A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

Efficient implementations of a pseudodynamical stochastic filtering strategy for static elastography

A computationally efficient pseudodynamical filtering setup is established for elasticity imaging (i.e., reconstruction of shear modulus distribution) in soft-tissue organs given statically recorded and partially measured displacement data. Unlike a regularized quasi-Newton method (QNM) that needs inversion of ill-conditioned matrices, the authors explore pseudodynamic extended and ensemble Kalman filters (PD-EKF and PD-EnKF) that use a parsimonious representation of states and bypass explicit regularization by recursion over pseudotime. Numerical experiments with QNM and the two filters suggest that the PD-EnKF is the most robust performer as it exhibits no sensitivity to process noise covariance and yields good reconstruction even with small ensemble sizes.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Huffman Binary Coding of WLN Symbols for File-Compression

Construction of Huffman binary codes for WLN symbols is described for the compression of a WLN file. Here, a parenthesized representation of the tree structure is used for computer encoding.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Purification of RNA polymerase from mycobacteria for optimized promoter-polymerase interactions

In vitro transcription analysis is important to understand the mechanism of transcription. Various assays for the analysis of initiation, elongation and termination form the basis for better understanding of the process. Purified RNA polymerase (RNAP) with high specific activity is necessary to carry out variety of these specific reactions. The RNAP purified from Mycobacterium smegmatis from exponential phase showed low promoter specificity in promoter-polymerase interaction studies. This is due to the presence of a large number of sigma factors during exponential phase and under-representation of sigma(A) required for house-keeping transcription. We describe an in vivo reconstitution of RNAP holoenzyme with sigma(A) and its purification, which resulted in holoenzyme with stoichiometric sigma(A) content. The reconstituted holoenzyme showed enhanced promoter-specific binding and promoter-specific-transcription activity compared to the enzyme isolated using standard procedure. Such in vivo reconstitution of stoichiometric holoenzyme could facilitate promoter-specific transcription assays, especially in organisms which encode a large number of sigma factors.

Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits

The angular-momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular-momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to nonlinear memory. We average the angular-momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular-momentum flux provides the final input needed for gravitational-wave phasing of binaries moving in quasi-elliptical orbits. We obtain the evolution of orbital elements under 3PN gravitational radiation reaction in the quasi-elliptic case. For small eccentricities, we give simpler limiting expressions relevant for phasing up to order e(2). This work is important for the construction of templates for quasi-eccentric binaries, and for the comparison of post-Newtonian results with the numerical relativity simulations of the plunge and merger of eccentric binaries.

Automated inspection of aircraft parts using a modified ICP algorithm

The application of computer-aided inspection integrated with the coordinate measuring machine and laser scanners to inspect manufactured aircraft parts using robust registration of two-point datasets is a subject of active research in computational metrology. This paper presents a novel approach to automated inspection by matching shapes based on the modified iterative closest point (ICP) method to define a criterion for the acceptance or rejection of a part. This procedure improves upon existing methods by doing away with the following, viz., the need for constructing either a tessellated or smooth representation of the inspected part and requirements for an a priori knowledge of approximate registration and correspondence between the points representing the computer-aided design datasets and the part to be inspected. In addition, this procedure establishes a better measure for error between the two matched datasets. The use of localized region-based triangulation is proposed for tracking the error. The approach described improves the convergence of the ICP technique with a dramatic decrease in computational effort. Experimental results obtained by implementing this proposed approach using both synthetic and practical data show that the present method is efficient and robust. This method thereby validates the algorithm, and the examples demonstrate its potential to be used in engineering applications.

Adsorption of Nitrogen on Activated Carbon-Refit of Experimental Data and Derivation of Properties Required for Design of Equipment

Volumetric method based adsorption measurements of nitrogen on two specimens of activated carbon (Fluka and Sarabhai) reported by us are refitted to two popular isotherms, namely, Dubunin−Astakhov (D−A) and Toth, in light of improved fitting methods derived recently. Those isotherms have been used to derive other data of relevance in design of engineering equipment such as the concentration dependence of heat of adsorption and Henry’s law coefficients. The present fits provide a better representation of experimental measurements than before because the temperature dependence of adsorbed phase volume and structural heterogeneity of micropore distribution have been accounted for in the D−A equation. A new correlation to the Toth equation is a further contribution. The heat of adsorption in the limiting uptake condition is correlated with the Henry’s law coefficients at the near zero uptake condition.

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

A unit cube in k dimensions (k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k where R-i (for 1 <= i <= k) is a closed interval of the form [a(i), a(i) + 1] on the real line. A graph G on n nodes is said to be representable as the intersection of k-cubes (cube representation in k dimensions) if each vertex of C can be mapped to a k-cube such that two vertices are adjacent in G if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G denoted as cub(G) is the minimum k for which G can be represented as the intersection of k-cubes. An interesting aspect about cubicity is that many problems known to be NP-complete for general graphs have polynomial time deterministic algorithms or have good approximation ratios in graphs of low cubicity. In most of these algorithms, computing a low dimensional cube representation of the given graph is usually the first step. We give an O(bw . n) algorithm to compute the cube representation of a general graph G in bw + 1 dimensions given a bandwidth ordering of the vertices of G, where bw is the bandwidth of G. As a consequence, we get O(Delta) upper bounds on the cubicity of many well-known graph classes such as AT-free graphs, circular-arc graphs and cocomparability graphs which have O(Delta) bandwidth. Thus we have: 1. cub(G) <= 3 Delta - 1, if G is an AT-free graph. 2. cub(G) <= 2 Delta + 1, if G is a circular-arc graph. 3. cub(G) <= 2 Delta, if G is a cocomparability graph. Also for these graph classes, there axe constant factor approximation algorithms for bandwidth computation that generate orderings of vertices with O(Delta) width. We can thus generate the cube representation of such graphs in O(Delta) dimensions in polynomial time.

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.

Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.

An alternate form of the ramberg-osgood formula for matrix displacement analysis

A new stress-strain law, which is a three parameter representation of stress in terms of strain has been proposed for the matrix displacement analysis of structures made of non-hookean materials. This formula has been utilized to study three typical problems. These studies brought out the effectiveness and suitability of this law for matrix displacement analysis.

Hardness of approximation results for the problem of finding the stopping distance in Tanner graphs

Tanner Graph representation of linear block codes is widely used by iterative decoding algorithms for recovering data transmitted across a noisy communication channel from errors and erasures introduced by the channel. The stopping distance of a Tanner graph T for a binary linear block code C determines the number of erasures correctable using iterative decoding on the Tanner graph T when data is transmitted across a binary erasure channel using the code C. We show that the problem of finding the stopping distance of a Tanner graph is hard to approximate within any positive constant approximation ratio in polynomial time unless P = NP. It is also shown as a consequence that there can be no approximation algorithm for the problem achieving an approximation ratio of 2(log n)(1-epsilon) for any epsilon > 0 unless NP subset of DTIME(n(poly(log n))).