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## Filters

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Book announcements

1993
*
Discrete Applied Mathematics
*

The enumeration

doi:10.1016/0166-218x(93)90134-a
fatcat:guesbjpz7fcb7nex3cwh2gfg4e
*of*N, and N + from the*characteristic**polynomial*. A*graph*-theoretical classification*of*conjugated hydrocarbons based*on*their spectral*characteristics*). ... Methods based*on*graphic*polynomials*(The*characteristic**polynomial*. The Acyclic*polynomial*. The permanental*polynomial*). The method based*on*the coefficients*of*nonbonding molecular orbitals. ...##
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Generalized characteristic polynomials of graph bundles

2008
*
Linear Algebra and its Applications
*

We show that the number

doi:10.1016/j.laa.2008.03.023
fatcat:lhs7hodvizf5looulutb2gv6ya
*of*spanning trees in a*graph*is the partial derivative (at (0,1))*of*the generalized*characteristic**polynomial**of*the*graph*. ... In this paper, we find computational formulae for generalized*characteristic**polynomials**of**graph*bundles. ... Its adjacency*matrix*, known as a "kite", is*one**of*important examples in*matrix**analysis*. The outline*of*this paper is as follows. ...##
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Shift-Enabled Graphs: Graphs Where Shift-Invariant Filters are Representable as Polynomials of Shift Operations

2018
*
IEEE Signal Processing Letters
*

However, the

doi:10.1109/lsp.2018.2849685
fatcat:6nikkuarhvb6leb4b2pez55j2i
*characteristic*and minimum*polynomials**of*the adjacency*matrix*must be identical for the property to hold. ... When extended to*graph*signal processing (GSP), this would mean that a shift-invariant*graph*filter can be represented as a*polynomial**of*the adjacency (shift)*matrix**of*the*graph*. ... A*graph*G is shift-enabled † if the*characteristic*and minimal*polynomials**of*its corresponding shift*matrix*S are equivalent, i.e., p S (λ) = m S (λ). ...##
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Thermodynamic characterization of networks using graph polynomials

2015
*
Physical Review E
*

Commencing from a

doi:10.1103/physreve.92.032810
pmid:26465531
fatcat:5srvx2ay3bh6lmkswh4kob33se
*representation**of**graph*structure based*on*a*characteristic**polynomial*computed from the normalized Laplacian*matrix*, we show how the*polynomial*is linked to the Boltzmann partition function ... ) characterization*of**graph*structure. ... A more convenient route is to adopt an alternative*graph**representation*based*on*a*characteristic**polynomial*. ...##
###
Efficient computation of Ihara coefficients using the Bell polynomial recursion

2012
*
Linear Algebra and its Applications
*

It is determined by the prime cycles

doi:10.1016/j.laa.2011.08.017
fatcat:znqlw4glgzgi7l7a5b77l4muxu
*of*a finite*graph*G = (V, E) and can be characterized in terms*of*a quasi*characteristic**polynomial**of*the adjacency*matrix*T*of*the oriented line*graph*associated ... The Ihara zeta function has proved to be a powerful tool in the*analysis**of**graph*structures. ... It can be expressed in terms*of*a quasi*characteristic**polynomial**of*the adjacency*matrix*T*of*the oriented line*graph*L(G) associated to G. ...##
###
The Companion Model – a Canonical Model in Graph Signal Processing
[article]

2022
*
arXiv
*
pre-print

We further show that, surprisingly, in the canonical model, convolution

arXiv:2203.13791v1
fatcat:mci63yfa2vbelb6i6cxtygjlcu
*of**graph*signals is fast convolution by the DSP FFT. ... This paper introduces a canonical*graph*signal model defined by a canonical*graph*and a canonical shift, the companion*graph*and the companion shift. ... Since 𝐶 comp is determined by the*characteristic**polynomial*Δ 𝐴 (𝑥), it only depends*on*the*graph*frequencies or eigenvalues*of*𝐴, not*on*the spectral modes or eigenvectors*of*𝐴. ...##
###
Visual Exploration of Polynomial Combination Based on Variant Measurement Model

2019
*
Journal of Applied Mathematics and Physics
*

It can be seen from the variant maps

doi:10.4236/jamp.2019.711203
fatcat:dv4eygk5lnfmdiziogkdgw33ly
*of*the*polynomial*that the graphical results under multiple conditions exhibit spatial symmetry, as well as special changes and fixed*characteristics**of*the points. ... The visualization*of*the final*polynomial*combination formula is presented in a two-dimensional color map mode. ... Acknowledgements I would like to thank my instructor, Professor Jeffrey Zheng, for his careful guidance*on*this paper and his care and concern. ...##
###
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
[chapter]

2010
*
Lecture Notes in Computer Science
*

Sketch

doi:10.1007/978-3-642-11266-9_19
fatcat:dibjikvj6rdhdmmwlysur2ibpu
*of*proof: a pathological*graph*instance G n : symbolic OBDD-*representation*is*polynomial*with respect to the number*of*Boolean variables the*characteristic*function*of*R, the set that consists*of*... Sketch*of*proof: a pathological*graph*instance G n : symbolic OBDD-*representation*is*polynomial*with respect to the number*of*Boolean variables the*characteristic*function*of*R, the set that consists*of*...*Polynomial*upper bound*on*the OBDD size*of*χ E (v i 1 ,...,in , v ℓ 1 ,... ...##
###
Multi-graph learning of spectral graph dictionaries

2015
*
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

In particular, we concentrate

doi:10.1109/icassp.2015.7178601
dblp:conf/icassp/ThanouF15
fatcat:ydiwq65bybderlfbada2tnqfga
*on**graph*atoms that are constructed*on**polynomials**of*the*graph*Laplacian. ... We propose to learn*graph*atoms and build*graph*dictionaries that provide sparse*representations*for classes*of*signals, which share common spectral*characteristics*but reside*on*the vertices*of*different ... These*characteristics*are reflected in a common dictionary structure that is constructed to be a*polynomial*function*of*the*graph*Laplacian*matrix*, and the coefficients*of*the*polynomials*are jointly learned ...##
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Weighted graph characteristics from oriented line graph polynomials

2009
*
2009 IEEE 12th International Conference on Computer Vision
*

We develop a novel method for extracting

doi:10.1109/iccv.2009.5459449
dblp:conf/iccv/RenWH09
fatcat:rfq77ktitjdkjmnzmfr4evbrg4
*graph**characteristics*from edge-weighted*graphs*, based*on*an extension*of*the Ihara zeta function from unweighted to edgeweighted*graphs*. ... We also present a spectral*analysis**of*the edge-weighted*graph*Ihara coefficients and indicate their advantages over*graph*spectral methods. ... Although the the zeta function draws*on*the*characteristic**polynomial**of*a*graph*and is hence akin to methods from algebraic*graph*theory, it first relies*on*a*graph*transformation. ...##
###
Spectral Analysis of Complex Laplacian Matrices
[chapter]

2004
*
Lecture Notes in Computer Science
*

Our spectral

doi:10.1007/978-3-540-27868-9_5
fatcat:xvowttehzjcohef7675pask6mi
*representation*is based*on*the eigendecomposition*of*the resulting Hermitian property*matrix*. The eigenvalues*of*the*matrix*are real while the eigenvectors are complex. ... This paper explores how to extend the spectral*analysis**of**graphs*to the case where the nodes and edges are attributed. To do this we introduce a complex Hermitian variant*of*the Laplacian*matrix*. ...*characteristics*to perform pattern*analysis**on*sets*of**graphs*and trees. ...##
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Discrete Signal Processing on Graphs

2013
*
IEEE Transactions on Signal Processing
*

This paper extends to signals

doi:10.1109/tsp.2013.2238935
fatcat:er2wivkywnapnfhfepx4lbxwmq
*on**graphs*DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral*representation*, Fourier transform, frequency response, and illustrates ... DSP*on**graphs*by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior*of*customers*of*a mobile service provider. ... The degree*of*the minimal*polynomial*satisfies deg m A (x) = N A = M−1 m=0 R m ≤ N. (42) The*characteristic**polynomial**of*the*matrix*A is defined as Fig. 1 . 1*Graph**representations*for different datasets ...##
###
Model Development for Analysis of Steam Power Plant Reliability
[chapter]

2017
*
Recent Improvements of Power Plants Management and Technology
*

The

doi:10.5772/intechopen.68285
fatcat:ak25o6oiyrh2fbxvvta5zdcxve
*graph*theoretical*analysis*and a graph's*characteristic**polynomial*are deployed as the basis for a system approach employed to develop a model for estimating the reliability index and evaluating the ... Computing a graph's*characteristic**polynomial*using three different methods, namely, the linearly independent cycles, the figure equation and the adjacent*matrix*, the approximate reliability*of*the system ... The*characteristic**polynomial**of*the*graph*is the*characteristic**polynomial**of*its adjacency*matrix*. ...##
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Symmetric Determinantal Representations in characteristic 2

2013
*
Linear Algebra and its Applications
*

This paper studies Symmetric Determinantal

doi:10.1016/j.laa.2013.04.022
fatcat:3n2hn7bi6zeblijittbvgklv4y
*Representations*(SDR) in*characteristic*2, that is the*representation**of*a multivariate*polynomial*P by a symmetric*matrix*M such that P=det(M), and where each ... We conclude by describing the case*of*Alternating Determinantal*Representations*in any*characteristic*. ... We once again work with the*graph**representation*instead*of*the*matrix**representation*. ...##
###
Polynomial Matrix Inequalities within Tame Geometry
[article]

2022
*
arXiv
*
pre-print

*Polynomial*

*matrix*inequalities can be solved using hierarchies

*of*convex relaxations, pioneered by Henrion and Lassere. ... In some cases, this might not be practical, and

*one*may need to resort to methods with local convergence guarantees, whose development has been rather ad hoc, so far. ... J.A. is supported by the Government

*of*Ireland Postgraduate Scholarship Programme GOIPG/2020/910

*of*the Irish Research Council. ...

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