information measures the curious case of the binary alphabet four problems related to information divergence measures defined on finite alphabets are considered in three of the cases we consider we illustrate a contrast that arises between the binary alphabet and larger alphabet settings this is surprising in some instances since characterizations for the larger alphabet settings do not generalize their binary alphabet counterparts in particular we show that f divergences are not the unique decomposable divergences on binary alphabets that satisfy the data processing inequality thereby clarifying claims that have previously appeared in the literature we also show that kullback leibler kl divergence is the unique bregman divergence which is also an f divergence for any alphabet size we show that kl divergence is the unique bregman divergence which is invariant to statistically sufficient transformations of the data even when nondecomposable divergences are considered like some of the problems we consider this result holds only when the alphabet size is at least three

alpha divergence is unique belonging to both f divergence and bregman divergence classes a divergence measure between two probability distributions or positive arrays positive measures is a useful tool for solving optimization problems in optimization signal processing machine learning and statistical inference the csiszar f divergence is a unique class of divergences having information monotonicity from which the dual alpha geometrical structure with the fisher metric is derived the bregman divergence is another class of divergences that gives a dually flat geometrical structure different from the alpha structure in general csiszar gave an axiomatic characterization of divergences related to inference problems the kullback leibler divergence is proved to belong to both classes and this is the only such one in the space of probability distributions this paper proves that the alpha divergences constitute a unique class belonging to both classes when the space of positive measures or positive arrays is considered they are the canonical divergences derived from the dually flat geometrical structure of the space of positive measures

geometry of deformed exponential families invariant dually flat and conformal geometries an information geometrical foundation is established for the deformed exponential families of probability distributions two different types of geometrical structures an invariant geometry and a flat geometry are given to a manifold of a deformed exponential family the two different geometries provide respective quantities such as deformed free energies entropies and divergences the class belonging to both the invariant and flat geometries at the same time consists of exponential and mixture families theq families are characterized from the viewpoint of the invariant and flat geometries the q exponential family is a unique class that has the invariant and flat geometries in the extended class of positive measures furthermore it is the only class of which the riemannian metric is conformally connected with the invariant fisher metric

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

relative information of type s csiszar s f divergence and information inequalities during past years dragomir has contributed a lot of work providing different kinds of bounds on the distance information and divergence measures in this paper we have unified some of his results using the relative information of type s and relating it with the csiszar s f divergence

the burbea rao and bhattacharyya centroids we study the centroid with respect to the class of information theoretic burbea rao divergences that generalize the celebrated jensen shannon divergence by measuring the non negative jensen difference induced by a strictly convex and differentiable function although those burbea rao divergences are symmetric by construction they are not metric since they fail to satisfy the triangle inequality we first explain how a particular symmetrization of bregman divergences called jensen bregman distances yields exactly those burbea rao divergences we then proceed by defining skew burbea rao divergences and show that skew burbea rao divergences amount in limit cases to compute bregman divergences we then prove that burbea rao centroids can be arbitrarily finely approximated by a generic iterative concave convex optimization algorithm with guaranteed convergence property in the second part of the paper we consider the bhattacharyya distance that is commonly used to measure overlapping degree of probability distributions we show that bhattacharyya distances on members of the same statistical exponential family amount to calculate a burbea rao divergence in disguise thus we get an efficient algorithm for computing the bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families improving over former specialized methods found in the literature that were limited to univariate or diagonal multivariate gaussians to illustrate the performance of our bhattacharyya burbea rao centroid algorithm we present experimental performance results for k means and hierarchical clustering methods of gaussian mixture models

three dimensional unstructured multigrid for the euler equations the three dimensional euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy the driving algorithm consists of an explicit vertex based finite element scheme which employs an edge based data structure to assemble the residuals the multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution variables residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation the addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm the preprocessing operation is shown to require a negligible fraction of the cpu time required by the overall solution procedure whereas gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350 000 vertices solutions using globally regenerated fine meshes as well as adaptively refined meshes are given

application of spectral methods for high frequency financial data to quantifying states of market participants abstract empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi dimensional time series with spectral distances introduced in a h sato physica a 382 2007 258 270 as a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth and that the similarities among best quotation rates are associated with those among quotation frequencies furthermore it is shown that the jensen shannon spectral divergence is proportional to a mean of the kullback leibler spectral distance both empirically and numerically it is confirmed that these spectral distances are connected with distributions for behavioural parameters of the market participants from numerical simulation this concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioural parameters of the market participants

an axiomatic characterization of a two parameter extended relative entropy the uniqueness theorem for a two parameter extended relative entropy is proven this result extends our previous one the uniqueness theorem for a one parameter extended relative entropy to a two parameter case in addition the properties of a two parameter extended relative entropy are studied

information geometry approach to parameter estimation in markov chains we consider the parameter estimation of markov chain when the unknown transition matrix belongs to an exponential family of transition matrices then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator further we also define a curved exponential family of transition matrices using a transition matrix version of the pythagorean theorem we give an asymptotically efficient estimator for a curved exponential family primary 62m05

implicit multiple grid solution of the compressible navier stokes equations using k epsilon turbulence closure in the present work an algorithm for the numerical solution of the two dimensional mass weighted ensemble averaged compressible navier stokes equations is presented turbulence closure for the reynolds stresses is obtained using a low reynolds n umber two equation k s model which includes near wall effects the same algorithm is used for the integration of both the navier stokes and the turbulence transport equations the algorithm consists of a basic explicit finite volume scheme whose convergence is accelerated using local time step ping and multiple grid techniques convergence is further enhanced by the use of an implicit residual smoothing technique applied both in the fine and the coarser grids the application of the numerical scheme to the solution of the k s equations is examined in detail comparisons of computations with experimental data are presented for three shock wave turbulent boundary layer interaction flows algorithm convergence rate and cpu time require ments are discussed he numerical solution of the navier stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work 1 interest is focused both on code applicability to variegated config urations and on computational rapidity although direct simulation of turbulent flows2 or large eddy numerical sim ulations using subgrid turbulence modeling 3 4 have appeared in the literature current status of algorithm development and computer power indicate that for practical applications the ensemble averaged navier stokes equations should be used in conjunction with transport equations for turbulence closure 5 7 algebraic or mixing length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear layer thickness and of the distance of each grid point from the solid boundary thus they lack both geometric invariance and locality which are highly desirable properties from a computational viewpoint when addressing complex flowfields with many interacting solid boundaries although research on reynolds stre ss transport closure appears quite promising 9 10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved also further research con cerning wall effects is required the more so since the use of wall functions is considered inadequate 11 on the other hand the use of two equation closures such as a 12 14 is quite widespread notwithstanding the fact that the use of the boussinesq hypothesis15 introduces a question able simplification of the flow physics 16 the major drawback of the k s model is probably the near wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence several variants of the original jones launder model12 have been developed in an attempt to improve upon near wall modeling some ten such models have been thor oughly examined in a critical review article by patel et al 17 who concluded that the models of launder and sharma 14

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

signal estimation and threshold optimization using an array of bithreshold elements we consider the problem of optimizing signal transmission through multichannel noisy devices we investigate an array of bithreshold noisy devices which is connected in parallel and convergent on a summing center utilizing the concept of noise induced linearization we derive an analytical approximation of the normalized power norm and clarify the relation between the optimum threshold and the standard deviation of noises we show that the optimum threshold value is 0 63 times the standard deviation of the noises this relation is applicable to both subthreshold and suprathreshold inputs

artificial dissipation models for the euler equations various artificial dissipation models that are used with central difference algorithms for the euler equations are analyzed for their effect on accuracy stability and convergence rates in particular linear and nonlinear models are investigated using an implicit approximate factorization code arc2d for transonic airfoils fully implicit application of the dissipation models is shown to improve robustness and convergence rates the treatment of dissipation models at boundaries will be examined it will be shown that accurate error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model i introduction t he solution of the euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme this is because the euler equations do not provide any natural dissipation mechanism such as viscosity in the navier stokes equations that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks a variety of numerical algorithms and computer codes for the euler equations have been developed methods such as maccormack s1 explicit

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

harmonic bayesian prediction under alpha divergence we investigate bayesian shrinkage methods for constructing predictive distributions we consider the multivariate normal model with a known covariance matrix and show that the bayesian predictive density with respect to stein s harmonic prior dominates the best invariant bayesian predictive density when the dimension is greater than or equal to 3 alpha divergence from the true distribution to a predictive distribution is adopted as a loss function

near wall k e computation of transonic turbomachinery flows with tip clearance acomputational methodforthenumericalintegration ofthefavre reynolds averaged three dimensionalcompressible navier stokes equations in axial turbomachinery using the launder sharma near wall k turbulence closure is developed the mean e ow and turbulence transport equations are discretized using a e nite volume method based on muscl van leere ux vector splitting with van albada limiters and are integrated in time using a fully coupled approximately factored implicit backward euler method the resulting scheme is robust and was found stable for local time steps of courant friedrichs lewy number cfl 20 the computational domain is discretized using a basic h o h grid the tip clearance gap is discretized using a e ne o type grid the radial distribution ofnodeswithin thetip clearancegap is independent of theblade rowo grid and a bufferoverlap grid is used to convey information boundary conditions at periodicity boundaries and at domain interfaces are treated using e ve phantom nodes this procedure ensures stability at high cfl results are presented for the nasa 37 rotor at an operating point near surge computations are compared with measurements both for blade to blade mach number contours and pitchwise distributions and for radial distributions downstream of the blades results are obtained using three grids of 10 6 2 10 6 and 3 10 6 points with 21 31 and 41 radial stations within the tip clearancegap respectively demonstratingthatresultsaregridindependent comparisonwithmeasurementsis satisfactory with theexception of pressureratio overestimation due to unsatisfactory prediction ofe ow separation by the turbulence model

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

limitations of the near wall k epsilon turbulence model comparisons are given at two different reynolds numbers between the measured turbulent kinetic energy in channel flow and the predictions of several near wall variants of the k e closure included among these are new calculations based on a form of the e equation that is consistent with the physically correct boundary condition it is observed that all of the approaches fail to account for the large peak k value in the wall region that is evident in the experimental data by contrasting the computed energy budget with its measured values it is shown that this defect may be attributed to a fundamental inconsistency in the commonly used model for the pressure diffu sion term in the k equation near the boundary he k e closure is widely utilized today in the prediction of the mean properties of turbulent flowfields in recent years extensions of its basic form have been developed to permit treatment of complex fluid motions such as those found in curved pipes 1 compressible boundary layers 2 com bustion chambers 3 etc a strong incentive for the continued development and application of the k e model has been the remarkable success it has achieved in the prediction of mean velocity fields in wall bounded shear flows such as occur in channels pipes and boundary layers 4 6 the success of the k e closure in these relatively simple flows is not complete however since the high accuracy obtained for mean velocity is not duplicated in the case of the turbulent kinetic energy k a notable defect4 7 9 is the 25 or more underprediction of the large peak k value shown by clark 10 and kreplin and eckelmann11 to occur at y 15 in a channel flow for ap plications where predictions of turbulence levels are impor tant such as in internal combustion engine simulations 12 this failure can be of great practical significance it may be expected that major errors in the prediction of k stem from deficiencies in the low turbulent reynolds number forms of the k e equations which have been developed for the region adjacent to boundaries jones and launder4 for mulated the first such model that permitted k and e to be calculated down to a solid wall without the use of wall func tions several more recent studies including those of lam and bremhorst 7 hassid and poreh 8 and chien 9 have at tempted to improve upon the jones and launder approach but these authors report only modest gains in the accuracy of k the object of the present study is to elucidate the cause of this discrepancy by making direct comparisons between the terms in the exact and modeled energy equations to ac complish this a set of new calculations was performed in which e was required to satisfy the physically correct bound ary condition at the wall it was revealed that the failure of the k e model to predict the correct peak k value is most likely due to reliance on a flawed model for the pressure velocity correlation in the k equation this relation will be shown to be inconsistent with the experimentally measured values of the exact term as found by kreplin and eckelmann 11 and may be directly implicated in suppressing the peak k value removal of this limitation should allow for better predictions of k near solid boundaries

the spl alpha em algorithm surrogate likelihood maximization using spl alpha logarithmic information measures a new likelihood maximization algorithm called the spl alpha em algorithm spl alpha expectation maximization algorithm is presented this algorithm outperforms the traditional or logarithmic em algorithm in terms of convergence speed for an appropriate range of the design parameter spl alpha the log em algorithm is a special case corresponding to spl alpha 1 the main idea behind the spl alpha em algorithm is to search for an effective surrogate function or a minorizer for the maximization of the observed data s likelihood ratio the surrogate function adopted in this paper is based upon the spl alpha logarithm which is related to the convex divergence the convergence speed of the spl alpha em algorithm is theoretically analyzed through spl alpha dependent update matrices and illustrated by numerical simulations finally general guidelines for using the spl alpha logarithmic methods are given the choice of alternative surrogate functions is also discussed

simulation of three dimensional turbulent flows on unstructured meshes a three dimensional navier stokes flow solver is developed on unstructured tetrahedral meshes for a turbulence closure a standard high reynolds number k e model with a wall function boundary condition is used the seven equations of motion are discretized and integrated in a tightly coupled manner the time integration is achieved using an explicit runge kutta time stepping scheme the inviscid flux terms are discretized based on a cell centered finite volume formulation with roe s flux difference splitting the numerical method is applied for flows on a two dimensional backward facing step and a three dimensional turbomachinery geometry the results are compared with analytical and experimental data for validations

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

multiple grid convergence acceleration of viscous and inviscid flow computations a multiple grid algorithm for use in efficiently obtaining steady solutions to the euler and navier stokes equations is presented the convergence of a simple explicit fine grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse grid information propagation method which rapidly eliminates transients from the computational domain this use of multiple gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent attached and separated subsonic viscous flows work reduction factors as large as eight in comparison to the basic fine grid algorithm have been obtained possibilities for further performance improvement are discussed

a strongly implicit procedure for the compressible navier stokes equations the strongly implicit procedure of stone is used to obtain numerical solutions of the compressible navier stokes equations in conservative form in contrast to the spatially split douglas gunn type methods the method is shown to be numerically stable for the three dimensional wave equation the method is applied to a variety of external and internal two dimensional flow problems involving shock wave boundary layer interaction for both laminar and turbulent flows the results are in good agreement with other methods and or experiments

a note on divergences in many areas of neural computation like learning optimization estimation and inference suitable divergences play a key role in this note we study the conjecture presented by amari 2009 and find a counterexample to show that the conjecture does not hold generally moreover we investigate two classes of divergence zhang 2004 weighted f divergence and weighted divergence and prove that if a divergence is a weighted f divergence as well as a bregman divergence then it is a weighted divergence this result reduces in form to the main theorem established by amari 2009 when

optimal performance of generalized heat engines with finite size baths of arbitrary multiple conserved quantities beyond independent and identical distribution scaling in quantum thermodynamics effects of finiteness of the baths have been less considered in particular there is no general theory which focuses on finiteness of the baths of multiple conserved quantities then we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths in the context of general theories of quantum thermodynamics the size of the baths has been given in terms of the number of identical copies of a system which does not cover even such a natural scaling as the volume in consideration of the asymptotic extensivity we deal with a generic scaling of the baths to naturally include the volume scaling based on it we derive a bound for the performance of generalized heat engines reflecting finite size effects of the baths which we call fine grained generalized carnot bound we also construct a protocol to achieve the optimal performance of the engine given by this bound finally applying the obtained general theory we deal with simple examples of generalized heat engines as for an example of non independent and identical distribution scaling and multiple conserved quantities we investigate a heat engine with two baths composed of an ideal gas exchanging particles where the volume scaling is applied the result implies that the mass of the particle explicitly affects the performance of this engine with finite size baths

a class of logistic type discriminant functions summary in two group discriminant analysis the neyman pearson lemma establishes that the roc receiver operating characteristic curve for an arbitrary linear function is everywhere below the roc curve for the true likelihood ratio the weighted area between these two curves can be used as a risk function for finding good discriminant functions the weight function corresponds to the objective of the analysis for example to minimise the expected cost of misclassification or to maximise the area under the roc the resulting discriminant functions can be estimated by iteratively reweighted logistic regression we investigate some asymptotic properties in the near logistic setting where we assume the covariates have been chosen such that a linear function gives a reasonable but not necessarily exact

information geometry of u boost and bregman divergence we aim at an extension of adaboost to u boost in the paradigm to build a stronger classification machine from a set of weak learning machines a geometric understanding of the bregman divergence defined by a generic convex function u leads to the u boost method in the framework of information geometry extended to the space of the finite measures over a label set we propose two versions of u boost learning algorithms by taking account of whether the domain is restricted to the space of probability functions in the sequential step we observe that the two adjacent and the initial classifiers are associated with a right triangle in the scale via the bregman divergence called the pythagorean relation this leads to a mild convergence property of the u boost algorithm as seen in the expectation maximization algorithm statistical discussions for consistency and robustness elucidate the properties of the u boost methods based on a stochastic assumption for training data

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

divergence measures based on the shannon entropy a novel class of information theoretic divergence measures based on the shannon entropy is introduced unlike the well known kullback divergences the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved more importantly their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds these bounds are crucial in many applications of divergence measures the measures are also well characterized by the properties of nonnegativity finiteness semiboundedness and boundedness

analysis of high resolution foreign exchange data of usd jpy for 13 years we analyze high resolution foreign exchange data consisting of 20 million data points of usd jpy for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations a conditional probability density analysis clearly shows the existence of trend following movements at time scale of 8 ticks about 1 minute

criticality and phase transition in stock price fluctuations we analyze the behavior of the u s s p 500 index from 1984 to 1995 and characterize the non gaussian probability density functions pdf of the log returns the temporal dependence of fat tails in the pdf of a ten minute log return shows a gradual systematic increase in the probability of the appearance of large increments on approaching black monday in october 1987 reminiscent of parameter tuning towards criticality on the occurrence of the black monday crash this culminates in an abrupt transition of the scale dependence of the non gaussian pdf towards scale invariance characteristic of critical behavior these facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index to account for time varying phase transitionlike and scale invariant critical like behavior

fluctuation scaling of quotation activities in the foreign exchange market abstract we study the scaling behavior of quotation activities for various currency pairs in the foreign exchange market the components centrality is estimated from multiple time series and visualized as a currency pair network the power law relationship between a mean of quotation activity and its standard deviation for each currency pair is found the scaling exponent and the ratio between common and specific fluctuations increase with the length of the observation time window t the result means that although for t 1 min the market dynamics are governed by specific processes and at a longer time scale t 100 min the common information flow becomes more important we point out that quotation activities are not independently poissonian for t 1 min and temporally or mutually correlated activities of quotations can happen even at this time scale a stochastic model for the foreign exchange market based on a bipartite graph representation is proposed

sided and symmetrized bregman centroids in this paper we generalize the notions of centroids and barycenters to the broad class of information theoretic distortion measures called bregman divergences bregman divergences form a rich and versatile family of distances that unifies quadratic euclidean distances with various well known statistical entropic measures since besides the squared euclidean distance bregman divergences are asymmetric we consider the left sided and right sided centroids and the symmetrized centroids as minimizers of average bregman distortions we prove that all three centroids are unique and give closed form solutions for the sided centroids that are generalized means furthermore we design a provably fast and efficient arbitrary close approximation algorithm for the symmetrized centroid based on its exact geometric characterization the geometric approximation algorithm requires only to walk on a geodesic linking the two left right sided centroids we report on our implementation for computing entropic centers of image histogram clusters and entropic centers of multivariate normal distributions that are useful operations for processing multimedia information and retrieval these experiments illustrate that our generic methods compare favorably with former limited ad hoc methods

divergence function duality and convex analysis from a smooth strictly convex function rn r a parametric family of divergence function d may be introduced d x y 4 1 2 1 2 x 1 2 y 1 2x 1 2y for x y int dom rn and for r with d 1 defined through taking the limit of each member is shown to induce an independent riemannian metric as well as a pair of dual connections which are generally nonflat except for 1 in the latter case d 1 reduces to the nonparametric bregman divergence which is representable using and its convex conjugate and becomes the canonical divergence for dually flat spaces amari 1982 1985 amari nagaoka 2000 this formulation based on convex analysis naturally extends the information geometric interpretation of divergence functions eguchi 1983 to allow the distinction between two different kinds of duality referential duality and representational duality when applied to not necessarily normalized probability densities the concept of conjugated representations of densities is introduced so that connections defined on probability densities embody both referential and representational duality and are hence themselves bidual when restricted to a finite dimensional affine submanifold the natural parameters of a certain representation of densities and the expectation parameters under its conjugate representation form biorthogonal coordinates the alpha representation indexed by now 1 1 is shown to be the only measure invariant representation the resulting two parameter family of divergence functionals d 1 1 1 1 induces identical fisher information but bidual alpha connection pairs it reduces in form to amari s alpha divergence family when 1 or when 1 but to the family of jensen difference rao 1987 when 1

statistical properties of the moving average price in dollar yen exchange rates we introduce a weighted moving average analysis for the tick by tick data of yen dollar exchange rates the weights are determined automatically for given data by applying the yule walker formula for autoregressive model although the data are non stationary the resulting moving average gives a quite nice property that the deviation around the moving average becomes a white noise the weights decay exponentially with time scale less than 2 min implying that dealers are watching only very recent market state

frequency analysis of tick quotes on the foreign exchange market and agent based modeling a spectral distance approach abstract high frequency financial data of the foreign exchange market eur chf eur gbp eur jpy eur nok eur sek eur usd nzd usd usd cad usd chf usd jpy usd nok and usd sek are analyzed by utilizing the kullback leibler divergence between two normalized spectrograms of the tick frequency and the generalized jensen shannon divergence among them the temporal structure variations of the similarity between currency pairs is detected and characterized a simple agent based model in which n market participants exchange m currency pairs is proposed the equation for the tick frequency is approximately derived theoretically based on the analysis of this model the spectral distance of the tick frequency is associated with the similarity of the behavior perception and decision of the market participants in exchanging these currency pairs

stability of explicit navier stokes procedures using k e and k e algebraic reynolds stress turbulence models abstract a three dimensional explicit navier stokes procedure has been developed for application to compressible turbulent flows including rotation effects in the present work a numerical stability analysis of the discrete coupled system of seven governing equations is presented order of magnitude arguments are presented for flow and geometric properties typical of internal flows including turbomachinery applications to ascertain the relative importance of grid stretching rotation and turbulence source terms and effective diffusivity on the stability of the scheme it is demonstrated through both analysis and corroborative numerical experiments that 1 it is quite feasible to incorporate efficiently a two equation k turbulence model in an explicit time marching scheme provided certain numerical stability constraints are enforced 2 the role of source terms due to system rotation on the stability of the numerical scheme is not significant when appropriate grids are used and realistic rotor angular velocities are specified 3 the direct role of source terms in the turbulence transport equations on the stability of the numerical scheme is not significant when appropriate grids are used and realistic freestream turbulence quantities are specified except in the earliest stages of iteration a result which is contrary to that generally perceived 4 there is no advantage to numerically coupling the two equation model system to the mean flow equation system in regard to convergence or accuracy 5 for some flow configurations including turbomachinery blade rows it is useful to incorporate the influence of artificial dissipation in the prescription of a local timestep 6 explicit implementation of an algebraic reynolds stress model arsm is intrinsically stable provided that the discrete two equation transport model which provides the necessary values of k and is itself stable

integration of stochastic models by minimizing α divergence when there are a number of stochastic models in the form of probability distributions one needs to integrate them mixtures of distributions are frequently used but exponential mixtures also provide a good means of integration this letter proposes a one parameter family of integration called integration which includes all of these well known integrations these are generalizations of various averages of numbers such as arithmetic geometric and harmonic averages there are psychophysical experiments that suggest that integrations are used in the brain the divergence between two distributions is defined which is a natural generalization of kullback leibler divergence and hellinger distance and it is proved that integration is optimal in the sense of minimizing divergence the theory is applied to generalize the mixture of experts and the product of experts to the mixture of experts the predictive distribution is also stated in the bayesian framework