an and or graph approach for two dimensional cutting problems abstract the problem of generating guillotine cutting patterns for a rectangular plate is studied and a type of structure is proposed for representing the solution of the problem called and or graph which is commonly used in the artificial intelligence environment to search the graph we combined two classical strategies depth first and hill climbing further some heuristics are considered and computational results are presented relating their performance on examples from both literature as well as randomly generated

an integrated cutting stock and sequencing problem in this paper an integrated problem formulated as an integer linear programming problem is presented to find an optimal solution to the cutting stock problem under particular pattern sequencing constraints the solution uses a lagrangian approach the dual problem is solved using a modified subgradient method a heuristic for the integrated problem is also presented the computational results obtained from a set of unidimensional instances that use these procedures are reported

maximum number of distinct and nonequivalent nonstandard squares in a word the combinatorics of nonstandard squares in a word depends on how the equivalence of halves of the square is defined we consider abelian squares parameterized squares and order preserving squares the word uv is an abelian parameterized order preserving square if u and v are equivalent in the abelian parameterized order preserving sense the maximum number of ordinary squares in a word is known to be asymptotically linear but the exact bound is still investigated we present several results on the maximum number of distinct squares for nonstandard factor equivalence relations let sq abel n and sq abel n denote the maximum number of abelian squares in a word of length n over an alphabet of size which are distinct as words and which are nonequivalent in the abelian sense respectively for 2 we prove that sq abel n n 2 sq abel n n 3 2 and sq abel n o n 11 6 we also give linear bounds for parameterized and order preserving squares for alphabets of constant size sq param n o 1 n sq op n o 1 n the upper bounds have quadratic dependence on the alphabet size for order preserving squares and exponential dependence for parameterized squares as a side result we construct infinite words over the smallest alphabet which avoid nontrivial order preserving squares and nontrivial parameterized cubes nontrivial parameterized squares cannot be avoided in an infinite word a preliminary version of this paper was published at dlt 2014 24 in this full version we improve or extend the bounds on all three kinds of squares

approximate case influence for the proportional hazards regression model with censored data a method is presented for approximating the influence of individual cases upon regression coefficient estimates obtained from the cox proportional hazards model observations can thus be identified which may greatly influence statistical inferences regarding the effects of prognostic factors upon survival time an example from a cancer clinical trial is given

strip generation algorithms for constrained two dimensional two staged cutting problems abstract the constrained two dimensional cutting c tdc problem consists of determining a cutting pattern of a set of n small rectangular piece types on a rectangular stock plate of length l and width w as to maximize the sum of the profits of the pieces to be cut each piece type i i 1 n is characterized by a length l i a width w i a profit or weight c i and an upper demand value b i the upper demand value is the maximum number of pieces of type i which can be cut on rectangle l w in this paper we study the two staged fixed orientation c tdc noted fc 2tdc it is a classical variant of the c tdc where each piece is produced in the final cutting pattern by at most two guillotine cuts and each piece has a fixed orientation we solve the fc 2tdc problem using several approximate algorithms that are mainly based upon a strip generation procedure we evaluate the performance of these algorithms on instances extracted from the literature

an exact two dimensional non guillotine cutting tree search procedure we consider the two dimensional cutting problem of cutting a number of rectangular pieces from a single large rectangle so as to maximize the value of the pieces cut we develop a lagrangean relaxation of a zero one integer programming formulation of the problem and use it as a bound in a tree search procedure subgradient optimization is used to optimize the bound derived from the lagrangean relaxation problem reduction tests derived from both the original problem and the lagrangean relaxation are given incorporating the bound and the reduction tests into a tree search procedure enables moderately sized problems to be solved

a partial robust ridge based regression model with fuzzy predictors responses abstract this paper extends the conventional semi parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1 outliers occur in data set 2 multicollinearity exists in predictors for this purpose the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function then inspired by the conventional local linear smoothing method a kernel based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology some common goodness of fit criteria are also used to examine the performance of the proposed method the effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study the proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses the numerical results clearly indicate that 1 the proposed method is not sensitive to the outliers 2 the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3 comparing to existing fuzzy multiple regressions the proposed model provides more efficient predictions

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

best first search methods for constrained two dimensional cutting stock problems best first search is a widely used problem solving technique in the field of artificial intelligence the method has useful applications in operations research as well here we describe an application to constrained two dimensional cutting stock problems of the following type a stock rectangle s of dimensions l w is supplied there are n types of demanded rectangles r1 r2 rn with the ith type having length li width wi value vi and demand constraint bi it is required to produce from the stock rectangle s ai copies of ri 1 i n to maximize a1v1 a2v2 anvn subject to the constraints ai bi only orthogonal guillotine cuts are permitted all parameters are integers a best first tree search algorithm based on wang s bottom up approach is described that guarantees optimal solutions and is more efficient than existing methods

implications of influence function analysis for sliced inverse regression and sliced average variance estimation sliced inverse regression sliced inverse regression ii and sliced average variance estimation are three related dimension reduction methods that require relatively mild model assumptions as an approximation for the relative influence of single observations from large samples the influence function is used to compare the sensitivity of the three methods to particular observational types the analysis carried out here helps to explain why there is a lack of agreement concerning the preferability of these dimension reduction procedures in general an efficient sample version of the influence function is also developed and evaluated

detecting influential measurements in a growth curves model this paper comprises a study of the influence of deleting measurements on growth curve estimates the problem of influential measurements is considered both at the inference level and at the design level a measure of detecting influential vs uninfluential measurements is proposed the influence analysis envisaged also serves as a means for comparing the robustness of various models to missing measurements and to different study designs the paper concludes with an illustrative application

a simple derivation of deletion diagnostic results for the general linear model with correlated errors a general simple and intuitive derivation is provided for diagnostics associated with the deletion of arbitrary subsets for the linear model with general covariance structure these are seen to be most simply expressed even for the well studied case of independent and identically distributed data in terms of a residual known variously as the conditional residual the deletion prediction residual and the cross validation residual particularly simple specializations arise when the subsets are of size 1 and of size 2 but the method is easy to apply for all subsets and to conditional deletions

influence diagnostics for linear measurement error models summary influence functions are used to show that extreme observations affect linear measurement error model estimators in directions orthogonal to and along the fitted plane rather than vertically and horizontally as with least squares estimators influence diagnostics patterned after those for least squares and derived for generalized linear models by pregibon 1981 are adapted to assess the influence of extreme observations on linear measurement error model estimators perturbation arguments and asymptotic theory are used to support the use of these diagnostics it is well known that least squares estimators are influenced by extreme observations in the response and predictor variables geometrically these influences are in directions defined by the axis of the response variable and the plane defined by the predictors as shown in 3 measurement error model estimators are affected in directions that are perpendicular to and along the fitted plane thus least squares influence diagnostics that measure the effects of observations in the vertical and the horizontal directions may fail to accurately indicate the true effects of extreme observations on measurement error model estimators kelly 1984 derives an influence function for a structural measurement error model in which the error distribution has finite fourth moments and the error covariance matrix is known up to a multiple with the aid of this influence function diagnostics such as cook s d are defined by analogy to the corresponding least squares equivalents fuller 1987 defines a measurement error model estimator of the hat matrix using estimated predictor variable values he also proposes using diagnostics and plotting techniques analogous to those of least squares with estimated model errors and estimated leverage values from the hat matrix miller 1989 provides partial theoretical justification for the use of these least squares based techniques by showing that the estimated model errors asymptotically are a gaussian process apart from these efforts little research has been conducted on influence diagnostics for measurement error models the derivation of influence diagnostics for measurement error models in this paper proceeds as follows measurement error model estimators are briefly described in 2 a more comprehensive discussion of these estimators is given by fuller 1987 ch 2 in 3 influence function arguments are used to establish the need for measurement error model diagnostics measurement error model estimators are expressed as iteratively reweighted least squares estimators in 4 leading to the adaptation of diagnostics for

assessing influence in multiple linear regression with incomplete data the problem of assessing influence and detecting influential cases in multiple linear regression with incomplete data is considered a case is said to be influential if appreciable changes in fitted regression coefficients occur when it is removed from the data a one step influence measure is derived based on the em algorithm for detecting cases that are influential in the maximum likelihood estimation of the regression coefficients results are compared with the complete data cook s distance measure techniques are demonstrated by examples

an approximation algorithm for solving unconstrained two dimensional knapsack problems abstract an efficient heuristic for solving two dimensional knapsack problems is proposed the algorithm selects an optimal subset of optimal generated strips by solving a sequence of one dimensional knapsack problems we show that the number of these knapsacks can be reduced to only four knapsacks the algorithm gives an excellent worst case experimental approximation ratio 0 98 and a high percentage of optimal solutions 91 from this heuristic we derive an approximation algorithm for which we prove some refined bounds and we show that its approximation ratio is 4 9 our numerical study on large size instances shows the efficiency of these algorithms for solving real world problems which are hardly handled by other known methods which are often limited by computer storage facilities

optimum influence of initial observations in regression models with ar 2 errors abstract this article considers an optimal procedure of identifying the influential observations in a regression model with ar 2 errors it develops some diagnostic techniques using a hat matrix the likelihood ratio and f test statistic have been discussed and an example of a constant mean model with ar 2 error shows its practical application in time series

problems in between words and abelian words k abelian avoidability we consider a recently defined notion of k abelian equivalence of words in connection with avoidability problems this equivalence relation for a fixed natural number k takes into account the numbers of occurrences of the different factors of length k and the prefix and the suffix of length k 1 we search for the smallest alphabet in which k abelian squares and cubes can be avoided respectively for 2 abelian squares this is four as in the case of abelian words while for 2 abelian cubes we have only strong evidence that the size is two as it is in the case of words however we are able to prove this optimal value only for 8 abelian cubes

influence and a quadratic form in the andrews pregibon statistic a quadratic form found in the andrews pregibon ap statistic may be decomposed into two terms one of the terms has a simple geometric interpretation that relates naturally to the expression of influence found in cook s statistic the measure of influence derived from the quadratic form is easy to compute once the two factors of the ap statistic have been found this measure suggests a computing strategy for diagnostics and leads to an exact relation between the ap statistic and cook s statistic

the dh kd algorithm a hybrid approach for unconstrained two dimensional cutting problems abstract we study both weighted and unweighted unconstrained two dimensional guillotine cutting problems we develop a hybrid approach which combines two heuristics from the literature the first one dh uses a tree search procedure introducing two strategies depth first search and hill climbing the second one kd is based on a series of one dimensional knapsack problems using dynamic programming techniques the dh kd algorithm starts with a good initial lower bound obtained by using the kd algorithm at each level of the tree search the proposed algorithm uses also the kd algorithm for constructing new lower bounds and uses another one dimensional knapsack for constructing refinement upper bounds the resulting algorithm can be seen as a generalization of the two heuristics and solves large problem instances very well within small computational time our algorithm is compared to morabito et al s algorithm the unweighted case and to beasley s 2 approach the weighted case on some examples taken from the literature as well as randomly generated instances

approximate inferences in multiresponse regression analysis summary we present an approximate inference procedure for the multiresponse regression model this can be used to determine approximate confidence regions or intervals and to formulate diagnostic tools such as standardized residuals and influence measures the overall approximation is based on approximations at two stages at the first stage the multiresponse regression model is replaced by a generalized least squares model using the estimated variance covariance matrix of the error terms at the second stage the nonlinear model functions are replaced by linear approximations

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

uniformly growing k th power free homomorphisms a string is called kth power free if it does not have xk as a nonempty substring for all nonnegative rational numbers k kth power free strings and kth power free homomorphisms are investigated and the shortest uniformly growing square free k 2 and cube free k 3 homomorphisms mapping into least alphabets with three and two letters are introduced it is shown that there exist exponentially many square free and cube free strings of each length over these alphabets sharpening the kth power freeness to the repetitive threshold rt n of n letter alphabets we provide arguments for the nonexistence of various rt n th power free homomorphisms

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

on some generalizations of abelian power avoidability we prove that 2 abelian cubes are avoidable over a binary alphabet and that 3 abelian squares are avoidable over a ternary alphabet answering positively to two questions of karhumaki et al we also show the existence of infinite additive cube free words on several ternary alphabets to achieve this we give sufficient conditions for a morphism to be k abelian n power free resp additive n power free and then we give several morphisms which respect these conditions additionally all our constructions show that the number of such words grows exponen tially as a corollary we get a new lower bound of 3 1 19 1 059526 for the growth rate of abelian cube free words