bluuebunny/crossref_metadata_2025 huggingface dataset:
A MULTI COMPARTMENTS MODEL OF NITRATE METABOLISM REGULATION IN PLANT ROOTS
Authors: ALEKHINA NATALIA D. , KHARITONASHVILI ELENA V. , RIZNICHENKO GALINA Yu. , PLUSNINA TATIANA Yu. , SIDOROV SERGEI V. , RUBIN ANDREI B.
Published: May 2003

A new concept illustrated by a corresponding mathematical model of nitrate metabolism regulation is proposed. The model is based on the root nitrate compartmentation in several functional pools: storage, metabolic and mobile (MobP) intended for translocation to shoots. Data on nitrate uptake, compartmentation, reduction in intact roots and translocation to shoots were obtained on steady state wheat seedlings grown at 25° and 12°C in the root zone. The net uptake, influx/efflux ratio, MobP size and translocation changed depending on the medium temperature. The oscillations of the net uptake rate, nitrate tissue concentration and its temperature modification were revealed. The scheme of regulation is based on the idea that net uptake through nitrate influx/efflux is under the control of the nitrate of MobP which size was dependent on the nitrate translocation into shoots. The mathematical model is represented by a system of ordinary differential equations simplified according to the time hierarchy of reactions. It has a limit cycle at definite values of parameters. The model postulates the mechanism of a positive feed-back regulation of newly absorbed nitrate transfer into translocated pool formed in the root cortex. Theoretical results are verified experimentally.
ON THE DYNAMICS OF COMPLEX SYSTEMS WITH RANDOM FLUCTUATIONS: A STATISTICAL FIELD THEORY APPROACH
Authors: D'AMBROGIO ENOS G.
Published: May 2003

A theoretical study based on the application of Fokker–Planck theory to the dynamics of a cell membrane model is presented. The role and the meaning of nonlinear interaction of electric-field-sensitive channels is discussed in the framework of the coupled mode theory of weakly ionized media. A phenomenological model of Malthus-Verhulst type is derived for the size of activating channels of a single ion species.
NETWORK ANALYSIS OF A BENTHIC FOOD WEB MODEL OF A PARTLY RECLAIMED ISLAND IN THE SUNDARBAN MANGROVE ECOSYSTEM, INDIA
Authors: RAY SANTANU , ULANOWICZ ROBERT E. , MAJEE N. C. , ROY A. B.
Published: May 2003

Network analysis is performed on a 14 species food web model of the ecosystem occupying a mudflat on a partly reclaimed island of the Sundarban mangrove ecosystem. The results demonstrate a dramatic difference between this heavily impacted mangrove ecosystem in its modes of primary and secondary production and its diminished role of detritus vis-a-vis its less disturbed counterparts. Unlike most benthic mangrove systems, the Sundarban bottom community receives a large contribution from the phytoplankton populations. In this system herbivory and detritivory are virtually equal, in contrast to the usual herbivory:detritivory ratio of 1:5. Anthropogenic impacts have changed the physiography of this system so as to increase the relative importance of zooplankton and meiobenthos as herbivores. Although a slight degree of omnivory is exhibited by the populations of larger organisms, all flows of each integer of trophic length into a food chain may be aggregated that represents the underlying trophic status of the starting food web. Only a small number of pathways of recycle can be identified (31), and the Finn cycling index for this system is quite low (8.4%). Litterfall comprises only 16% of the total system input, which is very little in comparison with most mangrove systems. Pathway redundancy is rather high in this ecosystem, indicating that the surviving system is probably highly resilient to further perturbations, as one might expect for a highly impacted system.
SUFFICIENT CONDITIONS FOR COORDINATION OF A FORCED BIOCHEMICAL SYSTEM WITH THE INTERPLAY OF ACTIVATION AND INHIBITION
Authors: LIU JUNLI
Published: May 2003

A system of ordinary differential equations representing a biochemical system with the interplay of enzyme activation and inhibition is studied. Each term of the equations describes an enzymatic reaction and has an upper limit — the maximum activity of the enzyme. The sufficient conditions for guaranteeing coordination of the system subject to any type, period and amplitude of external forcing are analytically derived. Numerical analysis using three types of external signals, namely rectangular, sinusoidal and noisy signals, supports the analytical results. The sufficient conditions require kinetic parameter values (in particular, maximum enzyme activities) be related, implying system coordination requires enzymes in the system properly work together. It is shown that, when the sufficient conditions are satisfied, the system always develop to a stable (possibly time-dependent) state when it is subject to any type, period and amplitude of external forcing. When not, whether system coordination is destroyed depends quantitatively on the parameter values and the type, period and amplitude of external signals. Once system coordination is destroyed by external forcing, the system does not have any stable state on phase plane, and one of the species concentrations accumulates infinitely. Finally, I discuss the implications of the results for understanding the coordination of nonlinear enzyme-catalysed reaction systems with the interplay of activation and inhibition, and the possible consequences of modulating such systems.
INDUSTRIAL POLLUTION AND ASTHMA: A MATHEMATICAL MODEL
Authors: GHOSH MINI
Published: May 2003

In this paper, some nonlinear mathematical models are proposed and analyzed to study the spread of asthma due to inhaled pollutants from Industry. The following two types of demographics are considered here; (i) population with constant immigration, (ii) population with logistic growth. In each type of demography, the following three cases have been considered regarding the release of pollutant into the environment; (i) when emission of the pollutant into the environment is constant, (ii) when emission of the pollutant is population dependent, and (iii) when emission of the pollutant is periodic. Using stability theory of differential equations and computer simulation, it is shown that due to an increase in the air pollutant, the asthmatic (diseased) population increases in the region under consideration.
GLOBAL ANALYSIS OF MARCZUK'S MODEL IN CASE OF STRONG IMMUNE SYSTEM
Authors: FORYŚ URSZULA
Published: May 2003

Some special cases of Marchuk's model of an infectious disease are studied. A paralysis effect is neglected, and the model reduces to 3 ordinary differential equations with time delay and initial data corresponding to a healthy organism infected by some dose of the antigen at time 0. It is proved that, if the immune system is very strong and the antigen reproduction rate is not too large, then every solution has a finite limit, which is equal to the stationary state describing the healthy organism. If the antigen reproduction rate is large, then all solutions have average values equal to the values corresponding to the chronic form of the disease.
IDENTIFICATION OF A COMPLEX NEUROPHYSIOLOGICAL SYSTEM USING THE MAXIMUM LIKELIHOOD APPROACH
Authors: KOTTI V. K. , RIGAS A. G.
Published: May 2003

In this work we use Generalized Linear Models (GLMs) in order to identify a complex neurophysiological system, called muscle spindle that involves stationary point processes. Three parameters are of interest because they describe the intrinsic properties of the system: the threshold, the recovery and the summation function. These parameters are included in the GLMs and their estimates are obtained by using the maximum likelihood approach. Two cases are examined. In the first case, there is no input present and it is shown that the system fires spontaneously. In the second case, the system is affected by the presence of a gamma motoneurone. It is shown that there is no spontaneous activity and the behavior of the system is excitatory. These results are in accordance with previous work. In the present work a new parameter, the carry over effect function is included in the model. The performance of the new model is compared with the previous results and it is shown that the addition of the carry over effect function in the model improves the results significantly.
CONTACT PROBES FOR MAP RECORDING: A COMPUTATIONAL STUDY
Authors: ATKINSON EVAN M. , TRAYANOVA NATALIA A.
Published: May 2003

In this computational study, we investigate the effects of a contact probe's design on the monophasic action potential (MAP) it records. Particularly, we focus on tip size and electrode geometry. A MAP is recorded when the tip of the contact probe is pressed against myocardial tissue and an action potential propagates through the tissue. Our 2-dimensional tissue model incorporates Luo–Rudy I membrane kinetics to simulate the transmembrane action potential (TAP), and the tissue injury induced by the contact probe is modeled after ischemic conditions. We compare our simulated MAPs to the TAPs in the model. Our results show that the correlation between MAP and TAP signals is affected by both the shape of the contact probe's active electrode and the size of the probe's tip. We found that an asymmetrical active electrode which records MAPs from the downstream region of injury (e.g., right side of injury for a wave propagating across the tissue from left to right) very accurately reflects the TAP of the healthy tissue. Further, our findings suggest that the optimal size for a contact probe's tip is between 0.64 and 1 mm 2. If the tip is very small (0.04 mm 2), the resulting region of injury is too small to maintain a stable transmembrane potential, and the recorded MAPs are distorted. On the other hand, very large probe tips (>1 mm 2) covered with standard active electrodes focus their measurements too much on the interior of the injury and thus do not accurately describe the behavior of the injury currents. The results of our study could have implications on the design of contact probes used for recording MAPs in vivo.
DETERMINISTIC AND STOCHASTIC ANALYSIS OF A NONLINEAR PREY-PREDATOR SYSTEM
Authors: BANDYOPADHYAY MALAY , CHAKRABARTI C. G.
Published: May 2003

The paper deals first with the deterministic analysis of stability and bifurcation of a non-linear model prey-predator system and then with the critical analysis of nonequilibrium fluctuation and stability of the model system under random perturbation including the comparative study of both deterministic and stochastic criteria of stability of the system.
REGULATION OF A PREY-PREDATOR FISHERY BY TAXATION: A DYNAMIC REACTION MODEL
Authors: KAR T. K. , CHAUDHURI K. S.
Published: May 2003

In a fully dynamic model of an open-access fishery, the level of fishery effort expands or contracts according as the net economic revenue (i.e., perceived rent) to the fisherman is positive or negative. A model reflecting this dynamic interaction between the perceived rent and the effort in a fishery, is called a dynamic reaction model. In this paper, we study a dynamic reaction model, in which the prey species is subjected to harvesting in the presence of a predator and a tax. It is also assumed that the gross rate of investment of capital in the fishery is proportional to the perceived rent. With this capital theoretic approach, the dynamical system consisting of the growth equations of the two species and also of the fishing effort is formulated. The steady state is determined and its stability is discussed. The object is to maximize the monetary social benefit as well as prevent the predator from extinction, keeping the ecological balance.
STOCHASTICS OF ORDER n IN BIOLOGICAL SYSTEMS: APPLICATIONS TO POPULATION DYNAMICS, THERMODYNAMICS, NONEQUILIBRIUM PHASE AND COMPLEXITY
Authors: JUMARIE GUY
Published: May 2003

In the present paper, a modeling in the complex space is combined with complex-valued fractional Brownian motion to get some new results in biological systems. The rational of this approach is as follows. Biological dynamics which evolve continuously in time but are not time differentiable, necessarily exhibit random properties. These random features appear also as a result of the randomness of the proper time of biological systems. Usually, this is taken into account by using white noises that is to say fractals of order two. Fractals of order n larger than two are more suitable for increments with large amplitudes, and they may be introduced by using either real-valued fractal noises with long range memory or Brownian motions with independent increments, which are necessarily complex-valued. In the later case, we are then led to describe biological systems in the complex plane. After some background on the complex-valued fractional Brownian motion, we shall deal successively with population growth, information thermodynamics of order n, nonequilibrium phase transition via fractal noises and complexity of Markovian processes via the concept of informational divergence.
SINGULARITY SPECTRUM OF NONPERIODIC TIME SERIES: SURROGATE DATA AND WAVELET TRANSFORM
Authors: NICOLLET M. , LEMARCHAND A. , DUMAS G. M. L.
Published: May 2003

We study the singularities of time series giving the evolution of the cool flame temperature of a hydrocarbon. Several tests using surrogate data and wavelet transform are applied to the original signals. The results suggest that the hypothesis of deterministic chaos cannot be ruled out in the original signals. The multifractal organization of their local singularities is proven.
FIRST PASSAGE TIME PROBLEM FOR BIASED CONTINUOUS-TIME RANDOM WALKS
Authors: RANGARAJAN GOVINDAN , DING MINGZHOU
Published: May 2003

We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias is constant. When the bias depends linearly on the position, the full FPT density function is derived in terms of Hermite polynomials and generalized Mittag-Leffler functions.
THE GEOMETRY OF PREFRACTAL RENORMALISATION: APPLICATION TO CRACK SURFACE ENERGIES
Authors: ADDISON PAUL S.
Published: May 2003

Natural fractal objects, unlike their mathematical counterparts, tend to exhibit power law scaling over a limited range of scales. In this paper a prefractal theoretical framework is constructed for natural fractal objects and illustrated through the application to natural crack surfaces. The prefractal model is linked with both traditional and current fractal methods for determining the energy of fracture. It is shown how the prefractal model gives the same size effect law as incorporated by existing recent fractal theories, but with the advantage of retaining the correct physical dimensions. The prefractal theory developed within the paper has general application to a range of other scientific and engineering problems.
AN EFFICIENT IMPLEMENTATION OF THE EXACT ENUMERATION METHOD FOR RANDOM WALKS ON SIERPINSKI CARPETS
Authors: FRANZ ASTRID , SCHULZKY CHRISTIAN , SEEGER STEFFEN , HOFFMANN KARL HEINZ
Published: May 2003

In the following, we present a highly efficient algorithm to iterate the master equation for random walks on effectively infinite Sierpinski carpets, i.e. without surface effects. The resulting probability distribution can, for instance, be used to get an estimate for the random walk dimension, which is determined by the scaling exponent of the mean square displacement versus time.

The advantage of this algorithm is a dynamic data structure for storing the fractal. It covers only a little bit more than the points of the fractal with positive probability and is enlarged when needed. Thus the size of the considered part of the Sierpinski carpet need not be fixed at the beginning of the algorithm. It is restricted only by the amount of available computer RAM. Furthermore, all the information which is needed in every step to update the probability distribution is stored in tables. The lookup of this information is much faster compared to a repeated calculation. Hence, every time step is speeded up and the total computation time for a given number of time steps is decreased.
MULTIFRACTAL MEASURES CHARACTERIZED BY THE ITERATIVE MAP WITH TWO CONTROL PARAMETERS
Authors: KIM KYUNGSIK , KIM G. H. , KONG Y. S.
Published: May 2003

A one-dimensional iterative map with two control parameters — the Kim–Kong map — is proposed. Our purpose is to investigate the characteristic properties of this map, and to discuss numerically the multifractal behavior of the normalized first passage time. Based especially on the Monte Carlo simulation, the normalized first passage time to arrive at the absorbing barrier after starting from an arbitrary site is mainly obtained in the presence of both absorption and reflection on a two-dimensional Sierpinski gasket. We also discuss the multifractal spectra of the normalized first passage time, and the numerical result of the Kim–Kong model presented will be compared with that of the Sinai and logistic models.
FRACTAL GRAIN BOUNDARY MIGRATION
Authors: TAKAHASHI MIKI , NAGAHAMA HIROYUKI
Published: May 2003

Fractal analysis on experimentally recrystallized quartz grain boundaries has been employed to relate the grain boundary complexities with deformation conditions, such as strain rate and temperature. The fractal dimensional increment of the grain boundaries, defined as (D-1), and the degree of irregularity in grain boundaries, is proportional to the logarithmic of the Zener–Hollomon parameter that is defined by strain rate and temperature (the Arrhenius term). The physical mean of the empirical relationship can be explained theoretically by a new grain boundary migration model (GBM or cell dynamics model) extended by the fractal concepts and the dimension analysis. This is a more general model than the migration growth model for the fractal grain boundaries.
ON THE MODIFICATION OF FRACTAL SELF-SPACE DURING CELL DIFFERENTIATION OR TUMOR PROGRESSION
Authors: WALISZEWSKI PRZEMYSLAW , KONARSKI JERZY , MOLSKI MARCIN
Published: May 2003

A novel parameter called expansion coefficient has been defined to measure both connectivity and collectivity in a population of cells conquering the available space and self-organizing into tissue patterns of the higher order. Connectivity (i.e. interconnectedness) denotes that there are complex dynamic relationships, not just structural, static ones, in a population of cells enabling the emergence of global features in the system that would never appear in single cells existing out of the system. Collectivity denotes that all interconnected cells interact in a common mode.

Evolution of this coefficient during differentiation or tumor progression was investigated by the box-counting method. The population of control or retinoid-treated primary cancer cells cultured in the monolayer (i.e. quasi-2D) system possessed fractal dimension and self-similarity. However, the expansion coefficient was close to zero, indicating that connectivity was low, and no collective state emerged. A significant change of the coefficient occurred when primary cells formed aggregates, quasi-3D systems with increased connectivity, and during treatment of the aggregates with retinoid resulting in a collective state (i.e. in differentiation of cells). Those statistical features were lost during tumor progression. All populations of the secondary cancer cells possessed integer dimension and the expansion coefficient was equal to zero.
FRACTAL REALITY OF RANDOM DATA COMPRESSION FOR EQUAL-INTERVAL SERIES
Authors: CHEN JEN-CHUNG , LEE TZONG-YEANG
Published: May 2003

Many natural phenomena of equal-time and/or equal-space interval have been recorded. They exhibited features at many different scales of measurement — suggesting that they could be described as fractals. Two observed terrain elevation data were selected for this study. On the condition that data number was reduced properly, we used the fractal interpolation technique to reconstruct the "original" profile. The random mode was adopted for reducing the measured data. The variations of profiles compared with different ratios of data reduction and several statistics (as the first four moments) were used to test their overall properties. When data compression was as high as 70%, a resembling appearance by means of fractal reconstruction continued to exist. Its excellence appeared on the texture of profile and magnification of visualization.
THE BOUNDS AND THE DIMENSIONS OF THE GENERAL M AND J SETS
Authors: LIU XIANGDONG , HE XIQIN , ZHU WEIYONG
Published: May 2003

In this paper, the bounds of the general M and J sets were analytically calculated to solve the primary problem encountered in constructing the general M and J sets by the escape time algorithm. The fractal dimensions of some J sets were discussed.
WAVELET-BASED FRACTAL ANALYSIS OF ELECTRICAL POWER DEMAND
Authors: DEGAUDENZI M. E. , ARIZMENDI C. M.
Published: May 2003

We apply wavelet transform to study and compare the multifractal characteristics of two electrical power demand time series, corresponding to a whole continent and a touristic city. The fluctuations in power demand associated with weather conditions or population will be different in both places. Fractal analysis shows common characteristics such as the degree of persistence of power demand fluctuations or absence of chaos, as well as some slight differences.
POWER LAW FLUCTUATION GENERATOR BASED ON ANALOG ELECTRICAL CIRCUIT
Authors: SATO AKI-HIRO , TAKAYASU HIDEKI , SAWADA YASUJI
Published: May 2003

We constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit, fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory of a differential equation with both multiplicative and additive noises which describes the circuit is introduced. The circuit is composed of a noise generator, an analog multiplier and an integration circuit. Sequential outputs of the circuit are observed and their probability density function and autocorrelation coefficients are shown. It is found that correlation time of the autocorrelation coefficient is dependent on the power law exponent.
A GROWING NETWORK OF IDEAS
Authors: BENTLEY R. ALEXANDER , MASCHNER HERBERT D. G.
Published: May 2003

The term "self-organized criticality" in the scientific literature is shown to have spread in a fractal, tree-like process. The probability that one of the original papers will be cited in a subsequent paper is related to the random network growth of the entire field, much like the growth of the World Wide Web. This is in opposition to recent publications that argue for a multiplicative process in scientific publishing where publishing success is based on attributes directly inherent to the author.
GOODNESS OF FIT ON A MODIFIED RICHARDSON PLOT BY RESIDUAL ANALYSIS
Authors: PARKINSON IAN H. , FAZZALARI NIC L.
Published: May 2003

Modified Richardson plots obtained by a box counting method on outlines of trabecular bone were tested for linearity. The degree of deviation from true linearity was quantified. The results showed that although there was evidence of nonlinearity or serial correlation in the Richardson plots, the magnitude of deviation from true linearity was less than 0.3% for the residuals and less than 4% for the standard deviation of the residuals. This study shows that the modified box counting method for estimating overall fractal dimension or sectional fractal dimensions of trabecular bone is efficacious. The low magnitude of deviation from linearity confirms that over a defined range of scale the Richardson plot provides an accurate estimation of the fractal dimension of trabecular bone.
ANALYSIS OF C-PLANE FRACTAL IMAGES FROM z ← zα + c FOR (α < 0)
Authors: WANG XINGYUAN , LIU XIANGDONG , ZHU WEIYONG , GU SHUSHENG
Published: May 2003

This paper expounds the definition of the c-plane fractal images from the complex mapping z ← zα + c (α < 0). A series of interesting and intriguing fractal images are generated by changing a single parameter α. When symbol α is a negative integer, the fractal image is a planetary structure consisting of a central planet surrounded by satellite structures. The number of satellite structures equals (1 + | α |). For negative non-integer values of α, additional embryonic satellite structure, proportional in size to the fractional part of α, are observed. The position and size of the planet and the positions of the satellite structures are analytically estimated. The four evolutions of the c-plane fractal image are given for the first time. The reasons resulting in the four evolutions of the c-plane fractal images are analyzed.
MODELISATION OF 3-D MICROVASCULATURE BY INTERLACED DIFFUSION LIMITED AGGREGATION
Authors: FLEURY VINCENT , SCHWARTZ LAURENT
Published: May 2003

We present a model of 3-D vascular formation which is able to explain how the capillary system matures into two 3-D arborescent vasculatures which interdigitate in the distal parts, without forming direct shunts.
LARGE SCALE-INVARIANT FLUCTUATIONS IN NORMAL BLOOD CELL COUNTS: A SIGN OF CRITICALITY?
Authors: PERAZZO CARLOS A. , FERNANDEZ ELMER A. , CHIALVO DANTE R. , WILLSHAW PETER
Published: May 2003

All types of blood cells are formed by differentiation from a small self-maintaining population of pluri-potential stem cells in the bone marrow. Despite abundant information on the molecular aspects of division, differentiation, commitment and maturation of these cells, comparatively little is known about the dynamics of the system as a whole, and how it works to maintain this complex "ecology" in the observed normal ranges throughout life. Here we report unexpected large, scale-free, fluctuations detected from the first long-term analysis of the day-to-day variability of a healthy animal's blood cell counts measured over 1 000 days. This scale-invariance cannot be accounted for by current theoretical models, and resembles some of the scenarios described for self-organized criticality.
CHARACTERISTICS OF AEROSOL FORMATION IN THE FREE-MOLECULAR REGIME
Authors: TERAO TAKAMICHI , TERAOKA TAKUMI , NAKAYAMA TSUNEYOSHI
Published: May 2003

We study aerosol growth phenomena in the free-molecular regime. The growth kinetics is clarified by two different approaches, such as the Smoluchowski equation and the cluster-cluster aggregation (CCA) model. The calculated results suggest that the Smoluchowski equation gives a correct description on the aerosol formation. We also study the light scattering intensity on aggregates with non-spherical monomers. The fractal dimension of aggregates does not depend on the microscopic detail of monomers, which confirms the theoretical prediction proposed by restricted hierarchical model.
IMAGE ZOOMING BY WAVELETS
Authors: REVATHY K. , RAJU G. , NAYAR S. R. PRABHAKARAN
Published: May 2003

Enlargement and reduction of images are often required in image processing. Popular methods for re-sizing are standard interpolation methods. Recently, wavelets and fractal-based methods are developed for re-sizing. In this paper, wavelet zooming algorithm based on pyramid algorithm for wavelet transformation is explained. Also performance analysis of wavelet-based zooming method is investigated. We find that wavelet zooming with enhanced coefficients gives better visual quality. The objective error analysis also agrees with this. Wavelet zooming has also been performed block-wise. A significant drawback of the method is that the scaling factor should be power of 2.
PHASE-PERIODIC STRUCTURES OF SELF-SIMILAR STAIRCASE FRACTALS
Authors: PAVLOVITCH BULAEV BORIS
Published: May 2003

The possibilities of investigating the self-similar staircase fractals in a discrete coordinate system are clearly very promising. Surprisingly, such fractals are found to have holographic properties. Some geometric shapes e.g. a circle or a quadrate, are produced by a well-defined boundary through generating the staircase fractals in 2D discrete space. The obtained "luminous boundaries" are remembered outer boundaries of any geometric form, regardless of the size. Actually, this process is similar to the photographing of an exterior form. Thus there is destruction of a natural phase-periodical structure of the fractal. The staircase fractals are subject to the same rules that apply in information theory. It is shown that the difference in sharpness of holographic shapes is a direct consequence of spectra informations of the forms.

The Hausdorff-Besicovitch dimension for this fractal has been estimated to be 0.5. On this view, the structure of staircase fractals is that of a Cantor Set. As indicated in the picture, such fractal resembles a "goose-wing." Also, the self-similar staircase fractal has much in common with a set of straight lines in a discrete coordinate system.
PARETO'S LAW FOR INCOME OF INDIVIDUALS AND DEBT OF BANKRUPT COMPANIES
Authors: AOYAMA HIDEAKI , SOUMA WATARU , NAGAHARA YUICHI , OKAZAKI MITSUHIRO P. , TAKAYASU HIDEKI , TAKAYASU MISAKO
Published: May 2003

We analyze the distribution of income and income tax of individuals in Japan for the fiscal year 1998. From the rank-size plots, we find that the accumulated probability distribution of both data obey a power law with a Pareto exponent very close to -2. We also present an analysis of the distribution of the debts owed by bankrupt companies from 1997 to March 2000, which is consistent with a power law behavior with a Pareto exponent equal to -1. This power law is the same as that of the income distribution of companies. Possible implications of these findings for model building are discussed.
CONVERGENCE OF THE WEIERSTRASS-MANDELBROT PROCESS TO FRACTIONAL BROWNIAN MOTION
Authors: PIPIRAS VLADAS , TAQQU MURAD S.
Published: May 2003

In this work, we develop Mandelbrot's idea that Weierstrass's nowhere differentiable function can be modified and randomized to approximate fractional Brownian motion (FBM). Our approach covers the convergence of processes of a more general type and allows us to consider different dependence structures in the above randomization.
A GENERALIZED MANDELBROT SET FOR BICOMPLEX NUMBERS
Authors: ROCHON DOMINIC
Published: May 2003

We use a commutative generalization of complex numbers called bicomplex numbers to introduce bicomplex dynamics. In particular, we give a generalization of the Mandelbrot set and of the "filled-Julia" sets in dimensions three and four. Also, we establish that our version of the Mandelbrot set with quadratic polynomial in bicomplex numbers of the form w2 + c is identically the set of points where the associated generalized "filled-Julia" set is connected. Moreover, we prove that our generalized Mandelbrot set of dimension four is connected.
GREEN'S FUNCTIONS ON FRACTALS
Authors: KIGAMI JUN , SHELDON DANIEL R. , STRICHARTZ ROBERT S.
Published: May 2003

For a regular harmonic structure on a post-critically finite (p.c.f.) self-similar fractal, the Dirichlet problem for the Laplacian can be solved by integrating against an explicitly given Green's function. We give a recursive formula for computing the values of the Green's function near the diagonal, and use it to give sharp estimates for the decay of the Green's function near the boundary. We present data from computer experiments searching for the absolute maximum of the Green's function for two different examples, and we formulate two radically different conjectures for where the maximum occurs. We also investigate a local Green's function that can be used to solve an initial value problem for the Laplacian, giving an explicit formula for the case of the Sierpinski gasket. The local Green's function turns out to be unbounded, and in fact not even integrable, but because of cancelation, it is still possible to form a singular integral to solve the initial value problem if the given function satisfies a Hölder condition.
WAVELET-BASED MULTISCALING IN SELF-AFFINE RANDOM MEDIA
Authors: FRANTZISKONIS GEORGE , HANSEN ALEX
Published: May 2003

Wavelet analysis is used to determine particular properties of self-affine random media, i.e. ones with homogeneous increments. When such media are filtered through introducing upper and lower cutoffs — corresponding to the domain and sample support scales — interesting properties result from wavelet analysis. In particular, we show that the filtered media can be used for transferring information along scales. Furthermore, we show that a wavelet-based approach for determining the underlying Hurst exponent is highly efficient. Examples relating to size and surface effects in materials demonstrate applications of the relevant multiscaling. Finally, we show that the wavelet-based approach and a method based on mode superposition complement each other nicely.
FRACTAL BEHAVIOR OF TREE-LIKE NICKEL AND COBALT ELECTRODEPOSITS
Authors: IMRE ATTILA R. , BALÁZS LÁSZLÓ
Published: May 2003

Fractal dimensions (exterior Minkowski-Bouligand and box dimensions) for nickel and cobalt metal trees (electrodeposits) were determined. These trees usually exhibit fractal characteristic in the 30–1000 micrometer range with fractal dimensions strongly depending on the initial metal-ion concentration of the electrolyte.
THE FRACTAL DIMENSION OF TOKYO'S STREETS
Authors: RODIN VLADIMIR , RODINA ELENA
Published: May 2003

The following paper presents the results obtained during the analyses of the street structure of Tokyo, focusing on six districts: Shinjuku, Shibuya, Ikebukuro, Ueno, Nakano and Aoto. The length-area relation in the chosen zones shows the presence of the analogue of a fractal dimension. The fractal dimension appears in these high-density street zones branching within a limited territory.
COMPARISON OF RECENT METHODS OF ANALYZING HEART RATE VARIABILITY
Authors: SAERMARK K. , MOELLER M. , HINTZE U. , MOELGAARD H. , BLOCH THOMSEN P. E. , HUIKURI H. , MAKIKIALLIO T. , LEVITAN J. , LEWKOWICZ M.
Published: May 2003

We compare three recently applied methods for analyzing heart rate variability: detrended fluctuation analysis (DFA), multiresolution wavelet analysis (WAV) and detrended time series analysis (DTS). In the comparison, both scale-dependent and scale-independent measures are considered. In agreement with recent results by Thurner et al.,9 we conclude that scale-dependent measures are well suited to separate healthy subjects from patients with heart disease. However, as regards the use in Kaplan-Meier cumulative survival curves, scale-independent measures (generally slope values) clearly outperform scale dependent measures (generally rms values). The comparison is mainly based on a database containing recordings from 428 patients with heart disease (myocardial infarct) and on a database containing 105 healthy subjects and 11 heart patients.
DIFFUSION OF A PASSIVE IMPURITY THROUGH A POROUS MEDIA: FRACTAL MODEL
Authors: PARK YUNG
Published: May 2003

This paper is no longer available. Please contact "fractals@wspc.com"
UNIVERSAL STRUCTURE OF THE PERSONAL INCOME DISTRIBUTION
Authors: SOUMA WATARU
Published: May 2003

We investigate the Japanese personal income distribution in the high income range over the 112 years (1887–1998), and that in the middle income range over the 44 years (1955–1998). It is observed that the distribution pattern of the log-normal with power law tail is the universal structure. However, the indexes specifying the distribution differ from year to year. One of the index characterizing the distribution is the mean value of the log-normal distribution; the mean income in the middle income range. It is found that this value correlates linearly with the gross domestic product (GDP). To clarify the temporal change of the equality or inequality of the distribution, we analyze Pareto and Gibrat indexes, which characterize the distribution in the high income range and that in the middle income range, respectively. It is found for some years that there is no correlation between the high income and the middle income. It is also shown that the mean value of Pareto index equals to 2, and the change of this index is effected by the change of the asset price. From these analysis, we derive four constraints that must be satisfied by mathematical models.
π IN THE MANDELBROT SET
Authors: KLEBANOFF AARON
Published: May 2003

The Mandelbrot set is arguably one of the most beautiful sets in mathematics. In 1991, Dave Boll discovered a surprising occurrence of the number π while exploring a seemingly unrelated property of the Mandelbrot set.1 Boll's finding is easy to describe and understand, and yet it is not widely known — possibly because the result has not been rigorously shown. The purpose of this paper is to present and prove Boll's result.
SCALE INVARIANCE IN A PERTURBED EINSTEIN-DE SITTER COSMOLOGY
Authors: ABDALLA ELCIO , MOHAYAEE ROYA , RIBEIRO MARCELO B.
Published: May 2003

This paper seeks to check the validity of the apparent fractal conjecture,1,2 which states that the observed power-law behavior for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone. Since general relativity states that astronomical observations are carried out in this spacetime hypersurface, observables necessary for direct comparison with astronomical data must be calculated along it. Implementing this condition in the proposed set of observational relations profoundly changes the behavior of many observables in the standard cosmological models. In particular, the average density becomes inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analyzed by Ribeiro (1992b, 1993, 1994, 1995)3–6 for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by Abdalla and Mohayaee (1999),7 where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a decaying power-law like average density profile, meaning that the dust distribution of this cosmology has a scaling behavior compatible with the power-law profile of the density-distance correlation observed in the galaxy catalogues. These results show that, in the context of this work, the apparent fractal conjecture is correct.
FRACTAL-SKELETAL BASED CHANNEL NETWORK (F-SCN) IN A TRIANGULAR INITIATOR-BASIN
Authors: SAGAR B. S. DAYA , SRINIVAS D. , RAO B. S. PRAKASA
Published: May 2003

Fractal-skeletal based channel network (F-SCN) model, which describes how the boundary of the basin constrains the channel network evolution, produces a channel network pattern that obeys Horton's laws. The statistical features of this model conform well with real networks. For this F-SCN that depends on general shape of the initiator-basin, generating mechanism and rule, and the nature of skeletonization process, the estimation of fractal dimension (D) is Log RB Log RL. The estimated D, 1.76 is approximated to the observed value, 1.8.
ASYMMETRIC ANOMALOUS DIFFUSION: AN EFFICIENT WAY TO DETECT MEMORY IN TIME SERIES
Authors: GRIGOLINI PAOLO , PALATELLA LUIGI , RAFFAELLI GIACOMO
Published: May 2003

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where the waiting time distribution is an inverse power law with index μ. We focus our attention on μ<3, and we evaluate the scaling exponent δ of the time in the resulting diffusion process. We prove that δ gets its maximum value, δ=1, corresponding to the ballistic motion, at μ=2. We study the resulting diffusion process by means of joint use of the continuous time random walk and of the generalized central limit theorem (CLT), as well as adopting a numerical treatment. We show that rendering the diffusion process to be asymmetric yields the significant benefit of enhancing the value of the scaling parameter δ. Furthermore, this scaling parameter becomes sensitive to the power index μ in the whole region 1<μ<3. Finally, we show our method in action on real data concerning human heartbeat sequences.
A GENERALIZATION OF FRACTAL INTERPOLATION STOCHASTIC PROCESSES TO HIGHER DIMENSIONS
Authors: MAŁYSZ ROBERT
Published: May 2003

We generalize the notion of fractal interpolation functions (FIFs) to stochastic processes. We prove that the Minkowski dimension of trajectories of such interpolations for self-similar processes with stationary increments converges to 2-α.

We generalize the notion of vector-valued FIFs to stochastic processes. Trajectories of such interpolations based on an equally spaced sample of size n on the interval [0,1] converge to the trajectory of the original process. Moreover, for fractional Brownian motion and, more generally, for self-similar processes with stationary increments (α-sssi) processes, upper bounds of the Minkowski dimensions of the image and the graph converge to the Hausdorff dimension of the image and the graph of the original process, respectively.
SCALING IN COGNITION
Authors: MORARIU VASILE V. , COZA AUREL , CHIS MINERVA ALOUETTE , ISVORAN ADRIANA , MORARIU LAURA-CORNELIA
Published: May 2003

Conscious activity is generally consistent with a deterministic mode of action, however some activities demand randomness. The goal of this study was to find whether mind can produce randomness. We asked various human subjects, aged between 21 and 57, to produce sequences of random integers. The non-repetition of the terms in the series was the "algorithm" generally used by all the subjects. The series were analyzed by using spectral analysis (SA), detrended fluctuation analysis (DFA), information (I2) and approximate entropy (AE) and correlation dimension analysis (CDA). SA of the series revealed 1/fβ(-0.4<β<1) types of spectra. The α scaling exponent resulting from DFA ranged between 0.2 and 1.1. The maximum of the distribution of α was centered at about 0.62. This is equivalent to a quarter power law in spectral terms. A significant percentage of subjects were able to produce random series. I2 of mental series revealed short-range correlation for pairs of successive numbers in the series. The correlation decreased gradually and it disappeared at a delay step of about 7 which is the characteristic number of short memory. AE had a minimum value at α=1 and a maximum value at α=0.5 for mental and random series, respectively. CDA showed no presence of attractors in the series, therefore none of the randomness produced by the subjects was of deterministic origin. A comparison of the scaling exponents revealed that the mental series have a certain long-range characteristic which is common to the human language as evident in the literature writings.
COMPARATIVE STUDY OF FRACTAL BEHAVIOR IN QUASI-RANDOM AND QUASI-PERIODIC SPEECH WAVE MAP
Authors: SENGUPTA R. , DEY N. , NAG DIPALI , DATTA A. K.
Published: May 2003

Fractal behavior in the quasi-steady states of the two types of speech signals, namely, quasi-periodic and quasi-random, are studied. The signals of the first group consist of seven vowels and those for the second group consist of three variants each of three sibilants. Ten rendering of each of these signals by one native Bengali male speaker of 45 years of age are used as the signal database. Standard box-counting method is used for generating ln (pq) versus ln (1/r) curves. D0, Dq and the knee expanse (KE) of the curves, their interrelations and the projections on the source characteristics are the objects of analysis. D2>D0 is found to indicate locally dense nature of the map and are found to be associated mainly with some sibilants. Dq are found to be a family of simple polynomial functions of q for all signals. D0, Dq and KE are related to the nature of different signals and character of the sources generating the signals. The study of fractal dimensions and the generalized dimensions for these signals reveal intermittency behavior and multifractality, which indicate basically, turbulent source or sources for speech generation. That the quasi-periodic and the quasi-random sounds are fundamentally different is reflected in the behavior of generalized fractal dimensions.
AMBIGUITIES IN DETERMINATION OF SELF-AFFINITY IN THE AE-INDEX TIME SERIES
Authors: WATKINS N. W. , FREEMAN M. P. , RHODES C. S. , ROWLANDS G.
Published: May 2003

The interaction between the Earth's magnetic field and the solar wind plasma results in a natural plasma confinement system which stores energy. Dissipation of this energy through Joule heating in the ionosphere can be studied via the Auroral Electrojet (AE) index. The apparent broken power law form of the frequency spectrum of this index has motivated investigation of whether it can be described as fractal coloured noise. One frequently-applied test for self-affinity is to demonstrate linear scaling of the logarithm of the structure function of a time series with the logarithm of the dilation factor λ. We point out that, while this is conclusive when applied to signals that are self-affine over many decades in λ, such as Brownian motion, the slope deviates from exact linearity and the conclusions become ambiguous when the test is used over shorter ranges of λ. We demonstrate that non self-affine time series made up of random pulses can show near-linear scaling over a finite dynamic range such that they could be misinterpreted as being self-affine. In particular, we show that pulses with functional forms such as those identified by Weimer within the AL index, from which AE is partly derived, will exhibit nearly linear scaling over ranges similar to those previously shown for AE and AL. The value of the slope, related to the Hurst exponent for a self-affine fractal, seems to be a more robust discriminator for fractality, if other information is available.
FRACTAL CHARACTERIZATION OF THE TEMPORAL DISTRIBUTION OF AFTERSHOCKS ASSOCIATED WITH THE 1994MW6.7 NORTHRIDGE EARTHQUAKE
Authors: TELESCA LUCIANO , CUOMO VINCENZO , LAPENNA VINCENZO , MACCHIATO MARIA
Published: May 2003

Fractal analysis has been performed to investigate the aftershock activity that followed the 1994 MW6.7 Northridge earthquake (Southern California). The sequence analyzed is very long and the obtained fractal estimates seem very reliable. High degree of clustering is revealed by the calculation of the coefficient of variation CV≈ 3.2, and the autocorrelation function shows the presence of dependence among the inter-event times. The obtained value of the capacity dimension D ≈ 0.05 demonstrates that the temporal distribution of the aftershocks is strongly clusterized. Furthermore, we calculated the power-law exponent of the power spectral density of the seismic process, by means of the Allan Factor method and the count-based Periodogram method; the very high obtained values αAF≈ 1.53 and αS≈ 1.43 reveal the presence of high correlated time structures in the process.
THE BOUNDARY OF THE ATTRACTOR OF A RECURRENT ITERATED FUNCTION SYSTEM
Authors: DEKKING F. M. , VAN DER WAL P.
Published: May 2003

We prove for a subclass of recurrent iterated function systems (also called graph-directed iterated function systems) that the boundary of their attractor is again the attractor of a recurrent IFS. Our method is constructive and permits computation of the Hausdorff dimension of the attractor and its boundary.