On the optimality of misspecified spectral algorithms

In the misspecified spectral algorithms problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_{\rho}^{*}\|_{L^{\infty}} \alpha_{0}$ where $\alpha_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the spectral algorithms are optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that spectral algorithms are minimax optimal for any $\alpha_{0}-\frac{1}{\beta} < s < 1$, where $\beta$ is the eigenvalue decay rate of $\mathcal{H}$. We also give several classes of RKHSs whose embedding index satisfies $\alpha_0 = \frac{1}{\beta}$. Thus, the spectral algorithms are minimax optimal for all $s\in (0,1)$ on these RKHSs.Comment: 48 pages, 2 figure

Holographic Integrated Sensing and Communications: Principles, Technology, and Implementation

Integrated sensing and communication (ISAC) has attracted much attention as a promising approach to alleviate spectrum congestion. However, traditional ISAC systems rely on phased arrays to provide high spatial diversity, where enormous power-consuming components such as phase shifters are used, leading to the high power consumption of the system. In this article, we introduce holographic ISAC, a new paradigm to enable high spatial diversity with low power consumption by using reconfigurable holographic surfaces (RHSs), which is an innovative type of planar antenna with densely deployed metamaterial elements. We first introduce the hardware structure and working principle of the RHS and then propose a novel holographic beamforming scheme for ISAC. Moreover, we build an RHS-enabled hardware prototype for ISAC and evaluate the system performance in the built prototype. Simulation and experimental results verify the feasibility of holographic ISAC and reveal the great potential of the RHS for reducing power consumption. Furthermore, future research directions and key challenges related to holographic ISAC are discussed

Kernel interpolation generalizes poorly

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that for any $\varepsilon>0$, the generalization error of kernel interpolation is lower bounded by $\Omega(n^{-\varepsilon})$. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on sphere generalize poorly

On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression, the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently. However, most recent arguments on the learning curve are heuristic and are based on the 'Gaussian design' assumption. In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve: elaborating the effect and the interplay of the choice of the regularization parameter, the source condition and the noise. In particular, our results suggest that the 'benign overfitting phenomenon' exists in very wide neural networks only when the noise level is small

Machine Learning Solution to Organ-At-Risk Segmentation for Radiation Treatment Planning

In the treatment of cancer using ionizing radiation, it is important to design a treatment plan such that dose to normal, healthy organs is sufficiently low. Today, segmentation requires a trained human to carefully outline, or segment, organs on each slice of a treatment planning computed tomography (CT) scan but it is laborious, time-consuming, and contains intra- and inter-rater variability. Currently, existing clinical automation technology relies on atlas-based automation, which has limited segmentation accuracy. Thus the auto-segmentations require post process editing by an expert. In this paper, we propose a machine learning solution that shortens the segmentation time of organs-at-risk (OARs) in the thoracic cavity. The overall system will include preprocessing, model processing, and postprocessing steps to make the system easily integratable into the radiotherapy planning process. For our model, we chose to use a 3D deep convolutional neural network with a U-net based architecture because this machine learning strategy takes into account local spatial relationships, will restore the original image resolution and has been utilized in image segmentation, especially in medical image analysis. Training and testing were done with a 60 patient dataset of thoracic CT scans from the AAPM 2017 Grand Challenge. To assess and improve our system we calculated accuracy metrics (Dice similarity coefficient (DSC), mean surface distance (MSD)) and compared our model’s segmentation performance to that of an expert and the top two performing machine learning methods of the challenge. We explored using preprocessing steps such as cropping and image enhancement to improve the model segmentation accuracy. Our final model was able to segment the lungs as accurately as a dosimetrist and the heart and spinal cord within acceptable DSC ranges. All DSC values of the OARs from our method were as accurate as other machine learning methods. The DSC for the esophagus was below tolerable error for radiotherapy planning, but our mean surface distance was superior to other auto-segmentation methods. We were successful in significantly reducing manual segmentation time by developing a machine learning system. Though our approach still necessitates a single preparatory step of manually cropping anatomical regions to isolate segmentation volume, a general hospital technician could complete this task which removes the need of an expert for one time-consuming step of radiotherapy planning. Implementation of our methods to provide radiotherapy in lower-middle income countries brings us closer to accessibility of treatment for a wider population

Reconfigurable Holographic Surface: A New Paradigm to Implement Holographic Radio

Ultra-massive multiple-input multiple-output (MIMO) is one of the key enablers in the forthcoming 6G networks to provide high-speed data services by exploiting spatial diversity. In this article, we consider a new paradigm termed holographic radio for ultra-massive MIMO, where numerous tiny and inexpensive antenna elements are integrated to realize high directive gain with low hardware cost. We propose a practical way to enable holographic radio by a novel metasurface-based antenna, i.e., reconfigurable holographic surface (RHS). Specifically, RHSs incorporating densely packed tunable metamaterial elements are capable of holographic beamforming. Based on the working principle and hardware design of RHSs, we conduct full-wave analyses of RHSs and build an RHS-aided point-to-point communication platform supporting real-time data transmission. Both simulated and experimental results show that the RHS has great potential to achieve high directive gain with a limited size, thereby substantiating the feasibility of RHS-enabled holographic radio. Moreover, future research directions for RHS-enabled holographic radio are also discussed.Comment: 7 pages, 7 figure

Synthesis, Characterization, and Tribological Behavior of Oleic Acid Capped Graphene Oxide

Graphene oxide (GO) nanosheets were prepared by modified Hummers and Offeman methods. Furthermore, oleic acid (OA) capped graphene oxide (OACGO) nanosheets were prepared and characterized by means of Fourier transform-infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), and X-ray diffraction (XRD). At the same time, the friction and wear properties of OA capped graphite powder (OACG), OACGO, and oleic acid capped precipitate of graphite (OACPG) as additives in poly-alpha-olefin (PAO) were compared using four-ball tester and SRV-1 reciprocating ball-on-disc friction and wear tester. By the addition of OACGO to PAO, the antiwear ability was improved and the friction coefficient was decreased. Also, the tribological mechanism of the GO was investigated

Towards Ubiquitous Positioning by Leveraging Reconfigurable Intelligent Surface

The received signal strength (RSS) based technique is widely utilized for ubiquitous positioning due to its advantage of simple implementability. However, its accuracy is limited because the RSS values of adjacent locations can be very difficult to distinguish. Against this background, we propose the novel RSS-based positioning scheme enabled by reconfigurable intelligent surface (RIS). By modifying the reflection coefficient of the RIS, the propagation channels are programmed in such a way that the differences between the RSS values of adjacent locations can be enlarged to improve the positioning accuracy. New challenge lies in the selection of suitable reflection coefficients for high-accuracy positioning. To tackle this challenge, we formulate the RIS-aided positioning problem and design an iterative algorithm to solve the problem. The effectiveness of the proposed positioning scheme is validated through simulations