Quantitative single-cell splicing analysis reveals an ‘economy of scale’ filter for gene expression

In eukaryotic cells, splicing affects the fate of each pre-mRNA transcript, helping to determine whether it is ultimately processed into an mRNA, or degraded. The efficiency of splicing plays a key role in gene expression. However, because it depends on the levels of multiple isoforms at the same transcriptional active site (TAS) in the same cell, splicing efficiency has been challenging to measure. Here, we introduce a quantitative single-molecule FISH-based method that enables determination of the absolute abundances of distinct RNA isoforms at individual TASs. Using this method, we discovered that splicing efficiency behaves in an unexpected ‘economy of scale’ manner, increasing, rather than decreasing, with gene expression levels, opposite to a standard enzymatic process. This behavior could result from an observed correlation between splicing efficiency and spatial proximity to nuclear speckles. Economy of scale splicing represents a non-linear filter that amplifies the expression of genes when they are more strongly transcribed. This method will help to reveal the roles of splicing in the quantitative control of gene expression

Weight function for the quantum affine algebra Uq(sl^3)U_q(\hat{sl}_3)

We give a precise expression for the universal weight function of the quantum affine algebra $U_q(\hat{sl}_3)$. The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.Comment: 28 page

Asymptotic Theory of Rerandomization in Treatment-Control Experiments

Although complete randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. To supplement existing results, we develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and a truncated Gaussian random variable. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete randomization, rerandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the average causal effect, thereby revealing further advantages of rerandomization over complete randomization

Bound States of the Heavy Flavor Vector Mesons and Y(4008) and Z1+(4050)Z^{+}_1(4050)

The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{*}\bar{B}^{*}$ molecules should exist, and the $D^{*}\bar{D}^{*}$ bound states with the same quantum numbers very likely exist as well. However, the CP exotic ($1^{-+}$, $2^{+-}$) $B^{*}\bar{B}^{*}$ and $D^{*}\bar{D}^{*}$ states may not be bound by the one boson exchange potential. We find that the I=0 configuration is more deeply bound than the I=1 configuration, hence $Z^{+}_1(4050)$ may not be a $D^{*}\bar{D}^{*}$ molecule. Although Y(4008) is close to the $D^{*}\bar{D}^{*}$ threshold, the interpretation of Y(4008) as a $D^{*}\bar{D}^{*}$ molecule is not favored by its huge width. $1^{--}$ $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ states can be produced copiously in $e^{+}e^{-}$ annihilation, detailed scanning of the $e^{+}e^{-}$ annihilation data near the $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ threshold is an important check to our predictions.Comment: 17 pages,6 figur

Manin-Olshansky triples for Lie superalgebras

Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg, \fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for several series of Lie superalgebras \fa which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward superization of suitable Etingof--Kazhdan's results guarantee then the uniqueness of $q$-quantization of our Lie bialgebras. Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions. To find explicit solutions is a separate (open) problem. It is also an open problem to list (\`a la Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra \fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix

Finite-horizon H∞ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements

This technical note deals with the H∞ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the H∞ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon H∞ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

H-infinity state estimation for discrete-time complex networks with randomly occurring sensor saturations and randomly varying sensor delays

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, the state estimation problem is investigated for a class of discrete time-delay nonlinear complex networks with randomly occurring phenomena from sensor measurements. The randomly occurring phenomena include randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs) that result typically from networked environments. A novel sensor model is proposed to describe the ROSSs and the RVSDs within a unified framework via two sets of Bernoulli-distributed white sequences with known conditional probabilities. Rather than employing the commonly used Lipschitz-type function, a more general sector-like nonlinear function is used to describe the nonlinearities existing in the network. The purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that, for all probabilistic sensor saturations and sensor delays, the dynamics of the estimation error is guaranteed to be exponentially mean-square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an $H_{infty}$-norm. In terms of a novel Lyapunov–Krasovskii functional and the Kronecker product, sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method. A simulation example is provided to show the usefulness of the proposed state estimation conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61028008, 61134009, 61104125 and 60974030, the Natural Science Foundation of Universities in Anhui Province of China under Grant KJ2011B030, and the Alexander von Humboldt Foundation of Germany

Efficient equilibrium sampling of all-atom peptides using library-based Monte Carlo

We applied our previously developed library-based Monte Carlo (LBMC) to equilibrium sampling of several implicitly solvated all-atom peptides. LBMC can perform equilibrium sampling of molecules using the pre-calculated statistical libraries of molecular-fragment configurations and energies. For this study, we employed residue-based fragments distributed according to the Boltzmann factor of the OPLS-AA forcefield describing the individual fragments. Two solvent models were employed: a simple uniform dielectric and the Generalized Born/Surface Area (GBSA) model. The efficiency of LBMC was compared to standard Langevin dynamics (LD) using three different statistical tools. The statistical analyses indicate that LBMC is more than 100 times faster than LD not only for the simple solvent model but also for GBSA.Comment: 5 figure