Interpolation of graph signals using shift-invariant graph filters

2015 ◽  
Author(s):  
Santiago Segarra ◽  
Antonio G. Marques ◽  
Geert Leus ◽  
Alejandro Ribeiro
Keyword(s):  
Invariant Graph

scholarly journals Invariant Graph Partition Comparison Measures

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 504 ◽  
Author(s):  
Fabian Ball ◽  
Andreas Geyer-Schulz
Keyword(s):  
Invariant Measures ◽  
Automorphism Groups ◽  
Structural Difference ◽  
Equivalence Classes ◽  
Classical Counterpart ◽  
Symmetric Graphs ◽  
Invariant Graph ◽  
Partition Space ◽  
Comparison Measures ◽  
Pseudometric Space

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived.

scholarly journals On Invariant Graph Subspaces

2016 ◽  
Vol 85 (3) ◽  
pp. 399-425 ◽  
Author(s):  
Konstantin A. Makarov ◽  
Stephan Schmitz ◽  
Albrecht Seelmann
Keyword(s):  
Invariant Graph

scholarly journals On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case

2016 ◽  
Vol 100 (5-6) ◽  
pp. 761-773 ◽  
Author(s):  
S. Albeverio ◽  
A. K. Motovilov
Keyword(s):  
Adjoint Operator ◽  
Invariant Graph

scholarly journals Heterogeneous Graph Matching Networks for Unknown Malware Detection

2019 ◽  
Author(s):  
Shen Wang ◽  
Zhengzhang Chen ◽  
Xiao Yu ◽  
Ding Li ◽  
Jingchao Ni ◽  
...  
Keyword(s):  
Graph Matching ◽  
Malware Detection ◽  
False Positives ◽  
Graph Representation ◽  
Systematic Evaluation ◽  
Detection Algorithms ◽  
Training Samples ◽  
Invariant Graph ◽  
Training Cost ◽  
Malicious Program

Information systems have widely been the target of malware attacks. Traditional signature-based malicious program detection algorithms can only detect known malware and are prone to evasion techniques such as binary obfuscation, while behavior-based approaches highly rely on the malware training samples and incur prohibitively high training cost. To address the limitations of existing techniques, we propose MatchGNet, a heterogeneous Graph Matching Network model to learn the graph representation and similarity metric simultaneously based on the invariant graph modeling of the program's execution behaviors. We conduct a systematic evaluation of our model and show that it is accurate in detecting malicious program behavior and can help detect malware attacks with less false positives. MatchGNet outperforms the state-of-the-art algorithms in malware detection by generating 50% less false positives while keeping zero false negatives.

Invariant tori and topological entropy in Tonelli Lagrangian systems on the 2-torus

2015 ◽  
Vol 36 (6) ◽  
pp. 1989-2014 ◽  
Author(s):  
JAN PHILIPP SCHRÖDER
Keyword(s):  
Energy Level ◽  
Topological Entropy ◽  
Chaotic Dynamics ◽  
Large Scale ◽  
Invariant Tori ◽  
Critical Value ◽  
Lagrangian Systems ◽  
Fixed Energy ◽  
Invariant Graph ◽  
Rational Direction

We study the Euler–Lagrange flow of a Tonelli Lagrangian on the 2-torus$\mathbb{T}^{2}$at a fixed energy level${\mathcal{E}}\subset T\mathbb{T}^{2}$strictly above Mañé’s strict critical value. We prove that, if for some rational direction${\it\zeta}\in S^{1}$there is no invariant graph${\mathcal{T}}\subset {\mathcal{E}}$over$\mathbb{T}^{2}$for the Euler–Lagrange flow with the property that all orbits on${\mathcal{T}}$have an asymptotic direction equal to${\it\zeta}$, then there are chaotic dynamics in${\mathcal{E}}$. This implies that, if the topological entropy of the Euler–Lagrange flow in${\mathcal{E}}$vanishes, then in${\mathcal{E}}$there are invariant graphs for all asymptotic directions${\it\zeta}\in S^{1}$and integrable-like behavior on a large scale.

scholarly journals Non-smooth saddle-node bifurcations I: existence of an SNA

2014 ◽  
Vol 36 (4) ◽  
pp. 1130-1155 ◽  
Author(s):  
GABRIEL FUHRMANN
Keyword(s):  
Lyapunov Exponent ◽  
General Result ◽  
Sufficient Conditions ◽  
Positive Lyapunov Exponent ◽  
Hyperbolic Attractor ◽  
Interval Maps ◽  
Skew Products ◽  
Saddle Node ◽  
Invariant Graph

We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is equivalent to the existence of a sink-source orbit, that is, an orbit with positive Lyapunov exponent both forwards and backwards in time. The attractor itself is a non-continuous invariant graph with negative Lyapunov exponent, often referred to as ‘SNA’. In contrast to former results in this direction, our conditions are${\mathcal{C}}^{2}$-open in the fibre maps. By applying a general result about saddle-node bifurcations in skew-products, we obtain a conclusion on the occurrence of non-smooth bifurcations in the respective families. Explicit examples show the applicability of the derived statements.

scholarly journals GeniePath: Graph Neural Networks with Adaptive Receptive Paths

2019 ◽  
Vol 33 ◽  
pp. 4424-4431 ◽  
Author(s):  
Ziqi Liu ◽  
Chaochao Chen ◽  
Longfei Li ◽  
Jun Zhou ◽  
Xiaolong Li ◽  
...  
Keyword(s):  
Neural Networks ◽  
State Of The Art ◽  
Receptive Fields ◽  
Large Graphs ◽  
Graph Data ◽  
Invariant Graph ◽  
Graph Neural Networks ◽  
Yield State

We present, GeniePath, a scalable approach for learning adaptive receptive fields of neural networks defined on permutation invariant graph data. In GeniePath, we propose an adaptive path layer consists of two complementary functions designed for breadth and depth exploration respectively, where the former learns the importance of different sized neighborhoods, while the latter extracts and filters signals aggregated from neighbors of different hops away. Our method works in both transductive and inductive settings, and extensive experiments compared with competitive methods show that our approaches yield state-of-the-art results on large graphs.

Regularity of invariant graphs for forced systems

1999 ◽  
Vol 19 (1) ◽  
pp. 155-199 ◽  
Author(s):  
JAROSLAV STARK
Keyword(s):  
State Space ◽  
Extension Theorem ◽  
Invariant Set ◽  
Inertial Manifold ◽  
Input Space ◽  
Invariant Graph ◽  
Uniform Contraction ◽  
Whitney Extension ◽  
Fixed Input ◽  
Whitney Extension Theorem

Many applications of nonlinear dynamics involve forced systems. We consider the case where for a fixed input the driven system is contracting; this is for instance the situation in certain classes of filters, and in the study of synchronization. When this contraction is uniform, it can easily be shown that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space; this is a special case of the well known concept of an inertial manifold for more general systems. If the driving state space is a manifold and the contraction is sufficiently strong this invariant set is a normally hyperbolic manifold, and hence smooth. The aim of this paper is to extend this result in two directions: firstly, where we only have uniform contraction for a compact invariant set of input states, and secondly where the contraction rates are non-uniform (and hence defined by Liapunov exponents and analogous quantities). In both cases the invariant graph is only defined over closed subsets of the input space, and hence we need to define an appropriate notion of smoothness for such functions. This is done in terms of the Whitney extension theorem: a function is considered Whitney smooth if it satisfies the conditions of this theorem and hence can be extended to a smooth function of the whole input space.

scholarly journals The Reduced Neighborhood Topological Indices and Polynomial for the Treatment of COVID-19

2020 ◽  
Vol 11 (4) ◽  
pp. 11817-11832
Keyword(s):  
Graph Theory ◽  
Antiviral Agents ◽  
Molecular Graph ◽  
Topological Indices ◽  
Medical Sciences ◽  
Invariant Graph ◽  
Life Threatening

A graphical index is a numeric value corresponding to a structurally invariant graph, and in molecular graph theory, these invariants are known as topological indices. In the field of Chemical and Medical Sciences, the topological indices are used to study the chemical, biological, medical, and pharmaceutical features of drugs. Concerning the previous deadly diseases, the COVID-19 pandemic has been considered the biggest life-threatening issue that modern medicines have ever tackled. COVID-19 is immedicable, and even the existing treatments are only helping a certain group of sufferers. Scientists have tested available antiviral agents and got a favorable impact on recovering from the pandemic. Some of these antiviral agents are remdesivir, chloroquine, hydroxychloroquine, theaflavin, and dexamethasone. Keeping given the importance of topological indices in the study of pharmaceutical and chemical drugs, in this paper, we calculate the reduced neighborhood topological indices and RNM-polynomial of some of the antiviral agents remdesivir, chloroquine, hydroxychloroquine, theaflavin, and dexamethasone. The results thus obtained may be useful for finding new medicine and vaccine for the treatment of COVID-19.

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