Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Nuttier Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright (C) 2010 John Wiley & Sons, Ltd.

An enantiospecific approach to pinguisanes from (R)-carvone. Total synthesis of (+)-pinguisenol

Enantiospecific total synthesis of (+)-pinguisenol 1, a sesquiterpene containing a cis-1,2,6,7-tetramethylbicyclo[4.3.0]nonane carbon framework incorporating two vicinal quaternary carbon atoms and four cis-oriented methyl groups on four contiguous carbon atoms, isolated from a liverwort, is described. The orthoester Claisen rearrangement of the allyl alcohol 9, obtained from (R)-carvone, generates the ester 12. Intramolecular cyclopropanation of the diazo ketone 13, derived from the ester 12, furnishes the tricyclic ketone 7. Degradation of the isopropenyl group followed by regioselective reductive cyclopropane ring cleavage transforms compound 7 into the hydroxy ketone 21. Wolff–Kishner reduction of the hydroxy ketone 21 followed by oxidation and Grignard reaction furnishes pinguisenol (+)- 1.

Structure of 6,5'-anhydro-6-hydroxy-2',3' O-isopropylideneuridine

CI2HI4N206, Mr=282"3, orthorhombic,P21212 t, a = 10.412 (2), b = 14.936 (2), c =16.651(3),/k, V=2589.46A 3, Z--8, Din= 1.450, D x = 1.447 Mg m -3, 2(Cu Kct) = 1.5418/~, # =0.902mm -~, F(000)-- 1184.00, T= 293 K, R = 0.039, wR--0.038 for 2548 unique reflections with F > 3a(F). The two crystallographically independent molecules in the asymmetric unit have similar geome-tries with the ribose ring having an O(4')-exo, C(4')-endo pucker and the uracil base in the anti conformation.The geometry about the exocyclic C(4')-C(5') bond in both molecules is gauche-gauche. The dioxolane ring assumes twist conformations in both molecules.

The Structural Characterization of Folded Peptides Containing the Conformationally Constrained beta-Amino Acid Residue beta(2,2)Ac(6)c

Backbone alkylation has been shown to result in a dramatic reduction in the conformational space that is sterically accessible to a-amino acid residues in peptides. By extension, the presence of geminal dialkyl substituents at backbone atoms also restricts available conformational space for beta and ? residues. Five peptides containing the achiral beta 2,2-disubstituted beta-amino acid residue, 1-(aminomethyl)cyclohexanecarboxylic acid (beta 2,2Ac6c), have been structurally characterized in crystals by X-ray diffraction. The tripeptide Boc-Aib-beta 2,2Ac6c-Aib-OMe (1) adopts a novel fold stabilized by two intramolecular H-bonds (C11 and C9) of opposite directionality. The tetrapeptide Boc-Aib-beta 2,2Ac6c]2-OMe (2) and pentapeptide Boc-Aib-beta 2,2Ac6c]2-Aib-OMe (3) form short stretches of a hybrid a beta C11 helix stabilized by two and three intramolecular H-bonds, respectively. The structure of the dipeptide Boc-Aib-beta 2,2Ac6c-OMe (5) does not reveal any intramolecular H-bond. The aggregation pattern in the crystal provides an example of an extended conformation of the beta 2,2Ac6c residue, forming a polar sheet like H-bond. The protected derivative Ac-beta 2,2Ac6c-NHMe (4) adopts a locally folded gauche conformation about the C beta?Ca bonds (?=-55.7 degrees). Of the seven examples of beta 2,2Ac6c residues reported here, six adopt gauche conformations, a feature which promotes local folding when incorporated into peptides. A comparison between the conformational properties of beta 2,2Ac6c and beta 3,3Ac6c residues, in peptides, is presented. Backbone torsional parameters of H-bonded a beta/beta a turns are derived from the structures presented in this study and earlier reports.

Two timescale convergent Q-learning for sleep-scheduling in wireless sensor networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks. We study the problem of scheduling the sleep times of the individual sensors, where the objective is to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous stateaction spaces, in a manner similar to Fuemmeler and Veeravalli (IEEE Trans Signal Process 56(5), 2091-2101, 2008). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation. Feature-based representations and function approximation is necessary to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation architecture for the Q-values) is updated in an on-policy temporal difference algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model and this is useful in settings where the latter is not known. Our simulation results on a synthetic 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work.