Approximate Map Research Articles

Approximate conformal mapping of certain polygons onto a strip by the block method

The exponentially convergent block method, which the author has proposed and provided with a sound theoretical basis, is applied to the conformal mapping of a rectangle and two octagons onto a strip and of a Γ-shaped region onto a half-strip. The general scheme is shown to be improved by the use of analytic continuation, substitution of the complex variable, etc. It thus becomes possible to reduce the number of blocks used in the present case to one. The approximate conformal mapping is expressed in terms of elementary functions. Highly accurate practical results are presented.

The double scroll family

This paper provides a rigorous mathematical proof that the double scroll is indeed chaotic. Our approach is to derive a linearly equivalent class of piecewise-linear differential equations which includes the double scroll as a special case. A necessary and sufficient condition for two such piecewise-linear vector fields to be linearly equivalent is that their respective eigenvalues be a scaled version of each other. In the special case where they are identical, we have exact equivalence in the sense of linear conjugacy. An explicit normalform equation in the context of global bifurcation is derived and parametrized by their eigenvalues. Analytical expressions for various Poincare maps are then derived and used to characterize the birth and the death of the double scroll, as well as to derive an approximate one-dimensional map in analytic form which is useful for further bifurcation analysis. In particular, the analytical expressions characterizing various half-return maps associated with the Poincare map are used in a crucial way to prove the existence of a Shilnikov-type homoclinic orbit, thereby establishing rigorously the chaotic nature of the double scroll. These analytical expressions are also fundamental in our in-depth analysis of the birth (onset of the double scroll) and death (extinction of chaos) of the double scroll. The unifying theme throughout this paper is to analyze the double scroll system as an unfolding of a large family of piecewise-linear vector fields in R^3 . Using this approach, we were able to prove that the chaotic dynamics of the double scroll is quite common, and is robust because the associated horseshoes predicted from Shilnikov's theorem are structurally stable. In fact, it is exhibited by a large family (in fact, infinitely many linearlyequivalent circuits) of vector fields whose associated piecewise-linear differential equations bear no resemblance to each other. It is therefore remarkable that the normalized eigenvalues, which is a local concept, completely determine the system's global qualitative behavior.

Map location of the gene for a 130,000-dalton glycoprotein of bovine herpesvirus 1.

A bovine herpesvirus 1 variant (mar6) containing a mutation in a viral glycoprotein with a molecular weight of 130,000 (g130) was isolated by selecting for resistance to a neutralizing monoclonal antibody (130-6) directed against g130. Mar6 was completely resistant to neutralization by monoclonal antibody 130-6 in the presence and absence of complement, but was neutralized by polyvalent immune sera. The mar6 mutant synthesized and processed g130, but produced plaques which failed to react with monoclonal antibody 130-6 in an in situ immunoassay (black plaque). However, monoclonal antibody 130-6 was capable of binding and immunoprecipitating g130 from infected-cell extracts produced by lysis of mar6-infected cells with nonionic detergents. The mutation in mar6 was mapped by marker rescue with cloned bovine herpesvirus 1 restriction enzyme fragments to a 3.8-kilobase fragment at approximate map units 0.405 to 0.432. In addition, it was found that a DNA probe containing the glycoprotein B gene of herpes simplex type 1 hybridized uniquely to the same 3.8-kilobase fragment which was shown by marker rescue to contain the mutation site in the gene for bovine herpesvirus 1 g130.

Anaerobically induced genes of Escherichia coli.

A collection of anaerobically induced gene fusions were isolated, and representative isolates were characterized with respect to their regulatory properties, phenotypes, and approximate map locations. Four fusion strains that had defects in the anaerobic metabolism of asparagine or aspartate were found. These fusions were all repressed by alternate electron acceptors, ammonia, and glucose but were induced by other sugars. Several other fusion strains which demonstrated no observable phenotype showed diverse regulatory responses. The anaerobically induced fusions were scattered around the Escherichia coli chromosome more or less at random, suggesting that all the isolates examined were in separate genes.

An approximate Riemann Mapping Theorem in ? n

An approximate Riemann Mapping Theorem in ? n

Ising-like quality of the Potts model

A projection operator which maps the q-state Potts model onto an Ising model is investigated. The case of an approximate mapping between two-spin nearest-neighbour clusters on a d-dimensional hypercubic lattice is considered. In the ferromagnetic case, first-order transitions occur for q>qc(d)=1+exp(2KIc(d))>or=2, where KIc(d) is the critical Ising coupling. Among the results are qc(d) to exp(2/(d-1)) as d to 1+, qc(2)=3.41 and qc(3)=2.56. The antiferromagnetic Potts model has no long range order for q>2.

Chromosomal map position of genes encoding P adhesins in uropathogenic Escherichia coli.

Escherichia coli isolates from upper urinary tract infections frequently express adherence to human uroepithelium and D-mannose-resistant hemagglutination of human erythrocytes. Such adherence is usually associated with P pili encoded by the pap operon(s). In this paper, we report approximate chromosomal map positions for two copies of the pap operon. Only one copy expressed an adhesin capable of D-mannose-resistant hemagglutination, although both expressed P-related antigen.

Recombinants between vaccinia and ectromelia viruses bearing the specific pathogenicity markers of both parents.

Nineteen recombinants between vaccinia virus (VV) DNA-temperature-sensitive mutants and ectromelia virus (EMV) were characterized with respect to their biological properties and genome structure. Four of these recombinants acquired the pathogenicity for mice characteristic of EMV, while the pathogenicity for rabbits characteristic of VV was not only preserved, but even enhanced. Most unexpectedly, these recombinants with 'double pathogenicity', as well as four other recombinants, acquired a stable genetic trait which was not typical of the parental viruses, i.e., the ability to form haemorrhagic lesions on the chorioallantoic membrane of chick embryos. Approximate mapping of the genomes of these recombinants with restriction endonucleases showed that their DNA contained mostly VV sequences with a single detected insert of EMV DNA. In the 'double pathogenicity' recombinants, this insert was located in the central part of the genome, and its minimal size was about 16 Mdal.

Diffusion of electrons by coherent wavepackets

The momentum transfer and velocity diffusion of electrons periodically interacting with a coherent longitudinal wavepacket is considered. Applying the resonance overlap criterion, we establish the threshold for intrinsic stochasticity and the width of the stochastic region Δ v stoch in velocity space. Direct numerical integration of the single-particle dynamics and an approximate discrete mapping are used to corroborate the resonance overlap results and to find the short- and long-term momentum transfer and diffusion in the field. After the onset of stochasticity, we find a net induced current j ≈ Δ v stoch and in the weak-field regime (autocorrelation time ⪡ bounce time) an initial rate of change of the variance 〈π v 2〉 /2 t equal to the quasilinear-theory diffusion coefficient. In the strong-field regime momentum transfer and stochasticity persist owing to non-adiabatic transitions between trapped and untrapped states as the electron traverses the wavepacket. The diffusion coefficient substantially deviates from the quasilinear (≈ E 2) as well as from resonance broadening ( ≈E 3 2 ) scaling, while the scattering in velocity space tends to lose the local, diffusive nature characteristic of weak fields.

Specific labeling of protein domains with antibody fragments

Monovalent antibody Fab fragments, prepared from antisera raised against two different types of crystalline arrays made of either intact, or a proteolytic fragment of bacteriophage T4 major capsid protein, gp23*, were employed to stoichiometrically label different gp23* protein domains on the outer surface of a tubular variant (i.e., "polyheads") of bacteriophage T4 capsids. Computer filtrations of both negatively stained and freeze-dried/metal-shadowed specimens permitted approximate mapping of the Fab binding sites within the capsomere of the polyheads.

Differences exist between viral transcripts in cottontail rabbit papillomavirus-induced benign and malignant tumors as well as non-virus-producing and virus-producing tumors.

Five major cottontail rabbit papillomavirus-specific polyadenylated RNA species with sizes of 4.8, 2.6, 2.0, 1.3, and 0.9 kilobases (kb) were found in virus-producing tumors of cottontail rabbits (the natural host for the virus). Two of the RNA species (sizes, 2.0 and 1.3 kb) are indistinguishable with respect to size and map position from the RNA species detected previously in non-virus-producing benign and malignant tumors (Nasseri et al., J. Virol. 44:263-268, 1982). The 2.0-kb RNA in virus-producing benign tumors is more abundant than the 1.3-kb RNA. This, together with similar observations of benign non-virus-producing tumors, suggests that the predominance of the 2.0-kb RNA is a general feature of benign tumors. The change to a preferential synthesis of the 1.3-kb RNA appears to be a phenomenon of tumor progression from papillomas to carcinomas. Three transcripts of 4.8, 2.6, and 0.9 kb are unique to virus-producing tumors. The RNA molecules were mapped in two steps. First, hybridization of Northern blots with subgenomic probes revealed the approximate map position of the transcripts. Second, with nuclease S1 and exonuclease VII mapping procedures and end-labeled probes, the major exons of the 4.8-, 2.6-, 2.0-, and 1.3-kb RNAs were mapped precisely, and it is shown that all RNAs are transcribed from the same DNA strand. Both 1.3- and 2.0- kb RNAs consist of two exons which are separated by an identical 2.45-kb intron. The 5' ends of the 5'-proximal exons of the 2.0- and 1.3-kb RNAs map to positions 0.07 and 0.16, respectively. Some of the 2.0-kb RNA molecules, especially in the carcinoma, have an alternative 5' end at position 0.06. The 3' ends of both exons map to position 0.22, where two ends were found about seven nucleotides apart. The sizes of the 5'-proximal exons of the 2.0- and 1.3-kb RNAs are 1.23 and 0.48 kb, respectively. The 1.3- and 2.0-kb RNAs share a common 3'-proximal exon of 0.66 (0.61) kb. This exon has two 5' ends 50 nucleotides apart at map position 0.53 and a 3' end at map position 0.61. Only the 3'-proximal part of the 4.8- and 2.6-kb RNAs have been mapped precisely. Both RNAs share a common 3' end at position 0.99. The 2.6-kb RNA part consists of a single 1.59-kb exon which extends to map position 0.79.(ABSTRACT TRUNCATED AT 400 WORDS)

Construction and properties of intertypic poliovirus recombinants: First approximation mapping of the major determinants of neurovirulence

An attempt was made to map, in a general way, the region of the poliovirus genome that is responsible for the neurovirulent and attenuated phenotypes of different virus strains. A set of four recombinants was investigated, one described previously (E. A. Tolskaya, L. I. Romanova, M. S. Kolesnikova, and V. I. Agol, 1983, Virology 124,121–132) and three obtained in the present work with the following genetic structure: a 5′ end-ajdacent segment of the genome derived from either a virulent strain ( 452 62 3D), or from an attenuated strain (Leon-2) of poliovirus type 3, the remaining RNA sequences being derived from either a virulent strain (Mgr), or an attenuated strain (LSc-gr3) of poliovirus type 1. The crossover points in the recombinant genomes were centrally located, somewhere between the gene(s) that determines antigenic specificity of the virus and the locus that determines resistance of virus multiplication to low doses of guanidine. The recombinant nature of the newly selected clones was definitively established by mapping RNase T1 oligonucleotides of their genome. The recombinants were characterized with respect to their ability to produce infectious progeny and synthesize viral RNA at an elevated temperature. Neurovirulence of the recombinants was assayed by intracerebral inoculation of monkeys. Irrespective of the origin of the 3′ end-adjacent segment of the genome, the recombinants that inherited the 5′ end-adjacent segment from the neurovirulent parent were neurovirulent, whereas the recombinants with the 5′ end-adjacent segment derived from the attenuated parent were not. The results suggest that the major determinants of neurovirulence of these recombinants (and by inference, of their parental viruses) reside in the 5′ end-adjacent segment of poliovirus genome, known to code for capsid proteins.

MUTATIONS INDROSOPHILA MELANOGASTERAFFECTING PHYSIOLOGICAL AND BEHAVIOURAL RESPONSE TO MALATHION

AbstractMutants ofDrosophila melanogaster(Meigen) with altered resistance to the insecticide malathion were isolated and tested for their avoidance response to the insecticide. A correlation between sensitivity to the insecticide and increased avoidance was detected. Approximate chromosome map locations were determined for the loci of the mutations.

Ground‐Water Modeling in a Southwestern Alluvial Basin

ABSTRACTA two‐dimensional finite‐difference computer code was used to model the ground‐water flow system in an alluvial basin in southwest New Mexico. A three‐step approach was used to determine the transmissivity distribution for the model. First, values of the natural logarithm of transmissivity (In T) were interpolated from existing data using the kriging technique. This interpolation scheme also produced a map of standard deviations of the kriging errors. Second, a conventional flow net was drawn from steadystate water levels with the aid of the kriged hydraulic head distribution. Third, the approximate transmissivity map, the standard deviation map of the kriged In T values, and flow net were used to select the segment of each streamtube where transmissivity was known with greatest certainty (smallest In T kriging error). Then, transmissivities in other segments of the stream tubes were calculated from Darcy's Law. This distribution, when input to the numerical model, did not have to be altered appreciably during the calibration for a steady‐state and seven‐year transient period. Most of the transient calibration was accomplished by adjusting storage coefficients. Considering the uncertainty in the available pumping data, very good agreement was found between observed and predicted water levels during a four‐year model verification period.

Numerical Experiments on Solving Theodorsen’s Integral Equation for Conformal Maps with the Fast Fourier Transform and Various Nonlinear Iterative Methods

In [M. H. Gutknecht, Numer. Math., 36 (1981), pp. 405–429] we investigated several iterative methods for solving discretized versions of Theodorsen's nonlinear integral equation. Here we present corresponding numerical experiments and discuss some related questions, such as the application of a continuation method, the evaluation of the approximate mapping function, the selection of the appropriate type of approximation, and the use of preliminary maps to eliminate corners. Both the nonlinear SOR method and a related second order Euler method are seen to be very effective, even if the assumptions of the theory do not hold.

Approximate Mapping of Two-Dimensional Quantum-Spin Models on Staggered Eight-Vertex Models

Analytic results have been obtained for the thermodynamics of the two-dimensional $S=\frac{1}{2}$ $X\ensuremath{-}Y$ model using the simplest form of the generalized Trotter formula for the partition function. The model exhibits a phase transition of unconventional nature. It is claimed that this is one of the best descriptions given so far of the critical thermodynamics of the $S=\frac{1}{2}$ two-dimensional $X\ensuremath{-}Y$ model. Central in the present approach is the mapping of a family of two-dimensional $S=\frac{1}{2}$ models on staggered eight-vertex models having unconventional weights.

Approximate mapping of the two-impurity symmetric Anderson model in the local-moment regime to a classical problem

Using a path-integral formulation for the partition function the two-impurity symmetric Anderson model in the local-moment regime is mapped onto a problem of a classical four-component "Coulomb" gas interacting with a logarithmic potential. This can be viewed alternately as a problem of a general four-state spin system with inverse-square interaction in one dimension. The scaling equations for this model are derived and their implications for the properties of the Anderson model are pointed out. This mapping, although approximate, provides an explicit and physically interesting realization of a class of general $n$-state inverse-square spin systems in one dimension.

Temperature distributions in cladded configurations of complicated boundary shape

This paper deals with an approximate analytical solution of certain cladded shapes of basic interest in nuclear engineering technology. In one case a solution of Laplace's equation is obtained. In the other, a solution to a system of partial differential equations (Poisson's and Laplace's) is attained. An approximate conformal mapping approach is also used in both situations, and it is shown that the analytical predictions are in good agreement with the values obtained by means of a finite element code.

Commensurate-Incommensurate Transitions in Two Dimensions: Discrete Models and Square Symmetric Substrates

The phase diagram and the critical behavior of a discrete two-dimensional model of the commensurate-incommensurate transition is determined with use of an approximate mapping onto the six-vertex model. For an uniaxial substrate the critical behavior is that of the continuum case. For a square substrate either a single first-order transition or a second-order transition followed by a first-order transition is found.

Two deletions within genes for simian virus 40 structural proteins VP2 and VP3 lead to formation of abnormal transcriptional complexes.

The procedure developed by R. M. Fernandez-Muñoz et al. (J. Virol. 29:612-623, 1979) for isolating simian virus 40 (SV 40) chromatin free of disrupted previrions was optimized for preparing late transcriptional complexes, and these complexes were partially characterized. Transcriptional complexes derived from wild-type virus and from several deletion and temperature-sensitive mutants could be activated more than five-fold either by the anionic detergent Sarkosyl or by 300 mM ammonium sulfate, in agreement with the properties of SV40 transcriptional complexes prepared by other procedures. In contrast, complexes from cells infected with deletion mutants dl1261 or dl1262 were not activated at all by a high salt concentration, even though the extent of their activation by Sarkosyl was normal. Mutants dl1261 and dl1262 carry deletions of 54 and 36 base pairs, respectively, at an approximate map position of 0.91, which is within the overlapping genes for the virion proteins VP2 and VP3. The effects of these deletions on transcription in vitro indicate that VP2 or VP3 or both are bound to late transcriptional complexes in a way that affects the progress of initiated RNA polymerase. The properties of late transcriptional complexes derived from wild-type SV40 can be explained by the presence of the following two different kinds of complexes: (i) a minority class (about 20%), which is free of VP2 or VP3, active at low concentrations of ammonium sulfate in vitro, and responsible for late transcription in vivo, and (ii) a majority class (about 80%) with VP2 or VP3 bound, which is inactive at low salt concentrations both in vitro and in vivo but capable of being activated by high salt concentrations or by Sarkosyl. We propose that mutant VP2 and VP3 proteins from dl1261 and dl1262 bind to the majority class of late transcriptional complexes in a way that can be reversed by Sarkosyl but not by a high salt concentration.