When rule-based models need to count

Rule-based modelers dislike direct enumeration of cases when more efficient means of enumeration are available. We present an extension of the Kappa language which attaches to agents a notion of level. We detail two encodings that are more concise than the former practice

New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized

The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation fails to identify two `obviously' equal terms. If only the machine could decide a richer theory! We propose a way to decide theories which supplement evaluation with `$\nu$-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment. We study a simple -calculus with primitive fold, map and append operations on lists and develop in Agda a sound and complete decision procedure for an equational theory enriched with monoid, functor and fusion laws

A relaxation of Coq's guard condition

National audienceIn a convenient language to handle dependent algebraic data types, this article describes how commutative cuts are used to tackle dependency in pattern matching. It defines a new termination criteria by structural guard condition that allows commutative cuts. Everything exposed scales directly to the Coq proof assistant and describes its implementation. The proof of strong normalisation does not and is still work to do

Dynamic Influence Networks for Rule-based Models

We introduce the Dynamic Influence Network (DIN), a novel visual analytics technique for representing and analyzing rule-based models of protein-protein interaction networks. Rule-based modeling has proved instrumental in developing biological models that are concise, comprehensible, easily extensible, and that mitigate the combinatorial complexity of multi-state and multi-component biological molecules. Our technique visualizes the dynamics of these rules as they evolve over time. Using the data produced by KaSim, an open source stochastic simulator of rule-based models written in the Kappa language, DINs provide a node-link diagram that represents the influence that each rule has on the other rules. That is, rather than representing individual biological components or types, we instead represent the rules about them (as nodes) and the current influence of these rules (as links). Using our interactive DIN-Viz software tool, researchers are able to query this dynamic network to find meaningful patterns about biological processes, and to identify salient aspects of complex rule-based models. To evaluate the effectiveness of our approach, we investigate a simulation of a circadian clock model that illustrates the oscillatory behavior of the KaiC protein phosphorylation cycle.Comment: Accepted to TVCG, in pres

A determinantal point process approach to scaling and local limits of random Young tableaux

We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit description of the limiting surface of a uniform random Young tableau of shape $\lambda^0$, based on solving a complex-valued polynomial equation; (2) a simple criteria to determine if the limiting surface is continuous in the whole domain; (3) and a local limit result in the bulk of a random Poissonized Young tableau of shape $\lambda^0$. Our results have several consequences, for instance: they lead to explicit formulas for the limiting surface of $L$-shaped tableaux, generalizing the results of Pittel and Romik (2007) for rectangular shapes; they imply that the limiting surface for $L$-shaped tableaux is discontinuous for almost-every $L$-shape; and they give a new one-parameter family of infinite random Young tableaux, constructed from the so-called random infinite bead process

RuleVis: Constructing Patterns and Rules for Rule-Based Models

We introduce RuleVis, a web-based application for defining and editing "correct-by-construction" executable rules that model biochemical functionality, which can be used to simulate the behavior of protein-protein interaction networks and other complex systems. Rule-based models involve emergent effects based on the interactions between rules, which can vary considerably with regard to the scale of a model, requiring the user to inspect and edit individual rules. RuleVis bridges the graph rewriting and systems biology research communities by providing an external visual representation of salient patterns that experts can use to determine the appropriate level of detail for a particular modeling context. We describe the visualization and interaction features available in RuleVisand provide a detailed example demonstrating how RuleVis can be used to reason about intracellular interactions

Proving the absence of unbounded polymers in rule-based models

International audienceRule-based languages, such as Kappa and BNGL, allow for the description of very combinatorial models of interactions between proteins. A huge (when not infinite) number of different kinds of bio-molecular compounds may arise due to proteins with multiple binding and phosphorylation sites. Knowing beforehand whether a model may involve an infinite number of different kinds of bio-molecular compounds is crucial for the modeller. On the first hand, having an infinite number of kinds of bio-molecular compounds is sometimes a hint for modelling flaws: forgetting to specify the conflicts among binding rules is a common mistake. On the second hand, it impacts the choice of the semantics for the models (among stochastic, differential, hybrid). In this paper, we introduce a data-structure to abstract the potential unbounded polymers that may be formed in a rule-based model. This data-structure is a graph, the nodes and the edges of which are labelled with patterns. By construction, every potentially unbounded polymer is associated to at least one cycle in that graph. This data-structure has two main advantages. Firstly, as opposed to site-graphs, one can reason about cycles without enumerating them (by the means of Tarjan's algorithm for detecting strongly connected components). Secondly, this data-structures may be combined easily with information coming from additional reachability analysis: the edges that are labelled with an overlap that is proved unreachable in the model may be safely discarded

The rule-based model approach. A Kappa model for hepatic stellate cells activation by TGFB1

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A Kappa model for hepatic stellate cells activation by TGFB1

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