j,N-j+1)] -1/3N -2/3)≤ C exp[-(logN) cloglogN] for N large enough. (2) The proof of Dyson's conjecture (Dyson, 1962 [15]) which states that the time scale of the Dyson Brownian motion to reach local equilibrium is of order N -1 up to logarithmic corrections. (3) The edge universality holds in the sense that the probability distributions of the largest (and the smallest) eigenvalues of two generalized Wigner ensembles are the same in the large N limit provided that the second moments of the two ensembles are identical.
AU - László Erdös
AU - Yau, Horng-Tzer
AU - Yin, Jun
ID - 2770
IS - 3
JF - Advances in Mathematics
TI - Rigidity of eigenvalues of generalized Wigner matrices
VL - 229
ER -
TY - JOUR
AB - We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.
AU - László Erdös
AU - Hasler, David G
ID - 2771
IS - 5
JF - Journal of Statistical Physics
TI - Anderson localization at band edges for random magnetic fields
VL - 146
ER -
TY - JOUR
AB - We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all magnetic fields. The parameter β effectively determines the strength of the field. We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term vanishes. However for potentials with a Coulomb singularity, the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper (Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated magnetic field, Preprint, 2011) to prove the second order Scott correction to the ground state energy of large atoms and molecules.
AU - László Erdös
AU - Fournais, Søren
AU - Solovej, Jan P
ID - 2772
IS - 4
JF - Annales Henri Poincare
TI - Second order semiclassics with self generated magnetic fields
VL - 13
ER -
TY - JOUR
AB - Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2].
AU - László Erdös
AU - Yau, Horng-Tzer
ID - 2773
JF - Electronic Journal of Probability
TI - A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
VL - 17
ER -
TY - JOUR
AB - We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.
AU - László Erdös
AU - Fournais, Søren
AU - Solovej, Jan P
ID - 2774
IS - 3
JF - Communications in Mathematical Physics
TI - Scott correction for large atoms and molecules in a self-generated magnetic field
VL - 312
ER -
TY - JOUR
AB - The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the eigenvalue distributions are given by a log-gas with potential V and inverse temperature β = 1, 2, 4, corresponding to the orthogonal, unitary and symplectic ensembles. For β ∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model, but the statistical physics interpretation of the log-gas is still valid for all β > 0. The universality conjecture for invariant ensembles asserts that the local eigenvalue statistics are independent of V. In this article, we review our recent solution to the universality conjecture for both invariant and non-invariant ensembles. We will also demonstrate that the local ergodicity of the Dyson Brownian motion is the intrinsic mechanism behind the universality. Furthermore, we review the solution of Dyson's conjecture on the local relaxation time of the Dyson Brownian motion. Related questions such as delocalization of eigenvectors and local version of Wigner's semicircle law will also be discussed.
AU - László Erdös
AU - Yau, Horng-Tzer
ID - 2775
IS - 3
JF - Bulletin of the American Mathematical Society
TI - Universality of local spectral statistics of random matrices
VL - 49
ER -
TY - JOUR
AB - We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least 4 + ε moments.
AU - László Erdös
AU - Knowles, Antti
AU - Yau, Horng-Tzer
AU - Yin, Jun
ID - 2776
IS - 3
JF - Communications in Mathematical Physics
TI - Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues
VL - 314
ER -
TY - JOUR
AB - We consider a large neutral molecule with total nuclear charge Z in a model with self-generated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that Zα < 2/π, where α denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is fixed. The leading term in the energy asymptotics is independent of κ, it is given by the Thomas-Fermi energy of order Z7/3 and it is unchanged by including the self-generated magnetic field. We prove the first correction term to this energy, the so-called Scott correction of the form S(αZ)Z2. The current paper extends the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on the Scott correction for relativistic molecules to include a self-generated magnetic field. Furthermore, we show that the corresponding Scott correction function S, first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)], is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.
AU - László Erdös
AU - Fournais, Søren
AU - Solovej, Jan P
ID - 2777
IS - 9
JF - Journal of Mathematical Physics
TI - Relativistic Scott correction in self-generated magnetic fields
VL - 53
ER -
TY - JOUR
AB - We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification.
AU - Bourgade, Paul
AU - László Erdös
AU - Yau, Horng-Tzer
ID - 2778
IS - 9
JF - Journal of Mathematical Physics
TI - Bulk universality of general β-ensembles with non-convex potential
VL - 53
ER -
TY - JOUR
AB - We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters.
AU - László Erdös
AU - Hasler, David G
ID - 2779
IS - 8
JF - Annales Henri Poincare
TI - Wegner estimate for random magnetic Laplacian on ℤ 2
VL - 13
ER -
TY - JOUR
AB - When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow.
AU - Lapp, Tobias
AU - Rohloff, Martin
AU - Vollmer, Jürgen T
AU - Björn Hof
ID - 2802
IS - 5
JF - Experiments in Fluids
TI - Particle tracking for polydisperse sedimenting droplets in phase separation
VL - 52
ER -
TY - JOUR
AB - Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border.
AU - de Lózar, Alberto
AU - Mellibovsky, Fernando
AU - Avila, Marc
AU - Björn Hof
ID - 2803
IS - 21
JF - Physical Review Letters
TI - Edge state in pipe flow experiments
VL - 108
ER -
TY - JOUR
AB - The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution
AU - Blaschke, Johannes
AU - Lapp, Tobias
AU - Björn Hof
AU - Vollmer, Jürgen T
ID - 2804
IS - 6
JF - Physical Review Letters
TI - Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets
VL - 109
ER -
TY - CONF
AB - We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.
AU - Lampert, Christoph
ID - 2825
TI - Dynamic pruning of factor graphs for maximum marginal prediction
VL - 1
ER -