Related papers: Asymptotic Intrinsic Universality and Reprogrammab…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
This study focuses on finite-sample inference on the non-linear Bures-Wasserstein manifold and introduces a generalized bootstrap procedure for estimating Bures-Wasserstein barycenters. We provide non-asymptotic statistical guarantees for…
In this essay, I argue that explicit ethical machines, whose moral principles are inferred through a bottom-up approach, are unable to replicate human-like moral reasoning and cannot be considered moral agents. By utilizing Alan Turing's…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Recent breakthroughs in AI capability have been attributed to increasingly sophisticated architectures and alignment techniques, but a simpler principle may explain these advances: memory makes computation universal. Memory enables…
This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…
We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin's Omega number, halting probability, and program-size complexity. A classification of Turing machines…
Human behavior modeling is important for the design and implementation of human-automation interactive control systems. In this context, human behavior refers to a human's control input to systems. We propose a novel method for human…
The Turing Machine is the paradigmatic case of computing machines, but there are others such as analogical, connectionist, quantum and diverse forms of unconventional computing, each based on a particular intuition of the phenomenon of…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
In 1950, Alan Turing proposed replacing the question "Can machines think?" with a behavioral test: if a machine's outputs are indistinguishable from those of a thinking being, the question of whether it truly thinks can be set aside. This…
Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…