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On a glass of abstract polytopes constructed from binary codes

Egon Schulte
1990 Discrete Mathematics  
At the same time it allows interactions with the theory of buildings and diagram geometries (cf. [15, 11). The purpose of this note is to construct abstract polytopes from binary codes.  ...  By taking quotients P/C of 9 by suitable binary linear codes C interesting new abstract polytopes arise.  ...  Acknowledgement Finally I would like to thank A. Cohen and E. Shult for helpful discussion during the Finite Geometries Conference in Deinze (Belgium) in 1986.  ... 
doi:10.1016/0012-365x(90)90134-4 fatcat:433s5gsj6rcjzmagcw7xccksuq

Synthesis for multi-robot controllers with interleaved motion

Vasumathi Raman, Hadas Kress-Gazit
2014 2014 IEEE International Conference on Robotics and Automation (ICRA)  
The authors in [5] describe the automatic synthesis of control and communication strategies for a robotic team, from reactive task specifications of servicing requests in an environment.  ...  In contrast with the decentralized controllers presented in that work, this paper focuses on centralized controllers for a larger class of multi-robot tasks.  ...  The atomic controllers used to drive the team of robots from one configuration to another can be constructed using a method such as the one presented in [11] .  ... 
doi:10.1109/icra.2014.6907487 dblp:conf/icra/RamanK14 fatcat:5qkrjx7q2bgz3ip2eitajbjvoq

Recycling controllers

Hadas Kress-Gazit, Nora Ayanian, George J. Pappas, Vijay Kumar
2008 2008 IEEE International Conference on Automation Science and Engineering  
The problem of designing control schemes for teams of robots to satisfy complex high-level tasks is a challenging problem which becomes more difficult when adding constraints on relative locations of robots  ...  As a demonstration of this general approach we examine a task in which a group of robots sort different items to be recycled.  ...  Recall, from Problem 2.1, that we need to construct a motion control law u as well as an action activation policy π.  ... 
doi:10.1109/coase.2008.4626521 dblp:conf/case/Kress-GazitAPK08 fatcat:aibgrhua7fcrbitokeewxjhg6e

Temporal Logic Analysis of Gene Networks Under Parameter Uncertainty

GrÉgory Batt, Calin Belta, Ron Weiss
2008 IEEE Transactions on Automatic Control  
This approach has been implemented in a tool for robust verification of gene networks and applied to the tuning of a synthetic network built in E. coli.  ...  We consider models based on piecewise-multiaffine differential equations, dynamical properties expressed in temporal logic, and intervals for the values of uncertain parameters.  ...  Yordanov for contributions to the development of earlier versions of the mathematical model of the transcriptional cascade.  ... 
doi:10.1109/tac.2007.911330 fatcat:adlpf4b4tba7dgxamdfi5nwbwy

Robust Exponential Memory in Hopfield Networks

Christopher J. Hillar, Ngoc M. Tran
2018 Journal of Mathematical Neuroscience  
Abstract The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically coupled McCulloch-Pitts binary neurons interact to perform emergent  ...  storing collections of patterns X using a "one-shot" outer-product rule (OPR) for learning, which essentially assigns abstract synaptic weights between neurons to be their correlation, an early idea in  ...  Acknowledgements We thank Kilian Koepsell and Sarah Marzen for helpful comments that enhanced the quality of this work.  ... 
doi:10.1186/s13408-017-0056-2 pmid:29340803 pmcid:PMC5770423 fatcat:nbbhmyyb5nh3rc4dxbzyal272q

Robust exponential memory in Hopfield networks [article]

Christopher Hillar, Ngoc M. Tran
2015 arXiv   pre-print
In addition to providing a new set of error-correcting codes that achieve Shannon's channel capacity bound, these networks also efficiently solve a variant of the hidden clique problem in computer science  ...  , opening new avenues for real-world applications of computational models originating from biology.  ...  We thank Kilian Koepsell and Sarah Marzen for helpful comments that enhanced the quality of this work.  ... 
arXiv:1411.4625v2 fatcat:d73zerkhlbg7zfgk2ziftthdki

Geometric properties of a class of piecewise affine biological network models

Etienne Farcot
2005 Journal of Mathematical Biology  
Allowed transitions between these cells define a language on a finite alphabet.  ...  We first provide an analysis of a continuous-space, discrete-time dynamical system equivalent to the initial one, by the way of a transition map. This is similar to former studies.  ...  The author would like to thank one of the anonymous referees for his helpful and very detailed comments.  ... 
doi:10.1007/s00285-005-0360-4 pmid:16382313 fatcat:sxwnv5opmfbnxl3rkr3nejj5fi

Interior Point Methods for Combinatorial Optimization [chapter]

John E. Mitchell
1996 Applied Optimization  
ACKNOWLEDGEMENT The first author acknowledges support in part by ONR grant N00014-94-1-0391, and by a grant from the Dutch NWO and by Delft University of Technology for 1997-98, while visiting TWI/SSOR  ...  at Delft University of Technology.  ...  Inductive inference involves the following steps: (i) Inferring rules from examples, finding compact abstract models of data or hidden patterns in the data; (ii) Making predictions based on abstractions  ... 
doi:10.1007/978-1-4613-3449-1_11 fatcat:5utlmdqf4fbxpbrlvxdmblrgde

Interior Point Methods for Combinatorial Optimization [chapter]

John E. Mitchell, Panos M. Pardalos, Mauricio G. C. Resende
1998 Handbook of Combinatorial Optimization  
ACKNOWLEDGEMENT The first author acknowledges support in part by ONR grant N00014-94-1-0391, and by a grant from the Dutch NWO and by Delft University of Technology for 1997-98, while visiting TWI/SSOR  ...  at Delft University of Technology.  ...  Inductive inference involves the following steps: (i) Inferring rules from examples, finding compact abstract models of data or hidden patterns in the data; (ii) Making predictions based on abstractions  ... 
doi:10.1007/978-1-4613-0303-9_4 fatcat:jqlwni3hrbggze4w74hww2gsre

Minimum and Maximum Entropy Distributions for Binary Systems with Known Means and Pairwise Correlations

Badr Albanna, Christopher Hillar, Jascha Sohl-Dickstein, Michael DeWeese
2017 Entropy  
We provide upper and lower bounds on the entropy for the minimum entropy distribution over arbitrarily large collections of binary units with any fixed set of mean values and pairwise correlations.  ...  We also construct specific low-entropy distributions for several relevant cases.  ...  D. is grateful for support from the Hellman  ... 
doi:10.3390/e19080427 pmid:33535369 fatcat:hqgfl4rrejbfvj5hratztwwdra

PhD thesis: Homological Quantum Codes Beyond the Toric Code [article]

Nikolas P. Breuckmann
2018 arXiv   pre-print
We also introduce a novel decoder based on techniques from machine learning and image recognition to decode four-dimensional codes.  ...  We show how such surfaces can be constructed and enumerate all quantum codes derived from them which have less than 10.000 physical qubits.  ...  A binary linear classical (n, k)-code W is a subspace of dimension k of Z n 2 , were Z 2 denotes the field with two elements.  ... 
arXiv:1802.01520v1 fatcat:rrbxw235undqzn22p43baytnte

Cumulative index volumes 1–92

2000 Discrete Applied Mathematics  
Karlinger, A note on subtrees rooted along the primary path of a binary , L.  ...  Larcher 18 (1987) 309-3 13 Tietlvlinen, A., On the covering radius of long binary BCH codes (Note) 16 (1987) 75-77 Timkovsky, V.G., A polynomial-time algorithm for the two-machine unit-time release-date  ... 
doi:10.1016/s0166-218x(00)00210-9 fatcat:vvomn3k7hbbmliptwaczxk6wi4

Linear and quadratic reformulations of nonlinear optimization problems in binary variables

Elisabeth Rodríguez-Heck
2018 4OR  
The problem of optimizing a multilinear polynomial on binary variables without additional constraints arises in a variety of applications.  ...  We are interested in resolution methods based on reformulations of this nonlinear problem into a linear or a quadratic one, an approach that attempts to draw benefit from the existing literature on integer  ...  Abstract The problem of optimizing a multilinear polynomial on binary variables without additional constraints arises in a variety of applications.  ... 
doi:10.1007/s10288-018-0392-4 fatcat:wzpwrxoefrdplhkhsukddqcm7i

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
A v ariation of bundle methods is presented by means of which such a t ype of problems can be solved.In this variation a dynamic polyhedral model of dom is generated by means of normal vectors.In addition  ...  to the well known serious steps und null steps of bundle methods a third type of steps is used to generate the model of dom .  ...  Thus, model construction is a very complex task. Second, the complexity of this task is managed by the well known method of abstraction.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Symbolic numeric analysis of attractors in randomly generated piecewise affine models of gene networks

Etienne Farcot
2006 Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06  
Contrary to previous studies, the latter have several thresholds in each direction, a fact whose consequences on the number and nature of attractors is discussed.  ...  ABSTRACT The goal of this paper is to present and experiment the computer aided analysis of phase portraits of some ordinary differential equations.  ...  The author would like to thank two anonymous referees for their helpful and precise comments on this work.  ... 
doi:10.1145/1145768.1145787 dblp:conf/issac/Farcot06 fatcat:abhcodilhrcvncvvaygkhkgjc4
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