Optimal neighbourhood selection in structural equation models

We study the optimal sample complexity of neighbourhood selection in linear structural equation models, and compare this to best subset selection (BSS) for linear models under general design. We show by example that -- even when the structure is \emph{unknown} -- the existence of underlying structure can reduce the sample complexity of neighbourhood selection. This result is complicated by the possibility of path cancellation, which we study in detail, and show that improvements are still possible in the presence of path cancellation. Finally, we support these theoretical observations with experiments. The proof introduces a modified BSS estimator, called klBSS, and compares its performance to BSS. The analysis of klBSS may also be of independent interest since it applies to arbitrary structured models, not necessarily those induced by a structural equation model. Our results have implications for structure learning in graphical models, which often relies on neighbourhood selection as a subroutine

Residue theorem and summing over Kaluza-Klein excitations

Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluze-Klein modes in framework of warped extra dimension with the custodial symmetry $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_X\times P_{LR}$. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluze-Klein excitations in unified extra dimension. Additional, we analyze the possible connection between the propagators in five dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluze-Klein modes in four dimensional effective theory, and recover some relations presented in literature for warped and unified extra dimensions respectively. As an example, we demonstrate that the corrections from neutral Higgs to the Wilson coefficients of relevant operators for $B\rightarrow X_s\gamma$ contain the suppression factor $m_b^3m_s/m_{_{\rm w}}^4$ comparing with that from other sectors, thus can be neglected safely.Comment: 44 pages, no figur

Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue.

The dynamics of the RNA polymerase II (Pol II) backtracking process is poorly understood. We built a Markov State Model from extensive molecular dynamics simulations to identify metastable intermediate states and the dynamics of backtracking at atomistic detail. Our results reveal that Pol II backtracking occurs in a stepwise mode where two intermediate states are involved. We find that the continuous bending motion of the Bridge helix (BH) serves as a critical checkpoint, using the highly conserved BH residue T831 as a sensing probe for the 3'-terminal base paring of RNA:DNA hybrid. If the base pair is mismatched, BH bending can promote the RNA 3'-end nucleotide into a frayed state that further leads to the backtracked state. These computational observations are validated by site-directed mutagenesis and transcript cleavage assays, and provide insights into the key factors that regulate the preferences of the backward translocation