Parameter Optimization of Multi-Agent Formations based on LQR Design

In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and by the linear quadratic regulation(LQR) controllers, the upper bound of the cost function is minimized. For systems with homogeneous agents interconnected over sparse graphs, distributed controllers are proposed that inherit the same underlying graph as the one among agents. For the more general case, a relaxed optimization problem is considered so as to eliminate the nonlinear constraints. Using the subgradient method, interaction parameters among agents are optimized under the constraint of a sparse graph, and the optimum of the cost function is a better result than the one when agents interacted only through the control channel. Numerical examples are provided to validate the effectiveness of the method and to illustrate the geometrical performance of the system.Comment: Submitte

Control of Multi-Agent Formations with Only Shape Constraints

This paper considers a novel problem of how to choose an appropriate geometry for a group of agents with only shape constraints but with a flexible scale. Instead of assigning the formation system with a specific geometry, here the only requirement on the desired geometry is a shape without any location, rotation and, most importantly, scale constraints. Optimal rigid transformation between two different geometries is discussed with especial focus on the scaling operation, and the cooperative performance of the system is evaluated by what we call the geometries degrees of similarity (DOS) with respect to the desired shape during the entire convergence process. The design of the scale when measuring the DOS is discussed from constant value and time-varying function perspectives respectively. Fixed structured nonlinear control laws that are functions on the scale are developed to guarantee the exponential convergence of the system to the assigned shape. Our research is originated from a three-agent formation system and is further extended to multiple (n > 3) agents by defining a triangular complement graph. Simulations demonstrate that formation system with the time-varying scale function outperforms the one with an arbitrary constant scale, and the relationship between underlying topology and the system performance is further discussed based on the simulation observations. Moveover, the control scheme is applied to bearing-only sensor-target localization to show its application potentials.Comment: Submitte

Non-Chiral S-Matrix of N=4 Super Yang-Mills

We discuss the construction of non-chiral S-matrix of four-dimensional N=4 super Yang-Mills using a non-chiral superspace. This construction utilizes the non-chiral representation of dual superconformal symmetry, which is the natural representation from the point of view of the six-dimensional parent theory. The superspace in discussion is projective superspace constructed by Hatsuda and Siegel, and is based on a half coset U(2,2|4)/U(1,1|2)^2_+. We obtain the non-chiral representation of the five-point and general n-point MHV and anti-MHV amplitude. The non-chiral formulation can be straightforwardly lifted to six dimensions, which is equivalent to massive amplitudes in four dimensions.Comment: 30 pages, 2 figure

Exponential stability of nonhomogeneous matrix-valued Markovian chains

In this paper, we characterize the stability of matrix-valued Markovian chains by periodic data.Comment: 12 page

CP and CPT Violating Parameters Determined from the Joint Decays of C=+1C=+1 Entangled Neutral Pseudoscalar Mesons

Entangled pseudoscalar neutral meson pairs have been used in studying CP violation and searching CPT violation, but almost all the previous works concern $C=-1$ entangled state. Here we consider $C=+1$ entangled state of pseudoscalar neutral mesons, which is quite different from $C=-1$ entangled state and provides complementary information on symmetry violating parameters. After developing a general formalism, we consider three kinds of decay processes, namely, semileptonic-semileptonic, hadronic-hadronic and semileptonic-hadronic processes. For each kind of processes, we calculate the integrated rates of joint decays with a fixed time interval, as well as asymmetries defined for these joint rates of different channels. In turn, these asymmetries can be used to determine the four real numbers of the two indirect symmetry violating parameters, based on a general relation between the symmetry violating parameters and the decay asymmetries presented here. Various discussions are made on indirect and direct violations and the violation of $\Delta {\cal F} =\Delta Q$ rule, with some results presented as theorems.Comment: 22 pages, to appear in PR

Devaney's chaos revisited

In this note, we give several equivalent definitions of Devaney's chao

Chaos expansion of 2D parabolic Anderson model

We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the annealed density function of the polymer in a white noise environment.Comment: 11 pages, minor revision

Selection of the Regularization Parameter in the Ambrosio-Tortorelli Approximation of the Mumford-Shah Functional for Image Segmentation

The Ambrosio-Tortorelli functional is a phase-field approximation of the Mumford-Shah functional that has been widely used for image segmentation. The approximation has the advantages of being easy to implement, maintaining the segmentation ability, and $\Gamma$-converging to the Mumford-Shah functional. However, it has been observed in actual computation that the segmentation ability of the Ambrosio-Tortorelli functional varies significantly with different values of the parameter and it even fails to $\Gamma$-converge to the original functional for some cases. In this paper we present an asymptotic analysis on the gradient flow equation of the Ambrosio-Tortorelli functional and show that the functional can have different segmentation behavior for small but finite values of the regularization parameter and eventually loses its segmentation ability as the parameter goes to zero when the input image is treated as a continuous function. This is consistent with the existing observation as well as the numerical examples presented in this work. A selection strategy for the regularization parameter and a scaling procedure for the solution are devised based on the analysis. Numerical results show that they lead to good segmentation of the Ambrosio-Tortorelli functional for real images.Comment: 22 page

Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization

We consider the stochastic composition optimization problem proposed in \cite{wang2017stochastic}, which has applications ranging from estimation to statistical and machine learning. We propose the first ADMM-based algorithm named com-SVR-ADMM, and show that com-SVR-ADMM converges linearly for strongly convex and Lipschitz smooth objectives, and has a convergence rate of $O( \log S/S)$, which improves upon the $O(S^{-4/9})$ rate in \cite{wang2016accelerating} when the objective is convex and Lipschitz smooth. Moreover, com-SVR-ADMM possesses a rate of $O(1/\sqrt{S})$ when the objective is convex but without Lipschitz smoothness. We also conduct experiments and show that it outperforms existing algorithms

AutoSlim: Towards One-Shot Architecture Search for Channel Numbers

We study how to set channel numbers in a neural network to achieve better accuracy under constrained resources (e.g., FLOPs, latency, memory footprint or model size). A simple and one-shot solution, named AutoSlim, is presented. Instead of training many network samples and searching with reinforcement learning, we train a single slimmable network to approximate the network accuracy of different channel configurations. We then iteratively evaluate the trained slimmable model and greedily slim the layer with minimal accuracy drop. By this single pass, we can obtain the optimized channel configurations under different resource constraints. We present experiments with MobileNet v1, MobileNet v2, ResNet-50 and RL-searched MNasNet on ImageNet classification. We show significant improvements over their default channel configurations. We also achieve better accuracy than recent channel pruning methods and neural architecture search methods. Notably, by setting optimized channel numbers, our AutoSlim-MobileNet-v2 at 305M FLOPs achieves 74.2% top-1 accuracy, 2.4% better than default MobileNet-v2 (301M FLOPs), and even 0.2% better than RL-searched MNasNet (317M FLOPs). Our AutoSlim-ResNet-50 at 570M FLOPs, without depthwise convolutions, achieves 1.3% better accuracy than MobileNet-v1 (569M FLOPs). Code and models will be available at: https://github.com/JiahuiYu/slimmable_networksComment: tech repor