@inproceedings{1227, abstract = {Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction significantly determines the level of confidence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sufficient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiaffine system to be based on a set of multivariate polynomials. Hence, a rectangular partition defined in terms of polynomials of the form (xi − c) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.}, author = {Kong, Hui and Bartocci, Ezio and Bogomolov, Sergiy and Grosu, Radu and Henzinger, Thomas A and Jiang, Yu and Schilling, Christian}, location = {Grenoble, France}, pages = {128 -- 144}, publisher = {Springer}, title = {{Discrete abstraction of multiaffine systems}}, doi = {10.1007/978-3-319-47151-8_9}, volume = {9957}, year = {2016}, } @inproceedings{1230, abstract = {Concolic testing is a promising method for generating test suites for large programs. However, it suffers from the path-explosion problem and often fails to find tests that cover difficult-to-reach parts of programs. In contrast, model checkers based on counterexample-guided abstraction refinement explore programs exhaustively, while failing to scale on large programs with precision. In this paper, we present a novel method that iteratively combines concolic testing and model checking to find a test suite for a given coverage criterion. If concolic testing fails to cover some test goals, then the model checker refines its program abstraction to prove more paths infeasible, which reduces the search space for concolic testing. We have implemented our method on top of the concolictesting tool Crest and the model checker CpaChecker. We evaluated our tool on a collection of programs and a category of SvComp benchmarks. In our experiments, we observed an improvement in branch coverage compared to Crest from 48% to 63% in the best case, and from 66% to 71% on average.}, author = {Daca, Przemyslaw and Gupta, Ashutosh and Henzinger, Thomas A}, location = {St. Petersburg, FL, USA}, pages = {328 -- 347}, publisher = {Springer}, title = {{Abstraction-driven concolic testing}}, doi = {10.1007/978-3-662-49122-5_16}, volume = {9583}, year = {2016}, } @inproceedings{1234, abstract = {We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, including full linear temporal logic. The main idea is that we monitor each simulation run on the fly, in order to detect quickly if a bottom strongly connected component is entered with high probability, in which case the simulation run can be terminated early. As a result, our simulation runs are often much shorter than required by termination bounds that are computed a priori for a desired level of confidence on a large state space. In comparison to previous algorithms for statistical model checking our method is not only faster in many cases but also requires less information about the system, namely, only the minimum transition probability that occurs in the Markov chain. In addition, our method can be generalised to unbounded quantitative properties such as mean-payoff bounds.}, author = {Daca, Przemyslaw and Henzinger, Thomas A and Kretinsky, Jan and Petrov, Tatjana}, location = {Eindhoven, The Netherlands}, pages = {112 -- 129}, publisher = {Springer}, title = {{Faster statistical model checking for unbounded temporal properties}}, doi = {10.1007/978-3-662-49674-9_7}, volume = {9636}, year = {2016}, } @inproceedings{1256, abstract = {Simulink is widely used for model driven development (MDD) of industrial software systems. Typically, the Simulink based development is initiated from Stateflow modeling, followed by simulation, validation and code generation mapped to physical execution platforms. However, recent industrial trends have raised the demands of rigorous verification on safety-critical applications, which is unfortunately challenging for Simulink. In this paper, we present an approach to bridge the Stateflow based model driven development and a well- defined rigorous verification. First, we develop a self- contained toolkit to translate Stateflow model into timed automata, where major advanced modeling features in Stateflow are supported. Taking advantage of the strong verification capability of Uppaal, we can not only find bugs in Stateflow models which are missed by Simulink Design Verifier, but also check more important temporal properties. Next, we customize a runtime verifier for the generated nonintrusive VHDL and C code of Stateflow model for monitoring. The major strength of the customization is the flexibility to collect and analyze runtime properties with a pure software monitor, which opens more opportunities for engineers to achieve high reliability of the target system compared with the traditional act that only relies on Simulink Polyspace. We incorporate these two parts into original Stateflow based MDD seamlessly. In this way, safety-critical properties are both verified at the model level, and at the consistent system implementation level with physical execution environment in consideration. We apply our approach on a train controller design, and the verified implementation is tested and deployed on a real hardware platform.}, author = {Jiang, Yu and Yang, Yixiao and Liu, Han and Kong, Hui and Gu, Ming and Sun, Jiaguang and Sha, Lui}, location = {Vienna, Austria}, publisher = {IEEE}, title = {{From stateflow simulation to verified implementation: A verification approach and a real-time train controller design}}, doi = {10.1109/RTAS.2016.7461337}, year = {2016}, } @inproceedings{1335, abstract = {In this paper we review various automata-theoretic formalisms for expressing quantitative properties. We start with finite-state Boolean automata that express the traditional regular properties. We then consider weighted ω-automata that can measure the average density of events, which finite-state Boolean automata cannot. However, even weighted ω-automata cannot express basic performance properties like average response time. We finally consider two formalisms of weighted ω-automata with monitors, where the monitors are either (a) counters or (b) weighted automata themselves. We present a translation result to establish that these two formalisms are equivalent. Weighted ω-automata with monitors generalize weighted ω-automata, and can express average response time property. They present a natural, robust, and expressive framework for quantitative specifications, with important decidable properties.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, location = {Edinburgh, United Kingdom}, pages = {23 -- 38}, publisher = {Springer}, title = {{Quantitative monitor automata}}, doi = {10.1007/978-3-662-53413-7_2}, volume = {9837}, year = {2016}, } @inproceedings{1341, abstract = {In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.}, author = {Avni, Guy and Henzinger, Thomas A and Kupferman, Orna}, location = {Liverpool, United Kingdom}, pages = {153 -- 166}, publisher = {Springer}, title = {{Dynamic resource allocation games}}, doi = {10.1007/978-3-662-53354-3_13}, volume = {9928}, year = {2016}, } @inproceedings{1390, abstract = {The goal of automatic program repair is to identify a set of syntactic changes that can turn a program that is incorrect with respect to a given specification into a correct one. Existing program repair techniques typically aim to find any program that meets the given specification. Such “best-effort” strategies can end up generating a program that is quite different from the original one. Novel techniques have been proposed to compute syntactically minimal program fixes, but the smallest syntactic fix to a program can still significantly alter the original program’s behaviour. We propose a new approach to program repair based on program distances, which can quantify changes not only to the program syntax but also to the program semantics. We call this the quantitative program repair problem where the “optimal” repair is derived using multiple distances. We implement a solution to the quantitative repair problem in a prototype tool called Qlose (Quantitatively close), using the program synthesizer Sketch. We evaluate the effectiveness of different distances in obtaining desirable repairs by evaluating Qlose on programs taken from educational tools such as CodeHunt and edX.}, author = {D'Antoni, Loris and Samanta, Roopsha and Singh, Rishabh}, location = {Toronto, Canada}, pages = {383 -- 401}, publisher = {Springer}, title = {{QLOSE: Program repair with quantitative objectives}}, doi = {10.1007/978-3-319-41540-6_21}, volume = {9780}, year = {2016}, } @inproceedings{1391, abstract = {We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as "the first array cell contains the array length," and "the array contains equally many minimal and maximal elements." These properties cannot be expressed in quantified fragments of the theory of arrays, nor in the theory of concatenation. Using reduction to counter machines, we show that the satisfiability problem of AFL is PSPACE-complete, and with a natural restriction the complexity decreases to NP. We also show that adding either universal quantifiers or concatenation leads to undecidability. AFL contains terms that fold a function over an array. We demonstrate that folding, a well-known concept from functional languages, allows us to concisely summarize loops that count over arrays, which occurs frequently in real-life programs. We provide a tool that can discharge proof obligations in AFL, and we demonstrate on practical examples that our decision procedure can solve a broad range of problems in symbolic testing and program verification.}, author = {Daca, Przemyslaw and Henzinger, Thomas A and Kupriyanov, Andrey}, location = {Toronto, Canada}, pages = {230 -- 248}, publisher = {Springer}, title = {{Array folds logic}}, doi = {10.1007/978-3-319-41540-6_13}, volume = {9780}, year = {2016}, } @inproceedings{1421, abstract = {Hybridization methods enable the analysis of hybrid automata with complex, nonlinear dynamics through a sound abstraction process. Complex dynamics are converted to simpler ones with added noise, and then analysis is done using a reachability method for the simpler dynamics. Several such recent approaches advocate that only "dynamic" hybridization techniquesi.e., those where the dynamics are abstracted on-The-fly during a reachability computation are effective. In this paper, we demonstrate this is not the case, and create static hybridization methods that are more scalable than earlier approaches. The main insight in our approach is that quick, numeric simulations can be used to guide the process, eliminating the need for an exponential number of hybridization domains. Transitions between domains are generally timetriggered, avoiding accumulated error from geometric intersections. We enhance our static technique by combining time-Triggered transitions with occasional space-Triggered transitions, and demonstrate the benefits of the combined approach in what we call mixed-Triggered hybridization. Finally, error modes are inserted to confirm that the reachable states stay within the hybridized regions. The developed techniques can scale to higher dimensions than previous static approaches, while enabling the parallelization of the main performance bottleneck for many dynamic hybridization approaches: The nonlinear optimization required for sound dynamics abstraction. We implement our method as a model transformation pass in the HYST tool, and perform reachability analysis and evaluation using an unmodified version of SpaceEx on nonlinear models with up to six dimensions.}, author = {Bak, Stanley and Bogomolov, Sergiy and Henzinger, Thomas A and Johnson, Taylor and Prakash, Pradyot}, location = {Vienna, Austria}, pages = {155 -- 164}, publisher = {Springer}, title = {{Scalable static hybridization methods for analysis of nonlinear systems}}, doi = {10.1145/2883817.2883837}, year = {2016}, } @inproceedings{1439, abstract = {Fault-tolerant distributed algorithms play an important role in many critical/high-availability applications. These algorithms are notoriously difficult to implement correctly, due to asynchronous communication and the occurrence of faults, such as the network dropping messages or computers crashing. We introduce PSYNC, a domain specific language based on the Heard-Of model, which views asynchronous faulty systems as synchronous ones with an adversarial environment that simulates asynchrony and faults by dropping messages. We define a runtime system for PSYNC that efficiently executes on asynchronous networks. We formalize the relation between the runtime system and PSYNC in terms of observational refinement. The high-level lockstep abstraction introduced by PSYNC simplifies the design and implementation of fault-tolerant distributed algorithms and enables automated formal verification. We have implemented an embedding of PSYNC in the SCALA programming language with a runtime system for asynchronous networks. We show the applicability of PSYNC by implementing several important fault-tolerant distributed algorithms and we compare the implementation of consensus algorithms in PSYNC against implementations in other languages in terms of code size, runtime efficiency, and verification.}, author = {Dragoi, Cezara and Henzinger, Thomas A and Zufferey, Damien}, location = {St. Petersburg, FL, USA}, pages = {400 -- 415}, publisher = {ACM}, title = {{PSYNC: A partially synchronous language for fault-tolerant distributed algorithms}}, doi = {10.1145/2837614.2837650}, volume = {20-22}, year = {2016}, } @inproceedings{1524, abstract = {When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations. Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a λ-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude.}, author = {Beica, Andreea and Guet, Calin C and Petrov, Tatjana}, location = {Madrid, Spain}, pages = {173 -- 191}, publisher = {Springer}, title = {{Efficient reduction of kappa models by static inspection of the rule-set}}, doi = {10.1007/978-3-319-26916-0_10}, volume = {9271}, year = {2016}, } @inproceedings{1526, abstract = {We present the first study of robustness of systems that are both timed as well as reactive (I/O). We study the behavior of such timed I/O systems in the presence of uncertain inputs and formalize their robustness using the analytic notion of Lipschitz continuity: a timed I/O system is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions over timed words such as the timed version of the Manhattan distance and the Skorokhod distance. We consider two models of timed I/O systems — timed transducers and asynchronous sequential circuits. We show that K-robustness of timed transducers can be decided in polynomial space under certain conditions. For asynchronous sequential circuits, we reduce K-robustness w.r.t. timed Manhattan distances to K-robustness of discrete letter-to-letter transducers and show PSpace-completeness of the problem.}, author = {Henzinger, Thomas A and Otop, Jan and Samanta, Roopsha}, location = {St. Petersburg, FL, USA}, pages = {250 -- 267}, publisher = {Springer}, title = {{Lipschitz robustness of timed I/O systems}}, doi = {10.1007/978-3-662-49122-5_12}, volume = {9583}, year = {2016}, } @article{1705, abstract = {Hybrid systems represent an important and powerful formalism for modeling real-world applications such as embedded systems. A verification tool like SpaceEx is based on the exploration of a symbolic search space (the region space). As a verification tool, it is typically optimized towards proving the absence of errors. In some settings, e.g., when the verification tool is employed in a feedback-directed design cycle, one would like to have the option to call a version that is optimized towards finding an error trajectory in the region space. A recent approach in this direction is based on guided search. Guided search relies on a cost function that indicates which states are promising to be explored, and preferably explores more promising states first. In this paper, we propose an abstraction-based cost function based on coarse-grained space abstractions for guiding the reachability analysis. For this purpose, a suitable abstraction technique that exploits the flexible granularity of modern reachability analysis algorithms is introduced. The new cost function is an effective extension of pattern database approaches that have been successfully applied in other areas. The approach has been implemented in the SpaceEx model checker. The evaluation shows its practical potential.}, author = {Bogomolov, Sergiy and Donzé, Alexandre and Frehse, Goran and Grosu, Radu and Johnson, Taylor and Ladan, Hamed and Podelski, Andreas and Wehrle, Martin}, journal = {International Journal on Software Tools for Technology Transfer}, number = {4}, pages = {449 -- 467}, publisher = {Springer}, title = {{Guided search for hybrid systems based on coarse-grained space abstractions}}, doi = {10.1007/s10009-015-0393-y}, volume = {18}, year = {2016}, } @inproceedings{479, abstract = {Clinical guidelines and decision support systems (DSS) play an important role in daily practices of medicine. Many text-based guidelines have been encoded for work-flow simulation of DSS to automate health care. During the collaboration with Carle hospital to develop a DSS, we identify that, for some complex and life-critical diseases, it is highly desirable to automatically rigorously verify some complex temporal properties in guidelines, which brings new challenges to current simulation based DSS with limited support of automatical formal verification and real-time data analysis. In this paper, we conduct the first study on applying runtime verification to cooperate with current DSS based on real-time data. Within the proposed technique, a user-friendly domain specific language, named DRTV, is designed to specify vital real-time data sampled by medical devices and temporal properties originated from clinical guidelines. Some interfaces are developed for data acquisition and communication. Then, for medical practice scenarios described in DRTV model, we will automatically generate event sequences and runtime property verifier automata. If a temporal property violates, real-time warnings will be produced by the formal verifier and passed to medical DSS. We have used DRTV to specify different kinds of medical care scenarios, and applied the proposed technique to assist existing DSS. As presented in experiment results, in terms of warning detection, it outperforms the only use of DSS or human inspection, and improves the quality of clinical health care of hospital}, author = {Jiang, Yu and Liu, Han and Kong, Hui and Wang, Rui and Hosseini, Mohamad and Sun, Jiaguang and Sha, Lui}, booktitle = {Proceedings of the 38th International Conference on Software Engineering Companion }, location = {Austin, TX, USA}, pages = {112 -- 121}, publisher = {IEEE}, title = {{Use runtime verification to improve the quality of medical care practice}}, doi = {10.1145/2889160.2889233}, year = {2016}, } @inproceedings{1498, abstract = {Fault-tolerant distributed algorithms play an important role in many critical/high-availability applications. These algorithms are notoriously difficult to implement correctly, due to asynchronous communication and the occurrence of faults, such as the network dropping messages or computers crashing. Nonetheless there is surprisingly little language and verification support to build distributed systems based on fault-tolerant algorithms. In this paper, we present some of the challenges that a designer has to overcome to implement a fault-tolerant distributed system. Then we review different models that have been proposed to reason about distributed algorithms and sketch how such a model can form the basis for a domain-specific programming language. Adopting a high-level programming model can simplify the programmer's life and make the code amenable to automated verification, while still compiling to efficiently executable code. We conclude by summarizing the current status of an ongoing language design and implementation project that is based on this idea.}, author = {Dragoi, Cezara and Henzinger, Thomas A and Zufferey, Damien}, isbn = {978-3-939897-80-4 }, location = {Asilomar, CA, United States}, pages = {90 -- 102}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The need for language support for fault-tolerant distributed systems}}, doi = {10.4230/LIPIcs.SNAPL.2015.90}, volume = {32}, year = {2015}, } @inproceedings{1499, abstract = {We consider weighted automata with both positive and negative integer weights on edges and study the problem of synchronization using adaptive strategies that may only observe whether the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata.}, author = {Kretinsky, Jan and Larsen, Kim and Laursen, Simon and Srba, Jiří}, location = {Madrid, Spain}, pages = {142 -- 154}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Polynomial time decidability of weighted synchronization under partial observability}}, doi = {10.4230/LIPIcs.CONCUR.2015.142}, volume = {42}, year = {2015}, } @article{1501, abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph algorithms with quadratic complexity to compute the simulation relation. We present an automated technique for assume-guarantee style reasoning for compositional analysis of two-player games by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We show a tight link between two-player games and MDPs, and as a consequence the results for games are lifted to MDPs with qualitative properties. We have implemented our algorithms and show that the compositional analysis leads to significant improvements. }, author = {Chatterjee, Krishnendu and Chmelik, Martin and Daca, Przemyslaw}, journal = {Formal Methods in System Design}, number = {2}, pages = {230 -- 264}, publisher = {Springer}, title = {{CEGAR for compositional analysis of qualitative properties in Markov decision processes}}, doi = {10.1007/s10703-015-0235-2}, volume = {47}, year = {2015}, } @inproceedings{1502, abstract = {We extend the theory of input-output conformance with operators for merge and quotient. The former is useful when testing against multiple requirements or views. The latter can be used to generate tests for patches of an already tested system. Both operators can combine systems with different action alphabets, which is usually the case when constructing complex systems and specifications from parts, for instance different views as well as newly defined functionality of a~previous version of the system.}, author = {Beneš, Nikola and Daca, Przemyslaw and Henzinger, Thomas A and Kretinsky, Jan and Nickovic, Dejan}, isbn = {978-1-4503-3471-6}, location = {Montreal, QC, Canada}, pages = {101 -- 110}, publisher = {ACM}, title = {{Complete composition operators for IOCO-testing theory}}, doi = {10.1145/2737166.2737175}, year = {2015}, } @article{1538, abstract = {Systems biology rests on the idea that biological complexity can be better unraveled through the interplay of modeling and experimentation. However, the success of this approach depends critically on the informativeness of the chosen experiments, which is usually unknown a priori. Here, we propose a systematic scheme based on iterations of optimal experiment design, flow cytometry experiments, and Bayesian parameter inference to guide the discovery process in the case of stochastic biochemical reaction networks. To illustrate the benefit of our methodology, we apply it to the characterization of an engineered light-inducible gene expression circuit in yeast and compare the performance of the resulting model with models identified from nonoptimal experiments. In particular, we compare the parameter posterior distributions and the precision to which the outcome of future experiments can be predicted. Moreover, we illustrate how the identified stochastic model can be used to determine light induction patterns that make either the average amount of protein or the variability in a population of cells follow a desired profile. Our results show that optimal experiment design allows one to derive models that are accurate enough to precisely predict and regulate the protein expression in heterogeneous cell populations over extended periods of time.}, author = {Ruess, Jakob and Parise, Francesca and Milias Argeitis, Andreas and Khammash, Mustafa and Lygeros, John}, journal = {PNAS}, number = {26}, pages = {8148 -- 8153}, publisher = {National Academy of Sciences}, title = {{Iterative experiment design guides the characterization of a light-inducible gene expression circuit}}, doi = {10.1073/pnas.1423947112}, volume = {112}, year = {2015}, } @article{1539, abstract = {Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space. }, author = {Ruess, Jakob}, journal = {Journal of Chemical Physics}, number = {24}, publisher = {American Institute of Physics}, title = {{Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space}}, doi = {10.1063/1.4937937}, volume = {143}, year = {2015}, }