Heteroclinic Connections in the Kuramoto-Sivashinsky Equation: a Computer Assisted Proof

On the example of a finite dimensional approximation of the Kuramoto-Sivashinsky equation we show how topological methods may be successfully used in computer assisted proofs of the existence of heteroclinic connections in ordinary differential equations.     

Risk factors for adverse drug reactions during thiacetazone treatment of pulmonary tuberculosis in human immunodeficiency virus infected adults

It is well established that many continuously distributed traits have a heritable component. However, it is often difficult to communicate to the general public the meaning of quantitative estimates of heritability. To address this problem, the present paper introduces a heuristic for communicating heritability to nonscientific audiences. This heuristic involves adopting an extremely simplified model of inheritance and artificially (and somewhat arbitrarily) defining a cutoffs of "low environmental risk" and "affectation status." Using body weight and obesity as an example, we present a table which gives estimates of the proportion of obese persons who are "genetically obese" assuming varying levels of "environmental risk" for obesity and relative body weight scores for defining obesity. The resulting statistic may prove useful for lay audiences in understanding a heritability estimate.     

Analysis of the effect of structural defects on the fatigue strength of RFSSW joints using C‐scan scanning acoustic microscopy and SEM

Solid‐state refill friction stir spot welding (RFSSW) technology offers significant benefits in the fabrication of aluminium structures in the transport and aerospace industries. In this paper, the joining of 1.6‐mm‐thick Alclad 7075‐T6 aluminium alloy sheets is investigated. High‐cycle fatigue strength tests of single‐lap welded joints were carried out on an Instron E10000 testing machine with a limited number of cycles equal to 2 × 10⁶. The welding of overlap fatigue specimens was conducted using an RPS100 spot welder by Harms & Wende GmbH & Co KG. C‐mode scanning acoustic microscopy (C‐SAM) and scanning electron microscopy (SEM) were utilised to evaluate the joint quality and characterise the microstructure. The paper discusses the effect of the maximum load force and defects (voids, hook, kissing bond, bonding ligament, etc) associated with the material flow in the weld on the failure mechanism. Insufficient plasticisation of sheet material and mixing of the material in the weld area are crucial defects that influence the number of destructive cycles. The weld defects in the joint structure are a source of a decrease in the fatigue life compared with the fatigue life of defect‐free welds. It was also found that RFSSW joint defects can be effectively detected by the nondestructive C‐SAM method.     

Tsallis entropy in dual homogenization of random composites using the stochastic finite element method

This work concerns an application of the Tsallis entropy to homogenization problem of the fiber‐reinforced and also of the particle‐filled composites with random material and geometrical characteristics. Calculation of the effective material parameters is done with two alternative homogenization methods—the first is based upon the deformation energy of the Representative Volume Element (RVE) subjected to the few specific deformations, while the second uses explicitly the so‐called homogenization functions determined under periodic boundary conditions imposed on this RVE. Probabilistic homogenization is made with the use of three concurrent non‐deterministic methods, namely Monte‐Carlo simulation, iterative generalized stochastic perturbation technique as well as the semi‐analytical approach. The last two approaches are based on the Least Squares Method with polynomial basis of the statistically optimized order— this basis serves for further differentiation in the 10th‐order stochastic perturbation technique, while semi‐analytical method uses it in probabilistic integrals. These three approaches are implemented all as the extensions of the traditional Finite Element Method (FEM) with contrastively different mesh sizes, and they serve in computations of Tsallis entropies of the homogenized tensor components as the functions of input coefficient of variation.     

Design and characteristics of gellan gum beads for modified release of meloxicam

The aim of the presented work was to design, formulate and evaluate the properties of low-acyl gellan macro beads with the potential application as carriers for oral delivery of meloxicam (MLX) in the prophylaxis of colorectal cancer. The beads were obtained by means of ionotropic gelation technique. Calcium chloride (1.0%, 9.0?×?10^?2 M) was used as the cross-linking agent. Nine different polymer, drug and surfactant (Tween^®80) mixtures were used for production of the beads. The quantitative compositions of the mixtures were generated with the application of the Design of Experiments (DoE) modulus from the STATISTICA Software. The prepared formulations revealed 7.2–27.0% of drug loading and 29.2–50.7% drug encapsulation efficiency. It turned out that 0.5% amount of gellan gum in the mixtures was not sufficient to obtain spherical beads. The morphology and surface of the dried beads were analyzed by SEM. Raman spectra confirmed that MLX did not undergo structural changes during production of the beads. The swelling behavior and degradation of the beads were evaluated in three simulated gastrointestinal fluids at different pH (1.2; 4.5; 6.8). The MLX in vitro release studies were conducted on USP apparatus IV, working in the open loop mode. The obtained results showed that MLX release from the dried beads was pH-dependent. The formulations obtained from mixtures containing 1.0 and 1.5% of gellan may be considered as oral dosage forms for MLX, intended to omit the stomach and release the drug in the distal parts of the gastrointestinal tract.     

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Integrated motion planning and control for the purposes of maneuvering mobile robots under state- and input constraints is a problem of vital practical importance in applications of mobile robots such as autonomous transportation. Those constraints arise naturally in practice due to specifics of robot mechanical construction and the presence of obstacles in motion environment. In contrast to approaches focusing on feedback control design under the assumption of given reference motion or motion planning with neglection of subsequent feedback motion execution, we adopt a controller-driven motion planning paradigm, which has recently gained attention of many researchers. It postulates design of motion planning algorithms dedicated to specific feedback control policies, which compute a sequence of feedback control subtasks instead of classically planned open-loop controls or parametric paths. In this spirit, we propose a motion planning algorithm driven by the VFO (Vector Field Orientation) control law for the waypoint-following task. Presented analysis of the VFO control law reveals its beneficial properties, which are subsequently utilized to solve a generally nonlinear and non-convex optimal motion planning problem by formulating it as a mixed-integer linear program (MILP). The solution proposed in this paper yields a waypoint sequence, which is designed for execution by application of the VFO control law to drive a robot to a prescribed final configuration under an input constraint imposed by bounded curvature of robot motion and state constraints resulting from a convex decomposition of task space. Satisfaction of these constraints is guaranteed analytically and exactly, i.e., without utilization of numerical approximations. Moreover, for a given discrete set of possible waypoint orientations, the proposed algorithm computes plans optimal w.r.t. given cost functional, which can be any convex linear combination of quantities such as robot path length, curvature of robot motion, distance to imposed state constraints, etc. Furthermore, the planning algorithm exploits the possibility of both forward or backward movement of the robot to allow maneuvering in demanding environments. Generated waypoint sequences are a compact representation of a motion plan, which can be immediately executed with the VFO controller without any additional post-processing. Validity of the proposed approach has been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.     

Sampled suffix array with minimizers

Sampling (evenly) the suffixes from the suffix array is an old idea trading the pattern search time for reduced index space. A few years ago Claude et al. showed an alphabet sampling scheme allowing for more efficient pattern searches compared with the sparse suffix array, for long enough patterns. A drawback of their approach is the requirement that sought patterns need to contain at least one character from the chosen subalphabet. In this work, we propose an alternative suffix sampling approach with only a minimum pattern length as a requirement, which is more convenient in practice. Experiments show that our algorithm (in a few variants) achieves competitive time‐space tradeoffs on most standard benchmark data. Copyright © 2017 John Wiley & Sons, Ltd.     

A Bloom filter based semi‐index on q‐grams

We present a simple q‐gram based semi‐index, which allows to look for a pattern typically only in a small fraction of text blocks. Several space‐time tradeoffs are presented. Experiments on Pizza & Chili datasets show that our solution is up to three orders of magnitude faster than the Claude et al. (Journal of Discrete Algorithms 2012; 11 :37) semi‐index at a comparable space usage. Moreover, the construction of our data structure is fast and easily parallelizable. Copyright © 2016 John Wiley & Sons, Ltd.