Related papers: On Fields with Finite Information Density
A communication theory for a transmitter broadcasting to many receivers is presented. In this case energetic considerations cannot be neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit,…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and…
In this essay, we present a new understanding of the cosmological constant problem, built upon the realization that the vacuum energy density can be expressed in terms of a phase space volume. We introduce a UV-IR regularization which…
By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes,…
The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical…
Reconstructing the electric field from the measured voltages in an antenna, unfolding the antenna response, comes with several problems. Due to the noisiness of the signal it is often necessary to disregard part of the bandwidth of the…
We prove a new lower bound on the algorithmic information content of points lying on a line in $\mathbb{R}^n$. More precisely, we show that a typical point $z$ on any line $\ell$ satisfies \begin{equation*} K_r(z)\geq \frac{K_r(\ell)}{2} +…
In most inflationary models, space-time inflated to the extent that modes of cosmological size originated as modes of wavelengths at least several orders of magnitude smaller than the Planck length. Recent studies confirmed that, therefore,…
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
I have used the Hipparcos Input Catalog, together with Kurucz model stellar atmospheres, and information on the strength of the interstellar extinction, to create a model of the expected intensity and spectral distribution of the local…
In the article the formulas for the modeling of conservative fields in piecewise infinite plate with a thin inclusion found. The accuracy of the found formulas is of order equal to the thickness of the outer layer. The problem for higher…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
Using the temperature data from Planck we search for departures from a power-law primordial power spectrum, employing Bayesian model-selection and posterior probabilities. We parametrize the spectrum with $n$ knots located at arbitrary…
The properties of a dissipative system depend on the spectral density of the coupling to the environment. Mostly, the dependence on the low-frequency behavior is in the focus of interest. However, in order to avoid divergencies, it is also…
A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental ( $\sim$ Planck) length scale $\ell$. We develop a general formalism…