Bottom-up assembly of DNA nanostructures have been proposed for a variety of biotech uses ranging from targeted drug delivery to scaffolding of new materials. Units based on the rationally-designed 3D DNA motif, the tensegrity triangle, provide a wide range of DNA crystallographic assemblies. The sequence design possibilities of these building blocks give ever-increasing geometric complexities to form vast arrays of three-dimensional structures. We show an experimentally verified mathematical model that explains occurrences of diverse chiral topologies within the crystals. We also present methods based on periodic graphs and topological graph theory that enable design and analysis of various crystallographic constructs..

Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We examine what properties of uniform CA can be recovered by restricting the rule distribution to be (uniformly) recurrent, focusing on only 1D NUCA.

We show that a bijective NUCA with a uniformly recurrent rule distribution is reversible. We also show that if a NUCA is surjective and has a recurrent rule distribution, or if it is bijective, then it is balanced. We present an example of a NUCA which has a non-empty and non-residual set of equicontinuity points, and one which is not sensitive but has no equicontinuity points. Finally, we show that (positively) expansive NUCA are sensitive.

One of the most fundamental problems in tiling theory is the domino problem: given a set of tiles and tiling rules, decide if there exists a way to tile the plane. The problem is known to be undecidable in general.
In this paper, we focus on Wang tilesets.
We prove that the domino problem is decidable for robust tilesets, \emph{i.e.} tilesets that either cannot tile the plane or can by provably satisfying some particular invariant.
We establish that several famous tilesets considered in the literature are robust. We give arguments this is true for all tilesets unless they are produced from non-robust Turing machines: a Turing machine is said to be non-robust if it does not halt and furthermore does so non-provably.
As a side effect of our work, we provide a sound, relatively complete method for proving that a tileset can tile the plane.
Our analysis also provides explanations for the similarities between proofs in the literature for various tilesets, as well as of phenomena that have been observed experimentally in the systematic study of tilesets using computer methods.

In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a collection of Boolean entities (the automata) update their state depending on the states of others. Fixed points represent phenotypes such as cell differentiation. The interaction graph of a BAN captures the architecture of dependencies among its automata. A first seminal result is that cycles of interactions (so called feedbacks) are the engines of dynamical complexity. A second seminal result is that fixed points are invariant under block-sequential update modes, which update the automata following an ordered partition of the set of automata. In this article we study the ability of block-parallel update modes (dual to the latter) to break this fixed point invariance property, with a focus on the simplest feedback mechanism: the canonical positive cycle. We quantify numerically the creation of new fixed points, and provide families of block-parallel update modes generating exponentially many fixed points on this elementary structure of interaction.

Spiking neural P systems (SNP systems) in a formal way reflect the network of neurons communicating by electrical signal called spikes. Inspired by recent research in neuroscience investigating extrasynaptic activities of neurons using neuropeptides as signals, just recently wireless SNP systems (WSNP systems) have beennintroduced. In WSNP systems no direct communication structure for spikes as in
standard SNP systems is used; instead the neurons communicate by taking the spikes sent to the environment. Regular expressions associated with the rules in each neuron control their applicability. In the previous papers dealing with WSNP systems, finite input filters were used to control which packages of spikes are allowed to enter the neuron. In this paper, we now show that computational completeness can even be obtained by not using input filters any more. Moreover, we show that WSNP systems without input filters can be interpreted as a special normal
form of extended spiking neural P systems (ESNP systems). Finally we discuss how strings can be generated by WSNP systems without input filters.

The rapid and exponential growth of digital data - 90% of which has been generated in the last two years - poses a significant challenge for long-term storage due to limited resources, energy consumption, and the short lifespan of conventional storage media. Moreover, about 70% of this data is “cold,” rarely accessed and needing preservation for 10 years or more, further highlighting the need for durable and scalable storage solutions.
Recent advances identify DNA as a highly promising medium for next-generation data storage, offering an extraordinary theoretical capacity of up to 215 petabytes per gram and the potential for data stability over centuries through synthetic DNA encapsulated in specialized microcapsules. Retrieval is enabled by advanced sequencing technologies.
This presentation will review the current state of the art in DNA-based data storage, with a particular focus on the efficient compression and encoding of digital data into the quaternary code of DNA’s four nucleotides -Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). We will introduce JPEG DNA, an emerging standard specifically designed for image compression and coding tailored to DNA’s unique biochemical constraints.
We will also talk about the French initiative, the PEPR MoleculArXiv, which aims to bring together all French academic laboratories working in the field to build a DNA data storage proof of concept capable of writing 10 GB of data per day.

We introduce a framework that connects two discrete models of natural computing, cellular automata (CA) and reaction systems (RS). We define pattern graphs of a CA as one-out digraphs where vertices correspond to totally periodic configurations and edges reflect CA evolution. Using pattern graphs based on periodic configurations we show that every one-dimensional binary CA can be transformed into an RS via its zero-context graph and provide counterexamples for the converse. Modified techniques, such as increasing the number of states and subgraphs of pattern graphs, are used to transform arbitrary RS into CA.

We consider 2-state reversible gates that route tokens from input wires to output wires. Also known as Reversible Logic Elements with Memory (RLEMs), such gates have been studied extensively by Kenichi Morita and his co-authors. Through a series of results, they have shown that all non-degenerate 2-state RLEMs with ≥ 3 inputs are universal, meaning any of them can be used to build any other RLEM of any size and number of states. There are only four non-trivial gates with < 3 inputs, three of which have been proven to be non-universal. The one remaining gate, known as 2-17, has been conjectured to also be non-universal, but this has remained an open question since 2012.
Here we resolve this open question by showing that this extremely simple gate is in fact universal. This makes it the smallest universal reversible gate, and we name it the Morita gate in honor of Morita’s extensive foundational work in this area.

Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this simplicity leads to rich and diverse dynamical behaviors. CCAs have found applications in numerous scientific fields, including quantum computing, biology, social sciences, and cryptography. However, traditional CCAs assume complete certainty in the state of all cells, which limits their ability to model systems with inherent uncertainty. This paper introduces a novel generalization of CCAs, termed Cellular Automata on Measures (CAMs), which extends the classical framework to incorporate probabilistic uncertainty. In this setting, the state of each cell is described by a probability measure, and the local rule operates on configurations of such measures. In this paper, we provide a rigorous mathematical foundation for CAMs. This study lays the groundwork for future exploration of CAMs, offering a flexible and robust framework for modeling uncertainty in cellular automata and opening new directions for both theoretical analysis and practical applications.

This short paper is about the behavior of the cellular automaton (CA) obtained by the composition of two or more cellular automata. The general question we aim to face is: what is the relationship between a certain dynamical property of the CA obtained by the composition and the same (or other) property of each single CA appearing in the composition?

This work presents a fully integrated 45 nm CMOS System-on-Chip receiver designed for high-fidelity readout of transmon qubits. The study is structured in two main parts. The first focuses on quantum theoretical modelling, investigating the entanglement dynamics generated by transmon qubits coupled to transmission lines beside designing a novel Josephson Parametric Amplifier. The proposed JPA achieves a gain exceeding 24 dB and a compression point (P1dB) better than -92 dBm, operating effectively at cryogenic temperatures (~10 mK) to amplify ultra-low quantum signals. The second part addresses the analog readout circuitry that captures and processes the quantum chip output. This section includes a low-noise amplifier, a wideband voltage-controlled oscillator, a mixer, and an intermediate-frequency amplifier—all operating at room temperature. The system delivers a clean 200 MHz output suitable for digitization. Post-layout simulations demonstrate excellent noise performance (NF < 0.7 dB), high linearity, and broad frequency tunability, confirming the viability of the design for scalable quantum measurement applications.

We explore the application of the QUBO and Ising models to the integer factorization problem with implications for the security of public-key algorithms such as RSA. A key contribution is a program that applies existing algorithms to parameterize and simulate integer factorization through an Ising model in order to replicate previous works. Due to limited access to quantum hardware, we use classical heuristic methods to approximate solutions.

In classical computing, multiple different types of memory are used, such as read-only, or read/write, but a write-only memory is trivial, and cannot affect the output of a computation. In contrast, a write-only memory can play a non-trivial role in a quantum computation. In fact, it is frequently used in quantum algorithms, including in well known examples like factoring and phase estimation. Understanding how a quantum write-only memory works is helpful for the design of new algorithms, such as for simulating nonlinear differential equations.