Science Papers

                             

1. New Challenges for Classical and Quantum Probability

Source: Entropy, MDPI

Abstract: The discovery that any classical random variable with all moments gives rise to a full quantum theory (that in the Gaussian and Poisson cases coincides with the usual one) implies that a quantum–type formalism will enter into practically all applications of classical probability and
statistics. The new challenge consists in finding the classical interpretation, for different types of classical contexts, of typical quantum notions such as entanglement, normal order, equilibrium states, etc. As an example, every classical symmetric random variable has a canonically associated conjugate momentum. In usual quantum mechanics (associated with Gaussian or Poisson classical random
variables), the interpretation of the momentum operator was already clear to Heisenberg. How should we interpret the conjugate momentum operator associated with classical random variables outside the Gauss–Poisson class? The Introduction is intended to place in historical perspective the recent developments that are the main object of the present exposition.

 

2. Learning From Pseudo-Randomness With an Artificial Neural Network—Does God Play Pseudo-Dice?

Source: IEEE

ABSTRACT Inspired by the fact that the neural network, as the mainstream method for machine learning, has brought successes in many application areas, here we propose to use this approach for decoding hidden correlation among pseudo-random data and predicting events accordingly. With a simple neural network structure and a typical training procedure, we demonstrate the learning and prediction power of the neural network in pseudo-random environments. Finally, we postulate that the high sensitivity and efficiency of the neural network may allow learning on a low-dimensional manifold in a high-dimensional space of pseudo-random events and critically test, if there could be any fundamental difference between quantum randomness and pseudo randomness, which is equivalent to the classic question: Does God play dice? (Note that this analogy was first made by Einstein in his famous quotation ‘‘God does not play dice with the universe’’. He believed in laws of nature, and hence, the meaning of God in this context was some mechanism responsible for the ways by which the universe evolves.) 

 

3. A neural network oracle for quantum nonlocality problems in networks

Source: Nature, Quantum Information

Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed probability distribution can be reproduced using only classical resources. This causal inference task is challenging even for simple networks, both analytically and using standard numerical techniques. We propose to use neural networks as numerical tools to overcome these challenges, by learning the classical strategies required to reproduce a distribution. As such, a neural network acts as an oracle for an observed behavior, demonstrating that it is classical if it can be learned. We apply our method to several examples in the triangle configuration. After demonstrating that the method is consistent with previously known results, we give solid evidence that a quantum distribution recently proposed by Gisin is indeed nonlocal as conjectured. Finally we examine the genuinely nonlocal distribution recently presented by Renou et al., and, guided by the findings of the neural network, conjecture nonlocality in a new range of parameters in these distributions. The method allows us to get an estimate on the noise robustness of all examined distributions.

 

4. Fractal Nature Bridge between Neural Networks and Graph Theory Approach within Material Structure Characterization 

Source: MDPI

Abstract: Many recently published research papers examine the representation of nanostructures and biomimetic materials, especially using mathematical methods. For this purpose, it is important that the mathematical method is simple and powerful. Theory of fractals, artificial neural networks
and graph theory are most commonly used in such papers. These methods are useful tools for applying mathematics in nanostructures, especially given the diversity of the methods, as well as their compatibility and complementarity. The purpose of this paper is to provide an overview of
existing results in the field of electrochemical and magnetic nanostructures parameter modeling by applying the three methods that are “easy to use”: theory of fractals, artificial neural networks and graph theory. We also give some new conclusions about applicability, advantages and disadvantages in various different circumstances.

  

Photo Courtesy of Solvay Conference 1927, Wikimedia Commons