Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Does retrograde cerebral perfusion via superior vena cava cannulation protect the brain?

OBJECTIVE: The retrograde cerebral perfusion via cannulation of the superior vena cava is a widespread method for optimising protection of the brain during hypothermic circulatory arrest. METHODS: In 14 cadavers (8 females, 6 males) of the local department of pathology, an examination was performed to check the competence of the valves of the internal jugular veins. After a complete preparation of the superior vena cava, the innominate vein and both internal jugular veins, ligating all side branches, a retrograde perfusion on 7 cadavers was installed, documenting flow and pressure of each internal jugular vein (IJV) in vitro. Afterwards, the veins were opened and their valves inspected. RESULTS: In all 14 cadavers, anatomically and functionally competent valves on the right proximal IJV were found. Only 1/14 cadaver had no valve in the left proximal IJV. Additional rudimentary and incompetent valves could be identified in 1/14 cadaver on the distal right IJV, and in 2/14 cadavers on the left IJV. Retrograde flow measurement of 7/14 cadavers revealed 0 ml/min in 4/7 cadavers, 6 ml/min in 1/7, 340 ml/min in 1/7 and 2500 ml/min in 1/7 cadaver. CONCLUSIONS: As a rule, anatomically and functionally competent valves in the proximal IJV are present. In human beings, they obstruct the direct retrograde inlet to the intracranial venous system, which suggests an unbalanced and unreliable perfusion of the brain. Therefore, retrograde cerebral perfusion by cannulating the superior vena cava may help flushing out embolism and supporting 'the cold jacket' of the brain. However, its effect of retrograde backflow cannot be a sign of adequate cerebral perfusion

Heart Valve Tissue Engineering: Concepts, Approaches, Progress, and Challenges

Potential applications of tissue engineering in regenerative medicine range from structural tissues to organs with complex function. This review focuses on the engineering of heart valve tissue, a goal which involves a unique combination of biological, engineering, and technological hurdles. We emphasize basic concepts, approaches and methods, progress made, and remaining challenges. To provide a framework for understanding the enabling scientific principles, we first examine the elements and features of normal heart valve functional structure, biomechanics, development, maturation, remodeling, and response to injury. Following a discussion of the fundamental principles of tissue engineering applicable to heart valves, we examine three approaches to achieving the goal of an engineered tissue heart valve: (1) cell seeding of biodegradable synthetic scaffolds, (2) cell seeding of processed tissue scaffolds, and (3) in-vivo repopulation by circulating endogenous cells of implanted substrates without prior in-vitro cell seeding. Lastly, we analyze challenges to the field and suggest future directions for both preclinical and translational (clinical) studies that will be needed to address key regulatory issues for safety and efficacy of the application of tissue engineering and regenerative approaches to heart valves. Although modest progress has been made toward the goal of a clinically useful tissue engineered heart valve, further success and ultimate human benefit will be dependent upon advances in biodegradable polymers and other scaffolds, cellular manipulation, strategies for rebuilding the extracellular matrix, and techniques to characterize and potentially non-invasively assess the speed and quality of tissue healing and remodeling

A critical role of RBM8a in proliferation and differentiation of embryonic neural progenitors

BACKGROUND: Nonsense mediated mRNA decay (NMD) is an RNA surveillance mechanism that controls RNA stability and ensures the speedy degradation of erroneous and unnecessary transcripts. This mechanism depends on several core factors in the exon junction complex (EJC), eIF4A3, RBM8a, Magoh, and BTZ, as well as peripheral factors to distinguish premature stop codons (PTCs) from normal stop codons in transcripts. Recently, emerging evidence has indicated that NMD factors are associated with neurodevelopmental disorders such as autism spectrum disorder (ASD) and intellectual disability (ID). However, the mechanism in which these factors control embryonic brain development is not clear. RESULT: We found that RBM8a is critical for proliferation and differentiation in cortical neural progenitor cells (NPCs). RBM8a is highly expressed in the subventricular zone (SVZ) of the early embryonic cortex, suggesting that RBM8a may play a role in regulating NPCs. RBM8a overexpression stimulates embryonic NPC proliferation and suppresses neuronal differentiation. Conversely, knockdown of RBM8a in the neocortex reduces NPC proliferation and promotes premature neuronal differentiation. Moreover, overexpression of RBM8a suppresses cell cycle exit and keeps cortical NPCs in a proliferative state. To uncover the underlying mechanisms of this phenotype, genome-wide RNAseq was used to identify potential downstream genes of RBM8a in the brain, which have been implicated in autism and neurodevelopmental disorders. Interestingly, autism and schizophrenia risk genes are highly represented in downstream transcripts of RBM8a. In addition, RBM8a regulates multiple alternative splicing genes and NMD targets that are implicated in ASD. Taken together, this data suggests a novel role of RBM8a in the regulation of neurodevelopment. CONCLUSIONS: Our studies provide some insight into causes of mental illnesses and will facilitate the development of new therapeutic strategies for neurodevelopmental illnesses. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13064-015-0045-7) contains supplementary material, which is available to authorized users

Tissue engineering of functional trileaflet heart valves from human marrow stromal cells

BACKGROUND: We previously demonstrated the successful tissue engineering and implantation of functioning autologous heart valves based on vascular-derived cells. Human marrow stromal cells (MSC) exhibit the potential to differentiate into multiple cell-lineages and can be easily obtained clinically. The feasibility of creating tissue engineered heart valves (TEHV) from MSC as an alternative cell source, and the impact of a biomimetic in vitro environment on tissue differentiation was investigated. METHODS AND RESULTS: Human MSC were isolated, expanded in culture, and characterized by flow-cytometry and immunohistochemistry. Trileaflet heart valves fabricated from rapidly bioabsorbable polymers were seeded with MSC and grown in vitro in a pulsatile-flow-bioreactor. Morphological characterization included histology and electron microscopy (EM). Extracellular matrix (ECM)-formation was analyzed by immunohistochemistry, ECM protein content (collagen, glycosaminoglycan) and cell proliferation (DNA) were biochemically quantified. Biomechanical evaluation was performed using Instron(TM). In all valves synchronous opening and closing was observed in the bioreactor. Flow-cytometry of MSC pre-seeding was positive for ASMA, vimentin, negative for CD 31, LDL, CD 14. Histology of the TEHV-leaflets demonstrated viable tissue and ECM formation. EM demonstrated cell elements typical of viable, secretionally active myofibroblasts (actin/myosin filaments, collagen fibrils, elastin) and confluent, homogenous tissue surfaces. Collagen types I, III, ASMA, and vimentin were detected in the TEHV-leaflets. Mechanical properties of the TEHV-leaflets were comparable to native tissue. CONCLUSION: Generation of functional TEHV from human MSC was feasible utilizing a biomimetic in vitro environment. The neo-tissue showed morphological features and mechanical properties of human native-heart-valve tissue. The human MSC demonstrated characteristics of myofibroblast differentiation

The Forgotten Tradition. How the Logical Empiricists missed the Philosophical Significance of the work of Riemann, Christoffel and Ricci

Abstract. The paper attempts to show how the Logical Empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the Logical Empiricists neglected the fact that Riemann’s revolutionary insight flourished rather in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that in the attempt to draw the line Riemann-Helmholtz-Poincaré-Einstein Logical Empiricists were led to argue that General Relativity raised mainly a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative line of development Riemann-Chritoffel-Ricci-Einstein shows on the contrary that the main philosophical issue raised by Einstein’s theory was rather that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality