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International audience; There is considerable interest in the rational design of controllable, bioinspired supramolecular systems as a potential means to create new biocompatible and functional materials able to mimic and build upon the characteristics of natural biopolymers. Here, we report the alcohol-controlled aqueous self-assembly of an amphiphilic helical oligourea foldamer (artificial folded oligomer) into a diverse array of tubular fibril architectures. Electron microscopy studies provide details of the morphological evolution of the foldamer nanostructures from protofibrils to fibers, with high resolution X-ray crystal structures providing an atomic-scale view of these assemblies, and solution studies indicating the assembly and morphology to be affected by alcohol polarity and concentration. Overall, the results we report here highlight oligourea foldamers as suitable building blocks for the formation of a diverse range of tubular morphologies in a controllable manner.

Consider the following FUN problem. Given m,s you want to divide m muffins among s students so that everyone gets m/(s) muffins; however, you want to maximize the minimum piece so that nobody gets crumbs. Let f(m,s) be the size of the smallest piece in an optimal procedure. We study the case where ceil(2m/s)=3 because (1) many of our hardest open problems were of this form until we found this method, (2) we have used the technique to generate muffin-theorems, and (3) we conjecture this can be used to solve the general case. We give (1) an algorithm to find an upper bound for f(m,s) when ceil(2m/s)(and some ways to speed up that algorithm if certain conjectures are true), (2) an algorithm that uses the information from (1) to try to find a lower bound on f(m,s) (a procedure) which matches the upper bound, (3) an algorithm that uses the information from (1) to generate muffin-theorems, and (4) an algorithm that we think works well in practice to find f(m,s) for any m,s.

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation., {"references":["D. S. Broomhead and D. Lowe, \"Multi-variable functional interpolation\nand adaptive networks,\" Complex Systems, vol. 2, pp. 321-355, 1988.","C. A. Miehelli, \"Interpolation of scattered data: distance matrices and conditionally\npositive definite functionsConstructive Approximation,\" 1986.","M. J. D. Powell, \"Radial basis functions for multivariate interpolation,\"\na review, In J.C. Mason and M.G. Cox, editors, Algorithms for Approximation,\nClarendon Press, Oxford, 1987.","V.D. Sanchez, A. (Ed.), \"Special Issue on RBF Networks, Part I,\"\nNeurocomputing 19, 1998.","V.D. Sanchez, A. (Ed.), \"Special Issue on RBF Networks, Part II,\"\nNeurocomputing 20, 1998.","Chen S, Cowan CFN, Grant PM, \"Orthogonal Least Square Learning\nAlgorithm for Radial Basis Function Networks,\" IEEE Transactions on\nNeural Networks, 1991.","D simon, \"Training radial basis neural networks with the extended\nKalman filter,\" Neurocomputing 48, 2002.","M.T. Musavi, W. Ahmed, K.H. Chan, K.B. Faris, D.M. Hummels, \"On\nthe Training of Radial Basis Function Classifiers\", Neural Networks 5,\n1992.","Bernhard Scholkopf, Kah-Kay Sung, Christopher JC Burges, Federico\nGirosi, Partha Niyogi, Tomaso Poggio, Vladimir Vapnik, \"Comparing\nsupport vector machines with Gaussian kernels to radial basis function\nclassifiers,\" Signal Processing, IEEE Transactions on, 1997.\n[10] D. Broomhead, D. Lowe \"Multivariable functional interpolation and\nadaptive networks,\" Complex Systems 2, 321-355, 1988.\n[11] S. Shah, F. Palmieri, M. Datum, \"Optimal filtering algorithms for fast\nlearning in feedforward neural networks,\" Neural Networks 5, 779-787,\n1992.\n[12] J. Sum, C. Leung, G. Young, W. Kan, \"On the Kalman filtering method\nin neural network training and pruning,\" IEEE Trans. Neural Networks\n10, 161-166, 1999.\n[13] Y. Zhang, X. Li, \"A fast U-D factorization-based learning algorithm\nwith applications to nonlinear system modeling and identification,\" IEEE\nTrans. Neural Networks 10, 930-938, 1999.\n[14] D. Obradovic, \"On-line training of recurrent neural networks with\ncontinuous topology adaptation,\" IEEE Trans. Neural Networks 7 , 222-\n228, 1996.\n[15] G. Puskorius, L. Feldkamp, \"Neurocontrol of nonlinear dynamical\nsystems with Kalman filter trained recurrent networks,\" IEEE Trans.\nNeural Networks 5 (1994) 279-297.\n[16] W. H. Kwon and S. Han, \"Receding Horizon Control,\" London, U.K.,\nSpringer-Verlag, 2005.\n[17] Choon Ki Ahn, Soo Hee Han, and Wook Hyun Kwon, \"H FIR Filters\nfor Linear Continuous-time State-space Systems,\" IEEE Signal Processing\nLetters, Vol. 13, No. 9, September, 2006.\n[18] Choon Ki Ahn, \"A New Solution to Induced l Finite Impulse Response\nFiltering Problem Based on Two Matrix Inequalities\" International Journal\nof Control, Taylor & Francis, Volume 87, Issue 2, 2014, pages 404-\n409.\n[19] Choon Ki Ahn, \"Strictly Passive FIR Filtering for State-space Models\nwith External Disturbance,\" International Journal of Electronics and\nCommunications, Elsevier, Volume 66, Issue 11, November 2012, Pages\n944-948.\n[20] Choon Ki Ahn, Soo Hee Han, andWook Hyun Kwon, \"H Finite Memory\nControls for Linear Discrete-time State-space Models,\" IEEE Transactions\non Circuits & Systems II, Vol. 54, No. 2, February, 2007.\n[21] Hyun Duck Choi, Choon Ki Ahn, Myo Taeg Lim, \"Time-domain\nFiltering for Estimation of Linear Systems with Colored Noises using\nRecent Finite Measurements,\" Measurement, Elsevier, Volume 46, Issue\n8, October 2013, Pages 2792-2797.\n[22] Choon Ki Ahn, \"Robustness Bound for Receding Horizon Finite Memory\nControl: Lyapunov-Krasovskii Approach,\" International Journal of\nControl, Taylor & Francis, Volume 85, Issue 7, 2012, pages 942-949."]}