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Almost Global Consensus on the $n$ -Sphere

Johan Markdahl, Johan Thunberg, Jorge Goncalves
2018 IEEE Transactions on Automatic Control  
The feedback laws are intrinsic gradients of a Lyapunov function and include the canonical gradient descent protocol as a special case.  ...  This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the case of the n-sphere for nN\{1} differs from those of the circle and SO (3) where the corresponding  ...  To that end, consider the following multi-agent system on the special orthogonal group SO(n). System 23.  ... 
doi:10.1109/tac.2017.2752799 fatcat:qhe4butcq5cgjcy3n7y4pvifty

Exact solutions to a class of feedback systems on SO(n)

Johan Markdahl, Xiaoming Hu
2016 Automatica  
This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on SO(n).  ...  The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix.  ...  Instead of solving a system with n 2 variables and 1 2 n(n − 1) degrees of freedom on the Lie group SO(n), a system that evolves on the Lie algebra so(n) is solved.  ... 
doi:10.1016/j.automatica.2015.10.023 fatcat:7f7hbzjxabat7f6foiurptdmai

Properties of the new N$$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity

Nikolay Bobev, Thomas Fischbacher, Krzysztof Pilch
2020 Journal of High Energy Physics  
Guided by the numerical data for that point, we obtain a consistent SO(3) × Z 2 -invariant truncation of the N = 8 theory to an N = 1 supergravity with three chiral multiplets.  ...  The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of  ...  Note that the generators h j are orthogonal to so(8) in su (8) .  ... 
doi:10.1007/jhep01(2020)099 fatcat:qste743jljdnvhi4u5hpzvsgfm

Discrete Control Systems [article]

Taeyoung Lee, Melvin Leok, N. Harris McClamroch
2007 arXiv   pre-print
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems.  ...  They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics.  ...  While it is common to parameterize the one-sphere by an angle, we develop parameterfree equations of motion in the special orthogonal group SO(2), which is a group of 2 × 2 orthogonal matrices with determinant  ... 
arXiv:0705.3868v1 fatcat:2tsfkbm4dbbapgemvoedzn3fdq

PoMiN: A Post-Minkowskian N-body Solver

Justin Feng, Mark Baumann, Bryton Hall, Joel Doss, Lucas Spencer, Richard Matzner
2018 Astrophysical Journal  
In this paper, we introduce PoMiN, a lightweight N-body code based on the post-Minkowskian N-body Hamiltonian of Ledvinka et. al., which includes general relativistic effects up to first order in Newton's  ...  We describe the methods we used to simplify and organize the Hamiltonian, and the tests we performed (convergence, conservation, and analytical comparison tests) to validate the code.  ...  ACKNOWLEDGMENTS This work was partially supported by the National Science Foundation under Grant No. PHY-1620610. We thank Mark Selover for his advice and feedback.  ... 
doi:10.3847/1538-4357/aac209 fatcat:usoocs7y25e5rfp6xw26hn6gnu

Vector Fields for Robot Navigation Along Time-Varying Curves in $n$-Dimensions

Vinícius M. Goncalves, Luciano C. A. Pimenta, Carlos A. Maia, Bruno C. O. Dutra, Guilherme A. S. Pereira
2010 IEEE Transactions on robotics  
Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to time-varying curves defined in n-dimensional spaces.  ...  We also present a methodology for construction of the target curve based on a given set of its samples.  ...  The two problems are essentially very similar, and so are the solutions found in the literature.  ... 
doi:10.1109/tro.2010.2053077 fatcat:ifhcxjffmrgcrhtfkcrs3lel4u

A new N=1 AdS4 Vacuum of Maximal Supergravity [article]

Nikolay Bobev, Thomas Fischbacher, Krzysztof Pilch
2019 arXiv   pre-print
Guided by the numerical data for that point, we obtain a consistent SO(3)xZ2-invariant truncation of the N=8 theory to an N=1 supergravity with three chiral multiplets.  ...  The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N=8, SO(8) gauged supergravity using Machine Learning software has led to a discovery of a new N=  ...  T.F. would like to thank Jyrki Alakuijala and Rahul Sukthankar for feedback and encouragement on this work, Moritz Firsching and Sameer Agarwal for useful discussions on homotopy continuation methods,  ... 
arXiv:1909.10969v2 fatcat:xeyalwjlobcylj5csjsnbuzeay

Synchronization with partial state coupling on SO(n) [article]

Alain Sarlette, Christian Lageman
2010 arXiv   pre-print
This paper studies autonomous synchronization of k agents whose states evolve on SO(n), but which are only coupled through the action of their states on one "reference vector" in Rn for each link.  ...  Thus each link conveys only partial state information at each time, and to reach synchronization agents must combine this information over time or throughout the network.  ...  From the previous paragraph, if rank L g = n(k − 1) then I n ⊗ L g is positive definite on the subspace of R kn 2 orthogonal to vec(C r s ), thus in particular on the subspace of vec(so(n) k ) orthogonal  ... 
arXiv:1011.6171v1 fatcat:n3j46yx2kfexder4djvp425baa

Variable coordination modes and catalytic dehydrogenation of B-phenyl amine–boranes

Amit Kumar, Isobel K. Priest, Thomas N. Hooper, Andrew S. Weller
2016 Dalton Transactions  
The binding mode of B-aryl substituted amine–boranes at {Rh(bisphoshine)}+ fragments can manipulated by variation of the P–Rh–P bite-angle.  ...  The theory of this paper relies critically on an assumption: So much redundancy is contained in the neural circuits for sensorimotor control that orthogonal solutions always exist, and these solutions  ...  →p = T →p k : [S1] Given that there are N weights, the system has a redundancy of Nk, meaning that the solution manifold is an (Nk)-dimensional manifold embedded in an N-dimensional space.  ... 
doi:10.1039/c6dt00197a pmid:26936754 fatcat:bo5dzkrdirhjldlnl63vp2qfum

N-body simulations of gravitational dynamics

W. Dehnen, J. I. Read
2011 The European Physical Journal Plus  
We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and  ...  We briefly touch upon the history of N-body simulations and their most important results.  ...  In the limit n → ∞, we converge on the implicit Hermite solution (17) .  ... 
doi:10.1140/epjp/i2011-11055-3 fatcat:scevhtqoq5cbzb4aokzvg2hliu

Bringing "New Science? into Careers Research

Polly Parker, Michael B Arthur
2002 M@n@gement  
THERE ARE LOOPS IN THE INTERCONNECTIONS Feedback loops are essential to the survival of complex social systems. Both positive and negative forms of feedback are necessary.  ...  get feedback on my skills and knowledge .715 spending time with people from whom I can learn .646 identifying and reaching people from whom I can learn .644 using relationships to gain feedback on my  ... 
doi:10.3917/mana.051.0105 fatcat:p65pbugyb5bp3givuy5fgm33nu

Mismatch-induced bit error rate in optical chaos communications using semiconductor lasers with electrooptical feedback

Y.C. Kouomou, P. Colet, L. Larger, N. Gastaud
2005 IEEE Journal of Quantum Electronics  
We analyze the influence of parameter mismatch between emitter and receiver systems on the bit error rate of an optical chaos communication scheme.  ...  Intensity hyperchaos is generated in the system by semiconductor lasers with electrooptical feedback.  ...  We have divided the mismatched parameters into two groups: the so-called "tuneable mismatches" corresponding to and on one hand, and the "filter mismatches" corresponding to the response times and on the  ... 
doi:10.1109/jqe.2004.839686 fatcat:giyhsxvp45ehpldzko3efmnyky

Extremum Seeking and Obstacle Avoidance on the Special Orthogonal Group

Jan Maximilian Montenbruck, Hans-Bernd Dürr, Christian Ebenbauer, Frank Allgöwer
2014 IFAC Proceedings Volumes  
In particular, we develop an extremum seeking control law for systems living on the special orthogonal group.  ...  We are motivated by the idea of finding feedback laws for rotations that only require transmission of scalar signals.  ...  Notation Rotation matrices are members of the special orthogonal group SO(3). We smoothly embed SO(3) into the R 3×3 matrices, i.e.  ... 
doi:10.3182/20140824-6-za-1003.01446 fatcat:zwp7wfiblnerbe56cus5ndt2mi

Interpolation-Based Multi-Mode Precoding for MIMO-OFDM Systems with Limited Feedback

N. Khaled, B. Mondal, R.W. Heath, F. Petre
2007 IEEE Transactions on Wireless Communications  
precoder frequency down-sampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction  ...  ) systems.  ...  The analytical impact analysis of the limited-feedback constraint on the system BER/MMSE performance is the topic of our current investigations.  ... 
doi:10.1109/twc.2007.05334 fatcat:bkd7tk5pzvar7jp7y6x7dsr2b4

Vol. 2 n. 3 | 2017 | SPECIAL ISSUE | FULL ISSUE

Luisa Bravo
2017 The Journal of Public Space  
I want also to acknowledge the invaluable contribution of Jiao Hong, Melanie Milicic, Angelo Bueno and Tanyalak Chalermtip for assistance with the analytical and documental work.  ...  I would also like to show my gratitude to the anonymous reviewers for their precious insights.  ...  an intrinsically orthogonal construction system.  ... 
doi:10.5204/jps.v2i3.128 fatcat:wjkhilcu6vgvzayoauzszwuy3u
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