set identification via quantile restrictions in short panels this paper studies the identifying power of conditional quantile restrictions in short panels with flxed efiects in contrast to classical flxed efiects models with conditional mean restrictions conditional quantile restrictions are not preserved by taking difierences in the regression equation over time this paper shows however that a conditional quantile restriction in conjunction with a weak conditional independence restriction provides bounds on quantiles of difierences in time varying unobservables across periods these bounds carry observable implications for model parameters which generally result in set identiflcation the analysis of these bounds includes conditions for point identiflcation of the parameter vector as well as weaker conditions that result in identiflcation of individual parameter components

logic test pattern generation using linear codes logic testing of today s integrated circuits is a task of increasing difficulty as the number of circuits or transistors packed onto a single chip grows higher and higher exhaustive pattern testing with adequate partitioning of logic has been explored regarding its potential in solving the problems in test pattern generation and fault coverage in this paper we propose a new method of simultaneously generating exhaustive test patterns for all possible input subsets each corresponding to an output up tq a specified size the method is based on the structure of linear polynomial codes and can be easily implemented by modifying existing shift registers in an lssd or scan path design to embody additional feedback connections this is particularly attractive since the implementation is compatible with the approach of self testing using pseudorandom patterns thus a very reasonable strategy is to combine limited exhaustive pattern testing with pseudorandom pattern testing ini cases where complete exhaustive testing is not practical

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

instrumental variable quantile regression a robust inference approach abstract in this paper we develop robust inference procedures for an instrumental variables model defined by y d u where d u is strictly increasing in u and u is a uniform variable that may depend on d but is independent of a set of instrumental variables z the proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely the use of the proposed procedures is illustrated through two empirical examples

estimating and testing a quantile regression model with interactive effects this paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables we provide conditions under which the slope parameter estimator is asymptotically gaussian monte carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate meth ods we discuss an approach to testing the model specification against a competing fixed effects specification the paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment the findings show that i a change in the gender composition of a class impacts differently low and high performing students ii while smaller classes are beneficial for low performers larger classes are beneficial for high performers iii reductions in class size do not seem to impact mean and median student performance iv the fixed effects specification is rejected in favor of the interactive effects specification

new lower bounds for asymmetric and unidirectional codes new lower bounds on the sizes of asymmetric codes and unidirectional codes are presented various methods are used three of them of special interest the first is a partitioning method that is a modification of a method used to construct constant weight codes the second is a combining codes method that is used to obtain a new code from a few others the third method is shortening by weights that is applied on symmetric codes or on codes generated by the combining codes method tables for the sizes of codes of length n

the complexity of fault detection problems for combinational logic circuits in this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability although major fault detection problems have been known to be in general np complete they were proven for rather complex circuits in this correspondence we show that these are still np complete even for monotone circuits and thus for unate circuits we show that for k level k 3 monotone unate circuits these problems are still np complete but that these are solvable in polynomial time for 2 level monotone unate circuits a class of circuits for which these fault detection problems are solvable in polynomial time is presented ripple carry adders decoder circuits linear circuits etc belong to this class a design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test points

capacity analysis for finite state markov mapping of flat fading channels in this paper time varying flat fading channels are modeled as first order finite state markov channels fsmc the effect of this modeling on the channel information capacity is addressed the approximation accuracy of the first order memory assumption in the markov model is validated by comparing the fsmc capacity with the channel capacity assuming perfect state information at the receiver side the results indicate that the first order markovian assumption is accurate for normalized doppler frequencies f sub d t spl lsim 0 01 in amplitude only quantization of the channel gain for noncoherent binary signaling in phase only and joint phase and amplitude quantization of the channel gain for coherent binary signaling the first order markovian assumption is accurate for f sub d t spl lsim 0 001 furthermore the effect of channel quantization thresholds on the fsmc capacity is studied in high signal to noise ratio snr conditions nonuniform two level amplitude quantization scheme outperforms equiprobable quantization method by 0 8 1 5 db

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

how robust is the n cube the n cube network is called faulty if it contains any faulty processor or any faulty link for any number k we want to compute the minimum number f n k of faults which is necessary for an adversary to make every n k dimensional subcube faulty reversely formulated the existence of an n k dimensional non faulty subcube can be guaranteed if there are less than f n k faults in the n cube in this paper several lower and upper bounds for f n k are derived such that the resulting gaps are small for instance if k 2 is constant then f n k q logn especially for k 2 and large n f n 2 a email protected a n 2 where a n logn 1 2 log log n 1 2 or if k w log log n then 2 k f n k 2 1 k with chosen arbitrarily small the aforementioned upper bounds are obtained by analysing the behaviour of an adversary who makes worst case distributions of a given number of faulty processors for k 2 the worst case distribution is obtained constructively in the general case the constructive methods presented in this paper lead to a rather bad upper bound which can be significantly improved by probabilistic arguments the bounds mentioned above change if the notions are relativized with respect to some given parallel fault checking procedure p in this case only subcubes which are possible outputs of p must be made faulty by the adversary the notion of directed chromatic index is defined in order to analyse the case k 2 relations between the directed chromatic index and the chromatic number are derived which are of interest in their own right

a discrete queue based model for capturing memory and soft decision information in correlated fading channels a discrete binary input 2q ary output communication channel with memory is introduced to judiciously capture both the statistical memory and the soft decision information of a time correlated discrete fading channel dfc used with antipodal signaling and soft output quantization of resolution q the discrete channel which can be explicitly described via its binary input process and a 2q ary noise process is shown to be symmetric thus admitting a simple expression for its capacity when its noise is stationary ergodic it is observed that considerable capacity gains can be achieved due to the channel s memory and the use of as few as 2 bits for soft decision over interleaving the channel to render it memoryless and hard decision demodulation q 1 the 2q ary noise process is next modeled via a queue based qb ball sampling mechanism to produce a mathematically tractable stationary ergodic markovian noise source the dfc is fitted by the qb noise model via an iterative procedure that minimizes the kullback leibler divergence rate between the dfc and qb noise sources modeling results measured in terms of channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions

capacity and coding for the gilbert elliott channels the gilbert elliott channel a varying binary symmetric channel with crossover probabilities determined by a binary state markov process is treated in general such a channel has a memory that depends on the transition probabilities between the states a method of calculating the capacity of this channel is introduced and applied to several examples and the question of coding is addressed in the conventional usage of varying channels a code suitable for memoryless channels is used in conjunction with an interleaver with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel the transmission rate is limited by the capacity of this memoryless channel which is often considerably less than the capacity of the original channel a decision feedback decoding algorithm that completely recovers this capacity loss is introduced it is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie aided channel the capacity of which equals that of the original channel the calculated random coding exponent of the genie aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel

energy efficiency in the low snr regime under queueing constraints and channel uncertainty energy efficiency of fixed rate transmissions is studied in the presence of queueing constraints and channel uncertainty it is assumed that neither the transmitter nor the receiver has channel side information prior to transmission the channel coefficients are estimated at the receiver via minimum mean square error mmse estimation with the aid of training symbols it is further assumed that the system operates under statistical queueing constraints in the form of limitations on buffer violation probabilities the optimal fraction of power allocated to training is identified spectral efficiency bit energy tradeoff is analyzed in the low power and wideband regimes by employing the effective capacity formulation in particular it is shown that the bit energy increases without bound in the low power regime as the average power vanishes a similar conclusion is reached in the wideband regime if the number of noninteracting subchannels grow without bound with increasing bandwidth on the other hand it is proven that if the number of resolvable independent paths and hence the number of noninteracting subchannels remain bounded as the available bandwidth increases the bit energy diminishes to its minimum value in the wideband regime for this case expressions for the minimum bit energy and wideband slope are derived overall energy costs of channel uncertainty and queueing constraints are identified and the impact of multipath richness and sparsity is determined

bounds and constructions for ternary constant composition codes the problem of determining the maximum size of a ternary code is considered under the restriction that each symbol should appear a given number of times in each codeword upper and lower bounds on the size of such codes under the hamming metric are discussed where the lower bounds follow from constructions of good codes some of the results are obtained by explicitly finding codes by computer search a table of exact values and best known bounds on the maximum size for codes of length at most 10 is presented

a combinatorial approach to x tolerant compaction circuits test response compaction for integrated circuits ics with scan based design for testability dft support in the presence of unknown logic values xs is investigated from a combinatorial viewpoint the theoretical foundations of x codes employed in an x tolerant compaction technique called x compact are examined through the formulation of a combinatorial model of x compact novel design techniques are developed for x codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values while requiring only small fan out the special class of x codes that results leads to an avoidance problem for configurations in combinatorial designs general design methods and nonconstructive existence theorems to estimate the compaction ratio of an optimal x compactor are also derived

interpolation and approximation of sparse multivariate polynomials over gf 2 a function f 0 1 n to 0 1 is called t sparse if the n variable polynomial representation of f over gf 2 contains at most t monomials such functions are uniquely determined by their values at the so called critical set of all binary n tuples of hamming weight geqq n lfloor log 2 t rfloor 1 an algorithm is presented for interpolating any t sparse function f given the values of f at the critical set the time complexity of the proposed algorithm is proportional to n t and the size of the critical set then the more general problem of approximating 1 sparse functions is considered in which case the approximating function may differ from f at a fraction varepsilon of the space 0 1 n it is shown that o t varepsilon cdot n evaluation points are sufficient for the deterministic varepsilon approximation of any t sparse function and that an order t varepsilon alpha t varepsilon cdot log n points are necessary for this purpose wh

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

the sprague grundy function for some nearly disjunctive sums of nim and silver dollar games abstract we introduce and analyse an extension of the disjunctive sum operation on some classical impartial games whereas the disjunctive sum describes positions formed from independent subpositions our operation combines positions that are not completely independent but interact only in a very restricted way we extend the games nim and silver dollar played by moving counters along one dimensional strips of cells by joining several strips at their initial cell we prove that in certain cases computing the sprague grundy function can be simplified to that of a simpler game with at most two tokens in each strip we give an algorithm that for each sprague grundy value g computes the positions of two token star nim whose sprague grundy values are g we establish that the sequence of differences of coordinates of g positions is ultimately periodic

a quantile correlated random coefficients panel data model abstract we propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data specifically we extend the correlated random coefficients representation of linear quantile regression e g koenker 2005 section 2 6 we show that panel data allows the econometrician to i introduce dependence between the regressors and the random coefficients and ii weaken the assumption of comonotonicity across them i e to enrich the structure of allowable dependence between different coefficients we adopt a fixed effects approach leaving any dependence between the regressors and the random coefficients unmodeled we motivate different notions of quantile partial effects in our model and study their identification for the case of discretely valued covariates we present analog estimators and characterize their large sample properties when the number of time periods t exceeds the number of random coefficients p identification is regular and our estimates are n consistent when t p our identification results make special use of the subpopulation of stayers units whose regressor values change little over time in a way which builds on the approach of graham and powell 2012 in this just identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size one purpose of these discrete bandwidth asymptotics is to approximate settings where covariates are continuously valued and as such there is only an infinitesimal fraction of exact stayers while keeping the convenience of an analysis based on discrete covariates when the mass of stayers shrinks with n identification is irregular and our estimates converge at a slower than n rate but continue to have limiting normal distributions we apply our methods to study the effects of collective bargaining coverage on earnings using the national longitudinal survey of youth 1979 nlsy79 consistent with prior work e g chamberlain 1982 vella and verbeek 1998 we find that using panel data to control for unobserved worker heterogeneity results in sharply lower estimates of union wage premia we estimate a median union wage premium of about 9 percent but with in a more novel finding substantial heterogeneity across workers the 0 1 quantile of union effects is insignificantly different from zero whereas the 0 9 quantile effect is of over 30 percent our empirical analysis further suggests that on net unions have an equalizing effect on the distribution of wages

limited feedback for temporally correlated mimo channels with other cell interference limited feedback improves link reliability with a small amount of feedback from the receiver to the transmitter in cellular systems the performance of limited feedback will be degraded in the presence of other cell interference when the base stations have limited or no coordination this paper establishes the degradation in sum rate of users in a cellular system due to uncoordinated other cell interference and feedback delay a goodput metric is defined as the rate when the bits are successfully received at the mobile station and used to derive an upper bound on the performance of limited feedback systems with delay this paper shows that the goodput gained from having delayed limited feedback decreases doubly exponentially as the delay increases the analysis is extended to precoded spatial multiplexing systems where it is shown that the same upper bound can be used to evaluate the decay in the achievable sum rate to reduce the effects of interference zero forcing interference nulling is applied at the receiver where it is shown that the effect of the interference on the achievable sum rate can be suppressed by nulling out the interferer numerical results show that the decay rate of the goodput decreases when the codebook quantization size increases and when the doppler shift in the channel decreases

exhaustive test pattern generation with constant weight vectors we develop in this paper a simple way of generating a test set which simultaneously provides exhaustive pattern testing with respect to all input subsets of a logic circuit up to a certain size it is shown that such a test set may be formed with vectors of a particular set of weights main theorems and examples are established and illustrated in the binary case for 2 value logic circuits and then generalized to nonbinary cases for multivalue logic circuits such test sets are simple in structure and become optimal in size in certain cases it is also shown that such a test set can be effectively implemented via a scan path type shifter

on greedy algorithms in coding theory we study a wide class of problems in coding theory for which we consider two different formulations in terms of incidence matrices and in terms of hypergraphs these problems are dealt with using a greedy algorithm due to stein 1974 and lovasz 1975 some examples including constructing covering codes codes for conflict resolution separating systems source encoding with distortion etc are given a unified treatment under certain conditions derandomization can be performed leading to an essential reduction in the complexity of the constructions

on the unbiased asymptotic normality of quantile regression with fixed effects abstract nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data in a large class of such models including probit proportional hazard and quantile regression to name just a few it is impossible to difference out the individual effects and inference is usually justified in a large n large t asymptotic framework however there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions such as probit and proportional hazard and quantile regression in the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n t that are very close to what is typically assumed in standard nonlinear panels our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data in terms of n t as other commonly used nonlinear panel data models thorough numerical experiments confirm our theoretical findings

generalized markov modeling for flat fading this paper investigates the properties of a method for obtaining markov models of unspecified order to be applied to narrow band fading channels with additive white gaussian noise the models are obtained by applying the context tree pruning algorithm to experimental or simulated sequences fading environments are identified in which the extension from first order to higher order models is justified the paper presents as examples the evaluation of the covariance function and the packet error distribution

recursive pseudoexhaustive test pattern generation a recursive technique for generating exhaustive patterns is presented the method is optimal i e in one experiment it covers exhaustively every block of k adjacent inputs in the first 2 sup k vectors implementation methods based on characteristic functions of test vectors are provided they include a parallel pattern generator employing an exclusive or array and two serial generators that can be easily adopted in a scan based built in self test environment

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

sieve instrumental variable quantile regression estimation of functional coefficient models abstract in this paper we consider sieve instrumental variable quantile regression ivqr estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates we estimate the functional coefficients by the sieve ivqr technique and establish the uniform consistency and asymptotic normality of the estimators based on the sieve estimates we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic we conduct simulations to evaluate the finite sample behavior of our estimator and test statistic and apply our method to study the estimation of quantile engel curves

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

linear interference cancellation in cdma based on iterative techniques for linear equation systems it has previously been shown that well known iterations for solving a set of linear equations correspond to linear interference cancellation structures here we suggest applying a block wise iteration that consists of an outer and an inner iteration the outer iteration used is the gauss seidel gs method while for the inner iteration we study direct matrix inversion the jacobi over relaxation iteration and the conjugate gradient iteration when a true inner iteration is used this approach allows for a timely derivation of the acceleration parameters required by advanced iterations the block iteration is based on a symbol level implementation which leads to the same detection delay profile for both parallel and serial structures at the expense of differences in the amount of serial processing required this is discussed in some detail and quantified for comparison the performance of the detectors is studied via computer simulations where it is found that the block approach can provide significantly faster convergence leading to improved detection delay over the simpler gs iteration the improvements are obtained at the expense of an increase in the required serial processing speed

orbit and coset analysis of the golay and related codes let b be a code of length n over a field f with automorphism group g b sub w denotes the subset of codewords of weight w the goal is to classify the vectors of f sup n into orbits under g and to determine their distances from the various subcodes b sub w this is done for the first order reed muller nordstrom robinson and hamming codes of length 16 the golay and shortened golay codes of lengths 22 23 24 and the ternary golay code of length 12

heuristic algorithms for constructing binary constant weight codes constant weight binary codes are used in a number of applications constructions based on mathematical structure are known for many codes however heuristic constructions unrelated to any mathematical structure can become of greater importance when the parameters of the code are larger this paper considers the problem of finding constant weight codes with the maximum number of codewords from a purely algorithmic perspective a set of heuristic and metaheuristic methods is presented and developed into a variable neighborhood search framework the proposed method is applied to 383 previously studied cases with lengths between 29 and 63 for these cases it generates 153 new codes with significantly increased numbers of codewords in comparison with existing constructions for 10 of these new codes the number of codewords meets a known upper bound and so these 10 codes are optimal as well as the ability to generate new best codes the approach has the advantage that it is a single method capable of addressing many sets of parameters in a uniform way

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

playing mastermind with many colors we analyze the general version of the classic guessing game mastermind with n positions and k colors since the case k l n1 e e 0 a constant is well understood we concentrate on larger numbers of colors for the most prominent case k e n our results imply that codebreaker can find the secret code with o nlog log n guesses this bound is valid also when only black answer pegs are used it improves the o nlog n bound first proven by chvatal we also show that if both black and white answer pegs are used then the o nlog log n bound holds for up to n2log log n colors these bounds are almost tight as the known lower bound of n shows unlike for k l n1 e simply guessing at random until the secret code is determined is not sufficient in fact we show that an optimal nonadaptive strategy deterministic or randomized needs nlog n guesses

typical rounding problems the linear discrepancy problem is to round a given 0 1 vector x to a binary vector y such that the rounding error with respect to a linear form is small i e such that a x y is small for some given matrix a the combinatorial discrepancy problem is the special case of x 1 2 1 2 t a famous result of beck and spencer math programming 30 1984 88 as well as lovasz et al european j combin 7 1986 151 shows that the linear discrepancy problem is not much harder than this special case any linear discrepancy problem can be solved with at most twice the maximum rounding error among the discrepancy problems of the submatrices of a in this paper we strengthen this result for the common situation that the discrepancy of submatrices having n0 columns is bounded by cn0 for some c 0 0 1 in this case we improve the constant by which the general problem is harder than the discrepancy one from 2 down to 2 2 3 we also find that a random vector has expected linear discrepancy 2 1 2 cn only hence in the typical situation that the discrepancy is decreasing for smaller matrices the linear discrepancy problem is even less difficult compared to the discrepancy one than assured by previous results we also obtain the bound lindisc a x 2 2 21 1 c x 1 our proofs use a reduction to pusher chooser games

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

new bounds for binary covering arrays using simulated annealing covering arrays cas are combinatorial structures specified as a matrix of n rows and k columns over an alphabet on v symbols such that for each set of t columns called the strength of the array every t tuple of symbols is covered recently they have been used to represent interaction test suites for software testing given that they provide economical sized test cases while still preserving important fault detection capabilities this paper introduces an improved implementation of a simulated annealing algorithm called isa for constructing cas of strengths three through six over a binary alphabet i e binary cas extensive experimentation is carried out using 127 well known benchmark instances for assessing its performance with respect to an existing simulated annealing implementation a greedy method and five state of the art algorithms the results show that our algorithm attains 104 new bounds and equals the best known solutions for the other 23 instances consuming reasonable computational time furthermore the implications of using these results as ingredients to recursive constructions are also analyzed

the cell probe complexity of succinct data structures we consider time space tradeoffs for static data structure problems in the cell probe model with word size 1 the bit probe model in this model the goal is to represent n bit data with s n r bits such that queries of a certain type about the data can be answered by reading at most t bits of the representation ideally we would like to keep both s and t small but there are tradeoffs between the values of s and t that limit the possibilities of keeping both parameters small in this paper we consider the case of succinct representations where s n r for some email protected n for a boolean version of the problem of polynomial evaluation with preprocessing of coefficients we show a lower bound on the redundancy query time tradeoff of the form r 1 t email protected n logn in particular for very small redundancies r we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure up to a logarithmic factor we show similar lower bounds for problems satisfying a certain combinatorial properties of a coding theoretic flavor and obtain r 1 t email protected n for certain problems previously no w m lower bounds were known on t in the general model for explicit boolean problems even for very small redundancies by restricting our attention to systematic or index structures f satisfying f x email protected email protected x for some map f where denotes concatenation we show similar lower bounds on the redundancy query time tradeoff for the natural data structuring problems of prefix sum and substring search

quantile regression methods for recursive structural equation models abstract two classes of quantile regression estimation methods for the recursive structural equation models of chesher 2003 identification in nonseparable models econometrica 71 1405 1441 are investigated a class of weighted average derivative estimators based directly on the identification strategy of chesher is contrasted with a new control variate estimation method the latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class an application of the methods to the study of the effect of class size on the performance of dutch primary school students shows that i reductions in class size are beneficial for good students in language and for weaker students in mathematics ii larger classes appear beneficial for weaker language students and iii the impact of class size on both mean and median performance is negligible

lexicographic codes error correcting codes from game theory lexicographic codes or lexicodes are defined by various versions of the greedy algorithm the theory of these codes is closely related to the theory of certain impartial games which leads to a number of surprising properties for example lexicodes over an alphabet of size b 2 a are closed under addition while if b 2 2 a the lexicodes are closed under multiplication by scalars where addition and multiplication are in the nim sense explained in the text hamming codes and the binary golay codes are lexieodes remarkably simple constructions are given for the steiner systems s 5 6 12 and s 5 8 24 several record breaking constant weight codes are also constructed

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

hamming codes hypercube embeddings and fault tolerance in this paper we devise a special 1 error correcting code that enables us to embed the graph product of an n log n node hypercube and a log n node complete graph into in an n node hypercube with constant load dilation and congestion we apply the result to construct improved embeddings of trees and other structures in a hypercube and to design more efficient and robust algorithms for reconfiguring a hypercube around random or worst case faults the result has also been used subsequently by others to show that the n node hypercube can emulate all n node planar graphs with constant slowdown

the local lemma is asymptotically tight for sat the local lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science yet there are hardly any natural problems known where it provides an asymptotically tight answer the main theme of our article is to identify several of these problems among them a couple of widely studied extremal functions related to certain restricted versions of the k sat problem where the local lemma does give essentially optimal answers as our main contribution we construct unsatisfiable k cnf formulas where every clause has k distinct literals and every variable appears in at most 2 e o 1 2k k clauses the lopsided local lemma applied with an assignment of random values according to counterintuitive probabilities shows that this is asymptotically best possible the determination of this extremal function is particularly important as it represents the value where the corresponding k sat problem exhibits a complexity hardness jump from having every instance being a yes instance it becomes np hard just by allowing each variable to occur in one more clause the construction of our unsatisfiable cnf formulas is based on the binary tree approach of gebauer 2012 and thus the constructed formulas are in the class mu 1 of minimal unsatisfiable formulas having one more clause than variables the main novelty of our approach here comes in setting up an appropriate continuous approximation of the problem this leads us to a differential equation the solution of which we are able to estimate the asymptotically optimal binary trees are then obtained through a discretization of this solution the importance of the binary trees constructed is also underlined by their appearance in many other scenarios in particular they give asymptotically precise answers for seemingly unrelated problems like the european tenure game introduced by doerr 2004 and a search problem allowing a limited number of consecutive lies as yet another consequence we slightly improve the best known bounds on the maximum degree and maximum edge degree of a k uniform maker s win hypergraph in the neighborhood conjecture of beck

the k distinct language parameterized automata constructions abstract in this paper we pioneer a study of parameterized automata constructions for languages related to the design of parameterized algorithms we focus on the k distinct language l k k defined as the set of words of length k over an alphabet whose symbols are all distinct this language is implicitly related to several breakthrough techniques developed during the last two decades to design parameterized algorithms for fundamental problems such as k path and r dimensional k matching building upon the color coding divide and color and narrow sieves techniques we obtain the following automata constructions for l k we develop non deterministic automata nfas of sizes 4 k o k n o 1 and 2 e k o k n o 1 where the latter satisfies a bounded ambiguity property relevant to approximate counting as well as a non deterministic xor automaton nxa of size 2 k n o 1 where n we show that our constructions can be used to develop both deterministic and randomized algorithms for k path r dimensional k matching and module motif in a natural manner considering also their approximate counting variants our framework is modular and consists of two parts designing an automaton for k distinct and designing a problem specific automaton as well as an algorithm for deciding whether the intersection automaton s language is empty or for counting the number of accepting paths in it

error correcting codes in projective spaces via rank metric codes and ferrers diagrams coding in the projective space has received recently a lot of attention due to its application in network coding reduced row echelon form of the linear subspaces and ferrers diagram can play a key role for solving coding problems in the projective space in this paper we propose a method to design error correcting codes in the projective space we use a multilevel approach to design our codes first we select a constant weight code each codeword defines a skeleton of a basis for a subspace in reduced row echelon form this skeleton contains a ferrers diagram on which we design a rank metric code each such rank metric code is lifted to a constant dimension code the union of these codes is our final constant dimension code in particular the codes constructed recently by koetter and kschischang are a subset of our codes the rank metric codes used for this construction form a new class of rank metric codes we present a decoding algorithm to the constructed codes in the projective space the efficiency of the decoding depends on the efficiency of the decoding for the constant weight codes and the rank metric codes finally we use puncturing on our final constant dimension codes to obtain large codes in the projective space which are not constant dimension

random access communication and graph entropy a probabilistic problem that arises for conflict resolution in random access communication is treated an earlier conjecture is disproved and a technique for finding lower bounds on the number of graphs of given structure needed to cover all edges of a given graph is developed

randomization derandomization and antirandomization three games abstract three games are given between two players paul and carole with a common theme in each round paul does a split and carole chooses random play by carole allows a bound for the game value through derandomization this becomes a deterministic strategy for carole minimizing a weight function paul can use that same weight function to give a bound for the game value in the other direction

measuring teachability using variants of the teaching dimension in a typical algorithmic learning model a learner has to identify a target object from partial information conversely in a teaching model a teacher has to give information that allows the learners to identify a target object we devise two variants of the classical teaching model for boolean concept classes based on the teaching dimension and describe them by teaching dimension like combinatorial parameters in the first model the learners choose consistent hypotheses with least complexity we show that 1 decision lists are the harder to teach the longer they are and that 2 term dnfs are the harder to teach the more terms they have this contrasts with the teachability results for these classes in the teaching dimension model in our second model the learners choose consistent hypotheses based on the assumption that the teacher is optimal we show that monomials can be taught with a linear number of examples whereas some 1 decision lists need exponentially many

on construction of the 24 12 8 golay codes two product array codes are used to construct the 24 12 8 binary golay code through the direct sum operation this construction provides a systematic way to find proper 8 4 4 linear block component codes for generating the golay code and it generates and extends previously existing methods that use a similar construction framework the code constructed is simple to decode

six standard deviations suffice given n sets on n elements it is shown that there exists a two coloring such that all sets have discrepancy at most knl 2 k an absolute constant this improves the basic probabilistic method with which k c ln n l 2 the result is extended to n finite sets of arbitrary size probabilistic techniques are melded with the pigeonhole principle an alternate proof of the existence of rudin shapiro functions is given showing that they are exponential in number given n linear forms in n variables with all coefficients in 1 1 it is shown that initial values pl p e 0 1 may be approximated by el e 0 1 so that the forms have small error 1 we state our main result first in the language of linear forms theorem 1 let 1 1 li xl x l ailxl xe ai txn 1 i n be n linear forms in n variables with all laijl 1 then there exist e1 esl e 1 1 such that 1 2 li el e l ks for all i 1 i n here k is an absolute constant when all aij e 0 1 we may consider e1 aij as the incidence matrix for a family of n sets on n elements that is we may set ai j aij 1 given a two coloring say red and blue of 1 n the discrepancy disc x of a set x c 1 n is defined as the number of red points in x minus the number of blue points in x if we interpret si 1 as meaning i is to be colored red and ej 1 as blue then we obtain the following result corollary 2 let al an c 1 n then there exists a two coloring of 1 n so that 1 3 disc aj kw foralli 1 i n received by the editors july 1 1984 1980 muthemcltics subject clclssific ltion primary 05b20 secondary 41a28 42a61 this work was initiated while the author was an irex exchange fellow at the mathematical institute budapest and completed with support of the national science foundation for the many kindnesses and for the creative research environment provided by institute staff and colleagues koszonom szepen t1985 american mathematical society 0002 9947 85 1 00 25 per page

complex and integral laminated lattices in an earlier paper we studied real laminated lattices or z modules a where a is the lattice of even integers and a is obtained by stacking layers of a suitable n l dimensional lattice a as densely as possible keeping the same minimal norm the present paper considers two generalizations a complex and quaternionic lattices obtained by replacing z module by module where j may be the eisenstein gaussian or hurwitzian integers etc and b integral laminated lattices in which a is required to be an integral lattice with the prescribed minimal norm this enables us to give a partial answer to a question of j g thompson on integral lattices and to explain some of the computer generated results of plesken and pohst on this problem also a number of familiar lattices now arise in a canonical way for example the coxeter todd lattice is the 6 dimensional integral laminated lattice over z to of minimal norm 2 the paper includes tables of the best real integral lattices in up to 24 dimensions

on first order markov modeling for the rayleigh fading channel previous models for the received signal amplitude of the flat fading channel that use first order finite state markov chains are examined the stochastic properties of a proposed first order model based on these models are examined the limitations of using an information theoretic metric which is sometimes used to justify a first order markov chain as a sufficient model for very slowly fading channels are discussed a simple method of qualitatively comparing autocorrelation functions is instead proposed the usefulness of the first order markov chain in representing the flat fading channel is examined by looking at two specific problems in wireless system applications that represent two disparate cases the first case involves analysis over a short duration of time relative to the inverse of the normalized doppler frequency while the second involves analysis over a long duration of time contrary to previous reports the results indicate that first order markov chains are not generally suitable for very slowly fading channels rather first order markov chains can be suitable for very slowly fading applications which require analysis over only a short duration of time

covering arrays avoiding forbidden edges covering arrays cas can be used to detect the existence of faulty pairwise interactions between parameters or components in a software system the generalization considered here applies to the situation in which some input combinations are invalid a requirement quite common in software testing in this paper we study covering arrays avoiding forbidden edges cafes where certain pairwise interactions are forbidden while all others must be covered and we aim to minimize the number of tests we establish a theoretical framework for this problem by providing connections to the edge clique covering problem lower and upper bounds complexity results and a recursive construction we also give an algorithm for the case of binary alphabets

limited feedback beamforming over temporally correlated channels feedback of quantized channel state information csi called limited feedback enables transmit beamforming in multiple input multiple output mimo wireless systems with a small amount of overhead due to its efficiency beamforming with limited feedback has been adopted in several wireless communication standards prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected in this paper we consider temporally correlated channels and design single user transmit beamforming with limited feedback analytical results concerning csi feedback are derived by modeling quantized csi as a first order finite state markov chain these results include the information rate of the csi quantizer output the bit rate a csi feedback channel is required to support and the effect of feedback delay on throughput in particular based on the theory of markov chain convergence rate feedback delay is proved to reduce the throughput gain due to csi feedback at least exponentially furthermore an algorithm is proposed for csi feedback compression in time combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example

ulam s searching game with a fixed number of lies abstract paul tries to find an unknown x from l to n by asking q yes no questions in response carole may lie up to k times for k fixed and n q sufficiently large necessary and sufficient conditions are given for paul to win

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

inferences in panel data with interactive effects using large covariance matrices abstract we consider efficient estimation of panel data models with interactive effects which relies on a high dimensional inverse covariance matrix estimator by using a consistent estimator of the error covariance matrix we can take into account both cross sectional correlations and heteroskedasticity in the presence of cross sectional correlations the proposed estimator eliminates the cross sectional correlation bias and is more efficient than the existing methods the rate of convergence is also improved in addition we find that when the statistical inference involves estimating a high dimensional inverse covariance matrix the minimax convergence rate on large covariance estimations is not sufficient for inferences to address this issue a new doubly weighted convergence result is developed the proposed method is applied to the us divorce rate data we find that our more efficient estimator identifies the significant effects of divorce law reforms on the divorce rate and provides tighter confidence intervals than existing methods this provides a confirmation for the empirical findings of wolfers 2006 under more general unobserved heterogeneity

instrumental quantile regression inference for structural and treatment effect models we introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference these methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes we describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it we focus our discussion of inference on tests of distributional equality constancy of effects conditional dominance and exogeneity we apply the procedures to characterize the returns to schooling in the u s

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

european tenure games we study a variant of the tenure game introduced by spencer theoret comput sci 131 1994 415 in this version faculty is not fired but downgraded to the lowest rung instead for the upper bound we give a potential function argument showing that the value d of the game starting with d faculty on the first rung satisfies d log2d log2 log2d 1 98 we prove a nearly matching lower bound of log2d log2 log2d using a strategy that can be interpreted as an antirandomization of spencer s original game for d tending to infinity these bounds improve to log2d log2 log2d 1 o 1 d log2d log2 log2d 1 73 o 1 in particular the set of all d n such that the value of the game is precisely log2d log2 log2d 1 has lower density greater than 1 5

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries

intersecting codes and independent families a binary intersecting code is a linear code with the property that any two nonzero codewords have intersecting supports these codes appear in a wide variety of contexts and applications e g multiple access cryptography and information theory this paper is devoted partly to the study of intersecting codes and partly to their use in constructing large t independent families of binary vectors the latter subject has by now been extensively studied and has application in vlsi testing defect correction e biased probability spaces and derandomization by concatenation methods we construct codes with the highest known fate asymptotically we then generalize the concept to t wise intersecting codes we give bounds on the achievable rate of such codes both existential and constructive we show how t wise intersecting codes can be used to obtain t 1 independent families with this method we obtain improved asymptotical constructions of t independent families complexity issues are discussed

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated