On the existence of equiangular tight frames

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August undefined, 2024

WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular tight frames (if ... WebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ …

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Web6 de mar. de 2024 · We also develop a general framework of so-called harmonic BTFs and Steiner BTFs - which includes the equiangular cases, surprisingly, the development of … Webtight frame exists for each pair (d,N) with N ≤ 100 that meets the new conditions. The arguments also extend to deliver novel necessary conditions for the existence of … dallas assessor office

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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an N … Web3 Real equiangular tight frames In this section, we describe what is known about real equiangular tight frames. Throughout, we use ∃RETF(M,N) to denote the statement “there exists a real equiangular tight frame with parameters (M,N).” We start with some basic properties: Theorem 1 (see [39]). ∃RETF(M,N) implies each of the following: WebFinally, we mention a general necessary condition for the existence of equiangular tight frames. Compared to the local conditions described above, it is a global condition depending on solely the parameters n and m. Theorem 2.5 (Naimark, see e.g. [7]). dallas assessor iowa

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Web15 de out. de 2007 · We prove the existence of equiangular tight frames having n = 2 d-1 elements drawn from either C d or C d-1 whenever n is either 2 k-1 for k ∈ N, or a power of a prime such that n ≡ 3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2 d-element equiangular tight frame based on ... Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be found in [12,8,4,3,13,10,6,1,7,9,11]. A popular method to construct equiangular tight frames is based on conference matrices [8, 3,10]. bipolaris maydis life cycleWeb1 de out. de 2007 · Request PDF On the existence of equiangular tight frames An equiangular tight frame (ETF) is a d×N matrix that has unit-norm columns and … dallas asian chamber of commerce

"Webis an equiangular tight frame for R(M N). We call this the complementary equiangular tight frame. It follows that equiangular tight frames come in pairs and if M>2Nthen M<2(M N). So we only need to classify the equiangular tight frames for M>2N. Certain classes of equiangular tight frames always exist. Proposition 3.3: RN always has an 1. " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

Web12 de abr. de 2024 · Particularly, our choice of spark deficient Gabor frames over other classes of frames that may be spark deficient (e.g. equiangular tight frames ... Data-driven approaches could offer a performance advantage, but they assume the existence of a large training dataset with ground truths, which is not available in all cases; thus, ... WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and …

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Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 Web25 de fev. de 2009 · A survey on equiangular tight frames in the space $$ \\mathbb{R}^n $$ is presented. Several equivalent definitions of a tight frame are given. The …

Web9 de abr. de 2024 · a so-called equiangular tight frame if and only if this lower. bound is saturated, meaning in particular that the subnor-malised projectors {d. n ... deciding the existence of EAMs (see e.g. [68 ...

Web26 de fev. de 2014 · The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in ... Web1 de mar. de 2009 · The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular ...

WebAbstract: An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and orthogonal rows of norm sqrt(N/d). Its key property is that the absolute inner …

Web14 de set. de 2015 · Abstract. An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a ... bipolar is most likely to be characterized byWeb4 de ago. de 2015 · Neither the existence of SIC-POVMs in higher-dimensional Hilbert spaces nor the nonexistence of MUBs in a six-dimensional Hilbert space has been proved. On the other hand, conditional SIC-POVMs are considered as equiangular tight frames. The existence of equiangular tight frames is also studied in many literature (e.g., [8, … dallas assisted living centersWebEquiangular Tight Frames Let {x m} be a collection of N unit vectors in Cd with N ≥ d A lower bound on the maximum correlation between a pair of vectors: max m6= n hx m, x ni ≥ s N −d d(N −1) def= µ(d,N) The bound is met if and only if 1. The vectors are equiangular 2. The vectors form a tight frame bipolarity meaning in teluguWebtight frame exists for each pair (d,N) with N ≤ 100 that meets the new conditions. The arguments also extend to deliver novel necessary conditions for the existence of equiangular tight frames whose Gram matrices have entries drawn from a discrete set of complex numbers. Index Terms—tight frame, equiangular lines, optimal Grassman- bipolarity meaningWebThe Internet Archive offers over 20,000,000 freely downloadable books and texts. There is also a collection of 2.3 million modern eBooks that may be borrowed by anyone with a free archive.org account. Borrow a Book Books on Internet Archive are … bipolar is a diseaseWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … dallas assisted livingWebComplex Equiangular Tight Frames Joel A. Troppa aMathematics Department, The University of Michigan, 530 Church St., Ann Arbor, MI 48109-1043, USA ... First, one could demonstrate the existence of speciﬁc complex ETFs via constructive (or nonconstructive) means. Second, one could attempt to rule out the possibility that a complex bipolar is characterized by