Probing Strongly Interacting Electroweak Symmetry Breaking Mechanism at High Energy Collider

We sketch some of our recent studies on probing strongly interacting electroweak symmetry breaking mechanism at high energy colliders such as the CERN LHC and the future e(+)e(-) linear collider. The study includes both model-dependent and model-independent probes.Comment: 11-page LaTex file using procl.sty (included). Invited article published in Proc. Symp. on the Frontiers of Physics at Millennium, 8-11, Oct., 1999, Beijing, China, ed. Yue-Liang Wu and Jong-Ping Hsu (World Scientific, Singapore), pp.344-354. References adde

Probing the Electroweak Symmetry Breaking Mechanism at High Energy Colliders

We briefly review the recent developments of probing the electroweak symmetry breaking mechanism at high energy colliders such as the CERN LEP2, the Fermilab Tevatron, the CERN LHC and the e(+)e(-) linear colliders. Both weakly interacting and strongly interacting electroweak symmetry breaking mechanisms are concerned.Comment: 16-page LaTex file using procl.sty (included). Invited talk, published in Proc. International Workshop on Frontiers of Theoretical Physics, 2-5, Nov., 1999, Beijing, China, ed. Fumihiko Sakata, Ke Wu and En-Guang Zhao (World Scientific, Singapore), pp.17-34. References adde

Physics Overview

Recent developments of physics at the TeV energy scale, especially physics related to the electron-positron linear colliders are briefly reviewed. The topics include the present status of the standard model, Higgs physics, supersymmetry, strongly interacting electroweak symmetry breaking mechanism, and top quark physics.Comment: Talk presented at The First ACFA Workshop on Physics/Detector at the Linear Collider, Nov. 26-27, 1998, Tsinghua University, Beijing, China. 35 pages with 3 figures, using epsfig.sty and rotate.st

S-D Mixing and Searching for the psi(1P1) State at the Beijing Electron-Positron Coolider

The psi(1P1) state can be produced at the Beijing Electron-Positron Collider (BEPC) in the process psi'-->psi(1P1)+pi(0). We calculate the rate of this process taking account of the S-D mixing effect in psi'. It is shown that the rate is about a factor of 3 smaller than the simple result without considering the S-D mixing effect. Possible detecting channels are suggested and it is shown that psi(1P1) is able to be found with the accumulation of 30 million events of psi' at BEPC.Comment: 9-page RevTex file. Version for publication in Phys. Rev.

Ultimate Generalization to Monotonicity for Uniform Convergence of Trigonometric Series

Chaundy and Jolliffe [4] proved that if $\{a_{n}\}$ is a non-increasing (monotonic) real sequence with $\lim\limits_{n\to \infty}a_{n}=0$, then a necessary and sufficient condition for the uniform convergence of the series $\sum_{n=1}^{\infty}a_{n}\sin nx$ is $\lim\limits_{n\to \infty}na_{n}=0$. We generalize (or weaken) the monotonic condition on the coefficient sequence $\{a_{n}\}$ in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy and Jolliffe theorem in the complex space.Comment: 21 page

On L1L^{1}-Convergence of Fourier Series Under MVBVMVBV Condition

Let $f\in L_{2\pi}$ be a real-valued even function with its Fourier series $\frac{a_{0}}{2}+\sum_{n=1}^{\infty}a_{n}\cos nx,$ and let $S_{n}(f,x), n\geq 1,$ be the $n$-th partial sum of the Fourier series. It is well-known that if the nonnegative sequence $\{a_{n}\}$ is decreasing and $\lim\limits_{n\to \infty}a_{n}=0$, then $$\lim\limits_{n\to \infty}\Vert f-S_{n}(f)\Vert_{L}=0 {if and only if} \lim\limits_{n\to \infty}a_{n}\log n=0.$$ We weaken the monotone condition in this classical result to the so-called mean value bounded variation ($MVBV$) condition. The generalization of the above classical result in real-valued function space is presented as a special case of the main result in this paper which gives the $L^{1}$% -convergence of a function $f\in L_{2\pi}$ in complex space. We also give results on $L^{1}$-approximation of a function $f\in L_{2\pi}$ under the $$ condition.Comment: 13 Pages, Accepted by Canad. Math. Bul

Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method.Comment: This is an updated version of the publication "Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems," in IEEE Transactions on Automatic Control, vol. 60, no. 11, pp. 2917-2929, Nov. 2015. Few typos have been fixed in this versio

Quantum Theory of All-Optical Switching in Nonlinear Sagnac Interferometers

Recently, our group has demonstrated an ultrafast, low-loss, fiber-loop switch based on a nonlinear Sagnac-interferometer design, using which entangled photons were shown to be routed without any measurable degradation in their entanglement fidelity [Hall {\it et al.}, Phys. Rev. Lett. {\bf 106}, 053901 (2011)]. Such a device represents an enabling technology for a rich variety of networked quantum applications. In this paper we develop a comprehensive quantum theory for such switches in general, i.e., those based on nonlinear Sagnac interferometers, where the in-coupling of quantum noise is carefully modeled. Applying to the fiber-loop switch, the theory shows good agreement with the experimental results without using any fitting parameter. This theory can serve as an important guiding tool for configuring switches of this kind for future quantum networking applications.Comment: To appear in New J. Physic

Mode-resolved Photon Counting via Cascaded Quantum Frequency Conversion

Resources for the manipulation and measurements of high-dimensional photonic signals are crucial for implementing qu$d$it-based applications. Here we propose potentially high-performance, chip-compatible devices for such purposes by exploiting quantum-frequency conversion in nonlinear optical media. Specifically, by using sum-frequency generation in a $\chi^{(2)}$ waveguide we show how mode-resolved photon counting can be accomplished for telecom-band photonic signals subtending multiple temporal modes. Our method is generally applicable to any nonlinear medium with arbitrary dispersion property

Spectral Resolution Clustering for Brain Parcellation

We take an image science perspective on the problem of determining brain network connectivity given functional activity. But adapting the concept of image resolution to this problem, we provide a new perspective on network partitioning for individual brain parcellation. The typical goal here is to determine densely-interconnected subnetworks within a larger network by choosing the best edges to cut. We instead define these subnetworks as resolution cells, where highly-correlated activity within the cells makes edge weights difficult to determine from the data. Subdividing the resolution estimates into disjoint resolution cells via clustering yields a new variation, and new perspective, on spectral clustering. This provides insight and strategies for open questions such as the selection of model order and the optimal choice of preprocessing steps for functional imaging data. The approach is demonstrated using functional imaging data, where we find the proposed approach produces parcellations which are more predictive across multiple scans versus conventional methods, as well as versus alternative forms of spectral clustering