Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Iterative Forecasting of Financial Time Series: The Greek Stock Market from 2019 to 2024

Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time series's next value by analysing its past. The input financial data are assumed to be consistent with an α-stable Lévy motion. The computation of the scaling exponent and the value of α, which characterises the type of the α-stable Lévy motion, are crucial for the iterative scheme. These two indices can be determined at each iteration from the form of the structure function, for the computation of which we use the method of generalised moments. Their values are used for the creation of the corresponding α-stable Lévy noise, which acts as a seed for the stochastic component. Furthermore, the drift and diffusion terms are calculated at each iteration. The proposed model is general, allowing the kind of stochastic process to vary from one iterative step to another, and its applicability is not restricted to financial data. As a case study, we consider Greece's stock market general index over a period of five years, from September 2019 to September 2024, after the completion of bailout programmes. Greece's economy changed from a restricted to a free market over the chosen era, and its stock market trading increments are likely to be describable by an α-stable L'evy motion. We find that α=2 and the scaling exponent H varies over time for every iterative step we perform. The forecasting points follow the same trend, are in good agreement with the actual data, and for most of the forecasts, the percentage error is less than 2%.

Nanoscale Prognosis of Colorectal Cancer Metastasis from AFM Image Processing of Histological Sections

Early ascertainment of metastatic tumour phases is crucial to improve cancer survival, formulate an accurate prognostic report of disease advancement, and, most importantly, quantify the metastatic progression and malignancy state of primary cancer cells with a universal numerical indexing system. This work proposes an early improvement to metastatic cancer detection with 97.7 nm spatial resolution by indexing the metastatic cancer phases from the analysis of atomic force microscopy images of human colorectal cancer histological sections. The procedure applies variograms of residuals of Gaussian filtering and theta statistics of colorectal cancer tissue image settings. This methodology elucidates the early metastatic progression at the nanoscale level by setting metastatic indexes and critical thresholds based on relatively large histological sections and categorising the malignancy state of a few suspicious cells not identified with optical image analysis. In addition, we sought to detect early tiny morphological differentiations indicating potential cell transition from epithelial cell phenotypes of low metastatic potential to those of high metastatic potential. This metastatic differentiation, which is also identified in higher moments of variograms, sets different hierarchical levels for metastatic progression dynamics.

Universal Markers Unveil Metastatic Cancerous Cross-Sections at Nanoscale

Simple Summary

We propose the use of two universal morphometric indices whose synergetic potency leads to the classification of a cancerous tissue of a few nanometers in size as metastatic or non-metastatic. The method is label-free, operates on conventional histological cross-sections, recording surface height–height roughness by AFM, and detects nanoscale changes associated with the progress of carcinogenesis which are the output of combined statistical approaches, namely multifractal analysis and the generalized moments method. The benefit of this approach is at least two-fold. On the one hand, its application in the context of early diagnosis can increase the life expectancy of patients, and on the other hand, differentiation between metastatic and non-metastatic tissues at the singular cell level can lead to new methodologies to treat cancer biology and therapies.

Abstract

The characterization of cancer histological sections as metastatic, M, or not-metastatic, NM, at the cellular size level is important for early diagnosis and treatment. We present timely warning markers of metastasis, not identified by existing protocols and used methods. Digitized atomic force microscopy images of human histological cross-sections of M and NM colorectal cancer cells were analyzed by multifractal detrended fluctuation analysis and the generalized moments method analysis. Findings emphasize the multifractal character of all samples and accentuate room for the differentiation of M from NM cross-sections. Two universal markers emphatically achieve this goal performing very well: (a) the ratio of the singularity parameters (left/right), which are defined relative to weak/strong fluctuations in the multifractal spectrum, is always greater than 0.8 for NM tissues; and (b) the index of multifractality, used to classify universal multifractals, points to log-normal distribution for NM and to log-Cauchy for M tissues. An immediate large-scale screening of cancerous sections is doable based on these findings.