Related papers: Universal Computation Is 'Almost Surely' Chaotic
Today's most popular CPU can operate in two different computational modes for double precision computations. This fact is not very widely recognized among scientific computer users. The present paper reports the differences the modes bring…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
Although the emergence of a fully-functional quantum computer may still be far away from today, in the near future, it is possible to have medium-size, special-purpose, quantum devices that can perform computational tasks not efficiently…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
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…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantum computation increases by decreasing…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis:…