tree structured proportional hazards regression modeling a method for fitting piecewise proportional hazards models to censored survival data is described stratification is performed recursively using a combination of statistical tests and residual analysis the bootstrap is employed to keep the probability of a type i error the error of discovering two or more strata when there is only one of the method close to a predetermined value the proposed method can thus also serve as a formal goodness of fit test for the proportional hazards model real and simulated data are used for illustration

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

subgroup identification based on differential effect search a recursive partitioning method for establishing response to treatment in patient subpopulations we propose a novel recursive partitioning method for identifying subgroups of subjects with enhanced treatment effects based on a differential effect search algorithm the idea is to build a collection of subgroups by recursively partitioning a database into two subgroups at each parent group such that the treatment effect within one of the two subgroups is maximized compared with the other subgroup the process of data splitting continues until a predefined stopping condition has been satisfied the method is similar to interaction tree approaches that allow incorporation of a treatment by split interaction in the splitting criterion however unlike other tree based methods this method searches only within specific regions of the covariate space and generates multiple subgroups of potential interest we develop this method and provide guidance on key topics of interest that include generating multiple promising subgroups using different splitting criteria choosing optimal values of complexity parameters via cross validation and addressing type i error rate inflation inherent in data mining applications using a resampling based method we evaluate the operating characteristics of the procedure using a simulation study and illustrate the method with a clinical trial example copyright 2011 john wiley sons ltd

existence of a positive solution to kirchhoff type problems without compactness conditions abstract the existence of a positive solution to a kirchhoff type problem on r n is proved by using variational methods and the new result does not require usual compactness conditions a cut off functional is utilized to obtain the bounded palais smale sequences

the multiplicity of positive solutions for a class of nonlocal elliptic problem abstract in this paper using the theory of fixed point index we prove some results on the multiplicity of positive solutions for a class of nonlocal elliptic problem

adaptive methods for linear programming decoding detectability of failures of linear programming lp decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying lp problem in this paper we make a first step in studying this method and show that by starting from a simple lp problem and adaptively adding the necessary constraints the complexity of lp decoding can be significantly reduced in particular we observe that with adaptive lp decoding the sizes of the lp problems that need to be solved become practically independent of the density of the parity check matrix we further show that adaptively adding extra constraints such as constraints based on redundant parity checks can provide large gains in the performance

an investigation of missing data methods for classification trees applied to binary response data there are many different methods used by classification tree algorithms when missing data occur in the predictors but few studies have been done comparing their appropriateness and performance this paper provides both analytic and monte carlo evidence regarding the effectiveness of six popular missing data methods for classification trees applied to binary response data we show that in the context of classification trees the relationship between the missingness and the dependent variable as well as the existence or non existence of missing values in the testing data are the most helpful criteria to distinguish different missing data methods in particular separate class is clearly the best method to use when the testing set has missing values and the missingness is related to the response variable a real data set related to modeling bankruptcy of a firm is then analyzed the paper concludes with discussion of adaptation of these results to logistic regression and other potential generalizations

the admm penalized decoder for ldpc codes linear programming lp decoding for low density parity check codes was introduced by feldman et al and has been shown to have theoretical guarantees in several regimes furthermore it has been reported in the literature via simulation and via instanton analysis that lp decoding displays better error rate performance at high signal to noise ratios snr than does belief propagation bp decoding however at low snrs lp decoding is observed to have worse performance than bp in this paper we seek to improve lp decoding at low snrs while maintaining lp decoding s high snr performance our main contribution is a new class of decoders obtained by applying the alternating direction method of multipliers admm algorithm to a set of non convex optimization problems these non convex problems are constructed by adding a penalty term to the objective of lp decoding the goal of the penalty is to make pseudocodewords which are non integer vertices of the lp relaxation more costly we name this class of decoders admm penalized decoders for low and moderate snrs we simulate admm penalized decoding with ell 1 and ell 2 penalties we find that these decoders can outperform both bp and lp decoding for high snrs where it is difficult to obtain data via simulation we use an instanton analysis and find that asymptotically admm penalized decoding performs better than bp but not as well as lp unfortunately since admm penalized decoding is not a convex program we have not been successful in developing theoretical guarantees however the non convex program can be approximated using a sequence of linear programs an approach that yields a reweighted lp decoder we show that a two round reweighted lp decoder has an improved theoretical recovery threshold when compared with lp decoding in addition we find via simulation that reweighted lp decoding significantly attains lower error rates than lp decoding at low snrs

existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero we study the existence of changing sign solutions of an elliptic semilinear boundary value problem which arises as a limiting equation of the two species lotka volterra competing equations system using variational methods and a result of d aujourd hui we find conditions which are both sufficient and necessary for this existence problem

adaptive cut generation algorithm for improved linear programming decoding of binary linear codes linear programming lp decoding approximates maximum likelihood ml decoding of a linear block code by relaxing the equivalent ml integer programming ip problem into a more easily solved lp problem the lp problem is defined by a set of box constraints together with a set of linear inequalities called parity inequalities that are derived from the constraints represented by the rows of a parity check matrix of the code and can be added iteratively and adaptively in this paper we first derive a new necessary condition and a new sufficient condition for a violated parity inequality constraint or cut at a point in the unit hypercube then we propose a new and effective algorithm to generate parity inequalities derived from certain additional redundant parity check rpc constraints that can eliminate pseudocodewords produced by the lp decoder often significantly improving the decoder error rate performance the cut generating algorithm is based upon a specific transformation of an initial parity check matrix of the linear block code we also design two variations of the proposed decoder to make it more efficient when it is combined with the new cut generating algorithm simulation results for several low density parity check ldpc codes demonstrate that the proposed decoding algorithms significantly narrow the performance gap between lp decoding and ml decoding

on sign changing solution for some three point boundary value problems abstract in this paper an existence result of sign changing solution for some three point boundary value problems is obtained by using the fixed point index method

an integrated linear programming receiver for ldpc coded mimo ofdm signals this work investigates the joint detection and decoding of mimo ofdm signals traditional receivers either utilize disjoint serial detector and decoder or require turbo message passing between the two functional blocks of detection and decoding we present a novel approach that can jointly achieve detection and decoding of low density parity check ldpc coded multiple input multiple output mimo orthogonal frequency division multiplexing ofdm signals as a unified optimization algorithm our receiver integrates the mimo ofdm signal detection and the decoding of ldpc coded data by formulating a linear programming problem regardless of affine or nonaffine quadrature amplitude modulation qam mapping the proposed joint mimo ofdm detector and decoder achieves substantial performance gain over existing joint detection receivers of comparable computational complexity furthermore the proposed receiver also substantially outperforms the more traditional turbo receiver with only modest cost in complexity

classification trees with unbiased multiway splits two univariate split methods and one linear combination split method are proposed for the construction of classification trees with multiway splits examples are given where the trees are more compact and hence easier to interpret than binary trees a major strength of the univariate split methods is that they have negligible bias in variable selection both when the variables differ in the number of splits they offer and when they differ in the number of missing values this is an advantage because inferences from the tree structures can be adversely affected by selection bias the new methods are shown to be highly competitive in terms of computational speed and classification accuracy of future observations

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

decoding binary linear block codes using local search this paper presents a novel iterative hard decision decoding algorithm for binary linear block codes over a binary symmetric channel bsc the problem is formulated as a 0 1 integer programming problem which is known to be np hard when the crossover probability c of the channel is known the solution space of the decoding problem can be decreased to a sphere whose radius is related to c using the penalty function method the problem is reformulated on this reduced solution space then an iterative multi flip local search algorithm is designed to find the global solution of this decoding problem for a code with minimum distance d when the radius of the sphere is not greater than d 1 2 this algorithm has the maximum likelihood ml certificate property i e if the decoder outputs a codeword it is guaranteed to be the ml codeword compared to the probabilistic suboptimal iterative belief propagation bp decoder this approach has lower complexity and better performance numerical results show that in terms of speed and performance the proposed decoding method outperforms bp decoding in the error floor region

guessing facets polytope structure and improved lp decoder we investigate the structure of the polytope underlying the linear programming lp decoder introduced by feldman karger and wainwright we first show that for expander codes every fractional pseudocodeword always has at least a constant fraction of nonintegral bits we then prove that for expander codes the active set of any fractional pseudocodeword is smaller by a constant fraction than that of any codeword we further exploit these geometrical properties to devise an improved decoding algorithm with the same order of complexity as lp decoding that provably performs better the method is very simple it first applies ordinary lp decoding and when it fails it proceeds by guessing facets of the polytope and then resolving the linear program on these facets while the lp decoder succeeds only if the ml codeword has the highest likelihood over all pseudocodewords we prove that the proposed algorithm when applied to suitable expander codes succeeds unless there exists a certain number of pseudocodewords all adjacent to the ml codeword on the lp decoding polytope and with higher likelihood than the ml codeword we then describe an extended algorithm still with polynomial complexity that succeeds as long as there are at most polynomially many pseudocodewords above the ml codeword

using linear programming to decode binary linear codes a new method is given for performing approximate maximum likelihood ml decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel the decoding algorithm is based on a linear programming lp relaxation that is defined by a factor graph or parity check representation of the code the resulting lp decoder generalizes our previous work on turbo like codes a precise combinatorial characterization of when the lp decoder succeeds is provided based on pseudocodewords associated with the factor graph our definition of a pseudocodeword unifies other such notions known for iterative algorithms including stopping sets irreducible closed walks trellis cycles deviation sets and graph covers the fractional distance d sub frac of a code is introduced which is a lower bound on the classical distance it is shown that the efficient lp decoder will correct up to spl lceil d sub frac 2 spl rceil 1 errors and that there are codes with d sub frac spl omega n sup 1 spl epsi an efficient algorithm to compute the fractional distance is presented experimental evidence shows a similar performance on low density parity check ldpc codes between lp decoding and the min sum and sum product algorithms methods for tightening the lp relaxation to improve performance are also provided

adaptive linear programming decoding of nonbinary linear codes over prime fields in this work we consider adaptive linear programming alp decoding of linear codes over prime fields i e the finite fields mathbb f p of size p where p is a prime when used over a p ary input memoryless channel in particular we provide a general construction of valid inequalities using no auxiliary variables for the codeword polytope or the convex hull of the so called constant weight embedding of a single parity check spc code over any prime field the construction is based on sets of vectors called building block classes that are assembled to form the left hand side of an inequality according to several rules in the case of almost doubly symmetric valid classes we prove that the resulting inequalities are all facet defining while we conjecture this to be true if and only if the class is valid and symmetric valid symmetric classes impose certain symmetry conditions on the elements of the vectors from the class while valid doubly symmetric classes impose further technical symmetry conditions for p 3 there is only a single valid symmetric class and we prove that the resulting inequalities together with the so called simplex constraints give a complete and irredundant description of the codeword polytope of the embedded spc code for p 5 we show that there are additional facets beyond those from the proposed construction as an example for p 7 we provide additional inequalities that all define facets of the embedded codeword polytope the resulting overall set of linear in equalities is conjectured to be irredundant and complete such sets of linear in equalities have not appeared in the literature before have a strong theoretical interest and we use them to develop an efficient relaxed alp decoder for general non spc linear codes over prime fields the key ingredient is an efficient separation algorithm based on the principle of dynamic programming furthermore we construct a decoder for linear codes over arbitrary fields mathbb f q with q p m and m 1 by a factor graph representation that reduces to several instances of the case m 1 which results in general in a relaxation of the original decoding polytope finally we present an efficient cut generating algorithm to search for redundant parity checks to further improve the performance towards maximum likelihood decoding for short to medium block lengths numerical experiments confirm that our new decoder is very efficient compared to a static lp decoder for various field sizes check node degrees and block lengths

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

study of a nonlinear kirchhoff equation with non homogeneous material abstract in this paper we study a non homogeneous elliptic kirchhoff equation with nonlinear reaction term we analyze the existence and uniqueness of positive solution the main novelty is the inclusion of non homogeneous term making the problem without a variational structure we use mainly bifurcation arguments to get the results

on decoding of the 89 45 17 quadratic residue code in this paper three decoding methods of the 89 45 17 binary quadratic residue qr code to be presented are hard soft and linear programming decoding algorithms firstly a new hybrid algebraic decoding algorithm for the 89 45 17 qr code is proposed it uses the laplace formula to obtain the primary unknown syndromes as done in lin et al s algorithm when the number of errors v is less than or equal to 5 whereas gaussian elimination is adopted to compute the unknown syndromes when v 6 secondly an appropriate modification to the algorithm developed by chase is also given in this paper therefore combining the proposed algebraic decoding algorithm with the modified chase ii algorithm called a new soft decision decoding algorithm becomes a complete soft decoding of qr codes thirdly in order to further improve the error correcting performance of the code linear programming lp is utilized to decode the 89 45 17 qr code simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with lin et al s hard decoding algorithm and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate ber performance moreover the lp based decoding improves the error rate performance almost without increasing the decoding complexity when compared with the new soft decision decoding algorithm it provides a coding gain of 0 2 db at ber 2 x 10 6

ground state sign changing solutions for kirchhoff type problems in bounded domains abstract in the present paper we consider the existence of ground state sign changing solutions for a class of kirchhoff type problems 0 1 a b u 2 d x u f u x u 0 x where r n is a bounded domain with a smooth boundary n 1 2 3 a 0 b 0 and f c r r under some weak assumptions on f with the aid of some new analytical skills and non nehari manifold method we prove that 0 1 possesses one ground state sign changing solution u b and its energy is strictly larger than twice that of the ground state solutions of nehari type furthermore we establish the convergence property of u b as the parameter b 0 our results improve and generalize some results obtained by w shuai 2015 34

a uniqueness result for a nonlocal equation of kirchhoff type and some related open problem abstract we study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of kirchhoff type a b u 2 d x u f u in u 0 here is a bounded open set in r n with smooth boundary a b are positive real numbers and f r r is a continuous function in particular we give an answer to an open problem recently proposed by b ricceri

subgroup identification using covariate adjusted interaction trees we consider the problem of identifying subgroups of participants in a clinical trial that have enhanced treatment effect recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such subgroup identification the most commonly used recursive partitioning method the classification and regression tree algorithm first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all the subtrees of the large tree in the context of subgroup identification calculation of the splitting criteria and the evaluation measure used for final tree selection rely on comparing differences in means between the treatment and control arm when covariates are prognostic for the outcome covariate adjusted estimators have the ability to improve efficiency compared to using differences in averages between the treatment and control group this manuscript develops two covariate adjusted estimators that can be used to both make splitting decisions and for final tree selection the performance of the resulting covariate adjusted recursive partitioning algorithm is evaluated using simulations and by analyzing a clinical trial that evaluates if motivational interviews improve treatment engagement for substance abusers

identification of subgroups with differential treatment effects for longitudinal and multiresponse variables we describe and evaluate a regression tree algorithm for finding subgroups with differential treatments effects in randomized trials with multivariate outcomes the data may contain missing values in the outcomes and covariates and the treatment variable is not limited to two levels simulation results show that the regression tree models have unbiased variable selection and the estimates of subgroup treatment effects are approximately unbiased a bootstrap calibration technique is proposed for constructing confidence intervals for the treatment effects the method is illustrated with data from a longitudinal study comparing two diabetes drugs and a mammography screening trial comparing two treatments and a control copyright 2016 john wiley sons ltd

a new linear programming approach to decoding linear block codes in this paper we propose a new linear programming formulation for the decoding of general linear block codes different from the original formulation given by feldman the number of total variables to characterize a parity check constraint in our formulation is less than twice the degree of the corresponding check node the equivalence between our new formulation and the original formulation is proven the new formulation facilitates to characterize the structure of linear block codes and leads to new decoding algorithms in particular we show that any fundamental polytope is simply the intersection of a group of the so called minimum polytopes and this simplified formulation allows us to formulate the problem of calculating the minimum hamming distance of any linear block code as a simple linear integer programming problem with much less auxiliary variables we then propose a branch and bound method to compute a lower bound to the minimum distance of any linear code by solving a corresponding linear integer programming problem in addition we prove that for the family of single parity check spc product codes the fractional distance and the pseudodistance are both equal to the minimum distance finally we propose an efficient algorithm for decoding spc product codes with low complexity and maximum likelihood ml decoding performance

on decoding of the 73 37 13 quadratic residue code in this paper a method to search the set of syndromes indices needed in computing the unknown syndromes for the 73 37 13 quadratic residue qr code is proposed according to the resulting index sets one computes the unknown syndromes and thus finds the corresponding error locator polynomial by using an inverse free berlekamp massey bm algorithm based on the modified chase ii algorithm the performance of soft decision decoding for the 73 37 13 qr code is given this result is new moreover the error rate performance of linear programming lp decoding for the 73 37 13 qr code is also investigated and lp based decoding is shown to be significantly superior in performance to the algebraic soft decision decoding while requiring almost the same computational complexity in fact the algebraic hard decision and soft decision decoding of the 89 45 17 qr code outperforms that of the 73 37 13 qr code because the former has a larger minimal distance however experimental results indicate that the 73 37 13 qr code outperforms the 89 45 17 qr code with much fewer arithmetic operations when using the lp based decoding algorithms the pseudocodewords analysis partially explains this seemingly strange phenomenon

existence of a positive solution for a kirchhoff problem type with critical growth via truncation argument abstract in this paper we shall show an existence result of a positive solution for a kirchhoff problem type in a bounded domain of r n that is for the problem m u 2 d x u f x u u 2 2 u in u 0 on we shall study the asymptotic behavior of this solution when converges to infinity our approach is based on the variational method an appropriated truncated argument and a priori estimates to obtain the solution

ground states for the nonlinear kirchhoff type problems abstract in this paper we study the existence of ground states for the asymptotically periodic kirchhoff type problems with critical growth and three times growth the proof is based on the method of nehari manifold and concentration compactness principle in particular we improve the method of nehari manifold for kirchhoff type equations with three times growth

the sign changing solutions for nonlinear elliptic problem with carrier type abstract in this paper using the fixed point index method we are concerned with the existence of sign changing solutions of the following problem 0 1 a b u x d x u f u x in u x 0 x on where a 0 b 0 and r n is a bounded open set with smooth boundary and 1

a separation algorithm for improved lp decoding of linear block codes maximum likelihood ml decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an integer programming ip problem feldman relaxed this ip problem and presented linear programming lp based decoding in this paper we propose a new separation algorithm to improve the error correcting performance of lp decoding for binary linear block codes we use an ip formulation with indicator variables that help in detecting the violated parity checks we derive gomory cuts from the ip and use them in our separation algorithm an efficient method of finding cuts induced by redundant parity checks rpc is also proposed under certain circumstances we can guarantee that these rpc cuts are valid and cut off the fractional optimal solutions of lp decoding it is demonstrated on three ldpc codes and two bch codes that our separation algorithm performs significantly better than lp decoding and belief propagation bp decoding

sign changing solutions for a class of kirchhoff type problem in bounded domains abstract we are interested in the existence of least energy sign changing solutions for a class of kirchhoff type problem in bounded domains because the so called nonlocal term b u 2 d x u is involving in the equation the variational functional of the equation has totally different properties from the case of b 0 combining constraint variational method and quantitative deformation lemma we prove that the problem possesses one least energy sign changing solution u b moreover we show that the energy of u b is strictly larger than the ground state energy finally we regard b as a parameter and give a convergence property of u b as b 0

mathematical programming decoding of binary linear codes theory and algorithms mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches challenging established but often heuristic algorithms based on iterative message passing concepts from mathematical programming used in the context of decoding include linear integer and nonlinear programming network flows notions of duality as well as matroid and polyhedral theory this paper reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary input memoryless symmetric channels

subgroups from regression trees with adjustment for prognostic effects and postselection inference identification of subgroups with differential treatment effects in randomized trials is attracting much attention many methods use regression tree algorithms this article addresses 2 important questions arising from the subgroups how to ensure that treatment effects in subgroups are not confounded with effects of prognostic variables and how to determine the statistical significance of treatment effects in the subgroups we address the first question by selectively including linear prognostic effects in the subgroups in a regression tree model the second question is more difficult because it falls within the subject of postselection inference we use a bootstrap technique to calibrate normal theory t intervals so that their expected coverage probability averaged over all the subgroups in a fitted model approximates the desired confidence level it can also provide simultaneous confidence intervals for all subgroups the first solution is implemented in the guide algorithm and is applicable to data with missing covariate values 2 or more treatment arms and outcomes subject to right censoring bootstrap calibration is applicable to any subgroup identification method it is not restricted to regression tree models two real examples are used for illustration a diabetes trial where the outcomes are completely observed but some covariate values are missing and a breast cancer trial where the outcome is right censored

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

two positive solutions for the kirchhoff type elliptic problem with critical nonlinearity in high dimension abstract we investigate the kirchhoff type elliptic problem with critical nonlinearity 1 u 2 d x u u q u 2 1 u 0 in u 0 on where n 5 r n is a bounded domain with smooth boundary 0 r 2 2 n n 2 and q 1 2 1 we prove the existence of two solutions of it via the variational method since n 5 and 0 the uniqueness assertion for the associated limiting problem may fail this causes serious difficulties in controlling concentrating palais smale sequences we overcome these by introducing new techniques for a mountain pass type solution we utilize the limit function of the fibering maps of the concentrating palais smale sequence this tool is based on our careful setting of nehari type sets on the other hand a suitable modification to a concentrating minimizing sequence enables us to obtain a global minimum solution this is the first work which proves the multiplicity of positive solutions of the kirchhoff type critical problem in high dimension

lp decoding corrects a constant fraction of errors we show that for low density parity check ldpc codes whose tanner graphs have sufficient expansion the linear programming lp decoder of feldman karger and wainwright can correct a constant fraction of errors a random graph will have sufficient expansion with high probability and recent work shows that such graphs can be constructed efficiently a key element of our method is the use of a dual witness a zero valued dual solution to the decoding linear program whose existence proves decoding success we show that as long as no more than a certain constant fraction of the bits are flipped by the channel we can find a dual witness this new method can be used for proving bounds on the performance of any lp decoder even in a probabilistic setting our result implies that the word error rate of the lp decoder decreases exponentially in the code length under the binary symmetric channel bsc this is the first such error bound for ldpc codes using an analysis based on pseudocodewords recent work by koetter and vontobel shows that lp decoding and min sum decoding of ldpc codes are closely related by the graph cover structure of their pseudocodewords in their terminology our result implies that that there exist families of ldpc codes where the minimum bsc pseudoweight grows linearly in the block length

efficient admm decoding of ldpc codes using lookup tables linear programming decoding with the alternating direction method of multipliers admm is a promising decoding technique for low density parity check ldpc codes where the computational complexity of euclidean projections onto check polytopes becomes a prominent problem in this paper the problem is circumvented by building lookup tables luts and quantizing the inputs to approach approximate euclidean projections at low computational complexities to challenge the huge memory cost of luts we first propose two commutative compositions of euclidean projection and self map and show the existence of a small quantization range which does not alter the euclidean projection then we investigate the design and simplification of the luts by exploiting the commutative compositions and check node decomposition techniques an efficient algorithm for the lut based projection is demonstrated by using one simplification method simulation results show that for both the regular and irregular ldpc codes the admm decoding using lut based projection can substantially reduce the decoding time while maintaining the error rate performance at a comparatively large memory cost

on a class of problems involving a nonlocal operator in this paper we prove a result on existence of positive solution for a nonlocal elliptic problem by using a result on fixed point index theory and we establish another existence result which is proved by sub and supersolution and a comparison principle moreover we prove the existence uniqueness and asymptotic behaviour of the solutions for the evolution case

subgroup analysis via recursive partitioning subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest its goal is to determine the heterogeneity of the treatment effect across subpopulations in this paper we adapt the idea of recursive partitioning and introduce an interaction tree it procedure to conduct subgroup analysis the it procedure automatically facilitates a number of objectively defined subgroups in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect the standard cart breiman et al 1984 methodology is inherited to construct the tree structure also in order to extract factors that contribute to the heterogeneity of the treatment effect variable importance measure is made available via random forests of the interaction trees both simulated experiments and analysis of census wage data are presented for illustration

a general statistical framework for subgroup identification and comparative treatment scoring summary many statistical methods have recently been developed for identifying subgroups of patients who may benefit from different available treatments compared with the traditional outcome modeling approaches these methods focus on modeling interactions between the treatments and covariates while by pass or minimize modeling the main effects of covariates because the subgroup identification only depends on the sign of the interaction however these methods are scattered and often narrow in scope in this article we propose a general framework by weighting and a learning for subgroup identification in both randomized clinical trials and observational studies our framework involves minimum modeling for the relationship between the outcome and covariates pertinent to the subgroup identification under the proposed framework we may also estimate the magnitude of the interaction which leads to the construction of scoring system measuring the individualized treatment effect the proposed methods are quite flexible and include many recently proposed estimators as special cases as a result some estimators originally proposed for randomized clinical trials can be extended to observational studies and procedures based on the weighting method can be converted to an a learning method and vice versa our approaches also allow straightforward incorporation of regularization methods for high dimensional data as well as possible efficiency augmentation and generalization to multiple treatments we examine the empirical performance of several procedures belonging to the proposed framework through extensive numerical studies

on positive solutions of nonlocal and nonvariational elliptic problems abstract we will study the nonlocal and nonvariational elliptic problem a u q u h x f u in u 0 on by considering in two different results the cases n 1 and n 2 in both cases we will use fixed point theorems

a regression tree approach to identifying subgroups with differential treatment effects in the fight against hard to treat diseases such as cancer it is often difficult to discover new treatments that benefit all subjects for regulatory agency approval it is more practical to identify subgroups of subjects for whom the treatment has an enhanced effect regression trees are natural for this task because they partition the data space we briefly review existing regression tree algorithms then we introduce three new ones that are practically free of selection bias and are applicable to data from randomized trials with two or more treatments censored response variables and missing values in the predictor variables the algorithms extend the guide approach by using three key ideas i treatment as a linear predictor ii chi squared tests to detect residual patterns and lack of fit and iii proportional hazards modeling via poisson regression importance scores with thresholds for identifying influential variables are obtained as by products a bootstrap technique is used to construct confidence intervals for the treatment effects in each node the methods are compared using real and simulated data