Related papers: Characterising New Physics Models by Effective Dim…
Constraining the parameters of physical models with $>5-10$ parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
We present the quantum theory of the measurement of bosonic particles by multipixel detectors. For the sake of clarity, we specialize on beams of photons. We study the measurement of different spatial beam characteristics, as position and…
We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations…
Four-dimensional mass is determined in four-dimensional pseudo-Euclidean space as a physical invariant of that space. That invariant is discussed as an invariant of electromagnetic type. Finally, equations of Maxwell type are obtained for…
We introduce a mathematical framework for quantifying fine-tuning in general physical settings. In particular, we identify two distinct perspectives on fine-tuning, namely, a local and a global perspective --- and develop corresponding…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…
In this paper, we present a new cosmological model using fractal manifold. We prove that a space defined by this kind of manifold is an expanding space. This model provides us with consistent arguments pertaining to the relationship between…
Vessels are complex structures in the body that have been studied extensively in multiple representations. While voxelization is the most common of them, meshes and parametric models are critical in various applications due to their…
Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…
Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as…
For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Exact distribution of the moment estimator of shape parameter for the gamma distribution for small samples is derived. Order preserving properties of this estimator are presented.
In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.