Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms

Lidstone–Euler interpolation and related high even order boundary value problem

AbstractWe consider the Lidstone–Euler interpolation problem and the associated Lidstone–Euler boundary value problem, in both theoretical and computational aspects. After a theorem of existence and uniqueness of the solution to the Lidstone–Euler boundary value problem, we present a numerical method for solving it. This method uses the extrapolated Bernstein polynomials and produces an approximating convergent polynomial sequence. Particularly, we consider the fourth-order case, arising in various physical models. Finally, we present some numerical examples and we compare the proposed method with a modified decomposition method for a tenth-order problem. The numerical results confirm the theoretical and computational ones

Relationship between Interpolation and Differential Equations: A Class of Collocation Methods

In this chapter, the connection between general linear interpolation and initial, boundary and multipoint value problems is explained. First, a result of a theoretical nature is given, which highlights the relationship between the interpolation problem and the Fredholm integral equation for high-order differential problems. After observing that the given problem is equivalent to a Fredholm integral equation, this relation is used in order to determine a general procedure for the numerical solution of high-order differential problems by means of appropriate collocation methods based on the integration of the Fredholm integral equation. The classical analysis of the class of the obtained methods is carried out. Some particular cases are illustrated. Numerical examples are given in order to illustrate the efficiency of the method

Reduced sulfatide content in deferoxamine-induced senescent HepG2 cells

Iron chelators, such as deferoxamine, exert an anticancer effect by altering the activity of biomolecules critical for regulation of the cell cycle, cell metabolism, and apoptotic processes. Thus, iron chelators are sometimes used in combination with radio- and/or chemotherapy in the treatment of cancer. The possibility that deferoxamine could induce a program of senescence similar to radio- and/or chemotherapy, fostering adaptation in the treatment of cancer cells, is not fully understood. Using established biochemical techniques, biomarkers linked to lipid composition, and coherent anti-Stokes Raman scattering microscopy, we demonstrated that hepatocellular carcinoma-derived HepG2 cells survive after deferoxamine treatment, acquiring phenotypic traits and representative hallmarks of senescent cells. The results support the view that deferoxamine acts in HepG2 cells to produce oxidative stress-induced senescence by triggering sequential mitochondrial and lysosomal dysfunction accompanied by autophagy blockade. We also focused on the lipidome of senescent cells after deferoxamine treatment. Using mass spectrometry, we found that the deferoxamine-induced senescent cells presented marked remodeling of the phosphoinositol, sulfatide, and cardiolipin profiles, which all play a central role in cell signaling cascades, intracellular membrane trafficking, and mitochondria functions. Detection of alterations in glycosphingolipid sulfate species suggested modifications in ceramide generation, and turnover is frequently described in cancer cell survival and resistance to chemotherapy. Blockade of ceramide generation may explain autophagic default, resistance to apoptosis, and the onset of senescence

Pros and Cons of the SeHCAT Test in Bile Acid Diarrhea: A More Appropriate Use of an Old Nuclear Medicine Technique

Bile acid malabsorption (BAM) causing chronic diarrhea may be due to organic as well as functional disorders, and some of them were included under the general label of diarrheic-type irritable bowel syndrome (IBS-D). The 75-selenium homocholic acid taurine (SeHCAT) test is a nuclear medicine investigation considered to be the gold standard for the diagnosis of bile acid malabsorption (BAM). Many studies demonstrate that it could be effective in the clinical workout of chronic diarrhea due to different conditions. The SeHCAT test provides a quantitative assessment to estimate the severity of BAM and the possible response to therapy with bile acid sequestrants (BASs). However, there is no general agreement regarding its cutoff value and the test is not widely available. The aim of this review is to discuss the advantages and disadvantages of the SeHCAT test in clinical practice

The IASI Water Deficit Index to Monitor Vegetation Stress and Early Drying in Summer Heatwaves: An Application to Southern Italy

The boreal hemisphere has been experiencing increasing extreme hot and dry conditions over the past few decades, consistent with anthropogenic climate change. The continental extension of this phenomenon calls for tools and techniques capable of monitoring the global to regional scales. In this context, satellite data can satisfy the need for global coverage. The main objective we have addressed in the present paper is the capability of infrared satellite observations to monitor the vegetation stress due to increasing drought and heatwaves in summer. We have designed and implemented a new water deficit index (wdi) that exploits satellite observations in the infrared to retrieve humidity, air temperature, and surface temperature simultaneously. These three parameters are combined to provide the water deficit index. The index has been developed based on the Infrared Atmospheric Sounder Interferometer or IASI, which covers the infrared spectral range 645 to 2760 cm−1 with a sampling of 0.25 cm−1. The index has been used to study the 2017 heatwave, which hit continental Europe from May to October. In particular, we have examined southern Italy, where Mediterranean forests suffer from climate change. We have computed the index’s time series and show that it can be used to indicate the atmospheric background conditions associated with meteorological drought. We have also found a good agreement with soil moisture, which suggests that the persistence of an anomalously high water deficit index was an essential driver of the rapid development and evolution of the exceptionally severe 2017 droughts

Deep ensemble learning and transfer learning methods for classification of senescent cells from nonlinear optical microscopy images

The success of chemotherapy and radiotherapy anti-cancer treatments can result in tumor suppression or senescence induction. Senescence was previously considered a favorable therapeutic outcome, until recent advancements in oncology research evidenced senescence as one of the culprits of cancer recurrence. Its detection requires multiple assays, and nonlinear optical (NLO) microscopy provides a solution for fast, non-invasive, and label-free detection of therapy-induced senescent cells. Here, we develop several deep learning architectures to perform binary classification between senescent and proliferating human cancer cells using NLO microscopy images and we compare their performances. As a result of our work, we demonstrate that the most performing approach is the one based on an ensemble classifier, that uses seven different pre-trained classification networks, taken from literature, with the addition of fully connected layers on top of their architectures. This approach achieves a classification accuracy of over 90%, showing the possibility of building an automatic, unbiased senescent cells image classifier starting from multimodal NLO microscopy data. Our results open the way to a deeper investigation of senescence classification via deep learning techniques with a potential application in clinical diagnosis

3D cultures of primary astrocytes on Poly-L-lactic acid scaffolds

Tissue engineering is an emerging multidisciplinary field that aims at reproducing in vitro tissues with morphological and functional features similar to the biological tissue of the human body. Polymeric materials can be used in contact with biological systems in replacing destroyed tissue by transplantation [1]. Several biopolymers, including poly L (lactic acid) (PLLA), have been used in biomedical applications to set scaffolds with ductile proprieties and biodegradation kinetics [2]. In particular, the PLLA scaffold topography mimics the natural extracellular matrix and makes it a good candidate for neural tissue engineering. We report about of 3D system the PLLA porous scaffolds prepared via thermally-induced phase separation (TIPS) [3], and utilized as substrate for primary rat astrocytes 3D growth. Interestingly astrocytes adapt well to these porous matrices, not only remaining on the surface, but also penetrating inside the scaffolds. They colonize the matrix acquiring a typical star-like morphology; they form cell contacts and, in addition produce EVs as in vivo [4]. These results suggest that the chosen conditions could be a good starting point for 3D brain culture systems. PLLA scaffolds could be further enriched to host two or three different brain cell types, in order to set an in vitro model of blood brain barrier. The future use of co-culture systems may be involved in drug delivery studies, and in the formulation of new therapeutic strategies for the treatment of neurological diseases. [1]Langer R, Vacanti JP. Tissue engineering. Science. 1993; 260: 920 [2]Nejati E, et al. Appl. Sci. Manuf. 2008; 39: 1589–1596 [3]Scaffaro R, et al. J. Mech. Behav. Biomed. Mater. 2016; 54:8-20 [4]Schiera G, et al. Biomed Res Int 2015: 152926, 201

The Aurora-A/TPX2 axis directs spindle orientation in adherent human cells by regulating NuMA and microtubule stability

Mitotic spindle orientation is a crucial process that defines the axis of cell division, contributing to daughter cell positioning and fate, and hence to tissue morphogenesis and homeostasis.1,2 The trimeric NuMA/LGN/Gαi complex, the major determinant of spindle orientation, exerts pulling forces on the spindle poles by anchoring astral microtubules (MTs) and dynein motors to the cell cortex.3,4 Mitotic kinases contribute to correct spindle orientation by regulating nuclear mitotic apparatus protein (NuMA) localization,5-7 among which the Aurora-A centrosomal kinase regulates NuMA targeting to the cell cortex in metaphase.8,9 Aurora-A and its activator targeting protein for Xklp2 (TPX2) are frequently overexpressed in cancer,10-12 raising the question as to whether spindle orientation is among the processes downstream the Aurora-A/TPX2 signaling axis altered under pathological conditions. Here, we investigated the role of TPX2 in the Aurora-A- and NuMA-dependent spindle orientation. We show that, in cultured adherent human cells, the interaction with TPX2 is required for Aurora-A to exert this function. We also show that Aurora-A, TPX2, and NuMA are part of a complex at spindle MTs, where TPX2 acts as a platform for Aurora-A regulation of NuMA. Interestingly, excess TPX2 does not influence NuMA localization but induces a "super-alignment" of the spindle axis with respect to the substrate, although an excess of Aurora-A induces spindle misorientation. These opposite effects are both linked to altered MT stability. Overall, our results highlight the importance of TPX2 for spindle orientation and suggest that spindle orientation is differentially sensitive to unbalanced levels of Aurora-A, TPX2, or the Aurora-A/TPX2 complex

Excess TPX2 Interferes with Microtubule Disassembly and Nuclei Reformation at Mitotic Exit.

The microtubule-associated protein TPX2 is a key mitotic regulator that contributes through distinct pathways to spindle assembly. A well-characterised function of TPX2 is the activation, stabilisation and spindle localisation of the Aurora-A kinase. High levels of TPX2 are reported in tumours and the effects of its overexpression have been investigated in cancer cell lines, while little is known in non-transformed cells. Here we studied TPX2 overexpression in hTERT RPE-1 cells, using either the full length TPX2 or a truncated form unable to bind Aurora-A, to identify effects that are dependent-or independent-on its interaction with the kinase. We observe significant defects in mitotic spindle assembly and progression through mitosis that are more severe when overexpressed TPX2 is able to interact with Aurora-A. Furthermore, we describe a peculiar, and Aurora-A-interaction-independent, phenotype in telophase cells, with aberrantly stable microtubules interfering with nuclear reconstitution and the assembly of a continuous lamin B1 network, resulting in daughter cells displaying doughnut-shaped nuclei. Our results using non-transformed cells thus reveal a previously uncharacterised consequence of abnormally high TPX2 levels on the correct microtubule cytoskeleton remodelling and G1 nuclei reformation, at the mitosis-to-interphase transition