scholarly journals The lattice of balanced equivalence relations of a coupled cell network

2007 ◽  
Vol 143 (1) ◽  
pp. 165-183 ◽  
Author(s):  
IAN STEWART
Keyword(s):  
Network Architecture ◽  
Linear Chain ◽  
Cell System ◽  
Equivalence Relations ◽  
Locally Finite ◽  
Cell Network ◽  
Equality Relation ◽  
Coupled Cell Systems ◽  
Infinite Networks

AbstractA coupled cell system is a collection of dynamical systems, or ‘cells’, that are coupled together. The associated coupled cell network is a labelled directed graph that indicates how the cells are coupled, and which cells are equivalent. Golubitsky, Stewart, Pivato and Török have presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of the concept of a ‘balanced equivalence relation’, which depends solely on the network architecture. In their approach the network is assumed to be finite. We prove that the set of all balanced equivalence relations on a network forms a lattice, in the sense of a partially ordered set in which any two elements have a meet and a join. The partial order is defined by refinement. Some aspects of the theory make use of infinite networks, so we work in the category of networks of ‘finite type’, a class that includes all locally finite networks. This context requires some modifications to the standard framework. As partial compensation, the lattice of balanced equivalence relations can then be proved complete. However, the intersection of two balanced equivalence relations need not be balanced, as we show by a simple example, so this lattice is not a sublattice of the lattice of all equivalence relations with its usual operations of meet and join. We discuss the structure of this lattice and computational issues associated with it. In particular, we describe how to determine whether the lattice contains more than the equality relation. As an example, we derive the form of the lattice for a linear chain of identical cells with feedback.

scholarly journals Characterization of fundamental networks

2019 ◽  
Vol 150 (1) ◽  
pp. 453-474
Author(s):  
Manuela A. D. Aguiar ◽  
Ana P. S. Dias ◽  
Pedro Soares
Keyword(s):  
Network Architecture ◽  
Cell System ◽  
Hidden Symmetries ◽  
Network Construction ◽  
Cell Systems ◽  
Cell Network ◽  
A Cell ◽  
Network Synchrony ◽  
Coupled Cell Systems

AbstractIn the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that network. Subspaces defined by equalities of coordinates which are flow-invariant for any coupled cell system consistent with a network structure are called the network synchrony subspaces. Moreover, for every synchrony subspace, each network admissible system restricted to that subspace is a dynamical system consistent with a smaller network called a quotient network. We characterize networks such that: the network is a subnetwork of its fundamental network, and the network is a fundamental network. Moreover, we prove that the fundamental network construction preserves the quotient relation and it transforms the subnetwork relation into the quotient relation. The size of cycles in a network and the distance of a cell to a cycle are two important properties concerning the description of the network architecture. In this paper, we relate these two architectural properties in a network and its fundamental network.

scholarly journals Quasiharmonic classification of infinite networks

1980 ◽  
Vol 2 (4) ◽  
pp. 339-344 ◽  
Author(s):  
Maretsugu Yamasaki
Keyword(s):  
Infinite Networks

scholarly journals An aggregate method for thorax diseases classification

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bayu Adhi Nugroho
Keyword(s):  
Network Architecture ◽  
Classification Problem ◽  
Calculation Algorithm ◽  
Training Pattern ◽  
Deep Network ◽  
Network Training ◽  
Chest X Ray ◽  
Medical Image Classification ◽  
Positive Pattern

AbstractA common problem found in real-word medical image classification is the inherent imbalance of the positive and negative patterns in the dataset where positive patterns are usually rare. Moreover, in the classification of multiple classes with neural network, a training pattern is treated as a positive pattern in one output node and negative in all the remaining output nodes. In this paper, the weights of a training pattern in the loss function are designed based not only on the number of the training patterns in the class but also on the different nodes where one of them treats this training pattern as positive and the others treat it as negative. We propose a combined approach of weights calculation algorithm for deep network training and the training optimization from the state-of-the-art deep network architecture for thorax diseases classification problem. Experimental results on the Chest X-Ray image dataset demonstrate that this new weighting scheme improves classification performances, also the training optimization from the EfficientNet improves the performance furthermore. We compare the aggregate method with several performances from the previous study of thorax diseases classifications to provide the fair comparisons against the proposed method.

scholarly journals Time–frequency time–space LSTM for robust classification of physiological signals

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tuan D. Pham
Keyword(s):  
Time Series ◽  
Network Architecture ◽  
Time Series Data ◽  
Short Term Memory ◽  
Physiological Signals ◽  
Series Data ◽  
Time Frequency ◽  
Time Space ◽  
Deep Recurrent Neural Network

AbstractAutomated analysis of physiological time series is utilized for many clinical applications in medicine and life sciences. Long short-term memory (LSTM) is a deep recurrent neural network architecture used for classification of time-series data. Here time–frequency and time–space properties of time series are introduced as a robust tool for LSTM processing of long sequential data in physiology. Based on classification results obtained from two databases of sensor-induced physiological signals, the proposed approach has the potential for (1) achieving very high classification accuracy, (2) saving tremendous time for data learning, and (3) being cost-effective and user-comfortable for clinical trials by reducing multiple wearable sensors for data recording.

scholarly journals Automated Classification of Fake News Spreaders to Break the Misinformation Chain

Information ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 248
Author(s):  
Simone Leonardi ◽  
Giuseppe Rizzo ◽  
Maurizio Morisio
Keyword(s):  
Social Media ◽  
Network Architecture ◽  
Diffusion Mechanism ◽  
Automated Classification ◽  
Fake News ◽  
Neural Network Architecture ◽  
User Classification ◽  
The Social ◽  
Network Topologies

In social media, users are spreading misinformation easily and without fact checking. In principle, they do not have a malicious intent, but their sharing leads to a socially dangerous diffusion mechanism. The motivations behind this behavior have been linked to a wide variety of social and personal outcomes, but these users are not easily identified. The existing solutions show how the analysis of linguistic signals in social media posts combined with the exploration of network topologies are effective in this field. These applications have some limitations such as focusing solely on the fake news shared and not understanding the typology of the user spreading them. In this paper, we propose a computational approach to extract features from the social media posts of these users to recognize who is a fake news spreader for a given topic. Thanks to the CoAID dataset, we start the analysis with 300 K users engaged on an online micro-blogging platform; then, we enriched the dataset by extending it to a collection of more than 1 M share actions and their associated posts on the platform. The proposed approach processes a batch of Twitter posts authored by users of the CoAID dataset and turns them into a high-dimensional matrix of features, which are then exploited by a deep neural network architecture based on transformers to perform user classification. We prove the effectiveness of our work by comparing the precision, recall, and f1 score of our model with different configurations and with a baseline classifier. We obtained an f1 score of 0.8076, obtaining an improvement from the state-of-the-art by 4%.

scholarly journals Reachability Relations and the Structure of Transitive Digraphs

10.37236/115 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Norbert Seifter ◽  
Vladimir I. Trofimov
Keyword(s):  
Positive Integer ◽  
Negative Integer ◽  
Equivalence Relations ◽  
Basic Relation ◽  
Factor Graphs ◽  
Locally Finite ◽  
General Properties

In this paper we investigate reachability relations on the vertices of digraphs. If $W$ is a walk in a digraph $D$, then the height of $W$ is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed opposite to their orientation. Two vertices $u,v\in V(D)$ are $R_{a,b}$-related if there exists a walk of height $0$ between $u$ and $v$ such that the height of every subwalk of $W$, starting at $u$, is contained in the interval $[a,b]$, where $a$ ia a non-positive integer or $a=-\infty$ and $b$ is a non-negative integer or $b=\infty$. Of course the relations $R_{a,b}$ are equivalence relations on $V(D)$. Factorising digraphs by $R_{a,\infty}$ and $R_{-\infty,b}$, respectively, we can only obtain a few different digraphs. Depending upon these factor graphs with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ it is possible to define five different "basic relation-properties" for $R_{-\infty,b}$ and $R_{a,\infty}$, respectively. Besides proving general properties of the relations $R_{a,b}$, we investigate the question which of the "basic relation-properties" with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ can occur simultaneously in locally finite connected transitive digraphs. Furthermore we investigate these properties for some particular subclasses of locally finite connected transitive digraphs such as Cayley digraphs, digraphs with one, with two or with infinitely many ends, digraphs containing or not containing certain directed subtrees, and highly arc transitive digraphs.

scholarly journals USE OF GENETIC ALGORITHM IN DEEP NEURAL NETWORKS CONFIGURATION FOR THE PURPOSES OF COMPUTER ATTACKS CLASSIFICATION

2020 ◽  
pp. 104-117
Author(s):  
O.S. Amosov ◽  
◽  
S.G. Amosova ◽  
D.S. Magola ◽  
◽  
...  
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Network Architecture ◽  
Deep Neural Network ◽  
Deep Neural Networks ◽  
Classification Problem ◽  
Neural Network Architecture ◽  
Computer Attacks ◽  
Neural Network Technology

The task of multiclass network classification of computer attacks is given. The applicability of deep neural network technology in problem solving has been considered. Deep neural network architecture was chosen based on the strategy of combining a set of convolution and recurrence LSTM layers. Op-timization of neural network parameters based on genetic algorithm is proposed. The presented results of modeling show the possibility of solving the network classification problem in real time.

scholarly journals The Lattice of Definable Equivalence Relations in Homogeneous $n$-Dimensional Permutation Structures

10.37236/5980 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Samuel Braunfeld
Keyword(s):  
Distributive Lattice ◽  
Equivalence Relations ◽  
Electronic Journal ◽  
Finite Distributive Lattice ◽  
Linear Orders ◽  
Finite Dimensional ◽  
Homogeneous Structures ◽  
Special Case

In Homogeneous permutations, Peter Cameron [Electronic Journal of Combinatorics 2002] classified the homogeneous permutations (homogeneous structures with 2 linear orders), and posed the problem of classifying the homogeneous $n$-dimensional permutation structures (homogeneous structures with $n$ linear orders) for all finite $n$. We prove here that the lattice of $\emptyset$-definable equivalence relations in such a structure can be any finite distributive lattice, providing many new imprimitive examples of homogeneous finite dimensional permutation structures. We conjecture that the distributivity of the lattice of $\emptyset$-definable equivalence relations is necessary, and prove this under the assumption that the reduct of the structure to the language of $\emptyset$-definable equivalence relations is homogeneous. Finally, we conjecture a classification of the primitive examples, and confirm this in the special case where all minimal forbidden structures have order 2. 

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