Ensuring the safety of AI-enabled systems, particularly in high-stakes domains such as autonomous driving and healthcare, has become increasingly critical. Traditional formal verification tools fall short when faced with systems that embed both opaque, black-box AI components and complex stochastic dynamics. To address these challenges, we introduce LUCID (Learning-enabled Uncertainty-aware Certification of stochastIc Dynamical systems), a verification engine for certifying safety of black-box stochastic dynamical systems from a finite dataset of random state transitions. As such, LUCID is the first known tool capable of establishing quantified safety guarantees for such systems. Thanks to its modular architecture and extensive documentation, LUCID is designed for easy extensibility. LUCID employs a data-driven methodology rooted in control barrier certificates, which are learned directly from system transition data, to ensure formal safety guarantees. We use conditional mean embeddings to embed data into a Reproducing Kernel Hilbert Space (RKHS), where an RKHS ambiguity set is constructed that can be inflated to robustify the result to out-of-distribution behavior. A key innovation within LUCID is its use of a finite Fourier kernel expansion to reformulate a semi-infinite non-convex optimization problem into a tractable linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. LUCID thus offers a robust and efficient verification framework, able to handle the complexities of modern black-box systems while providing formal guarantees of safety. These unique capabilities are demonstrated on challenging benchmarks.

Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged as a key research focus in this rapidly evolving field. This paper explores Silq, a recent high-level quantum programming language, highlighting its strengths and unique features. We aim to share our insights on designing and implementing high-level quantum algorithms using Silq, demonstrating its practical applications and advantages for quantum programming.

Over the past 27 years, quantum computing has seen a huge rise in interest from both academia and industry. At the current rate, quantum computers are growing in size rapidly backed up by the increase of research in the field. Significant efforts are being made to improve the reliability of quantum hardware and to develop suitable software to program quantum computers. In contrast, the verification of quantum programs has received relatively less attention. Verifying programs is especially important in the quantum setting due to how difficult it is to program complex algorithms correctly on resource-constrained and error-prone quantum hardware. Research into creating verification frameworks for quantum programs has seen recent development, with a variety of tools implemented using a collection of theoretical ideas. This survey aims to be a short introduction into the area of formal verification of quantum programs, bringing together theory and tools developed to date. Further, this survey examines some of the challenges that the field may face in the future, namely the development of complex quantum algorithms.

The concept of barrier certificate has been developed recently in control theory to give formal guarantees on safety of a dynamical system. Neural mass models (NMMs) simulate the aggregated activity of neurons in the brain and have been used to model phenomena such as epilepsy. With a view to move towards novel treatments for epilepsy by investigating the application of control theory to epilepsy, we take one such NMM, the Wilson-Cowan (WC) model, and show that it is possible to automatically generate barrier certificates in both deterministic and non-deterministic cases, where the parameters of the model belong to an uncertainty set.

Microbial communities have vital roles in systems essential to human health and agriculture, such as gut and soil microbiomes, and there is growing interest in engineering designer consortia for applications in biotechnology (e.g., personalized probiotics, bioproduction of high-value products, biosensing). The capacity to monitor and model metabolite exchange in dynamic microbial consortia can provide foundational information important to understand the community level behaviors that emerge, a requirement for building novel consortia. Where experimental approaches for monitoring metabolic exchange are technologically challenging, computational tools can enable greater access to the fate of both chemicals and microbes within a consortium. In this study, we developed an in-silico model of a synthetic microbial consortia of sucrose-secreting Synechococcus elongatus PCC 7942 and Escherichia coli W. Our model was built on the NUFEB framework for Individual-based Modeling (IbM) and optimized for biological accuracy using experimental data. We showed that the relative level of sucrose secretion regulates not only the steady-state support for heterotrophic biomass, but also the temporal dynamics of consortia growth. In order to determine the importance of spatial organization within the consortium, we fit a regression model to spatial data and used it to accurately predict colony fitness. We found that some of the critical parameters for fitness prediction were inter-colony distance, initial biomass, induction level, and distance from the center of the simulation volume. We anticipate that the synergy between experimental and computational approaches will improve our ability to design consortia with novel function.

Despite increased understanding about psoriasis pathophysiology, currently there is a lack of predictive computational models. We developed a personalisable ordinary differential equations model of human epidermis and psoriasis that incorporates immune cells and cytokine stimuli to regulate the transition between two stable steady states of clinically healthy (non-lesional) and disease (lesional psoriasis, plaque) skin. In line with experimental data, an immune stimulus initiated transition from healthy skin to psoriasis and apoptosis of immune and epidermal cells induced by UVB phototherapy returned the epidermis back to the healthy state. Notably, our model was able to distinguish disease flares. The flexibility of our model permitted the development of a patient-specific "UVB sensitivity" parameter that reflected subject-specific sensitivity to apoptosis and enabled simulation of individual patients' clinical response trajectory. In a prospective clinical study of 94 patients, serial individual UVB doses and clinical response (Psoriasis Area Severity Index) values collected over the first three weeks of UVB therapy informed estimation of the "UVB sensitivity" parameter and the prediction of individual patient outcome at the end of phototherapy. An important advance of our model is its potential for direct clinical application through early assessment of response to UVB therapy, and for individualised optimisation of phototherapy regimes to improve clinical outcome. Additionally by incorporating the complex interaction of immune cells and epidermal keratinocytes, our model provides a basis to study and predict outcomes to biologic therapies in psoriasis.

Cyber-physical system models often feature stochastic behaviour that itself depends on uncertain parameters (e.g., transition rates). For these systems, verifying reachability amounts to computing a range of probabilities depending on how uncertainty is resolved. In general, this is a hard problem for which rigorous solutions suffer from the well-known curse of dimensionality. In this paper we focus on hybrid systems with random parameters whose distribution is subject to nondeterministic uncertainty. We show that for these systems the reachability probability is a smooth function of the nondeterministic parameters, and thus Gaussian processes can be used to approximate the reachability probability function itself very efficiently over its entire domain. Furthermore, we introduce a novel approach that exploits rigorous probability enclosures for training Gaussian processes. We apply our approaches to non-trivial hybrid systems case studies, and we empirically demonstrate their advantages with respect to standard statistical model checking.

We present NUFEB (Newcastle University Frontiers in Engineering Biology), a flexible, efficient, and open source software for simulating the 3D dynamics of microbial communities. The tool is based on the Individual-based Modelling (IbM) approach, where microbes are represented as discrete units and their behaviour changes over time due to a variety of processes. This approach allows us to study population behaviours that emerge from the interaction between individuals and their environment. NUFEB is built on top of the classical molecular dynamics simulator LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), which we extended with IbM features. A wide range of biological, physical and chemical processes are implemented to explicitly model microbial systems, with particular emphasis on biofilms. NUFEB is fully parallelised and allows for the simulation of large numbers of microbes (107 individuals and beyond). The parallelisation is based on a domain decomposition scheme that divides the domain into multiple sub-domains which are distributed to different processors. NUFEB also offers a collection of post-processing routines for the visualisation and analysis of simulation output. In this article, we give an overview of NUFEB's functionalities and implementation details. We provide examples that illustrate the type of microbial systems NUFEB can be used to model and simulate.

MOTIVATION: Biological systems are complex and challenging to model and therefore model reuse is highly desirable. To promote model reuse, models should include both information about the specifics of simulations and the underlying biology in the form of metadata. The availability of computationally tractable metadata is especially important for the effective automated interpretation and processing of models. Metadata are typically represented as machine-readable annotations which enhance programmatic access to information about models. Rule-based languages have emerged as a modelling framework to represent the complexity of biological systems. Annotation approaches have been widely used for reaction-based formalisms such as SBML. However, rule-based languages still lack a rich annotation framework to add semantic information, such as machine-readable descriptions, to the components of a model. RESULTS: We present an annotation framework and guidelines for annotating rule-based models, encoded in the commonly used Kappa and BioNetGen languages. We adapt widely adopted annotation approaches to rule-based models. We initially propose a syntax to store machine-readable annotations and describe a mapping between rule-based modelling entities, such as agents and rules, and their annotations. We then describe an ontology to both annotate these models and capture the information contained therein, and demonstrate annotating these models using examples. Finally, we present a proof of concept tool for extracting annotations from a model that can be queried and analyzed in a uniform way. The uniform representation of the annotations can be used to facilitate the creation, analysis, reuse and visualization of rule-based models. Although examples are given, using specific implementations the proposed techniques can be applied to rule-based models in general. AVAILABILITY AND IMPLEMENTATION: The annotation ontology for rule-based models can be found at http://purl.org/rbm/rbmo The krdf tool and associated executable examples are available at http://purl.org/rbm/rbmo/krdf CONTACT: [email protected] or [email protected].

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ δ-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for prostate cancer therapy.

We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an arbitrarily small interval which is guaranteed to contain the required probability. Standard (non-probabilistic) reachability is undecidable even for linear hybrid systems. In ProbReach we adopt the weaker notion of delta-reachability, in which the unsafe region is overapproximated by a user-defined parameter (delta). This choice leads to false alarms, but also makes the reachability problem decidable for virtually any hybrid system. In ProbReach we have implemented a probabilistic version of delta-reachability that is suited for hybrid systems whose stochastic behaviour is given in terms of random initial conditions. In this paper we introduce the capabilities of ProbReach, give an overview of the parallel implementation, and present results for several benchmarks involving highly non-linear hybrid systems.

In this paper we address the problem of verifying in stochastic hybrid systems temporal logic properties whose probability of being true is very small --- rare events. It is well known that sampling-based (Monte Carlo) techniques, such as statistical model checking, do not perform well for estimating rare-event probabilities. The problem is that the sample size required for good accuracy grows too large as the event probability tends to zero. However, several techniques have been developed to address this problem. We focus on importance sampling techniques, which bias the original system to compute highly accurate and efficient estimates. The main difficulty in importance sampling is to devise a good biasing density, that is, a density yielding a low-variance estimator. In this paper, we show how to use the cross-entropy method for generating approximately optimal biasing densities for statistical model checking. We apply the method with importance sampling and statistical model checking for estimating rare-event probabilities in stochastic hybrid systems coded as Stateflow/Simulink diagrams.

We show how statistical Model Checking can be used for verifying properties of analog circuits. As integrated circuit technologies scale down, manufacturing variations in devices make analog designs behave like stochastic systems. The problem of verifying stochastic systems is often difficult because of their large state space. Statistical Model Checking can be an efficient verification technique for stochastic systems. In this paper, we use sequential statistical techniques and model checking to verify properties of analog circuits in both the temporal and the frequency domain. In particular, randomly sampled system traces are sequentially generated by SPICE and passed to a trace checker to determine whether they satisfy a given specification, until the desired statistical strength is achieved.

We address the problem of model checking stochastic systems, i.e.~checking whether a stochastic system satisfies a certain temporal property with a probability greater (or smaller) than a fixed threshold. In particular, we present a novel Statistical Model Checking (SMC) approach based on Bayesian statistics. We show that our approach is feasible for hybrid systems with stochastic transitions, a generalization of Simulink/Stateflow models. Standard approaches to stochastic (discrete) systems require numerical solutions for large optimization problems and quickly become infeasible with larger state spaces. Generalizations of these techniques to hybrid systems with stochastic effects are even more challenging. The SMC approach was pioneered by Younes and Simmons in the discrete and non-Bayesian case. It solves the verification problem by combining randomized sampling of system traces (which is very efficient for Simulink/Stateflow) with hypothesis testing or estimation. We believe SMC is essential for scaling up to large Stateflow/Simulink models. While the answer to the verification problem is not guaranteed to be correct, we prove that Bayesian SMC can make the probability of giving a wrong answer arbitrarily small. The advantage is that answers can usually be obtained much faster than with standard, exhaustive model checking techniques. We apply our Bayesian SMC approach to a representative example of stochastic discrete-time hybrid system models in Stateflow/Simulink: a fuel control system featuring hybrid behavior and fault tolerance. We show that our technique enables faster verification than state-of-the-art statistical techniques, while retaining the same error bounds. We emphasize that Bayesian SMC is by no means restricted to Stateflow/Simulink models: we have in fact successfully applied it to very large stochastic models from Systems Biology.

BACKGROUND: Recent studies have found that overexpression of the High-mobility group box-1 (HMGB1) protein, in conjunction with its receptors for advanced glycation end products (RAGEs) and toll-like receptors (TLRs), is associated with proliferation of various cancer types, including that of the breast and pancreatic. RESULTS: We have developed a rule-based model of crosstalk between the HMGB1 signaling pathway and other key cancer signaling pathways. The model has been simulated using both ordinary differential equations (ODEs) and discrete stochastic simulation. We have applied an automated verification technique, Statistical Model Checking, to validate interesting temporal properties of our model. CONCLUSIONS: Our simulations show that, if HMGB1 is overexpressed, then the oncoproteins CyclinD/E, which regulate cell proliferation, are overexpressed, while tumor suppressor proteins that regulate cell apoptosis (programmed cell death), such as p53, are repressed. Discrete, stochastic simulations show that p53 and MDM2 oscillations continue even after 10 hours, as observed by experiments. This property is not exhibited by the deterministic ODE simulation, for the chosen parameters. Moreover, the models also predict that mutations of RAS, ARF and P21 in the context of HMGB1 signaling can influence the cancer cell's fate - apoptosis or survival - through the crosstalk of different pathways.

In this paper we aim at applying established formal methods techniques to a recent software area: quantum programming. In particular, we aim at providing a stepwise derivation of Grover's quantum search algorithm. Our work shows that, in principle, traditional software engineering techniques such as specification and refinement can be applied to quantum programs. We have chosen Grover's algorithm as an example because it is one of the two main quantum algorithms. The algorithm can find with high probability an element in an unordered array of length L in just O(radicL) steps (while any classical probabilistic algorithm needs Omega(L) steps). The derivation starts from a rigorous probabilistic specification of the search problem, then we stepwise refine that specification via standard refinement laws and quantum laws, until we arrive at a quantum program. The final program will thus be correct by construction.

In this paper a programming language, qGCL, is presented for the expression of quantum algorithms. It contains the features required to program a 'universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a refinement calculus supporting the verification and derivation of programs against their specifications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specification.