the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

a simplified min sum decoding algorithm for non binary ldpc codes non binary low density parity check codes are robust to various channel impairments however based on the existing decoding algorithms the decoder implementations are expensive because of their excessive computational complexity and memory usage based on the combinatorial optimization we present an approximation method for the check node processing the simulation results demonstrate that our scheme has small performance loss over the additive white gaussian noise channel and independent rayleigh fading channel furthermore the proposed reduced complexity realization provides significant savings on hardware so it yields a good performance complexity tradeoff and can be efficiently implemented

functional quantitative susceptibility mapping fqsm blood oxygenation level dependent bold functional magnetic resonance imaging fmri is a powerful technique typically based on the statistical analysis of the magnitude component of the complex time series here we additionally interrogated the phase data of the fmri time series and used quantitative susceptibility mapping qsm in order to investigate the potential of functional qsm fqsm relative to standard magnitude bold fmri high spatial resolution data 1 mm isotropic were acquired every 3 seconds using zoomed multi slice gradient echo epi collected at 7 t in single orientation so and multiple orientation mo experiments the latter involving 4 repetitions with the subject s head rotated relative to b0 statistical parametric maps spm were reconstructed for magnitude phase and qsm time series and each was subjected to detailed analysis several fqsm pipelines were evaluated and compared based on the relative number of voxels that were coincidentally found to be significant in qsm and magnitude spms common voxels we found that sensitivity and spatial reliability of fqsm relative to the magnitude data depended strongly on the arbitrary significance threshold defining activated voxels in spms and on the efficiency of spatio temporal filtering of the phase time series sensitivity and spatial reliability depended slightly on whether mo or so fqsm was performed and on the qsm calculation approach used for so data our results present the potential of fqsm as a quantitative method of mapping bold changes we also critically discuss the technical challenges and issues linked to this intriguing new technique

on optimal designs for nonlinear models a general and efficient algorithm finding optimal designs for nonlinear models is challenging in general although some recent results allow us to focus on a simple subclass of designs for most problems deriving a specific optimal design still mainly depends on numerical approaches there is need for a general and efficient algorithm that is more broadly applicable than the current state of the art methods we present a new algorithm that can be used to find optimal designs with respect to a broad class of optimality criteria when the model parameters or functions thereof are of interest and for both locally optimal and multistage design strategies we prove convergence to the optimal design and show in various examples that the new algorithm outperforms the current state of the art algorithms

a note on the de la garza phenomenon for locally optimal designs the celebrated de la garza phenomenon states that for a polynomial regression model of degree p 1 any optimal design can be based on at most p design points in a remarkable paper yang ann statist 38 2010 2499 2524 showed that this phenomenon exists in many locally optimal design problems for nonlinear models in the present note we present a different view point on these findings using results about moment theory and chebyshev systems in particular we show that this phenomenon occurs in an even larger class of models than considered so far

construction of quasi cyclic ldpc codes for awgn and binary erasure channels a finite field approach in the late 1950s and early 1960s finite fields were successfully used to construct linear block codes especially cyclic codes with large minimum distances for hard decision algebraic decoding such as bose chaudhuri hocquenghem bch and reed solomon rs codes this paper shows that finite fields can also be successfully used to construct algebraic low density parity check ldpc codes for iterative soft decision decoding methods of construction are presented ldpc codes constructed by these methods are quasi cyclic qc and they perform very well over the additive white gaussian noise awgn binary random and burst erasure channels with iterative decoding in terms of bit error probability block error probability error floor and rate of decoding convergence collectively particularly they have low error floors since the codes are qc they can be encoded using simple shift registers with linear complexity

codes on finite geometries new algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented the new construction methods result in a class of multistep majority logic decodable codes and three classes of low density parity check ldpc codes decoding methods for the class of majority logic decodable codes and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their tanner graphs are presented most of the codes constructed can be either put in cyclic or quasi cyclic form and hence their encoding can be implemented with linear shift registers

construction of nonbinary cyclic quasi cyclic and regular ldpc codes a finite geometry approach this paper presents five methods for constructing nonbinary ldpc codes based on finite geometries these methods result in five classes of nonbinary ldpc codes one class of cyclic ldpc codes three classes of quasi cyclic ldpc codes and one class of structured regular ldpc codes experimental results show that constructed codes in these classes decoded with iterative decoding based on belief propagation perform very well over the awgn channel and they achieve significant coding gains over reed solomon codes of the same lengths and rates with either algebraic hard decision decoding or kotter vardy algebraic soft decision decoding at the expense of a larger decoding computational complexity

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

optimal group testing designs for estimating prevalence with uncertain testing errors summary we construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity using optimal design theory for approximate designs we show that the most efficient design for simultaneously estimating the prevalence sensitivity and specificity requires three different group sizes with equal frequencies however if estimating prevalence as accurately as possible is the only focus the optimal strategy is to have three group sizes with unequal frequencies on the basis of a chlamydia study in the usa we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator we demonstrate that the locally d and ds optimal designs proposed have high efficiencies even when the prespecified values of the parameters are moderately misspecified

on the de la garza phenomenon deriving optimal designs for nonlinear models is in general challenging one crucial step is to determine the number of support points needed current tools handle this on a case by case basis each combination of model optimality criterion and objective requires its own proof the celebrated de la garza phenomenon states that under a p 1 th degree polynomial regression model any optimal design can be based on at most p design points the minimum number of support points such that all parameters are estimable does this conclusion also hold for nonlinear models if the answer is yes it would be relatively easy to derive any optimal design analytically or numerically in this paper a novel approach is developed to address this question using this new approach it can be easily shown that the de la garza phenomenon exists for many commonly studied nonlinear models such as the emax model exponential model three and four parameter log linear models emax pk1 model as well as many classical polynomial regression models the proposed approach unifies and extends many well known results in the optimal design literature it has four advantages over current tools i it can be applied to many forms of nonlinear models to continuous or discrete data to data with homogeneous or nonhomogeneous errors ii it can be applied to any design region iii it can be applied to multiple stage optimal design and iv it can be easily implemented

high rate quasi cyclic low density parity check codes derived from finite affine planes this paper shows that several attractive classes of quasi cyclic qc low density parity check ldpc codes can be obtained from affine planes over finite fields one class of these consists of duals of one generator qc codes presented here for codes contained in this class are the exact minimum distance and a lower bound on the multiplicity of the minimum weight codewords further it is shown that the minimum hamming distance of a code in this class is equal to its minimum additive white gaussian noise awgn pseudoweight also discussed is a class consisting of codes from circulant permutation matrices and an explicit formula for the rank of the parity check matrix is presented for these codes additionally it is shown that each of these codes can be identified with a code constructed from a constacyclic maximum distance separable code of dimension 2 the construction is similar to the derivation of reed solomon rs based ldpc codes presented by chen and djurdjevic experimental results show that a number of high rate qc ldpc codes with excellent error performance are contained in these classes

a matrix theoretic approach for analyzing quasi cyclic low density parity check codes a matrix theoretic approach for studying quasi cyclic codes based on matrix transformations via fourier transforms and row and column permutations is developed these transformations put a parity check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field the approach is amicable to the analysis and construction of quasi cyclic low density parity check codes since it takes into account the specific parity check matrix used for decoding with iterative message passing algorithms based on this approach the dimension of the codes and parity check matrices for the dual codes can be determined several algebraic and geometric constructions of quasi cyclic codes are presented as applications along with simulation results showing their performance over additive white gaussian noise channels decoded with iterative message passing algorithms

cyclic and quasi cyclic ldpc codes on constrained parity check matrices and their trapping sets this paper is concerned with construction and structural analysis of both cyclic and quasi cyclic codes particularly low density parity check ldpc codes it consists of three parts the first part shows that a cyclic code given by a parity check matrix in circulant form can be decomposed into descendant cyclic and quasi cyclic codes of various lengths and rates some fundamental structural properties of these descendant codes are developed including the characterization of the roots of the generator polynomial of a cyclic descendant code the second part of the paper shows that cyclic and quasi cyclic descendant ldpc codes can be derived from cyclic finite geometry ldpc codes using the results developed in the first part of the paper this enlarges the repertoire of cyclic ldpc codes the third part of the paper analyzes the trapping set structure of regular ldpc codes whose parity check matrices satisfy a certain constraint on their rows and columns several classes of finite geometry and finite field cyclic and quasi cyclic ldpc codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances consequently their error floor performances are dominated by their minimum distances

optimal design for goodness of fit of the michaelis menten enzyme kinetic function we construct efficient designs for the michaelis menten enzyme kinetic model capable of checking model assumptions an extended model called emax is also considered for this purpose this model is widely used in pharmacokinetics and reduces to the michaelis menten model for a specific choice of parameter settings our strategy is to find efficient designs for estimating the parameters in the emax model and at the same time test the validity of the michaelis menten model against the emax model by maximizing a minimum of the d or d1 efficiencies taken over a range of values for the nonlinear parameters in particular we show that such designs are a efficient for estimating parameters in the emax model b about 70 efficient for estimating parameters in the michaelis menten model c efficient for testing the michaelis menten model against the emax model and d robust with respect to misspecification of the unknown parameters in the nonlinear model

support points of locally optimal designs for nonlinear models with two parameters we propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model in contrast to the commonly used geometric approach we use an approach based on algebraic tools considerations are restricted to models with two parameters and the general results are applied to often used special cases including logistic probit double exponential and double reciprocal models for binary data a loglinear poisson regression model for count data and the michaelis menten model the approach which is also of value for multi stage experiments works both with constrained and unconstrained design regions and is relatively easy to implement

characterization of c l and ϕk optimal designs for a class of non linear multiple regression models optimal designs for multiple regression models are determined we consider a general class of non linear models including proportional hazards models with different censoring schemes the poisson and the negative binomial model for these models we provide a complete characterization of c optimal designs for all vectors c in the case of a single covariate for multiple regression with an arbitrary number of covariates c optimal designs for certain vectors c are derived analytically using some general results on the structure of optimal designs for multiple regression we determine l and k optimal designs for models with an arbitrary number of covariates

a revolving iterative algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes cyclic and quasi cyclic algebraic ldpc codes constructed based on finite fields finite geometries and combinatorial designs can achieve excellent performance in terms of error rate error floor and rate of decoding convergence with iterative decoding however the relatively high density of the parity check matrix of an algebraic cyclic or quasi cyclic ldpc code makes the hardware implementation complexity of the decoder quite large which may be a critical issue in practical applications this paper presents an effective reduced complexity algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes based on the block cyclic structure and cyclic grouping of the rows of their parity check matrices the decoding of a code is carried out based on a single small submatrix of the parity check matrix of the code in a revolving manner the proposed decoding algorithm significantly reduces the hardware implementation complexity and the size of memory required to store information

algebraic construction of quasi cyclic ldpc codes for the awgn and erasure channels this paper is concerned with construction of quasi cyclic qc low density parity check ldpc codes for three different types of channels the additive white gaussian noise the binary random erasure and the binary burst erasure channels two algebraic methods for systematic construction of qc ldpc codes are presented codes constructed perform well over all three types of channels

a modulated closed form solution for quantitative susceptibility mapping a thorough evaluation and comparison to iterative methods based on edge prior knowledge the aim of this study is to perform a thorough comparison of quantitative susceptibility mapping qsm techniques and their dependence on the assumptions made the compared methodologies were two iterative single orientation methodologies minimizing the l2 l1tv norm of the prior knowledge of the edges of the object one over determined multiple orientation method cosmos and anewly proposed modulated closed form solution mcf the performance of these methods was compared using a numerical phantom and in vivo high resolution 0 65 mm isotropic brain data acquired at 7 t using a new coil combination method for all qsm methods the relevant regularization and prior knowledge parameters were systematically changed in order to evaluate the optimal reconstruction in the presence and absence of a ground truth additionally the qsm contrast was compared to conventional gradient recalled echo gre magnitude and r2 maps obtained from the same dataset the qsm reconstruction results of the single orientation methods show comparable performance the mcf method has the highest correlation corrmcf 0 95 r2mcf 0 97 with the state of the art method cosmos with additional advantage of extreme fast computation time the l curve method gave the visually most satisfactory balance between reduction of streaking artifacts and over regularization with the latter being overemphasized when the using the cosmos susceptibility maps as ground truth r2 and susceptibility maps when calculated from the same datasets although based on distinct features of the data have a comparable ability to distinguish deep gray matter structures

a new multi edge metric constrained peg algorithm for designing binary ldpc code with improved cycle structure the progressive edge growth peg algorithm constructs an edge in each stage to maximize the variable node vn of interest s local girth in real time thus this vn s local girths after more than one edge is added to the current tanner graph tg setting may not be maximized relative to that tg setting to address this problem we define the multi edge local girth and edge trial and based on these definitions propose a new multi edge metric constrained peg algorithm mm pega to improve the design at each vn the mm pega constructs an edge in each stage that relative to the current tg setting can potentially maximize the vn of interest s local girth after a certain number up to the edge trial of edges are added to the tg setting we first analyze the properties of the multi edge local girth and then propose an algorithm for calculating the multi edge local girth we also propose a method for accelerating the mm pega moreover we generalize the mm pega for improving different peg like designs according to the theoretical analysis increasing the edge trial of the mm pega is expected to positively affect the cycle structure and the error performance of resulting low density parity check ldpc code this expectation is verified by simulations

on algebraic construction of gallager and circulant low density parity check codes this correspondence presents three algebraic methods for constructing low density parity check ldpc codes these methods are based on the structural properties of finite geometries the first method gives a class of gallager codes and a class of complementary gallager codes the second method results in two classes of circulant ldpc codes one in cyclic form and the other in quasi cyclic form the third method is a two step hybrid method codes in these classes have a wide range of rates and minimum distances and they perform well with iterative decoding

optimal designs for dose finding studies with an active control summary dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control in the past however research has focused mostly on experimental designs for placebo controlled dose finding studies to the best of our knowledge optimal designs for dose finding studies with an active control have not been considered so far as the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models the related design problem is different from what has been investigated before in the literature we present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control we determine explicitly the locally optimal designs for a broad class of models employed in such studies we also discuss robust design strategies and determine related bayesian and standardized minimax optimal designs we illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors

simultaneous phase unwrapping and removal of chemical shift spurs using graph cuts application in quantitative susceptibility mapping quantitative susceptibility mapping qsm is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility it relies on having a high quality field map typically acquired with a relatively long echo spacing and long final te applications of qsm outside the brain require the removal of fat contributions to the total signal phase however current water fat separation methods applied on typical data acquired for qsm suffer from three issues inadequacy when using large echo spacing over smoothing of the field maps and high computational cost in this paper the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves this method is referred as simultaneous phase unwrapping and removal of chemical shift spurs the result from spurs is then used as the initial guess for a voxel wise iterative decomposition of water and fat with echo asymmetric and least squares estimation ideal the estimated 3 d field maps are used to compute qsm in body regions outside of the brain such as the liver experimental results show substantial improvements in field map estimation water fat separation and reconstructed qsm compared to two existing water fat separation methods on 1 5t and 3t magnetic resonance human data with long echo spacing and rapid field map variation

quasi cyclic ldpc codes an algebraic construction this paper presents two new large classes of qc ldpc codes one binary and one non binary codes in these two classes are constructed by array dispersions of row distance constrained matrices formed based on additive subgroups of finite fields experimental results show that codes constructed perform very well over the awgn channel with iterative decoding based on belief propagation codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry ldpc codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low complexity reliability based iterative decoding algorithms such as binary message passing decoding algorithms non binary codes decoded with a fast fourier transform based sum product algorithm achieve significantly large coding gains over reed solomon codes of the same lengths and rates decoded with either the hard decision berlekamp massey algorithm or the algebraic soft decision kotter vardy algorithm they have potential to replace reed solomon codes in some communication or storage systems where combinations of random and bursts of errors or erasures occur

locally d optimal designs based on a class of composed models resulted from blending emax and one compartment models a class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic emax model is introduced the locally d optimal ld design for a 4 parameter composed model is found to be a saturated 4 point uniform ld design with the two boundary points of the design space in the ld design support for a 5 parameter composed model a su cient condition for the ld design to require the minimum number of sampling time points is derived robust ld designs are also investigated for both models it is found that an ld design with k parameters is equivalent to an ld design with k i1 parameters if the linear parameter in the two composed models is a nuisance parameter assorted examples of ld designs are presented research supported by national science foundation nsf grants dms 0103727 dms 0603761 and national institutes of health nih grant p50 at00155 jointly supported by national center for complementary and alternative medicine the o ce of dietary supplements the o ce of research on women s health and national institute of general medicine any opinions flndings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re ect the views of the nsf and the nih

construction of regular and irregular ldpc codes geometry decomposition and masking two algebraic methods for systematic construction of structured regular and irregular low density parity check ldpc codes with girth of at least six and good minimum distances are presented these two methods are based on geometry decomposition and a masking technique numerical results show that the codes constructed by these methods perform close to the shannon limit and as well as random like ldpc codes furthermore they have low error floors and their iterative decoding converges very fast the masking technique greatly simplifies the random like construction of irregular ldpc codes designed on the basis of the degree distributions of their code graphs

decoding algorithms for nonbinary ldpc codes over gf q in this letter we address the problem of decoding nonbinary low density parity check ldpc codes over finite fields gf q with reasonable complexity and good performance in the first part of the letter we recall the original belief propagation bp decoding algorithm and its fourier domain implementation we show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding in the second part of the letter we introduce a simplified decoder which is inspired by the min sum decoder for binary ldpc codes we called this decoder extended min sum ems we show that it is possible to greatly reduce the computational complexity of the check node processing by computing approximate reliability measures with a limited number of values in a message by choosing appropriate correction factors or offsets we show that the ems decoder performance is quite good and in some cases better than the regular bp decoder the optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution our simulations on ultra sparse codes over very high order fields show that nonbinary ldpc codes are promising for applications which require low frame error rates for small or moderate codeword lengths the ems decoder is a good candidate for practical hardware implementations of such codes

designing experiments with respect to standardized optimality criteria we introduce a new class of standardized optimality criteria which depend on standardized covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces

saturated locally optimal designs under differentiable optimality criteria we develop general theory for finding locally optimal designs in a class of single covariate models under any differentiable optimality criterion yang and stufken ann statist 40 2012 1665 1681 and dette and schorning ann statist 41 2013 1260 1267 gave complete class results for optimal designs under such models based on their results saturated optimal designs exist however how to find such designs has not been addressed we develop tools to find saturated optimal designs and also prove their uniqueness under mild conditions

transactions papers constructions of nonbinary quasi cyclic ldpc codes a finite field approach this paper is concerned with construction of efficiently encodable nonbinary quasi cyclic ldpc codes based on finite fields four classes of nonbinary quasi cyclic ldpc codes are constructed experimental results show that codes constructed perform well with iterative decoding using a fast fourier transform based q ary sum product algorithm and they achieve significant coding gains over reed solomon codes of the same lengths and rates decoded with either algebraic hard decision berlekamp massey algorithm or algebraic soft decision kotter vardy algorithm

near optimum universal belief propagation based decoding of low density parity check codes in this paper we propose a belief propagation bp based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified bp based algorithm the normalization factors can be obtained not only by simulation but also importantly theoretically this new bp based algorithm is much simpler to implement than bp decoding as it requires only additions of the normalized received values and is universal i e the decoding is independent of the channel characteristics some simulation results are given which show this new decoding approach can achieve an error performance very close to that of bp on the additive white gaussian noise channel especially for low density parity check ldpc codes whose check sums have large weights the principle of normalization can also be used to improve the performance of the max log map algorithm in turbo decoding and some coding gain can be achieved if the code length is long enough

construction of non binary quasi cyclic ldpc codes by arrays and array dispersions transactions papers this paper presents two algebraic methods for constructing high performance and efficiently encodable nonbinary quasi cyclic ldpc codes based on arrays of special circulant permutation matrices and multi fold array dispersions codes constructed based on these methods perform well over the awgn and other types of channels with iterative decoding based on belief propagation experimental results show that over the awgn channel these non binary quasi cyclic ldpc codes significantly outperform reed solomon codes of the same lengths and rates decoded with either algebraic hard decision berlekamp massey algorithm or algebraic soft decision kotter vardy algorithm also presented in this paper is a class of asymptotically optimal ldpc codes for correcting bursts of erasures codes constructed also perform well over flat fading channels non binary quasi cyclic ldpc codes have a great potential to replace reed solomon codes in some applications in communication environments and storage systems for combating mixed types of noises and interferences

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

algebraic quasi cyclic ldpc codes construction low error floor large girth and a reduced complexity decoding scheme this paper presents a simple and very flexible method for constructing quasi cyclic qc low density paritycheck ldpc codes based on finite fields the code construction is based on two arbitrary subsets of elements from a given field some well known constructions of qc ldpc codes based on finite fields and combinatorial designs are special cases of the proposed construction the proposed construction in conjunction with a technique known as masking results in codes whose tanner graphs have girth 8 or larger experimental results show that codes constructed using the proposed construction perform well and have low error floors also presented in the paper is a reduced complexity iterative decoding scheme for qc ldpc codes based on the section wise cyclic structure of their parity check matrices the proposed decoding scheme is an improvement of an earlier proposed reduced complexity iterative decoding scheme

optimal designs for rational models and weighted polynomial regression sion model of degree p with efficiency function 1 x are presented interest in these designs stems from the fact that they are equivalent to locally d optimal designs for inverse quadratic polynomial models for the unrestricted design space and p n the d optimal designs put equal masses on p 1 points which coincide with the zeros of an ultraspherical polynomial while for p n they are equivalent to d optimal designs for certain trigonometric regression models and exhibit all the curious and interesting features of those designs for the restricted design space 1 1 sufficient but not necessary conditions for the d optimal designs to be based on p 1 points are developed in this case the problem of constructing p 1 point d optimal designs is equivalent to an eigenvalue problem and the designs can be found numerically for n 1 and 2 the problem is solved analytically and specifically the d optimal designs put equal masses at the points 1 and at the p 1 zeros of a sum of n 1 ultraspherical polynomials a conjecture which extends these analytical results to cases with n an integer greater than 2 is given and is examined empirically 1 introduction weighted polynomial regression models with variance functions which depend on the explanatory variable have played and continue to play an important role in the development of classical optimal design theory the reasons for this are essentially twofold first there is a wealth of elegant mathematics associated with the construction of d optimal designs for many of these models in particular for certain classes of variance functions it is possible to show that the d optimal designs put equal masses on p 1 points of support where p is the degree of the polynomial embedded in the model and furthermore it is possible to use tools from the theory of differential equations and of canonical moments in order to establish that these support points coincide with the zeros of classical orthogonal polynomi

optimal designs for dose finding studies understanding and properly characterizing the dose response relationship is a fundamental step in the investigation of a new compound be it a herbicide or fertilizer a molecular entity an environmental toxin or an industrial chemical in this article we investigate the problem of deriving efficient designs for the estimation of target doses in the context of clinical dose finding we propose methods to determine the appropriate number and actual levels of the doses to be administered to patients as well as their relative sample size allocations more specifically we derive local optimal designs that minimize the asymptotic variance of the minimum effective dose estimate under a particular dose response model we investigate the small sample properties of these designs together with their sensitivity to a misspecification of the true parameter values and of the underlying dose response model through simulation finally we demonstrate that the designs derived for a fixed model are rather sensitive

shuffled iterative decoding shuffled versions of iterative decoding of low density parity check codes and turbo codes are presented the proposed schemes have about the same computational complexity as the standard versions and converge faster simulations show that the new schedules offer better performance complexity tradeoffs especially when the maximum number of iterations has to remain small

whole brain susceptibility mapping at high field a comparison of multiple and single orientation methods abstract optimisation and comparison of the performance of three different methods for calculating three dimensional susceptibility maps of the whole brain from gradient echo phase and modulus image data acquired at 7 t is described the methods studied are a multiple orientation method in which image data acquired with the head at several different angles to the main field are combined and two methods which use data acquired at a single orientation the first of these is based on exclusion of some k space data from the calculation through thresholding of the dipolar field kernel while the second incorporates a regularisation method that is based on using information from the modulus images the methods were initially optimised via analysis of data from a phantom containing different compartments of known susceptibility as part of this work a novel high pass filtering methodology was introduced to remove background fields from field maps based on phase data the optimised methods were successfully applied to high resolution 0 7 mm isotropic whole brain modulus and phase data acquired in vivo from five healthy male subjects 25 30 years of age the multiple orientation method yielded high quality susceptibility maps out performing the single orientation methods venous blood vessels as well as the substantia nigra and globus pallidus brain regions showed particularly high positive susceptibility offsets relative to surrounding tissue consistent with high deoxyhemoglobin and non heme iron content respectively to compare the performance of the different methods regions of interest were drawn in deep grey matter structures and in cortical grey and white matter the threshold based approach was fast and simple to use but underestimated susceptibility differences and showed significant artefacts due to noise amplification in difficult regions of k space the regularised single orientation method yielded contrast dependent on the choice of spatial priors but demonstrated the potential to yield susceptibility maps of a similar quality to those calculated using data acquired at multiple orientations to the field

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

a unified approach to the construction of binary and nonbinary quasi cyclic ldpc codes based on finite fields a unified approach for constructing binary and nonbinary quasi cyclic ldpc codes under a single framework is presented six classes of binary and nonbinary quasi cyclic ldpc codes are constructed based on primitive elements additive subgroups and cyclic subgroups of finite fields numerical results show that the codes constructed perform well over the awgn channel with iterative decoding

locally ϕp optimal designs for generalized linear models with a single variable quadratic polynomial predictor finding optimal designs for generalized linear models is a challenging problem recent research has identified the structure of optimal designs for generalized linear models with single or multiple unrelated explanatory variables that appear as first order terms in the predictor we consider generalized linear models with a single variable quadratic polynomial as the predictor under a popular family of optimality criteria when the design region is unrestricted our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure we show that the same conclusion holds with certain restrictions on the design region but in other cases a larger subclass may have to be considered in addition we derive explicit expressions for some d optimal designs

quasi cyclic ldpc codes an algebraic construction rank analysis and codes on latin squares quasi cyclic ldpc codes are the most promising class of structured ldpc codes due to their ease of implementation and excellent performance over noisy channels when decoded with message passing algorithms as extensive simulation studies have shown in this paper an approach for constructing quasi cyclic ldpc codes based on latin squares over finite fields is presented by analyzing the parity check matrices of these codes combinatorial expressions for their ranks and dimensions are derived experimental results show that with iterative decoding algorithms the constructed codes perform very well over the awgn and the binary erasure channels