Related papers: The tile assembly model is intrinsically universal
Generic coarse-grained models are designed such that they are (i) simple and (ii) computationally efficient. They do not aim at representing particular materials, but classes of materials, hence they can offer insight into universal…
We show that neural networks trained by evolutionary reinforcement learning can enact efficient molecular self-assembly protocols. Presented with molecular simulation trajectories, networks learn to change temperature and chemical potential…
The fabrication of nanomaterials involves self-ordering processes of functional molecules on inorganic surfaces. To obtain specific molecular arrangements, a common strategy is to equip molecules with functional groups. However, focusing on…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
Turing presented a general representation scheme by which to achieve artificial intelligence - unorganised machines. Significantly, these were a form of discrete dynamical system and yet such representations remain relatively unexplored.…
Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and…
The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied Totally Asymmetric Exclusion…
Inspired by the quest for shape-shifting structures in a range of applications, we show how to create morphable structural materials using a neutrally stable unit cell as a building block. This unit cell is a self-stressed hinged structure…
Research in Artificial Intelligence (AI) has focused mostly on two extremes: either on small improvements in narrow AI domains, or on universal theoretical frameworks which are usually uncomputable, incompatible with theories of biological…
We introduce the Neural Field Turing Machine (NFTM), a differentiable architecture that unifies symbolic computation, physical simulation, and perceptual inference within continuous spatial fields. NFTM combines a neural controller,…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
We give a complete classification of the infinite dimensional tilting modules over a tame hereditary algebra R. We start our investigations by considering tilting modules of the form T=R_U\oplus R_U /R where U is a union of tubes, and R_U…
Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…
Filter synthesis is an inverse problem that is traditionally approached rationally by considering spatially disjoint resonators, approximating them as lumped elements, and engineering the coupling of selected pairs. This approach strongly…
Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional materials is a developing field and has already resulted in the discovery of several rich and…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
An integral self-affine tile is the solution of a set equation $\mathbf{A} \mathcal{T} = \bigcup_{d \in \mathcal{D}} (\mathcal{T} + d)$, where $\mathbf{A}$ is an $n \times n$ integer matrix and $\mathcal{D}$ is a finite subset of…
Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural…