An approximate solution to the decentralized two-controller infinite-horizon scalar LQG problem: Part II- slow dynamics

Continuing the first part of the paper, we consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers. This paper focuses on the slow dynamics case when the eigenvalue of the system is small and prove that the single-controller optimal strategies ---linear strategies--- are constant ratio optimal among all distributed control strategies

Network Coding meets Decentralized Control: Network Linearization and Capacity-Stabilizablilty Equivalence

We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear time-invariant systems by appropriately restricting channels and coding schemes of network coding to be linear time-invariant, and the plant and controllers of decentralized control to be linear time-invariant as well. First, we apply linear system theory to network coding. This gives a novel way of converting an arbitrary relay network to an equivalent acyclic single-hop relay network, which we call Network Linearization. Based on network linearization, we prove that the fundamental design limit, mincut, is achievable by a linear time-invariant network-coding scheme regardless of the network topology. Then, we use the network-coding to view decentralized linear systems. We argue that linear time-invariant controllers in a decentralized linear system "communicate" via linear network coding to stabilize the plant. To justify this argument, we give an algorithm to "externalize" the implicit communication between the controllers that we believe must be occurring to stabilize the plant. Based on this, we show that the stabilizability condition for decentralized linear systems comes from an underlying communication limit, which can be described by the algebraic mincut-maxflow theorem. With this re-interpretation in hand, we also consider stabilizability over LTI networks to emphasize the connection with network coding. In particular, in broadcast and unicast problems, unintended messages at the receivers will be modeled as secrecy constraints

Young walls and graded dimension formulas for finite quiver Hecke algebras of type A2ℓ(2)A^{(2)}_{2\ell} and Dℓ+1(2)D^{(2)}_{\ell+1}

We study graded dimension formulas for finite quiver Hecke algebras $R^{\Lambda_0}(\beta)$ of type $A^{(2)}_{2\ell}$ and $D^{(2)}_{\ell+1}$ using combinatorics of Young walls. We introduce the notion of standard tableaux for proper Young walls and show that the standard tableaux form a graded poset with lattice structure. We next investigate Laurent polynomials associated with proper Young walls and their standard tableaux arising from the Fock space representations consisting of proper Young walls. Then we prove the graded dimension formulas described in terms of the Laurent polynomials. When evaluating at $q=1$, the graded dimension formulas recover the dimension formulas for $R^{\Lambda_0}(\beta)$ described in terms of standard tableaux of strict partitions.Comment: This is the final version to appear in the Journal of algebraic combinatoric

Classification based Grasp Detection using Spatial Transformer Network

Robotic grasp detection task is still challenging, particularly for novel objects. With the recent advance of deep learning, there have been several works on detecting robotic grasp using neural networks. Typically, regression based grasp detection methods have outperformed classification based detection methods in computation complexity with excellent accuracy. However, classification based robotic grasp detection still seems to have merits such as intermediate step observability and straightforward back propagation routine for end-to-end training. In this work, we propose a novel classification based robotic grasp detection method with multiple-stage spatial transformer networks (STN). Our proposed method was able to achieve state-of-the-art performance in accuracy with real- time computation. Additionally, unlike other regression based grasp detection methods, our proposed method allows partial observation for intermediate results such as grasp location and orientation for a number of grasp configuration candidates.Comment: 6 pages, 10 figures, Under revie

An approximate solution to the decentralized two-controller infinite-horizon scalar LQG problem: Part I- fast dynamics

We consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers, focusing on the fast dynamics case when the (scalar) eigenvalue of the system is large. It is shown that the best linear controllers' performance can be an arbitrary factor worse than the optimal performance. We propose a set of finite-dimensional nonlinear controllers, and prove that the proposed set contains an easy-to-find approximately optimal solution that achieves within a constant ratio of the optimal quadratic cost. The insight for nonlinear strategies comes from revealing the relationship between information flow in control and wireless information flow. More precisely, we discuss a close relationship between the high-SNR limit in wireless communication and fast-dynamics case in decentralized control, and justify how the proposed nonlinear control strategy can be understood as exploiting the generalized degree-of-freedom gain in wireless communication theory. For a rigorous justification of this argument, we develop new mathematical tools and ideas. To reveal the relationship between infinite-horizon problems and generalized MIMO Witsenhausen's counterexamples, we introduce the idea of geometric slicing. To analyze the nonlinear strategy performance, we introduce an approximate-comb-lattice model for the relevant random variables

Metal-insulator transitions in GdTiO3/SrTiO3 superlattices

The density functional plus U method is used to obtain the electronic structure, lattice relaxation and metal-insulator phase diagram of superlattices consisting of $m$ layers of Gadolinium Titanate (GdTiO$_{3}$) alternating with $n$ layers of Strontium Titanate (SrTiO$_{3}$). Metallic phases occur when the number of SrTiO$_3$ layers is large or the interaction $U$ is small. In metallic phases, the mobile electrons are found in the SrTiO$_3$ layers, with near-interface electrons occupying $xy$-derived bands, while away from the interface the majority of electrons reside in $xz/yz$ bands. As the thickness of the SrTiO$_3$ layers decreases or the on-site interaction U increases a metal-insulator transition occurs. Two different insulating states are found. When the number of SrTiO$_{3}$ layers is larger than one, we find an insulating state with two sublattice charge and orbital ordering and associated Ti-O bond length disproportionations. When the number of SrTiO$_{3}$ units per layer is one, a different insulating phase occurs driven by orbital ordering within the quasi one-dimensional $xz/yz$ bonding bands connecting Ti atoms across the SrO layer. In this phase there is no sublattice charge ordering or bond disproportionation. The critical U for the single-layer insulator is $\sim$ 2.5 eV, much less than critical U $\sim$ 3.5 eV required to drive the metal-insulator transition when the number of SrTiO$_3$ is larger than one. Inconsistencies between the calculation and the experiment suggest that many-body correlations may be important. A local inversion symmetry breaking around Ti atoms suggests the possibility of in-plane ferroelectric polarization in the insulating phase

Charge density distribution and optical response of the LaAlO3/SrTiO3 interface

We present calculations of the charge density profile, subband occupancy and ellipsometry spectra of the electron gas at the LaAlO3/SrTiO3 interface. The calculations employ self-consistent Hartree and random phase approximations, a tight binding parametrization of the band structure and a model for the optical phonon of SrTiO3. The dependence of the spatial structure and occupancy of subbands on the magnitude of the polarization charge at the interface and the dielectric function is determined. The interface-confined subbands may be labelled by the symmetry (xy, xz, or yz) of the Ti d-orbitals from which they mainly derive. The xy-derived band nearest the interface contains the major proportion of the electronic charge, but a large number of more distant, slightly occupied xy-derived bands are also found. Depending on the magnitude of the polarization charge, zero, one, or two xz/yz derived subbands are found. When present, these xz/yz bands give the dominant contribution to the long-distance tail of the interface charge. The response to applied ac electric fields polarized parallel and perpendicular to the interface is calculated and the results are presented in terms of ellipsometry angles. Two features are found: a dip in the spectrum near the LO feature of the STO phonon and a peak at the higher energy. We show that the form and magnitude of the dip is related to the Drude response of carriers moving in the plane of the interface while the peak arises from the plasmon excitation of the xz and yz electrons. The relation of the features of the subband occupancies and the in-plane conductivities is given.Comment: 18 pages, 6 figure

The finite-dimensional Witsenhausen counterexample

Recently, a vector version of Witsenhausen's counterexample was considered and it was shown that in that limit of infinite vector length, certain quantization-based control strategies are provably within a constant factor of the optimal cost for all possible problem parameters. In this paper, finite vector lengths are considered with the dimension being viewed as an additional problem parameter. By applying a large-deviation "sphere-packing" philosophy, a lower bound to the optimal cost for the finite dimensional case is derived that uses appropriate shadows of the infinite-length bound. Using the new lower bound, we show that good lattice-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the vector length. For Witsenhausen's original problem -- the scalar case -- the gap between regular lattice-based strategies and the lower bound is numerically never more than a factor of 8.Comment: 32 pages, 7 figures, 1 table. Presented at ConCom 2009, Seoul, Korea. Submitted to IEEE Transactions on Automatic Contro

Down-Scaling with Learned Kernels in Multi-Scale Deep Neural Networks for Non-Uniform Single Image Deblurring

Multi-scale approach has been used for blind image / video deblurring problems to yield excellent performance for both conventional and recent deep-learning-based state-of-the-art methods. Bicubic down-sampling is a typical choice for multi-scale approach to reduce spatial dimension after filtering with a fixed kernel. However, this fixed kernel may be sub-optimal since it may destroy important information for reliable deblurring such as strong edges. We propose convolutional neural network (CNN)-based down-scale methods for multi-scale deep-learning-based non-uniform single image deblurring. We argue that our CNN-based down-scaling effectively reduces the spatial dimension of the original image, while learned kernels with multiple channels may well-preserve necessary details for deblurring tasks. For each scale, we adopt to use RCAN (Residual Channel Attention Networks) as a backbone network to further improve performance. Our proposed method yielded state-of-the-art performance on GoPro dataset by large margin. Our proposed method was able to achieve 2.59dB higher PSNR than the current state-of-the-art method by Tao. Our proposed CNN-based down-scaling was the key factor for this excellent performance since the performance of our network without it was decreased by 1.98dB. The same networks trained with GoPro set were also evaluated on large-scale Su dataset and our proposed method yielded 1.15dB better PSNR than the Tao's method. Qualitative comparisons on Lai dataset also confirmed the superior performance of our proposed method over other state-of-the-art methods.Comment: 10 pages, 7 figures, 4 table

Real-Time, Highly Accurate Robotic Grasp Detection using Fully Convolutional Neural Networks with High-Resolution Images

Robotic grasp detection for novel objects is a challenging task, but for the last few years, deep learning based approaches have achieved remarkable performance improvements, up to 96.1% accuracy, with RGB-D data. In this paper, we propose fully convolutional neural network (FCNN) based methods for robotic grasp detection. Our methods also achieved state-of-the-art detection accuracy (up to 96.6%) with state-of- the-art real-time computation time for high-resolution images (6-20ms per 360x360 image) on Cornell dataset. Due to FCNN, our proposed method can be applied to images with any size for detecting multigrasps on multiobjects. Proposed methods were evaluated using 4-axis robot arm with small parallel gripper and RGB-D camera for grasping challenging small, novel objects. With accurate vision-robot coordinate calibration through our proposed learning-based, fully automatic approach, our proposed method yielded 90% success rate.Comment: This work was superceded by arXiv:1812.0776