IA Scholar Query: Fast computation of orthogonal Fourier-Mellin moments in polar coordinates.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 07 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Bootstrapping One-Loop Inflation Correlators with the Spectral Decomposition
https://scholar.archive.org/work/y46f3fdizrhqfbyqcj2z4624xm
Phenomenological studies of cosmological collider physics in recent years have identified many 1-loop inflation correlators as leading channels for discovering heavy new particles around or above the inflation scale. However, complete analytical results for these massive 1-loop correlators are currently unavailable. In this work, we embark on a program of bootstrapping inflation correlators with massive exchanges at 1-loop order, with the input of tree-level inflation correlators and the techniques of spectral decomposition in dS. As a first step, we present for the first time the complete and analytical results for a class of 4-point and 3-point inflation correlators mediated by massive scalar fields at the 1-loop order. Using the full result, we provide simple and reliable analytical approximations for the signals and the background in the squeezed limit. We also identify configurations of the scalar trispectrum where the oscillatory signal from the loop is dominant over the background.Zhong-Zhi Xianyu, Hongyu Zhangwork_y46f3fdizrhqfbyqcj2z4624xmMon, 07 Nov 2022 00:00:00 GMTUltrafast Image Retrieval from a Holographic Memory Disc for High-Speed Operation of a Shift, Scale, and Rotation Invariant Target Recognition System
https://scholar.archive.org/work/diwztsce4jc3tnraeroiy3ibdu
The hybrid opto-electronic correlator (HOC) architecture has been shown to be able to detect matches in a shift, scale, and rotation invariant (SSRI) manner by incorporating a polar Mellin transform (PMT) pre-processing step. Here we demonstrate the design and use of a thick holographic memory disc (HMD) for high-speed SSRI correlation employing an HOC. The HMD was written to have 1,320 stored images, including both unprocessed images and their PMTs. We further propose and demonstrate a novel approach whereby the HOC inputs are spatially shifted to produce correlation signals without requiring stabilization of optical phases, yielding results that are in good agreement with the theory. Use of this approach vastly simplifies the design and operation of the HOC, while improving its stability significantly. Finally, a real-time opto-electronic PMT pre-processor utilizing an FPGA is proposed and prototyped, allowing for the automatic conversion of images into their PMTs without additional processing delay.Julian Gamboa, Xi Shen, Tabassom Hamidfar, Selim M. Shahriarwork_diwztsce4jc3tnraeroiy3ibduMon, 07 Nov 2022 00:00:00 GMTFourier expansion of light-cone Eisenstein series
https://scholar.archive.org/work/cobsdya5vrfrhoov2kvkpeh2p4
In this work we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1-space. As a consequence we obtain results on location of all poles of these Eisenstein series as well as their supremum norms. We use this information to get new results on counting rational points on spheres.Dubi Kelmer, Shucheng Yuwork_cobsdya5vrfrhoov2kvkpeh2p4Wed, 14 Sep 2022 00:00:00 GMTA Principled Design of Image Representation: Towards Forensic Tasks
https://scholar.archive.org/work/tqng3a2n2naarmdpepuqugibgy
Image forensics is a rising topic as the trustworthy multimedia content is critical for modern society. Like other vision-related applications, forensic analysis relies heavily on the proper image representation. Despite the importance, current theoretical understanding for such representation remains limited, with varying degrees of neglect for its key role. For this gap, we attempt to investigate the forensic-oriented image representation as a distinct problem, from the perspectives of theory, implementation, and application. Our work starts from the abstraction of basic principles that the representation for forensics should satisfy, especially revealing the criticality of robustness, interpretability, and coverage. At the theoretical level, we propose a new representation framework for forensics, called Dense Invariant Representation (DIR), which is characterized by stable description with mathematical guarantees. At the implementation level, the discrete calculation problems of DIR are discussed, and the corresponding accurate and fast solutions are designed with generic nature and constant complexity. We demonstrate the above arguments on the dense-domain pattern detection and matching experiments, providing comparison results with state-of-the-art descriptors. Also, at the application level, the proposed DIR is initially explored in passive and active forensics, namely copy-move forgery detection and perceptual hashing, exhibiting the benefits in fulfilling the requirements of such forensic tasks.Shuren Qi, Yushu Zhang, Chao Wang, Jiantao Zhou, Xiaochun Caowork_tqng3a2n2naarmdpepuqugibgyTue, 06 Sep 2022 00:00:00 GMTMechanical structure of a spin-1 particle
https://scholar.archive.org/work/tubs74ov25f5vpceobekqh3ysa
We investigate the mechanical structure of a spin-1 particle. Introducing three different frameworks, i.e., the three-dimensional (3D) Breit frame, the two-dimensional (2D) Breit frame, and the 2D infinite momentum frame (equivalently the two-dimensional Drell-Yan frame), we scrutinize the 2D and 3D energy-momentum tensor (EMT) distributions in these frames. We first derive the EMT distributions in the 2D Breit frame by performing the Abel transformation. The mass distribution in the 2D Breit frame contains an additional monopole contribution induced geometrically. The pressure distribution in the 2D Breit frame also gets an induced monopole structure. When the Lorentz boost is carried out, the mass distribution in the 2D infinite-momentum frame acquires the induced dipole term. Similarly, we also have the induced dipole contributions to the pressure and shear-force densities. We visualize the 2D mass distributions when the spin-1 particle is polarized along the x- and z-axes. We observe that the 2D mass distribution in the infinite momentum frame exhibit clearly the induced dipole structure when the spin-1 particle is polarized along the x-axis. We also discuss the strong force fields inside a polarized spin-1 particle.June-Young Kim, Bao-Dong Sun, Dongyan Fu, Hyun-Chul Kimwork_tubs74ov25f5vpceobekqh3ysaTue, 02 Aug 2022 00:00:00 GMTShrinking the Semantic Gap: Spatial Pooling of Local Moment Invariants for Copy-Move Forgery Detection
https://scholar.archive.org/work/gheng2pfercbvnns2tm6qjwwcu
Copy-move forgery is a manipulation of copying and pasting specific patches from and to an image, with potentially illegal or unethical uses. Recent advances in the forensic methods for copy-move forgery have shown increasing success in detection accuracy and robustness. However, for images with high self-similarity or strong signal corruption, the existing algorithms often exhibit inefficient processes and unreliable results. This is mainly due to the inherent semantic gap between low-level visual representation and high-level semantic concept. In this paper, we present a very first study of trying to mitigate the semantic gap problem in copy-move forgery detection, with spatial pooling of local moment invariants for midlevel image representation. Our detection method expands the traditional works on two aspects: 1) we introduce the bag-of-visual-words model into this field for the first time, may meaning a new perspective of forensic study; 2) we propose a word-to-phrase feature description and matching pipeline, covering the spatial structure and visual saliency information of digital images. Extensive experimental results show the superior performance of our framework over state-of-the-art algorithms in overcoming the related problems caused by the semantic gap.Chao Wang, Zhiqiu Huang, Shuren Qi, Yaoshen Yu, Guohua Shenwork_gheng2pfercbvnns2tm6qjwwcuTue, 19 Jul 2022 00:00:00 GMTOn Gaussian multiplicative chaos and conformal field theory
https://scholar.archive.org/work/bhwea4esx5ci7euvz3qishl4ii
This thesis is concerned with conformally invariant stochastic processes in two dimensions and their applications to conformal field theory (CFT). The main probabilistic objects are the Gaussian free field (GFF) and the random geometries associated to it. Especially, we are interested in Gaussian multiplicative chaos (GMC), Schramm-Loewner evolution (SLE) and Liouville CFT, which can be understood as theories of random surfaces. From the point of view of physics, the idea of a "summing over surfaces" can be traced back to Polyakov's work on bosonic string theory. Indeed, the starting point of string theory is to replace a point particle by a one dimensional manifold (a string), so that one must replace the worldline by a worldsheet, i.e. an embedding of a surface into space-time. The path integral that Polyakov wrote down features a random conformal factor that should be described by the quantisation of the Liouville action. Therefore, this probability measure should describe random fluctuations around the uniform metric. Polyakov also suggested that the resulting quantum field theory should exhibit conformal invariance. This means that the Hilbert space of the theory should carry a projective unitary representation of the group of local conformal transformations, i.e. a unitary representation of the Virasoro algebra. Since it is an infinite dimensional Lie algebra, this is a huge constraint to put on a system and this led Belavin, Polyakov & Zamolodchikov to give an axiomatic framework for CFT based on the representation theory of the Virasoro algebra. Here, the game is somehow reversed: one tries to exhibit and classify all theories fitting in this framework. In particular, it is not even clear in the first place that such algebraic structures exist. In this context, Liouville theory is a success story in the interaction of algebra, geometry and probability. On the one hand, the algebraic point of view was successful in finding a theory fitting in the BPZ framework. On the other hand, it was unclear that t [...]Guillaume Baverez, Apollo-University Of Cambridge Repository, Jason Millerwork_bhwea4esx5ci7euvz3qishl4iiTue, 05 Apr 2022 00:00:00 GMTSelected topics in diffraction with protons and nuclei: past, present, and future
https://scholar.archive.org/work/sdzs2sjcvzdpxpzc5ivmqebjtu
We review a broad range of phenomena in diffraction in the context of hadron-hadron, hadron-nucleus collisions and deep inelastic lepton-proton/nucleus scattering focusing on the interplay between the perturbative QCD and non-perturbative models. We discuss inclusive diffraction in DIS, phenomenology of dipole models, resummation and parton saturation at low x, hard diffractive production of vector mesons, inelastic diffraction in hadron-hadron scattering, formalism of color fluctuations, inclusive coherent and incoherent diffraction as well as soft and hard diffraction phenomena in hadron-hadron/nucleus and photon-nucleus collisions. For each topic we review key results from the past and present experiments including HERA and the LHC. Finally, we identify the remaining open questions, which could be addressed in the continuing experiments, in particular in photon-induced reactions at the LHC and the future Electron-Ion Collider (EIC) in the US, Large Hadron electron Collider (LHeC) and Future Circular Collider (FCC) at CERN.L. Frankfurtwork_sdzs2sjcvzdpxpzc5ivmqebjtuWed, 23 Mar 2022 00:00:00 GMTStatistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
https://scholar.archive.org/work/gfut342wb5cl5injau266cp7ka
In this thesis, we study the detailed partonic content of the quantum states of a quark-antiquark color dipole subject to high-energy evolution, which are represented by a set of dipoles generated by a stochastic binary branching process, in the scattering off a large nucleus, and produce predictions for diffractive dissociation in electron-ion collisions, based on the dipole picture of QCD. Our main results are as follows. First, the scattering events of a color dipole, when parameters are set in such a way that the total cross section is small, are triggered by rare partonic fluctuations, which look different as seen from different reference frames. It turns out that the freedom to select a frame allows to deduce an asymptotic expression for the rapidity distribution of the first branching of the slowest parent dipole of the set of those which scatter. In another aspect, such study implies the importance of the characterization of particle distribution in the frontier region in the states generated by the QCD dipole branching, and more generally, by any one-dimensional branching random walk model. To this aim, we develop a Monte Carlo algorithm to generate the frontier region of a branching random walk. Furthermore, we are able to calculate the diffractive cross section demanding a minimal rapidity gap Y_0 and the distribution of rapidity gaps Y_gap in the diffractive dissociation of a small dipole off a large nucleus, in a well-defined parametric region. They are the asymptotic solutions to the so-called Kovchegov-Levin equation, which describes the diffractive dissociation at high energy. Finally, we present predictions for the rapidity gap distributionin realistic kinematics of future electron-ion machines, based on the numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling.Anh Dung Lework_gfut342wb5cl5injau266cp7kaTue, 01 Mar 2022 00:00:00 GMTA Zero-Watermark Scheme Based on Quaternion Generalized Fourier Descriptor for Multiple Images
https://scholar.archive.org/work/sb3a2mslpzed3pxzvwfdm44cvi
Most of the existing zero-watermark schemes for medical images are only appropriate for a single grayscale image. When they protect a large number of medical images, repeating operations will cause a significant amount of time and storage costs. Hence, this paper proposes an efficient zero-watermark scheme for multiple color medical images based on quaternion generalized Fourier descriptor (QGFD). Firstly, QGFD is utilized to compute the feature invariants of each color image, then the representative features of each image are selected, stacked, and reshaped to generate a feature matrix, which is then binarized to get a binary feature image. Copyright information can be converted into the copyright image by using QR code technology, which contains more information. Finally, the zero-watermark image is constructed by executing the XOR operation on the copyright image and the feature image scrambled by the Cat map. In the experiment, different parameters are selected to determine the maximum number of images that the proposed scheme can protect simultaneously while achieving good robustness. The experimental results demonstrate that the proposed scheme can effectively resist common attacks, geometric attacks and joint attacks, and effectively improve the operation efficiency of the algorithm, thus effectively decreasing the time and storage cost of copyright protection for lots of medical images.Baowei Wang, Weishen Wang, Peng Zhao, Naixue Xiongwork_sb3a2mslpzed3pxzvwfdm44cviOn the light-ray algebra in conformal field theories
https://scholar.archive.org/work/cde6zigx3vcznhys7yxvcjdfm4
We analyze the commutation relations of light-ray operators in conformal field theories. We first establish the algebra of light-ray operators built out of higher spin currents in free CFTs and find explicit expressions for the corresponding structure constants. The resulting algebras are remarkably similar to the generalized Zamolodchikov's W∞ algebra in a two-dimensional conformal field theory. We then compute the commutator of generalized energy flow operators in a generic, interacting CFTs in d > 2. We show that it receives contribution from the energy flow operator itself, as well as from the light-ray operators built out of scalar primary operators of dimension ∆ ≤ d − 2, that are present in the OPE of two stress-energy tensors. Commutators of light-ray operators considered in the present paper lead to CFT sum rules which generalize the superconvergence relations and naturally connect to the dispersive sum rules, both of which have been studied recently.Gregory P. Korchemsky, Alexander Zhiboedovwork_cde6zigx3vcznhys7yxvcjdfm4A friendly introduction to Fourier analysis on polytopes
https://scholar.archive.org/work/euftfnc5wjgihea4bts6etterm
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field. Of the many applications of these techniques, we have chosen to focus on the following topics: (a) formulations for the Fourier transform of a polytope (b) Minkowski and Siegel's theorems in the geometry of numbers (c) tilings and multi-tilings of Euclidean space by translations of a polytope (d) Computing discrete volumes of polytopes, which are combinatorial approximations to the continuous volume (e) Optimizing sphere packings, and their packing density (f) Iterating the divergence theorem to give new formulations for the Fourier transform of a polytope, with applications (g) Shannon sampling, in several variables We assume familiarity with Linear Algebra, with some Calculus and infinite series. Throughout, we introduce the topics gently, by giving many examples and exercises, so that this book is ideally suited for a course, or for self-study.Sinai Robinswork_euftfnc5wjgihea4bts6ettermFri, 31 Dec 2021 00:00:00 GMTAsymptotic Geometry of the Moduli Space of Parabolic SL(2,ℂ)-Higgs Bundles
https://scholar.archive.org/work/lxkl5admm5hkjeweptrsg6mjf4
Given a generic stable strongly parabolic SL(2,ℂ)-Higgs bundle (ℰ, φ), we describe the family of harmonic metrics h_t for the ray of Higgs bundles (ℰ, t φ) for t≫0 by perturbing from an explicitly constructed family of approximate solutions h_t^app. We then describe the natural hyperKähler metric on ℳ by comparing it to a simpler "semi-flat" hyperKähler metric. We prove that g_L^2 - g_sf = O(e^-γ t) along a generic ray, proving a version of Gaiotto-Moore-Neitzke's conjecture. Our results extend to weakly parabolic SL(2,ℂ)-Higgs bundles as well. In the case of the four-puncture sphere, we describe the moduli space and metric more explicitly. In this case, we prove that the hyperkähler metric is ALG and show that the rate of exponential decay is the conjectured optimal one, γ=4L, where L is the length of the shortest geodesic on the base curve measured in the singular flat metric |det φ|.Laura Fredrickson, Rafe Mazzeo, Jan Swoboda, Hartmut Weisswork_lxkl5admm5hkjeweptrsg6mjf4Wed, 22 Dec 2021 00:00:00 GMTColor Zero-Watermarking Algorithm for Medical Images Based on BEMD-Schur Decomposition and Color Visual Cryptography
https://scholar.archive.org/work/na4qt2d5mvgi7ht4txf6nxnuqm
With the widespread use of medical images in telemedicine, personal information may be leaked. The traditional zero-watermarking technology has poor robustness under large-scale attacks. At the same time, most of the zero-watermarking information generated is a binary sequence with a single information structure. In order to effectively solve the poor robustness problem of traditional zero-watermarking under large-scale attacks, a color zero-watermarking algorithm for medical images based on bidimensional empirical mode decomposition (BEMD)-Schur decomposition and color visual cryptography is proposed. Firstly, the color carrier image and the color copyright logo are decomposed into R, G, and B three color components, respectively, and the feature value of each sub-block are extracted by wavelet transform, BEMD decomposition, block operation, and Schur decomposition. Then, the R, G, and B components of the copyright logo are scrambled by Arnold scramble and converted into binary watermark information. Finally, a color visual cryptography scheme is proposed to generate two color shared images based on the carrier characteristics and copyright information. One shared image is used to generate a color zero-watermark, and the other is used for copyright authentication phase. Experimental results show that this algorithm has strong robustness and stability in resisting large-scale noise attacks, filtering attacks, JPEG compression, cropping attacks, and translation attacks at different positions. Compared with similar zero-watermarking algorithms, the robust performance is improved by about 10%, and it can adapt to more complex network environments.Deyang Wu, Miaomiao Wang, Jing Zhao, Jiayan Wang, Meiyu Zhong, Haichun Zheng, Sen Hu, Yong Tang, Changbo Qu, Jinwei Wangwork_na4qt2d5mvgi7ht4txf6nxnuqmMon, 20 Dec 2021 00:00:00 GMTThe Infrared Structure of Perturbative Gauge Theories
https://scholar.archive.org/work/7gxfsq4zevfgzfe7rs4yvll5dq
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders.Neelima Agarwal, Lorenzo Magnea, Chiara Signorile-Signorile, Anurag Tripathiwork_7gxfsq4zevfgzfe7rs4yvll5dqTue, 14 Dec 2021 00:00:00 GMT