Goldbach-Linnik type problems involving one prime, four prime cubes and powers of 2

In this paper, we prove that every pair of sufficiently large odd integers can be represented as a pair of a prime, four cubes of primes and $47$ powers of $2$.Comment: 16 page

Using MicroPET Imaging in Quantitative Verification of Acupuncture Effect in Ischemia Stroke Treatment

While acupuncture has survived several thousand years’ evolution of medical practice, its function still remains as a myth from the view point of modern medicine. Our goal in this paper is to quantitatively understand the function of acupuncture in ischemia stroke treatment. We carried out a comparative study using the Sprague Dawley rat animal model. We induced the focal cerebral ischemia in the rats using the middle cerebral artery occlusion (MCAO) procedure. For each rat from the real acupuncture group (n = 40), sham acupoint treatment group (n = 54), and blank control group (n = 16), we acquired 3-D FDG-microPET images at baseline, after MCAO, and after treatment (i.e., real acupuncture, sham acupoint treatment, or resting according to the group assignment), respectively. After verifying that the injured area is in the right hemisphere of the cerebral cortex in the brain by using magnetic resonance imaging(MRI) and triphenyl tetrazolium cchloride (TTC)-staining, we directly compared the glucose metabolism in the right hemisphere of each rat. We carried out t-test and permutation test on the image data. Both tests demonstrated that acupuncture had a more positive effect than non-acupoint stimulus and blank control (P < 0.025) in increasing the glucose metabolic level in the stroke-injured area in the brain, while there was no statistically significant difference between non-acupoint stimulus and blank control (P>0.15). The immediate positive effect of acupuncture over sham acupoint treatment and blank control is verified using our experiments. The long-term benefit of acupuncture needs to be further studied

Ultra-wideband THz/IR Metamaterial Absorber based on Doped Silicon

Metamaterial-based absorbers have been extensively investigated in the terahertz (THz) range with ever increasing performances. In this paper, we propose an all-dielectric THz absorber based on doped silicon. The unit cell consists of a silicon cross resonator with an internal cross-shaped air cavity. Numerical results suggest that the proposed absorber can operate from THz to mid-infrared, having an average power absorption of >95% between 0.6 and 10 THz. Experimental results using THz time-domain spectroscopy show a good agreement with simulations. The underlying mechanisms for broadband absorptions are attributed to the combined effects of multiple cavities modes formed by silicon resonators and bulk absorption in the substrate, as confirmed by simulated field patterns. This ultra-wideband absorption is polarization insensitive and can operate across a wide range of the incident angle. The proposed absorber can be readily integrated into silicon-based platforms and is expected to be used in sensing, imaging, energy harvesting and wireless communications systems.Comment: 6 pages, 5 figure

Hybrid Kinetics Embedding Framework for Dynamic PET Reconstruction

In dynamic positron emission tomography (PET) reconstruction, the importance of leveraging the temporal dependence of the data has been well appreciated. Current deep-learning solutions can be categorized in two groups in the way the temporal dynamics is modeled: data-driven approaches use spatiotemporal neural networks to learn the temporal dynamics of tracer kinetics from data, which relies heavily on data supervision; physics-based approaches leverage \textit{a priori} tracer kinetic models to focus on inferring their parameters, which relies heavily on the accuracy of the prior kinetic model. In this paper, we marry the strengths of these two approaches in a hybrid kinetics embedding (HyKE-Net) framework for dynamic PET reconstruction. We first introduce a novel \textit{hybrid} model of tracer kinetics consisting of a physics-based function augmented by a neural component to account for its gap to data-generating tracer kinetics, both identifiable from data. We then embed this hybrid model at the latent space of an encoding-decoding framework to enable both supervised and unsupervised identification of the hybrid kinetics and thereby dynamic PET reconstruction. Through both phantom and real-data experiments, we demonstrate the benefits of HyKE-Net -- especially in unsupervised reconstructions -- over existing physics-based and data-driven baselines as well as its ablated formulations where the embedded tracer kinetics are purely physics-based, purely neural, or hybrid but with a non-adaptable neural component.Comment: Under Revie

BundledSLAM: An Accurate Visual SLAM System Using Multiple Cameras

Multi-camera SLAM systems offer a plethora of advantages, primarily stemming from their capacity to amalgamate information from a broader field of view, thereby resulting in heightened robustness and improved localization accuracy. In this research, we present a significant extension and refinement of the state-of-the-art stereo SLAM system, known as ORB-SLAM2, with the objective of attaining even higher precision. To accomplish this objective, we commence by mapping measurements from all cameras onto a virtual camera termed BundledFrame. This virtual camera is meticulously engineered to seamlessly adapt to multi-camera configurations, facilitating the effective fusion of data captured from multiple cameras. Additionally, we harness extrinsic parameters in the bundle adjustment (BA) process to achieve precise trajectory estimation.Furthermore, we conduct an extensive analysis of the role of bundle adjustment (BA) in the context of multi-camera scenarios, delving into its impact on tracking, local mapping, and global optimization. Our experimental evaluation entails comprehensive comparisons between ground truth data and the state-of-the-art SLAM system. To rigorously assess the system's performance, we utilize the EuRoC datasets. The consistent results of our evaluations demonstrate the superior accuracy of our system in comparison to existing approaches

Design, fabrication and characterization of a MEMS gravity gradiometer

Gravity gradiometers have been developed to determine the gravity gradient for a number of terrestrial observations including oil and mineral exploration, measurement of the crustal anomaly, and archaeology since their first demonstration in the 1890s by the Hungarian physicist Lorand Eotvos. However, conventional gravity gradiometers weigh hundreds of kilograms to several tens. In order to integrate a gravity gradiometer into a weight- and volume-limited spacecraft or cube satellite, miniaturization becomes a priority. Microelectromechanical systems (MEMS) technologies offer a possible route. Only two MEMS gravity gradiometers have been developed so far but neither of them can be operated under Earth’s gravity to allow pre-flight validation. There are two possible approaches for implementation of a gravity gradiometer: differential-accelerometer and torsion-balance that depend on how the force difference is measured. For the former, the gravity gradient is determined by the difference between two accelerometers’ outputs divided by the separation. The latter transduces the force difference applied on two coupled masses as a torque, which is then balanced by a rotary suspension. The latter is approved to be a better option for implementing a MEMS gravity gradiometer. The aim of this thesis is to develop a torsion-balance-based MEMS gravity gradiometer for operation both on a satellite for planetary explorations and on Earth for airborne or shipborne gravity gradient surveys. The design rationales and noise analysis are introduced. With a feasibility study to achieve 1 Eo/rtHz, exploration for Mars gravitational field is possible. A seesaw-lever force-balancing suspension is designed to bear the gravity offset and to be compliant with respect to in-plane rotation but stiff with respect to other spurious vibrations. Closed-form solutions of gradiometer dynamics are derived and agree with finite element analysis (FEA) simulations and experimental results. Several prototypes of the MEMS gravity gradiometer based on this suspension are fabricated by through-wafer deep reactive-ion etching (DRIE) with their measured resonant frequencies varying from 6.6 Hz to 27 Hz. A normalized lateral capacitive array transducer (LCAT) is analysed. Its angular counterpart rotational capacitive array transducer (RCAT) is designed to be applied on the MEMS gravity gradiometer to determine the angular displacement induced by the gravity gradient. A frontend circuit is designed for the gravity gradiometer chip and implemented on a printed circuit board (PCB) that is also used to accommodate the MEMS chip. With the shortest paths from the MEMS chip to the front-end, the pre-amp noise is minimized. A conditioning circuit is designed to amplify, demodulate, and low-pass filter the pre-amplification signal. The MEMS gravity gradiometer chips were fabricated by four-mask processes on single-crystal silicon substrates using two metal layers insulated by a deposited silicon dioxide layer to form the RCAT, and using DRIE to etch through silicon wafers to define the mechanical structures. Both the stator and rotor dies were fabricated on the same wafer, singulated by pressing dicing-free features, and integrated by flip-chip technology. Then, the fully functional MEMS gravity gradiometer was characterized by a customized platform that provides angular accelerations. The transfer function of the gradiometer prototype was investigated and proved to be operational on Earth. Silicon suspensions suffer from changes in stiffness due to the temperature-dependent Young’s modulus of silicon. The sag displacement drift of a differential-accelerometer-based silicon gravity gradiometer due to temperature is problematic. A silicon/solder bilayer thermal actuator is developed to compensate the sag thermal-drift using the mismatching of the coefficient of thermal expansion of different materials. This design has been applied on a MEMS seismometer as a contribution to NASA’s InSight Mars mission.Open Acces

Latent Feature Relation Consistency for Adversarial Robustness

Deep neural networks have been applied in many computer vision tasks and achieved state-of-the-art performance. However, misclassification will occur when DNN predicts adversarial examples which add human-imperceptible adversarial noise to natural examples. This limits the application of DNN in security-critical fields. To alleviate this problem, we first conducted an empirical analysis of the latent features of both adversarial and natural examples and found the similarity matrix of natural examples is more compact than those of adversarial examples. Motivated by this observation, we propose \textbf{L}atent \textbf{F}eature \textbf{R}elation \textbf{C}onsistency (\textbf{LFRC}), which constrains the relation of adversarial examples in latent space to be consistent with the natural examples. Importantly, our LFRC is orthogonal to the previous method and can be easily combined with them to achieve further improvement. To demonstrate the effectiveness of LFRC, we conduct extensive experiments using different neural networks on benchmark datasets. For instance, LFRC can bring 0.78\% further improvement compared to AT, and 1.09\% improvement compared to TRADES, against AutoAttack on CIFAR10. Code is available at https://github.com/liuxingbin/LFRC.Comment: Tech repor

CAT:Collaborative Adversarial Training

Adversarial training can improve the robustness of neural networks. Previous methods focus on a single adversarial training strategy and do not consider the model property trained by different strategies. By revisiting the previous methods, we find different adversarial training methods have distinct robustness for sample instances. For example, a sample instance can be correctly classified by a model trained using standard adversarial training (AT) but not by a model trained using TRADES, and vice versa. Based on this observation, we propose a collaborative adversarial training framework to improve the robustness of neural networks. Specifically, we use different adversarial training methods to train robust models and let models interact with their knowledge during the training process. Collaborative Adversarial Training (CAT) can improve both robustness and accuracy. Extensive experiments on various networks and datasets validate the effectiveness of our method. CAT achieves state-of-the-art adversarial robustness without using any additional data on CIFAR-10 under the Auto-Attack benchmark. Code is available at https://github.com/liuxingbin/CAT.Comment: Tech repor