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Hardness Results for Structured Linear Systems [article]

Rasmus Kyng, Peng Zhang
2017 arXiv   pre-print
This result can be viewed either positively or negatively: either we will develop nearly-linear time algorithms for solving all systems of linear equations over the reals, or progress on the families we  ...  We show that if the nearly-linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly  ...  Acknowledgements We thank Richard Peng and Daniel Spielman for helpful comments and discussions and we thank Richard Peng for suggesting the example in Section 10.1 which demonstrates that the projection  ... 
arXiv:1705.02944v2 fatcat:stpvkn7jbrgk3p4utcfrtq34nu

On the complexity of the robust stability problem for linear parameter varying systems

Onur Toker
1997 Automatica  
We also comment on the use of these results for developing a non-polynomial-time algorithm for testing robust stability of linear parameter varying systems. 0 1997 Elsevier Science Ltd.  ...  Key Words-Linear parameter varying systems; robust stability; computational complexity.  ...  Acknowledgements-This work is supported by The Ohio State University, and The Dutch Institute of Systems and Control.  ... 
doi:10.1016/s0005-1098(97)00129-5 fatcat:xjmzintftzcebk2wrmbtbvbavi

Computational complexity analysis of set membership identification of a class of nonlinear systems

Mario Sznaier
2008 2008 47th IEEE Conference on Decision and Control  
This paper analyzes the computational complexity of set membership identification of a class of nonlinear systems consisting of the interconnection of a Linear Time Invariant plant and a static nonlinearity  ...  Its main result shows that, even in cases where a portion of the plant is known, the problem is generically NP-hard both in the number of experimental data points and in the number of inputs or outputs  ...  results above can be used to establish the following results concerning the computational complexity of two identification problems: Lemma 3: [20] Consider the Wiener system structure shown in Figure  ... 
doi:10.1109/cdc.2008.4738602 dblp:conf/cdc/Sznaier08 fatcat:c47x72dcurcddajro7fi4nd6ty

Effect of bond length fluctuations on crystal nucleation of hard bead chains [article]

Ran Ni, Marjolein Dijkstra
2012 arXiv   pre-print
We study the spontaneous nucleation and crystallization of linear and cyclic chains of flexibly connected hard spheres using extensive molecular dynamics simulations.  ...  More surprisingly, the resulting crystal nuclei possess a range of crystal morphologies including structures with a five-fold symmetry.  ...  We also find that the resulting crystal morphologies of bead chains with bond fluctuations resemble closely those for hard spheres including structures with five-fold symmetry.  ... 
arXiv:1204.5398v2 fatcat:v2r5sasotbdn7e472iryoi2jfa

On the Complexity of the Robust Stability Problem for Linear Parameter Varying Systems

Onur Toker
1996 IFAC Proceedings Volumes  
Citation for published version (APA): Toker, O. (1997). On the complexity of the robust stability problem for linear parameter varying systems.  ...  Acknowledgements-This work is supported by The Ohio State University, and The Dutch Institute of Systems and Control.  ...  robust stability und robust asymptotic stability problems for LPV systems In this section, A/B-hardness of stability and asymptotic stability problems for linear parameter varying systems, are proved.  ... 
doi:10.1016/s1474-6670(17)58211-7 fatcat:adigvkk6w5d5plboqq2ejjq3fq

Effect of bond length fluctuations on crystal nucleation of hard bead chains

Ran Ni, Marjolein Dijkstra
2013 Soft Matter  
Fig. 4 4 Typical configurations of the crystal structures for linear hard-sphere chains with chain length N ¼ 20 (a) and for ring-like polymers with N ¼ 3 (b) and N ¼ 5 (c).  ...  Fig. 5 shows p(cos q) for systems consisting of linear and cyclic bead chains with N ¼ 10.  ... 
doi:10.1039/c2sm26969d fatcat:utt3tfer7jcodhvklk2buv7424

Test of precision weak-link stage systems with large travel range and subnanometre-scale resolution

D. Shu, J. Maser
2010 Diamond Light Source Proceedings  
Based on an advanced structure design with the laminar overconstrained weak-link technique, we have designed and constructed a two-dimensional linear precision weak-link stage system for nanopositioning  ...  In this paper we present the preliminary test results of a linear precision weak-link stage system with subcentimetre travel range and subnanometre positioning resolution. † ., et al. 2006 Nanometer Linear  ...  Photon Source (APS) hard X-ray nanoprobe (Maser et al. 2006; ), we have developed a new twodimensional weak-link stage system for nanopositioning of a specimen holder for an MLL-based hard X-ray nanofocusing  ... 
doi:10.1017/s2044820110000729 fatcat:pgw6h45psrb3hfeyvz6k3gm2qi

The solid–liquid interfacial free energy of close-packed metals: Hard-spheres and the Turnbull coefficient

Brian B. Laird
2001 Journal of Chemical Physics  
We also show that the slope of this linear relationship can be determined with quantitative accuracy using a hard-sphere model, and that the correlation with the enthalpy of fusion reported by Turnbull  ...  follows as a consequence of the fact that the entropy of fusion for close-packed metals is relatively constant.  ...  Recently, we have determined via molecular-dynamics computer simulation, the structure 10 and solid-liquid interfacial free energy 11 for a system of hard-spheres.  ... 
doi:10.1063/1.1391481 fatcat:hicgmr7lq5bppmo57lqyxwt2vm

Collective Dynamics in Quasi-One-Dimensional Hard Disk System

Adrián Huerta, Taras Bryk, Victor M. Pergamenshchik, Andrij Trokhymchuk
2021 Frontiers in Physics  
Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of  ...  We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel.  ...  Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of  ... 
doi:10.3389/fphy.2021.636052 fatcat:ati4j5nb2zgwnl5x3f4bt3hfaq

Optimal Feedback Selection for Structurally Cyclic Systems with Dedicated Actuators and Sensors [article]

Shana Moothedath and Prasanna Chaporkar and Madhu N. Belur
2017 arXiv   pre-print
This paper solves the sparsest feedback selection problem for linear time invariant structured systems, a long-standing open problem in structured systems.  ...  We prove that finding a sparsest feedback selection is of linear complexity for the case of structurally cyclic systems with dedicated inputs and outputs.  ...  LINEAR COMPLEXITY ALGORITHM FOR SOLVING PROBLEM 1 The structured system (Ā,B,C) considered in the NP-hard proof given in [11] satisfies Assumption 1.  ... 
arXiv:1706.07928v2 fatcat:vzoytsblbbb4xlcbculx3ppjx4

Fluid–solid equilibria of flexible and linear rigid tangent chains from Wertheim's thermodynamic perturbation theory

Felipe J. Blas, Eduardo Sanz, Carlos Vega, Amparo Galindo
2003 Journal of Chemical Physics  
We have used the Einstein-crystal methodology, the Rahman-Parrinello technique, and the thermodynamic integration method for calculating the free energy and equation of state of linear rigid hard sphere  ...  The vapor-liquid equilibria are seen to disappear for linear rigid chains formed by more than 11 hard sphere segments that interact through an attractive van der Waals mean-field contribution; in other  ...  E.S. would like to thank the Ministerio de Educación y Cultura for the award of a PhD studentship ͑FPU͒.  ... 
doi:10.1063/1.1619936 fatcat:gp2llthtsvbg5jhhbowqgabeva

Improvement of Auto Checking Hardness Machine using Several Material Series of Aluminum Structural Frame: Case Study on Mitutoyo HR-522 Hardness Tester

Bernardus Plasenta Previo Caesar, Iwan Istanto, Pandu Sandi Pratama, Joung Hyung Cho, Aditya Rio Prabowo
2020 Procedia Structural Integrity  
For more effectively, it uses automatic operation in time and savings for other manual tools. The automated tool applies the 3-axes system mechanism using Festo linear actuator with the servo motor.  ...  For more effectively, it uses automatic operation in time and savings for other manual tools. The automated tool applies the 3-axes system mechanism using Festo linear actuator with the servo motor.  ...  All the linear drive motor system and linear guide system is detained by aluminum structural profile frame 45 inches.  ... 
doi:10.1016/j.prostr.2020.07.016 fatcat:n3tvrq3osvawvdgshhdbzppyy4

Page 4699 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
A negative result is provided which shows that the problem of checking if « = 0 is NP- hard. This result is much more negative than the known NP-hard result for the problem of checking if u < 1.  ...  ahead control, and model reference adaptive control for linear and non- linear systems.  ... 

Solid-liquid equilibrium for quadrupolar molecules

C. Vega, P.A. Monson
1995 Molecular Physics  
The reference system of quadrt/polar hard dumbbells is described using perturbation theory for the liquid and cell theory for the solid.  ...  Good agreement with simulation results of quadrupolar hard dumbbells is obtained through the theoretical description.  ...  On the basis of lattice energy calculations, English and Venables [38] also concluded that the e-N 2 structure is the stable one for linear quadrupolar systems when the quadrupole moment is sufficiently  ... 
doi:10.1080/00268979500101201 fatcat:ej5k7ckqvfa2jjkxbd3e4u2kri

Nonlinear systems identification with discontinuous nonlinearity

Mohamed Benyassi, Adil Brouri, Smail Slassi
2019 IAES International Journal of Robotics and Automation  
The entire nonlinear system is structured by Hammerstein model. Furthermore, the linear dynamic block is of any order and can be nonparametric.  ...  <span>In this paper, nonparametric nonlinear systems identification is proposed. The considered system nonlinearity is nonparametric and is of hard type.  ...  Presently, the nonlinear function f(.) is of hard type (Figure 2a -c) and the nonparametric linear block is of unknown structure.  ... 
doi:10.11591/ijra.v9i1.pp34-41 fatcat:jboezmq4r5a7hbhx3v2dkjkqyy
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