Karol Pąk · Formalized Mathematics · 2008
Linear Map of Matrices The paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finitedimensional vector space. Introduced are linear transformations over a finitedimensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations over a finite-dimensional vector space is the same as the rank of the matrix of that transformation.
Cited by 7Open access
Edmond Jonckheere · 1997
Abstract Computing the crossover amounts to solving the Nyquist equation f(p) = 0 + jO. Assuming this equation is defined over the polyhedron D × Ω, the natural approach to implement an ad hoc solution in the realm of finite computation is to map the vertex set {ai} of the domain D × Ω to the complex plane, ai↦ bi= f (ai), and then work with the piecewise-linear extension of the vertex transformation ai↦bi. A typical feature of the resulting map is that the image of a simplex is a convex polygon, so that this piecewise-linear extension is not, in general, simplicial. However, an attractive feature of the piecewise-linear extension is that computation of the approximate crossover can be formulated as a linear program. Next, since the piecewise-linear extension lacks simplicial property, the standard fixup would be to compute a simplicial approximation to the piecewise-linear map. However, a conceptually more elegant approach is to make the piecewise-linear extension itself simplicial relative to refined subdivisions of both D × Ω and N. The reward is that crossover computation on a simplicial piecewise-linear map amounts to pure combinatorics, and the need for a linear program is obviated. It follows that, in a certain sense, simplicial approximation and linear programming are equivalent.
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Yong-Jin Huang (17743399), Chun-Wei Chang (380018), Chih-hao Hsieh (28626) · Figshare · 2024
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Li Hua Yu, Beverley Anne. Nash · University of North Texas Digital Library (University of North Texas) · 2009
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
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Nie, Zuo-Ming, Zhang, Zhi-Fang, Wang, Dan et al. · Figshare · 2011
<b>Copyright information:</b>Taken from "Complete sequence and organization of nucleopolyhedrovirus, a -rich baculovirus"http://www.biomedcentral.com/1471-2164/8/248BMC Genomics 2007;8():248-248.Published online 24 Jul 2007PMCID:PMC1976136. The number and transcriptional direction of each ORF are labeled by arrows, indicating direction of transcription. Known baculovirus homologs are labeled in different colors. Polyhedrin was designed as the first ORF in reverse direction. AnpeNPV ORF numbers are shown below the arrows. The name of putative genes are shown upon the arrows. Homologous regions (s) are defined by blank boxes. As a comparison with AnpeNPV, the ORFs from CfMNPV and OpMNPV were included.
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Yu Zhang (12946), Wenjing Xu (183446), Guangjie Liu (141451) et al. · Figshare · 2021
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María Leticia Ferrelli (5675972), Matías Luis Pidre (5675975), Pablo Daniel Ghiringhelli (661198) et al. · Figshare · 2018
<p>Arrows represent orientations of predicted ORFs. Each ORF is designated by its number in the genome annotation. Those numbers that belong to well conserved baculovirus orthologs have been replaced by the particular descriptive names. ORFs categories are indicated in the figure with different colors. Transcription products corresponding to some ORFs (indicated by asterisks) were checked and detected by RT-PCR (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0202598#pone.0202598.s004" target="_blank">S1 Appendix</a>). Homologous repeat regions (<i>hrs</i>) are represented by black lines.</p>
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Nie, Zuo-Ming, Zhang, Zhi-Fang, Wang, Dan et al. · Figshare · 2011
<b>Copyright information:</b>Taken from "Complete sequence and organization of nucleopolyhedrovirus, a -rich baculovirus"http://www.biomedcentral.com/1471-2164/8/248BMC Genomics 2007;8():248-248.Published online 24 Jul 2007PMCID:PMC1976136. The number and transcriptional direction of each ORF are labeled by arrows, indicating direction of transcription. Known baculovirus homologs are labeled in different colors. Polyhedrin was designed as the first ORF in reverse direction. AnpeNPV ORF numbers are shown below the arrows. The name of putative genes are shown upon the arrows. Homologous regions (s) are defined by blank boxes. As a comparison with AnpeNPV, the ORFs from CfMNPV and OpMNPV were included.
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Camacho, Hugo, Rotermund, Kaja M., Slosar, Anže et al. · arXiv (Cornell University) · 2025
LuSEE-Night is a pathfinder radio telescope on the lunar far side employing four 3-m monopole antennas arranged as two horizontal cross pseudo-dipoles on a rotational stage and sensitive to the radio sky in the 1-50 MHz frequency band. LuSEE-Night measures the corresponding 16 correlation products as a function of frequency. While each antenna combination measures radiation coming from a large area of the sky, their aggregate information as a function of phase in the lunar cycle and rotational stage position can be deconvolved into a low-resolution map of the sky. We study this deconvolution using linear map-making based on the Wiener filter algorithm. We illustrate how systematic effects can be effectively marginalised over as contributions to the noise covariance and demonstrate this technique on beam knowledge uncertainty and gain fluctuations. With reasonable assumptions about instrument performance, we show that LuSEE-Night should be able to map the sub-50 MHz sky at a ~5-degree resolution.
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Kelsey A. Coffman (9707735), Gaelen R. Burke (9707738) · Figshare · 2020
<p>Each arrow indicates the genomic position of a DlEPV ORF, and the direction of the arrow corresponds to its strand orientation. Arrows are colored based on the putative functional category of each ORF as defined in the legend at the bottom of the map. Core Replication refers to the 45 poxvirus core genes identified in the DlEPV genome. Virulence: BRO refers to the 27 DlEPV BRO genes, Virulence: Homology indicates the 6 ORFs with similarity to known virulence genes, and Virulence: Early Promoter are the additional 34 putative virulence genes based on the presence of the conserved EPV early promoter sequence and no other assigned function.</p>
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Hugo Camacho, Kaja M. Rotermund, Anže Slosar et al. · The Open Journal of Astrophysics · 2026
LuSEE-Night is a pathfinder radio telescope on the lunar far side employing four 3-m monopole antennas arranged as two horizontal cross pseudo-dipoles on a rotational stage and sensitive to the radio sky in the 1-50 MHz frequency band. LuSEE-Night measures the corresponding 16 correlation products as a function of frequency. While each antenna combination measures radiation coming from a large area of the sky, their aggregate information as a function of phase in the lunar cycle and rotational stage position can be deconvolved into a low-resolution map of the sky. We study this deconvolution using linear map-making based on the Wiener filter algorithm. We illustrate how systematic effects can be effectively marginalised over as contributions to the noise covariance and demonstrate this technique on beam knowledge uncertainty and gain fluctuations. With reasonable assumptions about instrument performance, we show that LuSEE-Night should be able to map the sub-50 MHz sky at a ~5-degree resolution.
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Michail G. Lagoudakis, Instructor Prof, Ruth S. Day · 2007
this article, we adopt this extended notion of cognitive map, whereby it describes the way the state of a modeled system (whether this is the three-dimensional space or anything else) changes as a result of certain actions. In particular, we are interested in how the model (cognitive map) affects people&apos;s cognition when building linear plans in everyday situations
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H. Camacho, K. M. Rotermund, Anže Slosar et al. · ArXiv.org · 2025
LuSEE-Night is a pathfinder radio telescope on the lunar far side employing four 3-m monopole antennas arranged as two horizontal cross pseudo-dipoles on a rotational stage and sensitive to the radio sky in the 1-50 MHz frequency band. LuSEE-Night measures the corresponding 16 correlation products as a function of frequency. While each antenna combination measures radiation coming from a large area of the sky, their aggregate information as a function of phase in the lunar cycle and rotational stage position can be deconvolved into a low-resolution map of the sky. We study this deconvolution using linear map-making based on the Wiener filter algorithm. We illustrate how systematic effects can be effectively marginalised over as contributions to the noise covariance and demonstrate this technique on beam knowledge uncertainty and gain fluctuations. With reasonable assumptions about instrument performance, we show that LuSEE-Night should be able to map the sub-50 MHz sky at a ~5-degree resolution.
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Elena Bello-López (8887223), Ángeles Pérez-Oseguera (8989928), Walter Santos (10219142) et al. · Figshare · 2024
<p>The arrows in blue indicate genes encoding hypothetical proteins. The arrows in green indicate genes encoding proteins with functional annotations. The red bar filled with the letter “G” shows the fragment containing the minimal replication region of the plasmids. The purple bars indicate the other PCR products that were evaluated for replication function. The positions and names of the PCR primers used in this work are given in magenta.</p>
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Roberts, John A. G., Saito, Asaki, Vivaldi, Franco · arXiv (Cornell University) · 2021
We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs to the boundary between half-planes. These parameters consist of algebraic curves, determined by the symbolic dynamics of the itinerary that connects boundary points. We study the algebraic and geometrical properties of these curves, in relation with such a symbolic dynamics.
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Li, Yonghui, Yue, Chentao, Vucetic, Branka · arXiv (Cornell University) · 2025
In this paper, we propose a linear representation of BCJR maximum a posteriori probability (MAP) decoding of a rate 1/2 convolutional code (CC), referred to as the linear MAP decoding (LMAP). We discover that the MAP forward and backward decoding can be implemented by the corresponding dual soft input and soft output (SISO) encoders using shift registers. The bidrectional MAP decoding output can be obtained by combining the contents of respective forward and backward dual encoders. Represented using simple shift-registers, LMAP decoder maps naturally to hardware registers and thus can be easily implemented. Simulation results demonstrate that the LMAP decoding achieves the same performance as the BCJR MAP decoding, but has a significantly reduced decoding delay. For the block length 64, the CC of the memory length 14 with LMAP decoding surpasses the random coding union (RCU) bound by approximately 0.5 dB at a BLER of $10^{-3}$, and closely approaches both the normal approximation (NA) and meta-converse (MC) bounds.
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Al-Momani Ala'a · 2023
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Tyler D. P. Goralski (7506845), Conor C. Jenkins (14608819), Daniel J. Angelini (14608822) et al. · Figshare · 2023
<p>A) Day 1 only changes in expression, described by 37 genes (p = 0.005). B) Day 7 only changes in expression, described by 30 genes (p = 0.005). Linear regression analyses revealed that the transcriptomics data are more clearly described by examining Day 1 and Day 7 gene expression changes separately.</p>
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Yonghui Li, Chentao Yue, Branka Vucetic · 2025
In this paper, we propose a linear representation of BCJR maximum a posteriori probability (MAP) decoding of a rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 / 2$</tex> convolutional code (CC), referred to as the linear MAP decoding (LMAP). We discover that the MAP forward and backward decoding can be implemented by the corresponding dual soft input and soft output (SISO) encoders using shift registers. The bidrectional MAP decoding output can be obtained by combining the contents of respective forward and backward dual encoders. Represented using simple shift-registers, LMAP decoder maps naturally to hardware registers and thus can be easily implemented. Simulation results demonstrate that the LMAP decoding achieves the same performance as the BCJR MAP decoding, but has a significantly reduced decoding delay. For the block length 64, the CC of the memory length 14 with LMAP decoding surpasses the random coding union (RCU) bound by approximately 0.5 dB at a BLER of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^{-3}$</tex>, and closely approaches both the normal approximation (NA) and meta-converse (MC) bounds.
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Huicheng Zheng, Wei Shen · ACTA AUTOMATICA SINICA · 2009
摘要: 提出一种局部化的线性流形自组织映射方法, 可自主学习高维向量空间中的一组有序的低维线性流形. 与现有的基于Kohonen的自适应子空间自组织映射网络(Adaptive-subspace self-organizing map, ASSOM)方法相比较, 本文方法有效地克服了流形表达中出现的数据混淆现象, 网络中各神经元渐近学习各自区域内样本数据的平均向量和主元子空间, 数据表达更加清晰可辨. 实验中, 新方法对数据簇的分类准确率明显优于参与对比的其他三种方法, 其对手写体数字识别的准确率在MNIST训练集和测试集上分别达到了98.26\%和97.46\%. 关键词: 自组织映射 / 流形学习 / 手写体数字识别
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