Optimal Parameter Trajectory Estimation in Parameterized SDEs: An Algorithmic Procedure

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

Stress and strain-driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

This work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field.We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

ALWIN-Algorithmic Wiswesser Notation System for Organic Compounds

ALWIN, a new chemical notation system for organic compounds, based on the Wiswesser Line Notation, is described. Procedures and rules are given for constructing ALWIN for acyclic structures and cyclic structures, vi.?., benzene and Its derivatives, monocyclic, bicyclic, polycyclic, perifused, splro, bridged ring, and ring of rlngs systems. A new method called "tessellation" is introduced for the topological descrlptlon of fused and spiro ring systems. Also new concepts are introduced for describing bridged ring and ring of rlngs systems.

Synthesis of DEF ring skeleton of naulafine alkaloid

6, 8-Dichloro-4, 5-dihydro-2-methyl-[2, 7]acenaphthyridin-1-one (5), obtained from the. reaction of 5-cyano-2, 6-dihydroxy-3, 4-cyclopentenopyridine with Vilsmeier reagent, has been transformed to the key synthon 4a in two steps.

Tandem 5-exo-trig allyl and 3-exo-trig radical cyclisation and rearrangement to copa and ylanga type sesquiterpene skeleton

A novel tandem 5-exo-trig allyl and 3-exo-trig radical cyclisation and rearrangement to copa and ylanga type sesquiterpene skeleton is reported.

Advantage of the ether linkage between the positive charge and the cholesteryl skeleton in cholesterol-based amphiphiles as vectors for gene delivery

Twelve novel cationic cholesterol derivatives with different linkage types between the cationic headgroup and the cholesteryl backbone have been developed. These have been tested for their efficacies as gene transfer agents as mixtures with dioleoyl phosphatidylethanolamine (DOPE). A pronounced improvement in transfection efficiency was observed when the cationic center was linked to the steroid backbone using an ether type bond. Among these, cholest-5-en-3b-oxyethane-N, N,N-trimethylammonium bromide (2a) and cholest-5-en-3b-oxyethane-N, N-dimethyl-N-2-hydroxyethylammonium bromide (3d) showed transfection efficiencies considerably greater than commercially available reagents such as Lipofectin or Lipofectamine. To achieve transfection, 3d did not require DOPE. Increasing hydration at the headgroup level for both ester- and ether-linked amphiphiles resulted in progressive loss of transfection efficiency. Transfection efficiency was also greatly reduced when a 'disorder'-inducing chain like an oleyl (cis-9-octadecenyl) segment was added to these cholesteryl amphiphiles. Importantly, the transfection ability of 2a with DOPE in the presence of serum was significantly greater than for a commercially available reagent, Lipofectamine. This suggests that these novel cholesterol-based amphiphiles might prove promising in applications involving liposome-mediated gene transfection. This investigation demonstrates the importance of structural features at the molecular level for the design of cholesterol-based gene delivery reagents that would aid the development of newer, more efficient formulations based on this class of molecules.

Formulas for algorithmic computation of impedance matrix using general circuit constants

A set of formulas is derived from general circuit constants which facilitates formation of the impedance matrix of a power system by the bus-impedance method. The errors associated with the lumpedparameter representation of a transmission line are thereby eliminated. The formulas are valid for short lines also, if the relevant general circuit constants are employed. The mutual impedance between the added line and the existing system is not considered, but the approach suggested can well be extended to it.

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Algorithmic aspects of k-tuple total domination in graphs

For a fixed positive integer k, a k-tuple total dominating set of a graph G = (V. E) is a subset T D-k of V such that every vertex in V is adjacent to at least k vertices of T Dk. In minimum k-tuple total dominating set problem (MIN k-TUPLE TOTAL DOM SET), it is required to find a k-tuple total dominating set of minimum cardinality and DECIDE MIN k-TUPLE TOTAL DOM SET is the decision version of MIN k-TUPLE TOTAL DOM SET problem. In this paper, we show that DECIDE MIN k-TUPLE TOTAL DOM SET is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that MIN k-TUPLE TOTAL DOM SET can be solved in polynomial time. We also propose some hardness results and approximation algorithms for MIN k-TUPLE TOTAL DOM SET problem. (c) 2012 Elsevier B.V. All rights reserved.

An Approach to a Bislactone Skeleton: A Scalable Total Synthesis of (+/-)-Penifulvin A

An efficient and scalable total synthesis of the architecturally challenging sesquiterpenoid (+/-)-penifulvin A has been accomplished via a 12-step sequence with an overall yield of 16%. For the construction of this structurally complex tetracyclic molecule, the key steps used included 1,4-conjugate addition, a Pd(0) catalyzed cross-coupling reaction between an enol phosphate and trimethyl aluminum, Claisen rearrangement using the Johnson orthoester protocol, Ti(III)-mediated reductive epoxide opening-cyclization, Lewis acid catalyzed epoxy-aldehyde rearrangement, and finally a substrate controlled oxidative cascade lactonization process.

An Algorithmic Characterization of Polynomial Functions over Z(pn)

In this paper we consider polynomial representability of functions defined over , where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over is polynomially representable or not, and (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240-266, 1921) and Carlitz (Acta Arith. 9(1), 67-78, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case.

Efficient use of correlation entropy for analysing time series data

The correlation dimension D 2 and correlation entropy K 2 are both important quantifiers in nonlinear time series analysis. However, use of D 2 has been more common compared to K 2 as a discriminating measure. One reason for this is that D 2 is a static measure and can be easily evaluated from a time series. However, in many cases, especially those involving coloured noise, K 2 is regarded as a more useful measure. Here we present an efficient algorithmic scheme to compute K 2 directly from a time series data and show that K 2 can be used as a more effective measure compared to D 2 for analysing practical time series involving coloured noise.

A pattern adaptive thinning algorithm

A simple sequential thinning algorithm for peeling off pixels along contours is described. An adaptive algorithm obtained by incorporating shape adaptivity into this sequential process is also given. The distortions in the skeleton at the right-angle and acute-angle corners are minimized in the adaptive algorithm. The asymmetry of the skeleton, which is a characteristic of sequential algorithm, and is due to the presence of T-corners in some of the even-thickness pattern is eliminated. The performance (in terms of time requirements and shape preservation) is compared with that of a modern thinning algorithm.

Closo versus Hypercloso Metallaboranes: A DFT Study

The structures and electronic relationship of 9-, 10-, 11-, and 12-vertex closo and hypercloso (isocloso) etallaboranes are explored using OFT calculations. The role of the transition metal in stabilizing the hypercloso borane structures is explained using the concept of orbital compatibility. The hypercloso structures, C6H6MBn-1Hn-1 (n = 9-12; M = Fe, Ru, and Os) are taken as model complexes. Calculations on metal free polyhedral borane BnHn suggest that n vertex hypercloso structures need only n skeleton electron pairs (SEPs), but the structure will have one or more six-degree vertices, whereas the corresponding closo structures with n + 1 SEPs have only four- and five-degree vertices. This high-degree vertex of hypercloso structures can be effectively occupied by transition metal fragments with their highly diffused orbitals. Calculations further show that a heavy transition metal with more diffused orbitals prefers over a light transition metal to form hypercloso geometry, This is in accordance with the fact that there are more experimentally characterized hypercloso structures with the heavy transition metals. The size of the exohedral ligands attached to the metal atom also plays a role in deciding the stability of the hypercloso structure. The interaction between the borane and the metal fragments in the hypercloso geometry is analyzed using the fragment molecular orbital approach. The interconversion of the closo and hypercloso structures by the addition and removal of the electrons is also discussed in terms of the correlation diagrams.