Stochastic fragments: A framework for the exact reduction of the stochastic semantics of rule-based models

In this paper, we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein protein interaction networks. Our approach consists in quotienting the state space of networks. Yet interestingly, we do not apply the widelyused strong lumpability criterion which imposes that two equivalent states behave similarly with respect to the quotient, but a weak version of it. More precisely, our framework detects and proves some invariants about the dynamics of the system: indeed the quotient of the state space is such that the probability of being in a given state knowing that this state is in a given equivalence class, is an invariant of the semantics. Then we introduce an individual-based stochastic semantics (where each agent is identified by a unique identifier) for the programs of a rulebased language (namely Kappa) and we use our abstraction framework for deriving a sound population-based semantics and a sound fragments based semantics, which give the distribution of the traces respectively for the number of instances of molecular species and for the number of instances of partially defined molecular species. These partially defined species are chosen automatically thanks to a dependency analysis which is also described in the paper

Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Automatic Verification of Finite Precision Implementations of Linear Controllers

We consider the problem of verifying finite precision implementation of linear time-invariant controllers against mathematical specifications. A specification may have multiple correct implementations which are different from each other in controller state representation, but equivalent from a perspective of input-output behavior (e.g., due to optimization in a code generator). The implementations may use finite precision computations (e.g. floating-point arithmetic) which cause quantization (i.e., roundoff) errors. To address these challenges, we first extract a controller\u27s mathematical model from the implementation via symbolic execution and floating-point error analysis, and then check approximate input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of floating-point controller implementation in C language using the combination of techniques such as symbolic execution and convex optimization problem solving. We demonstrate the scalability of our approach through evaluation with randomly generated controller specifications of realistic size

Genetic counselling for psychiatric disorders: accounts of psychiatric health professionals in the United Kingdom

Genetic counselling is not routinely offered for psychiatric disorders in the United Kingdom through NHS regional clinical genetics departments. However, recent genomic advances, confirming a genetic contribution to mental illness, are anticipated to increase demand for psychiatric genetic counselling. This is the first study of its kind to employ qualitative methods of research to explore accounts of psychiatric health professionals regarding the prospects for genetic counselling services within clinical psychiatry in the UK. Data were collected from 32 questionnaire participants, and 9 subsequent interviewees. Data analysis revealed that although participants had not encountered patients explicitly demanding psychiatric genetic counselling, psychiatric health professionals believe that such a service would be useful and desirable. Genomic advances may have significant implications for genetic counselling in clinical psychiatry even if these discoveries do not lead to genetic testing. Psychiatric health professionals describe clinical genetics as a skilled profession capable of combining complex risk communication with much needed psychosocial support. However, participants noted barriers to the implementation of psychiatric genetic counselling services including, but not limited to, the complexities of uncertainty in psychiatric diagnoses, patient engagement and ethical concerns regarding limited capacity

Measuring β-diversity by remote sensing: a challenge for biodiversity monitoring

Biodiversity includes multiscalar and multitemporal structures and processes, with different levels of functional organization, from genetic to ecosystemic levels. One of the mostly used methods to infer biodiversity is based on taxonomic approaches and community ecology theories. However, gathering extensive data in the field is difficult due to logistic problems, especially when aiming at modelling biodiversity changes in space and time, which assumes statistically sound sampling schemes. In this context, airborne or satellite remote sensing allows information to be gathered over wide areas in a reasonable time. Most of the biodiversity maps obtained from remote sensing have been based on the inference of species richness by regression analysis. On the contrary, estimating compositional turnover (β‐diversity) might add crucial information related to relative abundance of different species instead of just richness. Presently, few studies have addressed the measurement of species compositional turnover from space. Extending on previous work, in this manuscript, we propose novel techniques to measure β‐diversity from airborne or satellite remote sensing, mainly based on: (1) multivariate statistical analysis, (2) the spectral species concept, (3) self‐organizing feature maps, (4) multidimensional distance matrices, and the (5) Rao's Q diversity. Each of these measures addresses one or several issues related to turnover measurement. This manuscript is the first methodological example encompassing (and enhancing) most of the available methods for estimating β‐diversity from remotely sensed imagery and potentially relating them to species diversity in the field

Process Simulation and Control Optimization of a Blast Furnace Using Classical Thermodynamics Combined to a Direct Search Algorithm

Several numerical approaches have been proposed in the literature to simulate the behavior of modern blast furnaces: finite volume methods, data-mining models, heat and mass balance models, and classical thermodynamic simulations. Despite this, there is actually no efficient method for evaluating quickly optimal operating parameters of a blast furnace as a function of the iron ore composition, which takes into account all potential chemical reactions that could occur in the system. In the current study, we propose a global simulation strategy of a blast furnace, the 5-unit process simulation. It is based on classical thermodynamic calculations coupled to a direct search algorithm to optimize process parameters. These parameters include the minimum required metallurgical coke consumption as well as the optimal blast chemical composition and the total charge that simultaneously satisfy the overall heat and mass balances of the system. Moreover, a Gibbs free energy function for metallurgical coke is parameterized in the current study and used to fine-tune the simulation of the blast furnace. Optimal operating conditions and predicted output stream properties calculated by the proposed thermodynamic simulation strategy are compared with reference data found in the literature and have proven the validity and high precision of this simulation

Mapping changing distributions of dominant species in oil-contaminated salt marshes of Louisiana using imaging spectroscopy

The April 2010 Deepwater Horizon (DWH) oil spill was the largest coastal spill in U.S. history. Monitoring subsequent change in marsh plant community distributions is critical to assess ecosystem impacts and to establish future coastal management priorities. Strategically deployed airborne imaging spectrometers, like the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), offer the spectral and spatial resolution needed to differentiate plant species. However, obtaining satisfactory and consistent classification accuracies over time is a major challenge, particularly in dynamic intertidal landscapes.Here, we develop and evaluate an image classification system for a time series of AVIRIS data for mapping dominant species in a heavily oiled salt marsh ecosystem. Using field-referenced image endmembers and canonical discriminant analysis (CDA), we classified 21 AVIRIS images acquired during the fall of 2010, 2011 and 2012. Classification results were evaluated using ground surveys that were conducted contemporaneously to AVIRIS collection dates. We analyzed changes in dominant species cover from 2010 to 2012 for oiled and non-oiled shorelines.CDA discriminated dominant species with a high level of accuracy (overall accuracy=82%, kappa=0.78) and consistency over three imaging dates (overall2010=82%, overall2011=82%, overall2012=88%). Marshes dominated by Spartina alterniflora were the most spatially abundant in shoreline zones (â¤28m from shore) for all three dates (2010=79%, 2011=61%, 2012=63%), followed by Juncus roemerianus (2010=11%, 2011=19%, 2012=17%) and Distichlis spicata (2010=4%, 2011=10%, 2012=7%).Marshes that were heavily contaminated with oil exhibited variable responses from 2010 to 2012. Marsh vegetation classes converted to a subtidal, open water class along oiled and non-oiled shorelines that were similarly situated in the landscape. However, marsh loss along oil-contaminated shorelines doubled that of non-oiled shorelines. Only S. alterniflora dominated marshes were extensively degraded, losing 15% (354,604m2) cover in oiled shoreline zones, suggesting that S. alterniflora marshes may be more vulnerable to shoreline erosion following hydrocarbon stress, due to their landscape position

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. © 2014 Hogg et al

Moment Semantics for Reversible Rule-Based Systems

International audienceWe develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the 'no-dangling-edge' condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree