PAR-1 Kinase Phosphorylates Dlg and Regulates Its Postsynaptic Targeting at the Drosophila Neuromuscular Junction

SummaryTargeting of synaptic molecules to their proper location is essential for synaptic differentiation and plasticity. PSD-95/Dlg proteins have been established as key components of the postsynapse. However, the molecular mechanisms regulating the synaptic targeting, assembly, and disassembly of PSD-95/Dlg are not well understood. Here we show that PAR-1 kinase, a conserved cell polarity regulator, is critically involved in controlling the postsynaptic localization of Dlg. PAR-1 is prominently localized at the Drosophila neuromuscular junction (NMJ). Loss of PAR-1 function leads to increased synapse formation and synaptic transmission, whereas overexpression of PAR-1 has the opposite effects. PAR-1 directly phosphorylates Dlg at a conserved site and negatively regulates its mobility and targeting to the postsynapse. The ability of a nonphosphorylatable Dlg to largely rescue PAR-1-induced synaptic defects supports the idea that Dlg is a major synaptic substrate of PAR-1. Control of Dlg synaptic targeting by PAR-1-mediated phosphorylation thus constitutes a critical event in synaptogenesis

Distributionally robust shortfall risk optimization model and its approximation

Utility-based shortfall risk measures (SR)have received increasing attention over the past few years for their potential to quantify the risk of large tail losses more effectively than conditional value at risk.In this paper, we consider a distributionally robust version of the shortfall risk measure (DRSR) where the true probability distribution is unknown and the worst distribution from an ambiguity set of distributions} is used to calculate the SR. We start by showing that the DRSR is a convex risk measure and under some special circumstance a coherent risk measure.We then move on to study an optimization problem with the objective of minimizing the DRSR of a random function and investigate numerical tractability of the optimization problem with the ambiguity set being constructed through $\phi$-divergence ball and Kantorovich ball. In the case when the nominal distribution in the balls is an empirical distribution constructed through iid samples,we quantify convergence of the ambiguity sets to the true probability distribution as the sample size increases under the Kantorovich metric and consequently the optimal values of the corresponding DRSR problems. Specifically, we show that the error of the optimal value is linearly bounded by the error of each of the approximate ambiguity sets and subsequently derive a confidence interval of the optimal value under each of the approximation schemes. Some preliminary numerical test results are reported for the proposed modeling and computational schemes

Convergence analysis for mathematical programs with distributionally robust chance constraint

Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability distribution is unknown, but it is possible to construct an ambiguity set of probability distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set. The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions. We start by deriving general convergence results under abstract conditions such as continuity of the robust probability function and uniform convergence of the robust probability functions and followed with detailed analysis of these conditions. Two sufficient conditions have been derived with one applicable to both continuous and discrete probability distribution and the other to continuous distribution. Case studies are carried out for ambiguity sets being constructed through moments and samples.Read More: https://epubs.siam.org/doi/10.1137/15M1036592<br/

Probability approximation schemes for stochastic programs with distributionally robust second order dominance constraints

Since the pioneering work by Dentcheva and Ruszczy?ski [Optimization with stochastic dominance constraints, SIAM J. Optim. 14 (2003), pp. 548–566], stochastic programs with second-order dominance constraints (SPSODC) have received extensive discussions over the past decade from theory of optimality to numerical schemes and practical applications. In this paper, we investigate discrete approximation of SPSODC when (a) the true probability is known but continuously distributed and (b) the true probability distribution is unknown but it lies within an ambiguity set of distributions. Differing from the well-known Monte Carlo discretization method, we propose a deterministic discrete approximation scheme due to Pflug and Pichler [Approximations for Probability Distributions and Stochastic Optimization Problems, International Series in Operations Research &amp; Management Science, Vol. 163, Springer, New York, 2011, pp. 343–387] and demonstrate that the discrete probability measure and the ambiguity set of discrete probability measures approximate their continuous counterparts under the Kantorovich metric. Stability analysis of the optimal value and optimal solutions of the resulting discrete optimization problems is presented and some comparative numerical test results are reported

Experimental realization of an optical digital comparator using silicon microring resonators

We propose and experimentally demonstrate a silicon photonic circuit that can perform the comparison operation of two-bit digital signals based on microring resonators (MRRs). Two binary electrical signals regarded as two operands of desired comparison digital signals are applied to three MRRs to modulate their resonances through the microheaters fabricated on the top of MRRs, respectively (here, one binary electrical signal is applied to two MRRs by a 1×2 electrical power splitter, which means that the two MRRs are modulated by the same binary electrical signal). The comparison results of two binary electrical signals can be obtained at two output ports in the form of light. The proposed device is fabricated on a silicon-on-insulator substrate using the complementary metal-oxide-semiconductor fabrication process, and the dynamic characterization of the device with the operation speed of 10 kbps is demonstrated successfully