multi adjoint t concept lattices the t concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non commutative fuzzy logic following the general techniques of formal concept analysis and based on the works by georgescu and popescu given a non commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways and this generates a pair of concept lattices in this paper we show that the information common to both concept lattices can be seen as a sublattice of the cartesian product of both concept lattices the multi adjoint framework can be applied to this general t concept lattice and its usefulness is illustrated by a working example

between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

notes on solution sets of inf t fuzzy relational equations on complete brouwerian lattices and fuzzy relational equations on complete brouwerian lattices this paper clarifies several hypotheses and results given in q q xiong and x p wang solution sets of fuzzy relational equations on complete brouwerian lattices information sciences 177 21 47574767 2007 and in q q xiong and x p wang fuzzy relational equations on complete brouwerian lattices information sciences 193 0 141152 2012 which in their current form are confusing and need to be improved

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

associatively tied implications we say that an implication operator a on a complete lattice l is associatively tied if there is a binary operation t on l that ties a that is the identity a a gamma a t holds for all in l this property extends to multiple valued logic the following equivalence in classical logic x y z x y z we show that in this case there exists an associative binary operation ta that ties a hence the nomenclature we study properties of that ta when a is associatively tied we then seek a characterization for the validity of associative tiedness for an implication a phrased in terms of a and two adjoints of it

trading classical communication quantum communication and entanglement in quantum shannon theory in this paper we give tradeoffs between classical communication quantum communication and entanglement for processing information in the shannon theoretic setting we first prove a unit resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation the optimal strategy mixes the three fundamental protocols of teleportation superdense coding and entanglement distribution we then provide an achievable rate region and a matching multiletter converse for the direct static capacity theorem this theorem applies to the scenario where a large number of copies of a noisy bipartite state are available in addition to consumption or generation of the above three noiseless resources our coding strategy involves a protocol that we name the classically assisted state redistribution protocol and the three fundamental protocols we finally provide an achievable rate region and a matching multiletter converse for the direct dynamic capacity theorem this theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources our coding strategy combines the classically enhanced father protocol with the three fundamental unit protocols

minimal solutions of general fuzzy relation equations on linear carriers an algebraic characterization abstract this paper considers a general fuzzy relation equation which has minimal solutions if it is solvable in this case an algebraic characterization is introduced which provides an interesting method to compute minimal solutions in this general setting moreover a comparison with other frameworks is also given

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

a resource framework for quantum shannon theory quantum shannon theory is loosely defined as a collection of coding theorems such as classical and quantum source compression noisy channel coding theorems entanglement distillation etc which characterize asymptotic properties of quantum and classical channels and states in this paper we advocate a unified approach to an important class of problems in quantum shannon theory consisting of those that are bipartite unidirectional and memoryless

conditional generalized estimating equations for the analysis of clustered and longitudinal data a common and important problem in clustered sampling designs is that the effect of within cluster exposures i e exposures that vary within clusters on outcome may be confounded by both measured and unmeasured cluster level factors i e measurements that do not vary within clusters when some of these are ill not accounted for estimation of this effect through population averaged models or random effects models may introduce bias we accommodate this by developing a general theory for the analysis of clustered data which enables consistent and asymptotically normal estimation of the effects of within cluster exposures in the presence of cluster level confounders semiparametric efficient estimators are obtained by solving so called conditional generalized estimating equations we compare this approach with a popular proposal by neuhaus and kalbfleisch 1998 biometrics 54 638 645 who separate the exposure effect into a within and a between cluster component within a random intercept model we find that the latter approach yields consistent and efficient estimators when the model is linear but is less flexible in terms of model specification under nonlinear models this approach may yield inconsistent and inefficient estimators though with little bias in most practical settings

on heterogeneous formal contexts we propose a new type of fuzzification for formal concept analysis that works with heterogeneous values in a context and illustrate this with an example we formulate and prove an appropriate counterpart to the so called basic theorem of a concept lattice we show that this is a generalization of the previous approaches it covers the so called generalized concept lattice and multi adjoint t concept lattices

universal coding for transmission of private information we consider the scenario in which alice transmits private classical messages to bob via a classical quantum channel part of whose output is intercepted by an eavesdropper eve we prove the existence of a universal coding scheme under which alice s messages can be inferred correctly by bob and yet eve learns nothing about them the code is universal in the sense that it does not depend on specific knowledge of the channel prior knowledge of the probability distribution on the input alphabet of the channel and bounds on the corresponding holevo quantities of the output ensembles at bob s and eve s end suffice

using concept lattice theory to obtain the set of solutions of multi adjoint relation equations an important goal in the fuzzy relation equations framework is to obtain the whole set of solutions this paper introduces algebraic properties in the multi adjoint concept lattice setting moreover using the relationship between these concept lattices and multi adjoint relation equations the complete set of solutions of these general equations is characterized and computed avoiding the necessity of considering minimal solutions

strong converse theorems using renyi entropies we use a renyi entropy method to prove strong converse theorems for certain information theoretic tasks which involve local operations and quantum or classical communication between two parties these include state redistribution coherent state merging quantum state splitting measurement compression with quantum side information randomness extraction against quantum side information and data compression with quantum side information the method we employ in proving these results extends ideas developed by sharma preprint arxiv 1404 5940 quant ph 2014 which he used to give a new proof of the strong converse theorem for state merging for state redistribution we prove the strong converse property for the boundary of the entire achievable rate region in the e q plane where e and q denote the entanglement cost and quantum communication cost respectively in the case of measurement compression with quantum side information we prove a strong converse theorem for the classical communication cost which is a new result extending the previously known weak converse for the remaining tasks we provide new proofs for strong converse theorems previously established using smooth entropies for each task we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a renyi generalization of the optimal rate hence we identify candidates for the strong converse exponents for each task discussed in this paper to prove our results we establish various new entropic inequalities which might be of independent interest these involve conditional entropies and mutual information derived from the sandwiched renyi divergence in particular we obtain novel bounds relating these quantities as well as the renyi conditional mutual information to the fidelity of two quantum states

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

multi adjoint relation equations definition properties and solutions using concept lattices this paper generalizes fuzzy relation equations following the multi adjoint philosophy moreover the solutions of these general fuzzy relation equations and the concepts of a multi adjoint property oriented concept lattice are related and several results are obtained from the theory of concept lattices as a consequence of this relevant relation more properties about these general equations can be proven from the theory of concept lattices and the algorithms developed to compute concept lattices can be used to obtain solutions furthermore an interesting application to fuzzy logic programming has been introduced in which an important problem in this topic has been interpreted in terms of solving a multi adjoint relation equation

on the dedekindmacneille completion and formal concept analysis based on multilattices the dedekindmacneille completion of a poset p can be seen as the least complete lattice containing p in this work we analyze some results concerning the use of this completion within the framework of formal concept analysis in terms of the poset of concepts associated with a galois connection between posets specifically we show an interesting property of the dedekindmacneille completion in that the completion of the concept poset of a galois connection between posets coincides with the concept lattice of the galois connection extended to the corresponding completions moreover we study the specific case when p has multilattice structure and state and prove the corresponding representation theorem

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

characterizing reducts in multi adjoint concept lattices abstract the construction of reducts that is minimal sets of attributes containing the main information of a database is a fundamental task in different frameworks such as in formal concept analysis fca and rough set theory rst this paper will be focused on a general fuzzy extension of fca called multi adjoint concept lattice and we present a study about the attributes generating meet irreducible elements and on the reducts in this framework from this study we introduce interesting results on the cardinality of reducts and the consequences in the classical case

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the paper deals with the isomorphism between the constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the essential point of the former approach encompasses the full diversification of data structures within a formal context in particular we use a different complete lattice for diverse objects a different complete lattice for diverse attributes and a different poset for diverse matrix fields the latter framework with heterogeneous hedges results in a reduction in the size of the corresponding concept lattice we present the properties of constraint heterogeneous approach that is associated with the fixpoints of hedges and we add remarks to the related studies

the logic of tied implications part 2 syntax an implication operator a is said to be tied if there is a binary operation t that ties a that is the identity a a a b z a t a b z holds for all a b z we aim at the construction of a complete predicate logic for prelinear tied adjointness algebras we realize this in three steps in the first step we establish a propositional calculus adjtpc complete for the class of all tied adjointness algebras on partially ordered sets without prelinearity and ignoring the lattice operations for that we supply a hilbert system based on seven axioms and one deduction rule modus ponens in the second and third steps we extend adjtpc to propositional and predicate calculi complete for prelinear tied adjointness algebras we apply a duality principle due to morsi in all three calculi through which we manage to cut down the number of proofs

attribute and size reduction mechanisms in multi adjoint concept lattices attribute reduction and size reduction in concept lattices are key research topics in formal concept analysis fca this paper combines both strategies in the multi adjoint concept lattice framework in order to simplify the information provided by the original context specifically we present three procedures which merge the attribute reduction and the size reduction by means of an irreducible cut concept lattice analyzing the obtained properties

efforts to adjust for confounding by neighborhood using complex survey data in social epidemiology one often considers neighborhood or contextual effects on health outcomes in addition to effects of individual exposures this paper is concerned with the estimation of an individual exposure effect in the presence of confounding by neighborhood effects motivated by an analysis of national health interview survey nhis data in the analysis we operationalize neighborhood as the secondary sampling unit of the survey which consists of small groups of neighboring census blocks thus the neighborhoods are sampled with unequal probabilities as are individuals within neighborhoods we develop and compare several approaches for the analysis of the effect of dichotomized individual level education on the receipt of adequate mammography screening in the analysis neighborhood effects are likely to confound the individual effects due to such factors as differential availability of health services and differential neighborhood culture the approaches can be grouped into three broad classes ordinary logistic regression for survey data with either no effect or a fixed effect for each cluster conditional logistic regression extended for survey data and generalized linear mixed model glmm regression for survey data standard use of glmms with small clusters fails to adjust for confounding by cluster e g neighborhood this motivated us to develop an adaptation we use theory simulation and analyses of the nhis data to compare and contrast all of these methods one conclusion is that all of the methods perform poorly when the sampling bias is strong more research and new methods are clearly needed

causal inference with generalized structural mean models summary we estimate cause effect relationships in empirical research where exposures are not completely controlled as in observational studies or with patient non compliance and self selected treatment switches in randomized clinical trials additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log linear models when accommodating binary data we propose the generalized structural mean model to overcome these limitations this is a semiparametric two stage model which extends the structural mean model to handle non linear average exposure effects the first stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure free outcomes in exposed subsets of the population for identification of the structural parameters a second stage nuisance model is introduced this takes the form of a classical association model for expected outcomes given observed exposure under the model we derive estimating equations which yield consistent asymptotically normal and efficient estimators of the structural effects we examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect the double logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self selected non compliance

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

effect of omitted confounders on the analysis of correlated binary data summary marginal analysis using the generalized estimating equation approach is widely applied to correlated observations as occur in studies with clusters and in longitudinal follow up of individuals in this article we investigate the effect of confounding in such models we assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y which can be binary or ordinal in order to investigate confounding arising from the omission of z a joint structure for x and z must be specified modeling normally distributed x z as sums of between and within individual or cluster components allows us to incorporate different degrees of betweenand within individual correlation such a structure includes as special cases cohort and period effects in longitudinal settings and random intercept models the latter situation corresponds to allowing z to vary only on the between individual or cluster level and to be uncorrelated with x and leads to attenuation of the coefficient of x in marginal models with the logit and probit links more complex situations occur when z is allowed to also vary on the within individual or cluster level and when z is correlated with x we examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z we derive general formulas and interpret the parameters and results in an ongoing cohort study testing for omitted covariates is also discussed

between within models for survival analysis a popular way to control for confounding in observational studies is to identify clusters of individuals e g twin pairs such that a large set of potential confounders are constant shared wit

multiply robust inference for statistical interactions a primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures when the main interest lies in the interaction this approach is not entirely satisfactory because it is prone to possibly severe bias when the main exposure effects or the associations between outcome and extraneous factors are misspecified in this article we consider conditional mean models with identity or log link that postulate the statistical interaction in terms of a finite dimensional parameter but are otherwise unspecified we show that estimation of the interaction parameter often is not feasible in this model because it requires nonparametric estimation of auxiliary conditional expectations given high dimensional variables we thus consider multiply robust estimation under a union model th

coding theorem and strong converse for quantum channels we present a new proof of holevo s 1973 1977 coding theorem for transmitting classical information through quantum channels and its strong converse the technique is largely inspired by wolfwitz s 1964 combinatorial approach using types of sequences as a byproduct of our approach which is independent of previous ones both in the coding theorem and the converse we can give a new proof of holevo s information bound

entanglement assisted capacity of a quantum channel and the reverse shannon theorem the entanglement assisted classical capacity of a noisy quantum channel c sub e is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel assuming that the sender and receiver have access to the resource of shared quantum entanglement which may be used up by the communication protocol we show that the capacity c sub e is given by an expression parallel to that for the capacity of a purely classical channel i e the maximum over channel inputs spl rho of the entropy of the channel input plus the entropy of the channel output minus their joint entropy the latter being defined as the entropy of an entangled purification of spl rho after half of it has passed through the channel we calculate entanglement assisted capacities for two interesting quantum channels the qubit amplitude damping channel and the bosonic channel with amplification attenuation and gaussian noise we discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel alone or in the presence of ancillary resources such as prior entanglement in the classical analog of entanglement assisted communication communication over a discrete memoryless channel dmc between parties who share prior random information we show that one parameter is sufficient i e that in the presence of prior shared random information all dmcs of equal capacity can simulate one another with unit asymptotic efficiency

partitioned gmm logistic regression models for longitudinal data correlation is inherent in longitudinal studies due to the repeated measurements on subjects as well as due to time dependent covariates in the study in the national longitudinal study of adolescent to adult health add health data were repeatedly collected on children in grades 7 12 across four waves thus observations obtained on the same adolescent were correlated while predictors were correlated with current and future outcomes such as obesity status among other health issues previous methods such as the generalized method of moments gmm approach have been proposed to estimate regression coefficients for time dependent covariates however these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time this assumption is not necessarily optimal in applications such as add health or health related data thus we depart from this assumption and instead use the partitioned gmm approach to estimate multiple coefficients for the data based on different time periods these extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship this approach offers a deeper understanding and appreciation into the effect of each covariate on the response we conduct simulation studies as well as analyses of obesity in add health rehospitalization in medicare data and depression scores in a clinical study the partitioned gmm methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data

syntax and semantics of multi adjoint normal logic programming abstract multi adjoint logic programming is a general framework with interesting features which involves other positive logic programming frameworks such as monotonic and residuated logic programming generalized annotated logic programs fuzzy logic programming and possibilistic logic programming one of the most interesting extensions of this framework is the possibility of considering a negation operator in the logic programs which will improve its flexibility and the range of real applications this paper introduces multi adjoint normal logic programming which is an extension of multi adjoint logic programming including a negation operator in the underlying lattice beside the introduction of the syntax and semantics of this paradigm we will provide sufficient conditions for the existence of stable models defined on a convex compact set of an euclidean space finally we will consider a particular algebraic structure in which sufficient conditions can be given in order to ensure the unicity of stable models of multi adjoint normal logic programs

an improved reductant calculus using fuzzy partial evaluation techniques partial evaluation pe is an automatic program transformation technique aiming to obtain among other advantages the optimization of a program with respect to parts of its input hence it is also known as program specialization this paper introduces the subject of pe into the field of fuzzy logic programming we define the concept of pe for multi adjoint logic programs and goals and apart from discussing the benefits achieved by this technique we also introduce in the fuzzy setting a completely novel application of pe which allows us the computation of reductants guaranteeing completeness properties without harming the computational efficiency reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties as observed in the specialized literature a multi adjoint logic program when interpreted on a partially ordered lattice has to include all its reductants in order to preserve the approximate completeness property this introduces severe penalties in the implementation of efficient multi adjoint logic programming systems not only the size of programs increases but also their execution time in this paper we define a refinement to the notion of reductant based on pe techniques that we call pe reductant we establish the main properties of pe reductants i e the classical concept of reductant and the new notion of pe reductant are both semantically and operationally equivalent and what is the best we demonstrate that our refined notion of pe reductant is even able to increase the efficiency of multi adjoint logic programs

channel simulation with quantum side information we study and solve the problem of classical channel simulation with quantum side information at the receiver this is a generalization of both the classical reverse shannon theorem and the classical quantum slepian wolf problem the optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the holevo information between the channel output and the quantum side information our main theorem has two important corollaries the first is a quantum generalization of the wyner ziv problem rate distortion theory with quantum side information the second is an alternative proof of the tradeoff between classical communication and common randomness distilled from a quantum state the fully quantum generalization of the problem considered is quantum state redistribution here the sender and receiver share a mixed quantum state and the sender wants to transfer part of her state to the receiver using entanglement and quantum communication we present outer and inner bounds on the achievable rate pairs

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

cryptographic distinguishability measures for quantum mechanical states this paper mostly expository in nature surveys four measures of distinguishability for quantum mechanical states this is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions namely the probability of an identification error the kolmogorov distance the bhattacharyya coefficient and the shannon 1948 distinguishability as defined through mutual information these measures have a long history of use in statistical pattern recognition and classical cryptography we obtain several inequalities that relate the quantum distinguishability measures to each other one of which may be crucial for proving the security of quantum cryptographic key distribution in another vein these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states this is a tool that may prove useful in the analysis of various quantum cryptographic protocols

multi adjoint property oriented and object oriented concept lattices this paper presents a generalisation of the classical property and object oriented concept lattices to a fuzzy environment based on the philosophy of the multi adjoint paradigm these concept lattices are generalisations of rough set theory used to consider two different sets the set of objects and the set of attributes to apply the corresponding modal operators as in formal concept analysis first of all the paper presents several specific properties of adjoint triples in which the duals of several supports are considered these properties are then used to introduce the multi adjoint property and object oriented concept lattices in which different adjoint triples can be used in non linear sets as well as the corresponding representation fundamental theorems moreover these lattices are related to the multi adjoint concept lattice in which negation operators are not needed as a result this relation allows the properties to be translated from one to another

rough set driven approach for attribute reduction in fuzzy formal concept analysis abstract the reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems two remarkable formal tools for extracting such information are rough set theory rst and formal concept analysis fca as well as their fuzzy generalizations this work introduces a new method to reduce attributes in fuzzy fca considering the reduction philosophy given in rst and studies its main properties this method allows us to carry out a deeper study of the relation between these two theories moreover the proposed methodology has been compared with other existing reduction mechanisms

tight uniform continuity bounds for quantum entropies conditional entropy relative entropy distance and energy constraints we present a bouquet of continuity bounds for quantum entropies falling broadly into two classes first a tight analysis of the alicki fannes continuity bounds for the conditional von neumann entropy reaching almost the best possible form that depends only on the system dimension and the trace distance of the states almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators as applications we give new proofs with tighter bounds of the asymptotic continuity of the relative entropy of entanglement er and its regularization e r infty as well as of the entanglement of formation ef using a novel quantum coupling of density operators which may be of independent interest we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation aka entanglement cost e c e f infty second we derive analogous continuity bounds for the von neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint most importantly systems of multiple quantum harmonic oscillators while without an energy bound the entropy is discontinuous it is well known to be continuous on states of bounded energy however a quantitative statement to that effect seems not to have been known here under some regularity assumptions on the hamiltonian we find that quite intuitively the gibbs entropy at the given energy roughly takes the role of the hilbert space dimension in the finite dimensional fannes inequality

analysis of longitudinal data with unmeasured confounders confounding in longitudinal or clustered data creates special problems and opportunities because the relationship between the confounder and covariate of interest may differ across and within individuals or clusters a well known example of such confounding in longitudinal data is the presence of cohort and period effects in models of aging in epidemiologic research we first formulate a data generating model with confounding and derive the distribution of the response variable unconditional on the confounder we then examine the properties of the regression coefficient for some analytic approaches when the confounder is omitted from the fitted model the expected value of the regression coefficient differs in across and within individual regression in the multivariate case within and between individual information is combined and weighted according to the assumed covariance structure we assume compound symmetry in the fitted covariance matrix and derive the variance bias and mean squared error of the slope estimate as a function of the fitted within individual correlation we find that even in this simplest multivariate case the trade off between bias and variance depends on a large number of parameters it is generally preferable to fit correlations somewhat above the true correlation to minimize the effect of between individual confounders or cohort effects period effects can lead to situations where it is advantageous to fit correlations that are below the true correlation the results highlight the trade offs inherent in the choice of method for analysis of longitudinal data and show that an appropriate choice can be made only after determining whether within or between individual confounding is the major concern

communicating over adversarial quantum channels using quantum list codes in this correspondence we study quantum communication in the presence of adversarial noise in this setting communicating with perfect fidelity requires a quantum code of bounded minimum distance for which the best known rates are given by the quantum gilbert varshamov qgv bound asking only for arbitrarily high fidelity and letting the sender and receiver use a secret key of length logarithmic in the number of qubits sent we find a dramatic improvement over the qgv rates in fact our protocols allow high fidelity transmission at noise levels for which perfect fidelity is impossible to achieve such rates we introduce fully quantum list codes which may be of independent interest

adjoint negations more than residuated negations negation operators are useful operators which have extensively been studied and used in different fuzzy settings such as in fuzzy logic this paper introduces a new and flexible kind of negation operator based on adjoint triples and which is called adjoint negation relative to a fixed element besides proving several interesting properties the comparison with weak negations studied by trillas esteva et al and pairs of weak negations introduced by georgescu and popescu is presented furthermore adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor

extrinsic and intrinsic data in quantum measurements asymptotic convex decomposition of positive operator valued measures we study the problem of separating the data produced by a given quantum measurement on states from a memoryless source which is unknown except for its average state described by a positive operator valued measure povm into a meaningful intrinsic and a not meaningful extrinsic part we are able to give an asymptotically tight separation of this form with the intrinsic data quantified by the holevo mutual information of a certain state ensemble associated to the povm and the source in a model that can be viewed as the asymptotic version of the convex decomposition of povms into extremal ones this result is applied to a similar separation therorem for quantum instruments and quantum operations in their kraus form finally we comment on links to related subjects we stress the difference between data and information in particular by pointing out that information typically is strictly less than data derive the holevo bound from our main result and look at its classical case we show that this includes the solution to the problem of extrinsic intrinsic data separation with a known source then compare with the well known notion of sufficient statistics the result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics an appendix collects several estimates for mixed state fidelity and trace norm distance that seem to be new in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity

fuzzy logic programming in this paper we consider the theory of fuzzy logic programming without negation our results cover logical systems with a wide variety of connectives ranging from t norm and conorms through conjunctors and disjunctors and their residuals to aggregation operators rules of our programs are many valued implications we emphasize that in contrast to other approaches our logic is truth functional i e according to p hajek we work in fuzzy logic in narrow sense we prove the soundness and the completeness of our formal model we deal with applications to threshold computation abduction fuzzy unification based on similarity we show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations

strong converse for the classical capacity of entanglement breaking and hadamard channels via a sandwiched renyi relative entropy a strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel along with a corresponding achievability statement for rates below the capacity such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication here we show that such a strong converse theorem holds for the classical capacity of all entanglement breaking channels and all hadamard channels the complementary channels of the former these results follow by bounding the success probability in terms of a sandwiched renyi relative entropy by showing that this quantity is subadditive for all entanglement breaking and hadamard channels and by relating this quantity to the holevo capacity prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle

identifying the information gain of a quantum measurement we show that quantum to classical channels i e quantum measurements can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement if sufficient shared randomness is available this result generalizes winter s measurement compression theorem for fixed independent and identically distributed inputs to arbitrary inputs and more importantly it identifies the quantum mutual information of a measurement as the information gained by performing it independent of the input state on which it is performed our result is a generalization of the classical reverse shannon theorem to quantum to classical channels in this sense it can be seen as a quantum reverse shannon theorem for quantum to classical channels but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication respectively the proof is based on a novel one shot state merging protocol for classically coherent states as well as the postselection technique for quantum channels and it uses techniques developed for the quantum reverse shannon theorem

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

quantum data processing we prove a data processing inequality for quantum communication channels which states that processing a received quantum state may never increase the mutual information between input and output states

attribute reduction in multi adjoint concept lattices knowledge reduction is one of the key issues in formal concept analysis and there have been many studies on this topic the irreducible elements in a lattice are also very important since they form the basic information of a relational system moreover they are also important from the viewpoint of attribute reduction both topics are notably more complicated in a fuzzy setting since not only the size of the sets of attributes and objects influence the size of the fuzzy concept lattice but the truth value sets where the sets of objects attributes and the relation are evaluated are important this paper presents in the general fuzzy framework of multi adjoint concept lattices a characterization of the meet irreducible elements from which a classification of attributes and its application to attribute reduction is introduced