Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

A General Method for Targeted Quantitative Cross-Linking Mass Spectrometry

Chemical cross-linking mass spectrometry (XL-MS) provides protein structural information by identifying covalently linked proximal amino acid residues on protein surfaces. The information gained by this technique is complementary to other structural biology methods such as x-ray crystallography, NMR and cryo-electron microscopy[1]. The extension of traditional quantitative proteomics methods with chemical cross-linking can provide information on the structural dynamics of protein structures and protein complexes. The identification and quantitation of cross-linked peptides remains challenging for the general community, requiring specialized expertise ultimately limiting more widespread adoption of the technique. We describe a general method for targeted quantitative mass spectrometric analysis of cross-linked peptide pairs. We report the adaptation of the widely used, open source software package Skyline, for the analysis of quantitative XL-MS data as a means for data analysis and sharing of methods. We demonstrate the utility and robustness of the method with a cross-laboratory study and present data that is supported by and validates previously published data on quantified cross-linked peptide pairs. This advance provides an easy to use resource so that any lab with access to a LC-MS system capable of performing targeted quantitative analysis can quickly and accurately measure dynamic changes in protein structure and protein interactions

Pedagogías de la precariedad en el orden educativo neoliberal. Inseguridad y recomposición de las posibilidades en el actual contexto político-pedagógico

The aim of this article is to analyse how neoliberal principles in education create a state of precariousness. The question that will guide the problematisation and the argumentation of the work is: What is the «status» of precariousness in the current order and how does it manifest itself - expressly or inadvertently - in the contemporary educational field? In order to address this question, a theoretical-analytical exercise has been carried out based on a review of relevant literature on the relationship between neoliberalisation and education. As a central hypothesis, we propose that the processes of precarisation constitute an objective necessity for the expansion and reproduction of the new neoliberal order. In addition, this order requires the production of a specific type of subjectivity that normalizes «precariousness» as a new historical condition, producing a particular notion of subjectivity and agency. The intersection between objective needs and the production of a particular subjectivity is produced in the cultural space through «pedagogies of precariousness». The installation of such pedagogies in formal education systems will be verified through the analysis of three predominant figures: the entrepreneur, the apprentice of competences and the teacher as technician. Finally, it is analysed how a «pedagogy of possibilities» could be opposed to «pedagogies of precariousness», enabling other forms of educational relations and new political-pedagogical horizons

Paneth cell - rich regions separated by a cluster of Lgr5+ cells initiate crypt fission in the intestinal stem cell niche

The crypts of the intestinal epithelium house the stem cells that ensure the continual renewal of the epithelial cells that line the intestinal tract. Crypt number increases by a process called crypt fission, the division of a single crypt into two daughter crypts. Fission drives normal tissue growth and maintenance. Correspondingly, it becomes less frequent in adulthood. Importantly, fission is reactivated to drive adenoma growth. The mechanisms governing fission are poorly understood. However, only by knowing how normal fission operates can cancer-associated changes be elucidated. We studied normal fission in tissue in three dimensions using high-resolution imaging and used intestinal organoids to identify underlying mechanisms. We discovered that both the number and relative position of Paneth cells and Lgr5+ cells are important for fission. Furthermore, the higher stiffness and increased adhesion of Paneth cells are involved in determining the site of fission. Formation of a cluster of Lgr5+ cells between at least two Paneth-cell-rich domains establishes the site for the upward invagination that initiates fission