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Chronic metabolic diseases such as diabetes are characterized by delayed wound healing and a dysregulation of the inflammatory phase of wound repair. Our study focuses on changes in the payload of extracellular vesicles (EVs) communicating between immune cells and stromal cells in the wound bed, which regulate the rate of wound closure. Adoptive transfer of EVs from genetically defined mouse models are used here to demonstrate a functional and molecular basis for differences in the pro-reparative biological activity of diabetic (db/db) vs. wildtype EVs in wound healing. We identify several members of the Serpin family of serine protease inhibitors that are absent in db/db EVs, then we overexpress Serpin A1, F2 and G1 in EVs to evaluate their effect on wound healing in db/db mice. Serpins have an important role in regulating levels of elastase, plasmin and complement factors that coordinate immune cell signaling in full thickness wounds in a diabetic model. Here, we establish a novel therapeutic approach by engineering the payload of EVs based on proteomic analysis. Serpin-loaded EVs were used to rescue the Serpin deficiency identified by proteomics and promote wound healing in db/db mice, as well as evaluated how EVs affected extracellular matrix remodeling and the resolution of tissue injury. Therefore, we propose that the identification of EV payloads that are downregulated in diabetic wounds can be systematically analyzed for their functional activity and potential as a therapeutic, based on whether their re-expression in engineered EVs restores normal kinetics of tissue repair in chronic wounds. Graphical Abstract

A distance based measure of dependence is proposed for stable distributions that completely characterizes independence for a bivariate stable distribution. Properties of this measure are analyzed, and contrasted with the covariation and co-difference. A sample analog of the measure is defined and demonstrated on simulated and real data, including time series and distributions in the domain of attraction of a stable law.

A flexible class of multivariate generalized spherical distributions with star-shaped level sets is developed. To work in dimension above two requires tools from computational geometry and multivariate numerical integration. An algorithm to approximately simulate from these star-shaped distributions is developed; it also works for simulating from more general tessellations. These techniques are implemented in the R package gensphere.

Stable distributions have heavy tails that are asymptotically Paretian. Accurate computations of stable densities and distribution functions are used to analyze when the Paretian tail actually appears. Implications for estimation procedures are discussed. In addition to numerically locating the mode of a general stable distribution, analytic and numeric results are given for the mode. Extensive tables of stable percentiles have been computed; aspects of these tables and the appropriateness of infinite variance stable models are discussed.

Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the L p representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to “locally approximately independent increments.” Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs.