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Some Fundamentals of Mathematics of Blockchain
This book provides a foundation for the mathematics of blockchain. It is inspired by a general analysis and synthesis of the current knowledge of blockchain technology and starts by laying a foundation for the mathematics of blockchain. The aim is for research in the area of blockchain to lead their study from the construction highlighted in this book. First, the basis of a blockchain is set: block, transaction contents, block header, Merkle tree, nonce, Proof-of-Work. Connections with elliptic curves and cryptographic signatures are made. Second, the book ties this with a Graph and Matrix Theories approach and models the peer-to-peer relationship through the Bitcoin Network. Third, it is proposed further modelling, notably around halving, optimal storing, or diffusion of information, which are consequences of the mathematical foundation. The notion of Entropy of Privacy and the Particles model are introduced. Finally, the mathematical statements therein are proven and essential reminders can be found before each section, so the content can be accessible from a graduate level.
Computational and Mathematical Methods for Data Analysis in Biology and Finance
Mathematics are understood as a set of abstract ideas, in the measure of the real world - or reality - has no way to intervene. However, some observable mathematical facts in experimental or simulated data can be counter-intuitive. The PhD is divided into two parts: first, we mathematically study the matrices of the same type of the ones in biology and finance. In particular, we show the following counter-intuitive fact: for these matrices, the eigenvector associated with the highest eigenvalue is close to the sum of each row, column by column. We also discuss some applications to graph theory with many numerical simulations and data analysis.On the other hand, we will face the genetic contact problem: from a contact map, a real current challenge is to find the DNA 3D-structure. We propose several matrix analysis methods, which one show disjoinct areas in the nucleus where the DNA interactions are different. These areas are nuclear compartments. With other biological features, we characterize the biological function of each of the compartments. The analysis tools are the ones already used in finance to analyze the autocorrelation matrices, or even time series.
La définition de soi
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Il pendio dei noci
1918. Il sergente Julien Vertou osserva la neve che ancora ricopre il monte Grappa, in un aprile senza primavera. Lì dove si è spostata l'ultima linea di difesa italiana dopo Caporetto, gli alpini del battaglione Susa hanno allestito il loro campo. Ma Julien non è uno di loro, la cicatrice sulla mano destra racconta un'altra storia. Negli ultimi sedici anni, la Legione Straniera è stata il suo rifugio e la sua penitenza. Ciò che è stato prima non ha più importanza. Sono perduti i sogni, ed è perduto l'amore, che per una breve stagione gli ha fatto credere di poter inventare il futuro. La guerra che ha conosciuto sull'Atlante aveva una sola regola: uccidere per non farsi uccidere. Ma ...
Forms of Faith in Sixteenth-century Italy
This interdisciplinary volume gathers essays by leading international scholars in the fields of Italian Renaissance literature, music, history and history of art to address the fertile question of the relationship between religious change and shifting cultural forms in sixteenth-century Italy. Each contribution examines the effects of the profound religious changes that took place in the period on cultural forms, seeking to establish an 'aesthetics of reform' for the sixteenth century.
