相关论文: A Note on Positive Distributions in Gaussian Analy…
The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…
Considering second variations about a given minimizer of a causal variational principle, we derive positive functionals in space-time. It is shown that the strict positivity of these functionals ensures that the minimizer is nonlinearly…
A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of…
In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals.…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
The normal distribution is well-known for several results that it is the only to fulfil. The aim of the present paper is to show that many of these characterizations actually follow from the fact that the derivative of the log-density of…
I describe a version of so-called naive dimensional analysis, a rule for estimating the sizes of terms in an effective theory below the scale of chiral symmetry breaking induced by a strong gauge interaction. The rule is simpler and more…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].
We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with…
In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties…
This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…
We study the non-Gaussian tail of the probability distribution function of density in cosmological N-Body simulations for a variety of initial conditions. We compare the behaviour of the non-Gaussian tail in the real space with that in the…
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. They include all correlations within the system of particles and represent…