arXiv subjects

Juri Kolčák

Publications and source records attributed to Juri Kolčák.

6 recordsLinked to original sources

arXiv2026

Automating Observable Closure Analysis for Graph Transformation Models with MolFoundry

Graph transformations model changing systems, with applications in software, biology and chemistry, among others. We introduce MolFoundry, a graph transformation framework, and present a workflow for observable analysis that tracks the dynamics of local patterns through rule composition. Analysing rule compositions avoids the need to enumerate a potentially infinite state space. Building on rule-algebraic stochastic rewriting, MolFoundry's kernel composes rules with nested application conditions, including missing-edge constraints. Given rules, rates and query patterns, the algorithms iteratively identify auxiliary pattern counts and search for closure. Using exact counting identities supplied by graph-family backends, successful searches yield closed ordinary differential equations for average counts or, with justified individual jumps, finite event models describing joint changes and rates. We evaluate conditional composition and automated discovery of auxiliary observables against published calculations and independent rule application. Applications to aldol addition, copolymerization and chlorination show how the framework yields quantitative predictions directly from molecular graph rules.

cs.LO↗

arXiv2026

Automated Inference of Graph Transformation Rules

The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel method of the graph transformation model construction, combining generative and dynamical viewpoints to give a fully automated data-driven model inference method. The method takes the input dynamical properties, given as a "snapshot" of the dynamics encoded by explicit transitions, and constructs a compatible model. The obtained model is guaranteed to be minimal, thus framing the approach as model compression (from a set of transitions into a set of rules). The compression is permissive to a lossy case, where the constructed model is allowed to exhibit behavior outside of the input transitions, thus suggesting a completion of the input dynamics. The task of graph transformation model inference is naturally highly challenging due to the combinatorics involved. We tackle the exponential explosion by proposing a heuristically minimal translation of the task into a well-established problem, set cover, for which highly optimized solutions exist. We further showcase how our results relate to Kolmogorov complexity expressed in terms of graph transformation.

cs.DM↗

arXiv2025

Continuous Petri Nets for Fast Yield Computation: Polynomial-Time and MILP Approaches

Petri nets provide accurate analogues to chemical reaction networks, with places representing individual molecules (the resources of the system) and transitions representing chemical reactions which convert educt molecules into product molecules. Their natural affinity for modeling chemical reaction networks is, however, impeded by their computational complexity, which is at least PSpace-hard for most interesting questions, including reachability. Continuous Petri nets offer the same structure and discrete time as discrete Petri nets, but use continuous state-space, which allows them to answer the reachability question in polynomial time. We exploit this property to introduce a polynomial time algorithm for computing the maximal yield of a molecule in a chemical system. Additionally, we provide an alternative algorithm based on mixed-integer linear programming with worse theoretical complexity, but better runtime in practice, as demonstrated on both synthetic and chemical data.

cs.DM↗

arXiv2025

Continuous Petri Nets Faithfully Fluidify Most Permissive Boolean Networks

The analysis of biological networks has benefited from the richness of Boolean networks (BNs) and the associated theory. These results have been further fortified in recent years by the emergence of Most Permissive (MP) semantics, combining efficient analysis methods with a greater capacity of explaining pathways to states hitherto thought unreachable, owing to limitations of the classical update modes. While MPBNs are understood to capture any behaviours that can be observed at a lower level of abstraction, all the way down to continuous refinements, the specifics and potential of the models and analysis, especially attractors, across the abstraction scale remain unexplored. Here, we fluidify MPBNs by means of Continuous Petri nets (CPNs), a model of (uncountably infinite) dynamic systems that has been successfully explored for modelling and theoretical purposes. CPNs create a formal link between MPBNs and their continuous dynamical refinements such as ODE models. The benefits of CPNs extend beyond the model refinement, and constitute well established theory and analysis methods, recently augmented by abstract and symbolic reachability graphs. These structures are shown to compact the possible behaviours of the system with focus on events which drive the choice of long-term behaviour in which the system eventually stabilises. The current paper brings an important keystone to this novel methodology for biological networks, namely the proof that extant PN encoding of BNs instantiated as a CPN simulates the MP semantics. In spite of the underlying dynamics being continuous, the analysis remains in the realm of discrete methods, constituting an extension of all previous work.

cs.DM↗

arXiv2022

Efficient Modular Graph Transformation Rule Application

Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made feasible via the development of programming frameworks which makes the formalisms executable. The application of such frameworks to large networks of chemical reactions, however, poses unique computational challenges. One such characteristic is the inherent combinatorial nature of the graphs involved. The graphs consist of many connected components, representing individual molecules. While the existing methods for implementing graph transformations can be applied to such graphs, the combinatorics of constructing graph matches quickly becomes a computational bottleneck as the size of the chemical reaction network grows. In this contribution, we develop a new method of enumerating graph matches during graph transformation rule application. The method is designed to improve performance in such scenarios and is based on constructing graph matches in an iterative, component-wise fashion which allows redundant applications to be detected early and pruned. We further extend the algorithm with an efficient heuristic based on local symmetries of the graphs, which allow us to detect and discard isomorphic applications early. Finally, we conduct chemical network generation experiments on real-life as well as synthetic data and compare against the state-of-the-art algorithm in the field.

cs.DM↗

arXiv2022

Representing catalytic mechanisms with rule composition

Reaction mechanisms are often presented as sequences of elementary steps, such as codified by arrow pushing. We propose an approach for representing such mechanisms using graph transformation. In this framework, each elementary step is a rule for modifying a molecular graph and a mechanism is a sequence of such rules. To generate a compact representation of a multi-step reaction, we compose the rules of individual steps into a composite rule, providing a rigorous and fully automated approach to coarse-graining. While the composite rule retains the graphical conditions necessary for the execution of a mechanism, it also records information about transient changes not visible by comparing educts and products. By projecting the rule onto a single "overlay graph", we generalize Fujita's idea of an Imaginary Transition Structure from elementary reactions to composite reactions. The utility of the overlay graph construct is exemplified in the context of enzyme-catalyzed reactions. In a first application, we exploit mechanistic information in the Mechanism and Catalytic Site Atlas to construct overlay graphs of hydrolase reactions listed in the database. These graphs point at a spectrum of catalytic entanglement of enzyme and substrate, de-emphasizing the notion of a singular catalyst in favor of a collection of catalytic sites that can be distributed across enzyme and substrate. In a second application, we deploy composite rules to search the Rhea database for reactions of known or unknown mechanism that are, in principle, compatible with the mechanisms implied by the composite rules. We believe this work adds to the utility of graph-transformation formalisms in representing and reasoning about chemistry in an automated yet insightful fashion.

cs.DM↗