For over a century, immunology has masterfully discovered and dissected the components of our immune system, yet its collective behavior remains fundamentally unpredictable. In this perspective, we argue that building on the learnings of reductionist biology and systems immunology, the field is poised for a third revolution. This new era will be driven by the convergence of purpose-built, large-scale causal experiments and predictive, generalizable AI models. Here, we propose the Predictive Immunology Loop as the unifying engine to harness this convergence. This closed loop iteratively uses AI to design maximally informative experiments and, in turn, leverages the resulting data to improve dynamic, in silico models of the human immune system across biological scales, culminating in a Virtual Immune System. This engine provides a natural roadmap for addressing immunology's grand challenges, from decoding molecular recognition to engineering tissue ecosystems. It also offers a framework to transform immunology from a descriptive discipline into one capable of forecasting and, ultimately, engineering human health.
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.
Lattice geometry profoundly shapes physical phenomena such as subsystem symmetry and directed percolation (DP). Among various lattice geometries, hyperbolic lattices are characterized by constant negative curvature and non-Abelian translation symmetry, offering a rich platform for investigating this geometry-physics interplay. However, the exponentially growing lattice size and nontrivial translation symmetry make approaches developed for Euclidean lattices incompatible, a limitation particularly evident in uniform cellular automata (CA). To resolve this, we develop a higher-order non-uniform cellular automata (NUCA) algorithm applicable to both translationally invariant regular Euclidean and hyperbolic lattices. In the algorithm, the non-uniform update rules incorporate nontrivial geometric data through a lattice-deforming procedure. We demonstrate the broad applicability of our algorithm to hyperbolic lattices through several applications on the hyperbolic $\{5,4\}$ lattice. By applying a linear NUCA, we generate subsystem symmetry-protected topological (SSPT) states and spontaneous subsystem symmetry-breaking states associated with regular or irregular subsystem symmetries unatt
Recent findings show that single, non-neuronal cells are also able to learn signalling responses developing cellular memory. In cellular learning nodes of signalling networks strengthen their interactions e.g. by the conformational memory of intrinsically disordered proteins, protein translocation, miRNAs, lncRNAs, chromatin memory and signalling cascades. This can be described by a generalized, unicellular Hebbian learning process, where those signalling connections, which participate in learning, become stronger. Here we review those scenarios, where cellular signalling is not only repeated in a few times (when learning occurs), but becomes too frequent, too large, or too complex and overloads the cell. This leads to desensitisation of signalling networks by decoupling signalling components, receptor internalization, and consequent downregulation. These molecular processes are examples of anti-Hebbian learning and forgetting of signalling networks. Stress can be perceived as signalling overload inducing the desensitisation of signalling pathways. Aging occurs by the summative effects of cumulative stress downregulating signalling. We propose that cellular learning desensitisation
For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained. In some cases, one can construct the solution formula for the initial value problem by analyzing the spatiotemporal pattern generated by the rule and decomposing it into simpler segments which one can then describe algebraically. We show an example of a rule when such approach is successful, namely elementary rule 156. Solution of the initial value problem for this rule is constructed and then used to compute the density of ones after $n$ iterations, starting from a random initial condition. We also show how to obtain probabilities of occurrence of longer blocks of symbols.
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
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.
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
Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as practical reasons. Our contribution solidifies this connection in the case of non-uniform CAs (nuCAs), simulating a global update in the architecture of the Python package TensorFlow. Additionally, we demonstrate how the highly optimised out-of-the-box multiprocessing in TensorFlow offers interesting computational benefits, especially when simulating large numbers of nuCAs with many cells.
We offer detailed proofs of some properties of the Rule 60 cellular automaton on a ring with a Mersenne number circumference. We then use these properties to define a propagator, and demonstrate its use to construct all the ground state configurations of the classical Newman-Moore model on a square lattice of the same size. In this particular case, the number of ground states is equal to half of the available spin configurations in any given row of the lattice.
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
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is that this modification not always goes in the sense of decreasing the entropy.
In a recent paper Sutner proved that the first-order theory of the phase-space $\mathcal{S}_\mathcal{A}=(Q^\mathbb{Z}, \longrightarrow)$ of a one-dimensional cellular automaton $\mathcal{A}$ whose configurations are elements of $Q^\mathbb{Z}$, for a finite set of states $Q$, and where $\longrightarrow$ is the "next configuration relation", is decidable. He asked whether this result could be extended to a more expressive logic. We prove in this paper that this is actuallly the case. We first show that, for each one-dimensional cellular automaton $\mathcal{A}$, the phase-space $\mathcal{S}_\mathcal{A}$ is an omega-automatic structure. Then, applying recent results of Kuske and Lohrey on omega-automatic structures, it follows that the first-order theory, extended with some counting and cardinality quantifiers, of the structure $\mathcal{S}_\mathcal{A}$, is decidable. We give some examples of new decidable properties for one-dimensional cellular automata. In the case of surjective cellular automata, some more efficient algorithms can be deduced from results of Kuske and Lohrey on structures of bounded degree. On the other hand we show that the case of cellular automata give new results
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.
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.
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new type of cellular automata networks uses local rules with a fraction of long-range shortcuts derived from the properties of small-world networks. Simulations show that the self-organized criticality emerges naturally in the system for a given probability of shortcuts and transition occurs as the probability increases to some critical value indicating the small-world behaviour of the complex automata networks. Pattern formation of cellular automata networks and the comparison with equation-based reaction-diffusion systems are also discussed
Cellular vehicle-to-everything (V2X) communication is expected to herald the age of autonomous vehicles in the coming years. With the integration of blockchain in such networks, information of all granularity levels, from complete blocks to individual transactions, would be accessible to vehicles at any time. Specifically, the blockchain technology is expected to improve the security, immutability, and decentralization of cellular V2X communication through smart contract and distributed ledgers. Although blockchain-based cellular V2X networks hold promise, many challenges need to be addressed to enable the future interoperability and accessibility of such large-scale platforms. One such challenge is the offloading of mining tasks in cellular V2X networks. While transportation authorities may try to balance the network mining load, the vehicles may select the nearest mining clusters to offload a task. This may cause congestion and disproportionate use of vehicular network resources. To address this issue, we propose a game-theoretic approach for balancing the load at mining clusters while maintaining fairness among offloading vehicles. Keeping in mind the low-latency requirements of
An important question to be addressed regarding system control on a time interval $[0, T]$ is whether some particular target state in the configuration space is reachable from a given initial state. When the target of interest refers only to a portion of the spatial domain, we speak about regional analysis. Cellular Automata (CA) approach have been recently promoted for the study of control problems on spatially extended systems for which the classical approaches cannot be used. An interesting problem concerns the situation where the subregion of interest is not interior to the domain but a portion of its boundary. In this paper we address the problem of regional controllability of cellular automata via boundary actions, i.e., we investigate the characteristics of a cellular automaton so that it can be controlled inside a given region only acting on the value of sites at its boundaries.
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.
Numerous biological functions-such as enzymatic catalysis, the immune response system, and the DNA-protein regulatory network-rely on the ability of molecules to specifically recognize target molecules within a large pool of similar competitors in a noisy biochemical environment. Using the basic framework of signal detection theory, we treat the molecular recognition process as a signal detection problem and examine its overall performance. Thus, we evaluate the optimal properties of a molecular recognizer in the presence of competition and noise. Our analysis reveals that the optimal design undergoes a "phase transition" as the structural properties of the molecules and interaction energies between them vary. In one phase, the recognizer should be complementary in structure to its target (like a lock and a key), while in the other, conformational changes upon binding, which often accompany molecular recognition, enhance recognition quality. Using this framework, the abundance of conformational changes may be explained as a result of increasing the fitness of the recognizer. Furthermore, this analysis may be used in future design of artificial signal processing devices based on bio