### Browsing by Author "Sun, Wenbo"

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- Additive averages of multiplicative correlation sequences and applicationsDonoso, Sebastian; Le, Ahn N.; Moreira, Joel; Sun, Wenbo (Springer, 2023-04-01)
Show more We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ>0, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(an+b)1/(cn+d) ℓ: n ∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.Show more - Averages of completely multiplicative functions over the Gaussian integersDonoso, Sebastian; Le, Anh; Moreira, Joel; Sun, Wenbo (2024)
Show more - Bounds for Bilinear Analogues of the Spherical Averaging OperatorSovine, Sean Russell (Virginia Tech, 2022-05-12)
Show more This thesis contains work from the author's papers Palsson and Sovine (2020); Iosevich, Palsson, and Sovine (2022); and Palsson and Sovine (2022) with coauthors Eyvindur Palsson and Alex Iosevich. These works establish new $L^p$-improving, quasi-Banach, and sparse bounds for several bilinear and multilinear operators that generalize the linear spherical average to the multilinear setting, and maximal variants of these operators, with an emphasis on the triangle averaging operator and the bilinear spherical averaging operator.Show more - Decomposition of multicorrelation sequences and joint ergodicityDonoso, Sebastián; Moragues, Andreu Ferré; Koutsogiannis, Andreas; Sun, Wenbo (Cambridge University Press, 2023-05)
Show more We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure-preserving Z(d) -actions with multivariable integer polynomial iterates is the sum of a nilsequence and a nullsequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third, and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on Z(d) -systems.Show more - Distance Sets and Gap LemmaBoone, Zackary Ryan (Virginia Tech, 2022-05-26)
Show more Many problems in geometric measure theory are centered around finding conditions and structures on a set to guarantee that its distance set must be large. Two notions of structure that are of importance in this work are Hausdorff dimension and thickness. Recent progress has been made on generalizing the notion of thickness so part of this work also generalizes previous results using this new upgraded version of thickness. We also show why a famous conjecture about distance sets does not hold on the real line and thus, why this conjecture needs to happen in higher dimensions. Furthermore, we give explicit distance set and thickness calculations for a special class of self-similar sets.Show more - Joint ergodicity for functions of polynomial growth
Show more We provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates.Show more - The Mattila-Sjölin Problem for TrianglesRomero Acosta, Juan Francisco (Virginia Tech, 2023-05-08)
Show more This dissertation contains work from the author's papers [35] and [36] with coauthor Eyvindur Palsson. The classic Mattila-Sjolin theorem shows that if a compact subset of $mathbb{R}^d$ has Hausdorff dimension at least $frac{(d+1)}{2}$ then its set of distances has nonempty interior. In this dissertation, we present a similar result, namely that if a compact subset $E$ of $mathbb{R}^d$, with $d geq 3$, has a large enough Hausdorff dimension then the set of congruence classes of triangles formed by triples of points of $E$ has nonempty interior. These types of results on point configurations with nonempty interior can be categorized as extensions and refinements of the statement in the well known Falconer distance problem which establishes a positive Lebesgue measure for the distance set instead of it having nonempty interiorShow more - MVGCN: Multi-view Graph Convolutional Neural Network for Surface Defect Identification using 3D Point CloudWang, Yinan; Sun, Wenbo; Jin, Jionghua (Judy); Kong, Zhenyu (James); Yue, Xiaowei (2023-03)
Show more Surface defect identification is a crucial task in many manufacturing systems, including automotive, aircraft, steel rolling, and precast concrete. Although image-based surface defect identification methods have been proposed, these methods usually have two limitations: images may lose partial information, such as depths of surface defects, and their precision is vulnerable to many factors, such as the inspection angle, light, color, noise, etc. Given that a three-dimensional (3D) point cloud can precisely represent the multidimensional structure of surface defects, we aim to detect and classify surface defects using a 3D point cloud. This has two major challenges: (i) the defects are often sparsely distributed over the surface, which makes their features prone to be hidden by the normal surface and (ii) different permutations and transformations of 3D point cloud may represent the same surface, so the proposed model needs to be permutation and transformation invariant. In this paper, a two-step surface defect identification approach is developed to investigate the defects’ patterns in 3D point cloud data. The proposed approach consists of an unsupervised method for defect detection and a multi-view deep learning model for defect classification, which can keep track of the features from both defective and non-defective regions. We prove that the proposed approach is invariant to different permutations and transformations. Two case studies are conducted for defect identification on the surfaces of synthetic aircraft fuselage and the real precast concrete specimen, respectively. The results show that our approach receives the best defect detection and classification accuracy compared with other benchmark methods.Show more - Sarnak's Conjecture for nilsequences on arbitrary number fields and applicationsSun, Wenbo (Elsevier, 2023-02-15)
Show more We formulate the generalized Sarnak's Möbius disjointness conjecture for an arbitrary number field K, and prove a quantitative disjointness result between polynomial nilsequences (Φ(g(n)Γ))n∈ZD and aperiodic multiplicative functions on OK, the ring of integers of K. Here D=[K:Q], X=G/Γ is a nilmanifold, g:ZD→G is a polynomial sequence, and Φ:X→C is a Lipschitz function. This result, being a generalization of a previous theorem of the author in [44], requires a significantly different approach, which involves with multi-dimensional higher order Fourier analysis, multi-linear analysis, orbit properties on nilmanifold, and an orthogonality criterion of Kátai in OK. We also use variations of this result to derive applications in number theory and combinatorics: (1) we prove a structure theorem for multiplicative functions on K, saying that every bounded multiplicative function can be decomposed into the sum of an almost periodic function (the structural part) and a function with small Gowers uniformity norm of any degree (the uniform part); (2) we give a necessary and sufficient condition for the Gowers norms of a bounded multiplicative function in OK to be zero; (3) we provide partition regularity results over K for a large class of homogeneous equations in three variables. For example, for a,b∈Z﹨{0}, we show that for every partition of OK into finitely many cells, where K=Q(a,b,a+b), there exist distinct and non-zero x,y belonging to the same cell and z∈OK such that ax2+by2=z2.Show more - Spherical higher order Fourier analysis over finite fields I: equidistribution for nilsequencesSun, Wenbo (2024)
Show more - Total joint ergodicity for totally ergodic systemsKoutsogiannis, Andreas; Sun, Wenbo (2023)
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