More Like this

1. Chemical Biology Framework to Illuminate Proteostasis

   https://doi.org/10.1146/annurev-biochem-013118-111552  

   Sebastian, Rebecca M.; Shoulders, Matthew D. (June 2020, Annual Review of Biochemistry)

   null (Ed.)

   Protein folding in the cell is mediated by an extensive network of >1,000 chaperones, quality control factors, and trafficking mechanisms collectively termed the proteostasis network. While the components and organization of this network are generally well established, our understanding of how protein-folding problems are identified, how the network components integrate to successfully address challenges, and what types of biophysical issues each proteostasis network component is capable of addressing remains immature. We describe a chemical biology–informed framework for studying cellular proteostasis that relies on selection of interesting protein-folding problems and precise researcher control of proteostasis network composition and activities. By combining these methods with multifaceted strategies to monitor protein folding, degradation, trafficking, and aggregation in cells, researchers continue to rapidly generate new insights into cellular proteostasis. 

   more » « less
2. Analysis of an hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system

   https://doi.org/10.1051/m2an/2020015  

   Gong, Wei; Hu, Weiwei; Mateos, Mariano; Singler, John; Zhang, Yangwen (January 2020, ESAIM: Mathematical Modelling and Numerical Analysis)

   We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an $ L^2 $ penalty on the boundary control.  The contribution of this paper is twofold.  First, we obtain well-posedness and regularity results for the tangential Dirichlet control problem on a convex polygonal domain.  The analysis contains new features not found in similar Dirichlet control problems for the Poisson equation; an interesting result is that the optimal control has higher local regularity on the individual edges of the domain compared to the global regularity on the entire boundary.  Second, we propose and analyze a hybridizable discontinuous Galerkin (HDG) method to approximate the solution.  For convex polygonal domains, our theoretical convergence rate for the control is optimal with respect to the global regularity on the entire boundary.  We present numerical experiments to demonstrate the performance of the HDG method. 

   more » « less
3. Recursive State Machine Guided Graph Folding for Context-Free Language Reachability

   https://doi.org/10.1145/3591233  

   Lei, Yuxiang; Sui, Yulei; Tan, Shin_Hwei; Zhang, Qirun (June 2023, Proceedings of the ACM on Programming Languages)

   Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%. 

   more » « less
4. Computational approaches for extremal geometric eigenvalue problems

   C.-Y. Kao; B. Osting; and E ́. Oudet (January 2023, Handbook of numerical analysis)

   In an extremal eigenvalue problem, one considers a family of eigenvalue problems, each with discrete spectra, and extremizes a chosen eigenvalue over the family. In this chapter, we consider eigenvalue problems defined on Riemannian manifolds and extremize over the metric structure. For example, we consider the problem of maximizing the principal Laplace–Beltrami eigenvalue over a family of closed surfaces of fixed volume. Computational approaches to such extremal geometric eigenvalue problems present new computational challenges and require novel numerical tools, such as the parameterization of conformal classes and the development of accurate and efficient methods to solve eigenvalue problems on domains with nontrivial genus and boundary. We highlight recent progress on computational approaches for extremal geometric eigenvalue problems, including (i) maximizing Laplace–Beltrami eigenvalues on closed surfaces and (ii) maximizing Steklov eigenvalues on surfaces with boundary. 

   more » « less
5. Hidden convexity in the heat, linear transport, and Euler’s rigid body equations: A computational approach

   https://doi.org/10.1090/qam/1679  

   Kouskiya, Uditnarayan; Acharya, Amit (December 2024, Quarterly of Applied Mathematics)

   A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of Euler for the rotation of a rigid body about a fixed point. The formulation turns initial-(boundary) value problems into degenerate elliptic boundary value problems in (space)-time domains representing the Euler-Lagrange equations of suitably designed dual functionals in each of the above problems. We demonstrate reasonable success in approximating solutions of this range of parabolic, hyperbolic, and ODE primal problems, which includes energy dissipation as well as conservation, by a unified dual strategy lending itself to a variational formulation. The scheme naturally associates a family of dual solutions to a unique primal solution; such ‘gauge invariance’ is demonstrated in our computed solutions of the heat and transport equations, including the case of a transient dual solution corresponding to a steady primal solution of the heat equation. Primal evolution problems with causality are shown to be correctly approximated by noncausal dual problems. 

   more » « less