Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a theta modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the theta-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the theta-modified Pauli equation. We extract theta-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a theta modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

Multiple synchronous states in static delay-free mutually connected PLL networks

In many engineering applications, the time coordination of geographically separated events is of fundamental importance, as in digital telecommunications and integrated digital circuits. Mutually connected (MC) networks are very good candidates for some new types of application, such as wireless sensor networks. This paper presents a study on the behavior of MC networks of digital phase-locked loops (DPLLs). Analytical results are derived showing that, even for static networks without delays, different synchronous states may exist for the network. An upper bound for the number of such states is also presented. Numerical simulations are used to show the following results: (i) the synchronization precision in MC DPLLs networks; (ii) the existence of synchronous states for the network does not guarantee its achievement and (iii) different synchronous states may be achieved for different initial conditions. These results are important in the neural computation context. as in this case, each synchronous state may be associated to a different analog memory information. (C) 2010 Elsevier B.V. All rights reserved.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

EFFECTIVE NETWORKS FOR REAL-TIME DISTRIBUTED PROCESSING

This paper applies the concepts and methods of complex networks to the development of models and simulations of master-slave distributed real-time systems by introducing an upper bound in the allowable delivery time of the packets with computation results. Two representative interconnection models are taken into account: Uniformly random and scale free (Barabasi-Albert), including the presence of background traffic of packets. The obtained results include the identification of the uniformly random interconnectivity scheme as being largely more efficient than the scale-free counterpart. Also, increased latency tolerance of the application provides no help under congestion.

An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Assessing the impact of upper blepharoplasty on quality of life with a standardized questionnaire (QBleflaro): a pilot study

BACKGROUND: There is scarce literature on assessing surgical results and the impact of upper blepharoplasty on quality of life of patients. OBJECTIVE: To evaluate the impact on quality of life of patients submitted to upper blepharoplasty. METHODS: A prospective study using a standardized questionnaire applied to adult women submitted to upper blepharoplasty and evaluated 90 days later to estimate the surgical impact on quality of life and complications. RESULTS: Forty-one healthy adult females (median age of 53 years) were evaluated from June 2005 to March 2006. The questionnaire showed high internal consistency. The quality of life element with greater impact on the first postoperative week was related to physical appearance perception and that of lesser impact was associated to relationship with relatives and close friends. Hypertrophic scar was the main late complication. Satisfaction levels with the surgery were significantly related with absence of undesirable effects (p<0.01). CONCLUSIONS: The authors suggest a consistent tool to evaluate the impact of this surgical procedure on quality of life of patients. High satisfaction levels with upper blepharoplasty stood out. Keywords: Blepharoplasty; Quality of life; Patient satisfaction

Rhinometric evaluation of nasal cavity geometry and its relation to the upper arch transverse distance

The objective of this study was to evaluate children's respiratory patterns in the mixed dentition, by means of acoustic rhinometry, and its relation to the upper arch width development. Fifty patients were examined, 25 females and 25 males with mean age of eight years and seven months. All of them were submitted to acoustic rhinometry and upper and lower arch impressions to obtain plaster models. The upper arch analysis was accomplished by measuring the interdental transverse distance of the upper teeth, deciduous canines (measurement 1), deciduous first molars (measurement 2), deciduous second molars (measurement 3) and the first molars (measurement 4). The results showed that an increased left nasal cavity area in females means an increased interdental distance of the deciduous first molars and deciduous second molars and an increased interdental distance of the deciduous canines, deciduous first and second molars in males. It was concluded that there is a correlation between the nasal cavity area and the upper arch transverse distance in the anterior and mid maxillary regions for both genders.

An unusual, dwarf new species of Neotropical freshwater stingray, Plesiotrygon nana sp. nov., from the upper and mid Amazon basin: the second species of Plesiotrygon (Chondrichthyes: Potamotrygonidae)

A new species of the relatively poorly known Neotropical freshwater stingray genus Plesiotrygon Rosa, Castello & Thorson, 1987 is described from the main channel and smaller tributaries (Ríos Itaya and Pachitea) of the upper Amazon basin in Peru. The first specimen to be collected, however, was from much farther east in Rio Solimões in 1996, just down-river from Rio Purus (specimen unavailable for this study). Plesiotrygon nana sp. nov., is a very distinctive and unusually small species of freshwater stingray (Potamotrygonidae), described here mostly from three specimens representing different size classes and stages of sexual maturity. Plesiotrygon nana sp. nov., is distinguished from its only congener, P. iwamae Rosa, Castello & Thorson, 1987, by numerous unique features, including: dorsal coloration composed of very fine rosettes or a combination of spots and irregular ocelli; very circular disc and snout; very small and less rhomboidal spiracles; short snout and anterior disc region; narrow mouth and nostrils; denticles on dorsal tail small, scattered, not forming row of enlarged spines; adult and preadult specimens with significantly fewer tooth rows; fewer caudal vertebrae; higher total pectoral radials; very small size, probably not surpassing 250 mm disc length or width, males maturing sexually at around 180 mm disc length and 175 mm disc width; distal coloration of tail posterior to caudal stings usually dark purplish-brown; and features of the ventral lateral-line canals (hyomandibular canal very narrow, infraorbital and supraorbital canals not undulated, supraorbital and infraorbital loops small and narrow, supraorbital loop very short, not extending posteriorly to level of mouth, jugular and posterior infraorbital canals short, not extending caudally to first gill slits, subpleural loop very narrow posteriorly; absence of anterior and posterior subpleural tubules). To provide a foundation for the description of P. nana sp. nov., morphological variation in P. iwamae was examined based on all type specimens as well as newly collected and previously unreported material. Two specimens topotypic with the male paratype of P. nana sp. nov., referred to here as Plesiotrygon cf. iwamae, are also reported. Relationships of the new species to P. iwamae are discussed; further characters indicative of Plesiotrygon monophyly are proposed, but the genus may still not be valid. Plesiotrygon nana sp. nov., is commercialized with some regularity in the international aquarium trade from Iquitos (Peru), an alarming circumstance because nothing is known of its biology or conservation requirements.

A cave population of Isbrueckerichthys alipionis (Gosline, 1947) in the Upper Ribeira karst area, southeastern Brazil (Siluriformes: Loricariidae)

A cave population of the armored catfish Isbrueckerichthys alipionis is reported from the Santana Cave, in the rio Betari watershed, Upper Ribeira karst area, Iporanga, São Paulo State, southeastern Brazil. The cave population was compared to an epigean population of I. alipionis and no significant differences where found in morphology or degree of pigmentation. As the cave population is known for at least 30 years and is apparently isolated from epigean streams, it is classified as troglophilic. The discovery of this troglophilic species in the Santana Cave is an additional strong argument for the conservation of that cave.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.