arXiv subjects
Publications and source records attributed to Li Tan.
This paper is concerned with strong convergence of a tamed $θ$-Euler-Maruyama scheme for neutral stochastic differential delay equations with superlinearly growing coefficients. We not only prove the strong convergence of implicit schemes, but also reveal the convergence rate for these equations driven by Brownian motion and pure jumps, respectively.
This paper is concerned with strong convergence and almost sure convergence for neutral stochastic differential delay equations under non-globally Lipschitz continuous coefficients. Convergence rates of $θ$-EM schemes are given for these equations driven by Brownian motion and pure jumps respectively, where the drift terms satisfy locally one-sided Lipschitz conditions, and diffusion coefficients obey locally Lipschitz conditions, and the corresponding coefficients are highly nonlinear with respect to the delay terms.
The pressing demands of improving energy efficiency for high performance scientific computing have motivated a large body of software-controlled hard- ware solutions using Dynamic Voltage and Frequency Scaling (DVFS) that strategically switch processors to low-power states, when the peak processor performance is not necessary. Although OS level solutions have demonstrated the effectiveness of saving energy in a black-box fashion, for applications with variable execution characteristics, the optimal energy efficiency can be blundered away due to defective prediction mechanism and untapped load imbalance. In this paper, we propose TX, a library level race-to-halt DVFS scheduling approach that analyzes Task Dependency Set of each task in parallel Cholesky, LU, and QR factorizations to achieve substantial energy savings OS level solutions cannot fulfill. Partially giving up the generality of OS level solutions per requiring library level source modification, TX lever- ages algorithmic characteristics of the applications to gain greater energy savings. Experimental results on two power-aware clusters indicate that TX can save up to 17.8% more energy than state-of-the-art OS level solutions with negligible 3.5% on average performance loss.
The effect of structural constriction on molecular mobility is investigated by broadband dielectric spectroscopy (BDS) within three types of molecular arrangements: monomers, oligomers and self-assembled monolayers (SAMs). While disordered monomers exhibit a variety of cooperative and local relaxation processes, the constrained nanodomains of oligomers and highly ordered structure of monolayers exhibit much hindered local molecular fluctuations. Particularly, in SAMs, motions of the silane headgroups are totally prevented whereas the polar endgroups forming the monolayer canopy show only one cooperative relaxation process. This latter molecular fluctuation is, for the first time, observed independently from other overlapping dielectric signals. Numerous electrostatic interactions among those dipolar endgroups are responsible for the strong cooperativity and heterogeneity of the canopy relaxation process. Our data analyses also revealed that the bulkiness of dipolar endgroups can disrupt the organization of the monolayer canopy thus increasing their ability to fluctuate as temperature is increased.
Situation calculus has been widely applied in Artificial Intelligence related fields. This formalism is considered as a dialect of logic programming language and mostly used in dynamic domain modeling. However, type systems are hardly deployed in situation calculus in the literature. To achieve a correct and sound typed program written in situation calculus, adding typing elements into the current situation calculus will be quite helpful. In this paper, we propose to add more typing mechanisms to the current version of situation calculus, especially for three basic elements in situation calculus: situations, actions and objects, and then perform rigid type checking for existing situation calculus programs to find out the well-typed and ill-typed ones. In this way, type correctness and soundness in situation calculus programs can be guaranteed by type checking based on our type system. This modified version of a lightweight situation calculus is proved to be a robust and well-typed system.
In this paper, first-passage probability of Markov chains is used to get a strict proof of the existence of degree distribution of the LCD model presented by Bollobas (Random Structures and Algorithms 18(2001)). Also, a precise expression of degree distribution is presented.