Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Superhard Phases of Simple Substances and Binary Compounds of the B-C-N-O System: from Diamond to the Latest Results (a Review)

The basic known and hypothetic one- and two-element phases of the B-C-N-O system (both superhard phases having diamond and boron structures and precursors to synthesize them) are described. The attention has been given to the structure, basic mechanical properties, and methods to identify and characterize the materials. For some phases that have been recently described in the literature the synthesis conditions at high pressures and temperatures are indicated.Comment: Review on superhard B-C-N-O phase

Petiole and leaf blade analyses as nutritional status indicators of 'solo' and 'formosa' papaya trees

The absence of a literature consensus about parts of leaves, blade or petiole which would be most indicative of the nutritional status of papaya trees, has hindered the use of foliar analysis as a diagnosis tool for this crop. An experiment was carried out to compare the nutricional status evaluated using blades and petioles of 'solo' and 'formosa' papaya groups. A completely randomized block design was used to test six varieties, three of each group. Leaves were sampled every three months in five occasions. Recently matured leaves were separated in petioles and blades for the evaluation of N, NO3-, P, K, Ca, Mg, S, B, Cl, Fe, Mn and Zn concentrations. These concentrations were compared to those reported in the literature for this crop. The nutritional status diagnosis of the papaya plants, when made by means of blade or petiole leaves, led to different diagnoses showing the need of the definition of a single pattern. Blade has shown to be more effective than petiole for the diagnosis of the nutritional status, better differentiating the papaya tree varieties in relation to N, P, K and Cl, and not differing in relation to the other nutrients. It is here recommended to use the blade as indicator of the nutritional status of papaya plants.A ausência de um consenso na literatura sobre qual parte da folha, limbo ou pecíolo, seria a mais indicada para avaliação do estado nutricional do mamoeiro, dificulta o uso da análise foliar como ferramenta de diagnose para a cultura. Assim, foi conduzido um experimento para comparar a diagnose do estado nutricional efetuada pela análise do limbo e do pecíolo foliar de mamoeiros pertencentes aos grupos 'Solo' e 'Formosa'. Foi adotado o delineamento em blocos casualizados para avaliar seis variedades de mamoeiros, três de cada grupo. Foram retiradas amostras foliares em cinco épocas, a cada três meses. A folha recém-madura foi dividida em limbo e pecíolo, onde foram determinados os teores de N, NO3-, P, K, Ca, Mg, S, B, Cl, Fe, Mn e Zn. Estes teores foram comparados com os citados na literatura como adequados para a cultura. A diagnose do estado nutricional do mamoeiro quando efetuada por meio da análise do limbo ou do pecíolo foliar levou a diferentes diagnósticos mostrando a necessidade de definição de um único padrão. A análise do limbo foliar mostrou-se mais efetiva que a do pecíolo para diagnosticar o estado nutricional, diferenciando melhor as variedades de mamoeiro, em relação a N, P, K e Cl, não diferindo em relação aos demais nutrientes. Sendo assim, o limbo foliar deve ser utilizado como indicador do estado nutricional do mamoeiro

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at sNN=200\sqrt{s_{NN}} = 200 GeV

Identified mid-rapidity particle spectra of $\pi^{\pm}$, $K^{\pm}$, and $p(\bar{p})$ from 200 GeV p+p and d+Au collisions are reported. A time-of-flight detector based on multi-gap resistive plate chamber technology is used for particle identification. The particle-species dependence of the Cronin effect is observed to be significantly smaller than that at lower energies. The ratio of the nuclear modification factor ($R_{dAu}$) between protons $(p+\bar{p})$ and charged hadrons ($h$) in the transverse momentum range $1.2<{p_{T}}<3.0$ GeV/c is measured to be $1.19\pm0.05$(stat)$\pm0.03$(syst) in minimum-bias collisions and shows little centrality dependence. The yield ratio of $(p+\bar{p})/h$ in minimum-bias d+Au collisions is found to be a factor of 2 lower than that in Au+Au collisions, indicating that the Cronin effect alone is not enough to account for the relative baryon enhancement observed in heavy ion collisions at RHIC.Comment: 6 pages, 4 figures, 1 table. We extended the pion spectra from transverse momentum 1.8 GeV/c to 3. GeV/

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding