bluuebunny/crossref_metadata_2025 huggingface dataset:
HOMOCLINIC ORBITS AND THEIR BIFURCATIONS IN DYNAMICAL SYSTEMS WITH TWO DEGREES OF FREEDOM: A METHOD OF QUALITATIVE AND NUMERICAL ANALYSIS
Authors: ELEONSKY V.M. , KOROLEV V.G. , KULAGIN N.E. , SHIL’NIKOV L.P.
Published: November 2004

An efficient method of numerical and qualitative analysis of homoclinic trajectories in Hamiltonian systems (or systems possessing a first integral of the motion) with two degrees of freedom is suggested. It allows us to reduce the problem of finding homoclinic loops as intersections of two-dimensional stable and unstable manifolds of an equilibrium point in the four-dimensional phase space to the problem of finding intersections of one-dimensional manifolds (hereafter referred to as touch-curves) on a certain two-dimensional boundary surface. The application of this algorithm in a number of problems leading to Hamiltonian dynamical systems with two degrees of freedom to the analysis of bifurcations of homoclinic loops occurring under the variation of structural parameters, is illustrated.
ROUTES TO CHAOS IN BISTABLE SYSTEMS DURING MULTIPLE CROSSINGS OF A REGION OF HYSTERESIS
Authors: BELOGORTSEV A.B. , POLIASHENKO M. , TRETYAKOV O.A.
Published: November 2004

We study the behavior of nonlinear bistable systems as the parameters are slowly perturbed periodically. Using averaged equations, typical features of the transition from regular to chaotic dynamics are determined in an externally driven Duffing oscillator and in a system consisting of a van der Pol and a linear oscillator coupled resonantly. We find that general features of the transition to chaos in these models are in many respects similar. In both systems considered, chaotic regions, arising due to similar mechanisms, are situated inside or near the regions of bistability.
TWISTED SCROLL WAVES IN HETEROGENEOUS EXCITABLE MEDIA
Authors: PANFILOV ALEXANDER V. , KEENER JAMES P.
Published: November 2004

We study numerically the behavior of a scroll wave in a three-dimensional excitable medium with stepwise heterogeneity, using a FitzHugh Nagumo type model. We find that if the refractory periods in the two homogeneous subregions are sufficiently different, the scroll breaks into two scrolls rotating independently in each part of the medium. Eventually, the faster scroll eliminates the slower one leading to a stationary process, in which the scroll wave surviving in the region of faster recovery acts as a source for planar waves in the region of slower recovery.
ON ANALYTIC AND PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR OSCILLATORS
Authors: GALLAS JASON A.C.
Published: November 2004

We use the equations of motion for a particle moving in one dimension under the action of forces which vary cubically with displacement to discuss differential equations associated with double-periodic Jacobian elliptic functions. We show that analytic solutions for this dynamical system can be given in terms of Jacobian elliptic functions. These periodic functions are natural extensions of the well-known trigonometric functions.
TRANSITIONS IN DYNAMICAL REGIMES BY DRIVING: A UNIFIED METHOD OF CONTROL AND SYNCHRONIZATION OF CHAOS
Authors: KOCAREV LJUPCO , SHANG ALAIN , CHUA LEON O.
Published: November 2004

We propose a simple method for the synchronization and the control of chaos. A general qualitative description of the method is presented.
UNPOLARIZED LASER AND VECTORIAL TOPOLOGICAL DEFECTS
Authors: GIL L.
Published: November 2004

Using symmetry arguments, we derive a two-dimensional Vectorial Ginzburg-Landau equation ruling the slow space-and-time behavior of an unpolarized electromagnetic wave. Then a topological analysis is performed and the topological defect solutions of the vector field are described.
GLOBAL DYNAMICAL EQUATIONS AND LYAPUNOV EXPONENTS FROM NOISY CHAOTIC TIME SERIES
Authors: KADTKE JAMES B. , BRUSH JEFFREY , HOLZFUSS JOACHIM
Published: November 2004

We discuss the extraction of few-parameter, global dynamical models from noisy time series of chaotic systems. In particular, we consider the class of models which are approximations to sets of dynamical equations in the reconstructed phase space. We show that certain numerical methods significantly improve the quality of the resulting models, and central to these methods is the idea of eliminating model terms which are “dynamically insignificant” and add only numerical noise. For the purposes of the paper, we quantify model quality by the rather strict measure of its ability to recover the dynamical invariants of the original system, in particular, the Lyapunov spectrum. Consequently, we also postulate that by first extracting a global model, the Lyapunov spectrum of a generating system can be recovered from time series whose noise levels are much higher than current algorithms would allow. We present several numerical examples to demonstrate the above ideas.
ADAPTIVE FILTERING AND PREDICTION OF NOISY MULTIVARIATE SIGNALS: AN APPLICATION TO SUBANNUAL VARIABILITY IN ATMOSPHERIC ANGULAR MOMENTUM
Authors: KEPPENNE CHRISTIAN L. , GHIL MICHAEL
Published: November 2004

Principal component analysis (PCA) in the space and time domains is applied to filter adaptively the dominant modes of subannual (SA) variability of a 12-year long multivariate time series of Northern Hemisphere atmospheric angular momentum (AAM); AAM is computed in 23 latitude bands of equal area from operational analyses of the U.S. National Meteorological Center. PCA isolates the leading empirical orthogonal functions (EOFs) of spatial dependence, while multivariate singular spectrum analysis (M-SSA) yields filtered time series that capture the dominant low-frequency modes of SA variability.

The time series prefiltered by M-SSA lend themselves to prediction by the maximum entropy method (MEM). Whole-field predictions are made by combining the forecasts so obtained with the leading spatial EOFs obtained by PCA. The combination of M-SSA and MEM has predictive ability up to about a month. These methods are essentially linear but data-adaptive. They seem to perform well for short, noisy, multivariate time series, to which purely nonlinear, deterministically based methods are difficult to apply.
GAUSSIAN OUTPUT FROM CHAOTIC INPUT
Authors: MADRAS N. , HANSELL R.I.C. , BYERS R.E.
Published: November 2004

We present a simple deterministic model in which the appearance of Gaussian noise in the system is actually due to input from a small number of non-Gaussian chaotic subsystems. We explore some implications of this phenomenon, with particular attention to sources of noise in biological systems.
A GEOMETRIC MODEL FOR THE DUFFING OSCILLATOR
Authors: McCALLUM J.W.L. , GILMORE R.
Published: November 2004

A geometric model for the Duffing oscillator is constructed by analyzing the unstable periodic orbits underlying the chaotic attractors present at particular parameter values. A template is constructed from observations of the motion of the chaotic attractor in a Poincaré section as the section is swept for one full period. The periodic orbits underlying the chaotic attractor are found and their linking numbers are computed. These are compared with the linking numbers from the template and the symbolic dynamics of the orbits are identified. This comparison is used to validate the template identification and label the orbits by their symbolic dynamics.
INTERMITTENCY, PHASE RANDOMIZATION AND GENERALIZED FRACTAL DIMENSIONS
Authors: PROVENZALE ANTONELLO , VILLONE BARBARA , BABIANO ARMANDO , VIO ROBERTO
Published: November 2004

The procedure of Fourier phase randomization has been repeatedly proposed for distinguishing low-dimensional chaos from noise in a measured time series. Here we extend the use of this method and we show that phase randomization is a necessary step for assessing the presence of intermittency in a stochastic and/or turbulent system. This procedure allows us to distinguish between linear and nonlinear signals as well. As an example of application of this approach, we study the time series of positions of passively advected particles in 2D turbulence and we show that their apparent multifractality is not associated with intermittency. The results discussed here confirm the importance of understanding the phase spectrum, and of developing appropriate measures of the phase distribution, in the study of nonlinear systems.
IS CHAOS GENERIC IN ECONOMIC DATA?
Authors: JADITZ TED , SAYERS CHERA L.
Published: November 2004

This paper examines recent developments in nonlinear science in economics. Several claims of findings of chaos in economic data are reviewed. We discuss how each claim has been revised in light of further analysis, and point out several traps for empirical researchers in economic data. These traps suggest certain methodological refinements useful for researchers analyzing very small data sets, including diagnostic tests to detect ill conditioned data, filtering data to exclude nonchaotic alternatives, and nonparametric procedures to check the precision of parameter estimates. Most specialists in the field would say there is no conclusive evidence of chaos in economic or financial data.
RECURRING ANTI-PHASE SIGNALS IN COUPLED NONLINEAR OSCILLATORS: CHAOTIC OR RANDOM TIME SERIES?
Authors: TSANG KWOK YEUNG , SCHWARTZ IRA B.
Published: November 2004

We discovered the existence of a new type of high-dimensional attractor in coupled nonlinear oscillator systems. Due to the presence of neutrally stable directions on the attractor, there can be noise-driven phase space diffusion. Recurring anti-phase states are observed as coherent portions of the time series. The observed time series looks coherent for a while, then incoherent, and then coherent again. Although the time series “looks” chaotic, the Lyapunov exponents are not positive.
CONTROLLING CHAOS IN A SIMPLE AUTONOMOUS SYSTEM: CHUA’S CIRCUIT
Authors: JOHNSON G.A. , HUNT E.R.
Published: November 2004

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua’s circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua’s circuit’s double-scroll attractor, applying corrections in each of these regions during a single orbit.
AUTO- AND CHAOTIC OSCILLATIONS IN HYDRODYNAMICS OF NON-NEWTONIAN LIQUIDS
Authors: SH. AKHATOV I. , KHASANOV M. M , KHUSAINOV I. G.
Published: November 2004

A new approach for the description of the rheological behavior of non-Newtonian liquids (clay solutions, polymer solutions, paraffin containing oil) is developed. By this approach the hydrodynamic phenomena in non-Newtonian liquids depend on the nonlinear kinetics of destruction-reconstruction processes for connecting links between the structural elements of the medium. The mathematical model is based on a respective phenomenological nonlinear kinetic equation. For the description of the nonsteady motion of such liquids between the walls of a rotary viscometer, this equation is supplemented with the equation of motion of the liquid and the equation of motion of the mobile cylinder of the viscometer. A numerical analysis of the dependence of the solutions of this system on the number of revolutions per minute is made. According to this analysis auto- and chaotic oscillations of rotary viscometer readings are the consequence of the joint action of kinetic phenomena in the liquid and inertial properties of the mobile part of the viscometer. The numerical results are qualitatively compared with the experimental data.
ON THE COMPUTATION OF LOCAL BIFURCATION DIAGRAMS NEAR DEGENERATE HOPF BIFURCATIONS OF CERTAIN TYPES
Authors: MOIOLA JORGE LUIS
Published: November 2004

The computation of local bifurcation diagrams near degenerate Hopf bifurcations of certain types using feedback system theory and harmonic balance techniques is presented. This approach also provides the analytical expressions for the defining and the nondegeneracy conditions in the so-called frequency domain counterpart. A classical graphical method is easily adapted to carry on the continuation of the oscillatory branches to depict the local bifurcation diagrams. Moreover, several higher-order harmonic balance approximations are implemented to compare the accuracy of the computed solutions. The results are presented using local bifurcation diagrams, phase portrait plots and period diagrams, with similar ones obtained by using AUTO.
DYNAMICAL SYNTHESIS OF POINCARÉ MAPS
Authors: BROWN RAY , CHUA LEON O.
Published: November 2004

We present a theory of constructive Poincaré maps. The basis of our theory is the concept of irreducible nonlinear maps closely associated to concepts from Lie groups. Irreducible nonlinear maps are, heuristically, nonlinear maps which cannot be made simpler without removing the nonlinearity. A single irreducible map cannot produce chaos or any complex nonlinear effect. It can be implemented in an electronic circuit, and there are only a finite number of families of irreducible maps in any n-dimensional space. The composition of two or more irreducible maps can produce chaos and most of the maps studied today that produce chaos are compositions of two or more irreducible maps. The composition of a finite number of irreducible maps is called a completely reducible map and a map which can be approximated pointwise by completely reducible maps is called a reducible map. Poincaré maps from sinusoidally forced oscillators are the most familiar examples of reducible maps.

This theoretical framework provides an approach to the construction of "closed form" Poincaré maps having the properties of Poincaré maps of systems for which the Poincaré map cannot be obtained in closed form. In particular, we derive a three-dimensional ODE for which the Hénon map is the Poincaré map and show that there is no two-dimensional ODE which can be written down in closed form for which the Hénon map is the Poincaré map. We also show that the Chirikov (standard) map is a Poincaré map for a two-dimensional closed form ODE. As a result of our theory, these differential equations can be mapped into electronic circuits, thereby associating them with real world physical systems. In order to clarify our results with respect to the abstract mathematical concept of suspension, which says that every C1 invertible map is a Poincaré map, we introduce the concept of a constructable Poincaré map. Not every map is a constructable Poincaré map and this is an important distinction between dynamical synthesis and abstract nonlinear dynamics.

We also show how to use any one-dimensional map to induce a two-dimensional Poincaré map which is a completely reducible map and hence for a very broad class of maps that includes the logistic map we derive closed form ODEs for which these one-dimensional maps are "embedded" in a Poincaré map. This provides an avenue for the study of one-dimensional maps, such as the logistic map, as two-dimensional Poincaré maps that arise from square-wave forced electronic circuits.
SECURE COMMUNICATIONS VIA CHAOTIC SYNCHRONIZATION II: NOISE REDUCTION BY CASCADING TWO IDENTICAL RECEIVERS
Authors: LOZI RENÉ , CHUA LEON O.
Published: November 2004

The signal recovered from the first reported experimental secure communication system via chaotic synchronization contains some inevitable noise which degrades the fidelity of the original message. In this letter we show by computer experiments that this noise can be significantly reduced by cascading the output of the receiver in the original system into an identical copy of this receiver.
BRAIDS AND KNOTS IN DRIVEN OSCILLATORS
Authors: McROBIE F. A. , THOMPSON J. M. T.
Published: November 2004

We consider the application of braid and knot theory to single-degree-of-freedom driven oscillators, giving emphasis to the braids of periodic orbits contained in horseshoes. Using such concepts as braid type, relative rotations, Nielsen equivalence, knot polynomials, the reduced Burau representation and positive, regular and ambient isotopy, we illustrate how these can be put together to gain some understanding of bifurcation structure.
TRAVELLING WAVES WITH SPATIALLY RESONANT FORCING: BIFURCATIONS OF A MODIFIED LANDAU EQUATION
Authors: GLENDINNING PAUL , PROCTOR MICHAEL
Published: November 2004

Normal form equations are derived representing the effects of spatially resonant forcing on a bifurcation to travelling waves in a nonreflexionally invariant system. The equations also describe the effects of forcing on the van der Pol–Duffing equation. It is found that the forcing prevents the propagation of the wave if it is sufficiently strong: the transition to a nonuniformly propagating solution can occur either via an oscillatory bifurcation or due to a saddle node bifurcation on a closed invariant curve.
REGULAR AND CHAOTIC PULSATIONS IN LASER DIODE WITH DELAYED FEEDBACK
Authors: GRIGORIEVA E. V. , KASHCHENKO S. A.
Published: November 2004

The dynamics of a semiconductor laser with delayed feedback are investigated on the basis of single-mode rate equations with retarded argument. Spontaneous emission in lasing mode, limited bandwidth of optoelectronic feedback and the presence of an impurity with saturable absorption are also taken into account.

The existence of a hierarchy of multistable periodic attractors with different structures (slowly and rapidly oscillating ones) are found. Complex temporal structures: metastable chaotic regimes, quasiperiodic regimes and intermittency are obtained as a result of different bifurcations of multidimensional maps.
DERIVATIVES FOR THE STABLE AND UNSTABLE MANIFOLDS OF A Cr Diffeomorphism ofR2
Authors: BROWN RAY , CHUA LEON
Published: November 2004

We illustrate how to form the Taylor polynomial for a stable or unstable manifold when considered as a curve in the plane. Our method does not use power series or assume that the manifold is analytic as is done in the method of Poincaré. Instead we use simple calculus to obtain closed form expressions for the Taylor coefficients.
ROBUSTNESS AND SIGNAL RECOVERY IN A SYNCHRONIZED CHAOTIC SYSTEM
Authors: CUOMO KEVIN M. , OPPENHEIM ALAN V. , STROGATZ STEVEN H.
Published: November 2004

Recent papers have demonstrated that synchronization in the Lorenz system is highly robust to additive perturbation of the drive signal. This property has led to a concept known as chaotic signal masking and recovery. This paper presents experiments and an approximate analytical model that quantify and explain the observed robustness of synchronization in the Lorenz system. In particular, we explain why speech and other narrowband perturbations can be recovered faithfully, even though the synchronization error is comparable in power to the message itself.
FACILITATING THE MAINTENANCE OF SAFETY-CRITICAL SYSTEMS
Authors: GANNOD GERALD C. , CHENG BETTY H.C.
Published: November 2004

As software is increasingly used to control safety-critical systems, correctness becomes paramount. Formal methods in software development provide many benefits in the forward engineering aspect of software development. Reverse engineering is the process of constructing a high-level representation of a system from existing lower level instanti-ations of that system. Reverse engineering of program code into formal specifications facilitates the utilization of the benefits of formal methods in projects where formal methods may not have previously been used, thus facilitating the maintenance of safety-critical systems.
MODULARITY AND CORRECTNESS FOR LOGIC PROGRAMS AND KNOWLEDGE BASES
Authors: ANTONIOU GRIGORIS
Published: November 2004

A modularity concept for structuring and developing large logic programs and logical knowledge bases is presented. The concept is motivated from work in the field of algebraic specification, and enforces an extreme modularity discipline that goes beyond the one found in imperative or logic programming languages. As concrete programming languages (respectively knowledge representation formalisms), we consider Horn logic and equational logic programming. We give formal semantics for single modules and discuss correctness and verification issues. Large systems are constructed as interconnections of single modules. We introduce the so-called module operations of composition, actualization, and union, and give results concerning compositionality of semantics and correctness preservation.
A FORMALISM FOR STRUCTURED PLANNING OF A SOFTWARE PROJECT
Authors: CIMITILE A. , VISAGGIO G.
Published: November 2004

Some features of software create considerable problems as regards the management of its construction processes, which therefore requires suitable models. In the studies published up to now on this subject, various problems have remained unsolved, particularly the readability of the numerous independent components for each activity in the process, the help required by the manager for handling projects and the need to adapt models to risks and the software development environment. The model proposed in this paper offers a solution to these problems. The innovative aspects of the approach described are the location of all pertinent information in the products of the model in order to improve management, and a formal definition which makes it possible to control the internal coherence of the plan automatically using a flexible notation which is compatible with the knowledge of all participants in the production process.
REVERSE ENGINEERING DISTRIBUTED APPLICATIONS: AN EVENT ABSTRACTION TOOL
Authors: KUNZ THOMAS
Published: November 2004

Understanding the behavior of distributed applications is a very challenging task due to the complexity of these applications. To manage complexity, the top-down use of suitable abstraction hierarchies is frequently proposed. Given the complexity of distributed applications, manually deriving such abstraction hierarchies is not realistic. The execution of distributed applications is typically analyzed using an event-based approach. This paper discusses one tool that groups more primitive events into abstract events to derive a hierarchy of abstract events automatically. Ideally, these abstractions should reveal logical units of an application and their relations. To explore the abstraction hierarchies derived, an existing prototype visualization tool was modified to provide abstract visualizations. A user can navigate through these abstraction hierarchies, displaying an execution at various levels of abstraction. Examples of such abstract visualizations are given and discussed. In general, the abstractions derived automatically represent meaningful parts of the application: they can be interpreted in terms of the application domain. While the abstraction tool does not necessarily derive the best possible abstraction hierarchies in all cases, it performs the bulk of the work and provides good initial abstractions which can subsequently be refined manually.
SUPPORTING QUERIES ON SOURCE CODE: A FORMAL FRAMEWORK
Authors: PAUL SANTANU , PRAKASH ATUL
Published: November 2004

Querying source code interactively for information is a critical task in reverse engineering of software. However, current source code query systems succeed in handling only small subsets of the wide range of queries possible on code, trading generality and expressive power for ease of implementation and practicality. We attribute this to the absence of clean formalisms for modeling and querying source code. In this paper, we present an algebraic framework (Source Code Algebra or SCA) that forms the basis of our source code query system. The benefits of using SCA include the integration of structural and flow information into a single source code data model, the ability to process high-level source code queries (command-line, graphical, relational, or pattern-based) by expressing them as equivalent SCA expressions, the use of SCA itself as a powerful low-level source code query language, and opportunities for query optimization. We present the SCA’s data model and operators and show that a variety of source code queries can be easily expressed using them. An algebraic model of source code addresses the issues of conceptual integrity, expressive power, and performance of a source code query system within a unified framework.
RESTRUCTURING PROGRAMS THROUGH PROGRAM SLICING
Authors: KIM HYEON SOO , KWON YONG RAE , CHUNG IN SANG
Published: November 2004

Software restructuring is recognized as a promising method to improve logical structure and understandability of a software system which is composed of modules with loosely-coupled elements. In this paper, we present methods of restructuring an ill-structured module at the software maintenance phase. The methods identify modules performing multiple functions and restructure such modules. For identifying the multi-function modules, the notion of the tightly-coupled module that performs a single specific function is formalized. This method utilizes information on data and control dependence, and applies program slicing to carry out the task of extracting the tightly-coupled modules from the multi-function module. The identified multi-function module is restructured into a number of functional strength modules or an informational strength module. The module strength is used as a criterion to decide how to restructure. The proposed methods can be readily automated and incorporated in a software tool.
EXECUTABLE SPECIFICATION AND ANALYSIS FOR THE DESIGN OF CONCURRENT OBJECT-ORIENTED SYSTEMS
Authors: DENG YI , CHANG SHI-KUO , LIN XIAOLA
Published: November 2004

This paper investigates the analysis of concurrent OO designs using a formal, executable specification technique called G-Net. After presenting an overview of the G-Net technique, we show how to use the G-Net notation to specify the concurrent OO systems. A formal transformation technique, which translates a G-Net specification to a semantically equivalent PrT-net, is presented. The resultant PrT-net can then be formally analyzed. The practical significance of this approach in fault-tolerant systems and distributed multimedia systems design is discussed.
PARTIAL EVALUATION FOR THE UNDERSTANDING OF FORTRAN PROGRAMS
Authors: BLAZY SANDRINE , FACON PHILIPPE
Published: November 2004

This paper describes a technique and a tool that support partial evaluation of FORTRAN programs, i.e., their specialization for specific values of their input variables. The authors’ aim is to understand old programs, which have become very complex due to numerous extensions. From a given FORTRAN program and these values of its input variables, the tool provides a simplified program, which behaves like the initial program for the specific values. This tool mainly uses constant propagation and simplification of alternatives to one of their branches. The tool is specified in terms of inference rules and operates by induction on the FORTRAN abstract syntax. These rules are compiled into Prolog by the Centaur/FORTRAN programming environment. The completeness and soundness of these rules are proven using rule induction.
ORTHOGONAL SHORTEST ROUTE QUERIES AMONG AXES PARALLEL RECTANGULAR OBSTACLES
Authors: ELGINDY HOSSAM , MITRA PINAKI
Published: November 2004

Given a set ℬ of n barriers, the shortest route query SRQ problem asks for a preprocessing of ℬ such that a description of the shortest route between two points (origin and destination) can be reported efficiently. In this manuscript we present efficient sequential and parallel algorithms for the SRQ problem where the barriers in ℬ are disjoint planar rectangles whose sides are parallel to the coordinate axes, and subsequent queries ask for the shortest L1 route between two arbitrary points which avoids the barriers in ℬ. The segments forming such route are also restricted to be parallel to the coordinate axes.

For this problem we we present sequential and parallel preprocessing algorithms which allow for reporting the shortest distance between two arbitrary query points in O( log n) time with a single processor. The route itself can also be constructed in time proportional to its number of segments. Our method is based on constructing three planar graphs, called carrier graphs, that contain the shortest route information in a succinct form. Each graph can then be searched using graph theoretic techniques. Using the same techniques we also present a parallel algorithm for computing the orthogonal shortest distance between two points among rectangular obstacles which runs in poly-logarithmic time using sub-quadratic number of processors on the CREW PRAM model of computation.
COMPUTATIONAL GEOMETRY COLUMN 22
Authors: O'ROURKE JOSEPH
Published: November 2004

The class of n2-hard geometric problems is described, with special concentration on detecting collinearities among a set of points in the plane.
A SURVEY OF OBJECT-SPACE HIDDEN SURFACE REMOVAL
Authors: DORWARD SUSAN E.
Published: November 2004

We present a survey of the hidden surface removal literature, focusing on object-space algorithms. We give a brief definition and history of the problem, followed by a discussion of problems and algorithms associated with the priority ordering of faces. We go on to examine object-space algorithms in order of increasing object complexity: xy-parallel rectangles, ordered triangles, c-oriented faces, c-oriented polyhedra, polyhedral terrains, and general polyhedra. We also review recent work on merging visibility maps and moving viewpoints. Finally, we present a list of open problems.
SUBPIXEL IMAGE REGISTRATION USING CIRCULAR FIDUCIALS
Authors: EFRAT ALON , GOTSMAN CRAIG
Published: November 2004

The design of fiducials for precise image registration is of major practical importance in computer vision, especially in automatic inspection applications. We analyze the sub-pixel registration accuracy that can, and cannot, be achieved by some rotation-invariant fiducials, and present and analyze efficient algorithms for the registration procedure. We rely on some old and new results from lattice geometry and number theory and efficient computational-geometric methods.
TRIANGULATING DISJOINT JORDAN CHAINS
Authors: BAR-YEHUDA REUVEN , CHAZELLE BERNARD
Published: November 2004

Recent advances on polygon triangulation have yielded efficient algorithms for a large number of problems dealing with a single simple polygon. If the input consists of several disjoint polygons, however, it is often desirable to merge them in preprocessing so as to produce a single polygon that retains the geometric characteristics of its individual components. We give an efficient method for doing so, which combines a generalized form of Jordan sorting with the efficient use of point location and interval trees. As a corollary, we are able to triangulate a collection of p disjoint Jordan polygonal chains in time O (n + p ( log p)1+ε), for any fixed ε > 0, where n is the total number of vertices. A variant of the algorithm gives a running time of O ((n + p log p) log log p). The performance of these solutions approaches the lower bound of Ω (n + p log p).
CONNECTIVITY AND SPECTRUM IN A GRAPH WITH A REGULAR AUTOMORPHISM GROUP OF ODD ORDER
Authors: SJOGREN JON A.
Published: November 2004

Let a finite group G of odd order n act regularly on a connected (multi-)graph Γ. That is, no group element other than the identity fixes any vertex. Then the “quotient graph” Δ under the action is the induced graph of orbits. We give a result about the connectivity of Γ and Δ in terms of their numbers of labeled spanning trees. In words, the spanning tree count of the graph is equal to n, the order of the given regular automorphism group, times the spanning tree count of the graph of orbits, times a perfect square integer. There is a dual result on the Laplacian spectrum saying that the multiset of Laplacian eigenvalues for the main graph is the disjoint union of the multiset for the quotient graph together with a multiset all of whose elements have even multiplicity. Specializing to the case of one orbit, we observe that a Cayley graph of odd order has spanning tree count equal to n times a square, and that that the Laplacian spectrum consists of the value 0 together with other doubled eigenvalues. These results are based on a study of matrices (and determinants) that consist of blocks of group-matrices. The generic determinant for such a matrix with the additional property of symmetry will have a dominanting square factor in its (multinomial) factorization. To show this, we make use of the Feit-Thompson theorem which provides a normal tower for an odd-order group, and perform a similarity conjugation with a fixed integer, unimodal matrix. Additional related results are given for certain group-matrices “twisted” by a group of automorphisms, generalizing the “g-circulants” of P.J. Davis.
ON SMALL LENGTH EQUATIONS OVER TORSION-FREE GROUPS
Authors: PRISHCHEPOV MATVEĬ I.
Published: November 2004

Let G be a group,  the free group generated by t and let r(t)∈G*. The equation r(t)=1 is said to have a solution over G if it has a solution in some group that contains G. There is a conjecture (attributed to F. Levin) that if G is a torsion-free group, then any equation has a solution over G. In this paper we verify this conjecture in the case when the sum of the absolute values of the exponent of t in r(t) is not greater than six.
OPTICAL BISTABILITY AND TRANSVERSE INHOMOGENITIES IN DIFFUSIVE SYSTEMS WITH INDUCED ABSORPTION
Authors: BURAK D. , GROHS J. , IßLER H. , KLINGSHIRN C.
Published: November 2004

In this contribution the systematic analysis of the steady-state absorptive optical bistability in a thin semiconductor film is given. The heat-conductivity equation with corresponding two-point boundary conditions is solved numerically and the analytical approximation of the switching intensity is given based on the theorem about lower bounds for critical parameters in nonlinear boundary-value problems. The influences of diffusion and of spatial inhomogenities of the excitation profiles in the sample on the input-output characteristic are analyzed in detail. The transverse nonuniformity of the system leads to a condition for the existence of bistability that differs significantly from the well known case of a spatially homogeneous excitation of the medium. The critical slowing down phenomenon is discussed analytically and compared to previous experimental results.
THE INVESTIGATIONS OF DIFFERENT NPP CRYSTAL SURFACE STRUCTURES BY AFM
Authors: WANG DA-WEN , YE CHENG , ZHAO JIAN-LIANG , BAI CHUN-LI
Published: November 2004

The investigations of nonlinear optical crystal surface structures have been reported in this paper for the first time. The AFM observations for cleavage (101) surface and (001) surface of NPP crystal indicate that the molecular arrangements on both of them are the same with its bulk structure, without any superstructure. And the phenyl and pyrrolidine rings in (001) surface can be distinguished. The angle between the molecular charge transfer axis and the binary axis obtained by AFM is 56°, closed to the optimal angle, which leads to the large nonlinear optical efficiency of NPP crystal.
LIGHT DIFFRACTION FROM MULTIFREQUENCY VOLUME GRATINGS IN ANISOTROPIC MEDIA
Authors: GALKIN O.N. , KRAVCHENKO V.I. , LIUSHENKO A.I. , PARKHOMENKO YU.N.
Published: November 2004

New principles of light anisotropic diffraction from complex (multifrequency) gratings have been studied theoretically and experimentally in case of two sound waves excited in the same volume. It has been shown that two different types of the intercombined multiphonon processes exist. Namely this peculiarity ensures reciprocity of the light transmission in opposite directions. Simultaneously qualitatively new (two-step) dependences of the diffracted electromagnetic wave intensity on sound frequency have been discovered.
SOLITON PROPAGATION IN SATURABLE NONLINEAR FIBRE COUPLERS — VARIATIONAL AND NUMERICAL RESULTS
Authors: PENG G.D. , CHU P.L. , ANKIEWICZ A.
Published: November 2004

The problem of optical soliton propagation in couplers with saturation of nonlinear refractive index is investigated using a simple variational approach. From this study, important features relating to optical switching and soliton eigen-states are revealed. For instance, a parameter, γ max , which characterizes the limiting effect of saturation in optical switching, is identified. We carry out numerical solutions to the problem and confirm that the approximate approach does give results agreeing with those from the simulation.
NEAR INFRARED NONLINEAR OPTICAL PHASE CONJUGATION IN PHOTOREFRACTIVE CRYSTALS AND SEMICONDUCTOR MATERIALS PART I: FUNDAMENTALS
Authors: SONDERER N. , GÜNTER P.
Published: November 2004

The concept of optical wavefront reversing as a tool for phase aberration correction is reviewed. Presenting the fundamental and basic nature of the nonlinear interaction of light with matter leading to optical phase conjugation, a theoretical description of the photorefractive effect is given with a special emphasis on the gain of a coupling experiment and the speed of the photorefractive effect. Optical phase conjugation configurations, designs, and enhancement techniques are described and summarized comparing the possibilities and disadvantages regarding specific applications in the near infrared.
ULTRASHORT PULSE SECOND-HARMONIC GENERATION IN OPTIMIZED NONLINEAR POLYMER THIN FILM STRUCTURES
Authors: SIDICK E. , DIENES A. , KNOESEN A.
Published: November 2004

Methods to optimize the generation of ultrashort second harmonic pulses are investigated. The goal is to maximize the conversion efficiency while maintaining a short pulse. The first method exploits the effects of anomalous-dispersion phase-matching. In a nonlinear polymer we show that an optimum concentration of chromophore exists that maximizes the conversion efficiency without causing unacceptable pulse-spreading. In the second method we use unipolar and bipolar quasi-phase-matched (QPM) structures to increase the nonlinear interaction length. Unipolar and bipolar QPM structures not only provide significant enhancement in ultrashort pulse second harmonic generation but also reduce the pulse distortion.
COHERENTIZATION CONDITION IN DOUBLE PHASE CONJUGATION VIA THIN LAYERS
Authors: ZEL’DOVICH B.Ya. , SAFONOV V.I.
Published: November 2004

Theoretical investigation of noise wave suppression in double phase conjugation via thin layers is carried out. Using methods of matrix and wave optics it is shown that if the distance between the lens and thin nonlinear layers is less than the double focus distance, then the conjugated wave is generated in the suggested scheme slightly above the threshold condition.
ON THE NON-NEWTONIAN INCOMPRESSIBLE FLUIDS
Authors: MÁLEK JOSEF , NEČAS JINDŘICH , RŮŽIČKA MICHAEL
Published: November 2004

The Navier-Stokes equations can be included as a special case into the class of non-Newtonian incompressible fluids with the nonlinear stress tensor τ=τ(e), the components of which satisfy the p-growth condition. Measure-valued solutions already exist for p>2n/(n+2). For the space periodic problem, the existence of the weak solution is then obtained for p>3n/(n+2). These solutions are regular and unique for p≥1+2n/(n+2).
MULTIPLE SOLUTIONS FOR INHOMOGENEOUS ELLIPTIC PROBLEMS ARISING IN ASTROPHYSICS
Authors: CALAHORRANO M. , DOBARRO F.
Published: November 2004

By variational and topological methods we prove the existence of a positive interval Λ such that for all λ∈Λ there exist at least three positive solutions of (1.1) on Ω=DR, where DR is a semidisk in [Formula: see text] with radius R and center (0, 0), h is a non-negative bounded smooth function and f: R→R is a function of type (tσ−tσ+α)χ[0, 1] (t) with σ>1 and α>0. Under some restrictions for f and h we show that Λ is independent of R, for R large enough. This type of problem arises in an astrophysical gravity-free model of solar flares given by J. Heyvaerts and others.
ON VIBRATIONS OF A BODY WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY
Authors: LOBO MIGUEL , PEREZ EUGENIA
Published: November 2004

We consider the asymptotic behavior of the vibration of a body occupying a region Ω⊂ℝ3. The density, which depends on a small parameter ε, is of order O(1) out of certain regions where it is O(ε–m) with m>2. These regions, the concentrated masses with diameter O(ε), are located near the boundary, at mutual distances O(η), with η=η(ε)→0. We impose Dirichlet (respectively Neumann) conditions at the points of ∂Ω in contact with (respectively, out of) the masses. For the critical size ε=O(η2), the asymptotic behavior of the eigenvalues of order O(εm−2) is described via a Steklov problem, where the ‘mass’ is localized on the boundary, or through the eigenvalues of a local problem obtained from the micro-structure of the problem. We use the techniques of the formal asymptotic analysis in homogenization to determine both problems. We also use techniques of convergence in homogenization, Semigroups theory, Fourier and Laplace transforms and boundary values of analytic functions to prove spectral convergence. In the same framework we study the case m=2 as well as the case when other boundary conditions are imposed on ∂Ω.
MIXED FINITE ELEMENT METHODS WITH CONTINUOUS STRESSES
Authors: BREZZI FRANCO , FORTIN MICHEL , MARINI L. DONATELLA
Published: November 2004

We present a modified mixed formulation for second order elliptic equations and linear elasticity problems which automatically satisfies the “ellipticity on the kernel” condition, i.e., one of the two compatibility conditions necessary to ensure stability and optimal error bounds (the other being the Inf-Sup condition). This modification differs from similar ones introduced by other authors in that it is independent of the mesh size. Moreover, it allows the use of continuous stresses.
A NUMERICAL HOMOTOPY METHOD AND INVESTIGATIONS OF A SPRING-MASS SYSTEM
Authors: DAVIDSON B.D. , STEWART D.E.
Published: November 2004

A numerical technique is developed to determine the behavior of periodic solutions to highly nonlinear non-autonomous systems of ordinary differential equations. The method is based on shooting in conjunction with a probability one homotopy method and an implementation of the topological index. It is shown that solutions may be characterized a priori in terms of an index and this is developed into a powerful numerical and investigative tool. This method is used to investigate the periodic solutions of a nonlinear fourth order system of differential equations. These equations describe the motion of a forced mechanical oscillator and are extremely difficult to evaluate numerically. Solutions are presented which could not be found using local methods. These include flip, saddle node and symmetry breaking pitchfork bifurcations.
SHARP ERROR ANALYSIS FOR CURVATURE DEPENDENT EVOLVING FRONTS
Authors: NOCHETTO RICARDO H. , PAOLINI MAURIZIO , VERDI CLAUDIO
Published: November 2004

The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter ε>0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order [Formula: see text] are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)-solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.
NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES
Authors: CLAIN S. , RAPPAZ J. , SWIERKOSZ M. , TOUZANI R.
Published: November 2004

We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel to the invariance axis. The model equations have current tension as prescribed data rather than current intensity. In particular, the formulation of the electromagnetic problem uses the magnetic field as the unknown function. The numerical method takes into account the time periodicity of the prescribed tension and deals with the two different time scales of electromagnetic and thermal phenomena.
NOGOOD RECORDING FOR STATIC AND DYNAMIC CONSTRAINT SATISFACTION PROBLEMS
Authors: SCHIEX THOMAS , VERFAILLIE GÉRARD
Published: November 2004

Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The notion of dynamic CSP (DCSP) [DD88] has been proposed to represent such evolutions. The problem we consider here is the solution maintenance problem in a DCSP.

Naively applying usual satisfaction algorithms to this problem results in redundant search and inefficiency. A general approach to suppress redundancies in case of both restrictions and relaxations is to concisely represent the frontier of the solution space and justifications of this frontier in terms of set of constraints. This paper proposes a new class of constraint recording algorithms called nogood recording that may be used for solving both dynamic CSPs and usual CSP (called static CSPs here). It offers an interesting compromise, polynomially bounded in space, between an ATMS-like (Assumption-based Truth Maintenance System) approach, that would give a precise and exhaustive description of the frontier, and the usual constraint satisfaction algorithms (that discover a new frontier at each execution). We first introduce the principles used for nogood generation and then examine various recording schemes, on top of different tree search algorithms, characterizing the tradeoffs between the amount of recorded constraints and the pruning achieved. We then present experimental results and comparisons with various existing techniques for solving static or dynamic CSP.
CONCEPT AND REALIZATION OF A HYBRID AI TOOL APPLIED TO COMPUTER VISION
Authors: DVORAK J. , BUNKE H.
Published: November 2004

Computer vision includes a variety of tasks of different natures, and there are many applications that have a strong need for knowledge representation and use. Typical knowledge representation methods used in computer vision include frames, rules, logic, constraints, and attributed prototype graphs. Although the advantages of hybrid approaches to knowledge representation have been recognized, no hybrid tool for high-level computer vision is available yet.

In this paper we first present a general framework for a hybrid knowledge representation tool. It is based on object-oriented programming and offers distinctive features such as high flexibility, coherence, and a clean integration of a collection of knowledge-based techniques. Then we give a brief overview of our computer vision tool VISTO, which was created along the framework discussed in the first part of the paper. With an application example we illustrate the use of VISTO and the advantages of hybrid knowledge representation in comparison to non-hybrid approaches.