generation and random generation from simple groups to maximal subgroups abstract let g be a finite group and let d g be the minimal number of generators for g it is well known that d g 2 for all non abelian finite simple groups we prove that d h 4 for any maximal subgroup h of a finite simple group and that this bound is best possible we also investigate the random generation of maximal subgroups of simple and almost simple groups by applying a recent theorem of jaikin zapirain and pyber we show that the expected number of random elements generating such a subgroup is bounded by an absolute constant we then apply our results to the study of permutation groups in particular we show that if g is a finite primitive permutation group with point stabilizer h then d g 1 d h d g 4

on the product of a nilpotent group and a group with non trivial center abstract it is proved that a finite group g a b which is a product of a nilpotent subgroup a and a subgroup b with non trivial center contains a non trivial abelian normal subgroup

some locally 3 arc transitive graphs constructed from triality abstract two new infinite families of locally 3 arc transitive graphs are constructed which have aut p 8 q as their automorphism group

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

on representing finite lattices as intervals in subgroup lattices of finite groups let mnbe the lattice of length 2 withn 1 atoms it is an open problem to decide whether or not every such lattice or indeed whether or not every finite lattice can be represented as an interval in the subgroup lattice of some finite group we complete the work of the second author lucchini by reducing this problem to a series of questions concerning the finite non abelian simple groups

separately accounting for uncertainties in rainfall and runoff calibration of event based conceptual hydrological models in small urban catchments using bayesian method 1 uncertainty analysis of hydrological models is usually based on model calibration and the bayesian method is a popular way to evaluate the uncertainty the traditional bayesian method usually uses lumped model residuals to form the likelihood function where uncertainty in inputs rainfall is not explicitly addressed this paper compares three approaches based on bayesian inferences considering rainfall uncertainty either implicitly or explicitly in calibration consistent parameter estimation and reliable quantification of predictive uncertainty are mainly examined when rainfall uncertainty is explicitly treated in calibration several rainfall observations at one minute time steps are grouped to share one multiplier to consider the possible observation errors the appropriate grouping strategy that balances the representativeness and the complexity of the problem is suggested the application of the methods considered in this study focuses on small urban catchments 200 ha with a small temporal scale 1 min time step in contrast to most literature studies dealing with larger catchments monitored at larger time steps it is found that uncertainty in rainfall has a minor contribution to the total uncertainty in runoff estimation and this minor role can be explained by the low pass filter effect of the linear reservoir model however the approach explicitly accounting for input uncertainty results in more informed knowledge for uncertainties related with hydrological model calibrations which can possibly provide an estimation of uncertainty attributed to rainfall records it should be noted that rainfall error estimates can compensate model structural uncertainty that is not explicitly addressed in this study

strong duality in nonconvex quadratic optimization with two quadratic constraints we consider the problem of minimizing an indefinite quadratic function subject to two quadratic inequality constraints when the problem is defined over the complex plane we show that strong duality holds and obtain necessary and sufficient optimality conditions we then develop a connection between the image of the real and complex spaces under a quadratic mapping which together with the results in the complex case lead to a condition that ensures strong duality in the real setting preliminary numerical simulations suggest that for random instances of the extended trust region subproblem the sufficient condition is satisfied with a high probability furthermore we show that the sufficient condition is always satisfied in two classes of nonconvex quadratic problems finally we discuss an application of our results to robust least squares problems

complex valued signal processing the proper way to deal with impropriety complex valued signals occur in many areas of science and engineering and are thus of fundamental interest in the past it has often been assumed usually implicitly that complex random signals are proper or circular a proper complex random variable is uncorrelated with its complex conjugate and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane while these assumptions are convenient because they simplify computations there are many cases where proper and circular random signals are very poor models of the underlying physics when taking impropriety and noncircularity into account the right type of processing can provide significant performance gains there are two key ingredients in the statistical signal processing of complex valued data 1 utilizing the complete statistical characterization of complex valued random signals and 2 the optimization of real valued cost functions with respect to complex parameters in this overview article we review the necessary tools among which are widely linear transformations augmented statistical descriptions and wirtinger calculus we also present some selected recent developments in the field of complex valued signal processing addressing the topics of model selection filtering and source separation

corruption of accuracy and efficiency of markov chain monte carlo simulation by inaccurate numerical implementation of conceptual hydrologic models conceptual rainfall runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics reliance on first order explicit fixed step integration methods leads to computationally cheap simulation models that are easy to implement computational speed is especially desirable for estimating parameter and predictive uncertainty using markov chain monte carlo mcmc methods confirming earlier work of kavetski et al 2003 we show here that the computational speed of first order explicit fixed step integration methods comes at a cost for a case study with a spatially lumped conceptual rainfall runoff model it introduces artificial bimodality in the marginal posterior parameter distributions which is not present in numerically accurate implementations of the same model the resulting effects on mcmc simulation include 1 inconsistent estimates of posterior parameter and predictive distributions 2 poor performance and slow convergence of the mcmc algorithm and 3 unreliable convergence diagnosis using the gelman rubin statistic we studied several alternative numerical implementations to remedy these problems including various adaptive step finite difference schemes and an operator splitting method our results show that adaptive step second order methods based on either explicit finite differencing or operator splitting with analytical integration provide the best alternative for accurate and efficient mcmc simulation fixed step or adaptive step implicit methods may also be used for increased accuracy but they cannot match the efficiency of adaptive step explicit finite differencing or operator splitting of the latter two explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically as the splitting method then loses its advantage

criteria for the solubility and non simplicity of finite groups abstract some criteria of the non simplicity of a finite group by graph theoretical terms are derived this is then used to establish conditions under which a finite group is soluble

complex linear quadratic systems for detection and array processing linear quadratic lq filters for detection and estimation are widely used in the real case we investigate their extension in the complex case which introduces various new questions in particular we calculate the optimum lq array receiver in a non gaussian environment by using the deflection criterion and evaluate some of its performance

a note on the solvability of groups abstract let m be a maximal subgroup of a finite group g and k l be a chief factor such that l m while k m we call the group m k l a c section of m and we define sec m to be the abstract group that is isomorphic to a c section of m for every maximal subgroup m of g assume that sec m is supersolvable then any composition factor of g is isomorphic to l 2 p or z q where p and q are primes and p 1 mod 8 this result answer a question posed by y wang s li c sections of maximal subgroups of finite groups j algebra 229 2000 86 94

cyclic quotients of transitive groups abstract let a be a transitive subgroup of s n we show that the largest cyclic quotient of a has order at most n this can be interpreted as an equivalent result about extensions of constants in the galois closure of a covering of curves over a finite field we also prove that the point stabilizer in a finite primitive permutation group always has a faithful orbit

a quaternion widely linear model for nonlinear gaussian estimation this paper deals with the nonlinear minimum mean squared error estimation problem by using a quaternion widely linear model on the basis of the information supplied by a gaussian signal and its square a quaternion observation process is defined and then by applying a widely linear processing an optimal estimator for the continuous time setting is provided the special structure of the estimator proves its superiority over the complex valued widely linear solution the continuous discrete version of the problem is also studied where the solution takes the form of a suboptimal estimator useful in practical applications in addition the particular case of signal plus noise is considered in which the suboptimal solution and its associated error can be implemented through an iterative algorithm two numerical simulation examples are presented showing the advantages of the proposed approach

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality 1 highly parameterized and cpu intensive groundwater models are increasingly being used to understand and predict flow and transport through aquifers despite their frequent use these models pose significant challenges for parameter estimation and predictive uncertainty analysis algorithms particularly global methods which usually require very large numbers of forward runs here we present a general methodology for parameter estimation and uncertainty analysis that can be utilized in these situations our proposed method includes extraction of a surrogate model that mimics key characteristics of a full process model followed by testing and implementation of a pragmatic uncertainty analysis technique called null space monte carlo nsmc that merges the strengths of gradient based search and parameter dimensionality reduction as part of the surrogate model analysis the results of nsmc are compared with a formal bayesian approach using the differential evolution adaptive metropolis dream algorithm such a comparison has never been accomplished before especially in the context of high parameter dimensionality despite the highly nonlinear nature of the inverse problem the existence of multiple local minima and the relatively large parameter dimensionality both methods performed well and results compare favorably with each other experiences gained from the surrogate model analysis are then transferred to calibrate the full highly parameterized and cpu intensive groundwater model and to explore predictive uncertainty of predictions made by that model the methodology presented here is generally applicable to any highly parameterized and cpu intensive environmental model where efficient methods such as nsmc provide the only practical means for conducting predictive uncertainty analysis

a polynomial bound for the orders of primitive solvable groups the structure of primitive solvable permutation groups has bee r thoroughly investigated since galois relying on the known structure theorems we determine the largest order a n of a primitive solvable group of degree ii theorem 3 in the course of the proof we obtain the largest order a n of a transitive solvable group of degree n as well theorem 2 although the formula describing the exact value of i is quite complicated we are able to give an asymptotic evaluation it turns out thar the order of a primitive solvable group of degree n is bounded by 24 12 for a constant c 3 24399 theorem i a similar asymptotic estimate obtained recentiy by babai cameron and pilfy 111 shows that the orders of those primitive permutation groups of degree iz in which all nonabelian simple sections have orders less than a iixed integer k are bounded by n where c c k depends on k only related estimates under the assumption of the classification of finite simple groups are given by cameron 2 strong motivation for such asymptotic estimates comes from recent results of luks 151 on the complexity of graph isomorphism testing the results of the present paper have immediate application to graphs of vaience k p we mean that the field multiplication can be defined on the k dimensional vector space over gf p so that this equ ality holds 127 002 8693 82 g g i27 i so2 gg g

a markov chain monte carlo scheme for parameter estimation and inference in conceptual rainfall runoff modeling a fully bayesian approach to parameter estimation and inference in conceptual rainfall runoff models crrms is presented computations are performed using a markov chain monte carlo mcmc method based on the metropolis hastings algorithm single site and block updating schemes are used for model parameters subject to nonnegativity restrictions as well as interval equality and order constraints diagnostics for the convergence of the markov chain and crrm assessment are also considered the mcmc approach produces samples from the joint posterior distribution of the model parameters this provides more information than single point estimates and avoids the need to use a normal approximation to the posterior as the basis for inference the methodology is demonstrated using an eight parameter conceptual rainfall runoff model and two case studies from southeastern australia the first case study considers a watershed with high runoff yield over a 12 year period the second case study considers a watershed with low yield over a 17 year period the results indicate that 1 bayesian methods provide an objective framework for model criticism and choice 2 the proposed strategies for handling constraints on model parameters are effective 3 the model parameters are sensitive to likelihood function selection 4 the conventional approach of using a power transformation and an autoregressive process to stabilize error variance and model dependence in the residuals may have limited success and 5 some care is required in the implementation of the mcmc approach and reliable results will be difficult to obtain when crrm complexity exceeds the limitations of the rainfall runoff data at hand a key finding is that the mcmc scheme presented herein provides a powerful means of identifying specific inadequacies in the structure of crrms

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

primitive permutation groups with a solvable 2 transitive subconstituent for a permutation group g acting on a finite set and a point a suborbit is an orbit of the point stabilizer g on the permutation group induced by g on is called a subconstituent of g moreover g is said to be uniprimitive if g is primitive but not 2 transitive in this paper we investigate uniprimitive permutation groups which have a solvable 2 transitive subconstituent we determine all such groups g which have a simple socle the affine case that is g has an elementary abelian socle are also discussed and an infinite family of affine primitive groups with non self paired 2 transitive subconstituents are presented

primitive permutation groups of bounded orbital diameter we give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs this is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive a key result is that in the almost simple case with socle of fixed lie rank apart from very specific cases there is such a diameter bound this is proved using recent results on the model theory of pseudofinite fields and difference fields

the maximal subgroups of the chevalley groups g2 q with q odd the ree groups 2g2 q and their automorphism groups

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

the probabilistic zeta function of finite simple groups abstract let g be a finite group there exists a uniquely determined dirichlet polynomial p g s such that if t n then p g t gives the probability of generating g with t randomly chosen elements we show that it may be recognized from the knowledge of p g s whether g frat g is a simple group

prime graph components of the simple groups of lie type over the field of even characteristic abstract we classify the connected components of the prime graphs of the simple groups of lie type over the field of even characteristic

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

a classification of the maximal subgroups of the finite alternating and symmetric groups following the classification of finite simple groups one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups that is of groups x such that x0 u x aut x for some finite non abelian simple group x0 the problem has been solved for most sporadic groups and groups of lie type of low rank see 19 sects 3 43 for discussion and references this paper is a contribution to the case where x0 is an alternating group a so that for n 6 x is a or s the maximal subgroups of a and s are known for several classes of degrees n

semi widely simulation and estimation of continuous time bbc eta proper quaternion random signals the repercussions of quaternion bbc eta properness on the continuous time simulation and estimation problems are studied as a first step a semi widely linear quaternion karhunen loeve expansion is derived then this series representation is used in both problems to give the solutions the simulation technique proposed is useful for transformations of nonstationary gaussian quaternion signals the estimation problem is also analyzed in a continuous discrete setting and by considering two different formulations the cambanis formulation and the signal plus noise model initially the estimators are developed on the basis of a semi widely linear processing afterwards the solutions are improved by incorporating the information supplied by the square quaternion observations and by using a semi widely nonlinear processing in this last scenario we assume gaussian observations and unknown probability distributions of the signal of interest

fixed point ratios in actions of finite classical groups iii abstract this is the first in a series of four papers on fixed point ratios in actions of finite classical groups our main result states that if g is a finite almost simple classical group and is a faithful transitive non subspace g set then either fpr x x g 1 2 for all elements x g of prime order or g is one of a small number of known exceptions here fpr x denotes the proportion of points in which are fixed by x in this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups a further application concerning monodromy groups of covers of riemann surfaces is also outlined

sylow s theorem for moufang loops abstract for finite moufang loops we prove an analog of the first sylow theorem giving a criterion for the existence of a p sylow subloop we also find the maximal order of p subloops in the moufang loops that do not possess p sylow subloops