On the Usability of Probably Approximately Correct Implication Bases

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph

Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

Discovering Implicational Knowledge in Wikidata

Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge. Besides providing a method for obtaining large real-world data sets for FCA, we sketch potential applications in offering semantic assistance for editing and curating Wikidata

Space Efficient Breadth-First and Level Traversals of Consistent Global States of Parallel Programs

Enumerating consistent global states of a computation is a fundamental problem in parallel computing with applications to debug- ging, testing and runtime verification of parallel programs. Breadth-first search (BFS) enumeration is especially useful for these applications as it finds an erroneous consistent global state with the least number of events possible. The total number of executed events in a global state is called its rank. BFS also allows enumeration of all global states of a given rank or within a range of ranks. If a computation on n processes has m events per process on average, then the traditional BFS (Cooper-Marzullo and its variants) requires $\mathcal{O}(\frac{m^{n-1}}{n})$ space in the worst case, whereas ou r algorithm performs the BFS requires $\mathcal{O}(m^2n^2)$ space. Thus, we reduce the space complexity for BFS enumeration of consistent global states exponentially. and give the first polynomial space algorithm for this task. In our experimental evaluation of seven benchmarks, traditional BFS fails in many cases by exhausting the 2 GB heap space allowed to the JVM. In contrast, our implementation uses less than 60 MB memory and is also faster in many cases

Formal concept analysis and structures underlying quantum logics

A Hilbert space $H$ induces a formal context, the Hilbert formal context $\overline H$, whose associated concept lattice is isomorphic to the lattice of closed subspaces of $H$. This set of closed subspaces, denoted $\mathcal C(H)$, is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of $\text{ChuCors}_{\mathcal H}$ of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Requirement-centric Approach to Web Service Modeling, Discovery, and Selection

Service-Oriented Computing (SOC) has gained considerable popularity for implementing Service-Based Applications (SBAs) in a flexible\ud and effective manner. The basic idea of SOC is to understand users'\ud requirements for SBAs first, and then discover and select relevant\ud services (i.e., that fit closely functional requirements) and offer\ud a high Quality of Service (QoS). Understanding users’ requirements\ud is already achieved by existing requirement engineering approaches\ud (e.g., TROPOS, KAOS, and MAP) which model SBAs in a requirement-driven\ud manner. However, discovering and selecting relevant and high QoS\ud services are still challenging tasks that require time and effort\ud due to the increasing number of available Web services. In this paper,\ud we propose a requirement-centric approach which allows: (i) modeling\ud users’ requirements for SBAs with the MAP formalism and specifying\ud required services using an Intentional Service Model (ISM); (ii)\ud discovering services by querying the Web service search engine Service-Finder\ud and using keywords extracted from the specifications provided by\ud the ISM; and(iii) selecting automatically relevant and high QoS services\ud by applying Formal Concept Analysis (FCA). We validate our approach\ud by performing experiments on an e-books application. The experimental\ud results show that our approach allows the selection of relevant and\ud high QoS services with a high accuracy (the average precision is\ud 89.41%) and efficiency (the average recall is 95.43%)

Pre-operative gastric ultrasound in patients at risk of pulmonary aspiration: a prospective observational cohort study.

Point-of-care gastric sonography offers an objective approach to assessing individual pulmonary aspiration risk before induction of general anaesthesia. We aimed to evaluate the potential impact of routine pre-operative gastric ultrasound on peri-operative management in a cohort of adult patients undergoing elective or emergency surgery at a single centre. According to pre-operative gastric ultrasound results, patients were classified as low risk (empty, gastric fluid volume ≤ 1.5 ml.kg-1 body weight) or high risk (solid, mixed or gastric fluid volume > 1.5 ml.kg-1 body weight) of aspiration. After sonography, examiners were asked to indicate changes in aspiration risk management (none; more conservative; more liberal) to their pre-defined anaesthetic plan and to adapt it if patient safety was at risk. We included 2003 patients, 1246 (62%) of which underwent elective and 757 (38%) emergency surgery. Among patients who underwent elective surgery, 1046/1246 (84%) had a low-risk and 178/1246 (14%) a high-risk stomach, with this being 587/757 (78%) vs. 158/757 (21%) among patients undergoing emergency surgery, respectively. Routine pre-operative gastric sonography enabled changes in anaesthetic management in 379/2003 (19%) of patients, with these being a more liberal approach in 303/2003 (15%). In patients undergoing elective surgery, pre-operative gastric sonography would have allowed a more liberal approach in 170/1246 (14%) and made a more conservative approach indicated in 52/1246 (4%), whereas in patients undergoing emergency surgery, 133/757 (18%) would have been managed more liberally and 24/757 (3%) more conservatively. We showed that pre-operative gastric ultrasound helps to identify high- and low-risk situations in patients at risk of aspiration and adds useful information to peri-operative management. Our data suggest that routine use of pre-operative gastric ultrasound may improve individualised care and potentially impact patient safety

Case report: Urolithiasis, nephrolithiasis and a urinary bladder malformation in a seven-month-old alpaca cria

Urolithiasis is a common condition in male small ruminants where predisposing factors have been identified. Occasionally, urolithiasis is diagnosed in South American camelids (SACs). However, nephrolithiasis is rarely diagnosed in ruminants. To our knowledge, this is the first report focusing on a combined appearance of nephrolithiasis and urolithiasis in an alpaca cria. A 7-month-old alpaca cria suffering from impaired urinary flow was presented for examination. On admission, the alpaca had a wet prepuce and showed a standing posture with a wide-based stance. Ultrasonographic examination of the abdomen showed a distended bladder. Clinical chemistry revealed azotemia and hypophosphatemia. After the first examination, repeated urination was observed. Conservative therapy using antibiotics, anti-inflammatory and spasmolytic drugs was started with the suspected diagnosis of urinary calculus. During the first 24 h, plasma concentrations of creatinine and urea decreased, but increased again during the following days. During the second day after admission, urination was not observed for 16 h while the concentration of urea and creatinine further increased. Therefore, the animal was euthanized due to financial concerns of the owner. Necropsy revealed that calculi were located in the left kidney as well as in the urethra. In addition, the animal exhibited uroperitoneum. The urinary bladder was intact, moderately distended with urine and showed a malformation, which was covered with a translucent mucosal membrane. Histologic examination revealed that this malformation was a bladder diverticulum. The extent to which the unilateral nephroliths affected the general condition and renal function of the animal is unclear, since the uroliths also cause azotemia, and abdominal pain. Further studies are needed for a better understanding of obstructive urinary disease in SACs

Query-Based Multicontexts for Knowledge Base Browsing: An Evaluation

In [7], we introduced the query-based multicontext theory, which allows to define a virtual space of views on ontological data. Each view is then materialised as a formal context. While this formal context can be visualised in a usual formal concept analysis framework such as Conexp or ToscanaJ, [7] also briefly described how the approach allowed the creation of a novel navigation framework for knowledge bases. The principle of this navigation is based on supporting the user in defining pertinent views. The purpose of this article is to discuss the benefits of the browsing interface. This discussion is performed, on the one hand, by comparing the approach to other Formal Concept Analysis based frameworks. On the other hand, it exposes the preliminary evaluation of the visualisation of formal contexts by comparing the display of a lattice to two other approaches based on trees and graphs

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Comment: 29 page