understanding the molecular machinery that regulates development of multicellular organisms is among the most fascinating problems of modern science. today , a growing experimental record about the regulatory mechanisms involved in development is accumulating , in particular in well - studied model - organisms as , e.g. , _ drosophila _ or _ hydra _ .still , the genomic details known today are not sufficient to derive dynamical models of developmental gene regulation processes in full detail .phenomenological models of developmental processes , on the other hand , are well established today .pioneering work in this field was done by turing , who in his seminal paper in 1952 considered a purely physico - chemical origin of biological pattern formation .his theory is based on an instability in a system of coupled reaction - diffusion equations . in this type of model , for certain parameter choices , stochastic fluctuations in the initial conditionscan lead to self - organization and maintenance of spatial patterns , e.g.  concentration gradients or periodic patterns .this principle has been successfully applied to biological morphogenesis in numerous applications . however , as current experiments make us wonder about the astonishingly high complexity of single regulating genes in development , they also seem to suggest that diffusion models will not be able to capture all details of developmental regulation , and point at a complex network of regulating interactions instead .the role of information processing in gene regulatory networks during development has entered the focus of theoretical research only recently .one pioneering study was published by jackson et al . in 1986 , who investigated the dynamics of spatial pattern formation in a system of locally coupled , identical dynamical networks . in this model ,gene regulatory dynamics is approximated by boolean networks with a subset of nodes communicating not only with nodes in the ( intracellular ) network , but also with some nodes in the neighboring cells .boolean networks are minimal models of information processing in network structures and have been discussed as models of gene regulation since the end of the 1960s .the model of jackson et al .  demonstrated the enormous pattern forming potential of local information processing , similar to _ direct contact induction _ as known in developmental biology .more recently , salazar - ciuadad et al . introduced a gene network model based on continuous dynamics and coupling their networks by direct contact induction .interestingly , they observe a larger variety of spatial patterns than turing - type models with diffusive morphogens , and find that patterns are less sensitive to initial conditions , with more time - independent ( stationary ) patterns .this matches well the intuition that networks of regulators have the potential for more general dynamical mechanisms than diffusion driven models .let us here therefore study interacting networks in pattern formation and in particular consider information - transfer - based processes . in , we introduced a simple stochastic cellular automata model of spatial pattern formation based on local information transfer , that performs de novo pattern formation by generating and regulating a domain boundary . in the followingwe will study how this very general mechanism could emerge as a result of interacting nodes in coupled identical networks , similar to gene regulation networks in interacting cells .the goal of this paper is twofold : first we will explore ways to map the earlier cellular automata model , onto dynamical networks ( boolean networks and threshold networks ) , motivated by the general observation of gene regulation networks in biological development ( section iii ) .secondly , we will give a more detailed account of the basic underlying mechanism , focusing on the stochastic dynamics ( section iv ) and on how the model was developed using a genetic algorithm ( appendix ) : in section iv , the statistical mechanics of noise - induced dynamics is studied in detail .numerical evidence for a first order phase transition at vanishing noise rate is given .a master equation for boundary readjustments is formulated and solved in the continuum limit .robustness against cell flow is studied numerically and in a mean field approximation . in the appendix ,the genetic algorithm applied for identification of model solutions is explained and statistical properties of different solutions are compared .let us first motivate and define the morphogenetic problem that we will use as a test case .then we undertake a three - step approach to find a genetic network model that solves this pattern formation problem . in the first step ,we summarize the properties of the cellular automata model introduced in .cellular automata as dynamical systems discrete in time and state space are known to display a wide variety of complex patterns and are capable of solving complex computational tasks , including universal computation .we searched for solutions ( i.e. rule tables which solve the problem ) by aid of a genetic algorithm ( for details , see appendix ) .candidate solutions have to fulfill four demands : their update dynamics has to generate a spatial pattern which 1 ) obeys a predefined scaling ratio , 2 ) is independent of the initial condition chosen at random , 3 ) is independent of the system size ( i.e. the number of cells ) and 4 ) is stationary ( a fixed point ) . in the second step ,this cellular automata rule table is `` translated '' into ( spatially coupled ) boolean networks , using binary coding of the cellular automata states .the logical structure of the obtained network is reduced to a minimal form , and then , in step three , translated into a threshold network .   a classical model organism for studies of position dependent gene activation is the fresh water polyp _ hydra _ , which has three distinct body regions - a head with mouth and tentacles , a body column and a foot region .the positions of these regions are accurately regulated along the body axis .the problem we shall focus on is sketched schematically in fig .[ hydraped ] for the example of the `` foot '' genes _pedibin _ and _ cn - nk2 _ .cn - nk2 is active only in the lowest foot region , the expression domain of pedibin extends a bit more towards the rump region , where it is turned off at some point , i.e.  the domain shows a sharp boundary .the relative position of the boundary is almost independent of the animal s size , i.e. the ratio ( as denoted in fig .[ hydraped ] ) is almost invariant under changes of body size .as the pedibin / cn - nk2 system presumably plays an important role in determining the foot region , this invariance appears to be an essential prerequisite for maintaining the correct body proportions ( proportion regulation ) and to establish the head - foot polarity .such regulation of position information is a quite general problem in biological development .an interesting problem is how the specific properties of this regulation can be achieved by a small network of regulatory genes and if so , whether local communication between the cells ( networks ) is sufficient .this basic question is the central motivation for the present study .in particular , we consider the simplified problem of regulating one domain as , for example , the foot region versus the rest of the body .we consider this as a one dimensional problem as first approximation to the well - defined head - foot - axis in _hydra_.  = n y  = n y  developmental processes exhibit an astonishing robustness .this often includes the ability of de novo pattern formation , e.g. , to regenerate a _hydra _ even after complete dissociation of the cell ensemble in a centrifuge .further , they are robust in the face of a steady cell flux : _ hydra _ cells constantly move from the central body region along the body axis towards the top and bottom , where they differentiate into the respective cell types according to their position on the head - foot axis .the global pattern of gene activity is maintained in this dynamic environment .let us take these observations as a starting point for a detailed study how the interplay of noise - induced regulatory dynamics and cell flow may stabilize a developmental system .   to define a model system that performs the pattern formation task of domain self - organization ,consider a one - dimensional cellular automaton with parallel update . cells are arranged on a one - dimensional lattice , and each cell is labeled uniquely with an index .each cell can take possible states .the state of cell is a function of its own state and of its neighbor s states and at time , i.e. \ ] ] with ( a cellular automaton with _neighborhood 3 _ ) . at the system boundaries , for simplicity we choose a discrete analogue of zero flux boundary conditions ,i.e. we set .other choices , e.g. asymmetric boundaries with cell update depending only on the inner neighbor cell , lead to similar results .the state evolution of course strongly depends on the choice of : for a three - state cellular automaton ( ) , there are possible update rules , each of which has a unique set of dynamical attractors .as we will show in the results section , is the minimal number of states necessary to solve the pattern formation problem formulated above .now we can formulate the problem we intend to solve as follows : find a set of functions ( update rules ) which , given a random initial vector , within update steps evolves the system s dynamics to a fixed point attractor with the property : \\\sigma_i \ne 2 \quad if \quad i \ge [ \alpha\cdot n_c ] \end{array}\right.\ ] ] where $ ] is the gauss bracket. the scaling parameter may take any value . for simplicity ,it is fixed here to .notice that does not depend on , i.e. we are looking for a set of solutions where the ratio of the domain sizes is _ invariant under changes of the system size_. this clearly is a non - trivial task when only local information transfer is allowed .the ratio is a _global property _ of the system , which has to emerge from purely local ( next neighbor ) interactions between the cell s states .one can now take a step further towards biological systems , by transferring the dynamics we found for a cellular automata chain onto cells in a line that communicate with each other , similar to biological cells .identifying states with cell types and assuming that the model cells have a network of regulators inside , each of them capable to reproduce the rules of a cellular automaton , we obtain a model mimicking basic properties of a biological genetic network in development .cellular automata rule tables can easily be translated into logical ( boolean ) networks , e.g. , for , two internal nodes can be used for binary coding of the cell states .one then has with .the so obtained rule tables are , by application of boolean logic , transformed into a minimized _ conjunctive normal form _ , which only makes use of the the three logical operators not , and and or with a minimal number of and operations .this is a rather realistic assumption for gene regulatory networks , as the and operation is more difficult to realize on the basis of interactions between transcription factors .other logical functions as , e.g. , xor , are even harder to realize biochemically .the structure of the constructed network and its biological interpretation is shown in fig .note that the up - down symmetry of the body axis is broken locally by a spatially asymmetric receptor distribution .perhaps the simplest model for transcriptional regulation networks are threshold networks , a subset of boolean networks , where logical functions are modeled by weighted sums of the nodes input states plus a threshold  .they have proven to be valuable tools to address questions associated to the dynamics and evolution of gene regulatory networks .any boolean network which has been reduced to its minimized form ( here , the conjunctive normal form ) , can be coded as a dynamical threshold network , with minimally three hierachies of information processing ( `` input layer '' : signals from the neighbor cells at time , `` hidden layer '' : logical processing of the signals , `` output layer '' : states of the two `` pattern genes '' in cell at time ) .the genes states now may take values , and likewise for the interaction weights one has for activating and inhibiting regulation , respectively , and if gene i does not receive an input from gene in cell .the dynamics then is defined as with for the `` hidden '' genes , where is the state of the _ output _ gene in cell ( there are no couplings between the genes in the `` hidden '' layer ) . the threshold is given by which implements a logical or operation .for the `` output '' ( pattern forming ) genes , one simply has .e. the weights are all set to one , and the ( negative ) threshold equals the number of inputs that gene receives from the `` hidden '' genes ( logical and ) .the first major outcome of the cellular automata model is that a number of different states is necessary and sufficient for this class of systems to solve the given pattern formation task .the update table of the fittest solution found during optimization runs , which solves the problem independent of system size for about 98 percent of ( randomly chosen ) initial conditions ( i.e. has fitness ) , is shown in table i. fig .[ ca1 g ] shows the typical update dynamics of this solution .the finite size scaling of the self - organized relative domain size as a function of the the number of cells is shown in fig .[ ndep ] . in the limit of large system sizes, converges towards the variance of vanishes with a power of , i.e. the relative size of fluctuations induced by different initial conditions becomes arbitrarily small with increasing system size .hence , the pattern self - organization in this system exhibits considerable robustness against fluctuations in the initial conditions .the main mechanism leading to stabilization at is a modulation of the traveling velocity of the right phase boundary in fig . 2 such that the boundary on average moves slightly more than one cell to the left per update step , whereas the left boundary moves one cell to the right exactly every third update step .the modulation of the right boundary can be seen as the result of interacting phase boundaries reminiscent of particle interactions .this picture of `` particle computation '' is a useful concept also in various other contexts .= n y  .rule table of most successful best cellular automata solution found during genetic algorithm search . in the left column ,the rule table index is shown , running from 0 to 26 , in the middle column the three input states at time are shown , the right column shows the corresponding output states at time . [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ]   =in the following we will study dynamics and robustness of the model with respect to noise .two kinds of perturbations frequently occur : stochastic update errors and external forces cased by a directed _ cell flow _due to cell proliferations .both types of perturbations are very common during animal development , e.g. , in _ hydra _ cells continuously move from the central body region along the body axis towards the top and bottom , and differentiate into the respective cell types along the way according to their position on the head - foot axis .let us define stochastic update errors with probability per cell , leading to an average error rate .interestingly , this stochastic noise starts moving `` particle '' excitations in the cellular automaton which , as a result indeed stabilize the developmental structure of the system . to prepare for the details of these effects ,define first how we measure the boundary position properly in the presence of noise .let us use a statistical method to measure the boundary position in order to get conclusive results also for high : starting at , we put a `` measuring frame '' of size over cell and the next cells , move this frame to the right and , for each , measure the fraction of cells with state within the frame .the algorithm stops when drops below and the boundary position is defined to be .it is easy to see that , for not too high , there are only two different quasi - particles ( i.e. state perturbations moving through the homogeneous phases ) , as shown in fig .[ particles ] . in the following ,these particles are called and .the particle is started in the phase by a stochastic error at some ) , moves to the right and , when reaching the domain boundary , readjusts it two cells to the left of its original position .the particle is started in the phase by a stochastic error at some and moves to the left .interaction with the domain boundary readjusts it one cell to the right .thus we find that the average position of the boundary is given by the rate equation i.e. .interestingly , for not too high error rates , is independent from and thus from .if we consider the average boundary position as a system - specific _ order parameter _ which is controlled by the two quasi - particles , then comparing the solution of eqn .( [ rate ] ) to the equilibrium position in the noiseless case indicates that the system undergoes a first order phase transition with respect to at .= n y  = n y  = n y  figs . [ pt0shift ] and[ pt0scal ] show noise dependence and finite size scaling of the transition . in case of a first order phase transition at , we would expect a shift of the transition point towards which is proportional to as well as a divergence of the slope at the transition point when is increased , i.e. when .the shift of is most easily measured by defining a lower and a upper boundary and , respectively ( fig .[ pt0shift ] ) ; when crosses these boundaries , two transition points and are obtained .we find that and with as expected ( fig .[ pt0scal ] ) , which implies that the difference scales as hence , because , indeed diverges when the sampling window size goes to infinity .the solution is stable only for . as shown in fig .[ particles ] , the interaction of a particle with the boundary needs only one update time step , whereas the boundary readjustment following a particle interaction takes three update time steps .hence , we conclude that the term on the right hand side of eqn . ( 10 ) , which gives the flow rate of particles at the boundary , for large will saturate at , leading to with the solution for . hence , there is a crossover from the solution to another solution vanishing with around .the finite size scaling term can be estimated from the following consideration : for , the average domain size created by `` pure chance '' is given by .if the measuring window has size , we obtain .to summarize , we find that the self - organized boundary position is given by with a first - order phase transition at and a crossover around .now let us consider the fluctuations of around given by the master equation with .( 15 ) determines the probability to find the boundary at position at update time step , given its position at time .this equation can be simplified as we are interested only in the _ stationary probability distribution _ of .it is easy to see that the error rate just provides a time scale for relaxation towards the stationary distribution and has no effect on the stationary distribution itself .therefore , we may consider the limit , divide through and neglect the last three terms on the right handside of eqn .( 14 ) ( which become zero in this limit ) .we obtain to study this equation , we consider the continuum limit .let us introduce the scaling variables , and the probability density . inserting these definitions into eqn .( 16 ) and ignoring all subdominant powers , we obtain a fokker - planck equation : the stationary solution of this equation is given by },\ ] ] i.e. in the long time limit , the probability density for the boundary position is a gaussian with mean : }.\ ] ] from eqn .( 18 ) we see that the variance of vanishes and the relative boundary position becomes sharp in the limit of large system sizes .[ fluct ] shows that this continuum approximation for provides very good correspondence with the numerically obtained probability distributions .the stochastic nature of boundary stabilization under noise is also reflected by the probability distribution of _ waiting times _ for boundary readjustments due to particle interactions : the particle production is a poisson process with the parameter and the waiting time distribution is given by with an average waiting time .[ wait ] shows the waiting time distributions for different error rates .= n y  in a biological organism , a pattern has to be robust not only with respect to dynamical noise , but also with respect , e.g. , to `` mechanical '' perturbations . in _ hydra _ , e.g. ,there is a steady flow of cells directed towards the animal s head and foot , due to continued proliferation of stem cells ; the stationary pattern of gene activity is maintained is spite of this cell flow .let us now study the robustness of the model with respect to this type of perturbation .let us consider a constant cell flow with rate , which is directed towards the left or the right system boundary . in eqn .( 9 ) , we now get an additional drift term on the left hand side : with the solution for the case of cell flow directed towards the left system boundary ( plus sign in eqn .( [ 20 ] ) ) .one observes that undergoes a second order phase transition at the critical value .below , the domain size vanishes , and above it grows until it reaches the value of the system without cell flow . for cell flowdirected towards the right system boundary ( minus sign in eqn .( [ 20 ] ) ) , we obtain in this case , the critical cell flow rate is given by , for cell flow rates larger than this value the -domain extends over the whole system , i.e.  .= n y  fig .[ cnflow ] compares the results of numerical simulations with the mean field approximation of eqn .( [ 20 ] ) . in numerical simulations , cell flowis realized by application of the translation operator to all cells with every time steps and leaving unchanged . in case of cell flow directed to the right system boundary , in the limit the boundary position detected in numerical simulations deviates from the mean field prediction , due to a boundary effect at the left system boundary ( stochastic production of finite lifetime stationary oscillators , leading to intermittent flows of particles through the system ) .  to summarize this part, we see that in the model stochastic errors in dynamical updates for indeed _ stabilize _ the global pattern against the mechanical stress of directed cell flow .in this paper we considered the dynamics of pattern formation motivated by animal morphogenesis and the largely observed participation of complex gene regulation networks in their coordination and control .we therefore chose a simple developmental problem to study toy models of interacting networks that control pattern formation and morphogenesis in this setting .in particular , the goal was to explore how networks can offer additional mechanisms beyond the standard diffusion based process of the turing instability .our results suggest that main functions of morphogenesis can be performed by dynamical networks without relying on diffusive biochemical signals , but using local signaling between neighboring cells .this includes solving the problem of generating global position information from purely local interactions .but also it goes beyond diffusion based models as it offers solutions to developmental problems that are difficult for such models and avoids their inherent problem of fine tuned model parameters. it may be not too far fetched to speculate that some developmental processes as , e.g. , the establishment of position information , may rely on this type of internal information processing rather than on interpretation of , e.g. , chemical gradients . as only ingredient to the present model , symmetry has to be broken locally by a spatially asymmetric receptor distribution , e.g. , as proposed in , to provide the necessary input information .also hybrid approaches are conceivable .for example such broken symmetry could be provided by a gradient , even without fine - tuning ( contrary to standard gradient - based models ) since only the direction of the gradient has to be read out .the network model derived here performs accurate regulation of position information and robust _ de novo _ pattern formation from random conditions , with a mechanism based on local information transfer rather than the turing instability .non - local information is transmitted through soliton - like quasi - particles instead of long - range gradients .two realizations as discrete dynamical networks , boolean networks and threshold networks , have been developed .the resulting networks have size and complexity comparable to developmental gene regulation modules as observed in animals , e.g. , _ drosophila _ or _ hydra _ . the threshold networks ( as models for transcriptional regulation networks ) process position information in a hierarchical manner ; in the present study , hierarchy levels were limited to three , but realizations with more levels of hierarchy , i.e. more `` pre - processing '' of information are also possible. similar hierarchical and modular organization are typical signatures of gene regulatory networks in organisms .robustness of the model is studied in detail for two types of perturbations , stochastic update errors ( noise ) and directed cell flow .a first order phase transition is observed for vanishing noise and a second order phase transition at increasing cell flow .fluctuations of the noise - controlled boundary position were studied numerically for finite size systems and analytically in the continuum limit .we find that the relative size of fluctuations vanishes with , which means that the boundary position becomes sharp in the limit of large system sizes .dynamics under cell flow is studied in detail numerically and analytically by a mean field approximation .a basic observation is that noise - induced perturbations act as quasi - particles that stabilize the pattern against the directed force of cell flow . at a critical cell flow rate, there is a second order phase transition towards a vanishing domain size or a domain extending over the whole system , depending on the direction of cell flow , respectively .several extensions of this model are conceivable . in the present model , the cell flow rate is considered as a free parameter , the global pattern , however , can be controlled easily by an appropriate choice of the error rate .this may suggest to extend the model by introduction of some kind of dynamical coupling between and , treating as a function of .interestingly , similar approaches have been studied by hogeweg and furusawa and kaneko : in both models of morphogenesis , the rate of cell divisions is controlled by cell differentiation and cell - to - cell signaling .dynamics in both models , however , is deterministic .an extension of our model as outlined above may open up for interesting studies how _ stochastic _ signaling events could control and stabilize a global expression pattern and cell flow as an integrated system .other possible extensions of the model concern the dimensionality : in two or three dimensions other mechanisms of symmetry breaking might be present , possibly leading to new , interesting dynamical effects .a java applet simulation of the model can be found at .we thank t.c.g .bosch , t.w .holstein , and u. technau for pointing us to current questions in hydra development . t.r . acknowledges financial support from the studienstiftung des deutschen volkes ( german national merit foundation ) .let us briefly recapitulate here how the rule table of the model has been obtained by the aid of a genetic algorithm .   in order to find a set of update rules that solve the problem as formulated in section ii , cellular automatahave been evolved using genetic algorithms .genetic algorithms are population - based search algorithms , which are inspired by the interplay of random mutations and selection as observed in biological evolution .starting from a randomly generated population of rule tables , the algorithm optimizes possible solutions by evaluating the fitness function - 1}\delta_{\sigma_i^n(t),2 } \right . \nonumber\\+ \sum_{i=[\alpha\cdot n_c]}^{n_c-1}\{1-\delta_{\sigma_i^n(t),2}\ } \right).\end{aligned}\ ] ] the optimization algorithm then is defined as follows :  1 .generate a random initial population  of rule tables .2 .  randomly assign system sizes to all rule tables .3 .  for each rule table , generate a random initial state vector .4 .  randomly mutate one entry of each rule table ( generating a population of mutants ) .iterate dynamics over time steps for and .evaluate and for all rule tables , averaging over the past update steps ( with an additional penalty term if does not converge to a fixed point ) .7 .  for each ,replace with , if .replace the least fit solution by a duplicate of the fittest one .9 .  go back to step 2 and iterate .the outcome of this search algorithm is a set of rule tables , which then can be `` translated '' into ( spatially coupled ) boolean networks or threshold networks with suitable thresholds .this yields a set of ( minimal ) dynamical networks which solve the pattern formation task by means of internal information processing .= n y  = n y  = n y   the genetic algorithm sketched above is run with the following parameter choices : , i.e. during ga runs the system size is varied randomly between and cells , and the population size is set to .[ evo ] shows the fitness of the highest fitness mutant and the average fitness of the population as a function of the number of successive mutation steps during optimization .a useful solution is found rather quickly ( after about 200 updates ) , with further optimization observed during futher 10000 generations . at timestep 10000 mutations are turned off , thus now the average fitness of the established population under random initial conditions and random fluctuations of the system size is tested .the average fitness indicates a surprisingly high robustness against fluctuations in the initial start pattern , indicating that the system is capable of _ de novo pattern formation_. in the `` fitness picture '' , fig .[ fitofn ] confirms that the dynamically regulated domain size ratio indeed is independent of system size ( proportion regulation ) , there is only a weak decay of the fitness at small values of .interestingly , one also observes that for regeneration of hydra polyps from random cell aggregates a minimum number of cells is required .the model suggests that this observation might be explained by the dynamics of an underlying pattern generating mechanism , i.e. that there has to be a minimum diversity in the initial condition for successful de novo pattern formation .an interesting question is how `` difficult '' it would be for an evolutionary process driven by random mutations and selection to find solutions for the pattern formation problem based on neighbor interactions between cells .as we showed above , the genetic algorithm finds the correct solution fast , however , this does not necessarily mean that biological evolution could access the same solution as fast .if there is only one , singular solution , evolution may never succeed finding it , as the genotype which already exists can not be modified in an arbitrary way without possibly destroying function of the organism ( _ developmental constrains _ ) . to illustrate this point, we generated an ensemble of different solutions with and performed a statistical analysis of the rule table structure .as one can see in fig .[ rulstat ] , some positions in the rule table are quite fixed , i.e. , there is not much variety in the outputs , whereas other positions are more variable .however , the output frequency distribution alone does not allow to really judge the `` evolvability '' of the solutions : if there are strong correlations between most of the rule table entries , evolutionary transitions from one solution to another would be almost impossible . to check this point , we studied statistical two point correlations between the rule table entries .the probability for finding state at position and state at rule table position is given by where is the kronecker symbol and runs over the statistical ensemble of size .the two point correlation between and then is defined as with and to obtain a proper normalization with respect to the two limiting cases of equal probabilities ( ) and for and for all other ) .[ rulcorr ] shows the frequency distribution of , averaged over all possible pairs .about 65% of rule table positions are strongly correlated ( ) , the rest shows correlation values between and .hence , we find that the space of solutions is restricted , nevertheless there is variability in several rule table positions . to summarize this aspect ,the pattern formation mechanism studied in this paper shows considerable robustness against rule mutations , however , a `` core module '' of rules is always fixed .interestingly , a similar phenomenon is observed in developmental biology : regulatory `` modules '' involved in developmental processes often are evolutionaryly very conservative , i.e. , they are shared by almost all animal phyla , while morphological variety is created by ( few ) taxon specific genes and `` rewiring '' of existing developmental modules .99 u. technau et al . , _ proc .( usa ) , * 97 * , 12127 ( 2000 ) .bosch , _ comp .biochem . and physiol .b _ , * 136 * , 185 ( 2003 ) .a.m. turing , _ phil .b _ , * 237 * , 37 ( 1952 ) . a. gierer and h. meinhardt , _ kybernetik _ * 12 * , 30 ( 1972 ) . h. meinhardt and a. gierer , _ bioessays _ * 22.8 * , 753 ( 2000 ) .bosch and k. khalturin , _canadian journal of zoology _ * 80 * , 1670 - 1677 ( 2002 ) .jackson , d. johnson and w.g .nash , _ j. theor. biol . _ * 119 * , 379 ( 1986 ) .kauffman , _* 22 * , 437 ( 1969 ) .kauffman , _ the origins of order : self - organization and selection in evolution _ , oxford university press , new york , 1993 .j. slack , _ mech .devel . _ * 41 * , 257 , 9100 - 9107 ( 1997 ) .i. salazar - ciudad , j. garcia - fernandez and r.v .j. theor .biol . _ * 205 * , ( 2000 ) .sole , i. salazar - ciuadad and j. garcia - fernandez , _ physica a _ * 305 * , 640 ( 2002 ) . t. rohlf and s. bornholdt , submitted ( 2003 ) ; cond - mat/0312366 . s. wolfram , _ rev ._ , * 55 * , 601 ( 1983 ) ; _ physica d _ , * 10 * , 1 ( 1984 ) ; _ nature _ ( london ) , * 311 * , 419 ( 1984 ) . s. thomsen , a. till , c. beetz , j. wittlieb , k. khalturin , and t.c.g. bosch , _ mech ._ , in press ( 2003 ). l. wolpert , _ j. theor_ , * 25 * , 37 ( 1952 ) .mller , pattern control in hydra : basic experiments and concepts . in : _experimental and theoretical advances in biological pattern formation _ , eds .othmer , p.k .maini , and j.d .murray , plenum press , new york ( 1993 ) .davidson , _ genomic regulatory systems .development and evolution ._ academic press ( 2001 ) .a. marciniac - czochra , _ j. biol .syst . _ * 11 * , 293 ( 2003 ) .krten , _ phys .a _ * 129(3 ) * , 157 ( 1988 ) . k.e .krten , _ j. phys .a _ * 1 21 * , l615-l619 ( 1988 ) .a. wagner , _ proc .usa _ * 91 * , 4387 - 4391 ( 1994 ) .s. bornholdt and k. sneppen , _ proc .r. soc .b _ * 267 * , 2281 - 2286 ( 2000 ) .s. bornholdt and t. rohlf , _ phys .lett . _ * 84 * , 6114 ( 2000 ) .t. rohlf and s. bornholdt , _ physica a _ * 310 * , 245 ( 2002 ) .t. rohlf and s. bornholdt , _ gene regulatory networks : a discrete model of dynamics and topological evolution _ , in : function and regulation of cellular systems : experiments and models , eds .a. deutsch , j. howard , m. falcke and w. zimmermann , 233 - 239 , birkhuser , basel ( 2004 ) .j.p . crutchfield and m.mitchell , _ proc .( usa ) , * 92 * , 10742 ( 1995 ) .mccluskey , _ bell syst .j. _ , * 35 * , 1417 - 1444 ( 1956 ). g. von dassow , e. meir , e.m . munro and g.m .odell , _ nature _ * 406 * , 188 - 192 ( 2000 ) . c. n. david and r. d. campbell , , 557 ( 1972 ) .p. hogeweg , _j. theor .* 203 * , 317 - 333 ( 2000 ) . c. furusawa and k. kaneko , _ phys ._ * 84 * , 6130 ( 2000 ) . c. furusawa and k. kaneko , _ j. theorbiol . _ * 224 * , 413 - 435 ( 2003 ) .m. mitchell , p. hraber and j.p .crutchfield , _ physica d _ 361 - 391 ( 1994 ) .holland , _ adaptation in natural and artificial systems ._ university of michigan press , ann arbor ( 1975 ) .

Abstract: based on a recently proposed non - equilibrium mechanism for spatial pattern formation we study how morphogenesis can be controlled by locally coupled discrete dynamical networks , similar to gene regulation networks of cells in a developing multicellular organism . as an example we study the developmental problem of domain formation and proportion regulation in the presence of noise and cell flow . we find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells . a further focus of this paper is a detailed study of noise - induced dynamics , which is a major ingredient of the control dynamics in the developmental network model . a master equation for domain boundary readjustments is formulated and solved for the continuum limit . evidence for a first order phase transition in equilibrium domain size at vanishing noise is given by finite size scaling . a second order phase transition at increased cell flow is studied in a mean field approximation . finally , we discuss potential applications . + pacs : 87.18.hf , 05.70.ln , 05.50.+q


started developing since 1995 to make communication at and near a human body .the whole idea behind developing these networks is to provide better health care services to critical patients and elderly people . with modern medicine and better lifestyle ,the average expectation of life is increased .now , society has more number of elder people , who need continuous monitoring and urgent medical aid .wbasn is excellent for this purpose with no or minimum intervention of humans .  besides the health monitoring of elder people and critical patients with life threatening issues, wbasn can also be used in many other fields where continuous and remote monitoring of the health is necessary .these fields include players in different sports , astronauts in space , pilots , etc .  for health monitoring of athletes and other players , parameters like respiratory rate , heart rate , blood oxygen , blood glucose , body temperature , etc .are important .another important issue with players is the fatigue of muscles .commercially many sensors are available for fatigue measurements in humans like temperature and heartbeat measuring sensors . however , the sensors measuring amount of lactic acid in muscles can provide the most accurate results .this is because , when a muscle feel lethargic it requires more oxygen and this requirement is fulfilled by producing lactic acid as a by product .the idea of accurately measuring the fatigue level in players can totally revolutionize the sports industry across the globe .the sports that include more physical exertion and include a team of players of different stamina , can especially be benefited .one of the most popular games that fall in this category is soccer .fans and admirers get very upset when their favorite players show bad performance because of fatigue .the sensors used for soccer players are in - vivo and also they should be of very small size for the ease of a player to show the performance . as the sensor has a very small size and low battery power , so ,the transmission rate of data is limited .generation and transmission of redundant data is minimized by using different threshold levels for sensors .data packet is only generated by the sensor node when the sensed value is equal to or above the provided threshold level .  in our proposed protocol the - fame, we use two threshold values for players fatigue measurement . for players fatigue measurement , we use a threshold for lactic acid level in the blood and a threshold for total distance travelled by the player . in the - fame, sensors send data when they sense fatigue .this data is then routed towards the nearest sink present at the boundary of the ground .most commonly used wireless technologies in wbasn are zigbee and bluetooth .zigbee was developed to address the need for small sized nodes , low energy consumption and low cost wireless networks .it has the ieee standard of 802.15.4 .it operates in the unlicensed bands of 868 mhz , 915 mhz and 2.4 ghz .our work begins by defining the work related with our technique in section ii .section iii includes the motivation for the proposed scheme . in section iv, we explain basic fatigue measuring parameter and mention the speed profile of a soccer player during the match .next , in section v , we show our proposed technique which limits the energy consumption of sensor nodes .we then present the simulation results of our technique in section vi , which depicts that it has minimum propagation delay and energy consumption .finally , we conclude our work in section vii .the field of wban is not quite latest and only little research work is done in it .those few research articles are mainly focused on patient s health monitoring . on the other side ,if research for wban employed for player s fatigue monitoring has been checked , very few work can be found .some of the articles on wban are listed below .  in ,kashif kifayat  present a design and implementation of a body area sensor network and a gaming platform to dynamically adapt the physiotherapy treatments .the proposed framework use three components side by side which includes a wireless sensor network ( wsn ) , a game and a data acquisition manager .wsn collect information from the patients and forward it to the data acquisition manager which then provides updates to the game .as , time passes and the patient shows better mobility , the game reaches its higher levels and become difficult .this is done to train patients accurately with the passage of time .m - attempt , show an energy efficient routing protocol for heterogeneous wbasn attached on a human body for continuous patient monitoring .sink is placed on the center of the body .m - attempt uses single hop data transmission for critical data and for normal data delivery to the sink , it uses multi - hop communication .it is a thermal aware protocol which when senses a hot - spot on the route , immediately change its route by skipping that node until it is back to its normal temperature .this will protect human tissues from being damaged .ashay dhamdhere  provide real time team monitoring for a soccer match . present different challenges for monitoring soccer players .they give their own design where , they divide team members into different categories on the basis of their position from sink and then calculate delay and resource consumption profile of wireless body area network ( wban ) for each team member , respectively .  l. de nardis  in use body area networks for soccer players to generate a realistic mobility model .each player has body area network ( ban ) , which provides player s position information throughout the game .the communication is done using inter - ban multi - hoping .they designed a new mobility model called dynamo and compared its delay and throughput with reference point group mobility model ( rpgm ) .  in , authors work on wban and the factors affecting the reliability of data .according to the paper , there are two main factors that affects the data reliability namely , data freshness and data accuracy .authors employed multiple sinks on a single human body to maintain freshness of data for remote monitoring of critical patients .the associated delays and packet loss also decrease because of their proposed scheme .yeongjoon gil  introduce a multi - body sensor platform for tele - medicine and emergency scenarios in .they present a prototype for their work .the results show that monitoring only a single parameter for a patient is not sufficient because , mostly diseases and ailments are interconnected .so , a framework for measuring multiple signals from a body is helpful specially when it is low power consuming and not harmful for any human tissue .authors in , , , and work on mac layer of the osi model and give a medium access control protocol for wban , give a through survey on energy efficient protocols for wban , present arm mobility for patients in wban , noise filtering for wban channel and provide localization technique for wban , respectively .zulkifli  implement heart rate monitoring algorithm for players , performing strenuous exercises .heart rate monitors ( hrm ) are commonly used as a training aid for sports persons . when hrms are incorporated with wban, they can provide continuous and accurate monitoring of players during hard exercises .authors in introduce a prototype system for remote monitoring of athlete s performance by providing live feedback .each player is equipped with sensors and a mobile device .some specific parameters are measured and then buffered locally .after a certain time period , the data will be forwarded using internet to the coaches .samuel j. lerer  provide a personnel management system for collecting vital health information in ice - hockey players .ice hockey is a very strenuous and a difficult game because of its requirements for high speed .the paper focuses on using inexpensive sensors for college students playing ice hockey .it uses a respiratory rate monitoring system and use audio processing on the collected data to find fatigue in players .miguel garcia  in propose a new remote monitoring mechanism for soccer players , called wireless soccer team monitoring ( wstm ) .they use multi - hoping topology for data routing in the network .two sinks are placed behind the goals and each player is equipped with a ban to calculate fatigue .in any sport , one of the major concerns is the fitness of a player . whereas , in team sports like soccer or hockey , fitness of each player is not only important but it is also considered a match winning criteria .the problem with these sports is that the fatigue level of a player is continuously changing during the play as it includes running , sprinting and many other tiring activities .so , there a mechanism is needed to constantly monitor each player in the team .whenever any critical condition occurs , coaches and health officials can immediately take precautionary measures to handle the situation and reduce the chance of any further injury .  in a protocol for soccer players monitoringis introduced which uses multi - hop routing to transmit data to the base station ( bs ) .however , large delay occurs when the player is not present near the bs . discuss player monitoring in ice hockey based on audio processing of respiratory data of players .however , monitoring respiratory data needs the use of microphones which creates difficulties for players .also , its processing creates long delays and produces less accurate results . keeping this in mind, we propose a new protocol called the - fame .our proposed protocol produces less propagation delays and increases the lifetime of the entire network .the standard size of a soccer ground can vary from 100 yards to 120 yards in length and from 60 yards to 80 yards in width .we choose a size of square yards for the soccer field .the total number of players from both teams are 22 i.e. 11 players per team .+  there are many game strategies but the most common are defensive and attacking .defensive game has 4 to 5 players in their own half and rest of the players are distributed according to the need . whereas , in attacking situation 4 players play in the other team s half to score more goals .the speed and fatigue analysis of players in the field is discussed in the following two subsections .a soccer match on average continues from 90 to 100 minutes . during this time, the total distance covered by a professional player is slightly more than 11 km per match ( nearly 7 miles ) .this distance is not only covered by running but , some sprinting is also performed as shown in the statistics provided in fig .1 . the average running speed of a player can vary from 10.3 km / hour .to 12.9 km / hour . during the possession of a ball , soccer players usually sprint and can achieve a speed of 25 km / hour .  a soccer player attempts approximately 100 sprints per match lasting about 2 - 5 seconds . on average , for a single match , the minimum work to rest ratio for a soccer player is 1:2 .soccer player s speed , direction and ball possession can all be compromised if he can not recover from the fatigue .if a player continues running instead of taking rest then , he can be seriously injured which can lead to permanent damage of muscle s tissues .so , to avoid this , a threshold for fatigue level must be defined beyond which , players can face serious health issues .+   muscle fatigue is commonly explained as the inability of muscles to generate any force .when humans perform any vigorous exercise or do sprinting or swimming , they begin to inhale faster to send more oxygen to the working muscles .a human body generates most of the energy using aerobic methods .but under some circumstances where , the amount of oxygen ( ) required is more than the need , the body uses anaerobic methods i.e. it uses glucose by a process called glycolysis to produce energy . in the process of glycolysis , glucose is metabolized into a substance called pyruvate . in presence of enough , pyruvateis further broken down to generate energy , but when there is a limited supply of in the body , pyruvate changes into lactate which will then be transformed into energy .the process is also explained in fig .if cells in the muscles do the above mentioned practice at high rates , i.e. for more than 3 minutes , lactic acid will start to accumulate into muscles .this shows that it is a good parameter to measure fatigue in a soccer player .the sensor used to measure lactic acid level , is an in - vivo sensor which includes a needle , pricking the muscle to draw blood .normal results show a value between 4.5 to 19.8 mg / dl ( 0.5 - 2.2mmol / l ) .where , mg / dl = milligrams per deciliter and mmol / l = millimoles per liter .the - fame works on the network layer of the standard osi model .we take two teams of 12 players each , for the experimentation .each player has an implanted sensor to collect his lactic acid level regularly as shown in fig .3 . in the - fame ,each player s fatigue information is transmitted whenever , the maximum threshold level for lactic acid in blood or distance covered during the match , reaches .this information is routed towards the sink using only a single hop .single hop or direct transmission will be useful for decreasing the propagation delay of the network .+  to support direct transmission mechanism , we use 6 sinks fixed at the boundaries of the ground whose locations are given in table i. multiple sinks in the field let the sensors consume less power during transmission of fatigue information ..location of sinks at the soccer ground [ cols="^,^,^ " , ]   in the - fame , we use direct transmission with multiple sinks to avoid the drain of battery . as a result , as shown in fig .6 , nodes live longer and need not to be changed frequently .however , in wstm sensor nodes die quickly as compared to our proposed protocol .the difference in results is because , wstm uses multi - hop scheme to route its data towards the sink , whereas , our protocol uses direct transmission method with multiple sinks in the field .stability period is the amount of time elapsed before the first sensor node in the network die .the - fame shows that the first node die nearly at 5100th round , as compared to the wstm protocol in which the first node is dying after 2700 rounds .these analysis show that the parameter known as the stability period , is very effective in order to clearly understand the true behaviour of any wireless network .fig.6 clearly reveals that our proposed protocol is 22 more stable than wstm .+   +   +  as explained earlier , in the - fame sensor nodes only transmit data to the sink when the threshold for fatigue is reached for the particular player . in nodessends data directly to the bs if it is at its minimum distance to bs , like in the case of a goal keeper , otherwise it uses other players as relay nodes to route data towards the bs . on the other hand , the - fame only uses direct transmission method to send data to the bs .hence , there are more packets generated in the network because of multi - hopping used in wstm as given in fig .7 .  in real worldno channel is an ideal channel and especially in the case of wireless medium , there is always some loss of data in the network because of multi - path effects like refraction , reflection and absorbtion etc . keeping this in mindwe have chosen a noisy channel for simulation purpose instead of an ideal one , to make it realistic with a packet drop probability of approximately 30 .8 shows the amount of packets dropped in the network before reaching any sink. packets received successfully at the sinks are roughly about 70 .the amount of packets received at all the sinks without any error is another important parameter to look for in the network .this parameter shows the accuracy of the protocol and network topology .this parameter for both protocols is presented in fig .+   +  residual energy shown in fig .10 depends on the overall life time of the sensors in the network . in wstm as , the nodes consume more energy during the communication process because of multi - hop scheme , so the residual energy deplete very quickly . whereas , in the - fame protocol , the nodes live longer despite of the fact that the nodes have very low initial energy in our proposed scheme .+   +  fig .11 compares the throughput of 2 schemes , the - fame and wstm .throughput of a network is given by the following equation :   from fig .11 we are confident to say that the packet delivery ratio is 8 better in the - fame as compared to wstm .throughput of the - fame , reveals that our proposed protocol is more efficient .it is very obvious from the fig .12 that the - fame has less propagation delay than wstm , because it uses direct transmission method to send information to the sink unlike wstm , which uses multi - hop and generates more delay .propagation delay is an important factor to handle in scenarios where , we want to send critical data more quickly .the - fame only transmits data when , a threshold for muscle fatigue is reached . in this respect , the - fameshould be preferred to achieve minimum propagation delays .in this paper , we present an energy efficient fatigue measuring protocol for soccer players using wbasn .direct transmission is selected to sent data to the bs to achieve minimum delay .the problem with direct transmission is more energy consumption , which is eradicated using multiple sinks along the border of the ground .we also use a composite parameter which consist of thresholds for lactic acid and distance covered by a player .the use of this composite parameter makes fatigue measurement more reliable .hence , the - fame gives better results in both energy and delay profiles as compared to multi - hop routing scheme . in future work, we will implement expected transmission count ( etx ) link metrics as demonstrated in     .99 kifayat , kashif , et al .`` body area networks for movement analysis in physiotherapy treatments . ''advanced information networking and applications workshops ( waina ) , 2010 ieee 24th international conference on .ieee , 2010 .javaid , nadeem , et al .`` m - attempt : a new energy - efficient routing protocol for wireless body area sensor networks . ''arxiv preprint arxiv:1303.5260 ( 2013 ) .dhamdhere , ashay , et al .`` experiments with wireless sensor networks for real - time athlete monitoring . '' local computer networks ( lcn ) , 2010 ieee 35th conference on .ieee , 2010 .de nardis , l. , d. domenicali , and m. di benedetto .`` mobility model for body area networks of soccer players . ''wireless technology conference ( euwit ) , 2010 european .ieee , 2010 .sampangi , raghav v. , shalini r. urs , and srinivas sampalli .`` a novel reliability scheme employing multiple sink nodes for wireless body area networks . ''wireless technology and applications ( iswta ) , 2011 ieee symposium on .ieee , 2011 .gil , yeongjoon , wanqing wu , and jungtae lee .`` a synchronous multi - body sensor platform in a wireless body sensor network : design and implementation . '' sensors 12.8 ( 2012 ) : 10381 - 10394 . rahim , a. , et al .`` adaptive - reliable medium access control protocol for wireless body area networks . ''sensor , mesh and ad hoc communications and networks ( secon ) , 2012 9th annual ieee communications society conference on .ieee , 2012 .javaid , nadeem , et al .`` energy efficient mac protocols in wireless body area sensor networks - a survey . ''arxiv preprint arxiv:1303.2072 ( 2013 ) .ain , q. , et al .`` modeling propagation characteristics for arm - motion in wireless body area sensor networks . ''broadband , wireless computing , communication and applications ( bwcca ) , 2012 seventh international conference on .ieee , 2012 .manzoor , b. , et al .`` noise filtering , channel modeling and energy utilization in wireless body area networks . ''high performance computing and communication and 2012 ieee 9th international conference on embedded software and systems ( hpcc - icess ) , 2012 ieee 14th international conference on .ieee , 2012 .javaid , nadeem , ayesha bibi , and zahoor ali khan .`` performance study of localization techniques in wireless body area sensor networks . ''trust , security and privacy in computing and communications ( trustcom ) , 2012 ieee 11th international conference on .ieee , 2012 .nsa , zulkifli , and fauzan khairi .`` xbee wireless sensor networks for heart rate monitoring in sport training . '' ( 2012 ) .baca , arnold , et al . `` a server - based mobile coaching system . ''sensors 10.12 ( 2010 ) : 10640 - 10662 .lerer , samuel j. , eric b. tieniber , and jonathan m. smith .`` building a wireless ice hockey personnel management system . ''philadelphia , pa , senior design project ( 2010 ) .garcia , miguel , et al .`` a wireless sensor network for soccer team monitoring . '' distributed computing in sensor systems and workshops ( dcoss ) , 2011 international conference on .ieee , 2011 .www.soccerperformance.org , ( 8 may 2013 ) www.scienceofsocceronline.com , ( 29 april 2013 ) www.sportsscientists.com , ( 29 april 2013 ) www.scientificamerican.com , ( 29 april 2013 ) www.nlm.nih.gov , ( 29 april 2013 )  n , javaid . a , khan . i.a , djouani .k , `` performance study of etx based wireless routing metrics , '' 2nd ieee international conference on computer , control and communications ( ic4 - 2009 ) , karachi , pakistan , pp.1 - 7 , 2009 .javaid , n. ; bibi , a. ; djouani , k. , `` interference and bandwidth adjusted etx in wireless multi - hop networks , '' globecom workshops ( gc wkshps ) , 2010 ieee , vol ., no . , pp.1638,1643 , 6 - 10 decdoi : 10.1109/glocomw.2010.5700217 .javaid , n. ; ullah , m. ; djouani , k. , `` identifying design requirements for wireless routing link metrics , '' global telecommunications conference ( globecom 2011 ) , 2011 ieee , vol ., no . , pp.1,5 , 5 - 9 dec . 2011 .doi : 10.1109/glocom.2011.6134360 .javaid , n. ; bibi , a. ; khan , z. a. ; djouani , k. , `` on using multiple quality link metrics with destination sequenced distance vector protocol for wireless multi - hop networks , '' electrical & computer engineering ( ccece ) , 2012 25th ieee canadian conference on , vol .pp.1,4 , april 29 2012-may 2 2012

Abstract: wireless body area sensor network ( wbasn ) is a technology employed mainly for patient health monitoring . new research is being done to take the technology to the next level i.e. player s fatigue monitoring in sports . muscle fatigue is the main cause of player s performance degradation . this type of fatigue can be measured by sensing the accumulation of lactic acid in muscles . excess of lactic acid makes muscles feel lethargic . keeping this in mind we propose a protocol reshold based nergy - efficient tigue asurement ( the - fame ) for soccer players using wbasn . in the - fame protocol , a composite parameter has been used that consists of a threshold parameter for lactic acid accumulation and a parameter for measuring distance covered by a particular player . when any parameters s value in this composite parameter shows an increase beyond threshold , the players is declared to be in a fatigue state . the size of battery and sensor should be very small for the sake of players best performance . these sensor nodes , implanted inside player s body , are made energy efficient by using multiple sinks instead of a single sink . matlab simulation results show the effectiveness of the - fame .   soccer , fatigue , lactic acid , multiple sinks , threshold .


there is a significant body of literature in statistics , econometrics and ecology dealing with the modeling of discrete responses under biased or preferential sampling designs .they are particularly popular in the natural sciences when species distributions are studied .such sample schemes may reduce the survey cost especially when one of the responses is rare .a large part of statistical literature concerns the case - control design , retrospective , choice - based or response - based sampling . in the simplest case a sample of cases and a sample of controls are available and for each observation a set of `` attributes / covariates '' is observed in both samples .then inference is carried out following standard statistical procedures .+ a case that has received increasing attention in the literature is the situation where the sample of controls is a random sample from the whole population with information only on the attributes and not on the response .this situation is fairly common in ecological studies where only species presence is recorded when field surveys are carried out . in the ecological literature , since the 1990 s such data are called _ presence only data _ ( see * ? ? ?* and references therein ) . define presence - only data as `` consisting only of observations of the organism but with no reliable data where the species was not found '' .atlases , museum and herbarium records , species lists , incidental observation databases and radio - tracking studies are examples of such data .+ in recent years we find a considerably growing literature describing approaches to the modeling of this type of data , among the many ecological papers we recall , , , , and , most notably , in the statistical literature , , , and . while in and to model the presence - only data poisson point processes are considered in the likelihood and bayesian framework respectively , in and a modified case - control logistic model is adopted in the likelihood and bayesian perspective respectively , in both papers there is no account for possible dependence structure in the observations . in asymptotic relations between the two approaches are discussed .+ a different approach , maxent , is based on the maximum entropy principle . in maxent the relative entropy between the distribution of covariates at locations where the species is present and the unconditional background distribution of covariates is maximized subject to some constrains concerning empirical statistics ( see philips et al . , 2006 , for details ) . as pointed by `` the maxent method requires knowledge of species prevalence for its estimator of occurrence to be consistent '' .+ in what follows we are going to use the name _ presence - only data _ when referring to the above sketched general problem of having information on the presence and covariates jointly on a sample from a population , while information on only the covariates is available on any sample from the same population .this work is developed in the same discrete setting as in and , i.e. , we have a population of independent units , no dependence structure , such as spatial correlation , is anticipated .we defer the treatment of this extension to a subsequent work .+ the main contribution of the paper is a new rigorous formalization of the logistic regression model with presence - only data that allows further insight into the inferential issues .this leads us to an algorithmic procedure that , among other results , returns a mcmc approximation of the response prevalence under general knowledge of the process generating the data .we also present a large simulation study involving 24,000 simulated datasets and comparing our approach to other two models representing optimal benchmarks .+ the paper is organized as follows .section [ sec : reglog ] introduces a general framework for the presence - only data problems , section [ sec : bayes ] presents our bayesian approach , section [ sec : mcmc ] describes the mcmc algorithm while results related to the simulation study are reported in section [ sec : sim ] .finally in section [ sec : conc ] some conclusions are drawn and future developments briefly described .the analysis of a binary response related to a set of explicative covariates is usually carried out through the use of the logistic regression where the logit of the conditional probability of occurrence is modeled as a function of covariates . in this section ,we first introduce a general framework for the modeling of presence - only data and then consider the case of the linear logistic regression .the approach proposed is built on two levels and we partially follow the formulation introduced by but adopting a bayesian scheme as in .let be a binary variable informing on the presence ( ) or absence ( ) of a population s attribute and let denote a set of highly informative , on the same attribute , covariates which are available on the same population .then , the presence - only problem can be formalized by considering a censorship mechanism that acts when observing the response , so that part of the population units are not reachable . in particular , we refer to the situation in which we are able to detect only a partial set of units on which the attribute of interest is present while the information on the covariates is available on the entire population . in this situation, we have to consider two types of uncertainty : the uncertainty due to the mechanism of censorship and the uncertainty due to the sampling procedure .moreover , since we are not able to collect a random sample of observable data , we need to adjust for the sampling mechanism through the use of a case - control scheme .+ in order to build a bayesian model , in this framework we adopt the following conceptual scheme in two levels .+     let be the subset of where we observe .a modified case - control design is applied so that a sample of presences , considered as cases , is selected from and a sample of `` contaminated '' controls is selected from the whole population , with all the covariates but no information on .   here, we can not approach the model construction using only a finite population approach because of the censoring mechanism that `` masks '' distributional information on already at the population level . by the introduction of level 1 we can describe the censored observations as random quantities generated by the model .hence , the problem of presence - only data can be formalized as a problem of missing data .   at the first level , we assume that the law is defined in terms of the conditional probability of occurrence , denoted by , when the covariates are .moreover , we consider that the relation between and is formalized through a regression function on the logit scale that is when the data are independently generated from , we denote by the empirical prevalence of the binary response in , expressed as the ratio of the number of presences to the size of the population , that is    at the second level , we adopt a case - control design modified for presence - only data in order to account for the specific sampling procedure considered .the use of the case - control scheme is necessary at all times when it is appropriate to select observations in fixed proportions with respect to the values of the response variable .this can occur when the attribute of interest represents a phenomenon that is rare among the units of the population as for example a rare disease or a rare exposure in epidemiological studies .+ now , let be a binary indicator of inclusion into the sample ( denotes that a unit is in the sample ) , let and be the inclusion probability of the absences and the presences , respectively . under the assumption that , given , the sampling mechanism is independent from the covariates , the conditional probability of occurrence is modified through the bayes rule as hence , the corresponding case - control regression function defined as the logit of is given by in particular , if the selection of cases ( ) and controls ( ) is made independently without replacement , the inclusion probabilities are given in terms of the empirical prevalence by and so that the equation becomes in our framework , since the response variable is already censored at the population level , the standard case - control design can not be adopted but it should be modified in such a way that a sample of presences is matched with an independent sample drawn from the entire population , named the _ background sample _ . remark that in this sample the response variable is unobserved and only the covariates are available .+ in this way , the complete sample is composed by a set of independent background data , where the response is not observed , drawn from the entire and by a set of independent observations selected from the sub - population of presences .this procedure implies that the reference population is augmented with its subset so that the total number of observations considered in the sampling scheme becomes . to illustrate the sampling framework we are going to adopt here ,let us consider the following situation : we can label population units of type only when they are isolated from units of type .this can be formalized by introducing a binary stratum variable such that indicates when an observation is drawn from the entire population while denotes the sampling from the sub - population .remark that implies whilst implies that is an unknown value .moreover , by construction is independent from the covariates , given the response .the introduction of the variable allows us to define the structure of the data at the population level and at the sample level in terms of presences / absences ( ) and known / unknown data ( ) , as reported in table [ tab1 ] and table [ tab2 ] .di lorenzo , b. , farcomeni , a. , and golini , n. ( 2011 ) . a bayesian model for presence - only semicontinuous data with application to prediction of abundance of taxus baccata in two italian regions ., * 16*(3 ) , 339356 .elith , j. , graham , c. h. , anderson , r. p. , dudik , m. , ferrier , s. , guisan , a. , hijmans , r. j. , huettmann , f. , leathwick , j. r. , lehmann , a. , li , j. , lohmann , l. g. , loiselle , b. a. , manion , g. , moritz , c. , nakamura , m. , nakazawa , y. , overton , j. m. , peterson , a. t. , phillips , s. j. , richardson , k. s. , scachetti - pereira , r. , schapire , r. e. , soberon , j. , williams , s. , wisz , m. s. , and zimmermann , n. e. ( 2006 ) .novel methods improve prediction of species distribution from occurence data . , * 29 * , 129151 .

Abstract: presence - only data are referred to situations in which , given a censoring mechanism , a binary response can be observed only with respect to on outcome , usually called _ presence_. in this work we present a bayesian approach to the problem of presence - only data based on a two levels scheme . a probability law and a case - control design are combined to handle the double source of uncertainty : one due to the censoring and one due to the sampling . we propose a new formalization for the logistic model with presence - only data that allows further insight into inferential issues related to the model . we concentrate on the case of the linear logistic regression and , in order to make inference on the parameters of interest , we present a markov chain monte carlo algorithm with data augmentation that does not require the a priori knowledge of the population prevalence . a simulation study concerning 24,000 simulated datasets related to different scenarios is presented comparing our proposal to optimal benchmarks .   [ [ keywords ] ] keywords : + + + + + + + + +  bayesian modeling , case - control design , data augmentation , logistic regression , markov chain monte carlo , population prevalence , presence - only data , simulation .


the complex dynamics of human social interactions lead to interesting phenomena , and inequalities at various levels often show up in course .the recent availability of huge amount of data ( empirical data from databases , electronic footprints , and sometimes large surveys ) for various forms of human social interactions has made it easier to uncover certain patterns present , to analyze them and investigate the reasons behind various socio - economic inequalities manifested in them .the age of _ big data _ has opened up new avenues and challenges , and scientists are in the quest to understand _ why _ certain things look like as they do and _ how _ do they happen .researchers are pooling in knowledge and techniques from various disciplines  , e.g. , statistics , applied mathematics , information theory , computer science , while tools of statistical physics have proved to be quite successful in better understanding of the precise ( spatio - temporal ) nature and origin of socio - economic inequalities prevalent in our society .more the data that is acquired and analyzed , more we become confident in addressing the _ _why__s , and __ how__s .statistical physics tells us that systems of a large number of interacting dynamical units collectively exhibit a behavior which is solely determined by only a few basic dynamical properties of the individual constituent units and of the embedding dimension , but is independent of all other details .this feature , which is specific to ` critical phenomena ' , as in continuous phase transitions , is known as _ universality _there is no shortage of empirical evidence that several social phenomena are characterized by simple emergent behavior out of the interactions of many individual constituent units . in recent times , a growing community of researchers have been analyzing large - scale social dynamics to uncover universal patterns and proposing simple microscopic models to describe them , very similar to the minimalistic models used in statistical physics to understand physical phenomena .these studies have revealed quite a few interesting patterns and behaviors in social systems , as in elections  , population growth  and economic growth  , income and wealth distributions , financial markets  , languages  , etc .( see refs . for a review ) .socio - economic inequality  usually concerns the existence of unequal ` wealth ' and ` fortunes ' accumulated due to complex dynamics and interactions within the society . usually containing structured and recurrent patterns of unequal distributions of goods , wealth , opportunities , and even rewards and punishments ,this is classically measured in terms of _ inequality of conditions _ , and _ inequality of opportunities_. the former refers to the unequal distribution of income , wealth , assets and material goods . while the latter refers to the unequal distribution of ` life chances ' .this is reflected in levels of education , health status , treatment done by the criminal justice system etc .socio - economic inequalities are mostly responsible for conflicts , wars , crises , oppressions , criminal activities , instability in political scenario and socio - political unrest , and that in turn affects economic growth  . historically as well as traditionally , economic inequalities have been extensively studied in the context of income and wealth  , although it is also measured for many quantities like energy consumption  .the studies of inequality in society  has been always very important , and is also a topic of contemporary focus and immediate global interest , drawing attention of researchers across disciplines economics , sociology , mathematics , statistics , demography , geography , graph theory , computer science , and not surprisingly , theoretical physics .quantifying socio - economic inequalities is a challenge , but is done in numerous ways .the probability distributions of various quantities , of course provide the most detailed measures .it is very common to find that most quantities display broad distributions most common are log - normals , power - laws or their combinations . for example, the distribution of income is usually found to be exponential for the bulk followed by a power law  for the top income range .however , such distributions can widely differ in their forms and details , and as such they are rather difficult to handle .this leads to the introduction of various _ indices _ like the gini  , theil  , pietra  and other socio - geometric indices  , which try to characterize various geometric features of these distributions using a single number .of course , each of these indices come with certain merits , and certain indices are more useful than others , depending on the context they are used in . in this articlewe will focus on the most common one , the gini index and a recently proposed index ( kolkata ) which has a nice , useful socio - geometric interpretation .-index is given by area of the shaded region , while the -index is computed from the coordinate of the point of intersection c ( ) of the lorenz curve and the diagonal perpendicular to the equality line .thus , while the -index measures the overall inequality in the system , the -index gives the fraction of wealth possessed by the fraction of richer population ., width=377 ]  the most commonly used measure to quantify socio - economic inequality is the gini index . to compute this , one has to consider the ` lorenz curve '  , which shows the cumulative proportion of ( poor to rich ) ordered individuals ( entries ) in terms of the cumulative share of their wealth . can of course represent income or assets of individuals but it can as well represent citation of articles , votes in favor of candidates , population of cities etc .it is first computed from a given statistical distribution or a dataset . the gini index ( ) ,defined as the ratio of the area enclosed between the lorenz curve and the equality line , to that below the equality line , taking values for absolute equality and for absolute inequality .let the area between ( i ) the lorenz curve and the equality line be represented as , and ( ii ) that below the lorenz curve be ( see fig .[ fig : lorenz ] ) . then the gini index is  .the recently introduced kolkata index ( symbolizing the extreme nature of social inequalities in kolkata ) or ` -index '  , is defined as the fraction such that fraction of people ( or papers ) possess fraction of highest incomes ( or citations )  .the empirical data on gini index from world bank data  for incomes over several years are given in fig .[ fig : emp_gini ] .the values seem to be mostly between and . in the later part of our article we will argue that the simple kinetic exchange models can even reproduce this feature .we also discuss here the specific case of the citation distributions .it was shown earlier  that the distribution of citations to papers within a discipline has a broad distribution , which is universal across broad scientific disciplines , by defining a relative indicator , where is the average citation within a discipline .our study  confirmed this case for academic institutions as well as journals across disciplines .studies on the statistics of human deaths from wars , conflicts and natural disasters shows that the form of the probability distribution for number of people killed exhibit power law decay for the largest sizes , the exponent values being quite similar .we argue if a common mechanism is responsible for similarity that is manifested .in view of the truly interdisciplinary nature of econophysics and sociophysics , it can be argued that some interdisciplinary visiting facilities for social and natural scientists are absolutely necessary today .these will provide scientists from different disciplines to interact over some long period , discuss and debate and develop in their own discipline . in the concluding part of this article , we argue about the need to establish a research institute dedicated to socio - economic problems with an interdisciplinary character , with some specific model in mind .in a recent study  , we were able to conclude that the citation distributions for articles published in different journals ( fig . [fig : plosfig14])b , as well as from different academic institutions ( fig .[ fig : plosfig14])a followed the same functional form , irrespective of time ( the year they are published ) and space ( institution ) .one has to carefully scale the probability distributions by their average , and the rescaled curves show excellent scaling collapse .the most of the resulting scaling curve fits to a lognormal function ,  \label{eq : ln}\ ] ] while the extreme right tail deviates from this and seem to fit more to a power law with a decay exponent around .   of citations rescaled by average number of citations to publications from 1990 for several several academic institutions .the scaled distribution fits very well to a lognormal for most of its range , with , .the largest citations do not follow the lognormal behavior , and seem to follow a power law : , with .( b ) probability distribution of citations rescaled by average number of citations to publications from 1990 for several academic journals .the scaled distribution function fits well to a lognormal function with , , while as for the lower range of .the largest citations fit well to a power law : , with .data is taken from ref ., title="fig:",width=226 ]  of citations rescaled by average number of citations to publications from 1990 for several several academic institutions .the scaled distribution fits very well to a lognormal for most of its range , with , .the largest citations do not follow the lognormal behavior , and seem to follow a power law : , with .( b ) probability distribution of citations rescaled by average number of citations to publications from 1990 for several academic journals .the scaled distribution function fits well to a lognormal function with , , while as for the lower range of .the largest citations fit well to a power law : , with .data is taken from ref ., title="fig:",width=226 ]   indices with number of papers and citations for academic institutions and journals . for larger number of papers or citations , the values seem to fluctuate less or converge around the mean values and respectively . for academic institutions ,the values are for gini and , while for the journals , the values are and .figure adapted from ref .width=302 ]  we additionally observed that for the academic institutions , gini index was and , which means around citations come from the top papers . for academic journals , , which means about citations come from the top papers .we further noted that gini and indices fluctuate less around respective mean values and as the number of articles or the number of citations became large ( fig .[ fig : plosfig6 ] ) . for academic institutions ,the values were for gini and . for journals ,the values are and .the huge variety of socio - economic data suggest that there might be a simple relation between the two seemingly different inequality measures  .analysis of the following were carried out : ( i ) citations of papers published from academic institutions and journals ( data from isi web of science  and reported in ref . ) , ( ii ) consumption expenditure data of india  , brazil  , italy  , income data from usa  , ( iii ) voting data from open list proportional elections  of italy , netherlands and sweden , _ first past the post _ election data for indian parliamentary elections and legislative assembly elections  , united kingdom  , canada  , bangladesh  , tanzania  , and ( iv ) city population data from ref .  .the relation seems to be perfectly linear for smaller values while it becomes non - linear at the limit of extreme inequality , i.e. , as or approaches unity ( fig .[ fig : gk_emp ] ) .the most striking feature is that the data from a variety of these sources hardly depart from a seemingly smooth curve .the -index and -index obey a linear relationship with  .there has been a attempt to explain the slope of the curve for small values . by approximating the lorenz curve as an arc of a circle  . this linear relationship( with the value of the slope ) can be argued to be more generally valid . if the lorenz curve in fig .[ fig : lorenz ] is taken as a parabola ( , as in case of normalized uniform distribution of income / wealth ; ) , one gets and , giving , the values of and satisfy the above relationship very well .the market models developed by physicists , specifically the kinetic exchange models  can provide an estimate of the relation between the inequality indices . in the cc model  , where an agent retains a ( same for all ) fraction of their income or wealth before going for any ( stochastic ) exchange ( call it trade or scattering ) with another agent , the dynamics is defined by \\m_j(t+1 ) = \lambda m_j(t)+(1-r)(1-\lambda)\left [ m_i(t)+m_j(t ) \right ] , \nonumber \label{eq : cc } \end{split}\ ] ] where is a random fraction in $ ] , drawn at each time step ( trade or exchange ) . and are the wealth of the agent at trading times and respectively . the steady state distribution of wealthis argued to be gamma distribution  with the peak position shifting to higher income or wealth as increases ( corresponds to gibbs or exponential distribution and approaches -function ) . the relationship for such distributionsis found to be linear ( fig . [fig : gk_models]a ) , obeying with .   vs. in cc and ccm models ( for agents ) .( a ) for cc model , varying parameter .the inset shows the plots of and in the range of .the points fit to with .( b ) for ccm model , varying parameter .the inset shows the variation of and in the range of .figure adapted from ref . , title="fig:",width=226 ]  vs. in cc and ccm models ( for agents ) .( a ) for cc model , varying parameter .the inset shows the plots of and in the range of .the points fit to with .( b ) for ccm model , varying parameter .the inset shows the variation of and in the range of .figure adapted from ref . , title="fig:",width=226 ]  in the ccm model  , each agent has a saving fraction drawn from a ( quenched ) distribution .following similar stochastic dynamics as in cc model , \\ m_j(t+1 ) = \lambda_j  m_j(t)+(1-r)\left [ ( 1-\lambda_i)(m_i(t)+(1-\lambda_j)m_j(t ) \right ] , \nonumber \label{eq : ccm } \end{split}\ ] ] one gets a steady state distribution of income or wealth with power law tails for large  . and computed for such distributions  given in inset of fig .[ fig : gk_models]b for varying range of .the relationship here is found to be nonlinear ( see fig . [fig : gk_models]b ) but very much around a similar linear relationship .the history of human civilization has been frequently shaped by events of wars , conflicts and disasters . in recent times , the scale of disaster events have increased remarkably . growingpopulation around the world has been seen as one of the reasons for the increase in counts of people affected by disaster events .a study on the statistics of human deaths from wars , conflicts as well as natural disasters shows that the probability distribution of number of people killed in natural disasters as well as man made situations exhibit similar universality in statistics with power law decay for the largest sizes , the exponent values being quite similar  , in the range of . comparing with natural disasters , where event sizes are measured in terms of physical quantities , like the energy released in earthquake , the volume of rainfall , the land area affected in forest fires , etc .also show striking similarities .these universal patterns in their statistics might suggest some subtle similarities in their mechanisms and dynamics .   of event size , measured by the number of human deaths in the corresponding event .( a ) _ man - made events _ : human deaths from conflicts during 1946 - 2008 , according to the prio database  ( using lowest estimates ) , dead according to the correlators of wars ( cow ) database  during 1816 - 2007 , dead in terror attack  during 1910 till july 2016 , and battle deaths according to ucdp database  during 1989 - 2014 . except the terrorist attack data ,all these distributions seem to have a power law tail with similar exponents .the straight line is a guide to the exponent value for comparison .( b ) _ natural disasters _ : human death from earthquakes , storms , wildfires , miscellaneous accidents , as well as all natural disasters listed in the emdat database  during 1900 - 2013 .the values of the exponents are in ( details in ref ., width=472 ]the gini index is the most popular among economists and sociologists , since it gives an overall measure of the inequality in a society . as evident from fig [ fig : lorenz ] , it requires accurate data for the entire lorenz curve to provide a measure of the shaded area enclosed by it and the equality line . the kolkata index being given by the intersection of the lorenz curve and the cross diagonal to the equality line .the linear relationship is extremely robust for not so high values of inequality and fits different forms of lorenz curve and hence , distributions of income , wealth , citations , etc . andthis robustness is also observed empirically ( fig .[ fig : gk_emp ] ) .we could even compare these findings with simple kinetic exchange models of wealth distributions , where the scaling relation between and was found to be also true .the relationship would be extremely useful to translate from one inequality measure to the other ; since fraction of people possess precisely fraction of the total wealth , translation of social inequality measures into -index language can be of major significance .one of our recent focus had been the inequality in citations for academic institutions and journals .although institutions and journals have their own ranking depending on the ` quality ' of research and publications that come out , get noticed and cited , we find that the form of the distribution function for citations is invariant with respect to the average citations , holding across institutions and over time as well . in terms of absolute inequality measures , roughly 75% citations come from the top 25% papers in case of academic institutions and 71% citations come from the top 29% papers for journals .we also discussed how the inequality statistics of deaths in social conflicts or wars compare with those in natural disasters .twenty years have passed since the formal coining of the term and hence the launch of econophysics as a research topic ( since 1995 ; see the entry by barkley rosser on econophysics in the new palgrave dictionary of economics  ) .furthermore , econophysics has been assigned the physics and astronomy classification scheme ( pacs ) number 89.65gh by the american institute of physics . however , regular interactions and collaborations between the communities of natural scientists and social scientists are rare . though interdisciplinary research papers on econophysics and sociophysics are regularly being published at a steady and healthy rate ( more than 1000 documents containing the explicit term econophysics " and more than 240 documents containing the explicit term sociophysics " in the years 2014 and 2015 according to google scholar ) and published mostly in physics journals , and a number of universities ( including universities of leiden , bern , paris and london )are offering the interdisciplinary courses on econophysics and sociophysics , not many clearly designated professor or other faculty positions for that matter are available yet ( except for econophysics in universities of leiden and london ) .neither there are any designated institutions on these interdisciplinary fields , nor separate departments or centres of studies for instance .we note however , happily in passing , a recently published highly acclaimed ( landmark " and masterful " ) economics book  by martin shubik ( seymour knox professor of mathematical institutional economics , emeritus , at yale university ) and eric smith ( santa fe institute ) discusses extensively on econophysics approaches and in general on the potential of interdisciplinary researches inspired by the developments in natural sciences .  in view of these, it seems it is time to try for an international centre for interdisciplinary studies on complexity in social and natural sciences ; specifically on econophysics and sociophysics .the model of the abdus salam international centre for theoretical physics ( ictp ) , trieste ( funded by unesco and iaea ) , could surely be helpful to guide us here .we are contemplating if an ictp - type interdisciplinary research institute could be initiated for researches on econophysics and sociophysics .we note that helbing ( eth , zurich ) and colleagues have been trying for an european union funded `` complex techno - socio - economic analysis centre '' or economic and social observatory " for the last five years ( see ref . containing the white papers arguing for the proposed centre ) .we are also aware that indian statistical institute had taken a decision to initiate a similar centre in india ( see the `` concluding remarks '' in ) .also there was an attempt for a similar asian centre in singapore , initiated in nyangyong technological university . in view of some recent enthusiasms at the japan - india heads of states or prime minister level , and signing of various agreements( predominantly for business deals , infrastructure development , technical science and also cultural exchanges ) by them , possibility of an indo - japan center for studies on complex systems is also being explored . in such bilateral ( indo - japan ) initiatives ,there are explicit memorandum of understandings already signed by the prime ministers .it did not have any economic or sociological study centres ever planned under such bilateral efforts .these proposals are for regular research centres on such interdisciplinary fields , where regular researchers will investigate such systems . however , in view of the extreme interdisciplinary nature of econophysics and sociophysics , such efforts may be complemented by another visiting centre model . unlike the above - mentioned kind of centres therefore this proposed centre may be just a visiting centre where natural and social scientists from different universities and institutions of the world can meet for extended periods to discuss and interact on various interdisciplinary issues and collaborate for such researches , following the original ictp model .  here , as in ictp , apart from a few ( say , about ten to start - with ) promising young researchers on econophysics and sociophysics as permanent faculty who will continue active research and active visiting scientist programmes ( in physics , economics and sociology ) etc .can be pursued , the faculty members , in consultation with the advisers from different countries , can choose the invited visitors and workshops or courses , on economics and sociological complexity issues , can be organized on a regular basis ( as for basic theoretical sciences in ictp or in newton centre , cambridge , etc . ) .we think , it is an appropriate time for the healthy growth of these new or evolving economic & sociological thinkings " including econophysics and sociophysics .we believe , tokyo would be the ideal location for such an international centre . in such new studies on social sciences , econophysics and sociophysics in particular, japan has already significantly large , active and established groups and hence , tokyo could be its natural location .we are extremely thankful to yuji aruka and taisei kaizoji for sharing with us many enthusiastic ideas on several collaboration projects .we are also grateful to sudip mukherjee for his help in preparing the manuscript .d. lazer , a. pentland , l. adamic , s. aral , a .-barabsi , d. brewer , n. christakis , n. contractor , j. fowler , m. gutmann , t. jebara , g. king , m. macy , d. roy , and m. van alstyne . computational social science . , 323(5915):721723 , 2009 .a. chatterjee .socio - economic inequalities : a statistical physics perspective . in _econophysics and data driven modelling of market dynamics , eds .f abergel , h. aoyama , b.k .chakrabarti , a. chakraborti , a. ghosh , _ , pages 287324 .new economic windows , springer , 2015 .inoue , a. ghosh , a. chatterjee , and b. k. chakrabarti .measuring social inequality with quantitative methodology : analytical estimates and empirical data analysis by gini and indices ., 429:184204 , 2015 .ibge . .http://www.ibge.gov.br/english/estatistica/populacao/condicaodevida/pof/2008_20  09_perfil_despesas / microdados.shtm [  http://www.ibge.gov.br/english/estatistica/populacao/condicaodevida/pof/2008_20  09_perfil_despesas / microdados.shtm ] , 2008 - 09 .accessed : september , 2015 .

Abstract: socio - economic inequality is measured using various indices . the gini ( ) index , giving the overall inequality is the most commonly used , while the recently introduced kolkata ( ) index gives a measure of fraction of population who possess top fraction of wealth in the society . this article reviews the character of such inequalities , as seen from a variety of data sources , the apparent relationship between the two indices , and what toy models tell us . these socio - economic inequalities are also investigated in the context of man - made social conflicts or wars , as well as in natural disasters . finally , we forward a proposal for an international institution with sufficient fund for visitors , where natural and social scientists from various institutions of the world can come to discuss , debate and formulate further developments .