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Many results in harmonic analysis and geometric measure theory ensure the existence of geometric configurations under the largeness of sets, which are sometimes specified via the ball condition and Fourier decay. Recently, Kuca, Opronon, Sahlsten, and Bruce, Pramanik proved a Sarkozy-like theorem, which removes the Fourier decay condition and shows that sets with large Hausdorff dimensions contain two-point patterns. This paper explores the existence of a three-point configuration that relies solely on the Hausdorff dimension., Comment: 11 pages

Any hypersurface in $\mathbb{R}^{d+1}$ has a Hausdorff dimension of $d$. However, the Fourier dimension depends on the finer geometric properties of the hypersurface. For example, the Fourier dimension of a hyperplane is 0, and the Fourier dimension of a hypersurface with non-vanishing Gaussian curvature is $d$. Recently, T. Harris showed that the Euclidean light cone in $\mathbb{R}^{d+1}$ has a Fourier dimension of $d-1$, which leads one to conjecture that the Fourier dimension of a hypersurface equals the number of non-vanishing principal curvatures. We prove this conjecture for all constant rank hypersurfaces. Our method involves substantial generalizations of Harris's strategy., Comment: 23 pages, 3 figures

Future lepton colliders such as the FCC-ee, CEPC, ILC, or a muon collider will collect large data samples that allow precision physics studies with unprecedented accuracy, especially when the data is collected by innovative state-of-the-art detectors. An electromagnetic calorimeter based on scintillating crystals, designed to separately record Cherenkov and scintillation light, can achieve precision measurements of electrons and photons without sacrificing jet energy resolution, given adequate light collection efficiency and separation. This paper presents initial measurements from a program aimed at developing such a calorimeter system for future colliders. We focus on using PbF2 crystals to enhance the understanding of Cherenkov light collection, marking the first step in this endeavor., Comment: 10 pages

The notions of Hausdorff and Fourier dimensions are ubiquitous in harmonic analysis and geometric measure theory. It is known that any hypersurface in $\mathbb{R}^{d+1}$ has Hausdorff dimension $d$. However, the Fourier dimension depends on the finer geometric properties of the hypersurface. For instance, the Fourier dimension of a hyperplane is 0, and the Fourier dimension of a hypersurface with non-vanishing Gaussian curvature is $d$. Recently, Harris has shown that the Euclidean light cone in $\mathbb{R}^{d+1}$ has Fourier dimension $d-1$, which leads one to conjecture that the Fourier dimension of a hypersurface equals the number of non-vanishing principal curvatures. We prove this conjecture for all $d$-dimensional cones and cylinders in $\mathbb{R}^{d+1}$ generated by hypersurfaces in $\mathbb{R}^d$ with non-vanishing Gaussian curvature. In particular, cones and cylinders are not Salem. Our method involves substantial generalizations of Harris's strategy.

Illumination variation has been a long-term challenge in real-world facial expression recognition(FER). Under uncontrolled or non-visible light conditions, Near-infrared (NIR) can provide a simple and alternative solution to obtain high-quality images and supplement the geometric and texture details that are missing in the visible domain. Due to the lack of existing large-scale NIR facial expression datasets, directly extending VIS FER methods to the NIR spectrum may be ineffective. Additionally, previous heterogeneous image synthesis methods are restricted by low controllability without prior task knowledge. To tackle these issues, we present the first approach, called for NIR-FER Stochastic Differential Equations (NFER-SDE), that transforms face expression appearance between heterogeneous modalities to the overfitting problem on small-scale NIR data. NFER-SDE is able to take the whole VIS source image as input and, together with domain-specific knowledge, guide the preservation of modality-invariant information in the high-frequency content of the image. Extensive experiments and ablation studies show that NFER-SDE significantly improves the performance of NIR FER and achieves state-of-the-art results on the only two available NIR FER datasets, Oulu-CASIA and Large-HFE.

With the strong robusticity on illumination variations, near-infrared (NIR) can be an effective and essential complement to visible (VIS) facial expression recognition in low lighting or complete darkness conditions. However, facial expression recognition (FER) from NIR images presents more challenging problem than traditional FER due to the limitations imposed by the data scale and the difficulty of extracting discriminative features from incomplete visible lighting contents. In this paper, we give the first attempt to deep NIR facial expression recognition and proposed a novel method called near-infrared facial expression transformer (NFER-Former). Specifically, to make full use of the abundant label information in the field of VIS, we introduce a Self-Attention Orthogonal Decomposition mechanism that disentangles the expression information and spectrum information from the input image, so that the expression features can be extracted without the interference of spectrum variation. We also propose a Hypergraph-Guided Feature Embedding method that models some key facial behaviors and learns the structure of the complex correlations between them, thereby alleviating the interference of inter-class similarity. Additionally, we have constructed a large NIR-VIS Facial Expression dataset that includes 360 subjects to better validate the efficiency of NFER-Former. Extensive experiments and ablation studies show that NFER-Former significantly improves the performance of NIR FER and achieves state-of-the-art results on the only two available NIR FER datasets, Oulu-CASIA and Large-HFE.

Vision Transformer (ViT) models have recently emerged as powerful and versatile models for various visual tasks. Recently, a work called PMF has achieved promising results in few-shot image classification by utilizing pre-trained vision transformer models. However, PMF employs full fine-tuning for learning the downstream tasks, leading to significant overfitting and storage issues, especially in the remote sensing domain. In order to tackle these issues, we turn to the recently proposed parameter-efficient tuning methods, such as VPT, which updates only the newly added prompt parameters while keeping the pre-trained backbone frozen. Inspired by VPT, we propose the Meta Visual Prompt Tuning (MVP) method. Specifically, we integrate the VPT method into the meta-learning framework and tailor it to the remote sensing domain, resulting in an efficient framework for Few-Shot Remote Sensing Scene Classification (FS-RSSC). Furthermore, we introduce a novel data augmentation strategy based on patch embedding recombination to enhance the representation and diversity of scenes for classification purposes. Experiment results on the FS-RSSC benchmark demonstrate the superior performance of the proposed MVP over existing methods in various settings, such as various-way-various-shot, various-way-one-shot, and cross-domain adaptation., Comment: SUBMIT TO IEEE TRANSACTIONS

Large-scale pre-trained transformers have demonstrated remarkable success in various computer vision tasks. However, it is still highly challenging to fully fine-tune these models for downstream tasks due to their high computational and storage costs. Recently, Parameter-Efficient Tuning (PETuning) techniques, e.g., Visual Prompt Tuning (VPT) and Low-Rank Adaptation (LoRA), have significantly reduced the computation and storage cost by inserting lightweight prompt modules into the pre-trained models and tuning these prompt modules with a small number of trainable parameters, while keeping the transformer backbone frozen. Although only a few parameters need to be adjusted, most PETuning methods still require a significant amount of downstream task training data to achieve good results. The performance is inadequate on low-data regimes, especially when there are only one or two examples per class. To this end, we first empirically identify the poor performance is mainly due to the inappropriate way of initializing prompt modules, which has also been verified in the pre-trained language models. Next, we propose a Pre-trained Visual Parameter-efficient (PVP) Tuning framework, which pre-trains the parameter-efficient tuning modules first and then leverages the pre-trained modules along with the pre-trained transformer backbone to perform parameter-efficient tuning on downstream tasks. Experiment results on five Fine-Grained Visual Classification (FGVC) and VTAB-1k datasets demonstrate that our proposed method significantly outperforms state-of-the-art PETuning methods.

The Large Hadron Collider (LHC) at CERN is expected to be upgraded to the High-Luminosity LHC (HL-LHC) by 2029 and achieve instantaneous luminosity around 5 - 7.5 $\times$ 10$^{34}$cm$^{-2}$ s$^{-1}$. This represents a more than 3-4 fold increase in the instantaneous luminosity compared to what has been achieved in Run 2. The New Small Wheel (NSW) upgrade is designed to be able to operate efficiently in this high background rate environment. In this article, we summarize multiple performance studies of the small-strip Thin Gap Chamber (sTGC) at high rate using nearly final front-end electronics. We demonstrate that the efficiency versus rate distribution can be well described by an exponential decay with electronics dead-time being the primary cause of loss of efficiency at high rate. We then demonstrate several methods that can decrease the electronics dead-time and therefore minimize efficiency loss. One such method is to install either a pi-network input filter or pull-up resistor to minimize the charge input into the amplifier. We optimized the pi-network capacitance and pull-up resistor resistance using the results from our measurements. The results shown here were not only critical to finalizing the components on the front-end board, but also are critical for setting the optimal operating parameters of the sTGC detector and electronics in the ATLAS cavern., Comment: to be submitted

The precise measurement of physics observables and the test of their consistency within the standard model (SM) are an invaluable approach, complemented by direct searches for new particles, to determine the existence of physics beyond the standard model (BSM). Studies of massive electroweak gauge bosons (W and Z bosons) are a promising target for indirect BSM searches, since the interactions of photons and gluons are strongly constrained by the unbroken gauge symmetries. They can be divided into two categories: (a) Fermion scattering processes mediated by s- or t-channel W/Z bosons, also known as electroweak precision measurements; and (b) multi-boson processes, which include production of two or more vector bosons in fermion-antifermion annihilation, as well as vector boson scattering (VBS) processes. The latter categories can test modifications of gauge-boson self-interactions, and the sensitivity is typically improved with increased collision energy. This report evaluates the achievable precision of a range of future experiments, which depend on the statistics of the collected data sample, the experimental and theoretical systematic uncertainties, and their correlations. In addition it presents a combined interpretation of these results, together with similar studies in the Higgs and top sector, in the Standard Model effective field theory (SMEFT) framework. This framework provides a model-independent prescription to put generic constraints on new physics and to study and combine large sets of experimental observables, assuming that the new physics scales are significantly higher than the EW scale., Comment: 55 pages; Report of the EF04 topical group for Snowmass 2021; v2: few typos corrected and references added

New front-end electronics including ASICs and FPGA boards are under development for the ATLAS Monitored Drift Tube (MDT) detector to handle the large data rates and harsh environment expected at high-luminosity LHC runs. A mobile Data Acquisition (miniDAQ) system is designed to perform integration tests of these front-end electronics. In addition, it will be used for surface commissioning of 96 small-radius MDT (sMDT) chambers and for integration and commissioning of new front-end electronics on the present ATLAS MDT chambers. Details of the miniDAQ hardware and firmware are described in this article. The miniDAQ system is also used to read out new front-end electronics on an sMDT prototype chamber using cosmic muons and results obtained are shown., Comment: 10 pages, 12 figures

The ATLAS experiment will replace the present Small Wheel (SW) detector with a New Small Wheel detector (NSW) aiming to improve the performance of muon triggering and precision tracking in the endcap region at the High-Luminosity LHC. Small-strip Thin Gap Chamber (sTGC) is one of the two new detector technologies used in this upgrade. A few custom-designed ASICs are needed for the sTGC detector. We designed an sTGC ASIC interface board to test ASIC-to-ASIC communication and validate the functionality of the entire system. A test platform with the final readout system is set up and the whole sTGC readout chain is demonstrated for the first time. Key parameters in the readout chain are discussed and the results are shown., Comment: 11 pages, 7 figures