Policy-based inconsistency management in relational databases

Though inconsistency management in databases and AI has been studied extensively for years, it does not allow the user to specify how he wants to resolve inconsistencies. In real-world applications, users may want to manage or resolve inconsistencies based not only on the data, but their own knowledge of the risks involved in decision making based on faulty data. Each user should be empowered to use reasonable policies to deal with his data and his mission needs. In this paper, we start by providing an axiomatic definition of inconsistency management policies (IMPs) that puts this power in the hands of users. Any function satisfying these axioms is an IMP. We then define three broad families of IMPs, and derive several results that show (i) how these policies relate to postulates for the revision of belief bases and to recent research in the area of consistent query answering, and (ii) how they interact with standard relational algebra operators. Finally, we present several approaches to efficiently implement an IMP-based framework.     

Realizing irreducible semigroups and real algebras of compact operators

Let B(X) be the algebra of bounded operators on a complex Banach space X. Viewing B(X) as an algebra over R, we study the structure of those irreducible subalgebras which contain nonzero compact operators. In particular, irreducible algebras of trace-class operators with real trace are characterized. This yields an extension of Brauer-type results on matrices to operators in infinite dimensions, answering the question: is an irreducible semigroup of compact operators with real spectra realizable, i.e., simultaneously similar to a semigroup whose matrices are real?     

Some Remarks on the Algebra of Bounded Dirichlet Series

We consider here the algebra of functions which are analytic and bounded in the right half-plane and can moreover be expanded as an ordinary Dirichlet series. We first give a new proof of a theorem of Bohr saying that this expansion converges uniformly in each smaller half-plane; then, as a consequence of the alternative definition of this algebra as an algebra of functions analytic in the infinite-dimensional polydisk, we first observe that it does not verify the corona theorem of Carleson; and then, we give in a deterministic way a new quantitative proof of the Bohnenblust-Hille optimality theorem, through the construction of a generalized Rudin-Shapiro sequence of polynomials. Finally, we compare this proof with probabilistic ones.     

Querying Historical Data Over Multiple Time-Lines

In a temporal database, time-varying relations may be defined over multiple time-lines with varying rates of sampling and/or progress, for instance, multiple time series. There is a need to represent such data in a temporal model and provide query languages. In this paper, we propose a clocked temporal relational algebra, called , which supports temporal relations based on multiple time-lines. In the underlying model, temporal relations (historical data) are defined over clocks which are subsequences of an assumed global time-line. The algebra is uniform, it is a consistent extension of the relational algebra, and it includes a number of temporal operators to combine data based on different time-lines, as well as extensions of the operators of the relational algebra. The semantics of an operation of depends on the clocks of the relations involved in the operation as well as the relations. We outline a formal interpretation of expressions of , which also represent clocked relations, and sketch a na?ve expression evaluation method.      

A remark on commutativity of the image of A-Valued analytic function

Let BL(?) be a complex Banach algebra of all bounded linear operators acting on the Hilbert space ?. J. Globevnik and I. Vidav proved that when the range of an operator-valued analytic function with domain of definition D ? ? consists of the normal operators, then f(D) is a commutative set in the algebra BL(?). The paper strengthens this result for the topological algebras.     

Bayesian network inference using marginal trees

Variable elimination (VE) and join tree propagation (JTP) are two alternatives to inference in Bayesian networks (BNs). VE, which can be viewed as one-way propagation in a join tree, answers each query against the BN meaning that computation can be repeated. On the other hand, answering a single query with JTP involves two-way propagation, of which some computation may remain unused. In this paper, we propose marginal tree inference (MTI) as a new approach to exact inference in discrete BNs. MTI seeks to avoid recomputation, while at the same time ensuring that no constructed probability information remains unused. Thereby, MTI stakes out middle ground between VE and JTP. The usefulness of MTI is demonstrated in multiple probabilistic reasoning sessions.     

Using Spreadsheet Simulation to Generate a Distribution of Forecasts for Electric Power Demand

Electric utilities commonly use econometric modelling for energy and power forecasting. In order to accommodate the uncertainties contained in the input variables, such forecasts are frequently made in three parts: a base forecast, assumed to be the most likely, and a high and a low forecast, often arbitrarily spaced on either side of the base forecast, giving a band of possible values for the forecast. Usually, a single point value forecast is then utilized rather than a distribution of possible forecast values. This paper describes how commercially available spreadsheet software was utilized to convert an econometric energy forecast into probabilistic demand and energy forecasts that incorporate weather variation, as well as other uncertain inputs.     

Homomorphisms of heterogeneous algebras

A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].     

Star partial order on B(H)

Let H be an infinite-dimensional complex Hilbert space and let B(H) be the algebra of all bounded linear operators on (H). In the paper the equivalent definition of the star partial order on B(H), using selfadjoint idempotent operators, is introduced. Also some properties of the generalized concept of order relations on B(H), defined with the help of idempotent operators, are investigated.     

Random Sampling Scattered Data with Multivariate Bernstein Polynomials

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L ^p convergence for these operators are studied, respectively.     

Topological function-theoretic proofs in spectral theory

In this paper, the spectral theorem and related characterizations of the spectrum and the spectral projections for bounded self adjoint and normal operators on a Hilbert space, are proved in purely topological —function theoretic terms. The basis for such a development, is the Gelfand—Naimark theorem for commutativeC ^*-algebras and the fact that the structure space of the (abelian) von Neumann algebra generated by the operator is a Stonean space.     

An introduction to forecasting with time series models

The use of ARIMA time series models in forecasting is reviewed. In connection with this, some important points about forecasting are discussed, including: (1) difficulties in forecasting by fitting and extrapolating a deterministic function of time; (2) the importance of providing reasonable measures of forecast accuracy; and (3) the need to incorporate subject matter knowledge with time series models when forecasting.     

Mixed-integer column generation algorithms and the probabilistic maximum satisfiability problem

The column generation approach to large-scale linear programming is extended to the mixed-integer case. Two general algorithms, a dual and a primal one, are presented. Both involve finding k-best solutions to combinatorial optimization subproblems. Algorithms for these subproblems must be tailored to each specific application. Their use is illustrated by applying them to a new combinatorial optimization problem with applications in Artificial Intelligence: Probabilistic Maximum Satisfiability. This problem is defined as follows: consider a set of logical sentences together with probabilities that they are true, assume this set of sentences is not satisfiable in the probabilistic sense, i.e., there is no probability distribution on the set of possible worlds (truth assignments to the sentences corresponding to at least one truth assignment to the logical variables they contain) such that for each sentence the sum of probabilities of the possible worlds in which it is true is equal to its probability of being true; determine a minimum set of sentences to be deleted in order to make the remaining set of sentences satisfiable. Computational experience with both algorithms is reported on.     

Sweedler 4维Hopf代数的Rota-Baxter代数结构

设H_4是Sweedler4维Hopf代数.本文根据Rota-Baxter算子的定义和性质,建立H_4的权为λ的Rota-Baxter算子在选定基下的矩阵元素满足的二次方程组.通过求解权λ=0时的二次齐次方程组和权λ=1时的二次非齐次方程组,给出了Rota-Baxter算子相应的矩阵形式.     

On some notions of spectra for quaternionic operators and for n-tuples of operators

The S-spectrum has been introduced for the definition of the S-functional calculus that includes both the quaternionic functional calculus and a calculus for n-tuples of nonnecessarily commuting operators. The notion of right spectrum for right linear quaternionic operators has been widely used in the literature, especially in the context of quaternionic quantum mechanics. Moreover, several results in linear algebra, like the spectral theorem for quaternionic matrices, involve the right spectrum. In this Note we prove that the two notions of S-spectrum and of right spectrum coincide.     

On the relevance of fuzzy sets for operations research

Every researcher in OR models knows that data in this field of human science are deterministic or random or uncertain. Of course, if measurements are available, the scientist must use such strong data but, in many case, a lot of data are weaker and subjectivity is necessary. To combine in a good way, at the best, taking account the present level of knowledge, it is what we can do. Fuzzy sets—and specially, fuzzy numbers—is a good tool for the OR analyst facing partial uncertainty and subjectivity. We are able to associate with several hybrid operators, probabilistic and uncertain data. Several processes and examples will be explained. The goal: to build a model faithful at the best and intelligible for the decision maker.     

Volterra type integral operators with homogeneous kernels in weighted <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-spaces

We consider multidimensional integral Volterra type operators with kernels homogeneous of degree (?n); the operators act in L _p -spaces with a submultiplicative weight. For these operators we obtain necessary and sufficient conditions of their invertibility. Besides, we describe the Banach algebra generated by the operators. For this algebra we construct the symbolic calculus, in terms of which we obtain an invertibility criterion of the operators.     

Differential operators on the free algebras

Following the definitions of the algebras of differential operators, ??-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in Lunts and Rosenberg (Selecta Math New Ser 3:335?C359, 1997), we describe these algebras on the free associative algebra. We further study their properties.     

Average Case Analysis in Database Problems

In a variety of applications ranging from environmental and health sciences to bioinformatics, it is essential that data collected in large databases are generated stochastically. This states qualitatively new problems both for statistics and for computer science. Namely, instead of deterministic (usually worst case) analysis, the average case analysis is needed for many standard database problems. Since both stochastic and deterministic methods and notation are used it causes additional difficulties for an investigation of such problems and for an exposition of results. We consider a general class of probabilistic models for databases and study a few problems in a probabilistic framework. In order to demonstrate the general approach, the problems for systems of database constraints (keys, functional dependencies and related) are investigated in more detail. Our approach is based on consequent using Rényi entropy as a main characteristic of uncertainty of distribution and Poisson approximation (Stein–Chen technique) of the corresponding probabilities.     

On operators commuting with Toeplitz operators modulo the compact operators

We prove that an operator on H² of the disc commutes modulo the compacts with all analytic Toeplitz operators if and only if it is a compact perturbation of a Toeplitz operator with symbol in H^∞ + C. Consequently, the essential commutant of the whole Toeplitz algebra is the algebra of Toeplitz operators with symbol in QC. The image in the Calkin algebra of the Toeplitz operators with symbol in H^∞ + C is a maximal abelian algebra. These results lead to a characterization of automorphisms of the algebra of compact perturbations of the analytic Toeplitz operators.