New Type of Coding Problem Motivated by Database Theory

The present paper is intended to survey the interaction between relational database theory and coding theory. In particular it is shown how an extremal problem for relational databases gives rise to a new type of coding problem. The former concerns minimal representation of branching dependencies that can be considered as a data mining type question. The extremal configurations involve d-distance sets in the space of disjoint pairs of k-element subsets of an n-element set X. Let X be an n-element finite set, 0 < k < n/2 an integer. Suppose that {A(1), B-1} and {A(2), B-2} are pairs of disjoint k-element subsets of X (that is, \A(1)\ = \B-1\ = \A(2)\ = \B-2\ = k, A(1) boolean AND B-1 = 0, A(2) boolean AND B-2 = 0). Define the distance of these pairs by d({A(1), B-1}, {A(2), B-2}) = min{\A(1) - A(2)\ + \B-1 - B-2\, \A(1) - B-2\ + \B-1 - A(2)\). (C) 2004 Elsevier B.V. All rights reserved

Process modelling for information system description

My previous experiences and some preliminary studies of the relevant technical literature allowed me to identify several reasons for which the current state of the database theory seemed unsatisfactory and required further research. These reasons included: insufficient formalism of data semantics, misinterpretation of NULL values, inconsistencies in the concept of the universal relation, certain ambiguities in domain definition, and inadequate representation of facts and constraints. The commonly accepted ’sequentiality’ principle in most of the current system design methodologies imposes strong restrictions on the processes that a target system is composed of. They must be algorithmic and must not be interrupted during execution; neither may they have any parallel subprocesses as their own components. This principle can no longer be considered acceptable. In very many existing systems multiple processors perform many concurrent actions that can interact with each other. The overconcentration on data models is another disadvantage of the majority of system design methods. Many techniques pay little (or no) attention to process definition. They assume that the model of the Real World consists only of data elements and relationships among them. However, the way the processes are related to each other (in terms of precedence relation) may have considerable impact on the data model. It has been assumed that the Real World is discretisable, i.e. it may be modelled by a structure of objects. The word object is to be interpreted in a wide sense so it can mean anything within the boundaries of this part of the Real World that is to be represented in the target system. An object may then denote a fact or a physical or abstract entity, or relationships between any of these, or relationships between relationships, or even a still more complex structure. The fundamental hypothesis was formulated stating the necessity of considering the three aspects of modelling - syntax, semantics and behaviour, and these to be considered integrally. A syntactic representation of an object within a target system is called a construct A construct which cannot be decomposed further (either syntactically or semantically) is defined to be an atom. Any construct is a result of the following production rules: construct ::= atom I function construct; function ::= atom I construct. This syntax forms a sentential notation. The sentential notation allows for extensive use of denotational semantics. The meaning of a construct may be defined as a function mapping from a set of syntactic constructs to the appropriate semantic domains; these in turn appear to be sets of functions since a construct may have a meaning in more than one class of objects. Because of its functional form the meaning of a construct may be derived from the meaning of its components. The issue of system behaviour needed further investigation and a revision of the conventional model of computing. The sequentiality principle has been rejected, concurrency being regarded as a natural property of processes. A postulate has been formulated that any potential parallelism should be constructively used for data/process design and that the process structure would affect the data model. An important distinction has been made between a process declaration - considered as a form of data or an abstraction of knowledge - and a process application that corresponds to a physical action performed by a processor, according to a specific process declaration. In principle, a process may be applied to any construct - including its own representation - and it is a matter of semantics to state whether or not it is sensible to do so. The process application mechanism has been explained in terms of formal systems theory by introducing an abstract machine with two input and two output types of channels. The system behaviour has been described by defining a process calculus. It is based on logical and functional properties of a discrete time model and provides a means to handle expressions composed of process-variables connected by logical functors. Basic terms of the calculus are: constructs and operations (equivalence, approximation, precedence, incidence, free-parallelism, strict-parallelism). Certain properties of these operations (e.g. associativity or transitivity) allow for handling large expressions. Rules for decomposing/integrating process applications, analogous in some sense to those forming the basis for structured programming, have been derived

Relationships between closure operations and choice functions - equivalent descriptions of a family of functional dependencies

The family of functional dependencies plays an important role in the relational database. The main goal of this paper is to investigate closure operations and choice functions. They are equivalent descriptions of family of functional dependencies. The main properties of and relationship between closure operations and choice functions are presented in this paper

Metaheuristics “In the Large”

Many people have generously given their time to the various activities of the MitL initiative. Particular gratitude is due to Adam Barwell, John A. Clark, Patrick De Causmaecker, Emma Hart, Zoltan A. Kocsis, Ben Kovitz, Krzysztof Krawiec, John McCall, Nelishia Pillay, Kevin Sim, Jim Smith, Thomas Stutzle, Eric Taillard and Stefan Wagner. J. Swan acknowledges the support of UK EPSRC grant EP/J017515/1 and the EU H2020 SAFIRE Factories project. P. GarciaSanchez and J. J. Merelo acknowledges the support of TIN201785727-C4-2-P by the Spanish Ministry of Economy and Competitiveness. M. Wagner acknowledges the support of the Australian Research Council grants DE160100850 and DP200102364.Following decades of sustained improvement, metaheuristics are one of the great success stories of opti- mization research. However, in order for research in metaheuristics to avoid fragmentation and a lack of reproducibility, there is a pressing need for stronger scientific and computational infrastructure to sup- port the development, analysis and comparison of new approaches. To this end, we present the vision and progress of the Metaheuristics “In the Large”project. The conceptual underpinnings of the project are: truly extensible algorithm templates that support reuse without modification, white box problem descriptions that provide generic support for the injection of domain specific knowledge, and remotely accessible frameworks, components and problems that will enhance reproducibility and accelerate the field’s progress. We argue that, via such principled choice of infrastructure support, the field can pur- sue a higher level of scientific enquiry. We describe our vision and report on progress, showing how the adoption of common protocols for all metaheuristics can help liberate the potential of the field, easing the exploration of the design space of metaheuristics.UK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) EP/J017515/1EU H2020 SAFIRE Factories projectSpanish Ministry of Economy and Competitiveness TIN201785727-C4-2-PAustralian Research Council DE160100850 DP20010236