Model Medicine is the science of understanding, diagnosing, treating, and preventing disorders in AI models, grounded in the principle that AI models -- like biological organisms -- have internal structures, dynamic processes, heritable traits, observable symptoms, classifiable conditions, and treatable states. This paper introduces Model Medicine as a research program, bridging the gap between current AI interpretability research (anatomical observation) and the systematic clinical practice that complex AI systems increasingly require. We present five contributions: (1) a discipline taxonomy organizing 15 subdisciplines across four divisions -- Basic Model Sciences, Clinical Model Sciences, Model Public Health, and Model Architectural Medicine; (2) the Four Shell Model (v3.3), a behavioral genetics framework empirically grounded in 720 agents and 24,923 decisions from the Agora-12 program, explaining how model behavior emerges from Core--Shell interaction; (3) Neural MRI (Model Resonance Imaging), a working open-source diagnostic tool mapping five medical neuroimaging modalities to AI interpretability techniques, validated through four clinical cases demonstrating imaging, compari
Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of quantum systems. Their negative curvature, exponential volume growth, and non-Abelian translation symmetry make them fundamentally distinct from Euclidean lattices and give rise to rich geometry-dependent physics, but also hinder the direct application of well-established analytical and computational approaches originally developed for physical systems defined on Euclidean lattices. To establish a unified framework for geometry-dependent physics on Euclidean and hyperbolic lattices, we develop \textit{higher-order non-uniform cellular automata} (NUCA) as a local-to-global construction for translationally invariant regular lattices. This construction derives geometry-dependent update rules through a lattice-deforming procedure that embeds hyperbolic lattices into a Euclidean square lattice, thereby encoding hyperbolic geometry while preserving physical locality. It thus provides a systematic route toward quantum and classical physics on hyperbolic lattices. We demonstrate the framework in three applications
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.
The complexity of the cells can be described and understood by a number of networks such as protein-protein interaction, cytoskeletal, organelle, signalling, gene transcription and metabolic networks. All these networks are highly dynamic producing continuous rearrangements in their links, hubs, network-skeleton and modules. Here we describe the adaptation of cellular networks after various forms of stress causing perturbations, congestions and network damage. Chronic stress decreases link-density, decouples or even quarantines modules, and induces an increased competition between network hubs and bridges. Extremely long or strong stress may induce a topological phase transition in the respective cellular networks, which switches the cell to a completely different mode of cellular function. We summarize our initial knowledge on network restoration after stress including the role of molecular chaperones in this process. Finally, we discuss the implications of stress-induced network rearrangements in diseases and ageing, and propose therapeutic approaches both to increase the robustness and help the repair of cellular networks.
With the increasing interest in deploying Artificial Intelligence in medicine, we previously introduced HAIM (Holistic AI in Medicine), a framework that fuses multimodal data to solve downstream clinical tasks. However, HAIM uses data in a task-agnostic manner and lacks explainability. To address these limitations, we introduce xHAIM (Explainable HAIM), a novel framework leveraging Generative AI to enhance both prediction and explainability through four structured steps: (1) automatically identifying task-relevant patient data across modalities, (2) generating comprehensive patient summaries, (3) using these summaries for improved predictive modeling, and (4) providing clinical explanations by linking predictions to patient-specific medical knowledge. Evaluated on the HAIM-MIMIC-MM dataset, xHAIM improves average AUC from 79.9% to 90.3% across chest pathology and operative tasks. Importantly, xHAIM transforms AI from a black-box predictor into an explainable decision support system, enabling clinicians to interactively trace predictions back to relevant patient data, bridging AI advancements with clinical utility.
The Oxford English Dictionary defines precision medicine as "medical care designed to optimize efficiency or therapeutic benefit for particular groups of patients, especially by using genetic or molecular profiling." It is not an entirely new idea: physicians from ancient times have recognized that medical treatment needs to consider individual variations in patient characteristics. However, the modern precision medicine movement has been enabled by a confluence of events: scientific advances in fields such as genetics and pharmacology, technological advances in mobile devices and wearable sensors, and methodological advances in computing and data sciences. This chapter is about bandit algorithms: an area of data science of special relevance to precision medicine. With their roots in the seminal work of Bellman, Robbins, Lai and others, bandit algorithms have come to occupy a central place in modern data science ( Lattimore and Szepesvari, 2020). Bandit algorithms can be used in any situation where treatment decisions need to be made to optimize some health outcome. Since precision medicine focuses on the use of patient characteristics to guide treatment, contextual bandit algorith
Starting from the working hypothesis that both physics and the corresponding mathematics and in particular geometry have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of our ordinary continuum physics and mathematics living on a smooth background, and perhaps more importantly find a way how this continuum limit emerges from the mentioned discrete structure. We model this underlying substratum as a structurally dynamic cellular network (basically a generalisation of a cellular automaton). We regard these continuum concepts and continuum spacetime in particular as being emergent, coarse-grained and derived relative to this underlying erratic and disordered microscopic substratum, which we would like to call quantum geometry and which is expected to play by quite different rules, namely generalized cellular automaton rules. A central role in our analysis is played by a geometric renormalization group which creates (among other things) a kind of sparse translocal network of correlations between the points in classical continuous space-time and under
Medical image analysis plays a key role in precision medicine as it allows the clinicians to identify anatomical abnormalities and it is routinely used in clinical assessment. Data curation and pre-processing of medical images are critical steps in the quantitative medical image analysis that can have a significant impact on the resulting model performance. In this paper, we introduce a precision-medicine-toolbox that allows researchers to perform data curation, image pre-processing and handcrafted radiomics extraction (via Pyradiomics) and feature exploration tasks with Python. With this open-source solution, we aim to address the data preparation and exploration problem, bridge the gap between the currently existing packages, and improve the reproducibility of quantitative medical imaging research.
The minimal number of inputs in the local function of a non-trivial cellular automaton is two. Such a function can be viewed as as a kind of binary operation. If this operation is associative, it forms, together with the set of states, a semigroup. There are 18 semigroups of order 3 up to equivalence, and they define 18 cellular automata rules with three states. We investigate these rules with respect to solvability and show that all of them are solvable, meaning that the state of a given cell after $n$ iterations can be expressed by an explicit formula. We derive the relevant formulae for all 18 rules using some additional properties possessed by particular semigroups of order 3, such as commutativity and idempotence.
We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers needed for directing random walkers in the diffusion process are generated with the help of rule 30. This CA produces density profiles which agree very well with solutions of the diffusion equation, and we discuss this agreement for two different boundary and initial conditions. We also show how our construction can be generalized to higher dimensions.
Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases include finite fields, finite commutative rings and finite commutative groups. In this paper, we provide methods to generalize these results to the broader case of group cellular automata, that is, the case where the state set is a finite (possibly non-commutative) finite group. The configuration space is not even necessarily the full shift but a subshift -- called a group shift -- that is a subgroup of the full shift on Z^d, for any number d of dimensions. We show, in particular, that injectivity, surjectivity, equicontinuity, sensitivity and nilpotency are decidable for group cellular automata, and non-transitivity is semi-decidable. Injectivity always implies surjectivity, and jointly periodic points are dense in the limit set. The Moore direction of the Garden-of-Eden theorem holds for all group cellular automata, while the Myhill direction fails in some cases. The proofs are based on effective projection operations on group shifts that are, in
With the increasing demand for vehicular data transmission, limited dedicated cellular spectrum becomes a bottleneck to satisfy the requirements of all cellular vehicle-to-everything (V2X) users. To address this issue, unlicensed spectrum is considered to serve as the complement to support cellular V2X users. In this paper, we study the coexistence problem of cellular V2X users and vehicular ad-hoc network~(VANET) users over the unlicensed spectrum. To facilitate the coexistence, we design an energy sensing based spectrum sharing scheme, where cellular V2X users are able to access the unlicensed channels fairly while reducing the data transmission collisions between cellular V2X and VANET users. In order to maximize the number of active cellular V2X users, we formulate the scheduling and resource allocation problem as a two-sided many-to-many matching with peer effects. We then propose a dynamic vehicle-resource matching algorithm (DV-RMA) and present the analytical results on the convergence time and computational complexity. Simulation results show that the proposed algorithm outperforms existing approaches in terms of the performance of cellular V2X system when the unlicensed sp
Federated Learning (FL) has emerged as a promising solution for privacy-enhancement and latency minimization in various real-world applications, such as transportation, communications, and healthcare. FL endeavors to bring Machine Learning (ML) down to the edge by harnessing data from million of devices and IoT sensors, thus enabling rapid responses to dynamic environments and yielding highly personalized results. However, the increased amount of sensors across diverse applications poses challenges in terms of communication and resource allocation, hindering the participation of all devices in the federated process and prompting the need for effective FL client selection. To address this issue, we propose Cellular Automaton-based Client Selection (CA-CS), a novel client selection algorithm, which leverages Cellular Automata (CA) as models to effectively capture spatio-temporal changes in a fast-evolving environment. CA-CS considers the computational resources and communication capacity of each participating client, while also accounting for inter-client interactions between neighbors during the client selection process, enabling intelligent client selection for online FL processes
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjectivity and injectivity is also established. The final part studies a strong form of equicontinuity property specially suited for non-uniform cellular automata.
To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. We describe new functions and tools in DDLab to generate iso-groups and iso-rules, for multi-value as well as binary, in one, two and three dimensions. These methods include filing, filtering, mutating, analysing dynamics by input-frequency and entropy, identifying the critical iso-groups for glider-gun/eater dynamics, and automatically classifying iso-rule-space. We illustrate these ideas and methods for two dimensional CA on square and hexagonal lattices.
The success of precision medicine requires computational models that can effectively process and interpret diverse physiological signals across heterogeneous patient populations. While foundation models have demonstrated remarkable transfer capabilities across various domains, their effectiveness in handling individual-specific physiological signals - crucial for precision medicine - remains largely unexplored. This work introduces a systematic pipeline for rapidly and efficiently evaluating foundation models' transfer capabilities in medical contexts. Our pipeline employs a three-stage approach. First, it leverages physiological simulation software to generate diverse, clinically relevant scenarios, particularly focusing on data-scarce medical conditions. This simulation-based approach enables both targeted capability assessment and subsequent model fine-tuning. Second, the pipeline projects these simulated signals through the foundation model to obtain embeddings, which are then evaluated using linear methods. This evaluation quantifies the model's ability to capture three critical aspects: physiological feature independence, temporal dynamics preservation, and medical scenario d
Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical systems. Each of the 256 ECA is labeled as rule $X$, where $X$ is an integer between $0$ and $255$. An important property, that is usually overlooked in computational studies, is that the composition of any two one-dimensional cellular automata is again a one-dimensional cellular automaton. In this chapter, we begin a systematic study of the composition of ECA. Intuitively speaking, we shall consider that rule $X$ has low complexity if the compositions $X \circ Y$ and $Y \circ X$ have small minimal memory sets, for many rules $Y$. Hence, we propose a new classification of ECA based on the compositions among them. We also describe all semigroups of ECA (i.e., composition-closed sets of ECA) and analyze their basic structure from the perspective of semigroup theory. In particular, we determine that the largest semigroups of ECA have $9$ elements, and have a subsemigroup of order $8$ that is $\mathcal{R}$-trivial, property which has been recently used to
Sustained rhythmic oscillations, pulsing dynamics, emerge spontaneously when the local connection scheme is randomised in 3-value cellular automata that feature"glider" dynamics. Time-plots of pulsing measures maintain a distinct waveform for each glider rule, and scatter plots of entropy/density and the density return-map show unique signatures, which have the characteristics of chaotic strange attractors. We present case studies, possible mechanisms, and implications for oscillatory networks in biology.
We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing universality or may turn out to be "too hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing-completness.