some novel developments in finite element procedures for gradient dependent plasticity summary improved algorithms are proposed for a gradient plasticity theory in which the laplacian of an invariant plastic strain measure enters the yield function particular attention is given to the type of finite elements that can be used within the format of gradient dependent plasticity assuming a weak satisfaction of the yield function mixed finite elements are developed in which the invariant plastic strain measure and the displacements are discretized two families of finite elements are developed one in which the invariant plastic strain measure is interpolated using c continuous polynomials and one in which penalty enhanced c continuous interpolants are used the performance of both families of finite elements is assessed numerically in one dimensional and two dimensional boundary value problems the regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated both for mesh refinement and for the directional bias of the grid lines

over nonlocal gradient enhanced plastic damage model for concrete abstract classical continuum models exhibit strong mesh dependency during softening one method to regularize the problem is to introduce a length scale parameter via the nonlocal formulation however standard nonlocal enhancement either by integral or gradient formulation may serve only as a partial localization limiter for many material models the over nonlocal formulation where the weight for the nonlocal value is greater than unity and the excesses compensated by assigning a negative weight to the local value is able to fully regularize certain material models when standard nonlocal enhancement fails to do so a plastic damage model for concrete is formulated with this over nonlocal enhancement via the gradient approach and the full regularizing capabilities demonstrated

on network coding for sum networks a directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources we call such a network a sum network it is shown that there exists a solvably and linear solvably equivalent sum network for any multiple unicast network and thus for any directed acyclic communication network it is also shown that there exists a linear solvably equivalent multiple unicast network for every sum network it is shown that for any set of polynomials having integer coefficients there exists a sum network which is scalar linear solvable over a finite field f if and only if the polynomials have a common root in f for any finite or cofinite set of prime numbers a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set the insufficiency of linear net work coding and unachievability of the network coding capacity are proved for sum networks by using similar known results for communication networks under fractional vector linear network coding a sum network and its reverse network are shown to be equivalent however under nonlinear coding it is shown that there exists a solvable sum network whose reverse network is not solvable

the inequality process as a wealth maximizing process abstract the one parameter inequality process opip long predates the saved wealth model swm to which it is isomorphic up to the different choice of stochastic driver of wealth exchange both are stochastic interacting particle systems intended to model wealth and income distribution the opip and other versions of the inequality process explain many aspects of wealth and income distribution but have gone undiscussed in econophysics the opip is a jump process with a discrete 0 1 uniform random variate driving the exchange of wealth between two particles while the swm as an extension of the stochastic version of the ideal gas model is driven by a continuous uniform random variate with support at 0 0 1 0 the opip s stationary distribution is a levy stable distribution attracted to the pareto pdf near the hot upper bound of the opip s parameter and attracted to the normal gaussian pdf toward the cool lower bound of a gamma pdf model approximating the opip s stationary distribution is heuristically derived from the solution of the opip the approximation works for 5 better as 0 the gamma pdf model has parameters in terms of the inequality process with distributed omega ipdo is a generalization of the opip in the ipdo each particle can have a unique value of its parameter i e particle i has i the meta model of the inequality process implies that smaller is associated with higher skill level among workers this hypothesis is confirmed in a test of the ipdo particle wealth gain or loss in the opip and ipdo is more clearly asymmetric than in the swm 0 time reversal asymmetry follows from asymmetry of gain and loss while the ipdo scatters wealth it also transfers wealth from particles with larger to those with smaller particles that according to the ipdo s meta model are more productive of wealth nourishing wealth production the smaller the harmonic mean of the i s in the ipdo population of particles the more wealth is concentrated in particles with smaller the less noise and the more signal there is in particle wealth and the deeper the time horizon of the process the ipdo wealth concentration mechanism is simpler than maxwell s demon

the κ generalized distribution a new descriptive model for the size distribution of incomes this paper proposes the generalized distribution as a model for describing the distribution and dispersion of income within a population formulas for the shape moments and standard tools for inequality measurement such as the lorenz curve and the gini coefficient are given a method for parameter estimation is also discussed the model is shown to fit extremely well the data on personal income distribution in australia and in the united states c 2008 elsevier b v all rights reserved

network coding for computing cut set bounds the following network computing problem is considered source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function f of the messages the objective is to maximize the average number of times f can be computed per network usage i e the computing capacity the network coding problem for a single receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver for network coding with a single receiver routing is known to achieve the capacity by achieving the network min cut upper bound we extend the definition of min cut to the network computing problem and show that the min cut is still an upper bound on the maximum achievable rate and is tight for computing using coding any target function in multi edge tree networks it is also tight for computing linear target functions in any network we also study the bound s tightness for different classes of target functions in particular we give a lower bound on the computing capacity in terms of the steiner tree packing number and a different bound for symmetric functions we also show that for certain networks and target functions the computing capacity can be less than an arbitrarily small fraction of the min cut bound

reversible and irreversible information networks it is shown that there exist information networks where messages can be sent utilizing network coding more easily in one direction than in the opposite direction this is valid even though each channel is assumed to have the same capacity in both directions it is shown that irreversible information networks only have solutions that use nonlinear network coding this correspondence argues that this result is more surprising than it might appear at first sight and that it follows using ideas resembling the path integral in quantum mechanics

average is over abstract the popular perception of statistical distributions is depicted by the iconic bell curve which comprises of a massive bulk of middle class values and two thin tails one of small left wing values and one of large right wing values the shape of the bell curve is unimodal and its peak represents both the mode and the mean thomas friedman the famous new york times columnist recently asserted that we have entered a human era in which average is over in this paper we present mathematical models for the phenomenon that friedman highlighted while the models are derived via different modeling approaches they share a common foundation inherent tipping points cause the models to phase shift from a normal bell shape statistical behavior to an anomalous statistical behavior the unimodal shape changes to an unbounded monotone shape the mode vanishes and the mean diverges hence i there is an explosion of small values ii large values become super large iii middle class values are wiped out leaving an infinite rift between the small and the super large values and iv average is over indeed

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

nonreversibility and equivalent constructions of multiple unicast networks we prove that for any finite directed acyclic network there exists a corresponding multiple unicast network such that for every alphabet each network is solvable if and only if the other is solvable and for every finite field alphabet each network is linearly solvable if and only if the other is linearly solvable the proof is constructive and creates an extension of the original network by adding exactly s 5m r 1 new nodes where in the original network m is the number of messages r is the average number of receiver nodes demanding each source message and s is the number of messages emitted by more than one source the construction is then used to create a solvable multiple unicast network which becomes unsolvable over every alphabet size if all of its edge directions are reversed and if the roles of source receiver pairs are reversed

investigating equality the renyi spectrum an equality index is a score quantifying the socioeconomic egalitarianism of the distribution of wealth in human societies the score takes values in the unit interval with the unit upper bound characterizing purely communist societies in this paper we explore the renyi spectrum a continuum of equality indices that i is based on the moments of the societies distributions of wealth ii unifies various measures of socioeconomic inequality including the theil and atkinson indices iii displays a collection of amicable analytic properties iv admits multiple renyi divergence representations and v provides a high resolution gauging of egalitarianism that is way beyond what can be offered by the common practice measures of socioeconomic inequality the gini and pietra indices at large the renyi spectrum is applicable in the context of any distribution of non negative sizes with a positive mean yielding a high resolution gauging of the distribution s inherent statistical heterogeneity

linear network codes and systems of polynomial equations if beta and gamma are nonnegative integers and f is a field then a polynomial collection p1 hellip pbeta sube z alpha1 hellip alphagamma is said to be solvable over f if there exist omega1hellip omegagamma isin f such that for all i 1 hellip beta we have pi omega1hellip omegagamma 0 we say that a network and a polynomial collection are solvably equivalent if for each field f the network has a scalar linear solution over f if and only if the polynomial collection is solvable over f koetter and medard s work implies that for any directed acyclic network there exists a solvably equivalent polynomial collection we provide the converse result namely that for any polynomial collection there exists a solvably equivalent directed acyclic network hence the problems of network scalar linear solvability and polynomial collection solvability have the same complexity the construction of the network is modeled on a matroid construction using finite projective planes due to maclane in 1936 a set psi of prime numbers is a set of characteristics of a network if for every q isin psi the network has a scalar linear solution over some finite field with characteristic q and does not have a scalar linear solution over any finite field whose characteristic lies outside of psi we show that a collection of primes is a set of characteristics of some network if and only if the collection is finite or co finite two networks n and n are is equivalent if for any finite field f n is scalar linearly solvable over f if and only if n is scalar linearly solvable over f we further show that every network is ls equivalent to a multiple unicast matroidal network

a dichotomy of functions f x y of correlated sources x y consider separate encoding of correlated sources x n x l cdots x n y n y l cdots y n for the decoder to reliably reproduce a function f x i y i n i 1 we establish the necessary and sufficient condition for the set of all achievable rates to coincide with the slepian wolf region whenever the probability density p x y is positive for all x y

nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity viscoplasticity and damage the construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the helmholtz free energy function of the constitutive material model the combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator within the small strain framework the choice of a quadratic potential w r t the gradient term provides the widely used helmholtz operator whose regularization properties are well known smoothing of discontinuities at interfaces and boundary layers in hardening materials and finite width localization bands in softening materials the objective is to review and propose nonlinear extensions of micromorphic and strain damage gradient models along two lines the first one introducing nonlinear relations between generalized stresses and strains the second one envisaging several classes of finite deformation model formulations the generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach additive split of some lagrangian strain measure or choice of a local objective rotating frame three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient a new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

function computation through a bidirectional relay we consider a function computation problem in a three node wireless network nodes a and b observe two correlated sources x and y respectively and want to compute a function f x y to achieve this nodes a and b send messages to a relay node c at rates r a and r b respectively the relay c then broadcasts a message to a and b at rate r c we allow block coding and study the achievable region of rate triples under both zero error and epsilon error as a preparation we first consider a broadcast network from the relay to a and b a and b have side information x and y respectively the relay node c observes both x and y and broadcasts an encoded message to a and b we want to obtain the optimal broadcast rate such that a and b can recover the function f x y from the received message and their individual side information x and y respectively for this problem we show equivalence between epsilon error and zero error computations this gives a rate characterization for zero error computation as a corollary this also gives a rate characterization for the relay network under zero error for a class of functions called component wise one to one functions when the support set of p xy is full for the relay network the zero error rate region for arbitrary functions is characterized in terms of graph coloring of some suitably defined probabilistic graphs we then give a single letter inner bound to this rate region furthermore we extend the graph theoretic ideas to address the epsilon error problem and obtain a single letter inner bound

measuring statistical heterogeneity the pietra index abstract there are various ways of quantifying the statistical heterogeneity of a given probability law statistics uses variance which measures the law s dispersion around its mean physics and information theory use entropy which measures the law s randomness economics uses the gini index which measures the law s egalitarianism in this research we explore an alternative to the gini index the pietra index which is a counterpart of the kolmogorov smirnov statistic the pietra index is shown to be a natural and elemental measure of statistical heterogeneity which is especially useful in the case of asymmetric and skewed probability laws and in the case of asymptotically paretian laws with finite mean and infinite variance moreover the pietra index is shown to have immediate and fundamental interpretations within the following applications renewal processes and continuous time random walks infinite server queueing systems and shot noise processes financial derivatives the interpretation of the pietra index within the context of financial derivatives implies that derivative markets in effect use the pietra index as their benchmark measure of statistical heterogeneity

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

measuring statistical evenness a panoramic overview motivated by the question how equal is the distribution of wealth within a given human population economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the lorenz curve and the following indices gini pietra hoover amato hirschman theil and atkinson these quantitative measures considered in the broader context of general data sets with positive values are in effect general gauges of statistical evenness while the application of gini s index grew beyond economics and reached diverse fields of science the aforementioned evenness toolbox has largely remained within the confines of the social sciences the aim of this paper is to expose this evenness toolbox to the physics community by presenting a comprehensive evenness based approach to a fundamental problem in science the measurement of statistical heterogeneity

an evaluation of higher order plasticity theories for predicting size effects and localisation conventional plasticity theories are unable to capture the observed increase in strength of metallic structures with diminishing size they also give rise to ill posed boundary value problems at the onset of material softening in order to overcome both deficiencies a range of higher order plasticity theories have been formulated in the literature the purpose of this paper is to compare existing higher order theories for the prediction of a size effect and the handling of localisation effects to this end size effect predictions for foils in bending are compared with existing experimental data furthermore a study of one dimensional harmonic incremental solutions from a uniform reference state allows one to assess the nature of material localisation as predicted by these competing higher order theories these analyses show that only one of the theories considered the fleck hutchinson strain gradient plasticity theory based upon the toupin mindlin strain gradient framework fleck n a hutchinson j w 1997 strain gradient plasticity adv appl mech 33 295 361 allows one to describe both phenomena the other theories show either nonphysical size effects or a pathologically localised post peak response

computation in multicast networks function alignment and converse theorems the classical problem in a network coding theory considers communication over multicast networks multiple transmitters send independent messages to multiple receivers that decode the same set of messages in this paper computation over multicast networks is considered each receiver decodes an identical function of the original messages for a countably infinite class of two transmitter two receiver single hop linear deterministic networks the computation capacity is characterized for a linear function modulo 2 sum of bernoulli sources a new upper bound is derived that is tighter than cut set based and genie aided bounds a matching inner bound is established via the development of a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality the decomposition theorem provides a conceptually simple proof of achievability that generalizes to l transmitter l receiver networks

on base field of linear network coding for a single source multicast network the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field in this paper we design a new class mathcal n of multicast networks and obtain an explicit formula for the linear solvability of these networks which involves the associated coset numbers of a multiplicative subgroup in a base field the concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size it further facilitates us to unveil infinitely many new multicast networks linearly solvable over gf q but not over gf q with q based on a subgroup order criterion in particular 1 for every k geq 2 an instance in mathcal n can be found linearly solvable over gf 2 2k but not over gf 2 2k 1 and 2 for arbitrary distinct primes p and p there are infinitely many k and k such that an instance in mathcal n can be found linearly solvable over gf p k but not over gf p k with p k

finite strain logarithmic hyperelasto plasticity with softening a strongly non local implicit gradient framework this paper addresses the extension of a eulerian logarithmic finite strain hyperelasto plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material it is shown that a logarithmic elasto plastic model with a strongly non local degrading yield stress exactly preserves the structure of its infinitesimal counterpart the strongly non local nature of the model makes it an attractive framework for the numerical solution of softening plasticity problems consistent constitutive tangent operators are derived for the particular case of hyperelasto j2 plasticity which are exactly equal to the corresponding infinitesimal tangent operators the finite element implementation along with the geometrically nonlinear contributions and the incremental solution strategy is outlined a benchmark example is solved illustrating the main differences between the purely elasto plastic case and the case with plastic damage finally the main model characteristics and its practical use are emphasized

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

exact repair mds code construction using interference alignment the high repair cost of n k maximum distance separable mds erasure codes has recently motivated a new class of mds codes called repair mds codes that can significantly reduce repair bandwidth over conventional mds codes in this paper we describe n k d exact repair mds codes which allow for any failed node to be repaired exactly with access to d survivor nodes where k d n 1 we construct exact repair mds codes that are optimal in repair bandwidth for the cases of k n 1 2 and d 2k 11 b k 3 our codes are deterministic and require a finite field size of at most 2 n k our constructive codes are based on interference alignment techniques

an ordered family of lorenz curves abstract a general method for building parametric functional families of lorenz curves generated from an initial lorenz curve which satisfies some regularity conditions is presented it is shown that these families can be ordered in a manner which leads to a hierarchy of lorenz curves the method starts from a generating lorenz curve l 0 p and builds the family by increasing the number of parameters which can be easily interpreted in terms of the elasticities of l 0 p the method is applied to a family we term the pareto family since they use the pareto lorenz curves as their generating curves the family is shown to contain an important number of classical lorenz curves used in the existing literature several properties of this family are analyzed these include the population function inequality measures and lorenz orderings a general method for the estimation of these family is given and applied to the pareto family finally an application is presented for data from various countries the results are very robust across data sources the pareto models fit very well in a number of applications

a class of non linearly solvable networks for each positive composite integer m a network is constructed which is solvable over an alphabet of size m but is not solvable over any smaller alphabet these networks have no linear solutions over any module alphabets and are not asymptotically linearly solvable over any finite field alphabets the networks capacities are all shown to equal one and their linear capacities are all shown to be bounded away from one for all finite field alphabets in addition if m is a non power of prime composite number then such a network is not solvable over any prime power size alphabet

polynomial time algorithms for multicast network code construction the famous max flow min cut theorem states that a source node s can send information through a network v e to a sink node t at a rate determined by the min cut separating s and t recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re encode the information they receive we demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed we give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity we extend these algorithms to integer capacities and to codes that are tolerant to edge failures

an implicit tensorial gradient plasticity model formulation and comparison with a scalar gradient model many rate independent models for metals utilize the gradient of effective plastic strain to capture size dependent behavior this enhancement sometimes termed as explicit gradient formulation requires higher order tractions to be imposed on the evolving elasto plastic boundary and the resulting numerical framework is complicated an implicit scalar gradient model was thus developed in peerlings peerlings r h j 2007 on the role of moving elastic plastic boundaries in strain gradient plasticity model simul mater sci eng 15 109 120 that has only c0 continuity requirements and its implementation is straightforward however both explicit and implicit scalar gradient models can be problematic when the effective plastic strains do not have smooth profiles to address this limitation an implicit tensorial gradient model is proposed in this paper based on the generalized micromorphic framework it is also demonstrated that the scalar and tensorial implicit gradient models give similar results when the effective plastic strains fluctuate smoothly

the sociogeometry of inequality part ii abstract the study of socioeconomic inequality is of prime economic and social importance and the key quantitative gauges of socioeconomic inequality are lorenz curves and inequality indices the most notable of the latter being the popular gini index in this series of papers we present a sociogeometric framework to the study of socioeconomic inequality in this part we focus on the gap between the rich and the poor which is quantified by gauges termed disparity curves we shift from disparity curves to disparity sets define inequality indices in terms of disparity sets and introduce and explore a collection of distance based and width based inequality indices stemming from the geometry of disparity sets we conclude with mean absolute deviation mad representations of the inequality indices established in this series of papers and with a comparison of these indices to the popular gini index

a generalization of the beta distribution with applications abstract this paper introduces a five parameter beta distribution gb which nests the generalized beta and gamma distributions and includes more than thirty distributions as limiting or special cases the generalized beta leads to an exponential generalized beta egb distribution which includes generalized forms of the logistics exponential gompertz and gumbell distributions and the normal as special cases the egb family of distributiosn provides the basis for partially adaptive estimation of econometric models with possibly skewed and leptokurtic error distributions applications of the models to investigating the distribution of income stock returns and in regression analysis are considered

probabilistic analysis of global performances of diagnostic tests interpreting the lorenz curve based summary measures several indices based on the receiver operating characteristic curve roc curve have previously been found to possess probabilistic interpretations however these interpretations are based on some unrealistic diagnostic scenarios in this paper the author presents a new approach using the lorenz curve the author found that the summary indices of the lorenz curve that is the pietra index and the gini index can be interpreted in several ways average change in post test probability per cent maximum prognostic information and probability of correct diagnosis these interpretations have a close tie with real world medical diagnosis suggesting that these indices are proper measures of test characteristics

inequality indicators and distinguishability in economics abstract money has a material counterpart such as banknotes or coins and an ideal expression monetary units in the latter case it is boson like individual incomes have no a priori limit and their units are not distinguishable from each other in economic processes individuals on the other hand usually occupy one job at a time which makes them akin to fermions we apply to individual incomes down to earth statistical calculations similar to those for quantum particles and obtain expressions for the cumulative distribution function probability density and lorenz function resulting from the simultaneous use of both statistics they provide extremely good fits to corresponding data on french income distributions on this basis we propose a new entropic inequality indicator

beyond lognormal inequality the lorenz flow structure abstract observed from a socioeconomic perspective the intrinsic inequality of the lognormal law happens to manifest a flow generated by an underlying ordinary differential equation in this paper we extend this feature of the lognormal law to a general lorenz flow structure of lorenz curves objects that quantify socioeconomic inequality the lorenz flow structure establishes a general framework of size distributions that span continuous spectra of socioeconomic states ranging from the pure communism extreme to the absolute monarchy extreme this study introduces and explores the lorenz flow structure analyzes its statistical properties and its inequality properties unveils the unique role of the lognormal law within this general structure and presents various examples of this general structure beyond the lognormal law the examples include the inverse pareto and pareto laws which often govern the tails of composite size distributions

about the modified gaussian family of income distributions with applications to individual incomes abstract in a recent paper in this journal q guo l gao distribution of individual incomes in china between 1992 and 2009 physica a 391 2012 5139 5145 a new family of distributions for modeling individual incomes in china was proposed this family is the so called modified gaussian mg distribution which depends on two parameters the mg distribution shows a satisfactory fit for the individual income data between 1992 and 2009 however for the practical use of this model with individual incomes it is necessary to know its probabilistic and statistical properties especially the corresponding inequality measures in this paper probabilistic functions and inequality measures of the mg distribution are obtained in closed form including the normalizing constant probability functions moments first degree stochastic dominance conditions relationships with other families of distributions and standard tools for inequality measurement lorenz and generalized lorenz curves and gini donaldson weymark kakwani and pietra indices several methods for parameter estimation are also discussed in order to illustrate all the previous formulations we have fitted individual incomes of spain for three years using the european community household panel survey concluding a static pattern of inequality since the gini index and other inequality measures remain constant over the study period

explicit expressions of the pietra index for the generalized function for the size distribution of income abstract the importance of the pietra index in socioeconomic systems and econophysics has been highlighted by eliazar and sokolov 2010 in this paper we obtain closed expressions for the pietra index for the generalized function for the size of income proposed by mcdonald 1984 this family is composed of three classes of distributions the generalized gamma distribution gg the generalized beta of the first kind gb1 and the generalized beta of the second kind gb2 for the different distributions we obtain closed and simple expressions of the pietra index which can be easily computed we also obtain the pietra index for other relevant income models including finite mixtures of distributions and the generalized distribution clementi et al 2008 finally two empirical applications with real income data are given

measuring social inequality with quantitative methodology analytical estimates and empirical data analysis by gini and k indices abstract social inequality manifested across different strata of human existence can be quantified in several ways here we compute non entropic measures of inequality such as lorenz curve gini index and the recently introduced k index analytically from known distribution functions we characterize the distribution functions of different quantities such as votes journal citations city size etc with suitable fits compute their inequality measures and compare with the analytical results a single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data and fit better to two distinct functions with a single crossover point here we provide general formulas to calculate these inequality measures for the above cases we attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures regarding the k index as an extra dimension both the lower and upper bounds of the gini index are obtained as a function of the k index this type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices