Thomas Nowak

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 calls, tool calls, and human control points, whose outcomes 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.

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.

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.

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.