Rearrangement Problem Research Articles

Bu3SnH mediated oxidative radical cyclisations: synthesis of 6H-benzo[c]chromen-6-ones †

Attempts to synthesise 6H-benzo[c]chromen-6-ones by Bu3SnH mediated cyclisation of o-(benzoyl)aryl radicals failed because of the preferred trans conformation of the ester. This problem was overcome by using cyclisation of o-(benzyloxy)aryl and o-[(aryloxy)methyl]aryl radicals to yield 6H-benzo[c]chromenes followed by oxidation to the 6H-benzo[c]chromen-6-ones. 3-Methoxy-6H-benzo[c]chromen-6-one 1, one of the main biologically active constituents of shilajit, a herbal medicine used in countries surrounding the Himalayan mountains, was synthesised using Bu3SnH mediated cyclisation of 1-benzyloxy-2,4-dibromo-5-methoxybenzene 31 to yield 3-methoxy-6H-benzo[c]chromene 25 followed by PCC oxidation of the 6-position. In order to avoid the problems of rearrangement, the aryl radical cyclisation must be designed such that whichever way the spirodienyl intermediate rearranges, the same product is obtained. For instance, the Bu3SnH mediated cyclisation of 1-iodo- and 1-bromo-2-(3-methoxyphenyloxymethyl)benzenes 22 and 23 respectively gave both the isomers, 1-methoxy-6H-benzo[c]chromenes 24 and 3-methoxy-6H-benzo[c]chromenes 25via rearrangement of the intermediate spirodienyl radical. The synthesised 6H-benzo[c]chromenes were oxidised in high yield to the corresponding 6H-benzo[c]chromen-6-ones. The mechanism of the ‘oxidative’ Bu3SnH mediated cyclisation is discussed.

Open problems and conjectures, optimal rearrangement problems related to discrete loaded strings

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.

Relationships of Fussell–Vesely and Birnbaum importance to structural importance in coherent systems

Abstract The notion of node criticality was introduced by Boland, Proschan and Tong to study the problem of optimal rearrangement of components in binary coherent systems. In this paper, we use this notion to study the importance of system components. We derive various relationships between the node criticality and the component importance measures due to Birnbaum, Fussell and Vesely, respectively. Some previous results due to Boland and Proschan, and Meng have been improved.

Neurosolver: Neuromorphic general problem solver

Most beautiful dreams of Artificial Intelligence are still unfulfilled, although some areas, for example Expert Systems, have made it through to the mainstream technology. In this paper, we propose a new approach to general problem solving that employs neuromorphic methods rather than these having their roots in formal logic. Our approach addresses many issues that are difficult to overcome in traditional, symbolic systems. The Neurosolver is a neural network based on a model of a biological cortical column. The cortical column has been found to play a fundamental role in information processing in the cerebral cortex. The model of the column presented in this paper exhibits similar functionality. The stress is laid on a cooperative behavior of many artificial columns interconnected in a network. The network is capable of recording behaviors: i.e., trajectories of time related events. These recorded trajectories let the network use time dependencies to perform breadth-first searches. The device can solve stimulus-response type problems in a given domain and because of that is called Neurosolver. A version of a blocks-world is used to explain and explore the capabilities of the Neurosolver. It has been shown that the Neurosolver can resolve any rearrangement problem in this environment. Furthermore, the network is adaptable and resistant to noisy training data. A discussion comparing the Neurosolver to symbolic systems is included. The prognosis for scaling to larger problems is analyzed.

Demethylation of trimethylantimony species in aqueous solution during analysis by hydride generation/gas chromatography with AAS and ICP MS detection

The method of hydride generation for the speciation of antimony compounds was examined with respect to the problem of molecular rearrangement'. Specifically, demethylation of trimethylstilbine during the analysis of trimethylantimony dichloride (Me3SbCl2) was studied. Previously published observations that enhanced demethylation takes place as a result of inadequate preconditioning of the analytical apparatus were found to be not reproducible. However, demethylation was enhanced as the pH decreased when using two different analytical methods: semi-continuous flow hydride generation–gas chromatography–atomic absorption spectrometry (HG– GC–AAS), and batch-type hydride generation– gas chromatography–inductively coupled plasma mass spectrometry (HG–GC–ICP MS). Applications of the hydride generation method to environmental samples revealed differences in analytical results at high and low pH, and enhanced demethylation taking place because of the matrix in a fungal extract sample. The authors recommend that researchers using the method of hydride generation for antimony compounds carefully test the reaction conditions with standard compounds and use the method of standard addition only. © 1998 John Wiley & Sons, Ltd.

Delivery of bacterial artificial chromosomes into mammalian cells with psoralen-inactivated adenovirus carrier.

Molecular biology has many applications where the introduction of large (>100 kb) DNA molecules is required. The current methods of large DNA transfection are very inefficient. We reasoned that two limits to improving transfection methods with these large DNA molecules were the difficulty of preparing workable quantities of clean DNA and the lack of rapid assays to determine transfection success. We have used bacterial artificial chromosomes (BACs) based on the Escherichia coli F factor plasmid system, which are simple to manipulate and purify in microgram quantities. Because BAC plasmids are kept at one to two copies per cell, the problems of rearrangement observed with YACs are eliminated. We have generated two series of BAC vectors bearing marker genes for luciferase and green fluorescent protein (GFP). Using these reagents, we have developed methods of delivering BACs of up to 170 kb into mammalian cells with transfection efficiency comparable to 5-10 kb DNA. Psoralen-inactivated adenovirus is used as the carrier, thus eliminating the problems associated with viral gene expression. The delivered DNA is linked to the carrier virus with a condensing polycation. Further improvements in gene delivery were obtained by replacing polylysine with low molecular weight polyethylenimine (PEI) as the DNA condensing agent.

Stereoselective Biotransformations in Synthesis of Some Pharmaceutical Intermediates

Publisher Summary The chapter provides some specific examples of stereoselective biotransformations to prepare chiral intermediates required for the synthesis of pharmaceutical drugs. The search for selective enzyme inhibitors and receptor agonists or antagonists is one of the keys for target-oriented research in the pharmaceutical industry. It is now known that in many cases only one stereoisomer of a drug substance is required for efficacy and the other stereoisomer is either inactive or exhibits considerably reduced activity. New drugs for the clinic should be homochiral to avoid the possibility of unnecessary side effects due to an undesirable stereoisomer. Chiral drug intermediates can be prepared by different routes. One is to obtain them from naturally occurring chiral synthons mainly produced by fermentation processes. Second is to carry out resolution of racemic compounds. This can be achieved by preferential crystallization of stereoisomers or diastereoisomers and by kinetic resolution of racemic compounds by chemical or biocatalytic methods. Chiral synthons can also be prepared by asymmetric synthesis by either chemical or biocatalytic processes using microbial cells or enzymes derived therefrom. The advantages of microbial or enzyme-catalyzed reactions over chemical reactions are that they are stereoselective and that they can be carried out at ambient temperature and atmospheric pressure. This minimizes problems of isomerization, racemization, epimerization, and rearrangement that generally occur during chemical processes. Microbial cells or enzymes derived therefrom can be immobilized and reused during many cycles. The chapter provides some specific examples of stereoselective biotransformations to prepare chiral intermediates required for the synthesis of pharmaceutical drugs.

Genome Rearrangements and Sorting by Reversals

Sequence comparison in molecular biology is in the beginning of a major paradigm shift—a shift from gene comparison based on local mutations (i.e., insertions, deletions, and substitutions of nucleotides) to chromosome comparison based on global rearrangements (i.e., inversions and transpositions of fragments). The classical methods of sequence comparison do not work for global rearrangements, and little is known in computer science about the edit distance between sequences if global rearrangements are allowed. In the simplest form, the problem of gene rearrangements corresponds to sorting by reversals, i.e., sorting of an array using reversals of arbitrary fragments. Recently, Kececioglu and Sankoff gave the first approximation algorithm for sorting by reversals with guaranteed error bound 2 and identified open problems related to chromosome rearrangements. One of these problems is Gollan’s conjecture on the reversal diameter of the symmetric group. This paper proves the conjecture. Further, the problem of expected reversal distance between two random permutations is investigated. The reversal distance between two random permutations is shown to be very close to the reversal diameter, thereby indicating that reversal distance provides a good separation between related and nonrelated sequences in molecular evolution studies. The gene rearrangement problem forces us to consider reversals of signed permutations, as the genes in DNA could be positively or negatively oriented. An approximation algorithm for signed permutation is presented, which provides a performance guarantee of $\tfrac{3}{2}$ . Finally, using the signed permutations approach, an approximation algorithm for sorting by reversals is described which achieves a performance guarantee of $\tfrac{7}{4}$.

The block distributed memory model

We introduce a computation model for developing and analyzing parallel algorithms on distributed memory machines. The model allows the design of algorithms using a single address space and does not assume any particular interconnection topology. We capture performance by incorporating a cost measure for interprocessor communication induced by remote memory accesses. The cost measure includes parameters reflecting memory latency, communication bandwidth, and spatial locality. Our model allows the initial placement of the input data and pipelined prefetching. We use our model to develop parallel algorithms for various data rearrangement problems, load balancing, sorting, FFT, and matrix multiplication. We show that most of these algorithms achieve optimal or near optimal communication complexity while simultaneously guaranteeing an optimal speed-up in computational complexity. Ongoing experimental work in testing and evaluating these algorithms has thus far shown very promising results.

Applications of matching and edge‐coloring algorithms to routing in clos networks

AbstractRearrangeable Clos networks have been studied in the literature in connection with telephone switching and communication networks. This paper examines the applicability of matching and edge‐coloring in bipartite graphs to the rearrangement problem in these networks. A survey of various matching and edge‐coloring algorithms is given, and these algorithms are evaluated for their suitability and effectiveness. It is shown that no single matching or edge‐coloring algorithm reported in the literature performs well over all Clos networks. It is further shown that the time complexity of the looping algorithm for Beneš networks is at least as good as any routing algorithm that can be obtained from matching or edge‐coloring. © 1994 by John Wiley & Sons, Inc.

Quantum rearrangement scattering calculations using the invariant imbedding method

We derive an algorithm to calculate quantum transmission and reflection amplitudes (S-matrix elements) for rearrangement reactions using the invariant imbedding method. Our approach can incorporate closed channels, treat complex potentials (to simulate decay), and can be used within an adiabatic representation (in which derivative coupling terms are present) or within a diabatic representation. The method can also be used to determine bound-state energies when only closed channels are present. The method is demonstrated on a rearrangement problem with two coupled potential surfaces (four channels) as a function of energy in the energy region from the lowest channel threshold through the highest channel threshold.

Strategic framework in environmental management: war and its aftermath

Strategic approaches to environmental management have in some parts of the world received an additional dimension: warfare and its aftermath. Warfare means not only loss of human life, loss of amenities, and diversion of materials and goods from regular use to logistic support for combatants, but also the disruption of the established administrative and legal system, designed to protect the environment. The paper advances two hypotheses: (i) that the acute damaging effects of war have their counterparts in environmental management malpractice, and (ii) that the aftermath leads to an ambiguous rearrangement of social, economic and environmental management priorities. An analysis is given of the additional cumulative effects of environmental loading as a consequence of warfare, and highlights the importance of the interface between the sciences and society in such specific circumstances. Transition from the centrally planned economies in the emerging states and societies of Central and Eastern Europe requires conceptual understanding of the time scales necessary and available. Within the time available there will be difficult management choices to be made, condensed into the problem of rearrangement of priorities within a legal system, harmonized with limited possibilities and needs on one side, and the requirements of contemporary environmental management principles and practices in the market economies of the western world.

Collisional approach to dynamics of resonance atomic states in an external field

The following aspects of the dynamics of an atomic state in an external stationary field are assessed: (i) the rearrangement problem; (ii) the description of the appropriate final-channel wavefunctions; (iii) the analytical properties of the transition amplitude into the continuum. The rearrangement problem was solved by the introduction of the effective Hamiltonian, the eigenstates of which include both the initial state and final states ('modified states of continuum spectrum' MSCS) which describe the potential part of the exact wavefunction of the scattering problem. It is shown that the amplitude of decay and transition into MSCS as functions of time have an exact representation as a sum of resonance terms defined by a set of resonance states and the matrix elements of the shift R-matrix operator. Analysing the following expansion basis sets: stationary states, Volkov-Keldysh states and coherent states it is shown that the most appropriate one is a modified set of Volkov-Keldysh states.

Parallel methods for solving fundamental file rearrangement problems

We present parallel algorithms for the elementary binary set operations that, given an EREW PRAM with k processors, operate on two sorted lists of total length n in O( n/ k + log n) time and O(k) extra space and are thus time-space optimal for any value of k ≤ n/(log n). Our methods are stable, require no information other than a record's key, and do not modify records as they execute.

Chiral sulfur-reagents for the preparation of optically active epoxides

Acyclic chiral sulfides which could be easily synthesized in both enantiomeric forms leading to poor yields and/or to racemic epoxides, Eliel's oxathiane reagent was used and proved to provide chiral trans diarylepoxides in high yield (70-80%) and enantiomeric purities up to 70-100%, with no rearrangement problems. It was also found that phase-transfer conditions were the easiest and the most efficient for these reactions.

An incremental algorithm for TDM switching assignments in satellite and terrestrial networks

The authors present an incremental algorithm for scheduling traffic in a general class of time-division multiplexed (TDM) switching systems used in satellite and terrestrial communication networks. Instead of recomputing the time slot assignment (TSA) for each frame of traffic, this algorithm computes a TSA for a new frame by modifying the known TSA of the previous frame. The algorithm takes O(M/sup 2/+cM) time for finding an optimal TSA in a hierarchical switching system, where M is the number of users and c is the number of changes between the traffic demands of two consecutive frames. The algorithm uses a two-step process. The first step transforms the TSA problem in the hierarchical switching system (HSS) into an equivalent TSA problem in a simple TDM switching system. The second step uses an incremental algorithm to find a TSA for the latter. The second step exploits the correspondence between the TSA problem and the rearrangement problem in a Clos three-stage network. When the traffic demands in consecutive frames overlap to a significant extent, the incremental algorithm provides considerable speedup over previous algorithms. >

Quantum behavior at a cusp, or how wave mechanics avoids a catastrophe

The quantum mechanical system whose potential is the cusp catastrophe function is canonical for the uniform asymptotic analysis of the Stokes phenomenon for four transition points. It is shown that across the singularity which marks the bifurcation from a single to two modes, quantum eigenlevels vary smoothly. Also, their derivatives and nonadiabatic coupling matrix elements are continuous with respect to control parameters. These matrix elements, which are of interest for the three-body rearrangement problem, clearly exhibit the ridge effect, i.e. a peaking astride potential maxima.

Faddeev approach to electron capture

The Faddeev-Watson-Lovelace scattering formalism is applied to the rearrangement problem in three-body collisions. In a second-order approximation, the transition operator is seen to generalize the second Born approximation by replacing each appearance of a two-body potential with a corresponding two-body transition operator, except for the first Born electron-nuclear potential term which remains the same. Application to electron capture in ion-atom collisions for both forward- and large-angle projectile scattering is discussed and the particular role of the internuclear potential in each case considered. Extension is made of results obtained within the second Born approximation, particularly the zero contribution of the internuclear potential at forward angles and the structure of critical-angle scattering. The treatment of initial- and final-state binding effects is also addressed. Differential capture cross sections for proton-hydrogen and proton-helium collisions in the MeV energy range are presented.

Rearranging data to maximize the efficiency of compression

We are concerned with rearranging the order in which data is stored in a database so as to maximize the amount of compression. We consider multi-attribute data defined over finite discrete domains (called categories) and seek an optimal permutation of the categories for each attribute. We study both deterministic and probabilistic models of data distribution. We show that the deterministic category rearrangement problem is NP-complete (for run length encoding compression methods) via a reduction to the rectilinear traveling salesman problem. For the probabilistic model, we show that the optimal category rearrangement for each attribute has the form of a double pipe organ, which is a generalized version of the well-known pipe organ arrangement found in earlier work on record placement on disk cylinders. For k-dimensional data we obtain an algorithm for finding the optimal arrangement which is O( n 2) for fixed k.

Structural and asymptotic properties of the eikonal approximation for electron capture

The authors develop the structural properties of the eikonal approximation (EA) to the electron capture process by comparison with the corresponding terms of the Born series. This allows one to extract the physical content of the EA and to point out the similarities and differences with Born-type expansions. In so doing they also pay attention to the interpretation of the two inequivalent (post and prior) forms of the EA. In the asymptotic regime, as nu to infinity , inspection of the eikonal amplitudes reveal that only the single and double scattering terms of the eikonal expansion contribute (to leading order) to the asymptotic cross section. This result appears to be shared by all multiple scattering descriptions of the charge exchange mechanism and underlines anew the special role played by the double-scattering term in the rearrangement problem.