On the support of measures in multiplicative free convolution semigroups

In this paper, we study the supports of measures in multiplicative free semigroups on the positive real line and on the unit circle. We provide formulas for the density of the absolutely continuous parts of measures in these semigroups. The descriptions rely on the characterizations of the images of the upper half-plane and the unit disc under certain subordination functions. These subordination functions are $\eta$-transforms of infinitely divisible measures with respect to multiplicative free convolution. The characterizations also help us study the regularity properties of these measures. One of the main results is that the number of components in the support of measures in the semigroups is a decreasing function of the semigroup parameter

Large Margin Neural Language Model

We propose a large margin criterion for training neural language models. Conventionally, neural language models are trained by minimizing perplexity (PPL) on grammatical sentences. However, we demonstrate that PPL may not be the best metric to optimize in some tasks, and further propose a large margin formulation. The proposed method aims to enlarge the margin between the "good" and "bad" sentences in a task-specific sense. It is trained end-to-end and can be widely applied to tasks that involve re-scoring of generated text. Compared with minimum-PPL training, our method gains up to 1.1 WER reduction for speech recognition and 1.0 BLEU increase for machine translation.Comment: 9 pages. Accepted as a long paper in EMNLP201

Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors

This thesis investigates Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closed-loop time-delay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the time-delay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of time-delay systems. Furthermore, the method of Saturated-Root Locus (S-RL) is extended to nonlinear time-delay systems. It turns out that, in a time-delay system, S-RL always terminates prematurely as opposed to a delay-free system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. The impact of increasing the time-delay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the efficacy of the approach

Substrate entering and product leaving trajectories predict an engulfing dynamic for the major conformational change of the β-lactam acylase

It is still a major challenge to acquire insight into the conformational changes between the ground state and the transition state of an enzyme, although conformational fluctuation within interconverting conformers has been widely investigated (1-4). Here, we utilize different enzymatic reactions in b-lactam acylase to figure out the substrate/product trajectories in the enzyme, thereby probing the overall conformational changes in transition state. First, an auto-proteolytic intermediate of cephalosporin acylase (EC 3.5.1.11) with partial spacer segment was identified. As a final proteolytic step, the deletion of this spacer segment was revealed to be a first-order reaction, suggesting an intramolecular Ntn mechanism for the auto-proteolysis. Accordingly, the different proteolytic sites in the acylase precursor indicate a substrate entering pathway along the spacer peptide. Second, bromoacyl-7ACA can interact with penicillin G acylase (EC 3.5.1.11) in two distinguish aspects, to be hydrolyzed as a substrate analogue and to affinity alkylate the conserved Trpb4 as a product analogue. The kinetic correlation between these two reactions suggests a channel opening from Serb1 to Trpb4, responsible for the main product leaving. These two reaction trajectories relaying at the active centre, together with the crystal structures (5-10), predict an engulfing dynamic involving pocket constriction and channel opening