Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

Origin of White and Brown Adipose Cells From Vascular Endothelium: A Dissertation

Obesity is associated with insulin resistance, dyslipidemia, and cardiovascular disease. The current obesity epidemic is the result of surplus energy consumption. Excess energy is stored in expanding adipose tissue. Adipose tissue growth entails the enlargement of existing adipocytes, the formation of new fat cells from preexisting progenitors, and the coordinated development of supporting vasculature. Identifying adipocyte progenitors and the mechanism of adipose tissue expansion is crucial for the development of new strategies to combat obesity and its complications. Though important progress has been made towards understanding the developmental origin of adipocytes, the identities of adipocyte progenitors are still not completely known. The main objective of this study is to determine whether endothelial cells of the adipose tissue can give rise to new adipocytes. Our results indicate that murine endothelial cells of adipose tissue are pluripotent and can potentially give rise to preadipocytes. Lineage tracing experiments using the VE-Cadherin-Cre transgenic mouse reveal localization of reporter genes in endothelial cells, preadipocytes and white and brown adipocytes. Moreover, capillary sprouts from human adipose tissue, which have predominantly endothelial cell characteristics, are found to express Zfp423, a preadipocyte determination factor. In response to PPARγ activation, endothelial characteristics of sprouting cells are progressively lost, and cells form structurally and biochemically defined adipocytes. Taken together, our data support an endothelial origin of a population of adipocytes. The ability of the vascular endothelium to give rise to adipocytes may explain how angiogenesis and adipogenesis can be temporally and spatially coordinated. Analysis of BAT and WAT revealed that adipose depots have distinct compositions of adipocyte progenitors. Of the CD45-CD29+Sca1+CD24+ progenitor population, only 17% and 52% express VE-Cadherin in WAT and BAT, respectively. Our data show that the number of these specific progenitors in BAT and WAT are highly variable and suggest that a considerable number of adipocytes progenitors may have a non-endothelial cell origin. Differences in composition and types of adipocyte progenitors may explain the differences in the adipocytes phenotypes that we observe in discrete depots. In brief, we find that the vascular endothelium gives rise to a population of brown and white fat cells, and that the number of endothelial-derived adipocyte progenitors residing in BAT and WAT is highly variable. These results expand our current understanding of adipose tissue growth, and, we hope, will accelerate the development of treatments for obesity-related complications

Transport properties in Simplified Double Exchange model

Transport properties of the manganites by the double-exchange mechanism are considered. The system is modeled by a simplified double-exchange model, i.e. the Hund coupling of the itinerant electron spins and local spins is simplified to the Ising-type one. The transport properties such as the electronic resistivity, the thermal conductivity, and the thermal power are calculated by using Dynamical mean-field theory. The transport quantities obtained qualitatively reproduce the ones observed in the manganites. The results suggest that the Simplified double exchange model underlies the key properties of the manganites.Comment: 5 pages, 5 eps figure

ZFOURGE: Extreme 5007A˚\AA emission may be a common early-lifetime phase for star-forming galaxies at z>2.5z > 2.5

Using the \prospector\ spectral energy distribution (SED) fitting code, we analyze the properties of 19 Extreme Emission Line Galaxies (EELGs) identified in the bluest composite SED in the \zfourge\ survey at $2.5 \leq z \leq 4$. \prospector\ includes a physical model for nebular emission and returns probability distributions for stellar mass, stellar metallicity, dust attenuation, and nonparametric star formation history (SFH). The EELGs show evidence for a starburst in the most recent 50 Myr, with the median EELG having a specific star formation rate (sSFR) of 4.6 Gyr$^{-1}$ and forming 15\% of its mass in this short time. For a sample of more typical star-forming galaxies (SFGs) at the same redshifts, the median SFG has a sSFR of 1.1 Gyr$^{-1}$ and forms only $4\%$ of its mass in the last 50 Myr. We find that virtually all of our EELGs have rising SFHs, while most of our SFGs do not. From our analysis, we hypothesize that many, if not most, star-forming galaxies at $z \geq 2.5$ undergo an extreme H$\beta$+[\hbox{{\rm O}\kern 0.1em{\sc iii}}] emission line phase early in their lifetimes. In a companion paper, we obtain spectroscopic confirmation of the EELGs as part of our {\sc MOSEL} survey. In the future, explorations of uncertainties in modeling the UV slope for galaxies at $z>2$ are needed to better constrain their properties, e.g. stellar metallicities.Comment: 11 pages, 5 figures (main figure is fig 5), accepted for publication in Ap

Integrable and superintegrable systems associated with multi-sums of products

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.Comment: 26 pages, submitted to Proceedings of the royal society