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Computation, mechanics and materials merge in biological systems, which can continually self-optimize through internal adaptivity across length scales, from cytoplasm and biofilms to animal herds. Recent interest in such material-based…
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Numerical optimization of complex systems benefits from the technological development of computing platforms in the last twenty years. Unfortunately, this is still not enough, and a large computational time is still necessary when…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
The rapidity and low power consumption of superconducting electronics makes them an ideal substrate for physical reservoir computing, which commandeers the computational power inherent to the evolution of a dynamical system for the purposes…
Quantum computers process information with the laws of quantum mechanics. Current quantum hardware is noisy, can only store information for a short time, and is limited to a few quantum bits, i.e., qubits, typically arranged in a planar…
A large multitude of scientific computing tools is available today. This article gives an overview of available tools and explains the main application fields. In addition basic principles of number representations in computing and the…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
We propose a modular quantum computation architecture based on utilizing multipartite entanglement. Each module consists of a small-scale quantum computer comprising data, memory and entangling qubits. Entangling qubits are used to…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
Computer modeling is essential to research on Advanced Accelerator Concepts (AAC), as well as to their design and operation. This paper summarizes the current status and future needs of AAC systems and reports on several key aspects of (i)…
Recent advances in metamaterials and fabrication techniques have revived interest in mechanical computing. Contrary to techniques relying on static deformations of buckling beams or origami-based lattices, the integration of wave scattering…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Qubit models and methods for improving the performance of software and hardware for analyzing digital devices through increasing the dimension of the data structures and memory are proposed. The basic concepts, terminology and definitions…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…