in this paper, we prove the hyers-ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. as a consequence, weobtain some random stability results in the sense of hyers-ulam-rassias.

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalisation group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that...

In this paper, we describe a new hidden Markov random field model, which we call hierarchical multi-data model, and which is based on a triplet of random fields (two hidden random fields and one observed field) in order to capture inter-scale and within-scale dependencies between various scales of resolution of wavelet-based texture features. We present a variation of the Iterated Conditional M...

We combine random forest (RF) and conditional random field (CRF) into a new computational framework, called random forest random field (RF). Inference of (RF) uses the Swendsen-Wang cut algorithm, characterized by MetropolisHastings jumps. A jump from one state to another depends on the ratio of the proposal distributions, and on the ratio of the posterior distributions of the two states. Prior...

A multi-agent Parrondo's model based on complex networks is used in the current study. For Parrondo's game A, the individual interaction can be categorized into five types of behavioral patterns: the Matthew effect, harmony, cooperation, poor-competition-rich-cooperation and a random mode. The parameter space of Parrondo's paradox pertaining to each behavioral pattern, and the gradual change of...

Most natural variables assume values at points within a spatiotemporal continuum. Each point in this continuum is represented by its space and time coordinates p = (s,t). Randomness of a natural variable manifests itself as an ensemble of possible realizations over the space/time continuum. This leads to the concept of the spatiotemporal random field (S/TRF) X(p), which is a collection of reali...

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a...

This paper considers an extension of probability space based on interval random variables. In this approach, first, a notion of interval random variable is introduced. Then, based on a family of continuous distribution functions with interval parameters, a concept of probability space of an interval random variable is proposed. Then, the mean and variance of an interval random variable are intr...

Abstract. Suitable macroscopic quantities are identified and used to assess the field distribution within a composite specimen of finite size with random microstructure. Composites made of N anisotropic dielectric materials are considered. The characteristic length scale of the microstructure relative to the length scale of the specimen is denoted by ε and realizations of the random composite m...