Symbolic Description Research Articles

Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark–Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of ‘rotational’ periodic solutions that display lens-chain structures for a general N-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.

Reversible Watermarking for Knowledge Digest Embedding and Reliability Control in Medical Images

To improve medical image sharing in applications such as e-learning or remote diagnosis aid, we propose to make the image more usable by watermarking it with a digest of its associated knowledge. The aim of such a knowledge digest (KD) is for it to be used for retrieving similar images with either the same findings or differential diagnoses. It summarizes the symbolic descriptions of the image, the symbolic descriptions of the findings semiology, and the similarity rules that contribute to balancing the importance of previous descriptors when comparing images. Instead of modifying the image file format by adding some extra header information, watermarking is used to embed the KD in the pixel gray-level values of the corresponding images. When shared through open networks, watermarking also helps to convey reliability proofs (integrity and authenticity) of an image and its KD. The interest of these new image functionalities is illustrated in the updating of the distributed users' databases within the framework of an e-learning application demonstrator of endoscopic semiology.

Systematic Methods for the Implementation of Nonlinear Wave-Digital Structures

Wave-digital (WD) structures containing adaptors with memory (characterized by port reflection filters) and nonlinear elements are suitable for the modeling of a wide range of nonlinear circuits and physical structures. In this paper, we propose two methods for automating the construction of algorithms that efficiently implement such structures, starting from their symbolic description. The former is based on the solution of state-space equations, while the latter is based on direct structural inspection. The state-space approach starts from the blockwise construction of a tableau matrix for the direct implementation of a generic WD structure and, for this reason, is here referred to as the wave tableau (WT) method. It has very general applicability as it works for a generic WD structure. The second technique (binary connection tree) implements a WD structure through a direct inspection (scanning) of the treelike topological representation of the reference model. Although valid for a slightly less general range of cases, this approach turns out to be much more efficient and flexible than that of the WT method. Such methods are particularly interesting for an interactive and immediate prototyping of physical models for the synthesis of sounds as they bring nonlinear WD structures with dynamic adaptors to a level of practical usability for a wide range of users while enabling the modeling of a wide variety of time-varying nonlinear physical models in an automatic fashion. The proposed solutions have been extensively tested on applications for the automatic modeling of acoustic interactions of musical interest.

FORECASTING OF BIFURCATION PHENOMENA IN DYNAMICS OF PULSE ENERGY CONVERTERS WITH PARAMETER UNCERTAINTIES

The results of bifurcation analysis seem to be used somehow or other as the basis of any method in nonlinear dynamics forecasting. The peculiarity of the problem setting in the paper is related to the fact that dynamics forecasting supposes the recognition of a bifurcation phenomenon before its beginning. In particular, this problem setting is important from the viewpoint of practical application of pulse energy converters (PEC). So, the necessity of real-time estimation of the direction of transient convergence appears. The complexity of such estimation is stipulated by the information on transients that is not mapped in bifurcation diagrams, and also time series do not contain preliminary information on a nonlinear dynamics picture. Moreover, PEC operation under parameter uncertainties leads to information on a bifurcation boundary location becomes fuzzy. The symbolic description of dynamical processes over time is offered with the purpose of the problem solution. This description is provided by the use of fractal regularities in the geometrical structures of phase trajectories, which are stipulated by the physical essence of both PWM process and transient convergence towards a limit cycle.

The topology of nested homoclinic and heteroclinic tangles

Homoclinic and heteroclinic tangles are fundamental phase space structures that help in organizing the transport defined by a chaotic map on a two-dimensional phase space. Previous work introduced the technique of “homotopic lobe dynamics” to study the topology of a homoclinic tangle. The present work generalizes homotopic lobe dynamics to describe the topology of a network of nested homoclinic and/or heteroclinic tangles. Using this theory, we demonstrate that the topological analysis of a network of nested tangles can lead to an efficient symbolic description of a chaotic phase space, even in the vicinity of islands of stability. By increasing the amount of topological information used (e.g. by introducing additional tangles at finer scales), this technique suggests an efficient route for defining accurate symbolic dynamics for phase spaces that exhibit a mixture of chaos and regularity.

A Hybrid Approach to Intricate Motion, Manipulation and Task Planning

We propose a representation and a planning algorithm able to deal with problems integrating task planning as well as motion and manipulation planning knowledge involving several robots and objects. Robot plans often include actions where the robot has to place itself in some position in order to perform some other action or to “modify” the configuration of its environment by displacing objects. Our approach aims at establishing a bridge between task planning and manipulation planning that allows a rigorous treatment of geometric preconditions and effects of robot actions in realistic environments. We show how links can be established between a symbolic description and its geometric counterpart and how they can be used in an integrated planning process that is able to deal with intricate symbolic and geometric constraints. Finally, we describe the main features of an implemented planner and discuss several examples of its use.

USING KNOWLEDGE REPRESENTATION FOR PERCEPTUAL ANCHORING IN A ROBOTIC SYSTEM

In this work we introduce symbolic knowledge representation and reasoning capabilities to enrich perceptual anchoring. The idea that encompasses perceptual anchoring is the creation and maintenance of a connection between the symbolic and perceptual description that refer to the same object in the environment. In this work we further extend the symbolic layer by combining a knowledge representation and reasoning (KRR) system with the anchoring module to exploit a knowledge inference mechanisms. We implemented a prototype of this novel approach to explore through initial experimentation the advantages of integrating a symbolic knowledge system to the anchoring framework in the context of an intelligent home. Our results show that using the KRR we are better able to cope with ambiguities in the anchoring module through exploitation of human robot interaction.

Proto-Plasm : parallel language for adaptive and scalable modelling of biosystems

This paper discusses the design goals and the first developments of Proto-Plasm, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the Proto-Plasm platform is still in its infancy. Its computational framework—language, model library, integrated development environment and parallel engine—intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. Proto-Plasm may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a Proto-Plasm program. Here we exemplify the basic functionalities of Proto-Plasm, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions.

Description of military apparatus in the Śrī-kālacakra-nāma-tantra-rāja

Russian Academy of Sciences, Institute of Oriental Studies, St. PetersburgIn the Śrī-kālacakra-nāma-tantra-rāja, a Buddhist treatise from the first half of the 11th century, there is a thematic fragment containing a description of military apparatus and their use in battles. In this article, the point of view that we are really dealing with a description of military apparatus and not with a symbolic description of the psychophysical practices of Buddhist yoga is developed. In our point of view, the reason for the subject of war being represented in this Buddhist work should be searched for in the reality of the tragic times in which the text was made―the times of destructive raids made on India by the ruler Mahmud of Ghazni. The article classifies the military apparatus mentioned in the Śrī-kālacakra-nāma-tantra-rāja, describes the basic technical characteristics of these mechanisms, and considers their function. The given subjects are considered with the drawing in the commentary Vimalaprabhā (11th century) and commentaries by Tibetan scholar Buton Rinchen Drub (1290–1364).

GetDP: a general finite‐element solver for the de Rham complex

AbstractGetDP is a high‐level finite element solver using mixed elements to discretize de Rham‐type complexes in one, two and three dimensions. This paper presents an overview of the structure of GetDP, highlighting the closeness between the organization of data defining a discrete problem and its symbolic mathematical description. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Temporal abstraction for feature extraction: A comparative case study in prediction from intensive care monitoring data

To compare two temporal abstraction procedures for the extraction of meta features from monitoring data. Feature extraction prior to predictive modeling is a common strategy in prediction from temporal data. A fundamental dilemma in this strategy, however, is the extent to which the extraction should be guided by domain knowledge, and to which extent it should be guided by the available data. The two temporal abstraction procedures compared in this case study differ in this respect. The first temporal abstraction procedure derives symbolic descriptions from the data that are predefined using existing concepts from the medical language. In the second procedure, a large space of numerical meta features is searched through to discover relevant features from the data. These procedures were applied to a prediction problem from intensive care monitoring data. The predictive value of the resulting meta features were compared, and based on each type of features, a class probability tree model was developed. The numerical meta features extracted by the second procedure were found to be more informative than the symbolic meta features of the first procedure in the case study, and a superior predictive performance was observed for the associated tree model. The findings indicate that for prediction from monitoring data, induction of numerical meta features from data is preferable to extraction of symbolic meta features using existing clinical concepts.

Reasoning about topological relations between regions with broad boundaries

Uncertain regions can be represented as having broad boundaries (BBRs) and their topological relations can be modeled by the extended 9-intersection. In order to satisfy the need for querying, managing, and processing BBRs, this study presents a 4-tuple representation of topological relations between BBRs, and a method in which the relations between simple regions with broad boundaries (SBBRs) are used to infer new topological information. The 4-tuple representation can distinguish the same topological relations as identified by the extended 9-intersection. Since the 4-tuple uses combinations of the basic topological relations between crisp regions to describe the relations between uncertain regions, the reasoning of topological relations between SBBRs can be obtained by combining the results of those between crisp regions. The reasoning mechanism can be used in several applications, such as to evaluate the consistency of topological relations between uncertain regions in multi-resolution spatial databases and to assess the consistency of a complete or incomplete symbolic description of a spatial scene.

Knowledge Extraction From Neural Networks Using the All-Permutations Fuzzy Rule Base: The LED Display Recognition Problem

A major drawback of artificial neural networks (ANNs) is their black-box character. Even when the trained network performs adequately, it is very difficult to understand its operation. In this letter, we use the mathematical equivalence between ANNs and a specific fuzzy rule base to extract the knowledge embedded in the network. We demonstrate this using a benchmark problem: the recognition of digits produced by a light emitting diode (LED) device. The method provides a symbolic and comprehensible description of the knowledge learned by the network during its training.

Supporting bi-cluster interpretation in 0/1 data by means of local patterns

Clustering or co-clustering techniques have been proved useful in many application domains. A weakness of these techniques remains the poor support for grouping characterization. As a result, interpreting clustering results and discovering knowledge from them can be quite hard. We consider potentially large Boolean data sets which record properties of objects and we assume the availability of a bi-partition which has to be characterized by means of a symbolic description. Our generic approach exploits collections of local patterns which satisfy some user-defined constraints in the data, and a measure of the accuracy of a given local pattern as a bi-cluster characterization pattern. We consider local patterns which are bi-sets, i.e., sets of objects associated to sets of properties. Two concrete examples are formal concepts (i.e., associated closed sets) and the so-called δ-bi-sets (i.e., an extension of formal concepts towards fault-tolerance). We introduce the idea of characterizing query which can be used by experts to support knowledge discovery from bi-partitions thanks to available local patterns. The added-value is illustrated on benchmark data and three real data sets: a medical data set and two gene expression data sets.

Special Section on Symbolic Methods for Complex Control Systems

Special Section on Symbolic Methods for Complex Control Systems

Symbolic Trajectory Description in Mobile Robotics

Autonomous mobile robot navigation systems are based on three principal kinds of techniques: map-based navigation, map-building-based navigation and mapless navigation. We propose a method for symbolic trajectory description in unknown indoor environments. The chosen form uses a panoramic description called fresco. The method uses distance measurements from a 2D laser range finder, digitises the robot's visibility area, eliminates superfluous data and reorients their presentation. The landmarks are then extracted and organised into the fresco which is validated by means of neighbourhood rules. As the robot moves in the environment, the frescoes are created and both the amount of new information a fresco carries out and its position in relation to the preceding ones are evaluated by means of two criteria. Only frescoes selected as enough informative are stored to describe the robot's route.

Engineering the brain

The target article presents a stimulating account for some of the most challenging issues in cognitive neuroscience. The theory solves in neural terms cognitive problems beyond the scope of previous models. But in many aspects the neural implementation is a quite literal translation of symbolic descriptions and therefore still lacks some of the truly self-organizing properties characteristic of biological networks.

Complementarity in Classical Dynamical Systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.

Symbolic Dynamics of Coupled Map Lattices

We present a method to reduce the [FORMULA: SEE TEXT] dynamics of coupled map lattices (CMLs) of N invertibly coupled unimodal maps to a sequence of N-bit symbols. We claim that the symbolic description is complete and provides for the identification of all fixed points, periodic orbits, and dense orbits as well as an efficient representation for studying pattern formation in CMLs. We give our results for CMLs in terms of symbolic dynamical concepts well known for one-dimensional chaotic maps, including generating partitions, Gray orderings, and kneading sequences. An example utilizing coupled quadratic maps is given.

Computer-Based Anatomy: A Prerequisite for Computer-Assisted Radiology and Surgery 1

The aim of the study is to show the possibilities opened up by three-dimensional (3D) computer-based models of the human body for education in anatomy, training of radiological and endoscopic examinations, and simulation of surgical procedures. Based on 3D data sets obtained from the Visible Human and/or clinical cases, virtual body models are created that provide an integrated spatial and symbolic description of the anatomy by using interactive color/intensity-based segmentation, ray casting visualization with subvoxel resolution, a semantic network for knowledge modeling, and augmented QuickTime VR (Apple Computer, Inc, Cupertino, CA) movies for presentation. From these models, various radiological, endoscopic, or haptic manifestations of the body can be derived. This is shown with examples from anatomy teaching, correlation of x-ray images with 3D anatomy for education in radiology, gastrointestinal endoscopy, correlation of ultrasound images with 3D anatomy in endoscopic ultrasonography, and simulation of drilling in temporal bone surgery. The presented models provide a means for realistic training in interpretation of radiological and endoscopic images of the human body. Furthermore, certain surgical procedures may be simulated realistically. Used as a complement to the current curriculum, these models have the potential to greatly decrease education times and costs.