An Exercise in Invariant-based Programming with Interactive and Automatic Theorem Prover Support

Invariant-Based Programming (IBP) is a diagram-based correct-by-construction programming methodology in which the program is structured around the invariants, which are additionally formulated before the actual code. Socos is a program construction and verification environment built specifically to support IBP. The front-end to Socos is a graphical diagram editor, allowing the programmer to construct invariant-based programs and check their correctness. The back-end component of Socos, the program checker, computes the verification conditions of the program and tries to prove them automatically. It uses the theorem prover PVS and the SMT solver Yices to discharge as many of the verification conditions as possible without user interaction. In this paper, we first describe the Socos environment from a user and systems level perspective; we then exemplify the IBP workflow by building a verified implementation of heapsort in Socos. The case study highlights the role of both automatic and interactive theorem proving in three sequential stages of the IBP workflow: developing the background theory, formulating the program specification and invariants, and proving the correctness of the final implementation.Comment: In Proceedings THedu'11, arXiv:1202.453

Mutual Mobile Membranes with Timers

A feature of current membrane systems is the fact that objects and membranes are persistent. However, this is not true in the real world. In fact, cells and intracellular proteins have a well-defined lifetime. Inspired from these biological facts, we define a model of systems of mobile membranes in which each membrane and each object has a timer representing their lifetime. We show that systems of mutual mobile membranes with and without timers have the same computational power. An encoding of timed safe mobile ambients into systems of mutual mobile membranes with timers offers a relationship between two formalisms used in describing biological systems

Quantifying the implicit process flow abstraction in SBGN-PD diagrams with Bio-PEPA

For a long time biologists have used visual representations of biochemical networks to gain a quick overview of important structural properties. Recently SBGN, the Systems Biology Graphical Notation, has been developed to standardise the way in which such graphical maps are drawn in order to facilitate the exchange of information. Its qualitative Process Diagrams (SBGN-PD) are based on an implicit Process Flow Abstraction (PFA) that can also be used to construct quantitative representations, which can be used for automated analyses of the system. Here we explicitly describe the PFA that underpins SBGN-PD and define attributes for SBGN-PD glyphs that make it possible to capture the quantitative details of a biochemical reaction network. We implemented SBGNtext2BioPEPA, a tool that demonstrates how such quantitative details can be used to automatically generate working Bio-PEPA code from a textual representation of SBGN-PD that we developed. Bio-PEPA is a process algebra that was designed for implementing quantitative models of concurrent biochemical reaction systems. We use this approach to compute the expected delay between input and output using deterministic and stochastic simulations of the MAPK signal transduction cascade. The scheme developed here is general and can be easily adapted to other output formalisms

On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a "delay as duration" approach, namely they are based on an interpretation of a delay as the elapsing time between the start and the termination of a chemical reaction. This interpretation is not suitable for some classes of biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a ``purely delayed'' interpretation of delays which provides better results on the considered model

Surgical and oncological outcomes of D1 versus D2 gastrectomy among elderly patients treated for gastric cancer

Introduction: Gastrectomy with D2 lymphadenectomy is considered standard treatment in gastric cancer (GC). Among Western patients, morbidity and mortality seem to increase in D2 relative to D1 lymphadenectomy. As elderly patients with co-morbidities are more prone to possible complications, it is unclear whether they benefit from D2 lymphadenectomy. This study aims to compare the short- and long-term results of D1 and D2 lymphadenectomy in elderly patients undergoing gastrectomy for GC. Methods: All elderly (> 75 years) patients undergoing gastrectomy with curative intent for GC during 2000-2015 were included and grouped according to the level of lymph node dissection into the D1 or D2 group. Short-term surgical outcome included the Comprehensive Complication Index (CCI) and 30-day mortality. Long-term outcomes comprised overall survival (OS), disease-specific survival (DSS), and disease-free survival (DFS). Cox regression was used in multivariable analyses. Results: In total, 99 elderly patients were included in the study (51 in D1 group, 48 in D2 group). The median follow-up was 32.5 months. Patients in the D1 group were older and had a higher American Society of Anesthesiologist (ASA) score. Both groups had similar burden of postoperative complications (CCI 20.9 versus 22.6, p = 0.26, respectively) and 90-day mortality (2% for both groups). The OS, DSS, and DFS were similar between groups. Multivariable analysis adjusted for potential confounders detected no difference in the survival between the D1 and D2 groups. Conclusions: Gastrectomy with D2 lymphadenectomy can be performed with low postoperative morbidity and mortality suggesting its use also in the elderly. Long-term outcomes seem similar but need further studies.Peer reviewe

Fältskiktsväxter i gran- och tallbestånd i södra Småland

Det svenska landskapet och dess markanvändning har förändrats kraftigt de senaste århundrandena, tät skogsmark har ersatt tidigare öppen mark och i södra Sverige har granen kommit att bli allt vanligare. Detta gör det intressant att undersöka vilka förutsättningar dagens skogslandskap skapar för växters livsmiljöer och om en signifikant skillnad mellan gran- och talldominerade skogar finns. Studien utgick från ett datamaterial över fältskiktsväxter som påträffats under en inventering av 30 granbestånd och 30 tallbestånd i södra Småland. Viktade indikatorvärden beräknades baserat på tabellvärden för ljus, markreaktion, fuktighet, temperatur och kväve. En lista sammanställdes över hävdgynnade växter och utifrån den så beräknades medeltäckningen av växterna beståndsvis. Tallbestånden hyste totalt sett mer fältvegetation än granbestånden. Ingen statistiskt signifikant skillnad konstaterades mellan gran- och tallbestånden för indikatorvärdena ljus, temperatur och markreaktion. Granbestånden fick ett signifikant högre medelvärde för fuktighet. För kväve var granbeståndens medelvärde högre än tallbestånden. Ingen signifikant skillnad i täckningsgrad av hävdgynnade växter kunde styrkas mellan gran- och tallbestånden. Tallbestånden fick ett lägre ljusvärde än väntat, vilket förmodligen beror på det stora inslaget av skuggtåliga risväxter. Skillnaden i fuktighetsvärde förklarades av granskogars mäktigare humusskikt och lägre solinstrålning. Skillnad i kvävevärde kan bero på den högre kvävedepositionen i granskogar. Många växtarter tycks vara generalister avseende temperatur och markreaktion vilket gav ett litet underlag att basera statistiken på, något som kan ha påverkat dessa värdens utfall. Trädslagsval föreföll ha en begränsad påverkan på täckningsgraden av hävdgynnade växter, skötsel och andra ståndortsfaktorer kan förmodligen vara av större betydelse.The Swedish landscape has changed in recent centuries; meadows and pastoral lands have become increasingly forested and in southern Sweden, Norway spruce has become more common. Thus, it is interesting to study which conditions contemporary forest landscapes are subjecting plants to, how it affects their habitats and if a significant difference between Norway spruce and Scots pine dominated forest stands exists. This study is based on data from a survey in southern Småland of the field vegetation in 60 stands, 30 dominated by Norway spruce and 30 by Scots pine. Ellenberg’s weighted indicator values were calculated based on table values for light, soil reaction, humidity, temperature and nitrogen. A list of plant species typically related to managed lands i.e. meadows and semi natural grasslands was compiled, and average plant coverage was calculated. Field vegetation abundance was generally higher in Scots pine stands. The indicator values of light, temperature and soil reaction showed no statistically significant difference between the two stand types. The Norway spruce stands showed significantly higher values for moisture and nitrogen. No significant difference between the two stand types was detected for the coverage of plants related to managed lands. The pine stands had a lower light value than expected, probably due to the large proportion of dwarf shrubs, such as Vaccinium myrtillus and V. vitis-idaea. Differences in moisture value may be due to the generally thicker humus layer and lower solar radiation characteristic for Norway spruce forests. Higher nitrogen values might be explained by the higher nitrogen deposition in Norway spruce forests. Many plants are seemingly generalists regarding temperature and soil reaction, which might have affected the results. Focal tree species does not seem to impact the coverage of plants related to managed lands, forest management and other stand factors may be of greater importance

Forest management in northern Fennoscandia: the need for solutions that mitigate conflicts during forest regeneration and increase the use of continuous cover forestry

Today, conflicts often occur in northern Fennoscandia (also known as Sápmi) between forestry and reindeer husbandry. Continuous cover forestry (CCF) is requested by both reindeer herding communities and the general public and is becoming more common, but the forest industry criticizes CCF for lower wood production. Mechanical site preparation (MSP) increases regeneration success and, thus, increases wood production in CCF. To reduce the conflict between forestry and reindeer husbandry, MSP in Sápmi should destroy as little ground lichen as possible. Today, there are no solutions for gentle and lichen-adapted MSP in CCF. Thus, there is a strong need to develop and test new technical solutions that increase regeneration success in a lichen-adapted way during CCF in Sápmi. We suggest that MSP solutions be developed which are gentle, work selectively and function in shelterwoods, gap cuts, and selection cutting stands. We envision that these solutions could fill the gap between the desired adaptivity on the part of the reindeer herding communities and the desired efficiency on the part of the forest industry. Such MSP technology would contribute to increased acceptance of CCF in the forest industry, higher biodiversity, and considerably reduce the conflict between forestry and reindeer herding communities

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453

Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking

Model-based mutation testing uses altered test models to derive test cases that are able to reveal whether a modelled fault has been implemented. This requires conformance checking between the original and the mutated model. This paper presents an approach for symbolic conformance checking of action systems, which are well-suited to specify reactive systems. We also consider nondeterminism in our models. Hence, we do not check for equivalence, but for refinement. We encode the transition relation as well as the conformance relation as a constraint satisfaction problem and use a constraint solver in our reachability and refinement checking algorithms. Explicit conformance checking techniques often face state space explosion. First experimental evaluations show that our approach has potential to outperform explicit conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582