A new approximation hierarchy for polynomial conic optimization

In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex cones, and we assume that all the feasible solutions are non-negative. This family of problems captures in particular polynomial optimization problems (POPs), polynomial semi-definite polynomial optimization problems (PSDPs) and polynomial second-order cone-optimization problems (PSOCPs). We propose a new general hierarchy of linear conic optimization relaxations inspired by an extension of Pólyaʼs Positivstellensatz for homogeneous polynomials being positive over a basic semi-algebraic cone contained in the non-negative orthant, introduced in Dickinson and Povh (J Glob Optim 61(4):615-625, 2015). We prove that based on some classic assumptions, these relaxations converge monotonically to the optimal value of the original problem. Adding a redundant polynomial positive semi-definite constraint to the original problem drastically improves the bounds produced by our method. We provide an extensive list of numerical examples that clearly indicate the advantages and disadvantages of our hierarchy. In particular, in comparison to the classic approach of sum-of-squares, our new method provides reasonable bounds on the optimal value for POPs, and strong bounds for PSDPs and PSOCPs, even outperforming the sum-of-squares approach in these latter two cases.V članku obravnavamo polinomske konične optimizacijske probleme, kjer je dopustna množica definirana z omejitvami, da morajo biti dani polinomski vektorji v danih nepraznih zaprtih konveksnih stožcih. Dodatno morajo dopustne rešitve zadoščati pogoju nenegativnosti. Ta družina problemov zajema zlasti klasične probleme polinomske optimizacije (POP), probleme polinomske semidefinitne optimizacije (PSDP) in probleme polinomske optimizacije nad stožci drugega reda (PSOCP). Predlagamo novo splošno hierarhijo linearnih koničnih optimizacijskih poenostavitev, ki naravno sledijo iz razširitve Pólya-jevega izreka o pozitivnosti iz Dickinson in Povh (J Glob Optim 61 (4): 615-625, 2015). Ob nekaterih klasičnih predpostavkah te poenostavitve monotono konvergirajo k optimalni vrednosti izvirnega problema. Kot zanimivost pokažemo, da dodajanje posebne redundantne omejitve k osnovnemu problemu ne spremeni optimalne rešitve tega problema, a bistveno izboljša kvaliteto poenostavitev. V članku tudi predstavimo obsežen seznam številčnih primerov, ki jasno kažejo na prednosti in slabosti naše hierarhije

MACHINE LEARNING TOOLS IN THE ANALYZE OF A BIKE SHARING SYSTEM

Advanced models, based on artificial intelligence and machine learning, are used here to analyze a bike-sharing system. The specific target was to predict the number of rented bikes in the Nova Mesto (Slovenia) public bike share scheme. For this purpose, the topological properties of the transport network were determined and related to the weather conditions. Pajek software was used and the system behavior during a 30-week period was investigated. Open questions were, for instance: how many bikes are shared in different weather conditions? How the network topology impacts the bike sharing system? By providing a reasonable answer to these and similar questions, several accurate ways of modeling the bike sharing system which account for both topological properties and weather conditions, were developed and used for its optimization

Local Projections of Low-Momentum Potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment

Scaling laws for the elastic scattering amplitude

The partial differential equation for the imaginary part of the elastic scattering amplitude is derived. It is solved in the black disk limit. The asymptotical scaling behavior of the amplitude coinciding with the geometrical scaling is proved. Its extension to preasymptotical region and modifications of scaling laws for the differential cross section are considered.Comment: 6 p. arXiv admin note: substantial text overlap with arXiv:1206.547

Baryons in Holographic QCD

We study the baryon in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system. In holographic QCD, the baryon appears as a topologically non-trivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton as Brane-induced Skyrmion. Some review of $D4/D8/\bar{D8}$ holographic QCD is presented from the viewpoints of recent hadron physics and phenomenologies. Four-dimensional effective theory with pions and $\rho$ mesons is uniquely derived from the non-abelian Dirac-Born-Infeld (DBI) action of $D8$ brane with $D4$ supergravity background, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and $\rho$-meson fields, we derive the energy functional and the Euler-Lagrange equation of Brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the pion profile $F(r)$ and the $\rho$-meson profile $G(r)$ of the Brane-induced Skyrmion, and estimate its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without $\rho$ mesons. We analyze interaction terms of pions and $\rho$ mesons in Brane-induced Skyrmion, and consider the role of $\rho$-meson component appearing in baryons.Comment: 28 pages, 11 figure

Vlasov Description Of Dense Quark Matter

We discuss properties of quark matter at finite baryon densities and zero temperature in a Vlasov approach. We use a screened interquark Richardson's potential consistent with the indications of Lattice QCD calculations. We analyze the choices of the quark masses and the parameters entering the potential which reproduce the binding energy (B.E.) of infinite nuclear matter. There is a transition from nuclear to quark matter at densities 5 times above normal nuclear matter density. The transition could be revealed from the determination of the position of the shifted meson masses in dense baryonic matter. A scaling form of the meson masses in dense matter is given.Comment: 15 pages 4 figure

Non-Perturbative QCD Treatment of High-Energy Hadron-Hadron Scattering

Total cross-sections and logarithmic slopes of the elastic scattering cross-sections for different hadronic processes are calculated in the framework of the model of the stochastic vacuum. The relevant parameters of this model, a correlation length and the gluon condensate, are determined from scattering data, and found to be in very good agreement with values coming from completely different sources of information. A parameter-free relation is given between total cross-sections and slope parameters, which is shown to be remarkably valid up to the highest energies for which data exist.Comment: 60 pages, Heidelberg preprin

Recomendações técnicas para a reprodução do tambaqui.

Das espécies nativas brasileiras, o tambaqui (Colossoma macropomum) é a mais produzida em cativeiro. Quase a totalidade da produção desse animal puro ocorre nos estados da região Norte do Brasil, com destaque para Rondônia. No Mato Grosso, existe grande produção do híbrido tambacu (tambaqui x pacu-caranha, Piaractus mesopotamicus). Isso se deve à popularidade do pacu-caranha na bacia do rio Paraguai e do repasse de tecnologia, no início dos anos 1980, do Centro Nacional de Pesquisa e Conservação de Peixes Continentais (Cepta), que recomendava a produção do híbrido com o objetivo de explorar o potencial de crescimento do tambaqui associado à resistência do pacu a temperaturas amenas. Atualmente, outro híbrido bastante produzido é o tambatinga, cruzamento de duas espécies amazônicas (tambaqui x pirapitinga, Piaractus brachypomus) com características produtivas parecidas com as do tambacu, mas com destaque para a cor prateada e o opérculo avermelhado, os quais chamam a atenção do consumidor. Desse modo, este manual vai tratar exclusivamente da tecnologia aplicada à reprodução do tambaqui, desenvolvida pela UFRGS, UEM e UFMT com apoio da Embrapa, por meio do Programa de Melhoramento Genético de Organismos Aquáticos, no âmbito do projeto AQUABRASIL.bitstream/item/83462/1/Doc-212-RecomendacoesTecnicasReproducaoTambaqui.pd

Energy Demand in Agricultural Biomass Production in Parana state, Brazil

Energy flow analysis is an interesting approach to assess and to improve sustainability of agricultural production systems, represented by the economy of energy resources and other inputs translated into energy terms. This type of analysis can complement the economic view contributing to more efficient production systems. Moreover, assessing crops with traditional food use may play an important role in energy provision. Energy efficiency tools were applied in order to determine the energy demand as well as the efficiency of the biomass production of several forage crops in mechanized systems conducted at Paraná state, Brazil. Material flow, input and output energy, energy balance, energy return over investment and embodied energy were used and identified that maize and sorghum were the crops that uses energy in the most efficient way, represented by the best results at net energy availability, profitability and embodied energy at the final product. Oat and ryegrass were the crops the presented the least efficient energy uses in the biomass production systems.   Keywords: Bioenergy, energy indicators, sustainability, embodied energy. &nbsp

Hadronic sizes and observables in high-energy scattering

The functional dependence of the high-energy observables of total cross section and slope parameter on the sizes of the colliding hadrons predicted by the model of the stochastic vacuum and the corresponding relations used in the geometric model of Povh and H\"ufner are confronted with the experimental data. The existence of a universal term in the expression for the slope, due purely to vacuum effects, independent of the energy and of the particular hadronic system, is investigated. Accounting for the two independent correlation functions of the QCD vacuum, we improve the simple and consistent description given by the model of the stochastic vacuum to the high-energy pp and pbar-p data, with a new determination of parameters of non-perturbative QCD. The increase of the hadronic radii with the energy accounts for the energy dependence of the observables.Comment: Latex, using Revtex.style . 2 ps figures. To be published in Physical Review D , July 199