Hypoxic pre-conditioning increases the infiltration of endothelial cells into scaffolds for dermal regeneration pre-seeded with mesenchymal stem cells.

Many therapies using mesenchymal stem cells (MSC) rely on their ability to produce and release paracrine signals with chemotactic and pro-angiogenic activity. These characteristics, however, are mostly studied under standard in vitro culture conditions. In contrast, various novel cell-based therapies imply pre-seeding MSC into bio-artificial scaffolds. Here we describe human bone marrow-derived MSC seeded in Integra matrices, a common type of scaffold for dermal regeneration (SDR). We show and measured the distribution of MSC within the SDR, where cells clearly establish physical interactions with the scaffold, exhibiting constant metabolic activity for at least 15 days. In the SDR, MSC secrete VEGF and SDF-1α and induce transwell migration of CD34(+) hematopoietic/endothelial progenitor cells, which is inhibited in the presence of a CXCR4/SDF-1α antagonist. MSC in SDR respond to hypoxia by altering levels of angiogenic signals such as Angiogenin, Serpin-1, uPA, and IL-8. Finally, we show that MSC-containing SDR that have been pre-incubated in hypoxia show higher infiltration of endothelial cells after implantation into immune deficient mice. Our data show that MSC are fully functional ex vivo when implanted into SDR. In addition, our results strongly support the notion of hypoxic pre-conditioning MSC-containing SDR, in order to promote angiogenesis in the wounds

Lecture 14: Randomized Algorithms for Least Squares Problems

The emergence of massive data sets, over the past twenty or so years, has lead to the development of Randomized Numerical Linear Algebra. Randomized matrix algorithms perform random sketching and sampling of rows or columns, in order to reduce the problem dimension or compute low-rank approximations. We review randomized algorithms for the solution of least squares/regression problems, based on row sketching from the left, or column sketching from the right. These algorithms tend to be efficient and accurate on matrices that have many more rows than columns. We present probabilistic bounds for the amount of sampling required to achieve a user-specified error tolerance. Along the way we illustrate important concepts from numerical analysis (conditioning and pre-conditioning), probability (coherence, concentration inequalities), and statistics (sampling and leverage scores). Numerical experiments illustrate that the bounds are informative even for small problem dimensions and stringent success probabilities. To stress-test the bounds, we present algorithms that generate \u27adversarial\u27 matrices\u27 for user-specified coherence and leverage scores. If time permits, we discuss the additional effect of uncertainties from the underlying Gaussian linear model in a regression problem

Universal characteristics of deep neural network loss surfaces from random matrix theory

This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning gradient descent algorithms. We also present insights into deep neural network loss surfaces from quite general arguments based on tools from statistical physics and random matrix theory.Comment: 42 page

Entanglement, non-Markovianity, and causal non-separability

Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: non-Markovianity, entanglement, and causal indefiniteness.Comment: 14 pages, 8 figure