We consider the performance of Glauber dynamics for the random cluster model with real parameter $q\gt 1$ and temperature $\beta \gt 0$. Recent work by Helmuth, Jenssen, and Perkins detailed the ordered/disordered transition of the model on random $\Delta$-regular graphs for all sufficiently large $q$ and obtained an efficient sampling algorithm for all temperatures $\beta$ using cluster expansion methods. Despite this major progress, the performance of natural Markov chains, including Glauber dynamics, is not yet well understood on the random regular graph, partly because of the non-local nature of the model (especially at low temperatures) and partly because of severe bottleneck phenomena that emerge in a window around the ordered/disordered transition. Nevertheless, it is widely conjectured that the bottleneck phenomena that impede mixing from worst-case starting configurations can be avoided by initialising the chain more judiciously. Our main result establishes this conjecture for all sufficiently large $q$ (with respect to $\Delta$). Specifically, we consider the mixing time of Glauber dynamics initialised from the two extreme configurations, the all-in and all-out, and obtain a pair of fast mixing bounds which cover all temperatures $\beta$, including in particular the bottleneck window. Our result is inspired by the recent approach of Gheissari and Sinclair for the Ising model who obtained a similar flavoured mixing-time bound on the random regular graph for sufficiently low temperatures. To cover all temperatures in the RC model, we refine appropriately the structural results of Helmuth, Jenssen and Perkins about the ordered/disordered transition and show spatial mixing properties ‘within the phase’, which are then related to the evolution of the chain.

OBJECTIVES/SPECIFIC AIMS: The primary aim is to assess differences in therapeutic effect between MSC and EPC EVs on acute ischemic rat hearts through delivery in a biocompatible and shear-thinning hydrogel. Primary outcomes for therapeutic assessment include an in-vitro angiogenesis assay and in-vivo hemodynamic analysis, mainly identifying differences in ejection fraction and contractility. Secondary hemodynamic outcomes include cardiac output, stroke volume, and end-diastolic pressure volume relationship (EDPVR). Secondary structural outcomes include post-mortem scar analysis and immunohistochemistry (IHC) staining for angiomyogenesis. METHODS/STUDY POPULATION: MSCs and EPCs will be cultured according to previously published protocols. EVs will be isolated from cultured cell lines through precipitation methods with polyethylene glycol. EVs will be qualitatively analyzed with nanoparticle tracking analysis (NTA) and flow cytometry. The shear thinning hydrogel (STG) will be constructed using a hyaluronic backbone conjugated to adamantane or beta-cyclodextrin, ultimately facilitating guest-host interactions with shear thinning properties. Controls and treatment groups mixed with the hydrogel will be injected into the border zone of infarcted Wistar rat hearts immediately following a left anterior descending artery ligation. Hemodynamic assessment will be performed at four weeks through left ventricular catheter based pressure-volume recordings. Ex-vivo analysis will include scar thickness assessment using Masson collagen staining and IHC stain for vessel (anti-vonWillebrand factor; anti-Isolectin) and myocyte formation (anti-cardiac Troponin I). RESULTS/ANTICIPATED RESULTS: We hypothesize that, in-vitro, MSC-EVs will demonstrate non-inferior angiogenic potential as compared to EPC-EVs. We posit that MSC-EVs will demonstrate superior therapeutic effect to EPC-EVs in-vivo as measured by functional hemodynamics and structural assessment. We have successfully isolated MSC and EPC EVs and have validated uniformity across EV populations (Figure 1). Preliminary data from the angiogenesis assay (n=3) demonstrated that MSC-EV and EPC-EV produce non-significantly different angiogenic potential as measured by number of vascular meshing extremes (p=0.144) and length of master vascular segment (p=0.193), with significant differences compared to either positive or negative controls. DISCUSSION/SIGNIFICANCE OF IMPACT: Novel regenerative therapies are needed for patients with a history of AMI given current limitations to therapy and sequelae of ischemic heart disease. Delivery of extracellular vesicles through a shear-thinning gel is a novel “off-the-shelf” translational approach to address the current clinical need.

A dramatic paradigm shift has occurred in European and German hate-speech laws, from their nineteenth-century origins in repressive campaigns against the Left to their present association with pluralism, tolerance, and minority rights. This article rethinks the timing and causes of that shift, arguing that, contrary to the prevailing scholarship, the decade of the 1890s—not 1945—constituted the first key turning point toward a human-rights model of hate-speech law. Departing from a more traditional legal historiography focused on formal legal institutions and laws, the article examines law “from below” as social and political practice. The results show how, in the 1890s, a new vision of hate speech began to take shape when a grassroots Jewish defense movement began to appropriate and reshape the law in order to oppose antisemites. In theoretical terms, the article's method of examining the interaction of law and politics shows that from the 1840s onward, the politics surrounding hate-speech law refutes simple binary constructions that cast German legal culture as “dignitarian” and distinct from U.S. “libertarianism.”

Pregnancy and lactation are times of additional demand for Ca. Ca is transferred across the placenta for fetal skeletal mineralisation, and supplied to the mammary gland for secretion into breast milk. In theory, these additional maternal requirements could be met through mobilisation of Ca from the skeleton, increased intestinal Ca absorption efficiency, enhanced renal Ca retention or greater dietary Ca intake. The extent to which any or all of these apply, the underpinning biological mechanisms and the possible consequences for maternal and infant bone health in the short and long term are the focus of the present review. The complexities in the methodological aspects of interpreting the literature in this area are highlighted and the inter-individual variation in the response to pregnancy and lactation is reviewed. In summary, human pregnancy and lactation are associated with changes in Ca and bone metabolism that support the transfer of Ca between mother and child. The changes generally appear to be independent of maternal Ca supply in populations where Ca intakes are close to current recommendations. Evidence suggests that the processes are physiological in humans and that they provide sufficient Ca for fetal growth and breast-milk production, without relying on an increase in dietary Ca intake or compromising long-term maternal bone health. Further research is needed to determine the limitations of the maternal response to the Ca demands of pregnancy and lactation, especially among mothers with marginal and low dietary Ca intake, and to define vitamin D adequacy for reproductive women.