Related papers: Rotations and Statistics
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
The bending of lightrays by the gravitational field of a ``lens'' that is moving relative to the observer is calculated within the approximation of weak fields, small angles and thin lenses. Up to first order in $v/c$ -- and assuming the…
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These…
The effects on the spin state of an electron in a time independent electric field are examined. The probability of spin flipping is calculated, and other effects are studied using the minimally coupled Dirac equation.
A new modelling approach shows how the Earth's hidden vibrations may drive global weather dynamics and atmospheric pressure variations, hinting that the planet's own beat could be imprinted on our climate. The atmospheric rotational…
The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the…
Using experimental techniques, we study properties of the "circumcenter map", which, upon $n$ iterations sends an $n$-gon to a scaled and rotated copy of itself. We also explore the topology of area-expanding and area-contracting regions…
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
We evaluate determinants of "spiral" matrices, which are matrices in which entries are spiralling from the centre of the matrices towards the outside, with prescribed increments from one entry to the next depending on whether one moves…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term {\it \`a la} Poynting-Robertson entering the equations of…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
It is demonstrated that any statistics can be represented by an attractor of the solution to a corresponding systen of ODE coupled with its Liouville equation. Such a non-Newtonian representation allows one to reduce foundations of…
How can we tell whether an image has been mirrored? While we understand the geometry of mirror reflections very well, less has been said about how it affects distributions of imagery at scale, despite widespread use for data augmentation in…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
Detailed calculations of spin rotation by the Earth's gravitational field in a frozen-spin ring are presented in three different coordinate systems and used (a) to show that the systematic error caused by gravitation in a proposed electric…