TY - BOOK
AB - 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.
AU - Davenport, Harold
AU - Timothy Browning
ID - 210
T2 - Analytic methods for diophantine equations and diophantine inequalities
TI - Analytic methods for diophantine equations and diophantine inequalities
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
ID - 211
IS - 6
JF - Bulletin of the London Mathematical Society
TI - Equal sums of like polynomials
VL - 37
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
AU - Heath-Brown, Roger
ID - 212
IS - 584
JF - Journal fur die Reine und Angewandte Mathematik
TI - Counting rational points on hypersurfaces
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
AU - Heath-Brown, Roger
ID - 214
IS - 2
JF - Mathematische Zeitschrift
TI - Plane curves in boxes and equal sums of two powers
VL - 251
ER -
TY - JOUR
AB - 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.
AU - Timothy Browning
ID - 217
IS - 2
JF - Journal of Number Theory
TI - The density of rational points on a certain singular cubic surface
VL - 119
ER -
TY - JOUR
AB - 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.
AU - Schwartz, Joel W
AU - Gaia Novarino
AU - Piston, David W
AU - DeFelice, Louis J
ID - 2307
IS - 19
JF - Journal of Biological Chemistry
TI - Substrate binding stoichiometry and kinetics of the norepinephrine transporter
VL - 280
ER -
TY - BOOK
AB - 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ID - 2335
T2 - The mathematics of the Bose gas and its condensation
TI - The mathematics of the Bose gas and its condensation
VL - 34
ER -
TY - CHAP
AB -
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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Benedicks, Michael
ED - Jones, Peter W
ED - Smirnov, Stanislav
ED - Winckler, Björn
ID - 2336
T2 - Perspectives in Analysis
TI - The quantum-mechanical many-body problem: The Bose gas
VL - 27
ER -
TY - JOUR
AB - 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2359
IS - 8
JF - Physical Review Letters
TI - Justification of c-number substitutions in bosonic hamiltonians
VL - 94
ER -
TY - JOUR
AB - The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2361
IS - 6
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Stronger subadditivity of entropy
VL - 71
ER -
TY - JOUR
AB - 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.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2362
IS - 5
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Ground state energy of the low density Fermi gas
VL - 71
ER -
TY - JOUR
AB - 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.
AU - Ambühl, Christoph
AU - Uli Wagner
ID - 2427
IS - 3
JF - Theory of Computing Systems
TI - The Clique problem in intersection graphs of ellipses and triangles
VL - 38
ER -
TY - CONF
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 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.
AU - Fiat, Amos
AU - Levy, Meital B
AU - Matoušek, Jiří
AU - Pach, Elchanan M
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
AU - Welzl, Emo
ID - 2428
TI - Online conflict-free coloring for intervals
ER -
TY - JOUR
AB - 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.
AU - Billou, Ikram
AU - Xu, Jian
AU - Wildwater, Marjolein
AU - Willemsen, Viola
AU - Paponov, Ivan A
AU - Jirí Friml
AU - Heldstra, Renze
AU - Aida, Mitsuhiro
AU - Palme, Klaus J
AU - Scheres, Ben
ID - 2455
IS - 7021
JF - Nature
TI - The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots
VL - 433
ER -
TY - CHAP
AU - Dubová, J
AU - Hejátko, Jan
AU - Jirí Friml
ED - Meyers, Robert A
ID - 2463
T2 - Encyclopedia of Molecular Cell Biology and Molecular Medicine
TI - Reproduction, plants
VL - 12
ER -
TY - CHAP
AU - Jirí Friml
AU - Wiśniewska, Justyna
ED - Fleming, Andrew J.
ID - 2464
T2 - Intercellular Communication in Plants
TI - Auxin as an intercellular signal
VL - 16
ER -
TY - JOUR
AB - In the ant Cardiocondyla obscurior, wingless males compete with nestmate males for access to female mating
partners, leading to local mate competition (LMC). Queen number varies between colonies, resulting in
variation in the strength of LMC. Cremer & Heinze (2002, Proceedings of the Royal Society of London, Series B,
269, 417–422) showed that colonies responded to increasing queen number by producing a less femalebiased
sex ratio, as predicted by LMC theory. However, the proximate mechanisms responsible for this
variation in the sex ratio could not be determined because the study was restricted to adult sex ratios.With
LMC, the primary sex ratio (proportion of haploid eggs laid by the queen) is expected to be female biased,
which lowers the conflict between queens and workers over sex allocation. We compared the primary sex
ratios laid by queens in monogynous and in polygynous experimental colonies of C. obscurior. The
proportion of haploid eggs laid by queens was significantly lower in single-queen than in multiple-queen
colonies. Furthermore, queens rapidly adjusted their primary sex ratios to changes in colony queen
number. This is the first report of an adaptive adjustment of the primary sex ratio in response to LMC by
ant queens.
AU - De Menten, Ludivine
AU - Cremer, Sylvia
AU - Heinze, Jürgen
AU - Aron, Serge
ID - 3915
IS - 5
JF - Animal Behaviour
TI - Primary sex ratio adjustment by ant queens in response to local mate competition
VL - 69
ER -
TY - JOUR
AB - Divergent reproductive interests of males and females often cause sexual conflict [1] and [2]. Males of many species manipulate females by transferring seminal fluids that boost female short-term fecundity while decreasing their life expectancy and future reproductivity [3] and [4]. The life history of ants, however, is expected to reduce sexual conflict; whereas most insect females show repeated phases of mating and reproduction, antqueens mate only during a short period early in life and undergo a lifelong commitment to their mates by storing sperm [5]. Furthermore, sexual offspring can only be reared after a sterile worker force has been built up [5]. Therefore, the males should also profit from a long female lifespan. In the antCardiocondyla obscurior, mating indeed has a positive effect on the lifetime reproductive success of queens. Queens that mated to either one fertile or one sterilized male lived considerably longer and started laying eggs earlier than virgin queens. Only queens that received viable sperm from fertile males showed increased fecundity. The lack of a trade-off between fecundity and longevity is unexpected, given evolutionary theories of aging [6]. Our data instead reveal the existence of sexual cooperation in ants.
AU - Schrempf, Alexandra
AU - Heinze, Jürgen
AU - Cremer, Sylvia
ID - 3916
IS - 3
JF - Current Biology
TI - Sexual cooperation: mating increases longevity in ant queens
VL - 15
ER -
TY - JOUR
AB - Resident dendritic cells (DC) within the T cell area of the lymph node take up soluble antigens that enter via the afferent lymphatics before antigen carrying DC arrive from the periphery. The reticular network within the lymph node is a conduit system forming the infrastructure for the fast delivery of soluble substances from the afferent lymph to the lumen of high endothelial venules (HEVs). Using high-resolution light microscopy and 3D reconstruction, we show here that these conduits are unique basement membrane-like structures ensheathed by fibroblastic reticular cells with occasional resident DC embedded within this cell layer. Conduit-associated DC are capable of taking up and processing soluble antigens transported within the conduits, whereas immigrated mature DC occur remote from the reticular fibers. The conduit system is, therefore, not a closed compartment that shuttles substances through the lymph node but represents the morphological equivalent to the filtering function of the lymph node.
AU - Sixt, Michael K
AU - Kanazawa, Nobuo
AU - Selg, Manuel
AU - Samson, Thomas
AU - Roos, Gunnel
AU - Reinhardt, Dieter
AU - Pabst, Reinhard
AU - Lutz, Manfred
AU - Sorokin, Lydia
ID - 3933
IS - 1
JF - Immunity
TI - The conduit system transports soluble antigens from the afferent lymph to resident dendritic cells in the T cell area of the lymph node
VL - 22
ER -
TY - CONF
AB - We present an efficient algorithm for generating a small set of coarse alignments between interacting proteins using meaningful features on their surfaces. The proteins are treated as rigid bodies, but the results are more generally useful as the produced configurations can serve as input to local improvement algorithms that allow for protein flexibility. We apply our algorithm to a diverse set of protein complexes from the Protein Data Bank, demonstrating the effectivity of our algorithm, both for bound and for unbound protein docking problems.
AU - Wang, Yusu
AU - Agarwal, Pankaj K
AU - Brown, Paul
AU - Herbert Edelsbrunner
AU - Rudolph, Johannes
ID - 3982
TI - Coarse and reliable geometric alignment for protein docking
ER -