Microalgae are promising cell factories for sustainable production of biofuel, high-value compounds, and wastewater bioremediation. However, their industrial deployment requires robust prediction of biomass productivity across the wide range of light and nutrient conditions encountered in photobioreactors. Mechanistic models typically assume constant growth parameters, limiting their accuracy across varying cultivation conditions. Conversely, response surface methodology (RSM) captures parameter variability across conditions but lacks dynamics and can yield biologically implausible predictions under untested cultivation conditions. This study introduces a hybrid model that embeds biologically interpretable Monod-type surfaces into a logistic growth model, allowing maximum growth rate and carrying capacity to vary independently and continuously with light intensity and nutrient availability. Validated on 1315 growth curves of Chlamydomonas reinhardtii grown mixotrophically, the model predicts full time series under previously untested light-nutrient combinations at 2 scales: flask (50mL, R2=0.94) and microplate (200µL, R2=0.84), consistently outperforming three established mechanistic models. Six global parameters replace up to 50 condition-specific ones, substantially reducing the experimental effort. We further demonstrate that microplate-derived parameter surfaces can be mapped onto flask-scale surfaces through simple transformations (R2≥0.94), providing a basis for scale-up from high-throughput data to bench-scale cultivation. The framework offers a practical tool to optimize microalgal cultivation at laboratory scale, with preliminary evidence supporting its transferability across culture volumes.

The Centralized Training with Decentralized Execution (CTDE) paradigm has become increasingly popular in multi-agent reinforcement learning and is widely adopted in recent works. However, decentralized policies operate under partial observations and may achieve suboptimal performance compared to centralized policies, while naive centralized policies often struggle to scale with larger numbers of agents. To address these limitations, we introduce Centralized Permutation Equivariant (CPE) learning, a scalable centralized training and execution (CTE) framework that transforms standard CTDE algorithms by replacing decentralized execution with a fully centralized policy, while retaining their centralized training components. Our policy network is built upon a Global–Local Permutation Equivariant (GLPE) architecture, which is lightweight, computationally efficient, and agent-number-agnostic at the architectural level. Empirical results show that CPE can be seamlessly integrated with both value decomposition and actor–critic methods, consistently improving the performance of classical CTDE approaches across cooperative benchmarks such as MPE, SMAC, and RWARE, while matching state-of-the-art performance on RWARE. These results suggest that scalable centralized execution constitutes a promising alternative to decentralized policies in coordination-intensive MARL settings.

Bursty transcription in single cells typically produces over-dispersed, skewed, and sometimes heavy-tailed expression distributions that are explained by two-state Markov models of the promoters. While the gold standard for simulation is exact stochastic sampling with Gillespie’s algorithm, obtaining thousands of timed traces is computationally costly. Surrogate models based on stochastic differential equations (SDEs) are widely used to speed up this simulation process. An example is the Chemical Langevin Equation based on Gaussian noise, which, however, does not capture heavy-tailed noise. In this work, we present a unified SDE framework that combines deterministic drift, Gaussian fluctuations, and additive sporadic jumps of arbitrary distributions, and provide an open-source Python implementation, bcrnnoise. The framework subsumes standard surrogate models and allows for vectorized generation of batches of transcription traces. We assess computational speed and accuracy of common surrogate models along with new models, showing that high accuracy can be obtained while reducing computational cost up to two orders of magnitude.

We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Θ (n^2) and has the optimal number of n states in a population of n agents. The existing protocol has the additional property that it becomes silent, i.e., the agents’ states eventually stop changing. Observing that any silent protocol solving self-stabilizing leader election requires Ω (n) expected parallel time, we introduce a silent protocol that uses optimal O(n) parallel time and states. Without any silence constraints, we show that it is possible to solve self-stabilizing leader election in asymptotically optimal expected parallel time of O(log n) , but using at least exponential states (a quasipolynomial number of bits). All of our protocols (and also that of Cai et al.) work by solving the more difficult ranking problem: assigning agents the ranks 1,… ,n .

The inherent stochastic fluctuations in signalling molecules of gene regulatory networks (GRNs) add unpredictability, complicating the design of robust synthetic GRNs that must function within precise ranges. Multi-stable GRNs, such as toggle switches, are central to systems like biosensors and logic gates, but can fail owing to unintended transitions between stable states caused by the fluctuations. Despite their importance, tools to characterize the probability distributions around stable states remain limited. We present a mathematical framework for analysing these multi-stable systems using continuous-time Markov chains (CTMCs) and quasi-stationary distributions (QSDs). This framework is broadly applicable, requiring only that the state space is connected, making it applicable to a variety of systems. We apply the framework to a toggle-switch design from the literature, identifying parameter thresholds at which systems transition from frequent stochastic switching (hours) to stable operation (years to decades), consistent with current experimental insights. We further present upper-bound calculations of false-positive/false-negative rates for population-level biosensor dynamics as supplementary results.

Multi-agent systems built on large language models (LLMs) are difficult to reason about. Coordination errors such as deadlocks or type-mismatched messages are often hard to detect through testing. We introduce a domain-specific language for specifying agent coordination based on message sequence charts (MSCs). The language separates message-passing structure from LLM actions, whose outputs remain unpredictable. We define the syntax and semantics of the language and present a syntax-directed projection that generates deadlock-free local agent programs from global coordination specifications. We illustrate the approach with a diagnosis consensus protocol and show how coordination properties can be established independently of LLM nondeterminism. We also describe a runtime planning extension in which an LLM dynamically generates a coordination workflow for which the same structural guarantees apply. An open-source Python implementation of our framework is available as ZipperGen.

We compare lightweight automata-based models (n-grams) with neural architectures (LSTM, Transformer) for next-activity prediction in streaming event logs. Experiments on synthetic patterns and five real-world process mining datasets show that n-grams with appropriate context windows achieve comparable accuracy to neural models while requiring substantially fewer resources. Unlike windowed neural architectures, which show unstable performance patterns, n-grams provide stable and consistent accuracy. While we demonstrate that classical ensemble methods like voting improve n-gram performance, they require running many agents in parallel during inference, increasing memory consumption and latency. We propose an ensemble method, the promotion algorithm, that dynamically selects between two active models during inference, reducing overhead compared to classical voting schemes. On real-world datasets, these ensembles match or exceed the accuracy of non-windowed neural models with lower computational cost.

We introduce the problem of asymptotic subspace consensus, which requires the outputs of processes to converge onto a common subspace while remaining inside the convex hull of initial vectors.This is a relaxation of asymptotic consensus in which outputs have to converge to a single point, i.e., a zero-dimensional affine subspace. We give a complete characterization of the solvability of asymptotic subspace consensus in oblivious message adversaries. In particular, we show that a large class of algorithms used for asymptotic consensus gracefully degrades to asymptotic subspace consensus in distributed systems with weaker assumptions on the communication network. We also present bounds on the rate by which a lower-than-initial dimension is reached.

We study model checking for an epistemic metric temporal logic with past, interpreted over finite Büchi automata under synchronous perfect recall. The logic is motivated by observation-based verification problems such as diagnosis and opacity, where an observer sees only a projection of an execution and reasons about events that may have occurred earlier. These requirements use no alternation between different agents' knowledge. We therefore consider the agent-alternation-free fragment, in which nested knowledge operators must refer to the same agent. We show that model checking for this fragment is EXPSPACE-complete. The lower bound already holds with one agent, one occurrence of the knowledge operator, and no non-trivial metric bounds. For the upper bound, we combine temporal test automata with perfect-recall observers. Because past formulas may have different truth values on indistinguishable histories ending in the same system state, the observer must track temporal automaton states in addition to system states.

We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus. In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., Ω (√(nlog n)) , where n is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of Ω (n) . To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.

Permutation equivariance (PE) is a property widely present in mathematics and machine learning. Classic deep reinforcement learning (DRL) algorithms, such as Deep Q-Network (DQN), require thorough exploration of the state space to achieve optimal performance. For a PE problem such as the Multi-Armed Bandit (MAB), the PE property helps reduce the space that needs to be explored. This paper proposes PEDQN, a PE DRL framework based on DQN that applies a PE neural network structure. Our MAB experiments show that PEDQN has clear advantages over DQN with a fully connected network and achieves the same or better performance than UCB1 when tested in the same environment as the training. Additionally, PE-based architectures can adapt to varying input sizes, with pretrained models accelerating learning in new environments.

Biochemical Reaction Networks (BCRNs) model species and their interactions via reactions. They have been extensively used in chemistry and extended to biological settings by generalizing the reactions' kinetics. However, detailed models of biochemical processes tend to result in complex BCRN models. We present the Meta-species Oriented Biosystem Syntax (MobsPy), a language designed to simplify the modeling process using the concept of meta-species. Meta-species are constructed using a bottom-up approach from base species, which represent elementary, simple characteristics. These characteristics are then combined to create meta-species with all their complex behavior. The combined species have characteristics that are the Cartesian product of the base species' characteristics and feature inheritance of reactions involving the base species. New reactions can involve all the states of a meta-species or only a subset that is selected via a query. In particular, reactions of meta-species can express a state change of one of the reactants. MobsPy is deployed as a Python package. We showcase its modeling capabilities by building concise models for biochemical systems from the literature.

The Centralized Training with Decentralized Execution (CTDE) paradigm has gained significant attention in multi-agent reinforcement learning (MARL) and is the foundation of many recent algorithms. However, decentralized policies operate under partial observability and often yield suboptimal performance compared to centralized policies, while fully centralized approaches typically face scalability challenges as the number of agents increases. We propose Centralized Permutation Equivariant (CPE) learning, a centralized training and execution framework that employs a fully centralized policy to overcome these limitations. Our approach leverages a novel permutation equivariant architecture, Global-Local Permutation Equivariant (GLPE) networks, that is lightweight, scalable, and easy to implement. Experiments show that CPE integrates seamlessly with both value decomposition and actor-critic methods, substantially improving the performance of standard CTDE algorithms across cooperative benchmarks including MPE, SMAC, and RWARE, and matching the performance of state-of-the-art RWARE implementations.

Thresholded hybrid systems are restricted dynamical systems, where the current mode, and hence the ODE system describing its behavior, is solely determined by externally supplied digital input signals and where the only output signals are digital ones generated by comparing an internal state variable to a threshold value. An attractive feature of such systems is easy composition, which is facilitated by their purely digital interface. A particularly promising application domain of thresholded hybrid systems is digital integrated circuits: Modern digital circuit design considers them as a composition of Millions and even Billions of elementary logic gates, like inverters, OR and AND. Since every such logic gate is eventually implemented as an electronic circuit, however, which exhibits a behavior that is governed by some ODE system, thresholded hybrid systems are ideally suited for making the transition from the analog to the digital world rigorous. In this paper, we prove that the mapping from digital input signals to digital output signals is continuous for a large class of thresholded hybrid systems. Moreover, we show that, under some mild conditions regarding causality, this continuity also continues to hold for arbitrary compositions, which in turn guarantees that the composition faithfully captures the analog reality. By applying our generic results to some recently developed thresholded hybrid gate models, both for single-input single-output gates like inverters and for a two-input CMOS NOR gate, we show that they are continuous. Moreover, we provide a novel thresholded hybrid model for the two-input NOR gate, which is not only continuous but also, unlike the existing one, faithfully models all multi-input switching effects.

Biological systems are mastering the art of composing cells into colonies, tissues, and organisms. This article reviews striking similarities and differences between such biological systems and distributed computing systems, where computational units are composed to form larger systems with the goal of increasing computational power, enhancing system robustness, or overcoming spatial distances. A problem that recurs in many contexts in distributed systems is obtaining a consistent view of part of the system by its agents. Such problems, known as agreement problems in distributed computing, have been extensively studied across different computational models, varying, for example, in the extent to which the network is stable or dynamic. Motivated by the importance of agreement problems, we discuss examples ranging from simple to more complex cases, the latter in the context of optimization: agents solving graph optimization problems, searching for optima in arbitrary loss landscapes, and applying gradient-based techniques closely related to widely adopted artificial neural networks. We then discuss the reverse direction: distributed systems implemented with biological material. In particular, we detail a theoretical distributed computing model and algorithm targeted toward implementation in bacterial populations. We conclude with an outlook on what we consider the beginning of a promising intersection between distributed computing and biology, highlighting opportunities for both understanding natural systems and engineering novel distributed systems, both biological and in silico.

We present a Python-based framework for event-log prediction in streaming mode, enabling predictions while data is being generated by a business process. The framework allows for easy integration of streaming algorithms, including language models like n-grams and LSTMs, and for combining these predictors using ensemble methods. Using our framework, we conducted experiments on various well-known process-mining data sets and compared classical batch with streaming mode. Though, in batch mode, LSTMs generally achieve the best performance, there is often an n-gram whose accuracy comes very close. Combining basic models in ensemble methods can even outperform LSTMs. The value of basic models with respect to LSTMs becomes even more apparent in streaming mode, where LSTMs generally lack accuracy in the early stages of a prediction run, while basic methods make sensible predictions immediately.

Coordinated actions of cells in microbial communities and multicellular organisms enable them to perform complex tasks otherwise difficult for single cells. This has inspired biological engineers to build cellular consortia for larger circuits with improved functionalities while implementing communication systems for coordination among cells. Here, we investigate the signalling dynamics of a phage-mediated synthetic DNA messaging system and couple it with CRISPR interference to build distributed circuits that perform logic gate operations in multicellular bacterial consortia. We find that growth phases of both sender and receiver cells, as well as resource competition between them, shape communication outcomes. Leveraging the easy programmability of DNA messages, we build eight orthogonal signals and demonstrate that intercellular CRISPRi (i-CRISPRi) regulates gene expression across cells. Finally, we multiplex the i-CRISPRi system to implement several multicellular logic gates that involve up to seven cells and take up to three inputs simultaneously, with single- and dual-rail encoding: NOT, YES, AND and AND-AND-NOT. The communication system developed here lays the groundwork for implementing complex biological circuits in engineered bacterial communities, using phage signals for communication.

We provide a complete characterization of both uniform and non-uniform deterministic consensus solvability in distributed systems with benign process and communication faults using point-set topology. More specifically, we non-trivially extend the approach introduced by Alpern and Schneider in 1985, by introducing novel fault-aware topologies on the space of infinite executions: the process-view topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. Consensus is solvable in a given model if and only if the sets of admissible executions leading to different decision values is disconnected in these topologies. By applying our approach to a wide range of different applications, we provide a topological explanation of a number of existing algorithms and impossibility results and develop several new ones, including a general equivalence of the strong and weak validity conditions.