Department Seminars & Colloquia
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De novo mutations provide a powerful source of information for identifying risk genes associated with phenotypes under selection, such as autism spectrum disorder (ASD), obsessive-compulsive disorder (OCD), congenital heart disease, and schizophrenia (SCZ). However, identifying de novo variants is costly, as it requires trio-based sequencing to obtain parental genotypes. To address this limitation, we propose a method to infer inheritance class using only offspring genetic data. In our new integrated model, we evaluate variation in case and control samples, attempt to distinguish de novo mutations from inherited variation, and incorporate this information into a gene-based association framework. We validate our method through ASD gene identification, demonstrating that it provides a robust and powerful approach for identifying risk genes.
This is a reading seminar presented by the graduate student, Mr. Taeyoon Woo. Following the lecture note of Yuri Manin, he will study K_0 of schemes, and its essential properties, such as functoriality, projective bundle formula, filtrations, relationship to Picard group, blow-up squares, Chern classes, Todd classes and the Grothendieck-Riemann-Roch theorem.
A knot bounds an oriented compact connected surface in the 3-sphere, and consequently in the 4-ball. The 4-genus of a knot is the minimal genus among all such surfaces in the 4-ball, and the 4-genus of a link is defined analogously. In this talk, I will discuss lower bounds on the 4-genus derived from Cheeger-Gromov-von Neumann rho-invariants. This is joint work with Jae Choon Cha and Min Hoon Kim.
Abstract: In this talk, we discuss the global-in-time existence of strong solutions to the one-dimensional compressible Navier-Stokes system. Classical results establish only local-in-time existence under the assumption that the initial data are smooth and the initial density remains uniformly positive. These results can be extended to global-in-time existence using the relative entropy and Bresch-Desjardins entropy under the same hypotheses. This approach allows for possibly different end states and degenerate viscosity.
Reference: A. Mellet and A. Vasseur, Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. SIAM J. Math. Anal., 39(4):1344–1365, 2007/08.
Abstract :
When a plane shock hits a wedge head on, it experiences a reflection diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. In particular, the C^{1,1}-regularity is optimal for the solution across the pseudo-sonic circle and at the point where the pseudo-sonic circle meets the reflected shock where the wedge has large-angle. Also, one can obtain the C^{2,\alpha} regularity of the solution up to the pseudo-sonic circle in the pseudo-subsonic region.
Reference :
Myoungjean Bae, Gui-Qiang Chen, and Mikhail Feldman. "Regularity of solutions to regular shock reflection for potential flow." (2008)
Gui-Qiang Chen and Mikhail Feldman. "Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow"