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We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
In the Quantum Supremacy regime, quantum computers may overcome classical machines on several tasks if we can estimate, mitigate, or correct unavoidable hardware noise. Estimating the error requires classical simulations, which become…
Approximate Bayesian Computation (ABC) is a family of statistical inference techniques, which is increasingly used in biology and other scientific fields. Its main benefit is to be applicable to models for which the computation of the model…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
In this review, we assess the use of Bayesian methods in model predictive control (MPC), focusing on neural-network-based modeling, control design, and uncertainty quantification. We systematically analyze individual studies and how they…
Recent advances in machine learning for medical imaging have led to impressive increases in model complexity and overall capabilities. However, the ability to discern the precise information a machine learning method is using to make…
Catastrophic forgetting has been the leading issue in the domain of lifelong learning in artificial systems. Current artificial systems are reasonably good at learning domains they have seen before; however, as soon as they encounter…
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…
We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases of the Bayesian posterior of a synthesis problem. This new…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
We show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective…
Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical"…
Computer models are widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical…
Can a Turing Machine simulate the human mind? If the Church-Turing thesis is assumed to be true, then a Turing Machine should be able to simulate the human mind. In this paper, I challenge that assumption by providing strong mathematical…