mass concentration and aging in the parabolic anderson model with doubly exponential tails we study the non negative solution u u x t to the cauchy problem for the parabolic equation partial t u vardelta u xi u on mathbb z d times 0 infty with initial data u x 0 mathsf 1 0 x here vardelta is the discrete laplacian on mathbb z d and xi xi z z in mathbb z d is an i i d random field with doubly exponential upper tails we prove that for large t and with large probability most of the total mass u t sum x u x t of the solution resides in a bounded neighborhood of a site z t that achieves an optimal compromise between the local dirichlet eigenvalue of the anderson hamiltonian vardelta xi and the distance to the origin the processes t mapsto z t and t mapsto tfrac 1 t log u t are shown to converge in distribution under suitable scaling of space and time aging results for z t as well as for the solution to the parabolic problem are also established the proof uses the characterization of eigenvalue order statistics for vardelta xi in large sets recently proved by the first two authors

delocalising the parabolic anderson model through partial duplication of the potential the parabolic anderson model on mathbb z d with i i d potential is known to completely localise if the distribution of the potential is sufficiently heavy tailed at infinity in this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin in the case of potential distribution with polynomial tail decay we exhibit a surprising phase transition in the model as the decay exponent varies for large values of the exponent the model completely localises as in the i i d case by contrast for small values of the exponent we show that the model may delocalise more precisely we show that there is an event of non negligible probability on which the solution has non negligible mass on two sites

finding maximum likelihood estimates of patterned covariance matrices by the em algorithm some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates in such cases the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables the advantage of this perspective is that the em algorithm can be used to calculate the desired maximum likelihood estimates for the original problem two examples are presented

general balance and treatment permutations abstract many equi replicate designs whether ordinary block designs or multi stratum designs have a structure which is left unchanged by a group g of permutations of the treatments this group g is often used in the construction of the design a survey of the properties of such designs is given and useful necessary conditions on g are found for such a design to be generally balanced if g is abelian then the necessary conditions are satisfied in this case explicit formulas for the efficiency factors are given

long time tails in the parabolic anderson model with bounded potential we consider the parabolic anderson problem t u u u on 0 z d with random i i d potential z z zd and the initial condition u 0 1 our main assumption is that esssup 0 0 depending on the thickness of the distribution prob 0 close to its essential supremum we identify both the asymptotics of the moments of u t 0 and the almost sure asymptotics of u t 0 as t in terms of variational problems as a by product we establish lifshitz tails for the random schrodinger operator at the bottom of its spectrum in our class of distributions the lifshitz exponent ranges from d 2 to the power law is typically accompanied by lower order corrections

which logic is the real fuzzy logic this paper is a contribution to the discussion of the problem whether there is a fuzzy logic that can be considered as the real fuzzy logic we give reasons for taking imtl bl email protected and ev l fuzzy logic with evaluated syntax as those fuzzy logics that should be indeed taken as the real fuzzy logics

analysis of artificial neural network learning near temporary minima a fuzzy logic approach artificial neural networks anns are often trained using gradient descent algorithms such as backpropagation an important problem in the learning process is the slowdown incurred by temporary minima tm we analyze this problem for an ann trained to solve the exclusive or problem the network is transformed into the equivalent all permutations fuzzy rule base farb which provides a symbolic representation of the knowledge embedded in the network after each learning step we develop a mathematical model for the evolution of the fuzzy rule base parameters during learning in the vicinity of tm we show that the rule base becomes singular and tends to remain singular in the vicinity of tm the analysis of the fuzzy rule base suggests a simple remedy for overcoming the slowdown in the learning process incurred by tm this is based on slightly perturbing the desired output values in the training examples so that they are no longer symmetric simulations demonstrate the effectiveness of this approach in reducing the time spent in the vicinity of tm

the universality classes in the parabolic anderson model we discuss the long time behaviour of the parabolic anderson model the cauchy problem for the heat equation with random potential on mathbb z d we consider general i i d potentials and show that exactly four qualitatively different types of intermittent behaviour can occur these four universality classes depend on the upper tail of the potential distribution 1 tails at that are thicker than the double exponential tails 2 double exponential tails at studied by gartner and molchanov 3 a new class called almost bounded potentials and 4 potentials bounded from above studied by biskup and konig the new class 3 which contains both unbounded and bounded potentials is studied in both the annealed and the quenched setting we show that intermittency occurs on unboundedly increasing islands whose diameter is slowly varying in time the characteristic variational formulas describing the optimal profiles of the potential and of the solution are solved explicitly by parabolas respectively gaussian densities our analysis of class 3 relies on two large deviation results for the local times of continuous time simple random walk one of these results is proved by brydges and the first two authors in bhk04 and is also used here to correct a proof in bk01

a method for constructing balanced incomplete block designs with nested rows and columns summary a general method for constructing balanced incomplete block designs with nested rows and columns is presented many designs are obtained in which none of the treatmentblock treatment row and treatment column incidence matrices is the incidence matrix of a balanced incomplete block design if the method of construction is applied to a generally balanced design then the resulting design is also generally balanced

the analysis of multistratum and spatially correlated repeated measures data summary in repeated measures experiments on animals the animals are often housed in pens and as well as the correlation between measurements over time the induced correlation due to the pen effect must be taken into account current research in the analysis of field experiments is focused on the use of spatial methods if in addition we have repeated measurements over time we need to take into account both the temporal and spatial dependence an approach is presented for the analysis of repeated measures data when an additional level of dependence exists we consider both the complete and incomplete data situations and discuss estimation based on residual maximum likelihood the procedures are illustrated using data from two experiments

optimal design with many blocking factors designs for sets of experimental units with many blocking factors are studied it is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form in consequence a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest in a sense which is made precise in the paper this encompasses several previous results for optimal designs with more than one blocking factor and applications to many other situations are given

joining models with commutative orthogonal block structure abstract mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas a mixed model is a model with orthogonal block structure obs when its variance covariance matrix is of all the positive semi definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix models with commutative orthogonal block structure cobs are a special case of obs in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance covariance matrix using the algebraic structure of cobs based on commutative jordan algebras of symmetric matrices and the cartesian product we build up complex models from simpler ones through joining in order to analyse together models obtained independently this commutativity condition of cobs is a necessary and sufficient condition for the least square estimators lse to be best linear unbiased estimators blue whatever the variance components since joining cobs we obtain new cobs the good properties of estimators hold for the joined models

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

nested generalized cyclic row column designs summary a nested row column design has v treatments arranged in b blocks each comprising pq units grouped into p rows and q columns a class of designs based on a cyclical method of construction is defined the canonical efficiency factors of such nested generalized cyclic row column designs are examined efficient designs are tabulated for 5 v 15 p 3 q 7 and r v where r bpq v is the number of replications of each treatment row column designs are used to eliminate heterogeneity in two directions more generally an experiment may have several blocks each containing pq plots arranged in p rows and q columns where the blocks may represent a further blocking factor or provide replications of the basic row column design these designs are called nested row column designs since rows and columns are nested within blocks the lattice square designs introduced by yates 1940 are examples of such designs a general analysis and the concept of balance have been considered by singh dey 1979 several series of balanced nested row column designs have been given by singh dey 1979 street 1981 and agrawal prasad 1982a preece 1967 provides a table of nested balanced incomplete block designs and a number of these designs can also be used as balanced nested row column designs other series based on partially balanced designs have been given by street 1981 and agrawal prasad 1982b jarrett hall 1982 gave some examples of small designs based on cyclic and generalized cyclic methods of con struction which they suggested could provide useful alternatives to nearest neighbour designs and methods as an example of a balanced nested row column design consider the following design given by singh dey 1979 for five treatments 0 1 2 3 4 arranged in five blocks of two rows and two columns

rectangular lattice designs efficiency factors and analysis rectangular lattice designs are shown to be generally balanced with respect to a particular decomposition of the treatment space efficiency factors are calculated and the analysis including recovery of interblock information is outlined the ideas are extended to rectangular lattice designs with an extra blocking factor

marginal permutation invariant covariance matrices with applications to linear models the goal of the present paper is to perform a comprehensive study of the covariance structures in balanced linear models containing random factors which are invariant with respect to marginal permutations of the random factors we shall focus on model formulation and interpretation rather than the estimation of parameters it is proven that permutation invariance implies a specific structure for the covariance matrices useful results are obtained for the spectra of permutation invariant covariance matrices in particular the reparameterization of random effects i e imposing certain constraints will be considered there are many possibilities to choose reparameterization constraints in a linear model however not every reparameterization keeps permutation invariance the question is if there are natural restrictions on the random effects in a given model i e such reparameterizations which are defined by the covariance structure of the corresponding factor examining relationships between the reparameterization conditions applied to the random factors of the models and the spectrum of the corresponding covariance matrices when permutation invariance is assumed restrictions on the spectrum of the covariance matrix are obtained which lead to sum to zero reparameterization of the corresponding factor

average efficiency factors and adjusted orthogonality in multidimensional designs summary an upper bound is given for the average efficiency factor of a connected multidimensional design it is shown that when the design has adjusted orthogonality its average efficiency factor is a simple function of the average efficiency factors of its component designs

are fuzzy sets a reasonable tool for modeling vague phenomena in the paper the indeterminacy phenomenon is discussed that is a phenomenon having two facets uncertainty and vagueness we argue that fuzzy sets are a reasonable mathematical tool for modeling of the latter the necessary sound foundations of their theory can now be more easily established because of significant progress reached in the formal theory of fuzzy logic further direction in the development of fuzzy set theory is also discussed

fuzzy sets the approximation of semisets abstract this paper deals with alternative set theory which substantially departs from classical set theory the main notion of it a semiset is proposed to model the same intuitive notion as fuzzy set but it is more general the reasonable tool for grasping semisets could be provided by fuzzy sets whose applicability is beyond discussion in the paper reasons for such an approximation are given and two ways how to provide it are proposed the fact that the membership function is modeled within the theory should be stressed at the end some problems and an indication for further investigation are discussed

optimal nested row column designs with specified components we consider nested row column designs where each of the row and column component designs is specified for the case that each of the component designs has second order balance we define such a nested row column design to be special if it is generally balanced with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components we show that if any special row column design exists then it is a optimal over all nested row column designs with the given components

geometric characterization of intermittency in the parabolic anderson model we consider the parabolic anderson problem tu u x u on r z d with localized initial condition u 0 x 0 x and random i i d potential under the assumption that the distribution of 0 has a double exponential or slightly heavier tail we prove the following geometric characterisation of intermittency with probability one as t 1 the overwhelming contribution to the total mass p x u t x comes from a slowly increasing number of islands which are located far from each other these islands are local regions of those high exceedances of the eld in a box of side length 2t log 2 t for which the local principal dirichlet eigenvalue of the random operator is close to the top of the spectrum in the box we also prove that the shape of in these regions is non random and that u t is close to the corresponding positive eigenfunction this is the geometric picture suggested by localization theory for the anderson hamiltonian

covariance hypotheses which are linear in both the covariance and the inverse covariance both the covariance and the inverse covariance are products of models each of which consists of either i independent identically distributed random vectors which have a covariance with a real complex or quaternion structure or ii independent identically distributed random vectors with a parametrization of the covariance which is given by means of the clifford algebra the models i are well known for models ii we have found under the assumption that the distribution is nornal the exact distributions of the maximum likelihood estimates and the likelihood ratio test statistics 1 introduction the purpose of the present paper is to describe for the family of normal distributions the structure of those statistical hypotheses models which are linear in both the covariance and the inverse covariance in section 2 we show that under such a hypothesis the problem of maximum likelihood estimation of the covariance has an explicit solution and that these hypotheses are parametrized by jordan algebras quadratic subspaces based on the theory of jordan algebras it is then possible to give a canonical form for such hypotheses in section 3 we show that the jordan algebras are products of so called simple jordan algebras and in section 4 we prove that the hypotheses can be decomposed into products of hypotheses parametrized by simple jordan algebras the simple jordan algebras are classified according to their so called degree the only simple jordan algebras of degree 1 is the set of real numbers and corresponding to that we have the hypothesis under which the covariance is proportional to a known covariance in section 5 we give a canonical form for the hypotheses which are parametrized by simple jordan algebras of degree greater than 3 it tums out that these hypotheses are equivalent to those consisting of independent identically distributed random vectors which have a covariance with a real complex or quatemion structure and the distributions of the maximum likelihood estimates are given by wishart 1928 goodman 1963 and andersson 1975 respectively the statistical hypotheses which are parametrized by simple jordan algebras of degree 2 are new and in section 6 we give a complete solution to the problems of maximum likelihood inference it turns out that the distribution problems are not more complicated than those for the two dimensional normal distribution the mathematical structure of the hypotheses is closely related to the theory of spinors in quantum mechanics based on that theory we give a canonical form for such hypotheses in section 7

correlation structure of intermittency in the parabolic anderson model consider the cauchy problem u x t t u x t x d t 0 with initial condition u x 0 1 and with the anderson hamiltonian here is the discrete laplacian 0 is a diffusion constant and x x d is an i i d random field taking values in gartner and molchanov 1990 have shown that if the law of 0 is nondegenerate then the solution u is asymptotically intermittent in the present paper we study the structure of the intermittent peaks for the special case where the law of 0 is in the vicinity of the double exponential prob 0 s exp e s s here 0 is a parameter that can be thought of as measuring the degree of disorder in the field our main result is that for fixed x y d and t the correlation coefficient of u x t and u y t converges to w 2 l2 z d w x z w y z in this expression while w d is given by w v d with v the unique centered ground state i e the solution in l2 with minimal l 2 norm of the 1 dimensional nonlinear equation v 2 v log v 0 the uniqueness of the ground state is actually proved only for large but is conjectured to hold for any 0 empty it turns out that if the right tail of the law of 0 is thicker or thinner than the double exponential then the correlation coefficient of u x t and u y t converges to x y resp the constant function 1 thus the double exponential family is the critical class exhibiting a nondegenerate correlation structure

parabolic problems for the anderson model the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

asymptotic distributions in the testing and estimation of the missing data multivariate normal linear patterned mean and correlation matrix abstract techniques used by szatrowski 1979 1983 to solve the testing and estimation problem for linear patterned covariance are used to obtain results for the linear patterned correlation problem in the presence of missing data iterative algorithms are given for finding the maximum likelihood estimates mle asymptotic distributions of the mle and likelihood ratio statistics lrs are obtained using the delta method

generalized dispersion matrices for covariance structural analysis abstract matrices v that are linear combinations of linearly independent matrices k i are considered if the k matrices are simultaneously diagonalizable methods are given for deriving eigenroots eigenvalues of v and when the k i s are also a closed set under multiplication for deriving v 1 included are such cases as the k matrices being powers of a matrix or kronecker products of powers of matrices the methods are extensions of those used for dispersion matrices for balanced data variance components models applications in covariance structural analysis for real symmetric structured dispersion matrices and for other situations are discussed

causal inference without counterfactuals abstract a popular approach to the framing and answering of causal questions relies on the idea of counterfactuals outcomes that would have been observed had the world developed differently for example if the patient had received a different treatment by definition one can never observe such quantities nor assess empirically the validity of any modeling assumptions made about them even though one s conclusions may be sensitive to these assumptions here i argue that for making inference about the likely effects of applied causes counterfactual arguments are unnecessary and potentially misleading an alternative approach based on bayesian decision analysis is presented properties of counterfactuals are relevant to inference about the likely causes of observed effects but close attention then must be given to the nature and context of the query as well as to what conclusions can and cannot be supported empirically in particular even in the absence of statistical uncertainty such inferences m

balance and orthogonality in designs for mixed classification models a classification model is easiest to analyze when it has a balanced design many of the nice features of balanced designs are retained by error orthogonal designs which were introduced in a recent paper by the authors the present paper defines a kind of partially balanced design and shows that this partial balance is sufficient to ensure the error orthogonality of a mixed classification model results are provided that make the partial balance condition easy to check it is shown that for a maximal rank error orthogonal design the type i sum of squares for a random effect coincides with the type ii sum of squares

parallel sampling from big data with uncertainty distribution data are inherently uncertain in most applications uncertainty is encountered when an experiment such as sampling is to proceed the result of which is not known to us while leading to variety of potential outcomes with the rapid developments of data collection and distribution storage technologies big data have become a bigger than ever problem and dealing with big data with uncertainty distribution is one of the most important issues of big data research in this paper we propose a parallel sampling method based on hyper surface for big data with uncertainty distribution namely pshs which adopts a universal concept of minimal consistent subset mcs of hyper surface classification hsc our inspiration for handling uncertainties in sampling from big data depends on 1 the inherent structure of the original sample set is uncertain for us 2 boundary set formed of all the possible separating hyper surfaces is a fuzzy set and 3 the uncertainty of elements in mcs pshs is implemented based on mapreduce framework which is a current and powerful parallel programming technique used in many fields experiments have been carried out on several data sets including real world data from uci repository and synthetic data the results show that our algorithm shrinks data sets while maintaining identical distribution which is useful for obtaining the inherent structure of the data sets furthermore the evaluation criterions of speedup scaleup and sizeup validate its efficiency

a widely applicable extension of the random effects two way layout its definition and statistical analysis based on group invariance a type of data layout that may be considered as an extension of the two way random effects analysis of variance is characterized and modeled based on group invariance the data layout seems to be suitable for several scenarios in psychometrics including the one in which multiple measurements are taken on each of a set of variables and the measurements can be divided into exchangeable subsets the algebraic structure of the model is studied which leads to results that are applicable to such problems as estimating correlation matrix corrected for attenuation and testing symmetry hypotheses

fuzzy hyperbolic neural network with time varying delays in this paper the formula of fuzzy basis functions with time varying delays dfbf is firstly given based on the dfbf a novel fuzzy hyperbolic neural network with time varying delays dfhnn and its approximation properties are presented respectively by constructing an appropriate lyapunov krasovskii functional the stability of dfhnn is discussed and some new criteria concerning the global exponential stability of dfhnn are proposed finally three numerical examples are given to demonstrate the effectiveness of the obtained results

winograd s fourier transform via circulants abstract for small primes the minimal multiplication algorithms of winograd can be expressed as the eigenvalue eigenvector decomposition of the associated circulant matrix but forced into the real field

balance orthogonality and efficiency factors in factorial design on montre que 1 l equilibre general relativement a une structure factorielle et 2 la structure factorielle orthogonale sont essentiellement les memes pour des plans factoriels avec un systeme unique de blocs

what is an analysis of variance the analysis of variance is usually regarded as being concerned with sums of squares of numbers and independent quadratic forms of random variables in this paper an alternative interpretation is discussed for certain classes of dispersion models for finite or infinite arrays of random variables a form of generalized spectral analysis is described and its intuitive meaning explained the analysis gives a spectral decomposition of each dispersion in the class incorporating an analysis of the common variance and an associated orthogonal decomposition of each of the random variables one by product of this approach is a clear understanding of the similarity between the spectral decomposition for second order stationary processes and the familiar linear models with random effects

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

parabolic problems for the anderson model i intermittency and related topics the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t 0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

evaluating probabilistic data with a possibilistic criterion in land restoration decision making effects on the precision of results many decision making settings incorporate both possibilistic and probabilistic uncertainty in this study entropy is used as a common measure in quantifying both types of uncertainty this measure facilitates the direct comparison of the amounts of the two types of uncertainty in a given situation the main objective of this study is however to illustrate how in a decision making setting incorporating fuzzy membership function to represent possibilistic uncertainty leads to a more realistic assessment of the decision making problem at hand a methodology for the evaluation of land condition and for aiding the decision on restoration allocation and a case study is presented the methodology enables handling both types of uncertainty probabilistic uncertainty from the spatial simulation data and possibilistic uncertainty due to vagueness in land condition factor erosion status is selected as the land condition factor restoration allocation decision is based on fuzzy logic to reflect the continuous transition between different land conditions the analysis is done six times each time using a membership function with a different degree of fuzziness insights gathered from this study would relate to the risks associated with taking a decision in the presence of both types of uncertainty the comparison of the output of the analysis i e the loss associated with misclassification from six different trials reveals that the variance in the loss values decreases as more fuzziness is incorporated into the analysis in other words there is an inverse relation between the coefficient of variance of the loss values and the fuzziness incorporated into the analysis a more in depth analytical investigation is needed to understand if this observation is specific to this case study or a more general phenomenon

estimability of variance components when all model matrices commute abstract this paper deals with estimability of variance components in mixed models when all model matrices commute in this situation it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators if in addition the family of possible variance covariance matrices forms an orthogonal block structure then there are the same number of variance components as strata and the variance components are all estimable if and only if there are non zero residual degrees of freedom in each stratum we investigate the case where the family of possible variance covariance matrices while still commutative no longer forms an orthogonal block structure now the variance components may or may not all be estimable but there is no clear link with residual degrees of freedom whether or not they are all estimable there may or may not be uniformly best unbiased quadratic estimators of those that are estimable examples are given to demonstrate all four possibilities

an axiomatizable logical foundation for lattice ordered qualitative linguistic approach for reasoning with words it is commonsense that people do express think reason and make decision directly using linguistic terms in natural language rather than using numerical quantification how to establish the formalized approach imitating the common way of human being s to manipulate directly linguistic terms without numerical approximation to provide the rational decision is still an open research area investigations on the algebraic structure of linguistic term set for varied decision making applications especially in social science still lack a formalism for development of strict linguistic valued logic system as a theoretical foundation and its approximate reasoning scheme in practice to attain this goal we characterize and construct a typical structure of commonly used linguistic term sets in natural language by a lattice ordered algebra structure lattice implication algebra lia where lukasiewicz implication algebra as a special case of lia plays a substantial role by using lukasiewicz logic s axiomatizability in terms of pavelka type fuzzy logic we propose a new axiomatizable lattice ordered qualitative linguistic truth valued logic system based on lia to place an important foundation for further establishing formal linguistic truth valued logic based approximate reasoning and decision making with applications this proposed logic system has a distinct feature of handling comparable or incomparable linguistic terms directly without numerical quantification will be especially beneficial for perception based decision making processes it attempts to enhance the quantitative theory of decision science with qualitative algebraic and logic oriented approaches to achieve reasoning with words

localization for random walks among random obstacles in a single euclidean ball place an obstacle with probability 1 p independently at each vertex of mathbb z d and run a simple random walk before hitting one of the obstacles for d ge 2 and p strictly above the critical threshold for site percolation we condition on the environment where the origin is contained in an infinite connected component free of obstacles and we show that for environments with probability tending to one as n rightarrow infty there exists a unique discrete euclidean ball of volume d log 1 p n asymptotically such that the following holds conditioned on survival up to time n we have that at any time t in epsilon n n n for some epsilon n rightarrow n rightarrow infty 0 with probability tending to one the simple random walk is in this ball this work relies on and substantially improves a previous result of the authors on localization in a region of volume poly logarithmic in n for the same problem

valid restricted randomization for unbalanced designs sufficient conditions for strong validity of randomization are given for designs whose block structure corresponds to an association scheme these conditions generalize previous results for orthogonal designs and balanced designs applications to restricted randomization of neighbour balanced designs are discussed

extremal theory for spectrum of random discrete schrodinger operator iii localization properties in this paper we study the asymptotic localization properties with high probability of the kth eigenfunction associated with the kth largest eigenvalue k 1 fixed of the multidimensional anderson hamiltonian in torus v increasing to the whole of lattice denote by z k v v the site at which the kth largest value of potential is attained it is well known that if the tails of potential distribution are heavier than the double exponential function and satisfies additional regularity and continuity conditions at infinity then the kth eigenfunction is asymptotically delta function at the site z k v localization centre for some random k v k 1 we study the asymptotic behavior of the index v k by distinguishing between three cases of the tails of potential distribution i for the heavy tails including gaussian v k is asymptotically bounded ii for the light tails but heavier than the double exponential the index v k unboundedly increases like v o 1 iii finally for the double exponential tails with high disorder the index v k behaves like a power of v for weibull s and fractional double exponential types distributions associated with the case ii we obtain the first order expansion formulas for log v k

semi latin squares and related designs summary a semi latin square for t kn symbols is a rectangular arrangement with n rows and t columns these latter being grouped into sets each containing k consecutive columns each symbol occurs exactly once in each row and exactly once in each set of columns yates 1935 previous authors seem not to have considered the combinatorial possibilities of semi latin squares for each pair of values k and t the semi latin squares can be classified into species or main classes akin to the species of latin squares the classification considered in this note disregards the ordering of the k symbols to be fouind where any row intersects any set of columns for k 2 and t 4 6 and 8 the numbers of species are 1 2 and 10 respectively the relationship between semi latin squares trojan squares and certain partially balanced incomplete block designs with two associate classes is discussed the relevant semi regular designs of clatworthy 1973 are examined to see which can be obtained from semi latin trojan squares and some enumerations of squares obtainable from the semi regular designs are reported

updating formula in an analysis of variance model summary methods for updating the inverse of the information matrix in a regression analysis after deleting or adding one or more points have been known and used for many years in this paper these methods are extended to the case of interchanging two points in an analysis of variance model the results have important applications in the construction of experimental designs

fuzzy class theory the paper introduces a simple yet powerful axiomatization of zadeh s notion of fuzzy set based on formal fuzzy logic the presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics its essence is elementary fuzzy set theory cast as two sorted first order theory over fuzzy logic which is generalized to simple type theory we show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism in this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed however we also demonstrate how to add structure to the universe of discourse within our framework

decomposition tables for experiments i a chain of randomizations one aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space initially we establish the notation and methods for evaluating an experiment with a single randomization starting with two structures or orthogonal decompositions of the data space we describe how to combine them to form the overall decomposition for a single randomization experiment that is structure balanced the relationships between the two structures are characterized using efficiency factors the decomposition is encapsulated in a decomposition table then for experiments that involve multiple randomizations forming a chain we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment in particular it is proven that the properties of the design for such an experiment are derived in a straightforward manner from those of the individual designs we show how to formulate an extended decomposition table giving the sources of variation their relationships and their degrees of freedom so that competing designs can be evaluated

exact tests that recover interblock information in balanced incomplete blocks designs abstract consider a balanced incomplete blocks design in which treatment effects are fixed and blocks are random assume that the number of blocks is greater than i the number of treatments the objective is to test the null hypothesis that there are no differences in treatment effects other null hypotheses are that v treatment contrasts are 0 where v may be any number from 1 to i 1 the usual exact test for no treatment effects is the f test based entirely on intrablock estimates a long standing problem has been to find good exact tests that use both intrablock and interblock estimates e g see houtman and speed 1983 p 1078 scheffe 1959 p 175 in this study such exact tests are found furthermore they are easy to implement and perform much better than the usual f test

a two cities theorem for the parabolic anderson model the parabolic anderson problem is the cauchy problem for the heat equation partial derivative t u t z delta u t z xi z u t z on 0 infinity x z d with random potential xi z z is an element of z d we consider independent and identically distributed potentials such that the distribution function of z converges polynomially at infinity if u is initially localized in the origin that is if u 0 z 1 0 z we show that as time goes to infinity the solution is completely localized in two points almost surely and in one point with high probability we also identify the asymptotic behavior of the concentration sites in terms of a weak limit theorem

symmetry based inference in an instrumental variable setting we describe exact inference based on group invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model it is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form when applied to the linear model this exact inference provides a unified approach to a variety of parametric and distribution free tests in particular we consider exact instrumental variable inference based on symmetry assumptions the unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification in a multivariate instrumental variables context generalizations of anderson rubin confidence sets are considered

circulants inversion of circulants and some related matrix algebras abstract the spectral theory for circulants over r or c is discussed followed by a discussion of inversion of circulants the algebraic theory of one generator matrix algebras and applications to circulants and some related algebras are presented the theory of symmetric functions plays an important role thus the latter methods apply over arbitrary commutative rings

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

decomposition and bayesian analysis of invariant normal linear models abstract using the theory of linear group representations we analyse the normal linear model with known sampling covariance structure invariant under a symmetry group and sampling mean structure equivariant under the same group in particular assuming an invariant normal prior distribution on the parameter space the problem of bayesian inference is shown to decompose naturally into several independent subproblems within any such subproblem if additional irreducibility conditions hold it is shown that the posterior expectation of any parameter is a fixed scalar multiple of its unique unbiased estimator and similarly the posterior covariance of any two parameters is a fixed scalar multiple of the prior covariance the theoretical framework is illustrated with reference to experimental designs

extremal theory for spectrum of random discrete schrodinger operator ii distributions with heavy tails we study the asymptotic structure of the first k largest eigenvalues k v and the corresponding eigenfunctions k v of a finite volume anderson model discrete schrodinger operator mathcal h v kappa delta v xi cdot on the multidimensional lattice torus v increasing to the whole of lattice provided the distribution function f of i i d potential satisfies condition log 1 f t o t3 and some additional regularity conditions as t for z v denote by 0 z the principal eigenvalue of the single peak hamiltonian v z z in l2 v and let lambda 0 k v be the kth largest value of the sample 0 in v we first show that the eigenvalues k v are asymptotically close to lambda 0 k v we then prove extremal type limit theorems i e poisson statistics for the normalized eigenvalues k v bv av where the normalizing constants av 0 and bv are chosen the same as in the corresponding limit theorems for lambda 0 k v the eigenfunction k v is shown to be asymptotically completely localized as v at the sites zk v v defined by lambda 0 z k v lambda 0 k v proofs are based on the finite rank in particular rank one perturbation arguments for discrete schrodinger operator when potential peaks are sparse

on general balance in row column designs summary the purpose of this paper is to clarify the relationships between general balance in a row column design the commutivity of the information matrices of the row and column components and the concept of adjusted orthogonality the class of row column generalized cyclic incomplete block designs is defined and a characterization is given of the subclass having general balance

reasoning about mathematical fuzzy logic and its future this paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author our goal is to think of the state of the art in mathematical fuzzy logic mfl and to outline some of the tasks on which in the author s opinion mfl should focus in the future in our discussion we will mention not only the basic theory but also its extension called fuzzy logic in broader sense flb the paradigm of the latter is to be the logic of natural human reasoning whose most essential characteristic is the use of natural language besides brief description of flb we will also mention some of its applications on the basis of that we will ponder on other possible directions for research namely the possibility of using fln as a metatheory of fuzzy mathematics as a proper tool for modeling of the main manifestations of the phenomenon of vagueness and as a reasonable tool for developing models of linguistic semantics

determination of α resolution in lattice valued first order logic lf x key issues for resolution based automated reasoning in lattice valued first order logic lf x are investigated with truth values in a lattice valued logical algebraic structure lattice implication algebra lia the determination of resolution at a certain truth value level called a resolution in lf x is proved to be equivalently transformed into the determination of a resolution in lattice valued propositional logic lp x based on lia the determination of a resolution of any quasi regular generalized literals and constants under various cases in lp x is further analyzed specified and subsequently verified hence the determination of a resolution in lf x can be accordingly solved to a very broad extent which not only lays a foundation for the practical implementation of automated reasoning algorithms in lf x but also provides a key support for a resolution based automated reasoning approaches and algorithms in lia based linguistic truth valued logics

generalized inverses of circulant and generalized circulant matrices abstract an expression for the moore penrose inverse of certain singular circulants by s r searle is generalized to include all circulants similar expressions are given for the moore penrose inverse of block circulants with circulant blocks level q circulants k circulants where k 1 and certain other matrices which are the product of a permutation matrix and a circulant expressions for other generalized inverses are given

symmetry models and hypotheses for structured data layouts on peut utiliser des proprietes de symetrie pour deriver des tests valides d hypotheses nulles et pour construire des modeles statistiques appropries pour les donnees on developpe des idees generales et on les illustre dans le contexte d une classification a deux criteres

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

inversion of circulant matrices over z m in this paper we consider the problem of inverting an n n circulant matrix with entries over zm we show that the algorithm for inverting circulants based on the reduction to diagonal form by means of fft has some drawbacks when working over zm we present three different algorithms which do not use this approach our algorithms require different degrees of knowledge of m and n and their costs range roughly from n log n log log n to n log2 n log log n log m operations over zm we also present an algorithm for the inversion of finitely generated bi infinite toeplitz matrices the problems considered in this paper have applications to the theory of linear cellular automata