Programs as Transformations of Algebraic Theories (Extended Abstract)

Term algebras have been widely used in the theory of abstract data types. Here, the concept of canonical term algebra is generalized to the notion of canonical term functor, which is useful for various aspects of abstract data type specifications. In particular, we show how canonical term functors provide a constraint mechanism in loose specifications and how they constitute a junction between axiomatic and constructive approaches. These concepts are the semantic base for the specification development language ASPIK which has been implemented as a core component of an integrated software development and verification system.

Data interoperability is an ongoing challenge for global open data initiatives. The machine-readable specification of data types for datasets will help address interoperability issues. Data types have typically been at the syntactical level such as integer, float and string, etc. in programming languages. The work presented in this paper is a model design for the semantic specification of data types, such as a topographic map. The work was conducted in the context of the Semantic Web. The model differentiates the semantic data type from the basic data type. The former are instances (e.g., topographic map) of a specific data type class that is defined in the developed model. The latter are classes (e.g., Image) of resource types in existing ontologies. A data resource is an instance of a basic data type and is tagged with one or more specific data types. The implementation of the model is given within an existing production data portal that enables one to register specific data types and use them to annotate data resources. Data users can obtain explicating assumptions or information inherent in a dataset through the specific data types of that dataset. The machine-readable information of specific data types also paves the way for further studies, such as dataset recommendation.

G. Gr¨atzer’s gives the following example in his monograph «Universal algebra». Let A be a universal algebra (with some family of operations Σ). Let us take an arbitrary set B ⊆ A. For all of the operations f ∈ Σ (let n be the arity of f) let us look how f transformas the elements of Bn. It is not necessary that f(B) ⊆ B, so in the general case B is not a subalgebra of A. But if we define partial operation as mapping from a subset of the set Bn into the set B. then B be a set with a family of partial operations defined on it. Such sets are called partial universal algebras. In our example B will be a partial universal subalgebra of the algebra A, which means the set B will be closed under all of the partial operations of the partial algebra B. So, partial algebras can naturally appear when studying common universal algebras. The concept of congruence of universal algebra can be generalized to the case of partial algebras. It is well-known that the congruences of a partial universal algebra A always from a lattice, and if A be a full algebra (i.e. an algebra) then the lattice of the congruences of A is a sublattice of the lattice of the equivalence relations on A. The congruence lattice of a partial universal algebra is its important characteristics. For the most important cases of universal algebra some results were obtained which characterize the algebras A without any congruences except the trivial congruences (the equality relation on A and the relation A2). It turned out that in the most cases, when the congruence lattice of a universal algebra is trivial the algebra itself is definitely not trivial. And what can we say about the algebras A whose equivalence relation is, vice versa, contains all of the equivalence relations on A? It turns out, in this case any operation f of the algebra A is either a constant (|f(A)| = 1) or a projection (f(x1, ..., xi, ..., xn) ≡ xi). Kozhukhov I. B. described the semigroups whose equivalence relations are one-sided congruences. It is interesting now to generalize these results to the case of partial algebras. In this paper the partial n-ary groupoids G are studied whose operations f satisfy the following condition: for any elements x1, ..., xk−1, xk+1, ..., xn ∈ G the value of the expression f(x1, ..., xk−1, y, xk+1, ..., xn) is defined for not less that three different elements y ∈ G. It will be proved that if any of the congruence relations on G is a congruence of the partial n-ary groupoid (G, f) then under specific conditions for G the partial operation f is not a constant.

From software architecture perspective, the software architecture is described by layer. We propose a model which is used abstract data type to formal describe elements of each layer of software architecture. Using the model mainly describes the relationship among elements of the software architecture. Based on the abstract data type theory, we can make operation on the model and we divide software architecture into four layers, which make the deep analyse and construction for the architecture easier. We also design a software architecture description language SADL which can be transformed into Java framework finally. SADL combines UML graphics and supports layer-description and refinement. All above work set up the basic of research for the software architecture.

Three versions of the lambda calculus are discussed: typed lambda calculus, untyped lambda calculus, and polymorphically typed lambda calculus. It is shown that the syntax for these calculi can be described as initial algebras for suitable endofunctors. Models of the first two calculi are described as in [Lambek and Scott 1985] and the Per model of the third is recalled. Algebraic types are described in terms of sketches. A main contribution of the paper is the internalization of the theory of sketches in the category Per. Sketches themselves, models of sketches, categories of models of sketches and the category of all models of all sketches can all be realized in this setting. Next, dinatural transformations are reviewed in the context of the category Per and the relation between certain end formulas and initial algebras for finite signatures is discussed. The point of the theory of algebraic semantics in Per is to provide a setting for thinking about algebraic types and algebraic operations in conjunction with logical types and polymorphic operations. Two specific examples are discussed and a general principle for combining algebraic and polymorphic operations is proposed.KeywordsNatural TransformationCategory TheoryLogical TypeDenotational SemanticGraph ObjectThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Data mining and knowledge discovery aim at finding useful information from typically massive collections of data, and then extracting useful knowledge from the information. To date a large number of approaches have been proposed to find useful information and discover useful knowledge; for example, decision trees, Bayesian belief networks, evidence theory, rough set theory, fuzzy set theory, kNN (k-nearest-neighborhood) classifier, neural networks, and support vector machines. However, these approaches are based on a specific data type. In the real world, an intelligent system often encounters mixed data types, incomplete information (missing values), and imprecise information (fuzzy conditions). In the UCI (University of California – Irvine) Machine Learning Repository, it can be seen that there are many real world data sets with missing values and mixed data types. It is a challenge to enable machine learning or data mining approaches to deal with mixed data types (Ching, 1995; Coppock, 2003) because there are difficulties in finding a measure of similarity between objects with mixed data type attributes. The problem with mixed data types is a long-standing issue faced in data mining. The emerging techniques targeted at this issue can be classified into three classes as follows: (1) Symbolic data mining approaches plus different discretizers (e.g., Dougherty et al., 1995; Wu, 1996; Kurgan et al., 2004; Diday, 2004; Darmont et al., 2006; Wu et al., 2007) for transformation from continuous data to symbolic data; (2) Numerical data mining approaches plus transformation from symbolic data to numerical data (e.g.,, Kasabov, 2003; Darmont et al., 2006; Hadzic et al., 2007); (3) Hybrid of symbolic data mining approaches and numerical data mining approaches (e.g.,, Tung, 2002; Kasabov, 2003; Leng et al., 2005; Wu et al., 2006). Since hybrid approaches have the potential to exploit the advantages from both symbolic data mining and numerical data mining approaches, this chapter, after discassing the merits and shortcomings of current approaches, focuses on applying Self-Organizing Computing Network Model to construct a hybrid system to solve the problems of knowledge discovery from databases with a diversity of data types. Future trends for data mining on mixed type data are then discussed. Finally a conclusion is presented.

Algorithmic specifications of abstract data types have been introduced in [Lo 81a]. While being strongly related to the algebraic specification method used by e. g. [GH 78a, GHM 78b, Mu 80] the algorithmic specification method avoids several of its problems; it provides for instance an elegant way for handling undefined and error values; moreover it is felt to be easier to use for the specification of non-trivial data types.

The development of correct specifications is a critical task in the software development process. An alternative approach for the development of specifications is described. The approach relies on a specification language for abstract data types and synthesis system. The system is capable of translating in abstract data type specification into an executable program. This process defines an alternative methodology that provides the necessary tools for the early testing of the specifications and for the development of prototypes and implementation models.

Despite of the observed Cloud Services' (CS) heterogeneity, e.g., different APIs (Application Programming Interface), different accounting and charging models, and different security and privacy levels, one common aspect is that CSs provide a large amount of storage. CSs provide generic storage when it accepts to store data in any data type (e.g., Dropbox, Amazon S3). CSs provides data-specific storage when it accepts to store data only represented in specific data types (e.g., Google Picasa, SoundCloud). Therefore, PiCsMu (Platform-independent Cloud Storage System for Multiple-Usage) was developed to (1) aggregate multiple CSs' storage despite of the accepted data type, (2) provide enhanced privacy, and (3) enable a Peer-to-Peer (P2P) file sharing network relying on CSs' storage instead of peers' storage. The demonstrator use case shows how a PiCsMu user can upload, download, and share files with other PiCsMu users, especially highlighting: (a) the hybrid approach used by the PiCsMu system, showing that data is stored in CSs and the P2P network acts as a management overlay; (b) the PiCsMu social capabilities, showing that PiCsMu users are able to find and share content to existing Online Social Network friends; and (c) the fragmentation and data encoding, showing that both processes enable higher privacy levels since data is stored in multiple different CSs and is imperceptible to CSs' data validation.

A technique for defining graphical depictions for all the data types defined in an algorithm is presented. The ability to display arbitrary combinations of an algorithm's data objects in a common frame of reference, coupled with interactive control of algorithm execution, provides a powerful way to understand algorithm behavior. Type definitions are constrained so that all primitive values occurring in data objects are assigned scalar types. A graphical display, including user interaction with the display, is modeled by a special data type. Mappings from the scalar types into the display model type provide a simple user interface for controlling how all data types are depicted, without the need for type-specific graphics logic.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Induction of descriptive models is one of the most important technologies in data mining. The expressiveness of descriptive models are of paramount importance in applications that examine the causality of relationships between variables. Most of the work on descriptive models has concentrated on less expressive approaches such as clustering algorithms or rule-based approaches that are limited to a particular type of data, such as association rule mining for binary data. However, in many applications its important to understand the structure of the produced model for further human evaluation. In this research we present a novel generalised rule induction method that allows the induction of descriptive and expressive rules directly from both categorical and numerical features.

FAIR (findability, accessibility, interoperability, and reusability) guiding principles seek the reuse of data and other digital research input, output, and objects (algorithms, tools, and workflows that led to that data) making them findable, accessible, interoperable, and reusable. GO FAIR - a bottom-up, stakeholder driven and self-governed initiative - defined a seven-step FAIRification process focusing on data, but also indicating the required work for metadata. This FAIRification process aims at addressing the translation of raw datasets into FAIR datasets in a general way, without considering specific requirements and challenges that may arise when dealing with some particular types of data. This scientific contribution addresses the architecture design of an open technological solution built upon the FAIRification process proposed by "GO FAIR" which addresses the identified gaps that such process has when dealing with health datasets. A common FAIRification workflow was developed by applying restrictions on existing steps and introducing new steps for specific requirements of health data. These requirements have been elicited after analyzing the FAIRification workflow from different perspectives: technical barriers, ethical implications, and legal framework. This analysis identified gaps when applying the FAIRification process proposed by GO FAIR to health research data management in terms of data curation, validation, deidentification, versioning, and indexing. A technological architecture based on the use of Health Level Seven International (HL7) FHIR (fast health care interoperability resources) resources is proposed to support the revised FAIRification workflow. Research funding agencies all over the world increasingly demand the application of the FAIR guiding principles to health research output. Existing tools do not fully address the identified needs for health data management. Therefore, researchers may benefit in the coming years from a common framework that supports the proposed FAIRification workflow applied to health datasets. Routine health care datasets or data resulting from health research can be FAIRified, shared and reused within the health research community following the proposed FAIRification workflow and implementing technical architecture.

Parallel graph-based anomaly detection technique for sequential data

We describe and empirically evaluate machine learning methods for the prediction of zinc binding sites from protein sequences. We start by observing that a data set consisting of single residues as examples is affected by autocorrelation and we propose an ad-hoc remedy in which sequentially close pairs of candidate residues are classified as being jointly involved in the coordination of a zinc ion. We develop a kernel for this particular type of data that can handle variable length gaps between candidate coordinating residues. Our empirical evaluation on a data set of non redundant protein chains shows that explicit modeling the correlation between residues close in sequence allows us to gain a significant improvement in the prediction performance.KeywordsSupport Vector MachineProtein Data BankSite TypeBonding StateMetal Binding SiteThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Artificial neural networks can learn to estimate extinction rates from molecular phylogenies