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We present the results of an experimental project, made at the University of Calabria, which uses computer simulations and scientific computational systems in teaching and learning the fundamentals of analytic mechanics, in particular the classical Lagrangian and Hamiltonian formulation of the matter. Starting with examples of classical dynamical systems we also introduced students to appreciate chaos concepts going step by step to more complex settings. The success obtained with the use of computer-based methodologies has been very clear and the final students' tests confirm it. In this paper, in particular, we compare the results obtained by four groups of students: the first two attended such an experimental course and employed computer support for their individual work at home, while the learning environment of the second two groups (the control ones) was based only on traditional classroom lectures with paper and pencil home activities. If on the one hand a better overall performance of the first two groups was evident, it is very interesting (and not so easy) to investigate how much in quantity and quality, the learning of the experimental groups differs from that of the other groups, and why. For example, we illustrate some relevant differences between them in the comprehension of the studied phenomena, in dealing with and solving the proposed problems, and also in the individual development of further personal ideas.

To protect participants' confidentiality, blockchains can be outfitted with anonymization methods. Observations of the underlying network traffic can identify the author of a transaction request, although these mechanisms often only consider the abstraction layer of blockchains. Previous systems either give topological confidentiality that may be compromised by an attacker in control of a large number of nodes, or provide strong cryptographic confidentiality but are so inefficient as to be practically unusable. In addition, there is no flexible mechanism to swap confidentiality for efficiency in order to accommodate practical demands. We propose a novel approach, the neural fairness protocol, which is a blockchain-based distributed ledger secured using neural networks and machine learning algorithms, enabling permissionless participation in the process of transition validation while concurrently providing strong assurance about the correct functioning of the entire network. Using cryptography and a custom implementation of elliptic curves, the protocol is designed to ensure the confidentiality of each transaction phase and peer-to-peer data exchange. [ABSTRACT FROM AUTHOR]

Literature considers under the name "unimaginable numbers" any positive integer going beyond any physical application. One of the most known methodologies to conceive such numbers is using hyper-operations, that is a sequence of binary functions defined recursively starting from the usual chain: addition - multiplication - exponentiation. The most important notations to represent such hyper-operations have been considered by Knuth, Goodstein, Ackermann and Conway as described in this work's introduction. Within this work we will give an axiomatic setup for this topic, and then try to find on one hand other ways to represent unimaginable numbers, as well as on the other hand applications to computer science, where the algorithmic nature of representations and the increased computation capabilities of computers give the perfect field to develop further the topic, exploring some possibilities to effectively operate with such big numbers. In particular, we will give some axioms and generalizations for the up-arrow notation and, considering a representation via rooted trees of the hereditary base-n notation, we will determine in some cases an effective bound related to "Goodstein sequences" using Knuth's notation. Finally, we will also analyze some methods to compare big numbers, proving specifically a theorem about approximation using scientific notation and a theorem on hyperoperation bounds for Steinhaus-Moser notation. [ABSTRACT FROM AUTHOR]

In this paper, a set of local energetic indices for an urban water distribution system is proposed, together with a mathematical organization of the matter which is also able to incorporate many of the well known (global) indicators. In fact, arranged such incoming indices in vectors and drawing on some notions of linear algebra and vector calculus, they are placed at the starting point of a mathematical framework that seems never used before for engineering-hydraulic purposes. It is then told how such a study and local treatment of a water network can be very useful, accurate and rich in information, and can be considered as a natural and simple theoretical development of a common global vision generally pursued so far: in particular, it is shown how it is possible to recover from the drawn layout, through suitable formulas, some of the most known and mainly used energetic parameters in a very clear and effective way. [ABSTRACT FROM AUTHOR]

In the analysis of drinking Water Distribution Networks (WDNs), performance indices are widely used tools for obtaining synthetic information about the WDN operating regime (pressures and flows). This paper presents applications of a series of local surplus indices that act in a new mathematical framework. This framework allows reworking many well-known performance and energetic indices and simultaneously allowing analysis of specific aspects of the WDN. The analyses are carried out using different resolutive hydraulic approaches: the Demand-Driven Analysis (DDA) and the Pressure-Driven Analysis (PDA), typical of software such as EPANET and WaterNetGen. The authors analyse the hypotheses necessary for the application of these models, and how these influence the results of both the hydraulic modeling and the resilience indices assessment. In particular, two resilience indices are reformulated through the new local surplus indices and all of them are then simulated in different conditions for a water network known in literature as the Kang and Lansey WDN. The solving model assumption effects are deepen, reporting graphical and numerical results for different consumption scenarios and the different hydraulic approaches used. [ABSTRACT FROM AUTHOR]