Computability of Probability Distributions and Distribution Functions

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence

Random Iteration Algorithm for Graph-Directed Sets

A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton\u27s theorem, it is shown that almost all sequences obtained by this algorithm reflect a probability measure which is invariant with respect to the system of contractions with probabilities

The apelin‑apelin receptor signaling pathway in fibroblasts is involved in tumor growth via p53 expression of cancer cells

Cancer-associated fibroblasts (CAFs) are pivotal in tumor progression. TP53-deficiency in cancer cells is associated with robust stromal activation. The apelin-apelin receptor (APJ) system has been implicated in suppressing fibroblast-to-myofibroblast transition in non-neoplastic organ fibrosis. The present study aimed to elucidate the oncogenic role of the apelin-APJ system in tumor fibroblasts. APJ expression and the effect of APJ suppression in fibroblasts were investigated for p53 status in cancer cells using human cell lines (TP53-wild colon cancer, HCT116, and Caco-2; TP53-mutant colon cancer, SW480, and DLD-1; and colon fibroblasts, CCD-18Co), resected human tissue samples of colorectal cancers, and immune-deficient nude mouse xenograft models. The role of exosomes collected by ultracentrifugation were also analyzed as mediators of p53 expression in cancer cells and APJ expression in fibroblasts. APJ expression in fibroblasts co-cultured with p53-suppressed colon cancer cells (HCT116sh p53 cells) was significantly lower than in control colon cancer cells (HCT116sh control cells). APJ-suppressed fibroblasts treated with an antagonist or small interfering RNA showed myofibroblast-like properties, including increased proliferation and migratory abilities, via accelerated phosphorylation of Sma- and Mad-related protein 2/3 (Smad2/3). In addition, xenografts of HCT116 cells with APJ-suppressed fibroblasts showed accelerated tumor growth. By contrast, apelin suppressed the upregulation of phosphorylated Smad2/3 in fibroblasts. MicroRNA 5703 enriched in exosomes derived from HCT116sh p53 cells inhibited APJ expression, and inhibition of miR-5703 diminished APJ suppression in fibroblasts caused by cancer cells. APJ suppression from a specific microRNA in cancer cell-derived exosomes induced CAF-like properties in fibroblasts. Thus, the APJ system in fibroblasts in the tumor microenvironment may be a promising therapeutic target.Saiki H., Hayashi Y., Yoshii S., et al. The apelin‑apelin receptor signaling pathway in fibroblasts is involved in tumor growth via p53 expression of cancer cells. International Journal of Oncology 63, 139 (2023); https://doi.org/10.3892/ijo.2023.5587

Sequential Computability of a Function. Effective Fine Space and Limiting Recursion

We consider real sequences in I = [0, 1) and real functions on I. It is first shown that, as for real sequences from I, R-computability (computability with respect to the Euclidean topology) implies “ weak Fine-computability.” Using this result, we show that “ Fine­sequential computability” and “ -sequential computability” are equivalent for effectively locally Fine-continuous functions as well as for Fine-continuous functions

Fine-computable Functions on the Unit Square and their Integral

We discuss the integral and Fubini's Theorem for a Fine-computable function F(x, y) on the upper-right open unit square [0, 1) x [0,1). The core objective is Fine-computability of f(x) = ∫ [0,1) F(x,y)dy as a function of x ∈ [0,1)

Computability of Probability Distributions and Characteristic Functions

As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of characteristic functions is computable. As for the onvergence problem, the effectivized Glivenko's theorem holds. Effectivizations of Bochner's theorem and de Moivre-Laplace central limit theorem are also proved

Computability of Probability Distributions and Characteristic Functions

As a part of our works on effective properties of probability distributions,we deal with the corresponding characteristic functions. A sequence ofprobability distributions is computable if and only if the correspondingsequence of characteristic functions is computable. As for the onvergenceproblem, the effectivized Glivenko's theorem holds. Effectivizations ofBochner's theorem and de Moivre-Laplace central limit theorem are also proved