Gauge invariance and classical dynamics of noncommutative particle theory

We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed; in particular, the motion in the constant magnetic field is studied in detail. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3299296]

Continuous structural transitions in quasi-one-dimensional classical Wigner crystals

We study the structural phase transitions in confined systems of strongly interacting particles. We consider infinite quasi-one-dimensional systems with different pairwise repulsive interactions in the presence of an external confinement following a power law. Within the framework of Landau's theory, we find the necessary conditions to observe continuous transitions and demonstrate that the only allowed continuous transition is between the single-and the double-chain configurations and that it only takes place when the confinement is parabolic. We determine analytically the behavior of the system at the transition point and calculate the critical exponents. Furthermore, we perform Monte Carlo simulations and find a perfect agreement between theory and numerics.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

In this paper, employing the Ito stochastic Schrodinger equation, we extend Bell's beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm's causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm's causal dynamics regarding stationary states in quantum mechanics.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

Support vector machines for detecting age-related changes in running kinematics

Age-related changes in running kinematics have been reported in the literature using classical inferential statistics. However, this approach has been hampered by the increased number of biomechanical gait variables reported and subsequently the lack of differences presented in these studies. Data mining techniques have been applied in recent biomedical studies to solve this problem using a more general approach. In the present work, we re-analyzed lower extremity running kinematic data of 17 young and 17 elderly male runners using the Support Vector Machine (SVM) classification approach. In total, 31 kinematic variables were extracted to train the classification algorithm and test the generalized performance. The results revealed different accuracy rates across three different kernel methods adopted in the classifier, with the linear kernel performing the best. A subsequent forward feature selection algorithm demonstrated that with only six features, the linear kernel SVM achieved 100% classification performance rate, showing that these features provided powerful combined information to distinguish age groups. The results of the present work demonstrate potential in applying this approach to improve knowledge about the age-related differences in running gait biomechanics and encourages the use of the SVM in other clinical contexts. (C) 2010 Elsevier Ltd. All rights reserved.

Tracking 10-year competitive winning performance of judo athletes across age groups

Little information is available concerning early specialization and competitive success in judo across the early training years. Thus, the present objective was to verify the stability of individual competitive performance of a state-level championship for judo athletes who had been previously successful. For this, 406 athletes from six age groups (9 to 20+ years old) of each sex were followed for 10 years. Using recorded data from the Sao Paulo State Judo Federation beginning in 1999, the scores and standings for these judo players were analyzed. The proportion of medal winners during this period was not constant, differing from the grand mean in all groups of both 204 males and 202 females. At the end of this period, only 7% of the male and 5% of the female athletes had maintained their competitive levels. Successful competitive performance in early judo competition was not associated with success later in adulthood.

Cultivation of hitherto-uncultured bacteria belonging to the Verrucomicrobia subdivision 1 from the potato (Solanum tuberosum L.) rhizosphere

The role of dominant bacterial groups in the plant rhizosphere, e.g., those belonging to the phyla Acidobacteria and Verrucomicrobia, has, so far, not been elucidated, and this is mainly due to the lack of culturable representatives. This study aimed to isolate hitherto-uncultured bacteria from the potato rhizosphere by a combination of cultivation approaches. An agar medium low in carbon availability (oligotrophic agar medium) and either amended with potato root exudates or catalase or left unamended was used with the aim to improve the culturability of bacteria from the potato rhizosphere. The colony forming unit numbers based on colonies and microcolonies were compared with microscopically determined fluorescence-stained cell numbers. Taxonomical diversity of the colonies was compared with that of library clones made from rhizosphere DNA, on the basis of 16S rRNA gene comparisons. The oligotrophic media amended or not with catalase or rhizosphere extract recovered up to 33.6% of the total bacterial numbers, at least seven times more than the recovery observed on R2A. Four hitherto-uncultured Verrucomicrobia subdivision 1 representatives were recovered on agar, but representatives of this group were not found in the clone library. The use of oligotrophic medium and its modifications enabled the growth of colony numbers, exceeding those on classical agar media. Also, it led to the isolation of hitherto-uncultured bacteria from the potato rhizosphere. Further improvement in cultivation will certainly result in the recovery of other as-yet-unexplored bacteria from the rhizosphere, making these groups accessible for further investigation, e.g., with respect to their possible interactions with plants.

The relationship of flow cytometry results with classical measures of bacterial counts in raw refrigerated milk

Bulk milk was collected from 100 farms throughout the year and analysed after storage for either 24, 48 or 72 h, using flow cytometry. The total bacterial counts obtained by two methods - flow cytometry and standard plate count were compared and the conversion relationship between them was assessed: the results showed no effect of the age of the samples relationship between these two methods.

Classical and alternative components of the mitochondrial respiratory chain in pathogenic fungi as potential therapeutic targets

The frequency of opportunistic fungal infection has increased drastically, mainly in patients who are immunocompromised due to organ transplant, leukemia or HIV infection. In spite of this, only a few classes of drugs with a limited array of targets, are available for antifungal therapy. Therefore, more specific and less toxic drugs with new molecular targets is desirable for the treatment of fungal infections. In this context, searching for differences between mitochondrial mammalian hosts and fungi in the classical and alternative components of the mitochondrial respiratory chain may provide new potential therapeutic targets for this purpose.

Evaluation of curcumin and cisplatin-induced DNA damage in PC12 cells by the alkaline comet assay

A very appropriate method for antigenotoxicity evaluation of antioxidants is the comet assay, since this analytical method detects initial DNA lesions that are still subject to repair; in other words, lesions that are very associated to damages resulting from the generation and subsequent action of reactive species. However, a solid evaluation should be developed in order to avoid inexact interpretations. In our study, besides the association of curcumin with cisplatin, curcumin and cisplatin agents were also tested separately. Classical genotoxic compounds, when tested by the comet assay, present an increase in the nucleoid tail; however, the cisplatin treatment has resulted in a decrease of DNA migration. This was an expected effect, as the cross-links between cisplatin and DNA decrease the DNA electrophoretic mobility. A similar effect was observed with the curcumin treatment, which decreased the nucleoid tail. Such effect was not expected and reinforced the necessity of including in the study, separate treatment groups with potentially antigenotoxic substances. The comet assay results have been analyzed using specific software for image analysis, as well as the classical visual analysis, and we have observed that the effect of decrease in DNA electrophoretic mobility was more easily observed when the data were analyzed by the software.

Experimental study of the quantum driven pendulum and its classical analog in atom optics

We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck’s constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.