This article introduces the Ω counter, a frequency counter -- or a frequency-to-digital converter, in a different jargon -- based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the Ω counter on rigorous mathe…
In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true, it would represent a major fundamental breakthrough in comp…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in quantum protocols. The mathematical setting stipulates that the me…
The data describing a process of echo-image formation in bottlenose dolphin sonar perception were accumulated in our experimental explorations. These data were formalized mathematically and used in the computational model, comparative testing of which in echo-discrimination tasks revealed no less ca…
Q-variance (so-called) posits a statistical relationship $\mathbf{E}(σ^2 | z) = σ_0^2 + \tfrac{1}{2}z^2$ between an asset's volatility $σ^2$, 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 equivale…
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 Vallisn…
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…
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. P…
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. Howe…
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 si…