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Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…
Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular…
Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to…
Through periodic Training we can gradually buildup a reproducible responses in a disordered system where plasticity dominates over elasticity as is known in classical amorphous materials and soft matter 1, 6. Here we show that a similar…
Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This…
Soft machines display shape adaptation to external circumstances due to their intrinsic compliance. To achieve increasingly more responsive behaviors upon interactions without relying on centralized computation, embodying memory directly in…
We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
The motion of particles suspended in environmental turbulence is relevant to many scientific fields, from sediment transport to biological interactions to underwater robotics. At very small scales and simple shapes, we are able to…
Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for…
Studies of random organization models of monodisperse spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent…
In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations…
Masked generative models (MGMs) can generate tokens in parallel and in any order, unlike autoregressive models (ARMs), which decode one token at a time, left-to-right. However, MGMs process the full-length sequence at every sampling step,…
We consider a discrete system of $n$ simple indistinguishable devices, called \emph{agents}, forming a \emph{connected} shape $S_I$ on a two-dimensional square grid. Agents are equipped with a linear-strength mechanism, called a \emph{line…
We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary…
We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold…
We study a minimal cognitive flocking model, which assumes that the moving entities navigate using exclusively the available instantaneous visual information. The model consists of active particles, with no memory, that interact by a…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…