Algorithms for solving large random graphs

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Belief propagation on dense graphs with few strong links

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Classifying clinical decision making:interpreting nursing intuition, heuristics and medical diagnosis

This is the second of two linked papers exploring decision making in nursing. The first paper, 'Classifying clinical decision making: a unifying approach' investigated difficulties with applying a range of decision-making theories to nursing practice. This is due to the diversity of terminology and theoretical concepts used, which militate against nurses being able to compare the outcomes of decisions analysed within different frameworks. It is therefore problematic for nurses to assess how good their decisions are, and where improvements can be made. However, despite the range of nomenclature, it was argued that there are underlying similarities between all theories of decision processes and that these should be exposed through integration within a single explanatory framework. A proposed solution was to use a general model of psychological classification to clarify and compare terms, concepts and processes identified across the different theories. The unifying framework of classification was described and this paper operationalizes it to demonstrate how different approaches to clinical decision making can be re-interpreted as classification behaviour. Particular attention is focused on classification in nursing, and on re-evaluating heuristic reasoning, which has been particularly prone to theoretical and terminological confusion. Demonstrating similarities in how different disciplines make decisions should promote improved multidisciplinary collaboration and a weakening of clinical elitism, thereby enhancing organizational effectiveness in health care and nurses' professional status. This is particularly important as nurses' roles continue to expand to embrace elements of managerial, medical and therapeutic work. Analysing nurses' decisions as classification behaviour will also enhance clinical effectiveness, and assist in making nurses' expertise more visible. In addition, the classification framework explodes the myth that intuition, traditionally associated with nurses' decision making, is less rational and scientific than other approaches.

Interpreting "D.I.Y." documents:severance, release, trusts, certainty, vesting and undue influence

Comments on the Chancery Division decision in Wallbank v Price on whether a home-made ("DIY") document signed by a wife and purporting to revoke her rights as a beneficial joint tenant in the matrimonial home, which was acquired under the right-to-buy scheme, should be set aside for duress or undue influence. Details the court's analysis of the principles supporting a successful claim of undue influence, the nature of the DIY document, its meaning and its effect. Considers possible reasons for the parties' use of the document. Cases Wallbank v Price (2007) EWHC 3001 (Ch); (2008) 2 FLR 501 (Ch D (Birmingham)) : Royal Bank of Scotland Plc v Etridge (No.2) (2001) UKHL 44; (2002) 2 AC 773 (HL) : Paul v Constance (1977) 1 WLR 527 (CA (Civ Div)) Statutes Housing Act 1985

Message-passing for inference and optimization of real variables on sparse graphs

The inference and optimization in sparse graphs with real variables is studied using methods of statistical mechanics. Efficient distributed algorithms for the resource allocation problem are devised. Numerical simulations show excellent performance and full agreement with the theoretical results. © Springer-Verlag Berlin Heidelberg 2006.

On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

Learning Technology in Scheduling Based on the Mixed Graphs

We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

The topics they are a-changing - characterising topics with time-stamped semantic graphs

DBpedia has become one of the major sources of structured knowledge extracted from Wikipedia. Such structures gradually re-shape the representation of Topics as new events relevant to such topics emerge. Such changes make evident the continuous evolution of topic representations and introduce new challenges to supervised topic classification tasks, since labelled data can rapidly become outdated. Here we analyse topic changes in DBpedia and propose the use of semantic features as a more stable representation of a topic. Our experiments show promising results in understanding how the relevance of features to a topic changes over time.

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analyzed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Stretching the life of Twitter classifiers with time-stamped semantic graphs

Social media has become an effective channel for communicating both trends and public opinion on current events. However the automatic topic classification of social media content pose various challenges. Topic classification is a common technique used for automatically capturing themes that emerge from social media streams. However, such techniques are sensitive to the evolution of topics when new event-dependent vocabularies start to emerge (e.g., Crimea becoming relevant to War Conflict during the Ukraine crisis in 2014). Therefore, traditional supervised classification methods which rely on labelled data could rapidly become outdated. In this paper we propose a novel transfer learning approach to address the classification task of new data when the only available labelled data belong to a previous epoch. This approach relies on the incorporation of knowledge from DBpedia graphs. Our findings show promising results in understanding how features age, and how semantic features can support the evolution of topic classifiers.

Sequences of Maximal Degree Vertices in Graphs

2000 Mathematics Subject Classification: 05C35.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

An Inequality for Generalized Chromatic Graphs

Асен Божилов, Недялко Ненов - Нека G е n-върхов граф и редицата от степените на върховете му е d1, d2, . . . , dn, а V(G) е множеството от върховете на G. Степента на върха v бележим с d(v). Най-малкото естествено число r, за което V(G) има r-разлагане V(G) = V1 ∪ V2 ∪ · · · ∪ Vr, Vi ∩ Vj = ∅, , i 6 = j такова, че d(v) ≤ n − |Vi|, ∀v ∈ Vi, i = 1, 2, . . . , r е означено с ϕ(G). В тази работа доказваме неравенството ...

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.