@book{210, abstract = {Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.}, author = {Davenport, Harold and Browning, Timothy D}, pages = {140}, publisher = {Cambridge University Press}, title = {{Analytic Methods for Diophantine Equations and Diophantine Inequalities}}, doi = {10.1017/CBO9780511542893}, year = {2005}, } @article{211, abstract = {Let f ∈ ℤ[x] be a polynomial of degree d. The paucity of non-trivial positive integer solutions to the equation f(x1)+f(x 2)=f(x3)+f(x4) is established, provided that d ≤ 7$. Also the corresponding situation is investigated for equal sums of three like polynomials.}, author = {Timothy Browning}, journal = {Bulletin of the London Mathematical Society}, number = {6}, pages = {801 -- 808}, publisher = {John Wiley and Sons Ltd}, title = {{Equal sums of like polynomials}}, doi = {10.1112/S0024609305004741}, volume = {37}, year = {2005}, } @article{212, abstract = {For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Journal fur die Reine und Angewandte Mathematik}, number = {584}, pages = {83 -- 115}, publisher = {Walter de Gruyter and Co }, title = {{Counting rational points on hypersurfaces}}, doi = {https://doi.org/10.1515/crll.2005.2005.584.83}, year = {2005}, } @article{214, abstract = {Given an absolutely irreducible ternary form F, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Mathematische Zeitschrift}, number = {2}, pages = {233 -- 247}, publisher = {Unknown}, title = {{Plane curves in boxes and equal sums of two powers}}, doi = {10.1007/s00209-004-0719-z}, volume = {251}, year = {2005}, } @article{217, abstract = {We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface x1 x2 x3 = x4 (x1 + x2 + x3)2, has order of magnitude B (log B)6. This agrees with Manin's conjecture.}, author = {Timothy Browning}, journal = {Journal of Number Theory}, number = {2}, pages = {242 -- 283}, publisher = {Elsevier}, title = {{The density of rational points on a certain singular cubic surface}}, doi = {10.1016/j.jnt.2005.11.007}, volume = {119}, year = {2005}, } @article{2307, abstract = {The human norepinephrine (NE) transporter (hNET) attenuates neuronal signaling by rapid NE clearance from the synaptic cleft, and NET is a target for cocaine and amphetamines as well as therapeutics for depression, obsessive-compulsive disorder, and post-traumatic stress disorder. In spite of its central importance in the nervous system, little is known about how NET substrates, such as NE, 1-methyl-4-tetrahydropyridinium (MPP+), or amphetamine, interact with NET at the molecular level. Nor do we understand the mechanisms behind the transport rate. Previously we introduced a fluorescent substrate similar to MPP+, which allowed separate and simultaneous binding and transport measurement (Schwartz, J. W., Blakely, R. D., and DeFelice, L. J. (2003) J. Biol. Chem. 278, 9768-9777). Here we use this substrate, 4-(4-(dimethylamino)styrl)-N-methyl-pyridinium (ASP+), in combination with green fluorescent protein-tagged hNETs to measure substrate-transporter stoichiometry and substrate binding kinetics. Calibrated confocal microscopy and fluorescence correlation spectroscopy reveal that hNETs, which are homo-multimers, bind one substrate molecule per transporter subunit. Substrate residence at the transporter, obtained from rapid on-off kinetics revealed in fluorescence correlation spectroscopy, is 526 μs. Substrate residence obtained by infinite dilution is 1000 times slower. This novel examination of substrate-transporter kinetics indicates that a single ASP + molecule binds and unbinds thousands of times before being transported or ultimately dissociated from hNET. Calibrated fluorescent images combined with mass spectroscopy give a transport rate of 0.06 ASP +/hNET-protein/s, thus 36,000 on-off binding events (and 36 actual departures) occur for one transport event. Therefore binding has a low probability of resulting in transport. We interpret these data to mean that inefficient binding could contribute to slow transport rates.}, author = {Schwartz, Joel W and Gaia Novarino and Piston, David W and DeFelice, Louis J}, journal = {Journal of Biological Chemistry}, number = {19}, pages = {19177 -- 19184}, publisher = {American Society for Biochemistry and Molecular Biology}, title = {{Substrate binding stoichiometry and kinetics of the norepinephrine transporter}}, doi = {10.1074/jbc.M412923200}, volume = {280}, year = {2005}, } @book{2335, abstract = {This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.}, author = {Lieb, Élliott and Seiringer, Robert and Solovej, Jan and Yngvason, Jakob}, isbn = {978-3-7643-7336-8}, pages = {VIII, 203}, publisher = {Birkhäuser Verlag}, title = {{The Mathematics of the Bose gas and its Condensation}}, doi = {10.1007/b137508}, volume = {34}, year = {2005}, } @inbook{2336, abstract = { Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems.}, author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob}, booktitle = {Perspectives in Analysis}, editor = {Benedicks, Michael and Jones, Peter W and Smirnov, Stanislav and Winckler, Björn}, pages = {97 -- 183}, publisher = {Springer}, title = {{The quantum-mechanical many-body problem: The Bose gas}}, doi = {10.1007/3-540-30434-7_9}, volume = {27}, year = {2005}, } @article{2359, abstract = {The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review Letters}, number = {8}, publisher = {American Physical Society}, title = {{Justification of c-number substitutions in bosonic hamiltonians}}, doi = {10.1103/PhysRevLett.94.080401}, volume = {94}, year = {2005}, } @article{2361, abstract = {The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(ϱlnϱ) of a density matrix ϱ123 on the product of three Hilbert spaces satisfies S[ϱ123]- S[ϱ12]≤S[ϱ23]-S[ϱ2]. We strengthen this to S[ϱ123]-S[ϱ12] ≤αnα(S[ϱ23α]-S[ϱ2α]), where the nα are weights and the ϱ23α are partitions of ϱ23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.}, author = {Lieb, Élliott H and Robert Seiringer}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {6}, publisher = {American Physical Society}, title = {{Stronger subadditivity of entropy}}, doi = {10.1103/PhysRevA.71.062329}, volume = {71}, year = {2005}, } @article{2362, abstract = {Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground-state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa, where E0 is the energy of the noninteracting system and is the density. A similar formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.}, author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {5}, publisher = {American Physical Society}, title = {{Ground state energy of the low density Fermi gas}}, doi = {10.1103/PhysRevA.71.053605}, volume = {71}, year = {2005}, } @article{2427, abstract = {Intersection graphs of disks and of line segments, respectively, have been well studied, because of both practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate between disks and line segments, and show that the problem is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. Furthermore, the reduction immediately carries over to intersection graphs of triangles. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of convex objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounded.}, author = {Ambühl, Christoph and Uli Wagner}, journal = {Theory of Computing Systems}, number = {3}, pages = {279 -- 292}, publisher = {Springer}, title = {{The Clique problem in intersection graphs of ellipses and triangles}}, doi = {10.1007/s00224-005-1141-6}, volume = {38}, year = {2005}, } @inproceedings{2428, abstract = {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 several 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(√n) colors in the worst case. We then modify this approach, to obtain an efficient deterministic algorithm that uses a maximum of Θ(log 2 n) colors. Next, we present two randomized solutions. The first algorithm requires an expected number of at most O(log 2 n) colors, and produces a coloring which is valid with high probability, and the second one, which is a variant of our efficient deterministic algorithm, requires an expected number of at most O(log n log log n) colors but always produces a valid coloring. 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. The average-case behavior for disks, and cases involving other planar ranges, are still open.}, author = {Fiat, Amos and Levy, Meital B and Matoušek, Jiří and Pach, Elchanan M and Sharir, Micha and Smorodinsky, Shakhar and Uli Wagner and Welzl, Emo}, pages = {545 -- 554}, publisher = {SIAM}, title = {{Online conflict-free coloring for intervals}}, doi = {10.1137/S0097539704446682}, year = {2005}, } @article{2455, abstract = {Local accumulation of the plant growth regulator auxin mediates pattern formation in Arabidopsis roots and influences outgrowth and development of lateral root- and shoot-derived primordia. However, it has remained unclear how auxin can simultaneously regulate patterning and organ outgrowth and how its distribution is stabilized in a primordium-specif ic manner. Here we show that five PIN genes collectively control auxin distribution to regulate cell division and cell expansion in the primary root. Furthermore, the joint action of these genes has an important role in pattern formation by focusing the auxin maximum and restricting the expression domain of PLETHORA (PLT) genes, major determinants for root stem cell specification. In turn, PLT genes are required for PIN gene transcription to stabilize the auxin maximum at the distal root tip. Our data reveal an interaction network of auxin transport facilitators and root fate determinants that control patterning and growth of the root primordium.}, author = {Billou, Ikram and Xu, Jian and Wildwater, Marjolein and Willemsen, Viola and Paponov, Ivan A and Jirí Friml and Heldstra, Renze and Aida, Mitsuhiro and Palme, Klaus J and Scheres, Ben}, journal = {Nature}, number = {7021}, pages = {39 -- 44}, publisher = {Nature Publishing Group}, title = {{The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots}}, doi = {10.1038/nature03184}, volume = {433}, year = {2005}, } @inbook{2463, author = {Dubová, J and Hejátko, Jan and Jirí Friml}, booktitle = {Encyclopedia of Molecular Cell Biology and Molecular Medicine}, editor = {Meyers, Robert A}, pages = {249 -- 295}, publisher = {Wiley-Blackwell}, title = {{Reproduction, plants}}, doi = {10.1002/3527600906}, volume = {12}, year = {2005}, } @inbook{2464, author = {Jirí Friml and Wiśniewska, Justyna}, booktitle = {Intercellular Communication in Plants}, editor = {Fleming, Andrew J.}, publisher = {Wiley-Blackwell}, title = {{Auxin as an intercellular signal}}, volume = {16}, year = {2005}, } @misc{2647, abstract = {Our understanding of the role played by neurotransmitter receptors in the developing brain has advanced in recent years. The major excitatory and inhibitory neurotransmitters in the brain, glutamate and GABA, activate both ionotropic (ligand-gated ion channels) and metabotropic (G protein-coupled) receptors, and are generally associated with neuronal communication in the mature brain. However, before the emergence of their role in neurotransmission in adulthood, they also act to influence earlier developmental events, some of which occur prior to synapse formation: such as proliferation, migration, differentiation or survival processes during neural development. To fulfill these actions in the constructing of the nervous system, different types of glutamate and GABA receptors need to be expressed both at the right time and at the right place. The identification by molecular cloning of 16 ionotropic glutamate receptor subunits, eight metabotropic glutamate receptor subtypes, 21 ionotropic and two metabotropic GABA receptor subunits, some of which exist in alternatively splice variants, has enriched our appreciation of how molecular diversity leads to functional diversity in the brain. It now appears that many different types of glutamate and GABA receptor subunits have prominent expression in the embryonic and/or postnatal brain, whereas others are mainly present in the adult brain. Although the significance of this differential expression of subunits is not fully understood, it appears that the change in subunit composition is essential for normal development in particular brain regions. This review focuses on emerging information relating to the expression and role of glutamatergic and GABAergic neurotransmitter receptors during prenatal and postnatal development.}, author = {Luján, Rafael and Ryuichi Shigemoto and López-Bendito, Guillermina}, booktitle = {Neuroscience}, number = {3}, pages = {567 -- 580}, publisher = {Elsevier}, title = {{Glutamate and GABA receptor signalling in the developing brain}}, doi = {10.1016/j.neuroscience.2004.09.042}, volume = {130}, year = {2005}, } @article{2648, abstract = {Hyperpolarization-activated and cyclic nucleotide-gated (HCN) channels are involved in the control of neuronal excitability and plasticity. In this study, we used immunoblotting and immunohistochemical techniques to reveal the developmental expression and subcellular distribution of the HCN1 subunit in the cerebellar cortex. During postnatal development, the spatio-temporal expression of HCN1 correlated well with the morphological events occurring during the ontogenesis of cerebellar interneurons. Using immunoblotting techniques, HCN1 was weakly detected during the first postnatal week and continued to increase throughout postnatal development, peaking at postnatal day (P)15. At the light-microscopic level, HCN1 immunoreactivity was very weak until P7 whereas from P10-12 to adulthood it was strongly detected in the lower third of the molecular layer and in the Purkinje cell layer. HCN1 was present in axons running through the molecular layer and in the pericellular basket around Purkinje cells at P12, but in the periaxonal plexus (the pinceau) surrounding their initial segment only after P15. Using immunofluorescence, HCN1 colocalized with GAD65 and synaptophysin, demonstrating that the subunit was present in inhibitory axons and axon terminals. At the electron-microscopic level, in adulthood, HCN1 immunoparticles were detected at postsynaptic sites in basket and Purkinje cells but most immunoparticles were found at presynaptic sites in basket cell axons and in terminals. In the axon terminals, the distribution of HCN1 was relatively uniform along the extrasynaptic plasma membrane; this was confirmed using quantitative techniques. The present findings suggest that HCN1 channels may provide a significant route for modulating co-ordinated cerebellar synaptic transmission through basket cells.}, author = {Luján, Rafael and Albasanz, José L and Ryuichi Shigemoto and Juíz, José M}, journal = {European Journal of Neuroscience}, number = {8}, pages = {2073 -- 2082}, publisher = {Wiley-Blackwell}, title = {{Preferential localization of the hyperpolarization-activated cyclic nucleotide-gated cation channel subunit HCN1 in basket cell terminals of the rat cerebellum}}, doi = {10.1111/j.1460-9568.2005.04043.x}, volume = {21}, year = {2005}, } @article{2649, abstract = {The number of ionotropic receptors in synapses is an essential factor for determining the efficacy of fast transmission. We estimated the number of functional AMPA receptors at single postsynaptic sites by a combination of two-photon uncaging of glutamate and the nonstationary fluctuation analysis in immature rat Purkinje cells (PCs), which receive a single type of excitatory input from climbing fibers. Areas of postsynaptic membrane specialization at the recorded synapses were measured by reconstruction of serial ultrathin sections. The number of functional AMPA receptors was proportional to the synaptic area with a density of ∼ 1280 receptors/μm 2. Moreover, highly sensitive freeze-fracture replica labeling revealed a homogeneous density of immunogold particles for AMPA receptors in synaptic sites (910 ± 36 particles/μm 2) and much lower density in extrasynaptic sites (19 ± 2 particles/μm 2) in the immature PCs. Our results indicate that in this developing synapse, the efficacy of transmission is determined by the synaptic area.}, author = {Tanaka, Junichi and Matsuzaki, Masanori and Tarusawa, Etsuko and Momiyama, Akiko and Molnár, Elek and Kasai, Haruo and Ryuichi Shigemoto}, journal = {Journal of Neuroscience}, number = {4}, pages = {799 -- 807}, publisher = {Society for Neuroscience}, title = {{Number and density of AMPA receptors in single synapses in immature cerebellum}}, doi = {10.1523/JNEUROSCI.4256-04.2005}, volume = {25}, year = {2005}, } @article{2650, abstract = {Septohippocampal cholinergic neurons play key roles in learning and memory processes, and in the generation of hippocampal theta rhythm. The range of receptors for endogenous modulators expressed on these neurons is unclear. Here we describe GABAB 1a/b receptor (GABABR) and type 1 cannabinoid receptor (CB1R) expression in rat septal cholinergic [i.e. choline acetyltransferase (ChAT)-positive] cells. Using double immunofluorescent staining, we found that almost two-thirds of the cholinergic cells in the rat medial septum were GABABR positive, and that these cells had significantly larger somata than did GABABR-negative cholinergic neurons. We detected CB1R labelling in somata after axonal protein transport was blocked by colchicine. In these animals about one-third of the cholinergic cells were CB1R positive. These cells again had larger somata than CB1R-negative cholinergic neurons. The analyses confirmed that the size of GABABR-positive and CB 1R-positive cholinergic cells were alike, and all CB 1R-positive cholinergic cells were GABABR positive as well. CB1R-positive cells were invariably ChAT positive. All retrogradely labelled septohippocampal cholinergic cells were positive for GABABR and at least half of them also for CB1R. These data shed light on the existence of at least two cholinergic cell types in the medial septum: one expresses GABABR and CB1R, has large somata and projects to the hippocampus, whereas the other is negative for GABABR and CB1R and has smaller somata. The results also suggest that cholinergic transmission in the hippocampus is fine-tuned by endocannabinoid signalling.}, author = {Nyíri, Gábor and Szabadits, Eszter and Cserép, Csaba and Mackie, Ken P and Ryuichi Shigemoto and Freund, Tamás F}, journal = {European Journal of Neuroscience}, number = {11}, pages = {3034 -- 3042}, publisher = {Wiley-Blackwell}, title = {{GABAB and CB1 cannabinoid receptor expression identifies two types of septal cholinergic neurons}}, doi = {10.1111/j.1460-9568.2005.04146.x}, volume = {21}, year = {2005}, }