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Transient length in sequential iteration of threshold functions

F. Fogelman, E. Goles, G. Weisbuch
1983 Discrete Applied Mathematics  
Let F be a function from { 0, I}" into itself whose components are symmetric threshold functions. We give a general bound on the transient length for a sequential iteration on F.  ...  For this we use a monotonic operator analogous to the spin glass interaction energy (see in a similar context [l, 31).  ...  We denote T(F) = Max{ t(x) 1 XE (41)" }, and call it the transient length of F.  ... 
doi:10.1016/0166-218x(83)90105-1 fatcat:zyg7ec5jy5hrjnly3bwkjvs5ry

Sequential simulation of parallel iterations and applications

Maurice Tchuente
1986 Theoretical Computer Science  
We first show that the parallel evolution of a network of automata N can be sequentially simulated by another network N' whose local transition functions are the same as those of N.  ...  This result is used to unify and generalize some results on the dynamic behaviour of finite automata networks. R~sum~.  ...  On the contrary, since the Gauss-Seidel analogue of a threshold function is not a threshold function, sequential iterations may generate sequences with periods and transient lengths longer than parallel  ... 
doi:10.1016/0304-3975(86)90091-5 fatcat:uhuug3l6jjajda324mlbqncnyy

Decreasing energy functions as a tool for studying threshold networks

Eric Goles-Chacc, Françoise Fogelman-Soulie, Didier Pellegrin
1985 Discrete Applied Mathematics  
Block sequential iterations of threshold networks are studied through the use of a monotonic operator, analogous to the spin glass energy.  ...  This allows to characterize the dynamics: transient and fixed points.  ...  Sequential iterations of majority functions In this section, we will study sequential iterations of a particular class of threshold functions, namely majority functions, which have been introduced in the  ... 
doi:10.1016/0166-218x(85)90029-0 fatcat:g7uo5di7vnaq3i6glkleabrwki

Page 4841 of Mathematical Reviews Vol. , Issue 84k [page]

1984 Mathematical Reviews  
Transient length in sequential iteration of threshold functions. Discrete Appl. Math. 6 (1983), no. 1, 95-98.  ...  Authors’ summary: “Let F be a function from {0,1}" into itself whose components are symmetric threshold functions. We give a general bound on the transient length for a sequential iteration on F.  ... 

A variable threshold page procedure for detection of transient signals

Z.J. Wang, P. Willett
2005 IEEE Transactions on Signal Processing  
A Page test can be thought of as a repeated sequential test, and here we propose that each sequential test use a time-varying threshold.  ...  However, its application to unknown transient changes is less clear.  ...  Consider Page's test as an iterated sequential test with lower and upper thresholds 0 and h.  ... 
doi:10.1109/tsp.2005.857060 fatcat:jyvfa2aa6zacjfo3sjdkmceody

Page 414 of Neural Computation Vol. 8, Issue 2 [page]

1996 Neural Computation  
Transient length in sequential iterations of threshold functions. Discr. Appl. Math. 6, 95-98. Fogelman Soulié, F., Robert, Y., and Tchuente, M. 1987.  ...  Automata Networks in Computer Science: Theory and Applications. Manchester University Press, Manchester. Goles, E. 1982. Fixed point behavior of threshold functions on a finite set. SIAM ]. Alg.  ... 

Asymptotic Behavior of an Artificial Neural Network Defined on Multipartite Directed Graph

Majee
2010 OnLine Journal of Biological Sciences  
The convergence of such network was studied in the present research with the help of Lyapunov functional.  ...  Results: Attractors (fixed points) of such ANN and also limit cycles of different orders are investigated. Bounds of transient length of the neural network were also calculated.  ...  in nature the orbit of the synchronous iteration are only fixed point and /or cycle of length two.  ... 
doi:10.3844/ojbsci.2010.44.49 fatcat:cheabzg4ujalvod4urekgtjgxm

Dynamics of Discrete Time, Continuous State Hopfield Networks

Pascal Koiran
1994 Neural Computation  
This allows the length of a limit cycle to be bounded: the parallel iteration has cycles of length 1 or 2 only, and the sequential iteration has only fixed points.  ...  In this paper, we prove under mild hypotheses that any trajectory converges to a fixed point for the sequential iteration, and to a cycle of length 2 or a fixed point for the parallel iteration.  ... 
doi:10.1162/neco.1994.6.3.459 fatcat:xj3iilofuzgxjicenqjz47bwwm

Page 70 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
Moreover, in the particular case of majority rule, p = 1, and the transient length is bounded by the number of cells.  ...  The main mathematical tool presented in the book is the concept of Lyapunov functional defined by E(x‘) = —(x', A-x'~')+(b, x'+ x'-'), where A and b are the parameters of the threshold function.  ... 

Page 1602 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
We prove for synchronous iteration that there exist classes whose tran- sient length satisfies t > 2”/3 and for sequential iteration we obtain a transient length of order T > 2”/6.” 92c:68161 68T10 68Q25  ...  More precisely, we prove that there exists a class of symmetric networks with exponential transient, i.e., pos- sessing initial conditions whose transient length is > 2°", n being the number of cells of  ... 

Dynamics of positive automata networks

E. Goles Ch
1985 Theoretical Computer Science  
With an important class of automata networks we associate a Lyapunov function and by doing so we characterize its dynamic behaviour (transient and cycle lengths).  ...  As particular cases we study threshold and majority networks. * Partial support from FNC/1123 is gratefully acknowledged. 0304-3975/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)  ...  length of the iterative sequence {x(t); t 1> 0}: P (F) = max{p(x): x ~ Q"}, T(F) = max{t(x): x ~ Q"} the maximum period and transient length of the parallel iterative sequences associated with F. 24  ... 
doi:10.1016/0304-3975(85)90057-x fatcat:jyu6fglfobeojhjk3nk72iekcy

Joint Segmentation and Classification of Time Series Using Class-Specific Features

Z.J. Wang, P. Willett
2004 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
The computational burden is remarkably small, approximately linear with the length of the time series, and the method is nicely accurate in terms both of discovered number of segments and of segmentation  ...  In stage one, rough segmentations are implemented sequentially using a piecewise generalized likelihood ratio (GLR); in the second stage, the results from the first stage (both forward and backward) are  ...  probability density function (PDF) that approximates it when the transient is truly present.  ... 
doi:10.1109/tsmcb.2003.819486 pmid:15376851 fatcat:jnbfx66gt5ck3egbwezazpgzlu

PSPACE-Completeness of Majority Automata Networks [article]

Eric Goles, Pedro Montealegre, Ville Salo, Ilkka Törmä
2015 arXiv   pre-print
In particular, we show that the complexity of the problem of predicting an eventual state change in some vertex, given an initial configuration, is PSPACE-complete.  ...  We study the dynamics of majority automata networks when the vertices are updated according to a block sequential updating scheme.  ...  the transient length of the automata network A under the updating scheme S as the the greatest of these values: τ S (A) = max{τ S (x) : x ∈ {0, 1} V }.  ... 
arXiv:1501.03992v1 fatcat:rqypr3itkncidaujjyvk6xqjuu

PSPACE-completeness of majority automata networks

Eric Goles, Pedro Montealegre, Ville Salo, Ilkka Törmä
2016 Theoretical Computer Science  
In particular, we show that the complexity of the problem of predicting an eventual state change in some vertex, given an initial configuration, is PSPACE-complete.  ...  We study the dynamics of majority automata networks when the vertices are updated according to a block sequential updating scheme.  ...  the transient length of the automata network A under the updating scheme S as the the greatest of these values: τ S (A) = max{τ S (x) : x ∈ {0, 1} V }.  ... 
doi:10.1016/j.tcs.2015.09.014 fatcat:ua2jumar4bgs3cavptktjyaoby

Characterizing Configuration Spaces of Simple Threshold Cellular Automata [chapter]

Predrag T. Tosic, Gul A. Agha
2004 Lecture Notes in Computer Science  
"almost all" configurations, in both parallel and sequential cases, are transient states.  ...  We show that the temporal cycles exist only in case of (some) parallel simple threshold CA, but can never take place in sequential threshold CA.  ...  First, we need to define threshold functions, simple threshold functions, and the corresponding types of (S)CA.  ... 
doi:10.1007/978-3-540-30479-1_89 fatcat:ekqzxyzhxvgivbukux7zvhylaq
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