Division of Mathematical Sciences

In the Indo-Burma subduction zone the subducted and hanging-wall lithospheres interact strongly with the asthenosphere due to India-Asia plate convergence. Imaging the lithosphere-asthenosphere boundary (LAB) is therefore crucial for an in-depth understanding of the convergence process. Our Sp receiver function (RF) images built with dense array data reveal a regionally shallow LAB at an average depth of ~70 km, except beneath the Indo-Burma Ranges, where the Indian LAB dips eastward at an average of ~20° down to ~140 km; this dipping geometry is resolved primarily through SKS-derived RFs. Farther east, a positive velocity gradient emerges ~50-80 km beneath the Burma LAB, together they define an upper-asthenospheric low-velocity layer. Waveform modeling further indicates a sharp LAB, characterized by a Vs drop up to ~6-10% over <~20 km. Our RF results support a melt-rich LAB, potentially linked to the asthenospheric flow induced by the Indian plate subduction and subsequent rollback and/or tearing.

NMR prediction using ChemDoodle, NMR calculation withGaussian,and hands-on data collection using a benchtop NMR spectrometer wereexplored to assess their synergistic capacity in teaching NMR to organicchemistry students. Nine molecules representing functional groupscommonly encountered in undergraduate organic chemistry were selected.Spectra obtained using each of the three methods were incorporatedinto a laboratory exercise where students utilized all methods tolearn about NMR. Our approach combines experimental work with bothan approximation and theoretical calculation providing students witha more comprehensive understanding. Ultimately, students learned howto perform NMR spectroscopy and how different computational toolscan approach the problem in fundamentally different ways as outlinedbelow. Our qualitative analysis reveals that students engaged in higherorder thinking skills and reported several benefits to their learning.

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In this paper, we study corners in tree‐like and permutation tableaux. Tree‐like tableaux are in bijection with other combinatorial structures, including permutation tableaux, and have a connection to the partially asymmetric simple exclusion process (PASEP), an important model of an interacting particles system. In particular, in the context of tree‐like tableaux, a corner corresponds to a node occupied by a particle that could jump to the right while inner corners indicate a particle with an empty node to its left. Thus, the total number of corners represents the number of nodes at which PASEP can move, that is, the total current activity of the system. As the number of inner corners and regular corners is connected, we limit our discussion to just regular corners and show that asymptotically, the number of corners in a tableau of length n is normally distributed. Furthermore, since the number of corners in tree‐like tableaux is closely related to the number of corners in permutation tableaux, we will discuss the corners in the context of the latter tableaux. Finally, using analogous techniques, we prove a central limit theorem for the number of corners in symmetric tree‐like tableaux and type‐B permutation tableaux.

The rapid development of cryo-electron microscopy (cryo-EM) has led to the generation of significant low-resolution electron density data of biomolecules. However, the atomistic details of huge biomolecules usually cannot be obtained because it is very difficult to construct all-atom models for MD simulations. Thus, it is still a challenge to make use of the rich low-resolution cryo-EM data for computer simulation and functional study. In this study, we proposed a new method called Convolutional and K-means Coarse-Graining (CK-CG) for the efficient coarse-graining of large biological systems. Using the CK-CG method, we could directly map the cryo-EM data into coarse-grained (CG) beads. Furthermore, the CG beads were parameterized with an empirical harmonic potential to construct a new CG model. We subjected the CK-CG models of the fibrillar protein assemblies F-actin and collagen to external forces in pulling dynamic simulations to assess their mechanical response. The agreement between the estimated tensile stiffness between CG models and experiments demonstrates the validity of the CK-CG method. Thus, our method provides a practical strategy for the direct construction of a structural model from low-resolution data for biological function studies.

This article presents a weak Galerkin (WG) finite element method for the Cahn-Hilliard equation. The WG method makes use of piecewise polynomials as approximating functions, with weakly defined partial derivatives (first and second order) computed locally by using the information in the interior and on the boundary of each element. A stabilizer is constructed and added to the numerical scheme for the purpose of providing certain weak continuities for the approximating function. A mathematical convergence theory is developed for the corresponding numerical solutions, and optimal order of error estimates are derived. Some numerical results are presented to illustrate the efficiency and accuracy of the method.

SYNOPTIC ABSTRACTIn survival analysis and reliability, researchers are often interested in assessing the effects of different stress factors on the lifetime of experimental units. The model introduced in this article is motivated by a study of the effects of altitude and other risk factors on decompression sickness, a condition encountered when individuals are exposed to significant changes in environmental pressure. Unlike standard life-testing experiments, in this study, the levels of the stress factor, viz. altitude, are changed during the exposure duration. This is known as a step-stress test, a class of accelerated testing, widely used in material testing. Recently Kannan, Kundu, and Balakrishnan (2010) introduced the cumulative risk model as an alternative to the widely used cumulative exposure model. The new model allows for the inclusion of a lag period in the hazard function, a more realistic assumption in most applications. In this article, we consider the cumulative risk model assuming that the lifetime distributions of the experimental units follow Weibull distributions at the different levels of the risk factor. It is assumed that the level of the stress factor is changed only once during the exposure duration at a pre-fixed time τ1. The maximum likelihood and the least squares methods have been used to estimate the unknown parameters. Monte Carlo simulations are performed to compare the performances of the two different methods. We further propose the Bayes estimators of the unknown parameters of the model. To evaluate the performance of the model, one data set from the altitude decompression sickness experiment has been analyzed, and it is observed that the proposed model fits the data quite well.