Representation theorems obtained by mining across web sources for hints

Funding: JKFB partially supported by the Austrian Science Fund under FWF Meitner project M-3338.A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially behave in the same way, representation theorems typically provide insight and generate powerful techniques to study the involved structures, by cross-fertilising between the methodologies existing for each of the respective branches of mathematics. When the related structures have no obvious a priori connection, however, such results can be, by their own nature, elusive. Here, we show how data-mining across distinct web sources (including the Online Encyclopedia of Integer Sequences, OEIS), was crucial in the discovery of two original representation theorems relating event structures (mathematical structures commonly used to represent concurrent discrete systems) to families of sets (endowed with elementary disjointness and subset relations) and to full graphs, respectively. The latter originally emerged in the apparently unrelated field of bioinformatics. As expected, our representation theorems are powerful, allowing to capitalise on existing theorems about full graphs to immediately conclude new facts about event structures. Our contribution is twofold: on one hand, we illustrate our novel method to mine the web, resulting in thousands of candidate connections between distinct mathematical realms; on the other hand, we explore one of these connections to obtain our new representation theorems. We hope this paper can encourage people with relevant expertise to scrutinize these candidate connections. We anticipate that, building on the ideas presented here, further connections can be unearthed, by refining the mining techniques and by extending the mined repositories.Postprin

Computer aided verification of radiotherapy treatment plans

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Tackling polypharmacy : a multi-source decision support system

Managing the use of multiple medicines, also known as polypharmacy, is a challenge for physicians, pharmacists and patients alike, and is a particular concern for patients with multiple chronic conditions (aka multimorbidity). Patients with multimorbidity are often required to take a considerable number of medications for their different ongoing conditions, and managing/revising these medications effectively is a challenge. There is a need to periodically rearrange drugs taking into account patient’s preferences and avoiding adverse drug reactions. We present an incremental, constraint solver based framework for a clinical decision support system that makes it possible to check drug prescriptions using information from multiple sources, including a constraint database and patient records. We illustrate how it can be used to manage clinical conditions while reducing polypharmacy problems and undesired side effects in a patient-centric approach.Publisher PD

A flexible approach for finding optimal paths with minimal conflicts

This research is supported by EPSRC grant EP/M014290/1.Complex systems are usually modelled through a combination of structural and behavioural models, where separate behavioural models make it easier to design and understand partial behaviour. When partial models are combined, we need to guarantee that they are consistent, and several automated techniques have been developed to check this. We argue that in some cases it is impossible to guarantee total consistency, and instead we want to find execution paths across such models with minimal conflicts with respect to a certain metric of interest. We present an efficient and scalable solution to find optimal paths through a combination of the theorem prover Isabelle with the constraint solver Z3. Our approach has been inspired by a healthcare problem, namely how to detect conflicts between medications taken by patients with multiple chronic conditions, and how to find preferable alternatives automatically.Postprin

Mind the gap : addressing behavioural inconsistencies with formal methods

In complex system design, it is important to construct several design models focusing on different aspects of a system to gain a better understanding of individual component structure and behaviour. Scenarios of execution are commonly used to specify partial behaviour and interactions between a group of system objects or components. However, partial specifications may hide inconsistencies or an otherwise unintentionally incomplete or underspecified behavioural model. This paper proposes a new powerful technique combining constraint solvers and theorem provers to complete partial specifications and determine overall model inconsistencies. We use a true-concurrent model, namely labelled event structures, which can be used as the underlying semantics of widely used work flow or scenario-based languages. We show how an interplay between the theorem prover Isabelle and constraint solver Z3 can be used for detecting and solving partial specifications and inconsistencies over event structures.Postprin

Weaving true-concurrent aspects using constraint solvers

Large system models usually consist of several simpler models that can be understood more easily. Making changes to the behaviour of a component will likely affect several models and could introduce accidental errors. Aspects address this by modelling new functionality required in several places as an advice, which can be integrated with the original base models by specifying a pointcut. Before checking that the overall outcome is correct, we need to weave the cross-cutting advice into the base models, and obtain new augmented models. Although considerable research has been done to weave models, many such approaches are not fully automated. This paper looks at aspect weaving of scenario-based models, where aspects are given a true-concurrent semantics based on event structures. Our contribution is a novel formal automated technique for weaving aspects using the Z3-SMT solver. We compare the performance of Alloy and Z3 to justify our choice.Postprin

A novel EGs-based framework for systematic propositional-formula simplification

Funding: Bowles is partially supported by Austrian FWF Meitner Fellowship M-3338 N.This paper presents a novel simplification calculus for propositional logic derived from Peirce’s Existential Graphs’ rules of inference and implication graphs. Our rules can be applied to arbitrary propositional logic formulae (not only in CNF), are equivalence-preserving, guarantee a monotonically decreasing number of clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. We further show how this rule can be extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures. Finally, we discuss the complexity and implementation of our framework as a solver-agnostic algorithm to simplify Boolean satisfiability problems and arbitrary propositional formula.Postprin

Graph-based risk assessment and error detection in radiation therapy

Purpose : The objective of this study was to formalize and automate quality assurance (QA) in radiation oncology. QA in radiation oncology entails a multistep verification of complex, personalized radiation plans to treat cancer involving an interdisciplinary team and high technology, multivendor software and hardware. We addressed the pretreatment physics chart review (TPCR) using methods from graph theory and constraint programming to study the effect of dependencies between variables and automatically identify logical inconsistencies and how they propagate. Materials and Methods : We used a modular approach to decompose the TPCR process into tractable units comprising subprocesses, modules and variables. Modules represent the main software entities comprised in the radiation treatment planning workflow and subprocesses group the checks to be performed by functionality. Module‐associated variables serve as inputs to the subprocesses. Relationships between variables were modeled by means of a directed graph. The detection of errors, in the form of inconsistencies, was formalized as a constraint satisfaction problem whereby checks were encoded as logical formulae. The sequence in which subprocesses are visited was described in a activity diagram. Results : The comprehensive model for the TPCR process comprised 5 modules, 19 subprocesses and 346 variables, 225 of which were distinct. Modules included ”Treatment Planning System” and ”Record and Verify System”. Subprocesses included ”Dose Prescription”, ”Documents”, ”CT Integrity”, ”Anatomical Contours”, ”Beam Configuration”, ”Dose Calculation”, ”3D Dose Distribution Quality” and ”Treatment Approval”. Variable inconsistencies, their source and propagation are determined by checking for constraint violation and through graph traversal. Impact scores, obtained through graph traversal, combined with severity scores associated with an inconsistency, allow risk assessment. Conclusions : Directed graphs combined with constraint programming hold promise for formalizing complex QA processes in radiation oncology, performing risk assessment and automating the TPCR process. Though complex, the process is tractable.PostprintPeer reviewe

An integrated framework for verifying multiple care pathways

Common chronic conditions are routinely treated following standardised procedures known as clinical pathways. For patients suffering from two or more chronic conditions, referred to as multimorbidities, several pathways have to be applied simultaneously. However, since pathways rarely consider the presence of comorbidities, applying several pathways may lead to potentially harmful (medication) conflicts. This paper proposes an automated framework to detect, highlight and resolve conflicts in the treatments used for patients with multimorbidites. We use BPMN as a modelling language for capturing care guidelines. A BPMN model is transformed into an intermediate formal model capturing the possible unfoldings of the pathway. Through a combination of the constraint solver Z3 and the theorem prover Isabelle, we check the correctness of combined treatment plans. We illustrate the approach with an example from the medical domain and discuss future work.Postprin

Epistolary poetry by Dominican Toma Marinković Tomić (1710-1779)

U članku se na temelju literature, objavljenih izvora i arhivske građe prikazuje život i rad hrvatskog pjesnika, dominikanca Tome Marinkovića Tomića (1710-1779), koji je praktički nepoznat u povijesti hrvatske književnosti. Autor članka govori o njegovoj poslanici u safičkim strofama na hrvatskome jeziku, opisujući povod njezina nastanka, formu i opseg te iznoseći njezin kratki sadržaj. Naglašava se da je poslanica posebno zanimljiva zbog jezika i terminologije. Potom se prvi put objavljuje prijepis te poslanice, pri čemu se u bilješkama iznosi nekoliko nužnih razjašnjenja, vezanih uz terminologiju redovničkoga života. Poziva se povjesničare književnosti da posvete više pozornosti poslanici o. Tome Marinkovića Tomića, što je bilo nemoguće prije njezina objavljivanja, kako bi na taj način dobila pravo mjesto u povijesti hrvatske književnosti.Based on references, published sources and archival materials, the paper attempts to show the life and work of a Croatian poet, Dominican Toma Marinković Tomić (1710-1779), who is virtually unknown in the history of Croatian literature. The author of the paper is discussing his epistle in Sapphic stanzas in Croatian language, describing the cause of its emergence, its form and size, also briefly giving its plot outline. It is pointed out that the epistle is particularly interesting because of its language and terminology. The transcription of the epistle is also published for the first time, providing in the notes several necessary explanations regarding the terminology from priestly life. Literary historians are invited to pay more attention to the epistle written by father Toma Marinković Tomić, so that in that way it would receive a proper place in the history of Croatian literature, which was impossible before its publication