Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints

We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.Comment: 44 pages, 3 figure

A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control

Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

Tumour vascularization: sprouting angiogenesis and beyond

Tumour angiogenesis is a fast growing domain in tumour biology. Many growth factors and mechanisms have been unravelled. For almost 30 years, the sprouting of new vessels out of existing ones was considered as an exclusive way of tumour vascularisation. However, over the last years several additional mechanisms have been identified. With the discovery of the contribution of intussusceptive angiogenesis, recruitment of endothelial progenitor cells, vessel co-option, vasculogenic mimicry and lymphangiogenesis to tumour growth, anti-tumour targeting strategies will be more complex than initially thought. This review highlights these processes and intervention as a potential application in cancer therapy. It is concluded that future anti-vascular therapies might be most beneficial when based on multimodal anti-angiogenic, anti-vasculogenic mimicry and anti-lymphangiogenic strategies

CD34 marks angiogenic tip cells in human vascular endothelial cell cultures

The functional shift of quiescent endothelial cells into tip cells that migrate and stalk cells that proliferate is a key event during sprouting angiogenesis. We previously showed that the sialomucin CD34 is expressed in a small subset of cultured endothelial cells and that these cells extend filopodia: a hallmark of tip cells in vivo. In the present study, we characterized endothelial cells expressing CD34 in endothelial monolayers in vitro. We found that CD34-positive human umbilical vein endothelial cells show low proliferation activity and increased mRNA expression of all known tip cell markers, as compared to CD34-negative cells. Genome-wide mRNA profiling analysis of CD34-positive endothelial cells demonstrated enrichment for biological functions related to angiogenesis and migration, whereas CD34-negative cells were enriched for functions related to proliferation. In addition, we found an increase or decrease of CD34-positive cells in vitro upon exposure to stimuli that enhance or limit the number of tip cells in vivo, respectively. Our findings suggest cells with virtually all known properties of tip cells are present in vascular endothelial cell cultures and that they can be isolated based on expression of CD34. This novel strategy may open alternative avenues for future studies of molecular processes and functions in tip cells in angiogenesis

Multi-parametric assessment of the anti-angiogenic effects of liposomal glucocorticoids

Inflammation plays a prominent role in tumor growth. Anti-inflammatory drugs have therefore been proposed as anti-cancer therapeutics. In this study, we determined the anti-angiogenic activity of a single dose of liposomal prednisolone phosphate (PLP-L), by monitoring tumor vascular function and viability over a period of one week. C57BL/6 mice were inoculated subcutaneously with B16F10 melanoma cells. Six animals were PLP-L-treated and six served as control. Tumor tissue and vascular function were probed using MRI before and at three timepoints after treatment. DCE-MRI was used to determine Ktrans, ve, time-to-peak, initial slope and the fraction of non-enhancing pixels, complemented with immunohistochemistry. The apparent diffusion coefficient (ADC), T2 and tumor size were assessed with MRI as well. PLP-L treatment resulted in smaller tumors and caused a significant drop in Ktrans 48 h post-treatment, which was maintained until one week after drug administration. However, this effect was not sufficient to significantly distinguish treated from non-treated animals. The therapy did not affect tumor tissue viability but did prevent the ADC decrease observed in the control group. No evidence for PLP-L-induced tumor vessel normalization was found on histology. Treatment with PLP-L altered tumor vascular function. This effect did not fully explain the tumor growth inhibition, suggesting a broader spectrum of PLP-L activities