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[Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]SPEE [Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]SPEEColloque avec actes et comité de lecture. Internationale.; National audience; De manière générale les approches de type PIV nécessitent d'introduire un a priori sur la solution à estimer. Les méthodes locales imposent une uniformité du champ de vitesse dans un petit voisinage. Les approches globales introduisent un terme de régularisation qui peut être basé sur la dynamique des fluides. Nous montrons dans cette étude que l'introduction d'un a priori de type loi de puissance permet d'améliorer de façon significative les estimations du champ de vitesse vers les petites échelles. / PIV techniques need to introduce prior knowledge to estimate motion fields. Local approaches require window with constant velocity. Global approaches relies on a spatial regularization term which can be derived from the physics of fluids. In the present study we show that using regularizations based on turbulence power laws clearly provides accurate estimates down to the smal lest scales.

Bernoulli’s (1713) well-known Law of Large Numbers (LLN) establishes a legitimate one-way transition from mathematical probability to observed frequency. However, Bernoulli went one step further and abusively introduced the inverse proposition. Based on a careful analysis of Bernoulli’s original proof, this paper identifies this appealing, but illegitimate, inversion of LLN as a strong driver of confusion among probabilists. Indeed, during more than two centuries this “inference fallacy” hampered the emergence of rigorous mathematical foundations for the theory of probability. In particular, the confusion pertaining to the status of statistical inference was detrimental to both Laplace’s approach based on “equipossibility” and Mises’ approach based on “collectives”. Only Kolmogorov’s (1933) axiomatization made it possible to adequately frame statistical inference within probability theory. This paper argues that a key factor in Kolmogorov’s success has been his ability to overcome the inference fallacy., info:eu-repo/semantics/published

Bernoulli’s (1713) well-known Law of Large Numbers (LLN) establishes a legitimate one-way transition from mathematical probability to observed frequency. However, Bernoulli went one step further and abusively introduced the inverse proposition. Based on a careful analysis of Bernoulli’s original proof, this paper identifies this appealing, but illegitimate, inversion of LLN as a strong driver of confusion among probabilists. Indeed, during more than two centuries this “inference fallacy” hampered the emergence of rigorous mathematical foundations for the theory of probability. In particular, the confusion pertaining to the status of statistical inference was detrimental to both Laplace’s approach based on “equipossibility” and Mises’ approach based on “collectives”. Only Kolmogorov’s (1933) axiomatization made it possible to adequately frame statistical inference within probability theory. This paper argues that a key factor in Kolmogorov’s success has been his ability to overcome the inference fallacy.

We generate conservation laws for the one dimensional nonconservative Fokker–Planck (FP) equation, also known as the Kolmogorov forward equation, which describes the time evolution of the probability density function of position and velocity of a particle, and associate these, where possible, with Lie symmetry group generators. We determine the conserved vectors by a composite variational principle and then check if the condition for which symmetries associate with the conservation law is satisfied. As the Fokker–Planck equation is evolution type, no recourse to a Lagrangian formulation is made. Moreover, we obtain invariant solutions for the FP equation via potential symmetries.

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B 1 is used to signal the beginning of congestion while the lower threshold B 2 signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B 1 has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B 2 (smaller than B 1) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

National audience; Nous présentons dans cet article des algorithmes de classification prétopologique récemment développés, ainsi que l'introduction d'un nouvel algorithme original. Les algorithmes prétopologiques,principalement basés sur la fonction d'adhérence prétopologique et le concept de fermés permettent de classifier des données complexes non représentables dans un espace métrique. Après quelques rappels sur les notions de classification, nous proposons un algorithme exploitant la notion de distance basée sur la complexité de Kolmogorov dans un modèle prétopologique afin d'introduire un indice de similarité. Nous illustrerons celui-ci par une application permettant de saisir le degré de finesse que l'on peut obtenir avec une telle approche.

[Departement_IRSTEA]EA [TR1_IRSTEA]TEPSA / METFRI; International audience; Based on self-similar models of turbulence, we propose in this paper a multi-scale regularizer in order to provide a closure to the optic-flow estimation problem. Regularization is achieved by constraining motion increments to behave as a self-similar process. The associate constrained minimization problem results in a collection of first-order optic-flow regularizers acting at the different scales. The problem is optimally solved by taking advantage of lagrangian duality. Furthermore, an advantage of using a dual formulation, is that we also infer the regularization parameters. Since, the self-similar model parameters observed in real cases can deviate from theory, we propose to add in the algorithm a bayesian learning stage. The performance of the resulting optic-flow estimator is evaluated on a particle image sequence of a simulated turbulent flow. The self-similar regularizer is also assessed on a meteorological image sequence.

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines., info:eu-repo/semantics/published

[Notes_IRSTEA]Presentation PowerPoint (34 diapositives) [Departement_IRSTEA]EA [TR1_IRSTEA]TEPSA / METFRI; National audience; Une technique de flot optique contrainte par les cascades d'énergie pour améliorer l'estimation des petites échelles. Il montre comment introduire des a priori statistiques sur la turbulence dans les schémas d'analyse du mouvement dans les images. Pour cela il utilise les lois d'échelles des fonctions de structures qu'il introduit sous la forme d'un problème de minimisation sous contrainte. Il considère des incertitudes sur le modèle de cascade (prédictions de K41) et propose un apprentissage a posteriori des exposants des lois d'échelles. Une première validation de la méthode est montrée à partir d'une séquence d'images de particules dispersées dans une turbulence bidimensionnelle.

The article provides an historical survey of the early contributions on infinitely divisible distributions starting from the pioneering works of de Finetti in 1929 up to the canonical forms developed in the thirties by Kolmogorov, Levy and Khintchine. Particular attention is paid to single out the personal contributions of the above authors that were published in Italian, French or Russian during the period 1929-1938. In Appendix we report the translation from the Russian into English of a fundamental paper by Khintchine published in Moscow in 1937., 26 pages

A stochastic cellular automata simulator capable of spatiotemporal modeling of the crystallization and amorphization behavior of phase-change materials during the complex annealing cycles used in optical and electrical memory applications is presented. This is based on consideration of bulk and surface energies to generate rates of growth and decay of crystallites built up from "monomers" that may themselves be quite complex molecules. The approach uses a stochastic Gillespie-type time-stepping algorithm to deal with events that may occur on a very wide range of time scales. The simulations are performed at molecular length scale and using an approximation of local free energy changes that depend only on immediate neighbors. The approach is potentially capable of spanning the length scales between ab initio atomistic modeling methods, such as density functional theory, and bulk-scale methods, such the Johnshon-Mehl-Avrami-Kolmogorov formalism. As an example the model is used to predict the crystallization behavior in the chalcogenide Ge2 Sb2 Te5 alloy commonly used in phase-change memory devices. The simulations include annealing cycles with nontrivial spatial and temporal variations in temperature, with good agreement to experimental incubation times at low temperatures while modeling nontrivial crystal size distributions and melting dynamics at higher temperatures. � 2008 American Institute of Physics.

This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. David Freedman and Philip Stark's concept of model based probabilities is examined and is used as a bridge between the formal theory and applications., Comment: Published in at http://dx.doi.org/10.1214/193940307000000347 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency., new version to Phys. Rev. Lett

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2005, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2005, Bu çalışmada, Kolmogorov Uzaklık Tanımı ve k-NN sınıflandırıcısı kullanılarak müzik tarzı ve bestecisi bulunmuştur. Müzik parçaları arasındaki uzaklık hesaplanmadan önce müzik parçaları olarak kullanılan MIDI biçimli dosyalar ön işlemeden geçirilmiş ve matematiksel katar gösterilişleri elde edilmiştir. Farklı ön işleme metotları denenmiş ve her bir metodun başarımı k-NN sınıflandırıcısının hata düzeyine bakılarak ölçülmüştür. Ön işleme metotlarından çok seslilikten tek sesliliğe dönüşümün yapılması ve art arda gelen notalar arasındaki farkın alınması metodu en etkin metot olarak belirlenmiştir. Kullanılan test kümesinin elemanlarına bağlı olarak farklı örnekleme periyotlarında farklı başarım değerleri elde edilmiş ve en yüksek başarımın farklı türler için farklı örnekleme periyotlarında elde edildiği görülmüştür. Çalışmada %90’lara varan bir başarım elde edilmiştir. Sonuçları literatürdeki çalışmalarla karşılaştırdığımızda, sadece melodi ve ritmin kullanılarak bu kadar yüksek bir başarım elde edilmesi geliştirilen ön işleme metotlarının, kullanılan uzaklık tanımının ve sınıflandırıcısının etkinliğini göstermektedir., In this study genre and composer of music pieces are identified by using Kolmogorov Distance Measure and k-Nearest Neighbour (k-NN) classifier. The MIDI music input files are pre-processed into a mathematical string representation before the distance metric is computed. Different pre-processing techniques are considered and the performance of each technique is estimated by means of the test error of the k-NN classifier. As a pre-processing technique representing the music pieces in a monophonic format and taking the difference between notes in consecutive time intervals is found to be most effective. Different time interval lengths are found to be best for different classification tasks. Accuracy rates up to 90% are obtained. In comparison with the previous studies in the literature, this performance in classification accuracy by using only melody and rhythm shows the effectiveness of the developed preprocessing techniques, the distance measure and the classifier in music genre and composer classification., Yüksek Lisans, M.Sc.

A comparison of the "theory of random sequences" developed during the twentieth century and the axiomatic approach of probability theory proposed by Kolmogorov shows the importance of sigma-additivity as extension tool. Similarly, the Cauchy criterion appears to be an extension tool for mathematical analysis. The Dirichlet forms theory possesses also such an extension tool. They are the source of the fruitfulness of these languages and the condition of their creativity. A connection is given with the so-called Richard paradox.

In this thesis, we consider a robust state estimation problem for discrete-time, homogeneous, first-order, finite-state finite-alphabet hidden Markov models (HMMs). Based on Kolmogorov's Theorem on the existence of a process, we first present the Kolmogorov model for the HMMs under consideration. A new change of measure is introduced. The statistical properties of the Kolmogorov representation of an HMM are discussed on the canonical probability space. A special Kolmogorov measure is constructed. Meanwhile, the ergodicity of two expanded Markov chains is investigated. In order to describe the uncertainty of HMMs, we study probability distance problems based on the Kolmogorov model of HMMs. Using a change of measure technique, the relative entropy and the relative entropy rate as probability distances between HMMs, are given in terms of the HMM parameters. Also, we obtain a new expression for a probability distance considered in the existing literature such that we can use an information state method to calculate it. Furthermore, we introduce regular conditional relative entropy as an a posteriori probability distance to measure the discrepancy between HMMs when a realized observation sequence is given. A representation of the regular conditional relative entropy is derived based on the Radon-Nikodym derivative. Then a recursion for the regular conditional relative entropy is obtained using an information state method. Meanwhile, the well-known duality relationship between free energy and relative entropy is extended to the case of regular conditional relative entropy given a sub-[special character]-algebra. Finally, regular conditional relative entropy constraints are defined based on the study of the probability distance problem. Using a Lagrange multiplier technique and the duality relationship for regular conditional relative entropy, a finite horizon robust state estimator for HMMs with regular conditional relative entropy constraints is derived. A complete characterization of the solution to the robust state estimation problem is also presented.

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis is an experimental investigation of the passive scalar (species concentration) field in the far-field of round, axisymmetric, high Schmidt number (liquid phase), turbulent jets issuing into a quiescent reservoir, by means of a quantitative laser-induced fluorescence technique. Single-point concentration measurements are made on the jet centerline, at axial locations from 100 to 305 nozzle diameters downstream, and Reynolds numbers of 3,000 to 102,000, yielding data with a resolved temporal dynamic range up to [...], and capturing as many as 504 large-scale structure passages. Long-time statistics of the jet concentration are found to converge slowly. Between 100 and 300 large-scale structure passages are required to reduce the uncertainty in the mean to 1%, or so. The behavior of the jet varies with Reynolds number. The centerline concentration pdf's become taller and narrower with increasing Re, and the normalized concentration variances correspondingly decrease with Re. The concentration power spectra also evolve with Re. The behavior of the spectral slopes is examined. No constant -1 (Batchelor) spectral slope range is present. Rather, in the viscous region, the power spectra exhibit log-normal behavior, over a range of scales exceeding a factor of 40, in some cases. The frequency of the beginning of this log-normal range scales like [...] (Kolmogorov scaling). Mixing in the far-field is found to be susceptible to initial conditions. Disturbances in the jet plenum fluid and near the nozzle exit strongly influence the scalar variance, with larger disturbances causing larger variances, i.e., less homogeneous mixing. The plenum/nozzle geometry also influences the variance. These effects of initial conditions persist for hundreds of diameters from the nozzle exit, over hundreds of large scales. Mixing in these jets differs from gas-phase, order unity Sc, jet mixing. At low to moderate Re, the higher Sc jet is less well mixed. The difference is less pronounced at higher Re. Flame length estimates imply either an increase in entrainment and/or an increase in molecular mixing, with increasing Re. Experimental considerations such as buoyancy and resolution are shown not to influence these results.

A locally homogeneous representation for the two-point, second-order turbulent velocity fluctuation Rij(x,r) = 〈u′i(x)u′i(x+r)〉 is formulated in terms of three linearly independent structure tensors [Kassinos et al., J. Fluid Mech. 428, 213 (2001)]: Reynolds stress Bij, dimensionality Dij, and stropholysis Q*ijk. These structure tensors are single-point moments of the derivatives of vector stream functions that contain information about the directional and componential anisotropies of the correlation. The representation is a sum of several rotationally invariant component tensors. Each component tensor scales like a power law in r, while its variation in r/r depends linearly on the structure tensors. Continuity and self-consistency constraints reduce the number of degrees of freedom in the model to 17. A finite Re correction is introduced to the representation for separations of the order of Kolmogorov's length scale. To evaluate our representation, we construct a model correlation by fitting the representation to correlations calculated from direct numerical simulation (DNS) of homogeneous turbulence and channel flow. Comparison of the model correlation to the DNS data shows that the representation can capture the character of the anisotropy of two-point second-order velocity correlation tensors. © 2008 American Institute of Physics. 20

Kolmogorov has defined the complexity of a sequence of bits to be the minimal size of (the description of) a Turing machine which can regenerate the given sequence. This paper contains two notes on possible applications of this complexity notion to philosophy in general and the philosophy of science in particular. The first presents simplicism--a theory prescribing that people would tend to choose the simplest theory to explain observations, where "simple" is defined by (a version of) Kolmogorov's measure. The second suggests a reinterpretation of a simple observation, saying that reality is almost surely too complex to understand, terms such as "good" and "evil" almost surely too complex to define, and so forth.

A bibliography is given of works by Kolmogorov of statistical interest and of statistical papers by others that have cited his work. Also listed separately are bibliographies of Kolmogorov's works in all fields.

Consider the Hardy-type operator T: LP (a,b) → LP (a,b), -∞ ≤ a < b ≤ ∞, which is defined by (Tf)(x) = v(x) ∫ax u(t)f(t)dt. It is shown that ρn (T) = 1/n αP ∫ab u(x)v(x)+O(n-2), where ρn (T) stands for any of the following: the Kolmogorov n-width, the Gel'fand n-width, the Bernstein n-width or the nth approximation number of T.

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

The minimum distance (MD) functional defined by a distance $\mu$ is automatically robust over contamination neighborhoods defined by $\mu$. In fact, when compared to other Fisher-consistent functionals, the MD functional was no worse than twice the minimum sensitivity to $\mu$-contamination, and at least half the best possible breakdown point. In invariant settings, the MD functional has the best attainable breakdown point against $\mu$-contamination among equivariant functionals. If $\mu$ is Hilbertian (e.g., the Hellinger distance), the MD functional has the smallest sensitivity to $\mu$-contamination among Fisher-consistent functionals. The robustness of the MD functional is inherited by MD estimates, both estimates based on "weak" distances and estimates based on "strong" distances, when the empirical distribution is appropriately smoothed. These facts are general and apply not just in simple location models, but also in multivariate location-scatter and in semiparametric settings. Of course, this robustness is formal because $\mu$-contamination neighborhoods may not be large enough to contain realistic departures from the model. For the metrics we are interested in, robustness against $\mu$-contamination is stronger than robustness against gross errors contamination; and for "weak" metrics (e.g., $\mu = \text{Cramer-von Mises, Kolmogorov})$, robustness over $\mu$-neighborhoods implies robustness over Prohorov neighborhoods.

An asymptotic notion of robust tests is studied which is based on the requirement of equicontinuous error probabilities. If the test statistics are consistent, their robustness in Hampel's sense and robustness of the associated tests turn out to be equivalent. Uniform extensions are considered. Moreover, test breakdown points are defined. The main applications are on rank statistics: they are generally robust, under a slight condition even uniformly so; their points of final breakdown coincide with the breakdown points of the corresponding $R$ - estimators.

Andrey Nikolaevich Kolmogorov (1903 – 1987) was a Russian mathematician who contributed with his book Grundbegriffe der Wahrscheinlichkeitsrechnung to the foundations of probability theory and nature grounded human reasoning. Kolmogorov who was appointed a professor at Moscow University in 1931 has been able to publish this far-reaching monograph on probability theory in 1933. With this historical monograph, Kolmogorov built up probability theory in a rigorous way from fundamental axioms in a way comparable with Euclid's treatment of geometry. In this publication Kolmogoroff unfortunately did not contribute anything to the question whether there is a connection between geometry and probability theory. Download at: Archive, \href{https://doi.org/10.5281/zenodo.7883088}{Zenodo} \href{https://archive.org/details/foundationsofthe00kolm}{Archive}

Most statistical methods require assumptions about the populations from which samples are taken. Usually these methods measure the parameters, such as variance, standard deviations, means, etc., of the respective populations. One example is the assumption that a given population can be approximated closely with a normal curve. Since these assumptions are not always valid, statisticians have developed several alternate techniques known as nonparametric tests. The models of such tests do not specify conditions about population parameters. Certain assumptions, such as (1) observations are independent and (2) the variable being studied has underlying continuity, are associated with most nonparametric tests. However, these assumptions are weaker and less in number than those commonly associated with parametric tests.

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines.