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

Let Y be a closed and oriented 3-manifold. We define different versions of unfolded Seiberg-Witten Floer spectra for Y. These invariants generalize Manolescu's Seiberg-Witten Floer spectrum for rational homology 3-spheres. We also compute some examples when Y is a Seifert space.

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].

We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants (GCIs) is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function.

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N = 2 superconformal field theories. We also determine the mini-versal deformation of these singularities, and therefore solve the Coulomb branch spectrum and Seiberg-Witten solution.