The single-stranded RNA Flavivirus, Zika virus (ZIKV), has recently re-emerged and spread rapidly across the western hemispheres equatorial countries, primarily through Aedes mosquito transmission. While symptoms in adult infections appear to be self-limiting and mild, severe birth defects, such as microcephaly, have been linked to infection during early pregnancy. Recently, Tang et al. (Cell Stem Cell 2016, doi: 10.1016/j.stem.2016.02.016 ) demonstrated that ZIKV efficiently infects induced pluripotent stem cell (iPSC) derived human neural progenitor cells (hNPCs), resulting in cell cycle abnormalities and apoptosis. Consequently, hNPCs are a suggested ZIKV target. We analyzed the transcriptomic sequencing (RNA-seq) data (GEO: GSE78711) of ZIKV (Strain: MR766) infected hNPCs. For comparison to the ZIKV-infected hNPCs, the expression data from hNPCs infected with human cytomegalovirus (CMV) (Strain: AD169) was used (GEO: GSE35295). Utilizing a combination of Gene Ontology, database of human diseases, and pathway analysis, we generated a putative systemic model of infection supported by known molecular pathways of other highly related viruses. We analyzed RNA-sequencing data for transcript expression alterations in ZIKV-infected hNPCs, and then compared them to expression patterns of iPSC-derived hNPCs infected with CMV, a virus that can also induce severe congenital neurological defects in developing fetuses. We demonstrate for the first time that many of cellular pathways correlate with clinical pathologies following ZIKV infection such as microcephaly, congenital nervous

In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar—possibly infinite—graph with nonnegative combinatorial curvature and positive total curvature is a finite group, and give an upper bound estimate for the order of the group.

We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [14] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, $\max_{i,j} \E \abs{h_{ij}}^2$. As a consequence, we prove the universality of the local $n$-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width $W\gg N^{1-\e_n}$ with some $\e_n>0$ and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17,19,6].

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box  of side length $L$. We take the $limit N,L \to \infty $ while keeping the density $\rho = N/L^3 fixed and small. We prove a new lower bound for its ground state energy per particle $$ \frac{E(N,\Lambda)}{N} \ge 4 \pi a \rho [1- O(\rho^{1/3} | log \rho |^3) ] $$ as $\rho \to 0$, where $a$ is the scattering length of $V$.

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