Increased understanding of developmental disorders of the brain has shown that genetic mutations, environmental toxins and biological insults typically act during developmental windows of susceptibility. Identifying these vulnerable periods is a necessary and vital step for safeguarding women and their fetuses against disease causing agents during pregnancy and for developing timely interventions and treatments for neurodevelopmental disorders. We analyzed developmental time-course gene expression data derived from human pluripotent stem cells, with disease association, pathway, and protein interaction databases to identify windows of disease susceptibility during development and the time periods for productive interventions. The results are displayed as interactive Susceptibility Windows Ontological Transcriptome (SWOT) Clocks illustrating disease susceptibility over developmental time. Using this method, we determine the likely windows of susceptibility for multiple neurological disorders using known disease associated genes and genes derived from RNA-sequencing studies including autism spectrum disorder, schizophrenia, and Zika virus induced microcephaly. SWOT clocks provide a valuable tool for integrating data from multiple databases in a developmental context with data generated from next-generation sequencing to help identify windows of susceptibility.

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A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO 2 ) migration and storage [8]. Dual flux curves characterize the model, giving rise to flux discontinuities. One convex flux describes the invasion of the plume into pore space, and the other captures the flow as the plume leaves CO 2 bubbles behind, which are then trapped in the pore space. We investigate the method of characteristics, the structure of shock and rarefaction waves, and the result of binary wave interactions. The dual flux property introduces unexpected differences between the structure of these solutions and those of a scalar conservation law with a convex flux. During our analysis, we introduce a new construction of cross-hatch characteristics in regions of the space-time plane where the solution is constant, and there are two characteristic speeds. This construction is used to generalize the notion of the Lax entropy condition for admissible shocks, and is crucial to continuing the propagation of a shock wave if its speed becomes characteristic.

Recent theory of authors ascribes attenuation in typical marine mud sediments to be caused by viscous interaction of sea water with embedded silt particles. Influence of underlying clay matrix is regarded as passive and of minor importance. Present paper considers silt-less mud where clay particles are flocculated to a card-house structure, with the flocculation hypothesis yielding a porosity of 90%. During the passage of a sound wave, Van-der-Waals forces between platelets cause the matrix to move to-and-fro as a unit; viscous forces are insufficient to cause the matrix to move perfectly with the water. The silt-less theory assumes that the local force on the matrix is the sum of the viscous forces on the platelets in the matrix. Forces on clay particles, which are thin platelets, are given by a low-Reynolds flow theory initiated by Stokes, and further developed by Oberbeck, Lamb, and Brenner. For each particle there is a characteristic frequency inversely proportional to the platelet thickness, which turns out to be extremely high for clay. Consequently, at acoustic frequencies, the clay matrix moves nearly in lock-step with the fluid motion associated with the sound wave. The inevitable very-small slip leads to an attenuation that is proportional to the square of the frequency, but which is very small compared with that of mud with embedded silt-particles. Current idealized theory results in prediction of attenuation inversely proportional to viscosity and of nearly constant phase velocity. [Work supported by ONR.]

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