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Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
We show how to efficiently solve problems involving a quantitative measure, here called energy, as well as a qualitative acceptance condition, expressed as a B\"uchi or Parity objective, in finite weighted automata and in one-clock weighted…
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
This note is a contribution to the debate about the optimal algorithm for Economic Complexity that recently appeared on ArXiv [1, 2] . The authors of [2] eventually agree that the ECI+ algorithm [1] consists just in a renaming of the…
This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…
The optimization of Kernel-Target Alignment (TA) has been recently proposed as a way to reduce the number of hardware resources in quantum classifiers. It allows to exchange highly expressive and costly circuits to moderate size, task…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
A fitness landscape is a genetic space -- with two genotypes adjacent if they differ in a single locus -- and a fitness function. Evolutionary dynamics produce a flow on this landscape from lower fitness to higher; reaching equilibrium only…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
In this work, we formulate a new multi-task active learning setting in which the learner's goal is to solve multiple matrix completion problems simultaneously. At each round, the learner can choose from which matrix it receives a sample…
Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…
We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground state manifold of such models can be…
A key part of any evolutionary algorithm is fitness evaluation. When fitness evaluations are corrupted by noise, as happens in many real-world problems as a consequence of various types of uncertainty, a strategy is needed in order to cope…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions. We characterize safe and unsafe system states. We show that it is easy to recognize system…