Geometric Integrability of the Camassa-Holm Equation. II

It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.

Desing and Validation of a Light Inference System to Support Embedded Context Reasoning

Embedded context management in resource-constrained devices (e.g. mobile phones, autonomous sensors or smart objects) imposes special requirements in terms of lightness for data modelling and reasoning. In this paper, we explore the state-of-the-art on data representation and reasoning tools for embedded mobile reasoning and propose a light inference system (LIS) aiming at simplifying embedded inference processes offering a set of functionalities to avoid redundancy in context management operations. The system is part of a service-oriented mobile software framework, conceived to facilitate the creation of context-aware applications—it decouples sensor data acquisition and context processing from the application logic. LIS, composed of several modules, encapsulates existing lightweight tools for ontology data management and rule-based reasoning, and it is ready to run on Java-enabled handheld devices. Data management and reasoning processes are designed to handle a general ontology that enables communication among framework components. Both the applications running on top of the framework and the framework components themselves can configure the rule and query sets in order to retrieve the information they need from LIS. In order to test LIS features in a real application scenario, an ‘Activity Monitor’ has been designed and implemented: a personal health-persuasive application that provides feedback on the user’s lifestyle, combining data from physical and virtual sensors. In this case of use, LIS is used to timely evaluate the user’s activity level, to decide on the convenience of triggering notifications and to determine the best interface or channel to deliver these context-aware alerts.d

Geometric characteristics of conics in Bézier form

Derive coordinate-free expressions for geometric characteristics of conics written in Bézier form in terms of their control points and weights.

Multi-agent Architecture for Heterogeneous Reasoning under Uncertainty Combining MSBN and Ontologies in Distributed Network Diagnosis

This article proposes a MAS architecture for network diagnosis under uncertainty. Network diagnosis is divided into two inference processes: hypothesis generation and hypothesis confirmation. The first process is distributed among several agents based on a MSBN, while the second one is carried out by agents using semantic reasoning. A diagnosis ontology has been defined in order to combine both inference processes. To drive the deliberation process, dynamic data about the influence of observations are taken during diagnosis process. In order to achieve quick and reliable diagnoses, this influence is used to choose the best action to perform. This approach has been evaluated in a P2P video streaming scenario. Computational and time improvements are highlight as conclusions.

Distributed Fault Diagnosis Using Bayesian Reasoning in MAGNETO

Many of the emerging telecom services make use of Outer Edge Networks, in particular Home Area Networks. The configuration and maintenance of such services may not be under full control of the telecom operator which still needs to guarantee the service quality experienced by the consumer. Diagnosing service faults in these scenarios becomes especially difficult since there may be not full visibility between different domains. This paper describes the fault diagnosis solution developed in the MAGNETO project, based on the application of Bayesian Inference to deal with the uncertainty. It also takes advantage of a distributed framework to deploy diagnosis components in the different domains and network elements involved, spanning both the telecom operator and the Outer Edge networks. In addition, MAGNETO features self-learning capabilities to automatically improve diagnosis knowledge over time and a partition mechanism that allows breaking down the overall diagnosis knowledge into smaller subsets. The MAGNETO solution has been prototyped and adapted to a particular outer edge scenario, and has been further validated on a real testbed. Evaluation of the results shows the potential of our approach to deal with fault management of outer edge networks.

Towards Understanding Reasoning Complexity in Practice

Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologies

Aerodynamic study of airfoils geometric imperfections at low Reynolds number

The interest of this study is based on the observation that some manufacturing processes of various vehicles wings, such as unmanned aerial vehicle (UAV), or blades, such as wind turbine blades, or other devices that use aerodynamic profiles, produce imperfections in the leading edge or open trailing edge with bigger thickness than original airfoil, because, for example, they are manufactured in two parts, top surface and bottom surface and subsequently joined. In this last step might appear a sliding between the top surface and the bottom surface having a small step on the leading edge or a small thickness gain can occur on the trailing edge. Normally these imperfections are corrected through a refill and/or sanding processes using many hours of manual labor. Therefore the initial objective of this research is to determine the level of influence in the aerodynamic characteristics at low Reynolds numbers (Lissaman, 1981, Carmichael, 1981, Nagamatsu and Cuche, 1981, Schmitz, 1957, Cebeci, 1989, Mueller and Batill, 1982) of these imperfections in the manufacture, and determine whether there may be a value for which it would not be necessary to correct them

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Geometric tools in Juan de Álava's stonecutting workshop

Stonemasonry of the Gothic vault in its totality is based upon geometry of the line, whereas classic stereotomy relies on the comprehensive knowledge of the surface and the highly sophisticated sides of the voussoirs necessary for its vaults. It is obvious that this leap in the art of construction was paralleled and accompanied by an extension of the horizons of geometry. In Spain, it was made possible thanks to the centuries-old tradition of stone building begun in the most remote medieval times and to the presence of outstanding architects or stonemasons such as Juan de Álava, whose professional work surpassed the established limits and provided the art of building with new instruments.

Design and Validation of a Light Inference System to Support Embedded Context Reasoning

Embedded context management in resource-constrained devices (e.g. mobile phones, autonomous sensors or smart objects) imposes special requirements in terms of lightness for data modelling and reasoning. In this paper, we explore the state-of-the-art on data representation and reasoning tools for embedded mobile reasoning and propose a light inference system (LIS) aiming at simplifying embedded inference processes offering a set of functionalities to avoid redundancy in context management operations. The system is part of a service-oriented mobile software framework, conceived to facilitate the creation of context-aware applications?it decouples sensor data acquisition and context processing from the application logic. LIS, composed of several modules, encapsulates existing lightweight tools for ontology data management and rule-based reasoning, and it is ready to run on Java-enabled handheld devices. Data management and reasoning processes are designed to handle a general ontology that enables communication among framework components. Both the applications running on top of the framework and the framework components themselves can configure the rule and query sets in order to retrieve the information they need from LIS. In order to test LIS features in a real application scenario, an ?Activity Monitor? has been designed and implemented: a personal health-persuasive application that provides feedback on the user?s lifestyle, combining data from physical and virtual sensors. In this case of use, LIS is used to timely evaluate the user?s activity level, to decide on the convenience of triggering notifications and to determine the best interface or channel to deliver these context-aware alerts.

Analysis of the geometric altimetry to support aircraft optimal profiles within future 4D trajectory management

The use of barometric altimetry is to some extent a limiting factor on safety, predictability and efficiency of aircraft operations, and reduces the potential of the trajectory based operations capabilities. However, geometric altimetry could be used to improve all of these aspects. Nowadays aircraft altitude is estimated by applying the International Standard Atmosphere which differs from real altitude. At different temperatures for an assigned barometric altitude, aerodynamic forces are different and this has a direct relationship with time, fuel consumption and range of the flight. The study explores the feasibility of using sensors providing geometric reference altitude, in particular, to supply capabilities for the optimization of vertical profiles and also, their impact on the vertical Air Traffic Management separation assurance processes. One of the aims of the thesis is to assess if geometric altitude fulfils the aeronautical requirements through existing sensors. Also the thesis will elaborate on the advantages of geometric altitude over the barometric altitude in terms of efficiency for vertical navigation. The evidence that geometric altitude is the best choice to improve the efficiency in vertical profile and aircraft capacity by reducing vertical uncertainties will also be shown. In this paper, an atmospheric study is presented, as well as the impact of temperature deviation from International Standard Atmosphere model is analyzed in order to obtain relationship between geometric and barometric altitude. Furthermore, an aircraft model to study aircraft vertical profile is provided to analyse trajectories based on geometric altitudes.

Probabilistic reasoning with a bayesian DNA device based on strand displacement

We present a computing model based on the DNA strand displacement technique which performs Bayesian inference. The model will take single stranded DNA as input data, representing the presence or absence of a specific molecular signal (evidence). The program logic encodes the prior probability of a disease and the conditional probability of a signal given the disease playing with a set of different DNA complexes and their ratios. When the input and program molecules interact, they release a different pair of single stranded DNA species whose relative proportion represents the application of Bayes? Law: the conditional probability of the disease given the signal. The models presented in this paper can empower the application of probabilistic reasoning in genetic diagnosis in vitro.

An attitude-based reasoning strategy to enhance interaction with augmented objects

This paper describes a mobile-based system to interact with objects in smart spaces, where the offer of resources may be extensive. The underlying idea is to use the augmentation capabilities of the mobile device to enable it as user-object mediator. In particular, the paper details how to build an attitude-based reasoning strategy that facilitates user-object interaction and resource filtering. The strategy prioritizes the available resources depending on the spatial history of the user, his real-time location and orientation and, finally, his active touch and focus interactions with the virtual overlay. The proposed reasoning method has been partially validated through a prototype that handles 2D and 3D visualization interfaces. This framework makes possible to develop in practice the IoT paradigm, augmenting the objects without physically modifying them.

A Case Study of Geometric Modelling via 3-D Point Interpolation for the Bathymetry of the Rabasa Lakes (Alicante, Spain)

The interpolation of points by means of Information Technology programs appears as a technical tool of some relevancy in the hydrogeology in general and in the study of the humid zones in particular. Our approach has been the determination of the 3-D geometry of the humid zones of major depth of the Rabasa Lakes. To estimate the topography of the lake bed, we proceed to acquire information in the field by means of sonar and GPS equipment. A total of 335 points were measured both on the perimeter and in the lake bed. In a second stage, this information was used in a kriging program to obtain the bathymetry of the wetland. This methodology is demonstrated as one of the most reliable and cost-efficient for the 3-D analysis of this type of water masses. The bathymetric study of the zone allows us to characterize the mid- and long-term hydrological evolution of the lakes by means of depth-area-volume curves.