Multiplicity results for some elliptic problems with nonlinear boundary conditions involving variable exponents

In this paper we analyze an elliptic partial differential equation involving variable exponent growth conditions coupled with a nonlinear boundary condition. We show the existence of infinitely many bounded weak solutions provided there is a suitable oscillatory behavior of the nonlinearity either at infinity or at zero. Our proofs rely on a method due to Saint Raymond.     

A framework for reviewing domain specific conceptual models

Conceptual models are used in understanding and communicating the domain of interest during analysis phase of system development. As they are used in early phases, errors and omissions may propagate to later phases and may be very costly to correct. This paper proposes a framework for evaluating conceptual models when represented in a domain specific language based on UML constructs. The framework describes the main aspects to be considered when conceptual models are represented in a domain specific language, presents a classification of semantic issues and some evaluation indicators. The indicators can, in principle, identify situations in the models where inconsistencies or incompleteness might occur. Whether these are real concerns might depend on domain semantics, hence these are semantic, not syntactic checks. The use of the proposed review framework is illustrated in the context of two conceptual models in a domain specific notation, KAMA. With reviews based on the framework, it is possible to spot semantic issues which are not noticed by case tools and help the analyst to identify more information about the domain.     

EKF Based Attitude Estimation and Stabilization of a Quadrotor UAV Using Vanishing Points in Catadioptric Images

In recent years, Unmanned Air Vehicles (UAVs) have become more and more important. These vehicles are employed in many applications from military operations to civilian tasks. Under situations where global positioning system (GPS) and inertial navigation system (INS) do not function, or as an additional sensor, computer vision can be used. Having 360° view, catadioptric cameras might be very useful as they can be used as measurement units, obstacle avoidance sensors or navigation planners. Although many innovative research has been done about this camera, employment of such cameras in UAVs is very new. In this paper, we present the use of catadioptric systems in UAVs to estimate vehicle attitude using parallel lines that exist on many structures in an urban environment. After explanation of the algorithm, the UAV modeling and control will be presented. In order to increase the estimation and control speed an Extended Kalman Filter (EKF) and multi-threading are used and speeds up to 40 fps are obtained. Various simulations have been done to present the effectiveness of the estimation algorithms as well as the UAV controllers. A custom test stand has been designed to perform successful experiments on the UAV. Finally, we will present the experiments and the results of the estimation and control algorithms on a real model helicopter. EKF based attitude estimation and stabilization using catadioptric images has found to be a reliable alternative to other sensor usage.     

Soft groups and normalistic soft groups

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Akta? and Çag˜man [H. Akta?, N. Çag˜man, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726-2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms.     

Two-way D algorithm for path planning and replanning

Inspired by the Witkowski’s algorithm, we introduce a novel path planning and replanning algorithm — the two-way D^∗ (TWD^∗) algorithm — based on a two-dimensional occupancy grid map of the environment. Unlike the Witkowski’s algorithm, which finds optimal paths only in binary occupancy grid maps, the TWD^∗ algorithm can find optimal paths in weighted occupancy grid maps. The optimal path found by the TWD^∗ algorithm is the shortest possible path for a given occupancy grid map of the environment. This path is more natural than the path found by the standard D^∗ algorithm as it consists of straight line segments with continuous headings. The TWD^∗ algorithm is tested and compared to the D^∗ and Witkowski’s algorithms by extensive simulations and experimentally on a Pioneer 3DX mobile robot equipped with a laser range finder.     

Semi-globally Exponential Tracking Observer/Controller for Robots with Joint Hysteresis and Without Velocity Measurement

In this work, we consider a multiple degree of freedom robotic plant with joint hysteresis and without velocity measurement. We show, by construction, how a semi-globally exponential hysteresis observer/controller that assumes velocity measurement, a number of which we point out from the literature, can be combined/modified with a velocity observer to yield a combined semi-globally exponential tracking observer/controller. The resulting observer/controller estimates both the hysteresis state and the joint velocity. We prove that the combined estimation error and tracking error converges to zero semi-globally exponentially. One deemed contribution as compared to previous work for this same type of plant is that the usual requirement of velocity measurement has been removed; another is the proved semi-globally exponential result.     

Identifying mislabeled training data with the aid of unlabeled data

This paper presents a new approach for identifying and eliminating mislabeled training instances for supervised learning algorithms. The novelty of this approach lies in the using of unlabeled instances to aid the detection of mislabeled training instances. This is in contrast with existing methods which rely upon only the labeled training instances. Our approach is straightforward and can be applied to many existing noise detection methods with only marginal modifications on them as required. To assess the benefit of our approach, we choose two popular noise detection methods: majority filtering (MF) and consensus filtering (CF). MFAUD/CFAUD is the new proposed variant of MF/CF which relies on our approach and denotes majority/consensus filtering with the aid of unlabeled data. Empirical study validates the superiority of our approach and shows that MFAUD and CFAUD can significantly improve the performances of MF and CF under different noise ratios and labeled ratios. In addition, the improvement is more remarkable when the noise ratio is greater.     

A network approach to the French system of legal codes—part I: analysis of a dense network

We explore one aspect of the structure of a codified legal system at the national level using a new type of representation to understand the strong or weak dependencies between the various fields of law. In Part I of this study, we analyze the graph associated with the network in which each French legal code is a vertex and an edge is produced between two vertices when a code cites another code at least one time. We show that this network distinguishes from many other real networks from a high density, giving it a particular structure that we call concentrated world and that differentiates a national legal system (as considered with a resolution at the code level) from small-world graphs identified in many social networks. Our analysis then shows that a few communities (groups of highly wired vertices) of codes covering large domains of regulation are structuring the whole system. Indeed we mainly find a central group of influent codes, a group of codes related to social issues and a group of codes dealing with territories and natural resources. The study of this codified legal system is also of interest in the field of the analysis of real networks. In particular we examine the impact of the high density on the structural characteristics of the graph and on the ways communities are searched for. Finally we provide an original visualization of this graph on an hemicyle-like plot, this representation being based on a statistical reduction of dissimilarity measures between vertices. In Part II (a following paper) we show how the consideration of the weights attributed to each edge in the network in proportion to the number of citations between two vertices (codes) allows deepening the analysis of the French legal system.     

The Covering Law Model Applied to Dynamical Cognitive Science: A Comment on Joel Walmsley

In a 2008 paper, Walmsley argued that the explanations employed in the dynamical approach to cognitive science, as exemplified by the Haken, Kelso and Bunz model of rhythmic finger movement, and the model of infant preservative reaching developed by Esther Thelen and her colleagues, conform to Carl Hempel and Paul Oppenheim’s deductive-nomological model of explanation (also known as the covering law model). Although we think Walmsley’s approach is methodologically sound in that it starts with an analysis of scientific practice rather than a general philosophical framework, we nevertheless feel that there are two problems with his paper. First, he focuses only on the deductivenomological model and so neglects the important fact that explanations are causal. Second, the explanations offered by the dynamical approach do not take the deductive-nomological format, because they do not deduce the explananda from exceptionless laws. Because of these two points, Walmsley makes the dynamical explanations in cognitive science appear problematic, while in fact they are not.