The homologous recombination system of phage lambda. Pairing activities of beta protein

The red genes of phage lambda specify two proteins, exonuclease and beta protein, which are essential for its general genetic recombination in recA- cells. These proteins seem to occur in vivo as an equimolar complex. In addition, beta protein forms a complex with another polypeptide, probably of phage origin, of Mr 70,000. The 70-kDa protein appears to be neither a precursor nor an aggregated form of either exonuclease or beta protein, since antibodies directed against the latter two proteins failed to react with 70-kDa protein on Ouchterlony double diffusion analysis. beta protein promotes Mg2+-dependent renaturation of complementary strands (Kmiec, E., and Holloman, W. K. (1981) J. Biol. Chem. 256, 12636-12639). To look for other pairing activities of beta protein, we developed methods of purification to free it of associated exonuclease. Exonuclease-free beta protein appeared unable to cause the pairing of a single strand with duplex DNA; however, like Escherichia coli single strand binding protein (SSB), beta protein stimulated formation of joint molecules by recA protein from linear duplex DNA and homologous circular single strands. Like recA protein, but unlike SSB, beta protein promoted the joining of the complementary single-stranded ends of phage lambda DNA. beta protein specifically protected single-stranded DNA from digestion by pancreatic DNase. The half-time for renaturation catalyzed by beta protein was independent of DNA concentration, unlike renaturation promoted by SSB and spontaneous renaturation, which are second order reactions. Thus, beta protein resembles recA protein in its ability to bring single-stranded DNA molecules together and resembles SSB in its ability to reduce secondary structure in single-stranded DNA.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Multi-Tone Testing of Linear and Nonlinear Analog Circuits using Polynomial Coefficients

A method of testing for parametric faults of analog circuits based on a polynomial representation of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies in addition to DC. Classification or Cur is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. This testing method requires no design for test hardware as might be added to the circuit fly some other methods. The proposed method is illustrated for a benchmark elliptic filter. It is shown to uncover several parametric faults causing deviations as small as 5% from the nominal values.

Interactions of linear dicationic molecules with lipid A: structural requisites for optimal binding affinity

The structural determinants of the binding affinity of linear dicationic molecules toward lipid A have been examined with respect to the distance between the terminal cationic functions, the basicity, and the type of cationic moieties using a series of spermidine derivatives and pentamidine analogs by fluorescence spectroscopic methods, The presence of two terminal cationic groups corresponds to enhanced affinity, A distinct sigmoidal relationship between the intercationic distance and affinity was observed with a sharp increase at 11 Angstrom, levelling off at about 13 Angstrom. The basicity (pK) and nature of the cationic functions are poor correlates of binding potency, since molecules bearing primary amino, imidazolino, or guanido termini are equipotent, The interaction of pentamidine, a bisamidine drug, with lipid A, characterized in considerable detail employing the putative intermolecular excimerization of the drug, suggests a stoichiometry of 1:1 in the resultant complex, The binding is driven almost exclusively by electrostatic forces, and is dependent on the ionization states of both lipid A and the drug, Under conditions when lipid A is highly disaggregated, pentamidine binds specifically to bis-phosphoryl- but not to monophosphoryl-lipid A indicating that both phosphate groups of lipid A are necessary for electrostatic interactions by the terminal amidininium groups of the drug, Based on these data, a structural model is proposed for the pentamidine-lipid A complex, which may be of value in designing endotoxin antagonists from first principles.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Rare earth exchanged (Ce3+, La3+ and RE3+) H-Y zeolites as solid acid catalysts for the synthesis of linear alkyl benzenes

Rare earth exchanged H–Y zeolites were prepared by simple ion exchange methods at 353 K and have been characterized using different physicochemical techniques. A strong peak around 58 ppm in the 27Al{1H} MAS NMR spectra of these zeolites suggests a tetrahedral coordination for the framework aluminium. Small peak at or near 0 ppm is due to hexa-coordinated extra-framework aluminium and a shoulder peak near 30 ppm is a penta-coordinated aluminium species; [Al(OH)4]−. The vapor-phase benzene alkylation with 1-decene and 1-dodecene was investigated with these catalytic systems. Under the reaction conditions of 448 K, benzene/olefin molar ratio of 20 and time on stream 3 h, the most efficient catalyst was CeH–Y which showed more than 70% of olefin conversion with 48.5% 2-phenyldecane and 46.8%, 2-phenyldodecane selectivities with 1-decene and 1-dodecene respectively.

Asynchronous behaviour in some three-atom linear concerted radical-exchange reactions

A few simple three-atom thermoneutral radical exchange reactions (i.e. A + BC --> AB + C) are examined by ab initio SCF methods. Emphasis is laid on the detailed analysis of density matrices rather than on energetics. Results reveal that the sum of the bond orders of the breaking and forming bonds is not conserved to unity, due to development of free valence on the migrating atom 'B' in the transition state. Bond orders, free valence and spin densities on the atoms are calculated. The present analysis shows that the bond-cleavage process is always more advanced than the bond-formation process in the transition state. Further analysis shows a development of the negative spin density on the migrating atom 'B' in the transition state. The depletion of the alpha-spin density on the radical site "A" in the reactant during the reaction lags behind the growth of the alpha-spin density on the terminal atom "C" of the reactant bond, 'B-C' in the transition state. But all these processes are completed simultaneously at the end of the reaction. Hence, the reactions are asynchronous but kinetically concerted in most cases.

Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Phase space methods and the Hamilton-Jacobi form of dynamics

A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

An a priori error analysis of discontinuous Galerkin methods for a general elliptic problem is derived under a mild elliptic regularity assumption on the solution. This is accomplished by using some techniques from a posteriori error analysis. The model problem is assumed to satisfy a GAyenrding type inequality. Optimal order L (2) norm a priori error estimates are derived for an adjoint consistent interior penalty method.