Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of $SL(2,{\mathbb Z})$) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of an hyperbolic three-geometry associated with $q$-series in the computation of the string amplitudes.Comment: Revised version. References added, results remain unchanged. arXiv admin note: text overlap with arXiv:hep-th/0701156, arXiv:1105.4571, arXiv:1206.0664 by other author

High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations

We present the results of several parametrizations to two different ensemble of data on $pp$ total cross sections $\sigma_{tot}^{pp}$ at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC ($\sqrt s = 14$ TeV) is $\sigma_{tot}^{pp} = 113 \pm 5$ mb and from the other, $\sigma_{tot}^{pp}=140 \pm 7$ mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine $\rho(s)$ (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented.In all cases good descriptions of the experimental data are obtained.Comment: One formula added, one unit changed, small misprints corrected, final version to be published in Brazilian Journal of Physics; 13 pages, 8 figures, aps-revte

A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD

The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partition function constructed in d=4; the exponent 2S in the square of the wave functional plays the role of a d=3 Euclidean action. We start from a gauge-invariant conjecture for the infrared-dominant part of S, based on dynamical generation of a gluon mass M in d=4. We argue that the exact leading term, of O(M), in an expansion of S in inverse powers of M is a d=3 gauge-invariant mass term (gauged non-linear sigma model); the next leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass, which we constrain to be the same as M, and d=3 coupling are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio in d=3 of mass to coupling squared can be estimated from d=3 dynamics. This allows us to estimate the QCD coupling $\alpha_s(M^2)$ in terms of this strictly d=3 ratio; we find a value of about 0.4, in good agreement with an earlier theoretical value but a little low compared to QCD phenomenology. The wave functional for d=2+1 QCD has an exponent that is a d=2 infrared-effective action having both the gauge-invariant mass term and the field strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d=2 QCD would lead in d=3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), N-ality = 0 mod N representations are not confined.Comment: 15 pages, no figures, revtex

Dinâmica do carbono na regeneração natural em uma floresta manejada na Amazônia: estudo de caso Mil Madeiras Preciosas.

O futuro da Floresta Amazônica e as consequências que o desmatamento pode causar a mudança climática têm sido cada vez mais discutidos pela sociedade. Dessa forma, conhecer as consequências que as operações florestais irão trazer para a dinâmica das florestas manejadas é de extrema importância, mas precisamente nos termos da floresta está agindo como fonte ou sumidouro de carbono. Por esse motivo é importante estudar o ciclo do carbono na regeneração natural, já que a maior parte dos estudos de biomassa e carbono em florestas nativas se concentra na avaliação do estrato superior. Este trabalho utilizou dados de inventários florestais contínuos realizados na Fazenda Dois Mil, pertencente à empresa Mil Madeiras Preciosas, localizada no município de Itacoatiara-AM. O objetivo deste trabalho foi quantificar o estoque de carbono presente na regeneração natural de uma floresta manejada, assim como estudar a dinâmica do carbono e avaliar em diferentes períodos de monitoramento como a regeneração está se comportando após a exploração florestal.Dissertação (Mestrado em Ciências Florestais e Ambientais) - Universidade Federal do Amazonas, Manaus. Orientador: Dr. Celso Paulo de Azevedo; coorientadora: Dra. Cintia Rodrigues de Souza

Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space

We investigate the properties of eigenstates and local density of states (LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two-interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the non-ergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.Comment: 13 pages, 18 figure

Classical versus Quantum Structure of the Scattering Probability Matrix. Chaotic wave-guides

The purely classical counterpart of the Scattering Probability Matrix (SPM) $\mid S_{n,m}\mid^2$ of the quantum scattering matrix $S$ is defined for 2D quantum waveguides for an arbitrary number of propagating modes $M$. We compare the quantum and classical structures of $\mid S_{n,m}\mid^2$ for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincar\`{e} maps.Comment: 9 pages, 9 figure

Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size