TY - JOUR
AB - Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.
AU - Timothy Browning
ID - 223
IS - 1
JF - Monatshefte fur Mathematik
TI - Density of integer solutions to diagonal quadratic forms
VL - 152
ER -
TY - JOUR
AB - In many species, females show reduced expression of a trait that is under sexual selection in males, and this expression is thought to be maintained through genetic associations with the male phenotype. However, there is also the potential for the female trait to convey an advantage in intrasexual conflicts over resources. We tested this hypothesis in a feral population of Soay sheep, in which males and females have a polymorphism for horn development, producing either full (normal horned), reduced (scurred) or no (polled, females only) horns. During the lambing period, females who possessed horns were more likely to initiate and win aggressive interactions, independent of age, weight and birthing status. The occurrence of aggression was also context dependent, decreasing over the lambing period and associated with local density. Our results demonstrate that a trait that confers benefits to males during intrasexual competition for mates may also be used by females in intrasexual competition over resources: males use weaponry to gain mates, whereas females use weaponry to gain food.
AU - Robinson, Matthew Richard
AU - Kruuk, Loeske E.B
ID - 7753
IS - 6
JF - Biology Letters
SN - 1744-9561
TI - Function of weaponry in females: The use of horns in intrasexual competition for resources in female Soay sheep
VL - 3
ER -
TY - GEN
AB - These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.
AU - Browning, Timothy D
ID - 6321
T2 - arXiv
TI - The Manin conjecture in dimension 2
ER -
TY - CHAP
AB - This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected order of magnitude is established for a singular del Pezzo surface of degree four.
AU - Browning, Timothy D
ID - 6323
T2 - A Tribute to Gauss and Dirichlet
TI - An overview of Manin's conjecture for del Pezzo surfaces
VL - 7
ER -
TY - JOUR
AB - A 671 nm diode laser with a mode-hop-free tuning range of 40 GHz is described. This long tuning range is achieved by simultaneously ramping the external cavity length with the laser injection current. The laser output pointing remains fixed, independent of its frequency because of the cover slip cavity design. This system is simple, economical, robust, and easy to use for spectroscopy, as we demonstrate with lithium vapor and lithium atom beam experiments.
AU - Carr, Adra
AU - Serchest, Yancey
AU - Waitukaitis, Scott R
AU - Perreault, John
AU - Lonij, Vincent
AU - Cronin, Alexander
ID - 128
IS - 10
JF - Review of Scientific Instruments
TI - Cover slip external cavity diode laser
VL - 78
ER -
TY - CHAP
AB - This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, during the period April – July 2005. The authors are eminent experts in the field. Several subfields of the main topic are presented; the volume thus is particularly useful to get a broad overview of recent research developments.
AU - Browning, Timothy D
AU - Heath Brown, Roger
ED - Zannier, Umberto
ID - 167
T2 - Diophantine Geometry
TI - Simultaneous equal sums of three powers
VL - 4
ER -
TY - JOUR
AB - We explore the rich internal structure of Cs2 Feshbach molecules. Pure ultracold molecular samples are prepared in a CO2 -laser trap, and a multitude of weakly bound states is populated by elaborate magnetic-field ramping techniques. Our methods use different Feshbach resonances as input ports and various internal level crossings for controlled state transfer. We populate higher partial-wave states of up to eight units of rotational angular momentum (l -wave states). We investigate the molecular structure by measurements of the magnetic moments for various states. Avoided level crossings between different molecular states are characterized through the changes in magnetic moment and by a Landau-Zener tunneling method. Based on microwave spectroscopy, we present a precise measurement of the magnetic-field-dependent binding energy of the weakly bound s -wave state that is responsible for the large background scattering length of Cs. This state is of particular interest because of its quantum-halo character.
AU - Mark, Michael
AU - Ferlaino, Francesca
AU - Knoop, Steven
AU - Danzl, Johann G
AU - Kraemer, Tobias
AU - Chin, Cheng
AU - Nägerl, Hanns
AU - Grimm, Rudolf
ID - 1035
IS - 4
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Spectroscopy of ultracold trapped cesium Feshbach molecules
VL - 76
ER -
TY - JOUR
AB - The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.
As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.
For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.
AU - BÜHLER, OLIVER
AU - MULLER, Caroline J
ID - 9149
JF - Journal of Fluid Mechanics
KW - Mechanical Engineering
KW - Mechanics of Materials
KW - Condensed Matter Physics
SN - 0022-1120
TI - Instability and focusing of internal tides in the deep ocean
VL - 588
ER -
TY - GEN
AB - Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.
AU - Broderick,Tamara
AU - Dudik,Miroslav
AU - Gasper Tkacik
AU - Schapire,Robert E
AU - Bialek, William S
ID - 3742
T2 - ArXiv
TI - Faster solutions of the inverse pairwise Ising problem
VL - q-bio.QM
ER -
TY - JOUR
AB - We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with "anomalous" stochastic rates and (i) stabilise at "random carrying capacities", or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions. (c) 2006 Elsevier B.V. All rights reserved.
AU - de Vladar, Harold
AU - Pen, I.
ID - 4234
JF - Physica A
TI - Determinism, noise, and spurious estimations in a generalised model of population growth
VL - 373
ER -