Computable Analysis of Differential Equations (Invited Talk)

In this talk, we discuss some algorithmic aspects of the local and global existence theory for various ordinary and partial differential equations. We will present a sample of results and give some idea of the motivation and general philosophy underlying these results

From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty (Invited Talk)

Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds $Delta$ on the measurement errors. In this case, based on the measurement result $widetilde x$, we can only conclude that the actual (unknown) value $x$ of the desired quantity is in the interval $[widetilde x-Delta,widetilde x+Delta]$. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. To remedy this problem, in our previous papers, we proposed an extension of interval technique to {it set computations}, where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time

Semilattices, Domains, and Computability (Invited Talk)

As everyone knows, one popular notion of Scott domain is defined as a bounded complete algebraic cpo. These are closely related to algebraic lattices: (i) A Scott domain becomes an algebraic lattice with the adjunction of an (isolated) top element. (ii) Every non-empty Scott-closed subset of an algebraic lattice is a Scott domain. Moreover, the isolated ($=$ compact) elements of an algebraic lattice form a semilattice (under join). This semilattice has a zero element, and, provided the top element is isolated, it also has a unit element. The algebraic lattice itself may be regarded as the ideal completion of the semilattice of isolated elements. This is all well known. What is not so clear that is that there is an easy-to-construct domain of countable semilattices giving isomorphic copies of all countably based domains. This approach seems to have advantages over both ``information systems\u27\u27 or more abstract lattice formulations, and it makes definitions of solutions to domain equations very elementary to justify. The ``domain of domains\u27\u27 also has an immediate computable structure

INVITED PAPER ABSTRACTS

Teaching/Communication/Extension/Profession,

Invited article: Adaptability

For the last several decades, organizations have dealt with economic shifts using change management. Based on the new science, there are two major flaws with this approach. First, the word change implies an event with an ending. Second, it implies that change can be managed. In a world of economic volatility, this approach is no longer viable. The continuous climate of uncertainty and volatility demands another view, one that supports adaptability and resilience.Organization, alignment, speed of change, economic volatility, market shift, Total Quality Management, Business Reprocess Engineering, living systems, chaos, evolution, fifth discipline, learning organization, system thinking.