@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}, } @article{1740, abstract = {A systematic study of the morphology of self-organized islands in the InAs/GaAs(0 0 1) and Ge/Si(0 0 1) systems is presented, based on high-resolution scanning tunneling microscopy measurements. We demonstrate that in both cases two main island families coexist: smaller pyramids bound by one type of shallow facets and larger multifaceted domes. Their structure and facet orientation are precisely determined, thus solving a highly debated argument in the case of InAs/GaAs(0 0 1). The comparison between the two material systems reveals the existence of striking similarities that extend even to the nature of island precursors and to the islands that form when depositing InGaAs or GeSi alloys. The implications of these observations on a possible universal description of the Stranski-Krastanow growth mode are discussed with respect to recent theoretical results.}, author = {Costantini, Giovanni and Rastelli, Armando and Manzano, Carlos and Acosta-Diaz, P and Georgios Katsaros and Songmuang, Rudeeson and Schmidt, Oliver G and Von Känel, Hans and Kern, Klaus}, journal = {Journal of Crystal Growth}, number = {1-4}, pages = {38 -- 45}, publisher = {Elsevier}, title = {{Pyramids and domes in the InAs/GaAs (0 0 1) and Ge/Si (0 0 1) systems}}, doi = {10.1016/j.jcrysgro.2004.12.047}, volume = {278}, year = {2005}, } @article{1741, abstract = {SiGe islands move laterally on a Si(001) substrate during in situ postgrowth annealing. This surprising behavior is revealed by an analysis of the substrate surface morphology after island removal using wet chemical etching. We explain the island motion by asymmetric surface-mediated alloying. Material leaves one side of the island by surface diffusion, and mixes with additional Si from the surrounding surface as it redeposits on the other side. Thus the island moves laterally while becoming larger and more dilute.}, author = {Denker, Ulrich and Rastelli, Armando and Stoffel, Mathieu and Tersoff, Jerry and Georgios Katsaros and Costantini, Giovanni and Kern, Klaus and Jin-Phillipp, Neng Y and Jesson, David E and Schmidt, Oliver G}, journal = {Physical Review Letters}, number = {21}, publisher = {American Physical Society}, title = {{Lateral motion of SiGe islands driven by surface-mediated alloying}}, doi = {10.1103/PhysRevLett.94.216103}, volume = {94}, year = {2005}, } @article{1742, abstract = {The effects of substrate temperature, growth rate, and postgrowth annealing on the composition of Ge islands grown on Si(001) were investigated with a combination of selective wet chemical etching and atomic force microscopy. A simple kinetic model comprising only surface diffusion processes can explain all the experimentally observed compositional profiles for pyramid and dome islands grown in the 560-620°C range. From this model three-dimensional compositional maps were extracted. By performing annealing experiments a change in the composition of the domes was observed. This could be explained as the result of the islands' movement induced by alloying-driven energy minimization. Also in this case kinetically hindered bulk diffusion processes are not needed to explain the experimental observations.}, author = {Georgios Katsaros and Costantini, Giovanni and Stoffel, Mathieu and Esteban, Rubén and Bittner, Alexander M and Rastelli, Armando and Denker, Ulrich and Schmidt, Oliver G and Kern, Klaus}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {19}, publisher = {American Physical Society}, title = {{Kinetic origin of island intermixing during the growth of Ge on Si (001)}}, doi = {10.1103/PhysRevB.72.195320}, volume = {72}, year = {2005}, } @article{1743, abstract = {Laterally aligned multilayer GeSiSi islands grown on a patterned Si (001) substrate are disclosed by selective etching of Si in a KOH solution. This procedure allows us to visualize the vertical alignment of the islands in a three-dimensional perspective. Our technique reveals that partly coalesced double islands in the initial layer do not merge together, but instead gradually reproduce into well-separated double islands in upper layers. We attribute this effect to very thin spacer layers, which efficiently transfer the strain modulation of each island through the spacer layer to the surface. The etching rate of Si is reduced in tensile strained regions, which helps to preserve sufficient Si between the stacked islands to form a periodic array of freestanding and vertically modulated heterostructure pillars.}, author = {Zhong, Zheyang and Georgios Katsaros and Stoffel, Mathieu and Costantini, Giovanni and Kern, Klaus and Schmidt, Oliver G and Jin-Phillipp, Neng Y and Bauer, Günther}, journal = {Applied Physics Letters}, number = {26}, pages = {1 -- 3}, publisher = {American Institute of Physics}, title = {{Periodic pillar structures by Si etching of multilayer GeSi/Si islands}}, doi = {10.1063/1.2150278}, volume = {87}, year = {2005}, } @article{1744, abstract = {This paper presents optical duobinary and dicode signalling, as alternatives to the binary format, in order to improve the transmission performance in the presense of non-linear effects in a dense wavelength division multiplex (WDM) optical system. Duobinary signalling is applied to an optical system to explore the reduction of stimulated Brillouin scattering (SBS) effects. Duobinary signalling suppresses the SBS effects, and an eye-opening improvement of 0.25 to 1.2 dB is achieved relative to binary transmission over a range of input power levels. An experimental study demonstrates that duobinary modulation suppresses the four wave mixing (FWM) products of a dense WDM system by a maximum of 3 dB. The suppression is maintained over a range of channel spacings. An investigation of the impact of fibre dispersion on FWM products under binary, duobinary and dicode modulation in a dense WDM system is then performed, with interchannel spacing and optical power variation. This leads to the development of a set of guidelines for the application areas, in which it is appropriate to use duobinary or dicode modulation in WDM systems as a means of mitigating the impact of FWM.}, author = {Georgios Katsaros and Darwazeh, Izzat Z and Lane, Phil M}, journal = {IEE Proceedings - Optoelectronics}, number = {6}, pages = {344 -- 352}, publisher = {Institute of Electrical Engineers}, title = {{Non linear transmission effects in duobinary and dicode optical systems}}, doi = {10.1049/ip-opt:20045067}, volume = {152}, year = {2005}, }