The Differential Counting Polynomial

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common generalization of the dimension polynomial and the (algebraic) counting polynomial. Under mild additional asumptions, the differential counting polynomial decides whether a given set of solutions of a system of differential equations is the complete set of solutions

The Differential Dimension Polynomial for Characterizable Differential Ideals

We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it decides equality of characterizable differential ideals contained in each other

On the Ext-computability of Serre quotient categories

To develop a constructive description of $\mathrm{Ext}$ in categories of coherent sheaves over certain schemes, we establish a binatural isomorphism between the $\mathrm{Ext}$-groups in Serre quotient categories $\mathcal{A}/\mathcal{C}$ and a direct limit of $\mathrm{Ext}$-groups in the ambient Abelian category $\mathcal{A}$. For $\mathrm{Ext}^1$ the isomorphism follows if the thick subcategory $\mathcal{C} \subset \mathcal{A}$ is localizing. For the higher extension groups we need further assumptions on $\mathcal{C}$. With these categories in mind we cannot assume $\mathcal{A}/\mathcal{C}$ to have enough projectives or injectives and therefore use Yoneda's description of $\mathrm{Ext}$.Comment: updated bibliography and deleted remaining occurrences of "maximally

Thomas decompositions of parametric nonlinear control systems

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic behaviour of the system (in terms of observability, flatness, etc.). The constructive symbolic method is based on the differential Thomas decomposition into disjoint simple systems, in particular its elimination properties

On monads of exact reflective localizations of Abelian categories

In this paper we define Gabriel monads as the idempotent monads associated to exact reflective localizations in Abelian categories and characterize them by a simple set of properties. The coimage of a Gabriel monad is a Serre quotient category. The Gabriel monad induces an equivalence between its coimage and its image, the localizing subcategory of local objects.Comment: fixed Prop. 2.10, updated bibliograph

On Top of the Alveolar Epithelium: Surfactant and the Glycocalyx

Gas exchange in the lung takes place via the air-blood barrier in the septal walls of alveoli. The tissue elements that oxygen molecules have to cross are the alveolar epithelium, the interstitium and the capillary endothelium. The epithelium that lines the alveolar surface is covered by a thin and continuous liquid lining layer. Pulmonary surfactant acts at this air-liquid interface. By virtue of its biophysical and immunomodulatory functions, surfactant keeps alveoli open, dry and clean. What needs to be added to this picture is the glycocalyx of the alveolar epithelium. Here, we briefly review what is known about this glycocalyx and how it can be visualized using electron microscopy. The application of colloidal thorium dioxide as a staining agent reveals differences in the staining pattern between type I and type II alveolar epithelial cells and shows close associations of the glycocalyx with intraalveolar surfactant subtypes such as tubular myelin. These morphological findings indicate that specific spatial interactions between components of the surfactant system and those of the alveolar epithelial glycocalyx exist which may contribute to the maintenance of alveolar homeostasis, in particular to alveolar micromechanics, to the functional integrity of the air-blood barrier, to the regulation of the thickness and viscosity of the alveolar lining layer, and to the defence against inhaled pathogens. Exploring the alveolar epithelial glycocalyx in conjunction with the surfactant system opens novel physiological perspectives of potential clinical relevance for future research

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring $R$, i.e., a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over $R$. For a finitely generated maximal ideal $\mathfrak{m}$ in a commutative ring $R$ we show how solving (in)homogeneous linear systems over $R_{\mathfrak{m}}$ can be reduced to solving associated systems over $R$. Hence, the computability of $R$ implies that of $R_{\mathfrak{m}}$. As a corollary we obtain the computability of the category of finitely presented $R_{\mathfrak{m}}$-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a by-product, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu

Thomas Decomposition and Nonlinear Control Systems

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas\u27 algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas\u27 algorithm is used to illustrate the techniques on explicit examples

Murine and human pluripotent stem cell-derived cardiac bodies form contractile myocardial tissue in vitro

AimsWe explored the use of highly purified murine and human pluripotent stem cell (PSC)-derived cardiomyocytes (CMs) to generate functional bioartificial cardiac tissue (BCT) and investigated the role of fibroblasts, ascorbic acid (AA), and mechanical stimuli on tissue formation, maturation, and functionality.Methods and resultsMurine and human embryonic/induced PSC-derived CMs were genetically enriched to generate three-dimensional CM aggregates, termed cardiac bodies (CBs). Addressing the critical limitation of major CM loss after single-cell dissociation, non-dissociated CBs were used for BCT generation, which resulted in a structurally and functionally homogenous syncytium. Continuous in situ characterization of BCTs, for 21 days, revealed that three critical factors cooperatively improve BCT formation and function: both (i) addition of fibroblasts and (ii) ascorbic acid supplementation support extracellular matrix remodelling and CB fusion, and (iii) increasing static stretch supports sarcomere alignment and CM coupling. All factors together considerably enhanced the contractility of murine and human BCTs, leading to a so far unparalleled active tension of 4.4 mN/mm2 in human BCTs using optimized conditions. Finally, advanced protocols were implemented for the generation of human PSC-derived cardiac tissue using a defined animal-free matrix composition.ConclusionBCT with contractile forces comparable with native myocardium can be generated from enriched, PSC-derived CMs, based on a novel concept of tissue formation from non-dissociated cardiac cell aggregates. In combination with the successful generation of tissue using a defined animal-free matrix, this represents a major step towards clinical applicability of stem cell-based heart tissue for myocardial repair. © 2013 The Author