惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

月光博客
月光博客
小众软件
小众软件
爱范儿
爱范儿
Y
Y Combinator Blog
博客园 - Franky
美团技术团队
博客园 - 【当耐特】
The Cloudflare Blog
罗磊的独立博客
Hugging Face - Blog
Hugging Face - Blog
Jina AI
Jina AI
IT之家
IT之家
人人都是产品经理
人人都是产品经理
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
大猫的无限游戏
大猫的无限游戏
Apple Machine Learning Research
Apple Machine Learning Research
博客园 - 聂微东
WordPress大学
WordPress大学
V
Visual Studio Blog
博客园_首页
阮一峰的网络日志
阮一峰的网络日志
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
有赞技术团队
有赞技术团队

math.CO updates on arXiv.org

Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Extending the known families of scalable Huffman sequences
T. C. Petersen, D. M. Paganin, I. D. Svalbe · 2021-06-04 · via math.CO updates on arXiv.org

A canonical Huffman sequence is characterized by a zero inner-product between itself and each of its shifted copies, except at their largest relative shifts: their aperiodic auto-correlation then becomes delta-like, a single central peak surrounded by zeros, with one non-zero entry at each end. Prior work showed that the few known families of Huffman sequences (of length $N = 4n-1$, for integers $n > 1$, with continuously scalable elements) are based upon Fibonacci polynomials. Related multi-dimensional ($nD$) Huffman arrays were designed, as well as non-canonical quasi-Huffman arrays that also possess delta-like auto-correlations. We examined links between these discrete sequences and delta-correlated functions defined on the continuum, and provided simple non-iterative approaches to successfully deconvolve $nD$ data blurred by diffuse Huffman arrays. Here we describe new constructions for canonical Huffman sequences. Examples of length $N = 4n+1$, $N = 2n$ and families of arbitrary length are given, including scaled forms, as well as for Fibonacci-based arrays with perfect periodic auto-correlations, that are zero for all non-zero cyclic shifts. A generalization to include canonical sequences with complex scale factors invokes an equally useful dual form of delta-correlation. We also present $1D$ arrays with a much smaller dynamic range than those where the elements are built using Fibonacci recursion. When Huffman arrays (that are comprised of inherently signed values) are employed as diffuse probe beams for image acquisition, a new two-mask de-correlating step is described here that significantly reduces the total incident radiation dose compared to a prior method that added a positive pedestal-offset.