Consistent Systems of Finite Dimensional Distributions

In the paper we discuss the problem of description of random fields by means of systems of finite dimensional probability distributions. We present from a unified point of view a survey of the various such systems associated with random fields. Then general system of finite dimensional distributions with a suitable consistency condition is introduced. The properties, relations with other systems, as well as the problems of existence and uniqueness of the corresponding random fields are discussed

Notes on Ergodic Theory in Infinite Measure Spaces

This article is concerned with ergodic theory for transformations which preserve an infinite measure. In the first part we present an overview of the invertible case with a focus on weakly wandering sequences and their applications to number theory as it has developed over the last fifty years. The second part presents a very preliminary investigation into extending weakly wandering sequences to the non-invertible case. This consists primarily of a few examples which illustrate the complexities which arise in the non-invertible case

Does Proteomic Mirror Reflect Clinical Characteristics of Obesity?

Obesity is a frightening chronic disease, which has tripled since 1975. It is not expected to slow down staying one of the leading cases of preventable death and resulting in an increased clinical and economic burden. Poor lifestyle choices and excessive intake of “cheap calories” are major contributors to obesity, triggering type 2 diabetes, cardiovascular diseases, and other comorbidities. Understanding the molecular mechanisms responsible for development of obesity is essential as it might result in the introducing of anti-obesity targets and early-stage obesity biomarkers, allowing the distinction between metabolic syndromes. The complex nature of this disease, coupled with the phenomenon of metabolically healthy obesity, inspired us to perform data-centric, hypothesis-generating pilot research, aimed to find correlations between parameters of classic clinical blood tests and proteomic profiles of 104 lean and obese subjects. As the result, we assembled patterns of proteins, which presence or absence allows predicting the weight of the patient fairly well. We believe that such proteomic patterns with high prediction power should facilitate the translation of potential candidates into biomarkers of clinical use for early-stage stratification of obesity therapy

Does Proteomic Mirror Reflect Clinical Characteristics of Obesity?

Obesity is a frightening chronic disease, which has tripled since 1975. It is not expected to slow down staying one of the leading cases of preventable death and resulting in an increased clinical and economic burden. Poor lifestyle choices and excessive intake of “cheap calories” are major contributors to obesity, triggering type 2 diabetes, cardiovascular diseases, and other comorbidities. Understanding the molecular mechanisms responsible for development of obesity is essential as it might result in the introducing of anti-obesity targets and early-stage obesity biomarkers, allowing the distinction between metabolic syndromes. The complex nature of this disease, coupled with the phenomenon of metabolically healthy obesity, inspired us to perform data-centric, hypothesis-generating pilot research, aimed to find correlations between parameters of classic clinical blood tests and proteomic profiles of 104 lean and obese subjects. As the result, we assembled patterns of proteins, which presence or absence allows predicting the weight of the patient fairly well. We believe that such proteomic patterns with high prediction power should facilitate the translation of potential candidates into biomarkers of clinical use for early-stage stratification of obesity therapy

Hexakis(dimethylsulfoxide-O)-cobalt(II) hexatungstate, [Co(C₂H₆OS)₆][W₆O₁₉]: synthesis from aqueous dimethylsulfoxide solution, crystal structure determination, FT-IR and Raman spectroscopy analysis, and surface micromorphology

<p>The conditions necessary for formation of hexakis(dimethylsulfoxide-O)–cobalt(II) hexatungstate [Co(C₂H₆OS)₆][W₆O₁₉] in Co(NO₃)₂-–Na₂WO₄–HCl–H₂O–DMSO solution, acidified up to , were established. The synthesized salt was examined using chemical analysis, X-ray single crystal analysis, FT-IR and Raman spectroscopy, and scanning electron microscopy. By X-ray single-crystal analysis of [Co(C₂H₆OS)₆][W₆O₁₉] main crystallographic characteristics were revealed: triclinic, <i>C</i>2/<i>c</i>, <i>a</i> = 16.3318(9) Å, <i>b</i> = 14.9160(5) Å, <i>c</i> = 17.8291(10) Å, <i>β</i> = 112.104(6)°, <i>V</i> = 4024.1(3) ų at <i>T</i> = 293(2) K, <i>Z</i> = 4, <i>d</i>_Calcd = 3.194 g cm⁻³. The structure is built from isolated cationic complexes [Co(C₂H₆OS)₆]²⁺ and hexatungstate anions [W₆O₁₉]^2–.</p