We investigate linear operators between C?-algebras which approximately preserve involution and orthogonality, the latter meaning that for some ?>0 we have ??(x)?(y)????x??y? all positive x,y with xy=0. establish structural properties of such maps concerning approximate Jordan-like equations almost commutation relations. In situations (e.g. when codomain is finite-dimensional), show ? can be ap...

An inference graph can have many \deriva-tion strategies", each a particular ordering of the steps involved in reducing a given query to a sequence of database retrievals. An \optimal strategy" for a given distribution of queries is a complete strategy whose \expected cost" is minimal, where the expected cost depends on the conditional probabilities that each requested retrieval succeeds , give...

A satisscing search problem consists of a set of probabilistic experiments to be performed in some order, seeking a satisfying connguration of successes and failures. The expected cost of the search depends both on the success probabilities of the individual experiments, and on the search strategy, which speciies the order in which the experiments are to be performed. A strategy that minimizes ...

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that F is ε-approximately submodular if there exists a submodular function f such that (1−ε)f(S) ≤ F (S) ≤ (1+ε)f(S) for ...

Evaluating query predicates on data samples is the only way to estimate their selectivity in certain scenarios. Finding a guaranteed optimal query plan is not a reasonable optimization goal in those cases as it might require an infinite number of samples. We therefore introduce probably approximately optimal query optimization (PAO) where the goal is to find a query plan whose cost is near-opti...

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.