Towards a Mobile Three-dimensional Modelling System for Underground Structures

Robotica 2012: 12th International Conference on Autonomous Robot Systems and Competitions April 11, 2012, Guimarães, Portugal

Comparative analysis of two-dimensional electrophoresis maps (2-DE) of Helicobacter pylori from Brazilian patients with chronic gastritis and duodenal ulcer: a preliminary report

Helicobacter pylori is a bacterium recognized as the major cause of peptic ulcer and chronic gastritis. Recently, a proteome-based approach was developed to investigate pathogenic factors related to H. pylori. In this preliminary study, H. pylori strains were isolated from gastric biopsies of patients with chronic gastritis and duodenal ulcers. A partial proteomic analysis of H. pylori strains was performed by bacterial lyses and proteins were separated by two-dimensional gel electrophoresis (2-DE). A comparative analysis was performed to verify a differential protein expression between these two 2-DE maps. These data should be useful to clarify the role of different proteins related to bacterial pathogenesis. This study will be completed using a larger number of samples and protein identification of H. pylori by MALDI-TOF mass spectrometry.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Non-covalent and covalent protein labeling in two-dimensional gel electrophoresis.

Over the past decades, several sensitive post-electrophoretic stains have been developed for an identification of proteins in general, or for a specific detection of post-translational modifications such as phosphorylation, glycosylation or oxidation. Yet, for a visualization and quantification of protein differences, the differential two-dimensional gel electrophoresis, termed DIGE, has become the method of choice for a detection of differences in two sets of proteomes. The goal of this review is to evaluate the use of the most common non-covalent and covalent staining techniques in 2D electrophoresis gels, in order to obtain maximal information per electrophoresis gel and for an identification of potential biomarkers. We will also discuss the use of detergents during covalent labeling, the identification of oxidative modifications and review influence of detergents on finger prints analysis and MS/MS identification in relation to 2D electrophoresis.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

Differential epipolar constraint in mobile robot egomotion estimation

The estimation of camera egomotion is a well established problem in computer vision. Many approaches have been proposed based on both the discrete and the differential epipolar constraint. The discrete case is mainly used in self-calibrated stereoscopic systems, whereas the differential case deals with a unique moving camera. The article surveys several methods for mobile robot egomotion estimation covering more than 0.5 million samples using synthetic data. Results from real data are also given

Temporal variation of wing geometry in Aedes albopictus

Although native to the tropical and subtropical areas of Southeast Asia, Aedes albopictus is now found on five continents, primarily due to its great capacity to adapt to different environments. This species is considered a secondary vector of dengue virus in several countries. Wing geometric morphometrics is widely used to furnish morphological markers for the characterisation and identification of species of medical importance and for the assessment of population dynamics. In this work, we investigated the metric differentiation of the wings of Ae. albopictus samples collected over a four-year period (2007-2010) in São Paulo, Brazil. Wing size significantly decreased during this period for both sexes and the wing shape also changed over time, with the wing shapes of males showing greater differences after 2008 and those of females differing more after 2009. Given that the wings play sex-specific roles, these findings suggest that the males and females could be affected by differential evolutionary pressures. Consistent with this hypothesis, a sexually dimorphic pattern was detected and quantified: the females were larger than the males (with respect to the mean) and had a distinct wing shape, regardless of allometric effects. In conclusion, wing alterations, particularly those involving shape, are a sensitive indicator of microevolutionary processes in this species.

Limits on the validity of infinite length assumptions for modelling shallow landslides

The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two-dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25?m). However, it may also be valid even at much finer grid resolutions (e.g. 1?m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright (c) 2012 John Wiley & Sons, Ltd.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Are the light-harvesting I complexes from Rhodospirillum rubrum arranged around the reaction centre in a square geometry?

The basic photosynthetic unit containing the reaction centre and the light-harvesting I complex (RC-LHI) of the purple non-sulphur bacterium Rhodospirillum rubrum was purified and reconstituted into two-dimensional (2D) membrane crystals. Transmission electron microscopy using conventional techniques and cryoelectron microscopy of the purified single particles and of 2D crystals yielded a projection of the RC-LHI complex at a resolution of at least 1.6 nm. In this projection the LHI ring appears to have a square symmetry and packs in a square crystal lattice. The square geometry of the LHI ring was observed also in images of single isolated particles of the RC-LHI complex. However, although the LHI units are packed identically within the crystal lattice, a new rotational analysis developed here showed that the reaction centres take up one of four possible orientations within the ring. This fourfold disorder supports our interpretation of a square ring symmetry and suggests that a hitherto undetected component may be present within the photosynthetic unit.

Side-branch growth in two-dimensional dendrits. Part II: Phase-field model

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.