Oral Tau Aggregation Inhibitor for Alzheimer’s Disease : Design, Progress and Basis for Selection of the 16 mg/day Dose in a Phase 3, Randomized, Placebo-Controlled Trial of Hydromethylthionine Mesylate

Funding Information: We gratefully acknowledge the contribution of the scientific advisory board, study investigators, and the generosity of study participants. The authors thank EVERSANA™ for providing medical writing support, which was funded by TauRx Therapeutics in accordance with Good Publication Practice (GPP3) guidelines ( http://www.ismpp.org/gpp3 ). Publisher Copyright: © 2022, The Author(s).Peer reviewedPublisher PD

The Evolution of the Galaxy Stellar Mass Function at z= 4-8: A Steepening Low-mass-end Slope with Increasing Redshift

We present galaxy stellar mass functions (GSMFs) at $z=$ 4-8 from a rest-frame ultraviolet (UV) selected sample of $\sim$4500 galaxies, found via photometric redshifts over an area of $\sim$280 arcmin$^2$ in the CANDELS/GOODS fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data yet-to-date and the relatively large volume allow us to place a better constraint at both the low- and high-mass ends of the GSMFs compared to previous space-based studies from pre-CANDELS observations. Supplemented by a stacking analysis, we find a linear correlation between the rest-frame UV absolute magnitude at 1500 \AA\ ($M_{\rm UV}$) and logarithmic stellar mass ($\log M_*$) that holds for galaxies with $\log(M_*/M_{\odot}) \lesssim 10$. We use simulations to validate our method of measuring the slope of the $\log M_*$-$M_{\rm UV}$ relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over $z=$ 4-8, while the normalization of the trend exhibits a weak evolution toward lower masses at higher redshift. We combine the $\log M_*$-$M_{\rm UV}$ distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs, finding that the low-mass-end slope becomes steeper with increasing redshift from $\alpha=-1.55^{+0.08}_{-0.07}$ at $z=4$ to $\alpha=-2.25^{+0.72}_{-0.35}$ at $z=8$. The inferred stellar mass density, when integrated over $M_*=10^8$-$10^{13} M_{\odot}$, increases by a factor of $10^{+30}_{-2}$ between $z=7$ and $z=4$ and is in good agreement with the time integral of the cosmic star formation rate density.Comment: 27 pages, 17 figures, ApJ, in pres

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

Transcriptional regulation of the urokinase receptor (u-PAR) - A central molecule of invasion and metastasis

The phenomenon of tumor-associated proteolysis has been acknowledged as a decisive step in the progression of cancer. This short review focuses on the urokinase receptor (u-PAR), a central molecule involved in tumor-associated invasion and metastasis, and summarizes the transcriptional regulation of u-PAR. The urokinase receptor (u-PAR) is a heavily glycosylated cell surface protein and binds the serine protease urokinase specifically and with high affinity. It consists of three similar cysteine-rich repeats and is anchored to the cell membrane via a GPI-anchor. The u-PAR gene comprises 7 exons and is located on chromosome 19q13. Transcriptional activation of the u-PAR promoter region can be induced by binding of transcription factors (Sp1, AP-1, AP-2, NF-kappaB). One current study gives an example for transcriptional downregulation of u-PAR through a PEA3/ets transcriptional silencing element. Knowledge of the molecular regulation of this molecule in tumor cells could be very important for diagnosis and therapy in the near future

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes