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Combinatorial Resolution of Systems of Differential Equations. IV. Separation of Variables [chapter]

Pierre Leroux, Gérard X. Viennot
1988 Annals of Discrete Mathematics  
In the context of the combinatorial theory of ordinary differential equations recently introduced by the authors, a concrete interpretation is given to the classical method of separation of variables.  ...  This approach is then extended to more general equations and applied to systems of differential equations with forcing terms.  ...  this work was developed, the Natural Sciences and Engineering Research Council of Canada for financial assistance, and the organizers of the First Japan Conference on Graph Theory and Applications for  ... 
doi:10.1016/s0167-5060(08)70790-8 fatcat:xvabar4jwvgypemkohxnmoxova

Combinatorial resolution of systems of differential equations. IV. separation of variables

Pierre Leroux, Gérard X. Viennot
1988 Discrete Mathematics  
In the context of the combinatorial theory of ordinary differential equations recently introduced by the authors, a concrete interpretation is given to the classical method of separation of variables.  ...  This approach is then extended to more general equations and applied to systems of differential equations with forcing terms.  ...  this work was developed, the Natural Sciences and Engineering Research Council of Canada for financial assistance, and the organizers of the First Japan Conference on Graph Theory and Applications for  ... 
doi:10.1016/0012-365x(88)90213-0 fatcat:qjmkl53odfawpoegzktk67a5ma

Page 6398 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
(F-BORD) Combinatorial resolution of systems of differential equations. IV. Separation of variables. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986).  ...  {For the entire collection see MR 91m:05005.} 91m:05010 OSAI5 13F25 26A06 34A25 Bergeron, Francois (3-PQ); Reutenauer, Christophe (3-PQ) Combinatorial resolution of systems of differential equations.  ... 

Page 5 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
Mamedov, On the lattice of interpretability types of varieties (187-189); I. Mirchev, Separable and dominating sets of variables for functions (191-198); J.  ...  [Xiang Zhang*], Boundary value problems for vec- tor integral differential equations of singularly perturbed Volterra type (297-308); Ai Long Zheng and Fu Jun Wang, Stability and periodic bifurcation due  ... 

Author index

1988 Discrete Mathematics  
Viennot, Combinatorial resolution of systems of differential equations. IV. Separation of variables Lim, C.-K., see C.-L. Deng Loupekine, F. and J.J.  ...  Jr., Chromatic polynomials of generalized trees (72) 385-390 (72) 251-256 (72) 391-393 (72) 299-310 (72) 395-404 hexagonal systems (72) 405-415 (72) 225-236 (72) 35-47 (72) 163-166 (72  ... 
doi:10.1016/0012-365x(88)90234-8 fatcat:eslxmu3e3ne2tboojeam7psxti

Diagnosis of Breast Cancer using a Combination of Genetic Algorithm and Artificial Neural Network in Medical Infrared Thermal Imaging

Hossein Ghayoumi zadeh, Javad Haddadnia, Maryam Hashemian, Kazem Hassanpour
2013 Iranian Journal of Medical Physics  
Then these 8 parameters are used as input of our proposed combinatorial model which is formed using artificial neural network and genetic algorithm.  ...  The results indicate that the proposed combinatorial model produces optimum and efficacious parameters in comparison to other parameters and can improve the capability and power of globalizing the artificial  ...  The manager and staff of vasei hospital of sabzevar are also greatly appreciated for their efficient support regarding this study.  ... 
doi:10.22038/ijmp.2013.470 doaj:622c25df1d524e7c8cd7fc56ad3ec531 fatcat:gdtromqokvgoldu62aei7x5xh4

Relaxation and metastability in a local search procedure for the random satisfiability problem

Guilhem Semerjian, Rémi Monasson
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
For alpha > alpha_d, the system is trapped in some metastable state, and resolution occurs from escape from this state through crossing of a large barrier.  ...  Depending on the ratio alpha of constraints per variable, resolution takes a time T_res growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially (T_res \sim exp(N zeta(alpha)), alpha  ...  A3͒ The set of Kϩ1 linear coupled differential ͑A1͒ reduces to a partial differential equation on ⌽(x,t): ‫ץ‬⌽ ‫ץ‬t ͑ x,t ͒ϭϪ1ϩxϩ␣K͑ xϪ1 ͒⌽͑ x,t ͒ϩ␣͑ 1Ϫx 2 ͒ ‫ץ‬⌽ ‫ץ‬x ͑ x,t ͒. ͑  ... 
doi:10.1103/physreve.67.066103 pmid:16241300 fatcat:s2nmosr6hfaifaubb4q74ei7hu

Dynamic Optimization Strategies for Three-Dimensional Conflict Resolution of Multiple Aircraft

Arvind U. Raghunathan, Vipin Gopal, Dharmashankar Subramanian, Lorenz T. Biegler, Tariq Samad
2004 Journal of Guidance Control and Dynamics  
differential, algebraic, and control variables of the individual aircraft in that order, g., are the algebraic equalities, and gine are separation constraints between different pairs of aircraft.  ...  ., A“, AY), we obtain a candidate step by solving the following system of equations: H(w) Vic(w) —! | Vi c(w)?  ... 
doi:10.2514/1.11168 fatcat:3ljzyw4aerahbk5tuh4dgdpse4

String Topology: Background and Present State [article]

Dennis Sullivan
2007 arXiv   pre-print
The sum over all surface types of the top pseudomanifold chain yields a chain X satisfying the master equation dX + X*X = 0 where * is the sum over all gluings.  ...  The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each  ...  Actually, we think of such a master equation as a presentation of a free differential algebra generated by the X α with the differential on the generators defined by the master equation.  ... 
arXiv:0710.4141v1 fatcat:6d7u4xsmyvgjbmp63ztvgaoadm

Page 729 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Yurik], Separation of variables and construction of exact solutions of nonlinear wave equations (73-82); Leonid F. Barannyk [L. F.  ...  Wiltshire, Symmetries of systems of nonlinear reaction-diffusion equations (47-59); M. B. Abd-el-Malek, I. A. El-Awadi and S. M. A.  ... 

Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems [article]

Stephen Melczer, Bruno Salvy
2020 arXiv   pre-print
To our knowledge, this is the first completely automatic treatment and complexity analysis for the asymptotic enumeration of rational functions in an arbitrary number of variables.  ...  Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several variables (ACSV) makes it possible to compute asymptotic expansions  ...  Acknowledgments The authors would like to thank Mohab Safey El Din and Éric Schost for several discussions during the preparation of this work, and the anonymous referees for their close readings and helpful  ... 
arXiv:1905.04187v2 fatcat:urrhplwdzng2tj4abeeufccvby

Low power and massively parallel simulation of oscillatory biochemical networks on FPGA

Serge Le Thanh, Nicolas Lobato-Dauzier, Farad Khoyratee, Romain Beaubois, Teruo Fujii, Anthony Genot, Timothee Levi
2019 2019 IEEE Biomedical Circuits and Systems Conference (BioCAS)  
In order to reverse engineer networks and map their design space, dynamics needs to be simulated for many different parameters and topologies, leading to a combinatorial explosion that requires heavy computational  ...  It is crucial to compute the dynamics of a biochemical network from its kinetics and topology.  ...  ACKNOWLEDGMENT We would like to thank the MITI of CNRS (project DNA2 in Biomimetisme 2019).  ... 
doi:10.1109/biocas.2019.8919020 dblp:conf/biocas/ThanhLKBFGL19 fatcat:mvu2woqcs5agrl7lqcilhea7fe

Combinatorial Koszul Homology: Computations and Applications [article]

Eduardo Saenz-de-Cabezon
2008 arXiv   pre-print
of monomial ideals and apply it to describe the structure of monomial ideals.  ...  Describe algorithms to perform efficient computations of the homological invariants of monomial ideals.  ...  To obtain the prolongation R 2 of our equation, we have to formally differentiate the two equations of the system 4. 3 with respect to all the variables and add the result to R 1 .  ... 
arXiv:0803.0421v1 fatcat:nld7rtvthbbhrpyjcsj5tdhvci

The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

L. Grady, C.V. Alvino
2009 IEEE Transactions on Image Processing  
In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion  ...  In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, lowenergy solution  ...  equation by solving the system L R * f R * = −B T f R * . (16) In summary, the optimum for f R * and f R * may be produced by solving sparse, positive definite systems of linear equations for which many  ... 
doi:10.1109/tip.2009.2028258 pmid:19635698 fatcat:inyuw77aj5arbntnya2rtoimfe

Smooth curve extraction by mean field annealing

Laurent H�rault, Radu Horaud
1995 Annals of Mathematics and Artificial Intelligence  
Moreover, this cost function fits the constraints of a interacting spin system which in turn is a well suited physical model to solve hard combinatorial optimization problems.  ...  In this paper we attack the figure-ground discrimination problem from a combinatorial optimization perspective.  ...  Instead, the solution for the vector µ = [µ 1 , · · · , µ N ] may well be the stationary solution of the following system of N differential equations: τ dµ i dt = tanh N j=1 J ij µ j + δ i T − µ i (15)  ... 
doi:10.1007/bf01530832 fatcat:emf6htp6aff5pmcknopbmf6oiy
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