Variational approximations for stochastic dynamics on graphs

We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view of various (previously known) approximation schemes, and suggests quite a systematic way to improve the level of accuracy. We compare the different approximations with Monte Carlo simulations on a reversible (susceptible-infected-susceptible) discrete-time epidemic-spreading model on random graphs.Comment: 29 pages, 5 figures. Minor revisions. IOP-style

Noncommutative Geometry

Many of the different aspects of Noncommutative Geometry were represented in the talks. The list of topics that were covered includes in particular new insight into the geometry of a noncommutative torus, local index formulae in various situations, C*-algebras and dynamical systems associated with number theoretic structures, new methods in K-theory for noncommutative algebras as well as new progress in quantum field theory using concepts from noncommutative geometry

A Formal Concept Analysis approach to hierarchical description of malware threats

The problem of intelligent malware detection has become increasingly relevant in the industry, as there has been an explosion in the diversity of threats and attacks that affect not only small users, but also large organisations and governments. One of the problems in this field is the lack of homogenisation or standardisation in the nomenclature used by different antivirus programs for different malware threats. The lack of a clear definition of what a category is and how it relates to individual threats makes it difficult to share data and extract common information from multiple antivirus programs. Therefore, efforts to create a common naming convention and hierarchy for malware are important to improve collaboration and information sharing in this field. Our approach uses as a tool the methods of Formal Concept Analysis (FCA) to model and attempt to solve this problem. FCA is an algebraic framework able to discover useful knowledge in the form of a concept lattice and implications relating to the detection and diagnosis of suspicious files and threats. The knowledge extracted using this mathematical tool illustrates how formal methods can help prevent new threats and attacks. We will show the results of applying the proposed methodology to the identification of hierarchical relationships between malware.This work has been partially funded by the predoctoral contract FPU19/01467 (MCIU), the “VALID” project with reference PID2022- 140630NB-I00 (MCIN/ AEI/ 10.13039/ 501100011033) and the re- search project with reference PID2021-127870OB-I00 (MCIU/AEI/ ERDF, EU). Funding por open access charge: Universidad de Málaga / CBU

Structural Holes in Directed Fuzzy Social Networks

The structural holes have been a key issue in fuzzy social network analysis. For undirected fuzzy social networks where edges are just present or absent undirected fuzzy relation and have no more information attached, many structural holes measures have been presented, such as key fuzzy structural holes, general fuzzy structural holes, strong fuzzy structural holes, and weak fuzzy structural holes. There has been a growing need to design structural holes measures for directed fuzzy social networks, because directed fuzzy social networks where edges are attached by directed fuzzy relation would contain rich information. In this paper, we extend structural holes theory to directed fuzzy social network and propose the algorithm of unidirectional fuzzy structural holes and bidirectional fuzzy structural holes, which unveil more structural information of directed fuzzy social networks. Furthermore, we investigate the validness of the algorithm by illustrating this method to a case called G-Y Research Team and obtain reliable results, which provide strong evidences of the new measure’s utility

Concepts and analogies in cybernetics: Mathematical investigations of the role of analogy in concept formation and problem solving; with emphasis for conflict resolution via object and morphism eliminations

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We address two problematic areas of cybernetics; nam. Analogical Problem Solving (APS) and Analogical Learning (AL). Both these human faculties do unquestionably require Intelligence. In addition, we point out that shifting of representations is the main unified theme underlying these two intellectual tasks. We focus our attention on the formulation and clarification of the notion of analogy, which has been loosely treated and used in the literature; and also on its role in shifting of representations. We describe analogizing situations in a new representational scheme, borrowed from mathematics and modified and extended to cater for our targets. We call it k-structure, closely resembling semantic networks and directed graphs; the main components of it are the so-called objects and morphisms. We argue and substantiate the need for such a representation scheme, by analysing what its constituents stand for and by cataloguing its virtues, the main one being its visual appeal and its mathematical clarity, and by listing its disadvantages when it is compared to other representation systems. Emphasis is also given to its descriptive power and usefulness by implementing it in a number of APS and AL situations. Besides representation issues, attention is paid to intelligence mechanisms which are involved in APS and AL. A cornerstone in APS and a fundamental theme in AL is the 'skeletization of k-structures'. APS is conceived as 'harmonization of skeletons'. The methodology we develop involves techniques which are computer implemented and extensively studied in theoretic terms via a proposed theory for extended k-structures. To name but a few: 1. 'the separation of the context of a concept from the concept itself', based on the ideas of k-opens and k-spaces; 2, 'object and morphism elimination' of a controversial nature; and 3. 'conflict or deadlock or dilemma resolution' which naturally arises in a k-structure interaction. The overall system, is then applied to capture the essence of EVANS' (1963) analogy-type problems and WINSTOM (1970) learning-type situations. In our attempt not to be too informal, we use basic notions and terminology from abstract Algebra, Topology and Category theory. We rather tend to be "non-logical" (analogical) in EVANS' and WINSTON's sense; "non-numeric", in MESAROVIC (1970) terms (we rather deal with abstract conceptual entities); "non-linguistic" (we do not touch natural language); and "non-resolution" oriented, in the sense of BLEDSOE (1977). However, we give hints sometimes about logical deductive axiomatic systems, employing First Order Predicate Calculus (FOPC); and about semiotics, by which we denote syntactic-semantic-pragmatic features of our system and issues of the problem domains it is acting upon. We believe in what we call: shift from the traditional 'Heuristic search paradigm' era to the 'Analogy-paradigm' era underlying Artificial Intelligence and Cybernetics. We justify this merely by listing a number of A. I. works, which employ, in some way or another, the concept of analogy, over the last fifteen years or so, where a noticeable peak is obvious during the last years and especially in 1977. Finally, we hope that if the proposed conceptual framework and techniques developed do not straightforwardly constitute some kind of platform for Artificial Intelligence, at least it would give some insights into and illuminate our understanding of the two most fundamental faculties the human brain is occupied with; namely problem solving and learning

Conceptual graph-based knowledge representation for supporting reasoning in African traditional medicine

Although African patients use both conventional or modern and traditional healthcare simultaneously, it has been proven that 80% of people rely on African traditional medicine (ATM). ATM includes medical activities stemming from practices, customs and traditions which were integral to the distinctive African cultures. It is based mainly on the oral transfer of knowledge, with the risk of losing critical knowledge. Moreover, practices differ according to the regions and the availability of medicinal plants. Therefore, it is necessary to compile tacit, disseminated and complex knowledge from various Tradi-Practitioners (TP) in order to determine interesting patterns for treating a given disease. Knowledge engineering methods for traditional medicine are useful to model suitably complex information needs, formalize knowledge of domain experts and highlight the effective practices for their integration to conventional medicine. The work described in this paper presents an approach which addresses two issues. First it aims at proposing a formal representation model of ATM knowledge and practices to facilitate their sharing and reusing. Then, it aims at providing a visual reasoning mechanism for selecting best available procedures and medicinal plants to treat diseases. The approach is based on the use of the Delphi method for capturing knowledge from various experts which necessitate reaching a consensus. Conceptual graph formalism is used to model ATM knowledge with visual reasoning capabilities and processes. The nested conceptual graphs are used to visually express the semantic meaning of Computational Tree Logic (CTL) constructs that are useful for formal specification of temporal properties of ATM domain knowledge. Our approach presents the advantage of mitigating knowledge loss with conceptual development assistance to improve the quality of ATM care (medical diagnosis and therapeutics), but also patient safety (drug monitoring)

Learning dispositif and emotional attachment:a preliminary international investigation

This research investigated the significance of learning dispositif (LD) and emotional attachment (EA) on perceived learning success (LS) across a diaspora of Western, Russian, Asian, Middle Eastern and Chinese student cohorts. Foucault’s LD captures the disparate socio-cultural contexts, institutional milieus and more or less didactic teaching styles that moderate learning. EA is a multi-dimensional notion involving affective bonds that emerged in child psychology and spread to marketing and other fields. The sequential explanatory research reviewed the learning and EA literatures and generated an LD–EA framework to structure the quantitative phase of its mixed investigations. In 2017 and 2018, the research collected 150 responses and used a range of statistical techniques for quantitative analysis. It found that LS varied significantly across cohorts, intimating that dispositifs influence learning. Nonparametric analysis suggested that EA also influenced learning, but regressions were inconclusive. Exploratory techniques hint at a dynamic mix of emotional or cognitive motivations during the student learning journey, involving structural breaks in student/instructor relationships. Cluster analysis identified distinct student groupings, linked to years of learning. Separately, qualitative analysis of open-ended survey questions and expert interviews intimates that frequent teacher interactions can increase EA. The synthesis of quantitative with qualitative results and pedagogical reflection suggests that LD and EA both influence learning in a complex, dynamic system. The key constituents for EA are Affection, Connection, Social Presence (SP), Teaching Presence (TP) and Flow but student emotional engagement is conditioned by the socio-cultural milieu (LD) and associated factors like relationships and trust. Unlike in the Community of Learning framework, in the EA framework Cognitive Presence (CP) is an outcome of the interaction between these EA constituents, associated factors and the socio-cultural milieu. Finally, whilst awareness of culture and emotions is a useful pedagogical consideration, learning mainstays remain inclusive educational systems that identify student needs and support well-designed programmes. Within these, scaffolded modules should include a variety of engaging learning activities with non-threatening formative and trustworthy summative feedback. We acknowledge some statistical study limitations, but its tentative findings make a useful preliminary contribution