Deterministic Chaos

Disequilibrium is a common if not dominant condition in geomorphology and other environmental sciences. Because disequilibrium in a system implies a time lag, time steps and time delays in simple deterministic equations may reflect process, and such equations have been shown to result in chaos. After examining some models of hillslope and catchment development, we present an oversimplified model of a hillslope in which we calculate the elevation of a point at time t + 1 as a function (we consider both linear and nonlinear terms) of the difference in elevation between it and the next uphill and downhill points at time t. We show how this simple hillslope model will not produce chaos under one set of limiting conditions that do not include nonlinearity, but, without proof, we note that in most conditions the hillslope mode is so similar to other models in which chaos arises because of disequilibrium that chaotic behavior is a likely possibility. A formulation wherein the time step is in a weathering and/or erosion coefficient rather than the elevation is also proposed.

We propose a quantization of linear, volume preserving ,maps on the discrete and finite 3-torus T 3 N represented by elements of the group SL(3, Z N ). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three dimensional toroidal phase space and are characterized by invariant vectors a of T 3 N . We quantize all such flows which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a . The corresponding maps belong to the little group of a ∈ SL(3, Z N ) which is an SL(2, Z N ) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps, realize the metaplectic representation of SL(3, Z N ) on the discrete group of three dimensional magnetic translations i.e. the non-commutative 3-torus with deformation parameter the N -th root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three dimensional objects.

This research explores the concept of Informational Energy as a fundamental force influencing the structure and evolution of the universe. Unlike traditional energy forms, Informational Energy governs the order and entropy of systems, playing a critical role in both cosmic and quantum phenomena. The study proposes that before the Big Bang, the universe was governed by an informational framework—where mass, entropy, and velocity determined the stability of systems— and that the subsequent collapse of this framework triggered the explosive expansion of the Big Bang. By integrating principles from thermodynamics, quantum mechanics, and gravitational physics, this work establishes a mathematical foundation for Informational Energy and its effect on particle interactions, wavefunction behavior, and black hole mechanics. Furthermore, the research examines how Informational Energy influences quantum coherence, wavefunction collapse, and particle decay, offering new insights into the emergence of order from high-entropy states.

Understanding the "I" via time, rhythm and religion in Mozambique DENISE: Paulina Chiziane published her latest book in 2015 titled Ngoma Yethu 1 : O curandeiro e o novo testamento [WHICH LOSELY TRANSLATES TO: Our Drum/Rhythmic I: The traditional healer/nyanga and the new testament]. In a new writing phase the renown novelist now takes a different path from fiction to write about the present problems of her country: Mozambique. Chiziane does so with the collaboration of local experts in Traditional African Religion and Medicine. One of the prefatory notes claims that Chiziane opts for [AND I QUOTE] "um novo paradigma de escrita não propriamente ficcional mas contemplativo e reflexivo" [IN OUR TRANSLATION] [a new writing paradigm, one that is not merely fictional but contemplative and reflexive] (Ngomane, 2013: 9). With this in mind, for this project Chiziane chooses a traditional healer Mariana Martins to write Ngoma Yethu: O curandeiro e o novo testamento [Our Drum/Rhythmic I: The traditional healer/[OR IN THE RONGA? WORD] nyanga and the new testament]. WE PARTICULARLY USE THE WORD NYANGA BECAUSE IN RONGA IS A is a polysemic word in Changana that signifies simultaneously drum or rhythm, invoking spirits, and the preparation a sangoma traditional healer goes through. Both authors want to recover a sense of subjectivity of the African/Mozambican 'I' in relation to their traditional practices. However, these traditional practices since colonialism have been obscured, erased and mixed to the point of being indistinguishable from capitalist or neocolonial practices under the name of religion and spiritual healing. Both Chiziane and Martins want to open a debate on the problem of the [I QUOTE]"usurpação do ser e do ter" [usurpation of being and of having/owning] [END OF

A deterministic geometric approach, the fractal-multifractal (FM) method and faithful in encoding daily geophysical sets over a year, is used to describe records over multiple years. Looking for temporal trends on FM parameters that describes geometry of sets gathered over longer periods of time, this study presents FM descriptions of rainfall and streamflow and rainfall over five consecutive years optimizing deviations on accumulated sets. The results for 105 and 61 years of rainfall and runoff, respectively, near Sacramento, California illustrate that: (a) encoding of both types of data sets may be accomplished with reasonably small errors, and (b) predicting the geometry of both attributes is possible, even five years ahead, training a neural network on FM parameters. It is shown that the FM approach not only captures the accumulated sets over successive five years but also preserves other statistical attributes as well as the overall "texture" of the records.

When an s-polarized laser beam impinges on a homeotropically aligned ® lm of nematic liquid crystal at small incident angle, undamped oscillations of the molecular director may be produced. At high beam intensities the oscillations break up into deterministic chaos. Although this e ect has been known for a long time and the route to chaos has been qualitatively analysed, no detailed study of the actual molecular director motion has been carried out. We have designed an experimental apparatus to monitor the dynamics of the molecular director, as described by its two polar angles. We observed di erent dynamical regimes, depending on the laser intensity: steady states, ocillations, rotation and, at the highest laser intensities, deterministic chaos. Moreover, the transitions between the oscillation and rotation regimes are characterized by intermittency.

Recibido el 18 de febrero de 2006; aceptado el 1 de abril de 2006 We report on the experimental observation of chaotic behavior in the diffraction pattern of a homeotropically aligned nematic mixture. The heating effect of a linearly polarized laser beam induces the formation of an isotropic droplet at the centre of the beam. The joint action of the beam with a superimposed low frequency electric AC field produce a complex dynamics of the diffraction pattern. It undergoes a sequence of dynamical regimes occurring for well-defined threshold values of the beam's power, and the frequency and amplitude of the AC field. We measure a time series of intensity vs. time for a fixed location in the pattern. By using the algorithm of Wolf et al we determine the largest non-negative Lyapunov exponent λ 1 directly from the experimental time series, rather than analyzing the equations of motion of the system. The determined values of λ1 indicate chaotic behavior of the diffraction pattern for the unstable regime. The analysis of the time series suggests that the system follows a route to chaos through period doubling. Furthermore, from the calculated values of the correlation dimension, it was possible to identify this behavior as deterministic chaos.

A new methodology to characterize nonlinear systems is described. It is based on the measurement over the time series of two quantities: the "Dynamical order" and the "Self-correlation". The averaged "Scalar" and "Perpendicular" products are introduced to measure these quantities. While this approach can be applied to general nonlinear systems, the aim of this work is to focus on the characterization and modeling of chaotic systems. In order to illustrate the method, applications to a two-dimensional chaotic system and the modeling of real telephony traffic series are presented. Three important aspects are discussed: the use of the averaged "Scalar" product as supplement of the "Lyapunov exponent", the use of the averaged "Perpendicular" product as a refinement of the "Mutual information" and the reduction of m-dimensional systems to the study of only one dimension. This new conceptual framework introduc...

Some quite recent results from the area of Deterministic Chaos have considerable significance for practitioners of Information Theory. In 1959 Kolmogorov observed that Shannon’s probabilistic theory of information could be applied to symbolic encodings of the phase-space descriptions of physical non-linear dynamical systems so that one might characterise a process in terms of its Kolmogorov-Sinai entropy. Pesin’s theorem in 1977, proved that for certain deterministic non-linear dynamical systems exhibiting chaotic behaviour, the Kolmogorov-Sinai entropy h KS is given by the sum of the positive Lyapunov exponents for the process, i.e. h KS = ∑ i λ + i [3]. For a number of simple non-linear processes the Lyapunov exponents may be computed very precisely. Thus a non-linear dynamical systems may be viewed as an information source whose corresponding source entropy is accurately known. The existence of simple ‘calibrated’ sources such as the logistic map (ẋ = f(x) = rx(1−x)), [3] provide...

Workers in a bucket brigade production system perform unproductive travel when they walk to get more work from their colleagues. We introduce a new design of bucket brigades to reduce unproductive travel. Under the new design, each worker works on one side of an aisle when he proceeds in one direction and works on the other side when he proceeds in the reverse direction. We propose simple rules for workers to share work under the new design and find a sufficient condition for the system to self-balance. Numerical examples suggest that the improvement in throughput by the new design can be as large as 30%. Even with a 20% reduction in labor, the new design can still increase throughput by 7%.

Chaos has three important dynamic properties : the sensitive dependence on initial conditions, the intrinsic stochastic property and ergodicity. So it was applied to optimization problems. In most optimization methods such as the COA [1] and [4], variables chaos generated by different types of applications such as the Logistic, the application Tent, Lozi, Ikeda and others have shown very interesting results that random application. The main idea is to improve the convergence of the optimization chaotic. In this paper, a chaotic strategy is proposed based on a Hénon application chaotic. c © Electronic Journal of Theoretical Physics. All rights reserved.

Finite element simulations of bubbling gas-solid fluidized beds were performed using the two-fluid granular temperature model. A study was carried out to establish the number of equations necessary to describe the dynamics of this fluidized bed. In order to investigate the bubbles' behaviour and shape, several simulations were performed using differing numerical resolution. The main purpose of these investigations is to analyse, through numerical simulation, the dynamics of fluidized beds and to show how the application of deterministic chaos theory may be used to obtain the real dimensionality, or the number of degrees of freedom, of a simulated fluidized bed. Moreover, this type of statistical information can be used to quantify the similarities between experiment and simulation results.

We prove several results about the relations between injectivity and surjectivity for sand automata. Moreover, we begin the exploration of the dynamical behavior of sand automata proving that the property of nilpotency is undecidable. We believe that the proof technique used for this last result might reveal useful for many other results in this context.

We review the quantum transport of ultra-cold alkali atoms trapped in a one-dimensional optical lattice of double-potential wells, engineered through a combination of ac-Stark shifts and Zeeman interactions. The system is modelled numerically through analysis of the bandstructure and integration of the time-dependent Schrödinger equation. By these means we simulate coherent control of the atomic wavepackets. We present results from ongoing experiments on laser-cooled caesium, including the demonstration of quantum state preparation and preliminary evidence for coherent tunnelling. Entanglement between the internal and motional degrees of freedom allows us to access the tunnelling dynamics by Stern-Gerlach measurements of the ground state magnetic populations. A scheme to extend this into a full reconstruction of the density matrix for the ground state angular momentum is presented. We further consider the classical dynamics of our system, which displays deterministic chaos. This has important implications for the distinction between classical and quantum mechanical transport.

The Mediterranean climate patterns are characterized by the great rain variability between years combined whit recurrent drought periods and highly intense rain events. These last becomes critical in this area because incise, usually, immediately after the summer dry period, when the vegetation cover is less capable to protect the soil against rainfall aggressiveness and the wildfire period is finishing. These

We consider the problem of fast acquisition in magnetic resonance imaging (MRI). A recent breakthrough concept called compressed sensing (CS) shows that sparse or, more generally, compressible signals can be recovered from a small number of linear random measurements. CS, using random measurements, has also been successfully applied to MRI for fast acquisition. In a recent work, we have preliminarily employed deterministic chaos in CS that potentially offers a more practical and efficient CS framework. This paper adapts chaotic CS to MRI acquisition. In particular, we use chaotic logistic map for CS and adapt it to acquire the 2-dimensional MRI. In addition, we numerically analyze the performance of the proposed chaotic CS for MRI and show that it performs better random CS.

The Various physical mechanisms governing river flow dynamics act on a wide range of temporal and spatial scales. This spatio-temporal variability has been believed to be influenced by a large number of variables. In the light of this, an attempt was made in this paper to examine whether the daily flow sequence of the Benue River exhibits low-dimensional chaos; that is, if or not its dynamics could be explained by a small number of effective degrees of freedom. To this end, nonlinear analysis of the flow sequence was done by evaluating the correlation dimension based on phase space reconstruction and maximal Lyapunov estimation as well as nonlinear prediction. Results obtained in all instances considered indicate that there is no discernible evidence to suggest that the daily flow sequence of the Benue River exhibit nonlinear deterministic chaotic signatures. Thus, it may be conjectured that the daily flow time series span a wide dynamical range between deterministic chaos and periodic signal contaminated with additive noise; that is, by either measurement or dynamical noise. However, contradictory results abound on the existence of low-dimensional chaos in daily streamflows. Hence, it is paramount to note that if the existence of low-dimension deterministic component is reliably verified, it is necessary to investigate its origin, dependence on the space-time behavior of precipitation and therefore on climate and role of the inflow-runoff mechanism.

Non-averaged scalp-recorded brain potentials were analyzed in four right-handed humans while they were either silently reading a book, or in idle alert conditions. The dimensionality of chaotic strange attractors was estimated from the EEG at each of 14 scalp electrodes, using the point correlation dimension PD2 algorithm. When the subject was fully alert but not engaged in any specific task, PD2 was between 5.2 and 5.9. When the subject was silently reading a book, PD2 bifurcated to significantly higher values (6.6-6.9) in the left lateral anterior extrasylvian temporal cortex, but did not change in the adjacent left perisylvian cortex nor over the right side of the brain. The PD2 increases occurred without any significant change in vigilance level as assessed from the unchanged mean voltage of concomitant gamma (40 Hz) EEG oscillations. A small barely significant PD2 increase was only noticed in the left lateral precentral region. The increase of chaotic dimensionality in the left lateral extrasylvian temporal cortex during reading reflects enhanced processing operations in the semantic (Wernicke) areas and is in line with recent PET imaging data. These results provide for the first time evidence of a focal chaotic fractal dimension increase that is related to specific cognitive brain processing operations.

We report the observation and characterization of chaos in stimulated Brillouin scattering (SBS) generated in a single-mode fiber in the presence of weak external feedback. We establish that the noise, which initiates this process and dominates the emission near the SBS threshold, is dramatically suppressed from the onset of strong SBS emission, giving rise to various highly deterministic dynamical features.

Purchasing Power Parity is an important theory at the basis of a large number of economic models. However, the implication derived form the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies. In a recent paper, Serletis and Gogas (2000) show evidence of deterministic chaos in several OECD exchange rates. As a consequence, PPP rejections would be spurious. In this work, we follow a two-stage testing procedure to test for non-linearities and chaos in real exchange rates, using a new set of techniques designed by , under the denomination of Recurrence Quantification Analysis (RQA). Our conclusions differ slightly from Serletis and Gogas ( ), but they are also supportive of chaos for some exchange rates.

Complex systems and dynamics are present in many parts of daily life and branches of science. This participation is continuation of our previous research, that introduced a novelty method of visualization and possible control of complex networks, that are used to visualize dynamics of evolutionary algorithms. Selected evolutionary algorithms are used as an example in order to show how its behavior can be understood as complex network and controlled via conversion into CML system-a model based on mutually joined nonlinear n equations. The main aim of this investigation was to show that dynamics of evolutionary algorithms can be converted to CML system and then controlled. Selected results of evolutionary controlled CML system are discussed here.

This paper presents results of the utilization of selected discrete chaotic map, which is Dissipative standard map, as pseudo-random number generator for the differential evolution (DE) optimization algorithm and Particle Swarm Optimization (PSO) algorithm in the task of PID controller design for the selected 4 th order dynamical system. The results are compared with previously published results; both chaos driven heuristics with each other and finally the obtained results are compared with canonical PSO and DE versions, which do not utilize the chaos in the place of pseudo-random number generator.

The relationship between structure and behavior is central to System Dynamics, but effective tools required to understand that relationship still elude us. The current state of the art in the field of loop dominance analysis relies on either practitioner intuition and experience or complex algorithmic manipulation in the form of eigenvalue analysis or pathway participation metrics. This paper presents a new and distinct numeric method based on a different measure, the loop score, to determine the contribution of a loop to a model's behavior at each instant in time. This allows us to discover the origin of model behavior. The method was inspired by observations of the patterns in the changes of the values of variables during simulations and has been tested and refined using empirical evaluation on a variety of models. The method also offers a promising approach to the visualization and aggregation of simulation results.

Self-pulsing and deterministic chaos is observed in a single-mode, homogeneous-line, CO2 laser with an overall negative feedback, when the damping constant of the feedback loop is of the same order as the population decay rate. This represents a fundamental limitation of the general use of feedback schemes in high-stability laser applications. A theoretical model is shown to yield results in good agreement with the experimental ones, thus confirming the simple structure of the associated phase space.

This work is a study on the nature of a real load data set extracted as a time series. It checks whether the process that generates the loading graphics has any regularities and if so, where they can be detected. It still evaluates if the process presents non-periodical amplitudes of the frequencies that characterize them. The difference between these two kinds of behavior, finally, corresponds to the determination of the processes as regular or chaotic. In such case, as discussed here, a set of signals corresponding to load values taken in intervals of 15 min is provided and it is a matter of regression to their formation condition. In order to show how the time sale may affect the diagnosis of a system, another set obtained in intervals of 0.0083 s is analyzed. As a consequence, it is shown that chaos may be better identified if measures are obtained in short intervals of time. The analysis presented in this work is based upon the evaluation mechanisms of a chaotic process, which basically can be reduced to the calculation of Lyapunov exponents and to verifying the power spectra.

A simple and inexpensive mechanical model for the demonstration of chaos in a nonlinear deterministic system is described. Periodic, period-doubled, and chaotic motions are exhibited by the model in agreement with the solutions of its governing differential equation. The model is sufficiently free from long-term drifts to enable experimental Poincaré plots to be easily constructed. Such a simple mechanical model is shown to be ideal for use as a lecture room demonstration, as well as for a student laboratory.

Differential pressure fluctuations in gas-solid fluidized beds were analyzed by chaos analysis (construction of attractors, correlation dimension, Kolmogorov entropy) and mutual information. Experimental fluidization tests of three different particles were conducted. Two of them are from Geldart group B and one from Geldart group D. The fluidization experiments were performed in a cylindrical bed with 0.07 m i.d. and 1.0 m high. Pressure fluctuations were measured by three pressure transducers, and their signal time series were analyzed in the time domain (mean and standard deviation) and in the frequency domain (power spectra) for comparison and complementation of chaos analysis. Analyses in the time domain allowed a good estimation for determining whether or not the system is fluidized. The Fourier spectra provided more detailed information that could identify other phenomena such as the presence of bubbles. The chaos tools produced sensitive results, offering a qualitative and quantitative analysis for identification of the phenomena that occur in fluidization. Three different fluidization regimes could be indentified: multiple bubble bed, slugging bed, and exploding bubble bed.

We argue that any attempt to classify dynamical properties from nonlinear finite time-series data requires a mechanistic model fitting the data better than piecewise linear models according to standard model selection criteria. Such a procedure seems necessary but still not sufficient.

Many real phenomenona preserves the properties of chaotic dynamics. However, unambiguous determination of belonging to a group of chaotic systems is difficult and complex problem. The main purpose of this paper is to present compound method of time series classification which is basically directed to the detection of chaotic behaviors. The method has been designed for differentiation of three types of time series: chaotic, periodic and random. Our approach assumes, that more reliable information about the dynamics of the system will provide the compilation of several methods, than any individual. This paper focuses on choosing a good set of methods and analysis of their results. In our investigation, we used the following methods and indicators: time delay embedding, mutual information, saturation of system invariants, the largest Lyapunov exponent and Hurst exponent. We checked the validity of the methods applying them to three kinds of basic systems which generate chaotic, periodic and random time series. As a summary of this paper, all selected methods and indicators computed for generated times series have been summarized in the table, which gives the authors a possibility to conclude about type of observed behavior.

Many real phenomenona preserves the properties of chaotic dynamics. However, unambiguous determination of belonging to a group of chaotic systems is difficult and complex problem. The main purpose of this paper is to present compound method of time series classification which is basically directed to the detection of chaotic behaviors. The method has been designed for differentiation of three types of time series: chaotic, periodic and random. Our approach assumes, that more reliable information about the dynamics of the system will provide the compilation of several methods, than any individual. This paper focuses on choosing a good set of methods and analysis of their results. In our investigation, we used the following methods and indicators: time delay embedding, mutual information, saturation of system invariants, the largest Lyapunov exponent and Hurst exponent. We checked the validity of the methods applying them to three kinds of basic systems which generate chaotic, periodic and random time series. As a summary of this paper, all selected methods and indicators computed for generated times series have been summarized in the table, which gives the authors a possibility to conclude about type of observed behavior.

National Library of Canada Bibliothèque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395, nie Wellington OttawaON K1AON4 Ottawa ON K1A ON4 Canada Canada The author has granted a nonexclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sel1 copies of îhis thesis in rnicrofonn, paper or electronic formats. The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts from it rnay be printed or othenivike reproduced without the author's permission. L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique. L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation. This thesis is dedicated to the memory of Car1 Sagan whose book "Shadows of Forgotten Ancestors", CO-authored with his wife Ann Druyan, aroused my interest in the biological world. "When we no longer look at an organic bezng as a savage looks ut a shzp, as something wholly beyond hzs comp~ehension; when we regard every production of nature as one whzch has had a long history; when we conternplate every cornplex structure and instinct as the summing up of many contrivances, each usefuul to the possessor, in the same way as any great mechanicd invention 2s the svrnmzng up of the labour, the expen'ence, the renson. and even the blunders of nurnerous zuorkrnen: when we thus view each organic being, how far more interesting-i speak from experience-does the study of natural hastoy becorne!"

A class of differential equations, which captures the logical structure of discrete time logical switching networks composed of many elements, displays deterministic chaos if each element has many inputs. Statistical features of the dynamics are approximated by using a mean field Langevin-type equation with a random telegraph signal as a stochastic forcing function, and also by considering a random walk on an N-dimensional hypercube. [S0031-9007(97)03599-0]

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the numbers of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity or deterministic chaos.

Electroencephalogram (EEG) from dorsal cortex of lizard Gallotia galloti was analyzed at different temperatures to test the presence of fractal or nonlinear structure during open (OE) and closed eyes (CE), with the aim of comparing these results with those reported for human slow-wave sleep (SWS). Two nonlinear parameters characterizing EEG complexity [correlation dimension (D2)] and predictability [largest Lyapunov exponent (λ1)] were calculated, and EEG spectrum and fractal exponent β were determined via coarse graining spectral analysis. At 25°C, evidence of nonlinear structure was obtained by the surrogate data test, with EEG phase space structure suggesting the presence of deterministic chaos (D2 ∼6, λ1 ∼1.5). Both nonlinear parameters were greater in OE than in CE and for the right hemisphere in both situations. At 35°C the evidence of nonlinearity was not conclusive and differences between states disappeared, whereas interhemispheric differences remained for λ1. Harmonic powe...

The Various physical mechanisms governing river flow dynamics act on a wide range of temporal and spatial scales. This spatio-temporal variability has been believed to be influenced by a large number of variables. In the light of this, an attempt was made in this paper to examine whether the daily flow sequence of the Benue River exhibits low-dimensional chaos; that is, if or not its dynamics could be explained by a small number of effective degrees of freedom. To this end, nonlinear analysis of the flow sequence was done by evaluating the correlation dimension based on phase space reconstruction and maximal Lyapunov estimation as well as nonlinear prediction. Results obtained in all instances considered indicate that there is no discernible evidence to suggest that the daily flow sequence of the Benue River exhibit nonlinear deterministic chaotic signatures. Thus, it may be conjectured that the daily flow time series span a wide dynamical range between deterministic chaos and periodic signal contaminated with additive noise; that is, by either measurement or dynamical noise. However, contradictory results abound on the existence of low-dimensional chaos in daily streamflows. Hence, it is paramount to note that if the existence of low-dimension deterministic component is reliably verified, it is necessary to investigate its origin, dependence on the space-time behavior of precipitation and therefore on climate and role of the inflow-runoff mechanism.

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?

DETERMINISTIC' chaos is characterized by long-term unpredictability arising from an extreme sensitivity to initial conditions. Such behaviour may be undesirable, particularly for proces!ies dependent on temporal regulation. On the other hand, a chaotic !iY!item can be viewed as a virtually unlimited reservoir of periodic behaviour which may be accessed when appropriate feedback is applied to one of the system parameters 0 Feedback algorithms have now been successfully applied to stabilize periodic o!icillations in chaotic laserl, diode"', hydrodynamic4 and magnetoela!itic5 systems, and more recently in myocardial tissue6. Here we apply a mapbased, proportional-feedback algorithm7oll to stabilize periodic. Pefm.-nt _II 01 V G. Iso ~ of A1Y*8 o.n8try KoslUth L ~. PO Boa 7.

Should nonlinearity be found, the outcomes of each observation are compared to analyze the implications of each country in global, regional and local position of their competition in the continuously changing world of interdependency environment. The implications of nonlinearity finding in the three ASEAN countries capital markets to the current issues of AFAS on Financial Services, Harmonization among ASEAN countries capital markets in the ASEAN region and ASEAN integration and liberalization on Financial Services are analyzed. BDS statistic and R/S Analysis as our tools for nonlinearity testing are applied.

A rogue wave epidemiological pattern has been identified as a predominant pattern in COVID-19 epidemiological series with emergent chaotic attractors for different world regions. In the present work, we study People Republic of China’s daily new number of confirmed cases of COVID-19 from 2020-01-03 to 2023-10-27, which provides for a long series with a rogue wave pattern, and apply to this series multifractal analysis, smart topological data analysis and chaos theory, finding that the rogue wave pattern is linked to chaos-induced multifractal self-organized criticality, the source of the rogue wave is shown to be associated with an emergent three-dimensional chaotic attractor with a three winged structure, explaining the rogue wave dynamics, the reconstructed attractor is shown to have exploitable topological information that can be used by adaptive A.I. systems to predict the daily number of confirmed cases of COVID-19 with a high level of performance, the predictability is shown to decrease in a several days ahead prediction and to be linked to the attractor’s Lyapunov time, k-nearest neighbors’ graph analysis, persistent homology and ordinal partition graph analyses are also applied and researched in their relation to the predictability of the target series. The implications of the results for epidemiology, risk science, complexity research and healthcare planning are discussed.

A review of the literature reveals conflicting results regarding the existence and inherent nature of chaos in hydrological processes such as precipitation and streamflow, i.e. whether they are low dimensional chaotic or stochastic. This issue is examined further in this paper, particularly the effect that certain types of transformations, such as aggregation and sampling, may have on the identification of the dynamics of the underlying system. First, we investigate the dynamics of daily streamflows for two rivers in Florida, one with strong surface and groundwater storage contributions and the other with a lesser basin storage contribution. Based on estimates of the delay time, the delay time window, and the correlation integral, our results suggest that the river with the stronger basin storage contribution departs significantly from the behavior of a chaotic system, while the departure is less significant for the river with the smaller basin storage contribution. We pose the hypothesis that the chaotic behavior depicted on continuous precipitation fields or small time-step precipitation series becomes less identifiable as the aggregation (or sampling) time step increases. Similarly, because streamflows result from a complex transformation of precipitation that involves accumulating and routing excess rainfall throughout the basin and adding surface and groundwater flows, the end result may be that streamflows at the outlet of the basin depart from low dimensional chaotic behavior. We also investigate the effect of aggregation and sampling using series derived from the Lorenz equations and show that, as the aggregation and sampling scales increase, the chaotic behavior deteriorates and eventually ceases to show evidence of low dimensional determinism.

Given an infinite set X and a function f : X → X, the primal topology on X induced by f is the topology τ f = {U ⊆ X : f −1 (U) ⊆ U }. In this paper, we prove that there are 2 ω pairwise non-homemomorphic primal topologies on N. We also prove that an infinite set cannot have more than 2 ω pairwise non-homeomorphic primal topologies. We give a necessary and sufficient condition to guarantee that an Alexandroff topology be n-resolvable for an 2 ≤ n ∈ N. Other results on primal topologies are also given.

It is a pleasure to express thanks to the organizers of the conference who welcomed their German guests with an overwhelming hospitality after they had taken lots of trouble in inviting their German guests, finding financial support for the conference and accomodation for the guests, coordinating the Ukrainian speakers, replanning the conference after it had to be cancelled first for lack of money, then for the consequences of the Five Days in August. It is due to Igor V. Chernenko's and Mikhail V. Kuz'min's patience and perseverance that the conference participants eventually assembled safely at Vorzel'. The preparation of the conference would not have been successful without Dr. Wolfgang Döke, Vice Consul for Education and Science at the German Embassy at Kiev, who often served as a mail office when ordinary mail would not have been fast and secure enough to transport letters, papers, and floppy disks between Kiev and Koblenz. In the same way the support of Gerhard Kalab, my brother-in-law who works in Moscow for an important German firm, must be appreciated who also acted as a mail and telecommunications relais station between Kiev and Koblenz. Many a message would have got lost without the patient readiness of both of them to forward them by mail, telefax, and telephone. Our thanks go to the Association of Ukrainian Composers, whose recreation center in Vorzel' housed the conference, and especially to Mrs. Elena I. Kuts, the director of this center, and her personell, who hosted the German guests for five days. Another wholehearted thanks go to Galina S. Nechiporenko who prepared many of the texts of the Ukrainian authors for T E X, and to Olga Sinitsa who served the conference as a translator. She, of course, had to bear the greatest burden during the conference days since not every Ukrainian participant was fluent in English (and none of the German guests understood Russian or Ukrainian).

A framework for time series forecasting that integrates k-Nearest-Neighbors (kNN) and Differential Evolution (DE) is proposed. The methodology called NNDEF (Nearest Neighbor-Differential Evolution Forecasting) is based on knowledge shared from nearest neighbors with previous similar behaviour, which are then taken into account to forecast. NNDEF relies on the assumption that observations in the past similar to the present ones are also likely to have similar outcomes. The main advantages of NNDEF are the ability to predict complex nonlinear behavior and handling large amounts of data. Experiments have shown that DE can optimize the parameters of kNN and improve the accuracy of the predictions.

This paper presents an analytical, variable-conductivity, thermal model for single-point diamond precision machining of semi conductors. The model is used to calculate the temperature development during the simulated machining of silicon and germanium wafors. The heat generated at a tool-work piece contact is taken as the product of the coefficient of friction, the relative sliding speed, and the contact slrcas. Whereas, heat partition between the diamond abrasive and the work piece is obtained through a modified Jaeger-Blok analysis that incorporates the coupling of the thermal properties of the tool-work piece system. The results indicate that: for the ranges of nominal loads, cuffing speeds and, feeds encountered, the work piece surface teanpcrature rise is well below the thermal softening temperatures for these materials. This, has direct implications to the ductile removal mechanisms. The low values calculatext for the work surface arc shown to be c~amstmt with several calculations based on the analysis of convmtional machining.

This study deals with the seismic prognosis for Romanian territory on the base of several methods, more or less usual or generally accepted. As a final result, is revealed a potential increase of magnitude of events in our territory starting in 2024. At the same time, following the presented analyses, the possibility of producing a large-magnitude "crustal" earthquake is highlighted.
So far, numerous prognosis methods or models have been tested in world seismology, most of them based on statistical or astrophysical calculations, "formulas" that have not met the rigors of a reliable seismic forecasting. There have been researches and attempts to forecast earthquakes and in Romania, in particular generated by the Vrancea area. Such long- or medium-term forecasts based on statistic methods they were looking for a recurrence of large earthquakes. There are also other analyses which revealed a particular seismic evolution before some big earthquakes (such as the “seismic quiescence”). In the last decade there have also been attempts to highlight a precursor seismic series, based on analyses of seismic sequences that preceded major earthquakes (Italy, Japan) and also, a precursory seismic phenomenon called "seismic swarm" was highlighted.
Without the pretense that the present study would solve the problem of seismic forecasting, we brought some news. A novelty consists in the global analysis of the seismicity of the territory, of the three seismic clusters, crustal and the two subcrustal of the Vrancea seismogenic body (Grigore et al., 2008) which highlights the interrelationships between them. A deterministic method of earthquakes is discussed, analyzed and tested on several seismic sequences from the local, regional or global evolution, related to the important earthquakes in Romania, in time and space. The results of the advanced with reserves forecasts based on this method were also verified by a parallel analysis of the peak recurrence, taking into account the leveling of magnitudes and the dependence on potential generating factors, some of them cyclical - terrestrial tides, solar activity, large earthquakes on the globe, etc. Also, the seismic evolution from us is discussed in relation to the regional or global evolution based on some sequences and relative to the tectonic structure and the lateral transfer of stress. Following the analysis, a new model of the mechanism of the production of earthquakes in Vrancea is advanced, which can better verify its particular evolution in a global context, its sunken body evidently not being isolated.

We consider the fast acquisition problem in magnetic resonance imaging (MRI). Often, fast acquisition is achieved using parallel imaging (pMRI) techniques. It has been shown recently that compressed sensing (CS), which enables exact reconstruction of sparse or compressible signals from a small number of random measurements, can accelerate the speed of MRI acquisition because the number of measurements was small. Recently, the spread spectrum (SS) has been utilized to enhance the quality of reconstructed CS image. Also recently, chaotic CS approach potentially offers simpler hardware implementation. In this paper, we combine chaotic CS and spread spectrum technique in order to obtain a fast acquisition in MRI with enhanced quality of reconstructed image. The performance of the proposed method is analyzed using numerical simulation.