Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals

Canceling Quadratic Divergences in a Class of Two-Higgs-Doublet Models

The Newton-Wu conditions for the cancellation of quadratic divergences in a class of two-Higgs-doublet models are analyzed as to how they may be satisfied with a typical extension of the Standard Model of particle interactions.Comment: 5 pages, no figur

The Lit Review and Me

In this comic, the student reflects on the process of writing a “literature review,” a requirement for a course taught by Dean Scheibel called “Introduction of Research in Communication Studies.” The comics were created by students as a final course assignment. Students were instructed to create comics using photographs, drawings, or a computer program called Comic Life 3. The idea of reflection is important in education. These comics could be viewed as a response to reflective learning (or metacognition) about the idea of the literature review, or “research as inquiry.” Through reflection on what we do, we learn more deeply about our everyday experiences of life, death, love, God, and even literature reviews. Although “comix” have been the objects of critique by academics, these comics subject the work of the academy—the faculty member as teacher—to critique. Research is a process, and by having students reflect on the fears, errors, or mistakes made during that process they will experience new insights and discoveries

Differential Upregulation of BDNF mRNA in the Rat Hippocampus after Sing and Recurrent Hyperthermia-Induced Seizures

Thesis (M.D.) - Yale University, 2002

Weighted bounds for multilinear operators with non-smooth kernels

Let $T$ be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$. Our results are new even in the linear case

The Changing Needs for Higher Education Organizations Structure in Vietnam: Evidence From Japanese, Taiwanese, and Thai Universities

Organizational change is the process of changing the structure of the organization and the attitudes of members in the organization. During the last decade, both Vietnamese social and educational organizations have slowly changed in their organizational structure as a barrier to the development in the era of globalization and Internationalization in Vietnam. This paper is an attempt to discuss the factors which affect Vietnamese higher educational organization. Discussions on the viewpoint of higher educational organization structure of Japan, Taiwan, and Thailand. Furthermore, this paper will contribute to improve educational management, and serve as a useful reference for future higher education's school mergers

Two-State Migration of DNA in a structured Microchannel

DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In particular, the experimentally observed migration order of Lambda- and T2-DNA molecules is reproduced by the simulations. The simulation data indicate that the mobility may depend on the chain length in a nonmonotonic way at high electric fields. This is found to be the signature of a nonequilibrium phase transition between two different migration states, a slow one and a fast one, which can also be observed experimentally under appropriate conditions.Comment: Revised edition corresponding to the comments by the referees, submitted to Physical Review

The two-scale approach to hydrodynamic limits for non-reversible dynamics

In a recent paper by Grunewald et al., a new method to study hydrodynamic limits was developed for reversible dynamics. In this work, we generalize this method to a family of non-reversible dynamics. As an application, we obtain quantitative rates of convergence to the hydrodynamic limit for a weakly asymmetric version of the Ginzburg-Landau model endowed with Kawasaki dynamics. These results also imply local Gibbs behavior, following a method introduced in a recent paper by the second author

Stabilization Control of the Differential Mobile Robot Using Lyapunov Function and Extended Kalman Filter

This paper presents the design of a control model to navigate the differential mobile robot to reach the desired destination from an arbitrary initial pose. The designed model is divided into two stages: the state estimation and the stabilization control. In the state estimation, an extended Kalman filter is employed to optimally combine the information from the system dynamics and measurements. Two Lyapunov functions are constructed that allow a hybrid feedback control law to execute the robot movements. The asymptotical stability and robustness of the closed loop system are assured. Simulations and experiments are carried out to validate the effectiveness and applicability of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:1611.07112, arXiv:1611.0711