On the construction of a new generalization of Runge–Kutta methods

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Stochastic modelling and simulation of PTEN regulatory networks with miRNAs and ceRNAs

In this work, three genetic regulatory networks are considered, that model the post–transcriptional regulation of the PTEN onco suppressor gene, mediated by microRNAs and competitive endogenous RNAs, in glioblastoma multiforme, the most severe of brain tumours. We simulate solutions of the resulting stochastic differential systems and discuss the effects of this miRNA-fashioned regulation on PTEN expression

THE IMPORTANCE OF BEING MEAN

Many historical loci can be obtained through approaches that differ from classic methods built on their own pure description as loci. Aim of this work is to show how various algebraic curves can be obtained as the locus for particular midpoints, and how the consideration of the latter can give rise to a succession of homotheties, namely, contractions or dilations, of the original curve. What is important to underline is that points generating a locus possess the particular property of being midpoints of other pairs of points, or segments, stemming from a particular configurations of points and lines. This is illustrated here, by various examples

Nonlinear oscillators via \v{C}eby\v{s}\"ev quintic approximations

Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's relativistic oscillators and in non--relativistic models which deals with cables with an attached midpoint mass, or some harmonic Duffing oscillators.Comment: 15 pages, 9 figures, 3 table

On the chaotic nature of electro-discharge machining

The long-accepted thermoelectric model for electro-discharge machining is being brought into question. Several experimental facts prompt the proposal of a new theory based on the effect of gap pollution on the ignition of discharges. The first experimental proof comes from the recently reported observation of debris chains and clusters. In this view, each step of the process depends on the previous ones through a deterministic relation, even if the overall evolution is unpredictable. The paper establishes mathematical grounds for the abovementioned intuitions by setting up and solving a recursive equation for the machining energy employed at each discharge event. By means of numerical and algebraic tools, the above equation is studied and shows a chaotic evolution similar to that of the logistic map. Results reconcile the apparent paradox between deterministic nature and stochastic localization of the discharges and introduce a description of the chaotic dynamics of electro-discharge processes

A Computational Template for Three-Dimensional Modeling of the Vascular Scaffold of the Human Thyroid Gland

We recently designed an innovative scaffold-bioreactor unit for the bioengineering of a three-dimensional (3D) bioartificial human thyroid gland or its miniaturized replica as a part of a microfluidic chip test system.This device is based on the evidence that the 3D geometry of the intraglandular stromal/vascular scaffold (SVS; i.e., the fibrous and vascular matrix) of mammalian viscera plays a key role in guiding growth and differentiation of in vitro seeded cells. Therefore, we initiated a research program focused on computer-aided reconstruction of the 2nd to 4th order intralobar arterial network (IAN) of the human thyroid gland asa reliable surrogate for its 3D SVS, to be used as an input for rapid prototyping of a biomaterial replica. Tothis end, we developed a computational template that works within the Mathematica environment, giving rise to a quasi-fractal growth of the IAN distribution, constrained within an approximation of the thyroidl obe shape as a closed surface. Starting from edge detection of planar images of real human thyroid lobes acquired by in vivo real-time ultrasonography, we performed data approximation of the lobar profiles based on splines and Bezier curves, providing 3D lobar shapes as geometric boundaries for vessel growth by a diffusion-limited aggregation model. Our numerical procedures allowed for a robust connection between development of lobar arterial trees and thyroid lobe shape, led to a vascular self-similarity consistent with that of a cadaveric lobar arterial cast, and reproduced arterial vessels in a proportion not statistically different from that described for the real human thyroid gland. We conclude that our algorithmic template offers a reliable reproduction of the extremely complex IAN of the adult human thyroid lobe, potentially useful as a computational guidance for bioprinting of thyroid lobe matrix replicas. In addition, due to the simplicity and limited number of morphometrical parameters required by our system, we predict its application to the design of a number of patient-tailored human bioartificial organs and organs-on-chip,including parenchymal viscera and bones

Woven bone formation and mineralization by rat mesenchymal stromal cells imply increased expression of the intermediate filament desmin

BackgroundDisordered and hypomineralized woven bone formation by dysfunctional mesenchymal stromal cells (MSCs) characterize delayed fracture healing and endocrine –metabolic bone disorders like fibrous dysplasia and Paget disease of bone. To shed light on molecular players in osteoblast differentiation, woven bone formation, and mineralization by MSCs we looked at the intermediate filament desmin (DES) during the skeletogenic commitment of rat bone marrow MSCs (rBMSCs), where its bone-related action remains elusive.ResultsMonolayer cultures of immunophenotypically- and morphologically - characterized, adult male rBMSCs showed co-localization of desmin (DES) with vimentin, F-actin, and runx2 in all cell morphotypes, each contributing to sparse and dense colonies. Proteomic analysis of these cells revealed a topologically-relevant interactome, focused on cytoskeletal and related enzymes//chaperone/signalling molecules linking DES to runx2 and alkaline phosphatase (ALP). Osteogenic differentiation led to mineralized woven bone nodules confined to dense colonies, significantly smaller and more circular with respect to controls. It significantly increased also colony-forming efficiency and the number of DES-immunoreactive dense colonies, and immunostaining of co-localized DES/runx-2 and DES/ALP. These data confirmed pre-osteoblastic and osteoblastic differentiation, woven bone formation, and mineralization, supporting DES as a player in the molecular pathway leading to the osteogenic fate of rBMSCs.ConclusionImmunocytochemical and morphometric studies coupled with proteomic and bioinformatic analysis support the concept that DES may act as an upstream signal for the skeletogenic commitment of rBMSCs. Thus, we suggest that altered metabolism of osteoblasts, woven bone, and mineralization by dysfunctional BMSCs might early be revealed by changes in DES expression//levels. Non-union fractures and endocrine – metabolic bone disorders like fibrous dysplasia and Paget disease of bone might take advantage of this molecular evidence for their early diagnosis and follow-up

Multipotent adult rat, thyroid stem cells can be differentiated to follicular thyrocyte, and hepatocyte- like cells in 2D and 3D culture systems

We have recently characterized and differentiated towards endodermal and mesoder- mal lineages progenitor cells of the adult rat thyroid, expressing multipotency markers [1]. We have now assessed their clonogenicity, extent of side population, consistency of stem cell marker expression, and commitment to either follicular or hepatocyte-like lineages when in monolayer (2D), and suspension or Matrigel (3D). Colony forming unit (CFU)-like cultures were obtained by long-term subcultures of primary rat thyroid cells, under starvation conditions. CFU-like cultures seeded in Petri dishes by limiting dilution (1 cell / cm2) were observed to give rise to toluidine blue-positive, individual clones. In these cultures, quantitative densitometric analysis of immunoblotted Oct-3/4, Sca1, and GATA4 revealed an increase in stem cell markers ranging from 95% to 270% with respect to standard, primary thyroid cultures. In addition, using three different analytical techniques including DyeCycle Violet staining by flow cytometry, ABCG2 immunocytochemistry, and Hoechst 33342 histochemistry + the ABCG2 inhibitor, verapamil a side population involving 1-2% of CFU-like cultures was detected. Then, CFU-like cultures were differentiated using TSH, either in 2D or in 3D. Differentiated adherent cells resulted immunopositive for thyrocyte markers including thyroglobulin (TG), sodium-iodide symporter (NIS), and thyroperoxidase (TPO). Differentiation in suspension and in Matrigel gave rise to follicles with cells having ultrastructural features consistent with thyrocytes, and immunoreactivity (IR) for TG, NIS, and TPO. Finally, CFU-like cultures were differentiated in adherence to hepatocyte-like cells, resulting in pre-hepatocyte morphology, high periodic acid-Schiff reaction, and IR for α-fetoprotein and albumin. We conclude that our CFU-like thyroid cultures are enriched with a multipotent, stem cell population whose hepatic differentiation capacity has been revealed for the first time