O presente trabalho, propõe uma expressão analítica para estimar a probabilidade de perda de bytes em um único servidor de fila com chegadas de tráfego multirracial. Inicialmente, apresentamos a teoria necessária referente a processos multifractais, destacando o conceito de expoente de Hõlder. Em seguida, focalizamos nossa atenção na estimação dos momentos de segunda ordem para processos multifractais. Mais especificamente, assumimos que um modelo exponencial é adequado para representar a variância do processo sob diferentes escala de agregação. Dessa forma comparamos o desempenho da abordagem proposta com algumas outras abordagens (por exemplo, métodos baseados em monofractal, MSQ {Multi-Scale Queué) e CDTSQ {Criticai Dyadic Time-Scale Queue))usando traços de tráfegos reais. Além tusso, com base nos resultados da análise acima, propusemos uma nova estratégia de controle de admissão que leva em conta as características multifractais do tráfego. Comparamos a estratégia de controle de admissão proposta com outros métodos de controle de admissão amplamente utilizado na literatura (por exemplo, MVA, Perda Virtual e Capacidade Equivalente). Os resultados das simulações mostram que a proposta de estimação de probabilidade de perda é simples e precisa...

One reminds for all function f : n → the so-called (min, +)-wavelets which are lower and upper hulls build from (min, +) analysis [12, 13]. One shows that this analysis can be applied numerically to the Weierstrass and Weierstrass-Mandelbrot functions, and that one recovers their theoretical Hölder exponents and fractal dimensions.

We study the dynamics of skin laser Doppler flowmetry signals giving a peripheral view of the cardiovascular system. The analysis of Hölder exponents reveals that the experimental signals are weakly multifractal for young healthy subjects at rest. We implement the same analysis on data generated by a standard theoretical model of the cardiovascular system based on nonlinear coupled oscillators with linear couplings and fluctuations. We show that the theoretical model, although it captures basic features of the dynamics, is not complex enough to reflect the multifractal irregularities of microvascular mechanisms.

Multifractal properties of electrocardiographic inter-beat (RR) time-series offer insight into its long-term correlation structure, independently of RR variability. Here we quantify multifractal characteristics of RR data during 24-h diurnal-nocturnal activity in healthy participants. We tested the hypotheses that (1) age, gender and aerobic fitness influence RR multifractal properties, and that (2) these are influenced by circadian variation. Seventy adults (39 males) aged 19–58 years and of various fitness levels were monitored using 24-h ECG. Participants were dichotomized by median age and fitness for sub-group analysis. Gender and fitness were independent of age (p = 0.1, p > 0.5). Younger/older group ages were substantially different (p < 0.0005) and were independent of gender and fitness. Multifractality was quantified using the probability spectrum of Hölder exponents (h), from which modal h (h*) and the full-width and half-widths at half-maximum measures (FWHM, HWHM+, and HWHM−) were derived. FWHM decreased (p = 0.004) and h* increased (p = 0.011) in older people, indicating diminished long-range RR correlations and weaker anti-persistent behavior. Anti-persistent correlation (h*) was strongest in the youngest/fittest individuals and weakest in the oldest/least fit individuals (p = 0.015). Long-range correlation (HWHM+/FWHM) was strongest in the fittest males and weakest in the least fit females (p = 0.007–0.033). Multifractal RR characteristics in our healthy participants showed strong age-dependence...

Conference Paper; In this paper we introduce a new family of smooth, symmetric biorthogonal wavelet basis. The new wavelets are a generalization of the Cohen, Daubechies and Feauveau (CDF) biorthogonal wavelet systems. Smoothness is controlled independently in the analysis and synthesis bank and is achieved by optimization of the discrete finite variation (DFV) measure recently introduced for orthogonal wavelet design. The DFV measure dispenses with a measure of differentiability (for smoothness) which requires a large number of vanishing wavelet moments (e.g., Holder and Sobolev exponents) in favor of a smoothness measure that uses the fact that only a finite depth of the filter bank tree is involved in most practical applications. Image compression examples applying the new filters using the embedded wavelet zerotree (EZW) compression algorithm due to Shapiro shows that the new basis functions performs better when compared to the classical CDF 7/9 wavelet basis.

Knowing that a surface or profile can be characterized by numerous roughness parameters, the objective of this investigation was to present a methodology which aims to determine quantitatively and without preconceived opinion the most relevant pair of roughness parameters that describe an abraded surface. The methodology was firstly validated on simulated fractal profiles having different amplitudes and Hölder exponents and it was secondly applied to characterise different worn regions of a retrieved metallic femoral head articulated against an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup containing an embedded metallic fibber into its surface. The methodology consists in combining the recent Bootstrap method with the usual discriminant analysis. It was validated on simulated fractal profiles showing that, among more than 3000 pairs tested, the total amplitude Rt and the fractal dimension Δ is the most relevant pair of roughness parameters; parameters corresponding to the variables modulated in the analytical expression of the fractal function. The application of this methodology on a retrieved metallic femoral head shows that the most relevant pair of parameters for discriminating the different investigated worn regions is the arithmetic roughness parameter Ra paired with the mean peak height Rpm. This methodology finally helps in a better understanding of the scratch mechanism of this orthopedic bearing component.

We study linear co-cycles in GL(d,R) (or C) depending on a parameter (in a Lipschitz or Holder fashion) and establish Holder regularity of the Lyapunov exponents for the shift dynamics on the base. We also obtain rates of convergence of the finite volume exponents to their infinite volume limits. The technique is that developed jointly with Michael Goldstein for Schroedinger co-cycles. In particular, we extend the Avalanche Principle, which had been formulated originally for SL(2,R) co-cycles, to GL(d,R).

Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the Holder regularity is allowed to vary along the paths. In this paper, two kind of multi-parameter extensions of mBm are studied: one is isotropic while the other is not. For each of these processes, a moving average representation, a harmonizable representation, and the covariance structure are given. The Holder regularity is then studied. In particular, the case of an irregular exponent function H is investigated. In this situation, the almost sure pointwise and local Holder exponents of the multi-parameter mBm are proved to be equal to the correspondent exponents of H. Eventually, a local asymptotic self-similarity property is proved. The limit process can be another process than fBm.; Comment: 36 pages

In the present paper we give a positive answer to a question posed by Viana on the existence of positive Lyapunov exponents for symplectic cocycles. Actually, we prove that for an open and dense set of Holder symplectic cocycles over a non-uniformly hyperbolic diffeomorphism there are non-zero Lyapunov exponents with respect to any invariant ergodic measure with the local product structure.; Comment: 16 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1304.3794

(Revised version, January 2006. S. Gouezel pointed out that, when 1

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It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Holder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Holder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Holder exponent is no longer a useful parameter; Comment: 17 pages and 10 (png) figures

Consider the Banach manifold of real analytic linear cocycles with values in the general linear group of any dimension and base dynamics given by a Diophantine translation on the circle. We prove a precise higher dimensional Avalanche Principle and use it in an inductive scheme to show that the Lyapunov spectrum blocks associated to a gap pattern in the Lyapunov spectrum of such a cocycle are locally Holder continuous. Moreover, we show that all Lyapunov exponents are continuous everywhere in this Banach manifold, irrespective of any gap pattern in their spectra. These results also hold for Diophantine translations on higher dimensional tori, albeit with a loss in the modulus of continuity of the Lyapunov spectrum blocks.; Comment: 63 pages, 1 figure

This manuscript is a draft of work in progress, meant for network distribution only. It will be updated to a formal preprint when the numerical calculations will be accomplished. In this draft we develop a consistent closure procedure for the calculation of the scaling exponents $\zeta_n$ of the $n$th order correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents $\zeta_n$. This hierarchy was discussed in detail in a recent publication [V.S. L'vov and I. Procaccia, Phys. Rev. E, submitted, chao-dyn/9707015]. The scaling exponents in this set of equations cannot be found from power counting. In this draft we discuss in detail low order non-trivial closures of this infinite set of equations, and prove that these closures lead to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier-Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations...

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.; Comment: 20 pages, Latex

The paper is devoted to elaboration of a novel specific indicator based on the modified Holder exponents. This indicator has been used for forecasting critical points of financial time series and crashes of the USA stock market. The proposed approach is based on the hypothesis, which claims that before market critical points occur the dynamics of financial time series radically changes, namely time series become smoother. The approach has been tested on the stylized data and real USA stock market data. It has been shown that it is possible to forecast such critical points of financial time series as large upward and downward movements and trend changes. On this basis a new trading strategy has been elaborated and tested.; Comment: 15 pages, 9 figures

We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.; Comment: 15 pages, 4 figures. Comments are welcome. Minor fixes in the second version

We compute accurately the golden critical invariant circles of several area-preserving twist maps of the cylinder. We define some functions related to the invariant circle and to the dynamics of the map restricted to the circle (for example, the conjugacy between the circle map giving the dynamics on the invariant circle and a rigid rotation on the circle). The global H\"older regularities of these functions are low (some of them are not even once differentiable). We present several conjectures about the universality of the regularity properties of the critical circles and the related functions. Using a Fourier analysis method developed by R. de la Llave and one of the authors, we compute numerically the Holder regularities of these functions. Our computations show that -- withing their numerical accuracy -- these regularities are the same for the different maps studied. We discuss how our findings are related to some previous results: (a) to the constants giving the scaling behavior of the iterates on the critical invariant circle (discovered by Kadanoff and Shenker); (b) to some characteristics of the singular invariant measures connected with the distribution of iterates. Some of the functions studied have pointwise Holder regularity that is different at different points. Our results give a convincing numerical support to the fact that the points with different Holder exponents of these functions are interspersed in the same way for different maps...

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces. Bennett-Carbery-Christ-Tao have initiated the study of these inequalities for discrete Abelian groups and, in terms of suitable data, have characterized the set of all tuples of exponents for which such an inequality holds for specified data, as the convex polyhedron defined by a particular finite set of affine inequalities. In this paper we advance the theory of such inequalities for torsion-free discrete Abelian groups in three respects. The optimal constant in any such inequality is shown to equal $1$ whenever it is finite. An algorithm that computes the admissible polyhedron of exponents is developed. It is shown that nonetheless, existence of an algorithm that computes the full list of inequalities in the Bennett-Carbery-Christ-Tao description of the admissible polyhedron for all data, is equivalent to an affirmative solution of Hilbert's Tenth Problem over the rationals. That problem remains open. Applications to computer science will be explored in a forthcoming companion paper.; Comment: arXiv admin note: substantial text overlap with arXiv:1308.0068

We use unpublished and published VLBI results to investigate the geometry and the statistical properties of the velocity field traced by H2O masers in five galactic regions of star formation -- Sgr B2(M), W49N, W51(MAIN), W51N, and W3(OH). In all sources the angular distribution of the H2O hot spots demonstrates approximate self-similarity (fractality) over almost four orders of magnitude in scale, with the calculated fractal dimension d between (approximately) 0.2 and 1.0. In all sources, the lower order structure functions for the line-of-sight component of the velocity field are satisfactorily approximated by power laws, with the exponents near their classic Kolmogorov values for the high-Reynolds-number incompressible turbulence. These two facts, as well as the observed significant excess of large deviations of the two-point velocity increments from their mean values, strongly suggest that the H2O masers in regions of star formation trace turbulence. We propose a new conceptual model of these masers in which maser hot spots originate at the sites of ultimate dissipation of highly supersonic turbulence produced in the ambient gas by the intensive gas outflow from a newly-born star. Due to the high brightness and small angular sizes of masing hot spots and the possibility of measuring their positions and velocities with high precision...

We have shown elsewhere that the presence of mixed-culture growth of microbial species in fermentation processes can be detected with high accuracy by employing the wavelet transform. This is achieved because the crosses in the different growth processes contributing to the total biomass signal appear as singularities that are very well evidenced through their singularity cones in the wavelet transform; however, we used very simple two-species cases. In this work, we extend the wavelet method to a more complicated illustrative fermentation case of three microbial species for which we employ several wavelets of different number of vanishing moments in order to eliminate possible numerical artifacts. Working in this way allows filtering in a more precise way the numerical values of the Holder exponents; therefore, we were able to determine the characteristic Holder exponents for the corresponding crossing singularities of the microbial growth processes and their stability logarithmic scale ranges up to the first decimal in the value of the characteristic exponents. Since calibrating the mixed microbial growth by means of their Holder exponents could have potential industrial applications, the dependence of the Holder exponents on the kinetic and physical parameters of the growth models remains as a future experimental task.