The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a $2q$-state symmetric model, with two categories of $q$ states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second order dynamical system based on this model and show that the Kesten-Stigum reconstruction bound is not tight when $q \geq 4$.Comment: Accepted, to appear Journal of Statistical Physic

Perspective: "Relativity + Correlation + QED = Experiment''

The ultimate goal of electronic structure calculations is to make the left and right hand sides of the titled ``equation'' as close as possible. This requires high-precision treatment of relativistic, correlation, and quantum electrodynamics (QED) effects simultaneously. While both relativistic and QED effects can readily be built into the many-electron Hamiltonian, electron correlation is more difficult to describe due to the exponential growth of the number of parameters in the wave function. Compared with the spin-free case, spin-orbit interaction results in the loss of spin symmetry and concomitant complex algebra, thereby rendering the treatment of electron correlation even more difficult. Possible solutions to these issues are highlighted here.Comment: 3 figure

An Invitation to Linear Algebra

This is an OER textbook on linear algebra

Dual phosphorylation of Sin1 at T86 and T398 negatively regulates mTORC2 complex integrity and activity

Mammalian target of rapamycin (mTOR) plays essential roles in cell proliferation, survival and metabolism by forming at least two functional distinct multi-protein complexes, mTORC1 and mTORC2. External growth signals can be received and interpreted by mTORC2 and further transduced to mTORC1. On the other hand, mTORC1 can sense inner-cellular physiological cues such as amino acids and energy states and can indirectly suppress mTORC2 activity in part through phosphorylation of its upstream adaptors, IRS-1 or Grb10, under insulin or IGF-1 stimulation conditions. To date, upstream signaling pathways governing mTORC1 activation have been studied extensively, while the mechanisms modulating mTORC2 activity remain largely elusive. We recently reported that Sin1, an essential mTORC2 subunit, was phosphorylated by either Akt or S6K in a cellular context-dependent manner. More importantly, phosphorylation of Sin1 at T86 and T398 led to a dissociation of Sin1 from the functional mTORC2 holo-enzyme, resulting in reduced Akt activity and sensitizing cells to various apoptotic challenges. Notably, an ovarian cancer patient-derived Sin1-R81T mutation abolished Sin1-T86 phosphorylation by disrupting the canonical S6K-phoshorylation motif, thereby bypassing Sin1-phosphorylation-mediated suppression of mTORC2 and leading to sustained Akt signaling to promote tumorigenesis. Our work therefore provided physiological and pathological evidence to reveal the biological significance of Sin1 phosphorylation-mediated suppression of the mTOR/Akt oncogenic signaling, and further suggested that misregulation of this process might contribute to Akt hyper-activation that is frequently observed in human cancers