Integral Uniform Flows in Symmetric Networks

1998 ◽  
pp. 272-284
Author(s):  
Farhad Shahrokhi ◽  
László A. Székely
Keyword(s):  
Symmetric Networks

Absence of inflation symmetric commensurate states in inflation symmetric networks

1994 ◽  
Vol 4 (4) ◽  
pp. 605-614
Author(s):  
M. A. Itzler ◽  
R. Bojko ◽  
P. M. Chaikin
Keyword(s):  
Symmetric Networks

Adaptive Routing Strategy for Large Scale Rearrangeable Symmetric Networks

2010 ◽  
Vol 2 (2) ◽  
pp. 53-63 ◽  
Author(s):  
Amitabha Chakrabarty ◽  
Martin Collier ◽  
Sourav Mukhopadhyay
Keyword(s):  
Large Scale ◽  
Blocking Probability ◽  
Routing Algorithm ◽  
Adaptive Routing ◽  
Low Complexity ◽  
Deterministic Algorithms ◽  
Routing Strategy ◽  
The Status ◽  
Extensive Computation ◽  
Symmetric Networks

This paper proposes an adaptive unicast routing algorithm for large scale symmetric networks comprising 2 × 2 switch elements such as Bene?s networks. This algorithm trades off the probability of blocking against algorithm execution time. Deterministic algorithms exploit the rearrangeability property of Bene?s networks to ensure a zero blocking probability for unicast connections, at the expense of extensive computation. The authors’ algorithm makes its routing decisions depending on the status of each switching element at every stage of the network, hence the name adaptive routing. This method provides a low complexity solution, but with much better blocking performance than random routing algorithms. This paper presents simulation results for various input loads, demonstrating the tradeoffs involved.

scholarly journals Pattern Completion in Symmetric Threshold-Linear Networks

2016 ◽  
Vol 28 (12) ◽  
pp. 2825-2852 ◽  
Author(s):  
Carina Curto ◽  
Katherine Morrison
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Distance Geometry ◽  
Memory Encoding ◽  
Stable Fixed Point ◽  
Pattern Completion ◽  
Linear Networks ◽  
Firing Rate Models ◽  
Classical Distance ◽  
Symmetric Networks

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with constant external drive and discover constraints on the coexistence of fixed points involving different subsets of active neurons. In the case of symmetric networks, we prove the following antichain property: if a set of neurons [Formula: see text] is the support of a stable fixed point, then no proper subset or superset of [Formula: see text] can support a stable fixed point. Symmetric threshold-linear networks thus appear to be well suited for pattern completion, since the dynamics are guaranteed not to get stuck in a subset or superset of a stored pattern. We also show that for any graph G, we can construct a network whose stable fixed points correspond precisely to the maximal cliques of G. As an application, we design network decoders for place field codes and demonstrate their efficacy for error correction and pattern completion. The proofs of our main results build on the theory of permitted sets in threshold-linear networks, including recently developed connections to classical distance geometry.

On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets

2000 ◽  
Vol 12 (12) ◽  
pp. 2965-2989 ◽  
Author(s):  
Jiří Šíma ◽  
Pekka Orponen ◽  
Teemu Antti-Poika
Keyword(s):  
Computation Time ◽  
Network Size ◽  
Linear Increase ◽  
Convergence Time ◽  
Polynomial Time Approximation Algorithm ◽  
Asymmetric Networks ◽  
External Clock ◽  
Binary Networks ◽  
Computational Properties ◽  
Symmetric Networks

We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem for analog Hopfield nets is NP-hard and provide a polynomial time approximation algorithm for this problem in the case of binary nets. Finally, we show that symmetric analog nets with an external clock are computationally Turing universal.

Strongly Connected Spanning Subgraph for Almost Symmetric Networks

2017 ◽  
Vol 27 (03) ◽  
pp. 207-219
Author(s):  
A. Karim Abu-Affash ◽  
Paz Carmi ◽  
Anat Parush Tzur
Keyword(s):  
Directed Graph ◽  
Euclidean Distance ◽  
Directed Graphs ◽  
Minimum Weight ◽  
Shortest Paths ◽  
Strong Connectivity ◽  
Spanning Subgraph ◽  
Strongly Connected ◽  
Set Of Points ◽  
Symmetric Networks

In the strongly connected spanning subgraph ([Formula: see text]) problem, the goal is to find a minimum weight spanning subgraph of a strongly connected directed graph that maintains the strong connectivity. In this paper, we consider the [Formula: see text] problem for two families of geometric directed graphs; [Formula: see text]-spanners and symmetric disk graphs. Given a constant [Formula: see text], a directed graph [Formula: see text] is a [Formula: see text]-spanner of a set of points [Formula: see text] if, for every two points [Formula: see text] and [Formula: see text] in [Formula: see text], there exists a directed path from [Formula: see text] to [Formula: see text] in [Formula: see text] of length at most [Formula: see text], where [Formula: see text] is the Euclidean distance between [Formula: see text] and [Formula: see text]. Given a set [Formula: see text] of points in the plane such that each point [Formula: see text] has a radius [Formula: see text], the symmetric disk graph of [Formula: see text] is a directed graph [Formula: see text], such that [Formula: see text]. Thus, if there exists a directed edge [Formula: see text], then [Formula: see text] exists as well. We present [Formula: see text] and [Formula: see text] approximation algorithms for the [Formula: see text] problem for [Formula: see text]-spanners and for symmetric disk graphs, respectively. Actually, our approach achieves a [Formula: see text]-approximation algorithm for all directed graphs satisfying the property that, for every two nodes [Formula: see text] and [Formula: see text], the ratio between the shortest paths, from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] in the graph, is at most [Formula: see text].

Maximizing the Sum Rate in Symmetric Networks of Interfering Links

2010 ◽  
Vol 56 (9) ◽  
pp. 4471-4487 ◽  
Author(s):  
Sibi Raj Bhaskaran ◽  
Stephen V. Hanly ◽  
Nasreen Badruddin ◽  
Jamie S. Evans
Keyword(s):  
Sum Rate ◽  
Symmetric Networks
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