Symmetry has been a very useful tool to researchers in various scientific fields. At its most basic, symmetry refers to the invariance of an object to some transformation, or set of transformations. Usually one searches for, and uses information concerning an existing symmetry within given data, structure or concept to somehow improve algorithm performance or compress the search space. This thesis examines the effects of imposing or inducing symmetry on a search space. That is, the question being asked is whether only existing symmetries can be useful, or whether changing reference to an intuition-based definition of symmetry over the evaluation function can also be of use. Within the context of optimization, symmetry induction as defined in this thesis will have the effect of equating the evaluation of a set of given objects. Group theory is employed to explore possible symmetrical structures inherent in a search space. Additionally, conditions when the search space can have a symmetry induced on it are examined. The idea of a neighborhood structure then leads to the idea of opposition-based computing which aims to induce a symmetry of the evaluation function. In this context, the search space can be seen as having a symmetry imposed on it. To be useful, it is shown that an opposite map must be defined such that it equates elements of the search space which have a relatively large difference in their respective evaluations. Using this idea a general framework for employing opposition-based ideas is proposed. To show the efficacy of these ideas, the framework is applied to popular computational intelligence algorithms within the areas of Monte Carlo optimization, estimation of distribution and neural network learning. The first example application focuses on simulated annealing, a popular Monte Carlo optimization algorithm. At a given iteration, symmetry is induced on the system by considering opposite neighbors. Using this technique, a temporary symmetry over the neighborhood region is induced. This simple algorithm is benchmarked using common real optimization problems and compared against traditional simulated annealing as well as a randomized version. The results highlight improvements in accuracy, reliability and convergence rate. An application to image thresholding further confirms the results. Another example application, population-based incremental learning, is rooted in estimation of distribution algorithms. A major problem with these techniques is a rapid loss of diversity within the samples after a relatively low number of iterations. The opposite sample is introduced as a remedy to this problem. After proving an increased diversity, a new probability update procedure is designed. This opposition-based version of the algorithm is benchmarked using common binary optimization problems which have characteristics of deceptivity and attractive basins characteristic of difficult real world problems. Experiments reveal improvements in diversity, accuracy, reliability and convergence rate over the traditional approach. Ten instances of the traveling salesman problem and six image thresholding problems are used to further highlight the improvements. Finally, gradient-based learning for feedforward neural networks is improved using opposition-based ideas. The opposite transfer function is presented as a simple adaptive neuron which easily allows for efficiently jumping in weight space. It is shown that each possible opposite network represents a unique input-output mapping, each having an associated effect on the numerical conditioning of the network. Experiments confirm the potential of opposite networks during pre- and early training stages. A heuristic for efficiently selecting one opposite network per epoch is presented. Benchmarking focuses on common classification problems and reveals improvements in accuracy, reliability, convergence rate and generalization ability over common backpropagation variants. To further show the potential, the heuristic is applied to resilient propagation where similar improvements are also found.

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

<p>Establishing an axis of cell polarity is central to cell motility, tissue morphogenesis, and cell proliferation. A highly conserved group of polarity regulators is responsible for organizing a wide variety of polarized morphologies. One of the most widely expressed polarity regulators is the Rho-type GTPase Cdc42. In response to cell cycle cues the budding yeast <italic>Saccharomyces cerevisiae</italic> polarizes Cdc42p to a discrete site on the cell periphery. GTP-Cdc42p recruits a number of effectors that aid in the organization of a polarized actin cytoskeleton. The polarized actin cytoskeleton acts as tracks to facilitate the delivery of the secretory vesicles that will grow the bud, an essential process for an organism that proliferates by budding. We have employed treatment with the actin depolymerizing drugs Latrunculin A and B as well as high-speed timelapse microscopy of fluorescently labeled polarity proteins to characterize the assembly of the incipient bud site. </p><p>Often, ensuring that only a single axis of polarity is established is as important as generating asymmetry in the cell. Even in the absence of positional cues dictating the direction of polarization, many cells are still able to self-organize and establish one, and only one, polarity axis through a process termed symmetry breaking. Symmetry breaking is thought to employ positive feedback to amplify stochastic fluctuations in protein concentration into a larger asymmetry. To test whether singularity could be guaranteed by the amplification mechanism we re-wired yeast to employ a synthetic positive feedback mechanism. The re-wired cells could establish polarity, however they occasionally made two buds simultaneously, suggesting that singularity is guaranteed by the amplification mechanism.</p> / Dissertation

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A gauged SU(4) &#64258;avor symmetric hadronic Lagrangian with empirical hadron masses is constructed to study charmonium absorption and charmed hadron production in hadronic reactions. For the coupling constants, empirical values are used if available. Otherwise, they are determined from known coupling constants using the SU(4) relations. To take into account the &#64257;nite sizes of hadrons, form factors are introduced at strong interaction vertices with empirical cutoff parameters. For J/&#968;absorption by nucleons, we have included both two-and three-body final states and &#64257;nd that with a cutoff parameter of 1 GeV at interaction vertices involving charm hadrons, the cross section is at most 5 mb and is consistent with that extracted from J/&#968;production from both photo-and proton-nucleus reactions. We have also evaluated the cross sections for charmed hadron production from pion and rho meson interactions with nucleons. With the same cutoff parameter of 1 GeV at interaction vertices, we &#64257;nd that these cross sections have values of a few tenths of mb and are dominated bythe s-channel nucleon pole diagram. For charmed hadron production from proton-proton reactions, their cross sections including bothtwo-andthree-body &#64257;nal states are about 1 batcenter-of-mass energyof 11.5 GeV, which is comparable to the measured inclusive cross section in these reactions.Including photon as a U(1) gauge particle, we have extended the model to study charmed hadron production in photon-proton reactions with both two-and three-body &#64257;nal states included. For form factors, an overall one is introduced in each processin order to maintain the gauge invariance of the total amplitude. Fitting the cutoff parameter in the form factor to the measured total cross section for charmed hadron production in photon-proton reactions at a center-of-mass energy of 6 GeV, the ratio of the cross sections for two-body and three-body &#64257;nal states is consistent with available experimental data.This result is further compared with predictions from the leading-order perturbative QCD calculation. Knowledge of the cross sections for charmonium absorption byhadrons and for charmed hadron production in hadronic reactions is essential for understanding charm production in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC), where a quark-gluon plasma is expected to be formed during the initial hot dense stage.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 157-163). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph.D.)--University of Western Sydney, 2008. / A thesis presented to the University of Western Sydney, College of Health and Science, School of Computing and Mathematics, in fulfilment of the requirements for the degree of Doctor of Philosophy - Science. Includes bibliographies.

A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented.

Heavy ions are collided at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) in an effort to create a unique state of nuclear matter, where quarks and gluons can freely move over volumes larger than the typical size of a nucleon (typical scale of Quantum Chromodynamics, QCD). In this state, called a "Quark Gluon Plasma" (QGP), it is proposed Chiral symmetry is restored. The fact that Chiral symmetry is a symmetry of the Standard model and is broken at low energy (current energy scale of universe) makes the study of its possible very interesting. The analysis in this dissertation searches for signatures of chiral symmetry restoration at the phase transition between the QGP and the hadronic gas phase by using resonance particles as probes. Resonances may decay inside of hot dense matter due to their short lifetimes, and therefore their decay daughters carry away dynamical information such as the mass and decay width. Mass shift and width broadening are predicted signatures of chiral symmetry restoration. The [phi](1020) resonances reconstructed from the dielectron decay channel are investigated in this dissertation. This decay channel does not suffer scattering from the late hadronic medium due to the relatively small interaction cross section of leptons with hadrons. The disadvantage of this channel comes from the small branching ratio. Therefore, large statistics and clean Particle IDentification (PID) are necessary for this analysis. Those requirements were fulfilled with high luminosity beams at RHIC and the newly developed and installed Time Of Flight (TOF) detectors, which provide clear particle identification up to momentum of 2-3 GeV/c, as well as the large acceptance of the Solenoidal Tracker At RHIC (STAR) detector. In this dissertation, measurements of mass, width, transverse momentum spectrum, and yields of [phi][right arrow] e⁺e⁻ at mid-rapidity [mathematical symbols] from the STAR experiment in Au+Au collisions at [mathematical symbols]=200 GeV are presented and compared to a previously measured [phi] meson result from a hadronic decay channel. The possibility of medium modification which implies Chiral symmetry restoration is discussed. / text

The ATLAS Experiment is one of the four large detectors located at the Large Hadron Collider (LHC) at CERN in Geneva, Switzerland. In summer 2008, ATLAS is expected to start collecting data from proton-proton collisions at 14 TeV centre-of-mass energy. In the centre of the detector, the reconstruction of charged particle tracks is performed by silicon and drift tube based sub-detectors. In order to achieve the ATLAS physics goals the resolutions of the measured track parameters should not be degraded by more than 20% due to misalignment. Thus, the relative positions of the silicon detector elements have to be known to an accuracy of about 10 micrometers in the coordinate with the best measurement precision. This requirement can be achieved by track based alignment algorithms combined with measurements from hardware based alignment techniques. A robust track based alignment method based on track residual and overlap residual optimisation has been developed and implemented into the ATLAS offline software framework. The alignment algorithm has been used to align a test beam setup and also part of the final ATLAS detector using cosmic ray muons. Several simulation studies showed that the algorithm will be able to align the full detector with collision data. In addition to detector misalignments, limitations in the knowledge of the proton structure are going to affect physics discoveries at the LHC. Therefore, parton distribution uncertainties in high-mass Drell-Yan processes have been determined. This study includes the analysis of the forward-backward asymmetry. It has been performed on the level of next-to-leading order in both, Monte Carlo simulation using k-factors and parton distribution functions. This analysis is crucial for new physics searches with the ATLAS detector.