اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Star of David Rule
413
0
0.0
(
0
)
تأليف
Yidong Sun
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this note, a new concept called {em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are presented, one of which states that if a matrix is a $SDR$-matrix, then so is its matrix inverse (if exists).
قيم البحث
اقرأ أيضاً
We present a class of orderings L for which there exists a profile u of preferences for a fixed odd number of individuals such that Bordas rule maps u to L.
We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumars work on the equivariant coho
mology of the affine flag variety. We show that the cap operators for Pieri elements are the same as Pieri operators defined by Berg, Saliola and Serrano. This establishes the affine Pieri rule.
The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for desc
ribing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundarams Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule.
An odd-rule cellular automaton (CA) is defined by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF. We classify a
ll the odd-rule CAs defined by neighborhoods which are subsets of a 3 X 3 grid of square cells. There are 86 different CAs modulo trivial symmetries. When we consider only the different sequences giving the number of ON cells after n generations, the number drops to 48, two of which are the Moore and von Neumann CAs. This classification is carried out by using the meta-algorithm described in an earlier paper to derive the generating functions for the 86 sequences, and then removing duplicates. The fastest-growing of these CAs is neither the Fredkin nor von Neumann neighborhood, but instead is one defined by Odd-rule 365, which turns ON almost 75% of all possible cells.
Blind video deblurring restores sharp frames from a blurry sequence without any prior. It is a challenging task because the blur due to camera shake, object movement and defocusing is heterogeneous in both temporal and spatial dimensions. Traditional
methods train on datasets synthesized with a single level of blur, and thus do not generalize well across levels of blurriness. To address this challenge, we propose a dual attention mechanism to dynamically aggregate temporal cues for deblurring with an end-to-end trainable network structure. Specifically, an internal attention module adaptively selects the optimal temporal scales for restoring the sharp center frame. An external attention module adaptively aggregates and refines multiple sharp frame estimates, from several internal attention modules designed for different blur levels. To train and evaluate on more diverse blur severity levels, we propose a Challenging DVD dataset generated from the raw DVD video set by pooling frames with different temporal windows. Our framework achieves consistently better performance on this more challenging dataset while obtaining strongly competitive results on the original DVD benchmark. Extensive ablative studies and qualitative visualizations further demonstrate the advantage of our method in handling real video blur.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
