domain of definition of levermore s five moment system the simplest system in levermore s moment hierarchy involving moments higher than second order is the five moment closure it is obtained by taking velocity moments of the one dimensional boltzmann equation under the assumption that the velocity distribution is a maximum entropy function the moment vectors for which a maximum entropy function exists consequently make up the domain of definition of the system the aim of this article is a complete characterization of the structure of the domain of definition and the connected maximum entropy problem the space homogeneous case of the equation and numerical aspects are also addressed

new constructions for provably secure time bound hierarchical key assignment schemes a time bound hierarchical key assignment scheme is a method to assign time dependent encryption keys to a set of classes in a partially ordered hierarchy in such a way that each class in the hierarchy can compute the keys of all classes lower down in the hierarchy according to temporal constraints in this paper we propose new constructions for time bound hierarchical key assignment schemes which are provably secure with respect to key indistinguishability our constructions use as a building block any provably secure hierarchical key assignment scheme without temporal constraints and exhibit a tradeoff among the amount of private information held by each class the amount of public data the complexity of key derivation and the computational assumption on which their security is based moreover the proposed schemes support updates to the access hierarchy with local changes to public information and without requiring any private information to be re distributed

hausdorff moment problem and maximum entropy a unified approach hausdorff moment problem in the approach of maximum entropy is reconsidered some aspects as existence condition entropy convergence entropy decreasing stability are studied through a unified approach results known in literature and some new ones are illustrated

lyapunov exponents and the natural invariant density determination of chaotic maps an iterative maximum entropy ansatz we apply the maximum entropy principle to construct the natural invariant density and the lyapunov exponent of one dimensional chaotic maps using a novel function reconstruction technique that is based on the solution of the hausdorff moment problem via maximizing shannon entropy we estimate the invariant density and the lyapunov exponent of nonlinear maps in one dimension from a knowledge of finite number of moments the accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available furthermore we also consider a very complex example for which no exact analytical result for the invariant density is available a comparison of our results to those available in the literature is also discussed

a piecewise quadratic maximum entropy method for the statistical study of chaos abstract let the frobenius perron operator p s l 1 0 1 l 1 0 1 related to a nonsingular transformation s 0 1 0 1 have an invariant density f we propose a piecewise quadratic maximum entropy method for the numerical approximation of f the role of the partition of unity property of the quadratic functions for the numerical recovery of f has been depicted the proposed algorithm overcomes the ill conditioning shortage of the traditional maximum entropy method which only employs polynomials so that any number of moments can be used to increase the accuracy of the computed invariant density the convergence rate of the method is shown to be of order 3 numerical results are presented to justify the theoretical analysis of the method

another look at the regression discontinuity design the attractiveness of the regression discontinuity design rdd rests on its close similarity to a formal experimental design on the other hand it is of limited applicability since it is not often the case that units are assigned to the treatment group on the basis of an observable to the analyst pre program measure besides it only allows to identify the mean impact on a very specific sub population in this paper we show that the rdd straightforwardly generalizes to the instances in which the units eligibility is established on an observable pre program measure with eligible units allowed to freely self select into the program this set up also turns out very convenient to build a specification test on conventional non experimental estimators of the program mean impact data requirements are made explicit

controlling access in tree hierarchies abstract inspired from sandhu s scheme this paper presents a cryptographic key assignment scheme in tree hierarchies for access control initially the root security class is assigned an arbitrary secret key which is a 3 dimensional row vector any other security class s secret key can be generated or derived from its ancestor s secret key as needed in our scheme the secret key can be used directly as an encryption key or used as an encryption encryption key for generating an encryption key to encipher the owned information items our scheme preserves the advantages of sandhu s scheme such as a new security class can be defined easily and the size of secret key is fixed furthermore each security class can freely choose or change its encryption key for protecting the owned information items without altering the existing secret keys

approximate solution of fredholm integral equations by the maximum entropy method an approximate means of solving fredholm integral equations by the maximum entropy method is developed the fredholm integral equation is converted to a generalized moment problem whose approximate solution by maximum entropy methods has been successfully implemented in a previous paper by mead and papanicolaou l r mead and n papanicolaou j math phys 25 2404 1984 several explicit examples are given of approximate maximum entropy solutions of fredholm integral equations of the first and second kinds and of the wiener hopf type both the weaknesses and strengths of the method are discussed

solving differential equations by a maximum entropy minimum norm method with applications to fokker planck equations the method of maximum entropy minimum norm is utilized to produce a general method of solving differential equations the technique is a generalization and extension of previous work performed by baker jarvis j math phys 30 302 1989 it is found that introducing an additional constraint on the norm of the solution vector produces a probability distribution that is integrable over the entire real axis a number of simplifications occur in this extended method the lagrange multipliers and solution vector can be solved for explicitly thus eliminating the necessity of solving systems of nonlinear equations for the lagrange multipliers as was required in the previous approach it is shown that the solution obtained is equivalent to a minimum norm approximation the maximum entropy solution of differential equations with fourier moments is shown to be identical to a fourier series solution additionally the new method is applied to solving the random walk and fokker planck equations

a novel key management scheme for dynamic access control in a user hierarchy considering the solution of dynamic access problems in a user hierarchy a novel scheme based on one way hash function is proposed to manage the cryptographic keys in the paper the scheme attempts to achieve both efficiency and non iteration in deriving the successor s secret key besides the other issues in relation with dynamic access control problems such as adding deleting classes adding deleting relationships and changing secret keys can be held good to the scheme in view of security a competent central authority must provide the user a convenient way to change his her key at any time therefore the design toward the algorithm in the paper contains such a function what weight to mention especially among these characteristics of the scheme is the simplification of procedure in changing the private key and no other current keys need altering simultaneously

function reconstruction as a classical moment problem a maximum entropy approach we present a systematic study of the reconstruction of non negative functions via maximum entropy approach utilizing the information contained in a finite number of moments of the functions for testing the efficacy of the approach we reconstruct a set of functions using an iterative entropy optimization scheme and study the convergence profile as the number of moments is increased a wide variety of functions are considered that include a distribution with a sharp discontinuity an oscillatory function a distribution with singularities and finally a distribution with several spikes and fine structure the last example is important in the context of the determination of the natural density of the logistic map the convergence of the method is studied by comparing the moments of the approximated functions with the exact ones furthermore by varying the number of moments and iterations we examine to what extent the features of the functions such as the divergence behavior at singular points within the interval is reproduced the proximity of the reconstructed maximum entropy solution to the exact solution is examined via kullback leibler divergence and variation measures for different number of moments

high order entropy based closures for linear transport in slab geometry ii a computational study of the optimization problem we present a numerical algorithm to implement entropy based m n moment models in the context of a simple linear kinetic equation for particles moving through a material slab the closure for these models as is the case for all entropy based models is derived through the solution of a constrained convex optimization problem the algorithm has two components the first component is a discretization of the moment equations which preserves the set of realizable moments thereby ensuring that the optimization problem has a solution in exact arithmetic the discretization is a second order kinetic scheme which uses muscl type limiting in space and a strong stability preserving runge kutta time integrator the second component of the algorithm is a newton based solver for the dual optimization problem which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives the accuracy of the numerical solution to the dual problem plays a key role in the time step restric

maximum entropy in the hamburger moments problem the maximum entropy approach to the solution of the hamburger inverse problem of moments in which one seeks to recover a positive density function p x where x from the values of a finite n 1 of its moments is considered the obtained results show that unexpected upper bounds for the moments do not exist in the general hamburger finite moment problem unlike in the symmetric case previously considered some physical examples illustrating the use of partial information to determine the approximate function are presented

on the convergence of moment problems we study the problem of estimating a nonnegative density given a finite number of moments such problems arise in numerous practical applications as the number of moments increases the estimates will always converge weak as measures but need not converge weakly in l this is related to the existence of functions on a compact metric space which are not essentially riemann integrable in some suitable sense we characterize the type of weak convergence we can expect in terms of riemann integrability and in some cases give error bounds when the estimates are chosen to minimize an objective function with weakly compact level sets such as the bolzmann shannon entropy they will converge weakly in l when an lp norm 1 p is used as the objective the estimates actually converge in norm these results provide theoretical support to the growing popularity of such methods in practice

a maximum entropy method for solving frobenius perron operator equations let s 0 1 0 1 be a nonsingular transformation that preserves an absolutely continuous invariant measure with density f in this paper we develop a general algorithm for approximating f using the maximum entropy approach

on the application of maximum entropy to the moments problem the maximum entropy approach to the solution of classical inverse problem of moments in which one seeks to reconstruct a function p x where x 0 from the values of a finite set n 1 of its moments is studied it is shown that for n 4 such a function always exists while for n 2 and n 3 the acceptable values of the moments are singled out analytically the paper extends to the general case where the results were previously bounded to the case n 2

access control in user hierarchy based on elliptic curve cryptosystem this work proposes a novel key management method based on elliptic curve cryptosystem and one way hash function to solve dynamic access problems in a user hierarchy the proposed scheme attempts to derive the secret key of successors efficiently and non redundantly it includes functions such as insertion and removal of classes updating of their relationships and changing of secret keys the method utilizes a central authority which enables a user to change the secret key at will conveniently since the proposed method uses the elliptic curve cryptosystem which has a low computational cost and small key size its performance in terms of both security and efficiency is quite commendable therefore it can be anticipated that its use will be extended to wireless communication in the future

some physical features of the burr type xii distribution aspects related to driven nonequilibrium systems considered in beck cohen superstatistics bcs formalism and in addition the unbiased maximum entropy density estimation show the pertinence of considering the three parameter burr type xii distribution as a suitable way to describe stationary states of complex and nonequilibrium systems the above is shown following a variant to the procedure presented in the formulation of bcs which consists of the incorporation of an expanded boltzmann factor through the mittag leffler function on the other hand maximization of shannon boltzmann gibbs entropy and other generalized forms of entropy show that the burr type xii distribution may emerge as the least informative distribution for the mentioned systems

new developments of the extended quadrature method of moments to solve population balance equations abstract population balance models have a wide range of applications in many industrial fields as they allow accounting for heterogeneity among properties which are crucial for some system modelling they actually describe the evolution of a number density function ndf using a population balance equation pbe for instance they are applied to gas liquid columns or stirred reactors aerosol technology crystallisation processes fine particles or biological systems there is a significant interest for fast stable and accurate numerical methods in order to solve for pbes a class of such methods actually does not solve directly the ndf but resolves their moments these methods of moments and in particular quadrature based methods of moments have been successfully applied to a variety of systems point wise values of the ndf are sometimes required but are not directly accessible from the moments to address these issues the extended quadrature method of moments eqmom has been developed in the past few years and approximates the ndf from its moments as a convex mixture of kernel density functions kdfs of the same parametric family in the present work eqmom is further developed on two aspects the main one is a significant improvement of the core iterative procedure of that method the corresponding reduction of its computational cost is estimated to range from 60 up to 95 the second aspect is an extension of eqmom to two new kdfs used for the approximation the weibull and the laplace kernels all matlab source codes used for this article are provided with this article

from association to causation in observational studies the role of tests of strongly ignorable treatment assignment abstract if treatment assignment is strongly ignorable then adjustment for observed covariates is sufficient to produce consistent estimates of treatment effects in observational studies a general approach to testing this critical assumption is developed and applied to a study of the effects of nuclear fallout on the risk of childhood leukemia r a fisher s advice on the interpretation of observational studies was make your theories elaborate formally make causal theories sufficiently detailed that under the theory strongly ignorable assignment has testable consequences

a dynamic cryptographic key assignment scheme in a tree structure abstract in this paper we propose a dynamic cryptographic key assignment scheme based on newton s interpolation method and a predefined one way function all users are classified into disjoint sets of security classes that employ the relation of partial ordering that is a security class at higher level can derive from his own cryptographic key the keys of the other security class below him compared with the existing assignment schemes our scheme always produces economic cryptographic keys which are smaller than the keys generated by the previous work in a tree structure furthermore whenever a new security class is inserted into the user hierarchy system the corresponding keys can be determined without changing any existing keys therefore our scheme is suitable for practical implementation

a single key access control scheme in information protection systems abstract a new access control scheme for information protection systems is proposed it assigns every legal user just one integer key in such a way that employing a simple formula to the key of the user subject and the id number of the resource object yields the corresponding access right in the protection system

fourth order pseudo maximum likelihood methods we extend pml theory to account for information on the conditional moments up to order four but without assuming a parametric model to avoid a risk of misspecification of the conditional distribution the key statistical tool is the quartic exponential family which allows us to generalize the pml2 and qgpml1 methods proposed in gourieroux et al 1984 to pml4 and qgpml2 methods respectively an asymptotic theory is developed the key numerical tool that we use is the gauss freud integration scheme that solves a computational problem that has previously been raised in several fields simulation exercises demonstrate the feasibility and robustness of the methods

hamburger moment problem and maximum entropy on the existence conditions the existence of maximum entropy solution for the reduced hamburger moment problem is reconsidered existence conditions previously appeared in literature are revisited allowing an easy way to identifying the existence of maximum entropy solution the obtained results suggest that except for special sequences of moments unknown a priori the maximum entropy solution for the non symmetric reduced hamburger moment problem exists for practical purposes the replacing of the support r with a large enough finite interval finds a theoretical warranty the symmetric case may be formulated as follows once assigned the first 2m moments if maxent density does not exist conclusion drawn uniquely from numerical evidence maxent density with the first 2m 2 moments exists in such a case even if the first 2m moments are known we have to settle for a density which carries less information theoretical results are illustrated through some numerical examples

an efficient key assignment scheme for access control in a large leaf class hierarchy the employees of an organization are usually divided into different security classes to authorize the information retrieval and the number of leaf classes is substantially larger than the number of non leaf classes additionally the alternations in leaf classes are more frequent than in non leaf classes we proposed a new key assignment scheme for controlling the access right in a large poset partially ordered set hierarchy to reduce the required computation for key generation and derivation with the storage amount of data decreased

a practical computational framework for the multidimensional moment constrained maximum entropy principle the maximum entropy principle is a versatile tool for evaluating smooth approximations of probability density functions with a least bias beyond given constraints in particular the moment based constraints are often a common prior information about a statistical state in various areas of science including that of a forecast ensemble or a climate in atmospheric science with that in mind here we present a unified computational framework for an arbitrary number of phase space dimensions and moment constraints for both shannon and relative entropies together with a practical usable convex optimization algorithm based on the newton method with an additional preconditioning and robust numerical integration routine this optimization algorithm has already been used in three studies of predictability and so far was found to be capable of producing reliable results in one and two dimensional phase spaces with moment constraints of up to order 4 the current work extensively references those earlier studies as practical examples of the applicability of the algorithm developed below

coarse grained computation for particle coagulation and sintering processes by linking quadrature method of moments with monte carlo the study of particle coagulation and sintering processes is important in a variety of research studies ranging from cell fusion and dust motion to aerosol formation applications these processes are traditionally simulated using either monte carlo methods or integro differential equations for particle number density functions in this paper we present a computational technique for cases where we believe that accurate closed evolution equations for a finite number of moments of the density function exist in principle but are not explicitly available the so called equation free computational framework is then employed to numerically obtain the solution of these unavailable closed moment equations by exploiting through intelligent design of computational experiments the corresponding fine scale here monte carlo simulation we illustrate the use of this method by accelerating the computation of evolving moments of uni and bivariate particle coagulation and sintering through short simulation bursts of a constant number monte carlo scheme

ineligibles and eligible non participants as a double comparison group in regression discontinuity designs in a sharp regression discontinuity design rdd the participation status deterministically depends on whether a pre programme characteristic is above or below a specified threshold the attractiveness of such a design rests on close similarities with a formal experiment nevertheless it is of limited applicability since participation into a programme is seldom determined according to this rule besides in the presence of heterogeneous effects a sharp rdd only allows identification of mean effects for individuals around the threshold for participation two results are presented in this paper and they both partially overcome the two limitations described above we show that when individuals self select into participation conditional on some eligibility criteria a sharp rdd provides a natural framework to define a specification test for the non experimental estimation of programme effects for participants away from the threshold we also show that in this set up the regularity conditions required for the identification of the mean counterfactual outcome for participants marginally eligible for the programme are essentially the same as in a sharp rdd

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

on the application of maximum entropy to the moments problem the use of the maximum entropy condition to obtain a solution to the moments problem in which one seeks to reconstruct a function from the values of a finite set of its moments is of interest in a variety of physical applications unfortunately the standard analysis which is available and on which these applications are based takes as its starting point precise values of the moments whereas the physical applications involve imprecise data in this paper it will be shown how to solve the moments problem using the maximum entropy condition starting from imprecise data values with errors specified by a 2 function

construction of probability distributions in high dimension using the maximum entropy principle applications to stochastic processes random fields and random matrices the construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension this paper deals with the effective construction of the probability distribution in high dimension of a vector valued random variable using the maximum entropy principle the integrals in high dimension are then calculated in constructing the stationary solution of an ito stochastic differential equation associated with its invariant measure a random generator of independent realizations is explicitly constructed in this paper three fundamental applications are presented the first one is a new formulation of the stochastic inverse problem related to the construction of the probability distribution in high dimension of an unknown non stationary random time series random accelerograms for which the velocity response spectrum is given the second one is also a new formulation related to the construction of the probability distribution of positive definite band random matrices finally we present an extension of the theory when the support of the probability distribution is not all the space but is any part of the space the third application is then a new formulation related to the construction of the probability distribution of the karhunen loeve expansion of non gaussian positive valued random fields

maximum entropy formalism and analytic extrapolation the maximum entropy principle is used to obtain a new analytic extrapolation method just complementary to the pade type method which leads to rigorous upper and lower bounds on the extrapolated function on the cut complex plane among the large class of functions that could equally well represent an analytical function in the experimental region a choice is made of the unique function that maximizes the entropy functional associated to this set of functions the result is the least biased function compatible with the actual experimental data this extrapolation method is applied to kaon nucleon experimental data in order to obtain the most reasonable values for the kny coupling constants compatible with the available experimental data and analytical constraints

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

maximum entropy approach to classical hard sphere and hard disk equations of state the maximum entropy procedure for extrapolating series is applied to sum the known virial series for the hard disk and hard sphere fluids this procedure is found to produce numerical results more accurate than pade approximants and it agrees with monte carlo simulations of these systems the maximum entropy results extrapolate the series smoothly to densities arbitrarily near to maximum close packing and predict no singularities whatsoever

an efficient hierarchy scheme for determining relationships in information systems abstract in this paper a dynamic user hierarchy mechanism based on key pairs is proposed through careful design of keys we get an economic integer key pair for each user in our scheme the relationship between two users can be easily revealed by performing a simple formula to the key pair furthermore by applying our scheme whenever a new user is inserted into the user hierarchy system the corresponding key pair can be determined quickly without changing any existing key pairs

two dimensional distribution of streamwise velocity in open channel flow using maximum entropy principle incorporation of additional constraints based on conservation laws abstract this study derived the vertical and transverse distribution of streamwise velocity in open channels using the information theoretic concept involving the maximum entropy maxent principle moment constraints expressed by the conservation of mass momentum and energy and a hypothesis invoking the connection between probability and space domains through a generalized coordinate system explicit analytical solutions were obtained for velocity profiles using a non perturbation approach along with pade approximation the convergence of the series solution was shown both theoretically and numerically the lagrange multipliers arising through the application of maxent principle were obtained by minimizing a convex potential and the quasi newton method along with bfgs scheme was applied for solving the unconstrained optimization problem for applying the conservation laws the momentum and energy coefficients were found to influence the velocity profile in a channel cross section with the expressions of these coefficients the derived velocity equations were validated for a wide range of experimental and field data

on the failure of maximum entropy reconstruction for fredholm equations and other infinite systems we analyse several examples where the maximum entropy solution to a system of equations exists but fails to satisfy the natural dual formula these examples highlight the role that finiteness of the number of constraints has in the efficacy of maximum entropy type estimation and reconstruction we also provide two regularization processes which repair the problem

a maximum entropy method for solving the boundary value problem of second order ordinary differential equations we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent

maximum entropy in the problem of moments the maximum entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem in important special cases such as the hausdorff moment problem we establish necessary and sufficient conditions for the existence of a maximum entropy solution and examine the convergence of the resulting sequence of approximations a number of explicit illustrations are presented in addition to some elementary examples we analyze the maximum entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems we also briefly indicate possible applications to the lee yang theory of ising models to the summation of divergent series and so on the general conclusion is that maximum entropy provides a valuable approximation scheme a serious competitor of traditional pade like procedures

maximum entropy approximation for lyapunov exponents of chaotic maps let s 0 1 0 1 be a nonsingular chaotic map that preserves an integrable density f that describes the statistics of the orbits in this article we use the maximum entropy approach to approximate the density f and the corresponding lyapunov exponent

an optimal algorithm for assigning cryptographic keys to control access in a hierarchy a cryptographic scheme for controlling access to information within a group of users organized in a hierarchy was proposed in 1 the scheme enables a user at some level to compute from his own cryptographic key the keys of the users below him in the organization

the design of an arithmetic coding mechanism to determine relationships in a hierarchy abstract in this paper a dynamic user hierarchy mechanism based on arithmetic coding is proposed through careful design of keys some economic keys are obtained in our scheme the relationship between two users can be easily revealed by evaluating a simple formula to the relative key in addition whenever a new user is inserted into the user hierarchy system the corresponding keys can be determined quickly without changing the existing keys except for the last existing key furthermore the keys proposed by us are drastically reduced from the previous work

efficient numerical approximation of maximum entropy estimates a class of algorithms for approximation of the maximum entropy estimate of probability density functions on the basis of a finite number of sampled data is introduced the algorithms are presented as a finite sequence in order of increasing accuracy and decreasing computational efficiency in which the last element of the sequence is the exact maximum entropy estimate numerical and applicative examples are reported

observer participant models of neural processing a model is proposed in which the neuron serves as an information channel channel distortion occurs through the channel since the mapping from input boolean codes to output codes are many to one in that neuron outputs consist of just two distinguished states within the described model the neuron performs a decision making function decisions are made regarding the validity of a question passively posed by the neuron this question becomes defined through learning hence learning is viewed as the process of determining an appropriate question based on supplied input ensembles an application of the shannon information measures of entropy and mutual information taken together in the context of the proposed model lead to the hopfield neuron model with conditionalized hebbian learning rules neural decisions are shown to be based on a sigmoidal transfer characteristic or in the limit as computational temperature tends to zero a maximum likelihood decision rule the described work is contrasted with the information theoretic approach of linsker

calculation of maximum entropy densities with application to income distribution the maximum entropy approach is a flexible and powerful tool for density approximation this paper proposes a sequential updating method to calculate the maximum entropy density subject to known moment constraints instead of imposing the moment constraints simultaneously the sequential updating method incorporates the moment constraints into the calculation from lower to higher moments and updates the density estimates sequentially the proposed method is employed to approximate the size distribution of u s family income empirical evidence demonstrates the efficiency of this method

cryptanalysis and improvement of an access control in user hierarchy based on elliptic curve cryptosystem in a key management scheme for hierarchy based access control each security class having higher clearance can derive the cryptographic secret keys of its other security classes having lower clearances in 2008 chung et al proposed an efficient scheme on access control in user hierarchy based on elliptic curve cryptosystem information sciences 178 1 2008 230 243 their scheme provides solution of key management efficiently for dynamic access problems however in this paper we propose an attack on chung et al s scheme to show that chung et al s scheme is insecure against the exterior root finding attack we show that under this attack an attacker adversary who is not a user in any security class in a user hierarchy attempts to derive the secret key of a security class by using the root finding algorithm in order to remedy this attack we further propose a simple improvement on chung et al s scheme overall the main theme of this paper is very simple a security flaw is presented on chung et al s scheme and then a fix is provided in order to remedy the security flaw found in chung et al s scheme

higher order moments and the maximum entropy inference the thermodynamic limit approach according to jaynes 1963 statistical mechanics can be interpreted as a special type of statistical inference based on the principle of maximum entropy the result of such an inference depends on the available information about a given physical system but the principle itself does not decide what kind of information is essential and what is not the well known gibbs canonical state results from the principle when the statistical mean value of energy is supposed to be known the maximum entropy inference employing higher order moments of energy is examined from the point of view of the thermodynamic limit it is shown that the contribution to the total entropy arising from the extra information corresponding to the higher order moments is o n when n to infinity n v constant n is the number of particles and v is the volume consequently from a purely thermodynamic point of view this extra information is non essential and can be neglected in the maximum entropy procedure these conclusions also characterise the maximum entropy inference employing higher order moments of almost arbitrary extensive quantities one can say that the maximum entropy inference has a certain stability property with respect to information corresponding to higher order moments of extensive physical quantities

identification and estimation of treatment effects with a regression discontinuity design the regression discontinuity rd data design is a quasi experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables this data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment in the first application and discussion of the rd method thistlethwaite and campbell 1960 study the effect of student scholarships on career aspirations using the fact that awards are only made if a test score exceeds a threshold more recently van der klaauw 1997 estimates the effect of financial aid offers on students decisions to attend a particular college taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students grade point average and sat score angrist and lavy 1999 estimate the effect of class size on student test scores taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level finally black 1999 uses an rd approach to estimate parents willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries regression discontinuity methods have potentially broad applicability in economic research because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method although there have been several discussions and applications of rd methods in the literature important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions here we show that identifying conditions invoked in previous applications of rd methods are often overly strong and that treatment effects can be nonparametrically identified under an rd design by a weak functional form restriction the restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism we also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the wald estimator as an rd estimator

the maximum entropy method applied to stationary density computation abstract the maximum entropy method maxent is widely used in the context of the moment problem which appears naturally in many branches of physics and engineering it is used to numerically recover the density with least bias from finitely many known moments we introduce the basic idea behind this method and apply this method to approximating fixed densities of markov operators in stochastic analysis and frobenius perron operators in ergodic theory of chaotic dynamics

entropy densities with an application to autoregressive conditional skewness and kurtosis abstract the entropy principle yields for a given set of moments a density that involves the smallest amount of prior information we first show how entropy densities may be constructed in a numerically efficient way as the minimization of a potential next for the case where the first four moments are given we characterize the skewness kurtosis domain for which densities are defined this domain is found to be much larger than for hermite or edgeworth expansions last we show how this technique can be used to estimate a garch model where skewness and kurtosis are time varying we find that there is little predictability of skewness and kurtosis for weekly data

efficient provably secure hierarchical key assignment schemes a hierarchical key assignment scheme is a method to assign some private information and encryption keys to a set of classes in a partially ordered hierarchy in such a way that the private information of a higher class can be used to derive the keys of all classes lower down in the hierarchy in this paper we design and analyze hierarchical key assignment schemes which are provably secure and support dynamic updates to the hierarchy with local changes to the public information and without requiring any private information to be re distributed we first consider the problem of constructing a hierarchical key assignment scheme by using as a building block a symmetric encryption scheme we propose a new construction which is provably secure with respect to key indistinguishability requires a single computational assumption and improves on previous proposals then we show how to construct a hierarchical key assignment scheme by using as a building block a public key broadcast encryption scheme in particular one of our constructions provides constant private information and public information linear in the number of classes in the hierarchy