On computing joint invariants of vector fields

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}

Algorithms for Simultaneous Block Triangularization and Block Diagonalization of Sets of Matrices

A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. In a recent paper, a new method was proposed that gives an answer to that problem. In the present article conditions are given for the more general problem of putting set of matrices into block-diagonal form simultaneously. In addition, two algorithms for simultaneous block triangularization and block diagonalization of sets of matrices are presented and are applied to several concrete examples using the symbolic manipulation system Maple

Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page

The inverse problem for Lagrangian systems with certain non-conservative forces

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic forces. Our approach focusses primarily on obtaining coordinate-free conditions for the existence of a suitable non-singular multiplier matrix, which will lead to an equivalent representation of a given system of second-order equations as one of these Lagrangian systems with non-conservative forces.Comment: 28 page

On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda

Holonomy of Einstein Lorentzian manifolds

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This version is an extended part of the previous version; another part of the previous version is extended and submitted as arXiv:1001.444

Efficient Small Extracellular Vesicles (EV) Isolation Method and Evaluation of EV-Associated DNA Role in Cell-Cell Communication in Cancer

SIMPLE SUMMARY: Small extracellular vesicles (sEVs) released by all cell types function as a mediator in intercellular communication that can promote cell division and survival to remodel the tumor microenvironment to develop tumor invasion and metastasis. Even though dsDNA baggage is associated with all small EV populations, the functional role of EV-DNA in cancer remains poorly understood. This is due to a lack of methods allowing the efficient separation of small EVs (sEVs) from other non-sEV components. The main aim of our study was to develop an efficient sEV isolation method along with EV-associated DNA (EV-DNA) monitoring tool to evaluate the role of EV-DNA as a mediator of cell–cell communication in cancer. Our detailed small EV-DNA characterization confirmed that isolated sEVs using the TSU method (Tangential flow filtration + Size exclusion chromatography + Ultrafiltration) are free from contaminants such as cell-free and apoptotic bodies DNA, making TSU ideal for performing EV-DNA functional studies. Next, we revealed the exact EV-DNA distribution in the recipient cells using 3D image analysis and the association of EV-DNA with key cellular proteins, which may have an essential role in cancer. In the leukemia model, EV-DNA isolated from leukemia cell lines associated with mesenchymal stromal cells (MSCs), a crucial factor in the bone marrow (BM) microenvironment. ABSTRACT: Small extracellular vesicles (sEVs) play essential roles in intercellular signaling both in normal and pathophysiological conditions. Comprehensive studies of dsDNA associated with sEVs are hampered by a lack of methods, allowing efficient separation of sEVs from free-circulating DNA and apoptotic bodies. In this work, using controlled culture conditions, we enriched the reproducible separation of sEVs from free-circulated components by combining tangential flow filtration, size-exclusion chromatography, and ultrafiltration (TSU). EV-enriched fractions (F2 and F3) obtained using TSU also contained more dsDNA derived from the host genome and mitochondria, predominantly localized inside the vesicles. Three-dimensional reconstruction of high-resolution imaging showed that the recipient cell membrane barrier restricts a portion of EV-DNA. Simultaneously, the remaining EV-DNA overcomes it and enters the cytoplasm and nucleus. In the cytoplasm, EV-DNA associates with dsDNA-inflammatory sensors (cGAS/STING) and endosomal proteins (Rab5/Rab7). Relevant to cancer, we found that EV-DNA isolated from leukemia cell lines communicates with mesenchymal stromal cells (MSCs), a critical component in the BM microenvironment. Furthermore, we illustrated the arrangement of sEVs and EV-DNA at a single vesicle level using super-resolution microscopy. Altogether, employing TSU isolation, we demonstrated EV-DNA distribution and a tool to evaluate the exact EV-DNA role of cell–cell communication in cancer

The aortic root in repaired tetralogy of Fallot:Serial measurements and impact of losartan treatment

Background: Aortic root dilatation is common in adults with repaired tetralogy of Fallot (rTOF) and might lead to aortic dissection. However, little is known on progression of aortic dilatation and the effect of pharmaceutical treatment. This study aims to determine factors associated with aortic growth and investigate effects of losartan. Methods and results: We performed a prespecified analysis from the 1:1 randomized, double-blind REDEFINE trial. Aortic root diameters were measured at baseline and after 2.0 ± 0.3 years of follow-up using cardiovascular magnetic resonance (CMR) imaging. A total of 66 patients were included (68% men, age 40 ± 12 years, baseline aortic root 37 ± 6 mm, 32% aortic dilatation (>40 mm)). There was a trend towards slow aortic root growth (+0.6 ± 2.3 mm after two years, p = 0.06) (n = 60). LV stroke volume was the only factor associated with both a larger baseline aortic root (β: 0.09 mm/ml (95% C.I.:0.02, 0.15), p = 0.010) and with aortic growth during follow-up (β: 0.04 mm/ml (95% C.I.:0.005, 0.066), p = 0.024), after correction for age, sex, and body surface area using linear regression analysis. No treatment effect of losartan was found (p = 0.17). Conclusions: Aortic root dilatation was present in about one-third of rTOF patients. A larger LV stroke volume was associated with both a larger baseline aortic root and ongoing growth. Our findings provide no arguments for lower aortic diameter thresholds for prophylactic surgery compared to the general population

Archaeometric Study of the Historic Terrazzo Pavement of Prince Mohamed Ali Museum, Cairo, Egypt

This research will shed light on studying a terrazzo pavement in Prince Mohamed Ali Museum (the case study). The authors used visual inspection, stereo microscope, USB microscope, XRPD analysis, and SEM.EDX to identify its components, deterioration aspects and execution techniques. The XRPD and SEM.EDX results revealed that Portland cement was used in the three layers of terrazzo because of the detection of Hatrurite, Alite, Anorthite, Albite, Aragonite, etc. Many pigments were used in the topping terrazzo layer as; Goethite, Greenalite, Hematite, Azurite and Magnetite. The divider strips were made of brass alloy and the topping layer chips were prepared from basalt, marble and sea shells