An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Influence of interimplant distance on bone microstructure: A histomorphometric study in dogs

The microstructure of the crestal alveolar bone is important for both the maintenance of osseointegration and the location of the gingival soft tissues. The aim of this study was to evaluate and compare the bone microstructure of the alveolar bone and of the interimplant bone in implants inserted at different interimplant distances. The mandibular bilateral premolars of six dogs were extracted, and after 12 weeks, each dog received eight implants, for a total of 48 implants. Two pairs of implants, one for each hemiarch, were separated by 2 mm (group 1) and by 3 mm (group 2). After 12 weeks, the implants received temporary acrylic prostheses. After four more weeks, metallic crowns substituted the temporary prostheses. After an additional 8 weeks the animals were sacrificed and the hemimandibles were removed, dissected, and processed. The longitudinal collagen fiber orientation was 43.2% for the alveolar bone; it was 30.3% for the 2-mm group and 43.9% for the 3-mm group. There was a statistically significant difference between the 2-mm and 3-mm groups (p < .05). The orientation of transverse collagen fibers was 47.8% for the alveolar bone; it was 37.3% for the 2-mm group and 56.3% for the 3-mm group. There was a statistically significant difference between the 2-mm and 3-mm groups (p < .05). The marrow spaces were 34.87% for the alveolar bone, 52.3% for the 2-mm group, and 59.9% for the 3-mm group. There was a statistically significant difference between the alveolar bone and the 3-mm group (p < .05). The low mineral density index was 36.29 for the alveolar bone, 46.76 for the 2-mm group, and 17.91 for the 3-mm group. There was a statistically significant difference between the 2-mm and 3-mm groups (p < .05). The high mineral density was 87.57 for the alveolar bone, 72.58 for the 2-mm group, and 84.91 for the 3-mm group. There was a statistically significant difference between the alveolar bone and the 2-mm group (p < .05). The collagen fiber orientation resulted in statistically significant differences in both the 2-mm and 3-mm groups compared with the alveolar bone. The marrow spaces appeared significantly increased in the 3-mm group compared with the alveolar bone. The low mineral density index was significantly higher in the 2-mm group, while the high mineral density index was significantly higher in the alveolar bone. In conclusion, the interimplant distance should not be less than 3 mm.

SEM analysis of enamel surface treated by Er : YAG laser: Influence of irradiation distance

Background: Depending on the distance of laser tip to dental surface a specific morphological pattern should be expected. However, there have been limited reports that correlate the Er:YAG irradiation distance with dental morphology. Purpose: To assess the influence of Er:YAG laser irradiation distance on enamel morphology, by means of scanning electron microscopy (SEM). Methods: Sixty human third molars were employed to obtain discs (congruent to 1 mm thick) that were randomly assigned to six groups (n = 10). Five groups received Er:YAG laser irradiation (80 mJ/2 Hz) for 20 s, according to the irradiation distance: 11, 12, 14, 16, or 17 mm. and the control group was treated with 37% phosphoric acid for 15 s. The laser-irradiated discs were bisected. One hemi-disc was separated for superficial analysis without subsequent acid etching, and the other one, received the phosphoric acid for 15 s. Samples were prepared for SEM. Results: Laser irradiation at 11 and 12 min provided an evident ablation of enamel, with evident fissures and some fused areas. At 14, 16 and 17 mm the superficial topography was flatter than in the other distances. The subsequent acid etching on the lased-surface partially removed the disorganized tissue. Conclusions: Er:YAG laser in defocused mode promoted slight morphological alterations and seems more suitable for enamel conditioning than focused irradiation. The application of phosphoric acid on lased-enamel surface, regardless of the irradiation distance, decreased the superficial irregularities.

Shear strength of the bond to primary dentin: influence of Er:YAG laser irradiation distance

The aim of this study was to assess in vitro the influence of Er:YAG laser irradiation distance on the shear strength of the bond between an adhesive restorative system and primary dentin. A total of 60 crowns of primary molars were embedded in acrylic resin and mechanically ground to expose a flat dentin surface and were randomly assigned to six groups (n = 10). The control group was etched with 37% phosphoric acid. The remaining five groups were irradiated (80 mJ, 2 Hz) at different irradiation distances (11, 12, 16, 17 and 20 mm), followed by acid etching. An adhesive agent (Single Bond) was applied to the bonding sites, and resin cylinders (Filtek Z250) were prepared. The shear bond strength tests were performed in a universal testing machine (0.5 mm/min). Data were submitted to statistical analysis using one-way ANOVA and the Kruskal-Wallis test (p < 0.05). The mean shear bond strengths were: 7.32 +/- 3.83, 5.07 +/- 2.62, 6.49 +/- 1.64, 7.71 +/- 0.66, 7.33 +/- 0.02, and 9.65 +/- 2.41 MPa in the control group and the groups irradiated at 11, 12, 16, 17, and 20 mm, respectively. The differences between the bond strengths in groups II and IV and between the bond strengths in groups II and VI were statistically significant (p < 0.05). Increasing the laser irradiation distance resulted in increasing shear strength of the bond to primary dentin.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS: THE MAGNETIC FIELD GEOMETRY AND THE INFLUENCE OF THE WIND ON GIANT PLANET MIGRATION

By means of numerical simulations, we investigate magnetized stellar winds of pre-main-sequence stars. In particular, we analyze under which circumstances these stars will present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind. We show that the plasma-beta parameter (the ratio of thermal to magnetic energy densities) is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta(0) << 1. Using our self-consistent three-dimensional magnetohydrodynamics model, we estimate for these stellar winds the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter. In contrast to the findings of Lovelace et al., who estimated such timescales using the Weber and Davis model, our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on hot-Jupiters migration. Further simulations are necessary to investigate this result under more intense surface magnetic field strengths (similar to 2-3 kG) and higher coronal base densities, as well as in a tilted stellar magnetosphere.

Relation of genetic phylogeny and geographical distance of tick-borne encephalitis virus in central Europe

Tick-borne encephalitis virus (TBEV) is the most important arboviral agent causing disease of the central nervous system in central Europe. In this study, 61 TBEV E gene sequences derived from 48 isolates from the Czech Republic, and four isolates and nine TBEV strains detected in ticks from Germany, covering more than half a century from 1954 to 2009, were sequenced and subjected to phylogenetic and Bayesian phylodynamic analysis to determine the phylogeography of TBEV in central Europe. The general Eurasian continental east-to-west pattern of the spread of TBEV was confirmed at the regional level but is interlaced with spreading that arises because of local geography and anthropogenic influence. This spread is reflected by the disease pattern in the Czech Republic that has been observed since 1991. The overall evolutionary rate was estimated to be approximately 8x10(-4) substitutions per nucleotide per year. The analysis of the TBEV E genes of 11 strains isolated at one natural focus in Zd`ar Kaplice proved for the first time that TBEV is indeed subject to local evolution.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Shot Noise in a Spin-Diode Geometry

We apply the master equation technique to calculate shot noise in a system composed of single level quantum dot attached to a normal metal lead and to a ferromagnetic lead (NM-QD-FM). It is known that this system operates as a spin-diode, giving unpolarized currents for forward bias and polarized current for reverse bias. This effect is observed when only one electron can tunnel at a time through the dot, due to the strong intradot Coulomb interaction. We find that the shot noise also presents a signature of this spin-diode effect, with a super-Poissonian shot noise for forward and a sub-Poissonian shot noise for reverse bias voltages. The shot noise thus can provide further experimental evidence of the spin-rectification in the NM-QD-FM geometry.

SRTM resample with short distance-low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60 degrees north latitude and 56 degrees south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc-second (similar to 30m) for areas within the USA and at 3 arc-second (similar to 90m) resolution for the rest of the world. A resolution of 90m can be considered suitable for the small or medium-scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3"" to 1"". We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1"" model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1"" NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1"" surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline-interpolated surface still presented some noise and linear artifacts, which were removed by kriging.

PACKMOL: A Package for Building Initial Configurations for Molecular Dynamics Simulations

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the system`s overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules Must keep safe pairwise distances. Obtaining Such a molecular arrangement can be considered it packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules Must be greater than some specified tolerance. We have developed a code able to pack millions of atoms. grouped in arbitrarily complex molecules, inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straight forward. In addition. different atoms belonging to the same molecule may also be restricted to different spatial regions, in Such a way that more ordered molecular arrangements call be built, as micelles. lipid double-layers, etc. The packing time for state-of-the-art molecular dynamics systems varies front a few seconds to a few Minutes in a personal Computer. The input files are simple and Currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and call be downloaded front http://www.ime.unicamp.br/similar to martinez/packmol/. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 30: 2157-2164, 2009

Perfect Simulation of a Coupling Achieving the (d)over-bar-distance Between Ordered Pairs of Binary Chains of Infinite Order

We explicitly construct a stationary coupling attaining Ornstein`s (d) over bar -distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of i.i.d. sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.