The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion-nucleon scattering

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: 1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and 2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the $\Delta$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.Comment: 12 pages, 6 figures, using RevTEX4. References added, discussion extended, conclusions unchanged. To be published in Nuclear Physics

Rough Set Based Rule Evaluations and Their Applications

Knowledge discovery is an important process in data analysis, data mining and machine learning. Typically knowledge is presented in the form of rules. However, knowledge discovery systems often generate a huge amount of rules. One of the challenges we face is how to automatically discover interesting and meaningful knowledge from such discovered rules. It is infeasible for human beings to select important and interesting rules manually. How to provide a measure to evaluate the qualities of rules in order to facilitate the understanding of data mining results becomes our focus. In this thesis, we present a series of rule evaluation techniques for the purpose of facilitating the knowledge understanding process. These evaluation techniques help not only to reduce the number of rules, but also to extract higher quality rules. Empirical studies on both artificial data sets and real world data sets demonstrate how such techniques can contribute to practical systems such as ones for medical diagnosis and web personalization. In the first part of this thesis, we discuss several rule evaluation techniques that are proposed towards rule postprocessing. We show how properly defined rule templates can be used as a rule evaluation approach. We propose two rough set based measures, a Rule Importance Measure, and a Rules-As-Attributes Measure, %a measure of considering rules as attributes, to rank the important and interesting rules. In the second part of this thesis, we show how data preprocessing can help with rule evaluation. Because well preprocessed data is essential for important rule generation, we propose a new approach for processing missing attribute values for enhancing the generated rules. In the third part of this thesis, a rough set based rule evaluation system is demonstrated to show the effectiveness of the measures proposed in this thesis. Furthermore, a new user-centric web personalization system is used as a case study to demonstrate how the proposed evaluation measures can be used in an actual application

A comparison between the Pittsburgh and Michigan approaches for the binary PSO algorithm

IEEE Congress on Evolutionary Computation. Edimburgo, 5 september 2005This paper shows the performance of the binary PSO algorithm as a classification system. These systems are classified in two different perspectives: the Pittsburgh and the Michigan approaches. In order to implement the Michigan approach binary PSO algorithm, the standard PSO dynamic equations are modified, introducing a repulsive force to favor particle competition. A dynamic neighborhood, adapted to classification problems, is also defined. Both classifiers are tested using a reference set of problems, where both classifiers achieve better performance than many classification techniques. The Michigan PSO classifier shows clear advantages over the Pittsburgh one both in terms of success rate and speed. The Michigan PSO can also be generalized to the continuous version of the PSO

In-medium spectral change of omega mesons as a probe of QCD four-quark condensate

Within QCD sum rules at finite baryon density we show the crucial role of four-quark condensates for the in-medium modification of the omega meson spectral function. In particular, such a global property as the sign of the in-medium omega meson mass shift is found to be governed by a parameter which describes the strength of the density dependence of the four-quark condensate beyond mean-field approximation. To study self-consistently the broadening of the omega meson resonance we employ a hadron spectral function based on the omega meson propagator delivered by an effective chiral Lagrangian. Measurements of the omega meson spectral change in heavy-ion collisions with the HADES detector can reveal the yet unknown density dependence of the four-quark condensate

Probing the strange quark condensate by di-electrons from phi meson decays in heavy-ion collisions at SIS energies

QCD sum rules predict that the change of the strange quark condensate $<\bar s s>$ in hadron matter at finite baryon density causes a shift of the peak position of the di-electron spectra from $\phi$ meson decays. Due to the expansion of hadron matter in heavy-ion collisions, the $\phi$ peak suffers a smearing governed by the interval of density in the expanding fireball, which appears as effective broadening of the di-electron spectrum in the $\phi$ region. The emerging broadening is sensitive to the in-medium change of $<\bar s s>$. This allows to probe directly in-medium modifications of $$ via di-electron spectra in heavy-ion collisions at SIS energies with HADES

Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions

The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of low-energy VVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarized VVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the corresponding structure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted, where possible, with "data-driven" dispersive evaluations of low-energy structure quantities, such as nucleon polarizabilities. We find significant disagreements with dispersive evaluations at very low momentum-transfer $Q$; for example, in the slope of polarizabilities at zero momentum-transfer. By expanding the results in powers of the inverse nucleon mass, we reproduce the known "heavy-baryon" expressions. This serves as a check of our calculation, as well as demonstrates the differences between the manifestly Lorentz-invariant (B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.Comment: 31 pages, 11 figures, 1 table; supplemented material: 1 Mathematica notebook; minor modifications, published versio

QCD sum rules for D mesons in dense and hot nuclear matter

Open charm mesons (pseudo-scalar and scalar as well as axial-vector and vector) propagating or resting in nuclear matter display an enhanced sensitivity to the chiral condensate. This offers new prospects to seek for signals of chiral restoration, in particular in p-A and p-bar-A reactions as envisaged in first-round experiments by the CBM and PANDA collaborations at FAIR. Weinberg type sum rules for charming chiral partners are presented, and the distinct in-medium modifications of open-charm mesons are discussed. We also address the gluon condensates near Tc and their impact on QCD sum rules.Comment: 6 pages, 7 figures, conference proceeding