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Q-variance (so-called) posits a statistical relationship $\mathbf{E}(Ο^2 | z) = Ο_0^2 + \tfrac{1}{2}z^2$ between an asset's volatility $Ο^2$, as observed in a time interval $T$, and its (suitably scaled) return $z$ in the same interval. We here show that this relationship is {\em exactly equivalent} to to positing aβ¦
We address the two issues raised by Bayle, Vallisneri, Babak, and Petiteau (in their gr-qc document arXiv:2106.03976) about our matrix formulation of Time-Delay Interferometry (TDI) (arXiv:2105.02054) \cite{TDJ21}. In so doing we explain and quantify our concerns about the results derived by Vallisneri, Bayle, Babak anβ¦
The mathematical concept of q-deformations, in particular the one of qnumbers, is used to study the genetic code(s). After considering two kinds of q-numbers, for comparison, a phenomenological classification scheme of the genetic code together with its numerous minor variants is, first, established. Next, numbers descβ¦
In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation is assumed to depend on the "distance" between the codons. Preliminary general pβ¦
Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been studied in particular due to its simple form and versatility. However, these dynamic cβ¦
This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric model with a probabilistic model in a principled way. For simplicity, the geometβ¦
In the quiet backwaters of cs.CV, cs.LG and stat.ML, a cornucopia of new learning systems is emerging from a primordial soup of mathematics-learning systems with no need for external supervision. To date, little thought has been given to how these self-supervised learners have sprung into being or the principles that gβ¦
The problem of the determinism of Quantum Mechanics has been a main one during the 20th century. At the same time, in the context of Logic and Set Theory, the importance of ancient paradoxes as well as the appearance of many new ones, has shed light on and deeply influenced the foundations of Mathematics and somehow ofβ¦
The purpose of this paper is both to provide mathematical reinforcements to the paper [Mecozzi and Bellini : arXiv:1110.1253 [hep-ph]] by taking decoherence into consideration and to present some important problems related. We claim that neutrinos have superluminality as a latent possibility.β¦
We present a new explanation for a quantum eraser. Mathematical description of the traditional explanation needs quantum-superposition states. However, the phenomenon can be explained without quantum-superposition states by introducing unobservable potentials which can be identified as an indefinite metric vector. In aβ¦