on the computation of semiparametric estimates in limited dependent variable models abstract many semiparametric estimation methods for limited dependent variable models exist not all these estimates have a closed form solution and it is therefore necessary to consider numerical optimisation algorithms in those cases in this paper we discuss and compare several such algorithms for semiparametric estimates without a closed form solution

pareto and boltzmann gibbs behaviors in a deterministic multi agent system a b s t r a c t a deterministic system of interacting agents is considered as a model for economic dynamics the dynamics of the system is described by a coupled map lattice with nearest neighbor interactions the evolution of each agent results from the competition between two factors the agent s own tendency to grow and the environmental influence that moderates this growth depending on the values of the parameters that control these factors the system can display pareto or boltzmann gibbs statistical behaviors in its asymptotic dynamical regime the regions where these behaviors appear are calculated on the space of parameters of the system other statistical properties such as the mean wealth the standard deviation and the gini coefficient characterizing the degree of equity in the wealth distribution are also calculated

root exclusion from complex polydomains and some of its applications abstract a solution to an open research problem related to testing root exclusion of a real n dimensional polynomial n 1 from a subspace of n defined as a cartesian product n times of c c is given in this paper the solution is presented in two theorems which have application to several research problems related to robust relative multidimensional stability among them are the testing of robust relative stability of linear differential systems the testing of robust relative stability of linear delay differential systems and a complementary test for a robust stabilization algorithm several examples are presented to illustrate some of these applications

necessary and sufficient conditions for robust stability of discrete systems with coefficients depending continuously on two interval parameters abstract let a real polynomial in a complex variable whose coefficients are any given continuous functions of two real interval parameters be given necessary and sufficient conditions are derived for the polynomial to have all its zeros outside or inside the unit circle of the complex variable plane in a multi polynomial dependence of the coefficients on parameters the conditions involve in addition to a finite number of algebraic steps only resolving single variable fixed coefficients real polynomials

characterization of zero locations of polytopes of real polynomials given a stability region of a polytope of polynomials the edge theorem can be used to verify certain root clustering properties of the polytope the authors consider the inverse problem starting with a polytope of real polynomials they present a result that allows the construction of the smallest set of regions in the complex plane which characterizes its zero location

another simplification in multidimensional stability tests the main computational burden of checking stability of a multidimensional system is to check whether a multivariable polynomial has zeros on the distinguished boundary of a certain region of analyticity a transformation is performed yielding an expression which has zeros on the distinguished boundary if and only if the original polynomial has such zeros in some cases especially where a linear dependence of certain auxiliary variables defined in the text can be presented in terms of nonnegative integers the transformed expression is considerably simpler and its test is easier to perform than the original one examples are provided

n dimensional stability margins computation and a variable transformation stability margins for n dimensional n geq 2 linear discrete causal systems are defined following a definition suggested recently in the literature for n 2 these can serve as a measure in some sense for the tendency of a stable n d system to become unstable also presented is a new procedure for the computation of these stability margins which is explicitly formulated the computational complexity is equivalent to that of solving for one indeterminate a set of n 1 real equations in n 1 real indeterminates also an n dimensional expansion of a known variable transformation which preserves the core condition of stability is presented and used to considerably simplify n dimensional stability tests and stability margins computations for a class of special cases numerical examples are also provided

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

a root locus technique for linear systems with delay a new method of plotting the root loci is developed for the linear control system with delay in control or in state in case of the system with delay in control the root locus plot starts from neighborhoods of the open loop zeros instead of the open loop poles and thus the effect of time delay is easily handled in case of the system with delay in state the open loop poles are firstly found by applying the root locus method for the system with delay in control and then the desired root loci are found by starting the root loci plot from the open loop poles

exact computation of censored least absolute deviations estimator abstract we show that exact computation of the censored least absolute deviations clad estimator proposed by powell 1984 may be achieved by formulating the estimator as a linear mixed integer programming mip problem with disjunctive constraints we apply our approach to three previously studied datasets and find that widely used approximate optimization algorithms can lead to erroneous conclusions extensive simulations confirm that mip based computation using available solvers is effective for datasets typically encountered in econometric applications and that despite the proliferation of competitors clad remains a useful estimator

mmc techniques for limited dependent variables models implementation by the branch and bound algorithm we propose a finite sample approach to some of the most common limited dependent variables models the method rests on the maximized monte carlo mmc test technique proposed by dufour 1998 monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics journal of econometrics this issue we provide a general way for implementing tests and confidence regions we show that the decision rule associated with a mmc test may be written as a mixed integer programming problem the branch and bound algorithm yields a global maximum in finite time an appropriate choice of the statistic yields a consistent test while fulfilling the level constraint for any sample size the technique is illustrated with numerical data for the logit model c 2005 elsevier b v all rights reserved

qft template generation for time delay plants based on zero inclusion test abstract plant template generation is the key step in applying quantitative feedback theory qft to design robust control for uncertain systems in this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients the main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f t q f q t q q k 0 m 1 q k q k where f q g q h q e j g q and h q are both complex valued affine functions of the m dimensional real vector q and is a fixed frequency based on this condition an efficient algorithm which involves in the worst case evaluation of m algebraic inequalities and solution of m2m 1 one variable quadratic equations is developed for testing the zero inclusion of the value set f t q this zero inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution the proposed template generation technique has a linear computational complexity in resolution and is therefore more efficient than the parameter gridding and interval methods a numerical example illustrating the proposed technique and its computational superiority over the interval method is included

semiparametric estimation of a work trip mode choice model abstract a binary response model of choice between automobile and transit for travel to work is estimated using fixed and random coefficients probit specifications a semiparametric single index specification and a semiparametric specification that permits arbitrary heteroskedasticity of unknown form the estimation methods are maximum likelihood for the probit models semiparametric quasi maximum likelihood for the single index model and maximum score and smoothed maximum score for the arbitrarily heteroskedastic model specification tests result in rejection of the fixed coefficients probit and single index models but not of the random coefficients probit model and the semiparametric model with arbitrary heteroskedasticity

conditions on the boundary of the zero set and application to stabilization of systems with uncertainty abstract we describe an analytic method for finding the location of the zero set of a vector valued function which depends on m real variables and n complex parameters we apply the method to robust stabilization of multivariable linear feedback systems we find exact measures of the extent of permissible perturbations in the plant and or the compensator that maintain feedback stability

generation of robust root loci for linear systems with parametric uncertainties in an ellipsoid given a parametric polynomial family p s q n k 0 ak q sk q q q r m the robust root locus of p s q is defined as the two dimensional zero set p q s c p s q 0 for some q q in this paper we are concerned with the problem of generating robust root loci for the parametric polynomial family p s e whose polynomial coefficients depend polynomially on elements of the parameter vector q e which lies in an m dimensional ellipsoid e more precisely we present a computational technique for testing the zero inclusion exclusion of the value set p z e for a fixed point z in c and then apply an integer labelled pivoting procedure to generate the boundary of each subregion of the robust root locus p e the proposed zero inclusion exclusion test algorithm is based on using some simple sufficient conditions for the zero inclusion and exclusion of the value set p z e and subdividing the domain e iteratively furthermore an interval method is incorporated in the algorithm to spe

exact computation of max weighted score estimators abstract we show that exact computation of a family of max weighted score estimators including manski s max score estimator can be achieved efficiently by reformulating them as mixed integer programs mip with disjunctive constraints the advantage of our mip formulation is that estimates are exact and can be computed using widely available solvers in reasonable time in a classic work trip mode choice application our method delivers exact estimates that lead to a different economic interpretation of the data than previous heuristic estimates in a small monte carlo study we find that our approach is computationally efficient for usual estimation problem sizes

a simplified derivation of the zeheb walach 2 d stability test with applications to time delay systems zeheb and walach gave a stability test for n d systems for 2 d systems a simpler derivation is presented here using the results of decarlo et al it is then shown how the method may also be used to test for stability independent of delay of retarded time delay systems

robust stability and performance of interval plants abstract in this paper we consider the problem of robust performance for systems with unstructured and parametric perturbations the parametric uncertainty is modeled through a single input single output interval system description and the unstructured uncertainty through a norm bounded perturbation for this type of parametric robust performance we show that in order to synthesize a controller that achieves robust performance for a family of interval systems it is sufficient to synthesize that controller for a much smaller subset of the interval family regardless of the number of uncertain parameters in the original problem this reduced set is composed of thirty two one parameter families of systems a special class of controllers with stronger results is also presented

robustness analysis of polynomials with polynomial parameter dependency using bernstein expansion this paper considers the robust stability verification of polynomials with coefficients depending polynomially on parameters varying in given intervals two algorithms are presented both rely on the expansion of a multivariate polynomial into bernstein polynomials the first one is an improvement of the so called bernstein algorithm and checks the hurwitz determinant for positivity over the parameter set the second one is based on the analysis of the value set of the family of polynomials and profits from the convex hull property of the bernstein polynomials numerical results to real world control problems are presented showing the efficiency of both algorithms

on the spectral set for a family of polynomials the problem of generating the spectral set of two different families of polynomials p spherical families and polytopic families is discussed for the spherical case a closed form equation describing the boundary of the spectral set is obtained in the polytopic case a computationally feasible technique which requires only a two dimensional gridding of a bounded subset of the complex plane rather than a high dimensional gridding of the parameter set is shown two numerical examples are included

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

binary quantile regression with local polynomial smoothing abstract manski 1975 1985 proposed the maximum score estimator for the binary choice model under a weak conditional median restriction that converges at the rate of n 1 3 and the standardized version has a nonstandard distribution by imposing additional smoothness conditions horowitz 1992 proposed a smoothed maximum score estimator that often has large finite sample biases and is quite sensitive to the choice of smoothing parameter in this paper we propose a novel framework that leads to a local polynomial smoothing based estimator our estimator possesses finite sample and asymptotic properties typically associated with the local polynomial regression in addition our local polynomial regression based estimator can be extended to the panel data setting simulation results suggest that our estimators may offer significant improvement over the smoothed maximum score estimators

stability invariance of discrete and continuous multidimensional systems under some variable tranformations a variable transformation for stability tests of multidimensional discrete systems which was previously shown to retain a nonvanishing property of a multivariable polynomial on the distinguished boundary of the multidimensional unit ball is shown here to retain this property in the entire multidimensional unit ball also a new variable transformation is presented for stability tests of multidimensional continuous systems and is shown to retain the nonvanishing property on the finite part of the distinguished boundary of the right half hyperplane the multidimensional finite imaginary axis applying this new transformation some necessary conditions are derived for the nonvanishing of multivariable quadratic form polynomials on the finite multidimensional imaginary axis also explicit necessary and sufficient conditions are derived for this case where the dimensionality is two

an algorithm for computing multivariable root loci by pivoting an efficient and robust algorithm for computing multivariable root loci is proposed this algorithm solves a set of characteristic equations by pivoting the algorithm is based on kuhn s algorithm for finding roots of a polynomial by pivoting some theoretical results which validate the algorithm are obtained and several examples are computed to show the efficiency of the algorithm

fast computation of the multivariable stability margin for real interrelated uncertain parameters an alternative implementation of an algorithm for the computation of the multivariable stability margin to check the robust stability of feedback systems with real parametric uncertainty is proposed this method eliminates the need for the frequency search by reducing it to the testing of a finite number of conditions these conditions have a special structure that allows a significant improvement in the speed of computation

an overview of extremal properties for robust control of interval plants abstract this paper provides an overview of recent results on the problem of robust stability and performance of feedback control systems in the presence of plant perturbations the widely studied class of interval plants is considered and an effort is made to cover different types of plant perturbations by incorporating in addition to the interval plant description unstructured norm bounded perturbations extremality results for these classes of uncertain systems are provided in a unifying framework robust performance of control systems is addressed in the paper and a number of extremal results are given for the computation of the structured singular value function for feedback systems with interval plants also classical frequency response analysis for interval plant controller families of open loop transfer functions is surveyed with the aim of providing extremal results for the computation of specification parameters such as phase or gain margins and sensitivity and complementary sensitivity peaks

simple pivoting algorithm for root locus method of linear systems with delay a simple and efficient method for the computation of root loci is proposed the method solves characteristic equations by pivoting procedures the algorithm is simple and applicable to linear systems with time delay some theoretical results are given to validate the algorithm the efficiency of the method is shown by several numerical examples

on the maximum feasible subsystem problem iiss and iis hypergraphs we consider the max fs problem for a given infeasible linear system ax b determine a feasible subsystem containing as many inequalities as possible this problem which is np hard and also difficult to approximate has a number of interesting applications in a wide range of fields in this paper we examine structural and algorithmic properties of max fs and of irreducible infeasible subsystems iiss which are intrinsically related since one must delete at least one constraint from each iis to attain feasibility first we provide a new simplex decomposition characterization of iiss and prove that finding a smallest cardinality iis is very difficult to approximate then we discuss structural properties of iis hypergraphs i e hypergraphs in which each edge corresponds to an iis and show that recognizing iis hypergraphs subsumes the steinitz problem for polytopes and hence is np hard finally we investigate rank facets of the feasible subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system in particular using the iis hypergraph structural result we show that only two very specific types of rank inequalities induced by generalized antiwebs which generalize cliques odd holes and antiholes to general independence systems can arise as facets

a semiparametric structural analysis of the idling of cement kilns abstract this paper estimates the decision rule for idling capital at the micro firm level this is done for a cement kiln by using data from the us cement industry the decision rule for not operating a kiln at a given point in time is the standard rule do not operate if the average variable cost exceeds price the parameters of this discrete decision rule are semiparametrically estimated using the maximum score method and the estimates are then compared with the logit maximum likelihood estimates in terms of their values as well as predictions

operational characteristics of maximum score estimation abstract this paper reports on the operational characteristics of maximum score estimation of a linear model from binary response data a series of previous articles have shown that in theory the maximum score method makes possible binary response analysis under very weak distributional assumptions here we present evidence on the properties of maximum score estimation in practice after reviewing the known asymptotic theory of maximum score estimation the paper describes an algorithm for maximum score estimation and characterizes its performance then findings from a monte carlo study comparing maximum score and logit maximum likelihood estimation are reported finally the accuracy of bootstrap estimation of maximum score root mean square errors is evaluated

necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain linear time invariant systems with uncertain parameters are considered a test is given which is both necessary and sufficient for root clustering of a family of polytopic polynomials in a simply connected domain the test does not require checking a continuum of polynomials special cases include stability testing of continuous time systems and of discrete time systems with uncertain parameters as well as relative stability tests of such systems interval polynomials can also be handled as a special case

transition from pareto to boltzmann gibbs behavior in a deterministic economic model abstract the one dimensional deterministic economic model recently studied by gonzalez estevez et al j gonzalez estevez m g cosenza r lopez ruiz j r sanchez physica a 387 2008 4637 is considered on a two dimensional square lattice with periodic boundary conditions in this model the evolution of each agent is described by a map coupled with its nearest neighbors the map has two factors a linear term that accounts for the agent s own tendency to grow and an exponential term that saturates this growth through the control effect of the environment the regions in the parameter space where the system displays pareto and boltzmann gibbs statistics are calculated for the cases of the von neumann and the moore neighborhood it is found that even when the parameters in the system are kept fixed a transition from pareto to boltzmann gibbs behavior can occur when the number of neighbors of each agent increases

a fast technique for the generation of the spectral set of a polytope of polynomials denoting a polytope of polynomials by p s q where s is the complex variable and q r n are the coefficients we address the following problem given a bounding box q r n for q find the locus of points z in the complex plane such that p z q 0 for some q q the collection of such points describes the so called spectral set of the polytopic family of polynomials in this paper we describe a simple method for its generation following the approach of previous work we give a fast technique which exploits a two dimensional gridding of a bounded subset of the complex plane the number of elementary operations required by the proposed technique is o n when exploring the real axis and o n 2 when considering a single point in the complex plane

on possibilities of the extension of kharitonov s stability test for interval polynomials to the discrete time case it is shown that the kharitonov test for hurwitz stability of an interval polynomial does not extend in general to the discrete time case unless the degree n of the polynomial is not greater than two for n leq 3 a given monic interval polynomial has all roots inside the unit disk if all 2 3 8 extreme polynomials have that property instead of only four polynomials in kharitonov s test for n 4 it is shown by a counterexample that discrete time stability of all extreme polynomials does not guarantee the stability of the interval polynomial

a generalization of rudin s multivariable stability theorem rudin s n variable stability theorem requires testing in addition to a multidimensional condition on the distinguished boundary a single one variable condition a generalization of rudin s theorem is presented in this paper in which the single variable condition is replaced with n single variable conditions where 1 leq n leq n at one s choice the tradeoff is between simpler and a smaller number of single variable conditions the special case n 1 reduces to the original rudin theorem other special cases reduce to some well known stability theorems either with 1 or with n single variable conditions an example is provided where choosing n neq 1 n is advantageous from the computational point of view

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

simplifications in multidimensional stability margin computations previously published algorithms for the computation of multidimensional stability margins of discrete systems require a stability test of these systems before starting the computational algorithm in this correspondence it is shown that the multidimensional stability test may be replaced by single dimensional tests for one kind of stability margin and can be omitted completely for the second kind of stability margin

computation of the frequency response of systems with uncertain parameters a simplification abstract computation of all possible frequency responses of a linear system that depends on m uncertain parameters is the subject of this paper using a brute force approach this computation could be carried out using an m l dimensional parameter sweep i e there is the usual frequency sweep plus one sweep for each uncertain parameter a much simpler computational alternative is possible if the uncertain system s transfer function has a linear dependence on the parameters and if the set of possible parameter values has a polytopic structure for this class of uncertain systems it has previously been shown that for a single fixed frequency all possible responses can be determined using several 1 dimensional sweeps thus for a range of frequencies the obvious extension would involve several 2 dimensional sweeps however this obvious extension is not the simplest way to carry out the computation indeed this paper will show that all possible responses for a range of frequencies can be determined

efficient algorithm for computing qft bounds this article presents an efficient algorithm for computing quantitative feedback theory qft bounds for frequency domain specifications from plant templates which are approximated by a finite numb

stability margin of two dimensional continuous systems the margin of stability of two dimensional 2 d continuous systems is considered in particular the definition of the stability margins for a 2 d discrete system is extended to a 2 d continuous one two methods to compute the stability margin of 2 d continuous systems are presented illustrative examples are provided

root locus for siso dead time systems a continuation based approach we present a numerical method to plot the root locus of single input single output siso dead time systems with respect to the controller gain or the system delay we compute the trajectories of characteristic roots of the closed loop system on a prescribed complex right half plane we calculate the starting branch and boundary crossing roots of root locus branches inside the region we compute the root locus of each characteristic root based on a predictor corrector type continuation method to avoid the high sensitivity of roots with respect to the locus parameter in the neighborhood of branch points the continuation method relies on a natural parameterization of the root locus trajectory in terms of a distance in the characteristic root locus parameter space the method is numerically stable for high order siso dead time systems

zero sets of multiparameter functions and stability of multidimensional systems new theorems which can be used to find the zero set of a multiparameter rational function of a complex variable where the distinguished boundary of the parameters closed domain of definition is composed of piecewise smooth jordan arcs or curves are stated and proved the results are used to derive a new simplified procedure for a multi dimensional stability test presented for the continuous analog case as well as for the discrete digital case now proofs to huang s and strintzis theorems on multidimensional stability are also provided as an application of the theorems on zero sets

the robust root locus abstract in this paper a simple technique is described for generating the root loci of a feedback system which includes perturbations q rl entering affine linearly into the coefficients of the plant denoting the perturbed plant by p s q and the compensator by c s we address the following problem given a bounding set q rl for q find the locus of points z in the complex plane such that 1 kp z q c z 0 for some k 0 and some q q such points z are said to lie on the robust root locus one of the strengths of the technique presented in this paper is that it avoids the combinatoric explosion synonymous with gridding the l dimensional set q and plotting a large number of ordinary root loci associated with gridding the points instead the technique given here exploits only a 2 dimensional gridding of a bounded subset of the complex plane for the more general case when perturbations enter multilinearly into the coefficients a certain convex hull robust root locus is constructed finally the robust root locus technique is illustrated using a model of a supersonic transport plane

a method for computing the interval of delay values for which a differential delay system is stable a test for determining the interval of delay values for which delay differential system is asymptotically stable is presented i e an explicit method is given for calculating h such that for 0

a stopping rule for the computation of generalized method of moments estimators to obtain consistency and asymptotic normality a generalized method of moments gmm estimator typically is defined to be an approximate global minimizer of a gmm criterion function to compute such an estimator however can be problematic because of the difficulty of global optimization in consequence practitioners usually ignore the problem and take the gmm estimator to be the result of a local optimization algorithm this yields an estimator that is not necessarily consistent and asymptotically normal the use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function which makes it difficult to know when to stop the algorithm to alleviate these problems of global and local optimization we propose a stopping rule sr procedure for computing gmm estimators the sr procedure eliminates the need for global search with high probability and it provides an explicit sr for problems of stability that may arise with local optimization problems

a note on a computer aided root locus method it is shown that the computer aided root locus method suggested by pan and chao 3 can be more efficient reducing cumbersome complex arithmetics if one incorporates the bairstow technique for finding roots of real polynomials

competitively coupled maps and spatial pattern formation spatial pattern formation is a key feature of many natural systems in physics chemistry and biology the essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern this problem is most commonly studied using partial differential equations to model a reaction diffusion system of the type introduced by turing we report here on a much simpler and more robust model of spatial pattern formation which is formulated as a novel type of coupled map lattice in our model the local site dynamics are coupled through a competitive rather than diffusive interaction depending only on the strength of the interaction this competitive coupling results in spontaneous symmetry breaking of a homogeneous initial configuration and the formation of stable spatial patterns this mechanism is very robust and produces stable pattern formation for a wide variety of spatial geometries even when the local site dynamics is trivial

an algebraic criterion for robust stability of linear control systems a new robust stability test for linear control systems is described the condition at which robust stability is violated is transformed into an equivalent problem in which the existence of a real root of a multivariable polynomial is investigated this multivariable problem is reduced to that of the solvability of a set of univariable polynomial equations in real numbers for which a number of efficient numerical methods are available the use of the method is illustrated in the design of feedback control for an open loop unstable batch chemical reactor

local nonlinear least squares using parametric information in nonparametric regression abstract we introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model in effect we nonparametrically encompass the parametric model we obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model we establish the uniform consistency and derive the asymptotic distribution of the local parameter estimates and of the corresponding regression and derivative estimates for estimating the regression function our method has superior performance compared to the usual kernel estimators at or near the parametric model it is particularly well motivated for binary data using the probit or logit parametric model as a base we include an application to the horowitz 1993 journal of econometrics 58 49 70 transport choice dataset

predicting binary outcomes we address the issue of using a set of covariates to categorize or predict a binary outcome this is a common problem in many disciplines including economics in the context of a prespecified utility or cost function we examine the construction of forecasts suggesting an extension of the manski 1975 1985 maximum score approach we provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on conditional probability models the results are informative for both forecasting environments as well as program allocation where the value of including the participant in the program depends on how useful the program turns out to be for that participant