Line clipping revisited: Two efficient algorithms based on simple geometric observations

Two new line clipping algorithms, the opposite-corner algorithm and the perpendicular-distance algorithm, that are based on simple geometric observations are presented. These algorithms do not require computation of outcodes nor do they depend on the parametric representations of the lines. It is shown that the opposite-corner algorithm perform consistently better than an algorithm due to Nicholl, Lee, and Nicholl which is claimed to be better than the classic algorithm due to Cohen-Sutherland and the more recent Liang-Barsky algorithm. The pseudo-code of the opposite-corner algorithm is provided in the Appendix.

On some geometric invariants associated to the space of flat connections on an open space

A geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

The determination of spatial pattern in Dictyostelium discoideum

Free-living amoebae of the cellular slime mould Dictyostelium discoideum aggregate when starved and give rise to a long and thin multicellular structure, the slug. The slug resembles a metazoan embryo, and as with other embryos it is possible to specify a fate map. In the case of Dictyostelium discoideum the map is especially simple: cells in the anterior fifth of the slug die and form a stalk while the majority of those in the posterior differentiate into spores. The genesis of this anterior-posterior distinction is the subject of our review. In particular, we ask: what are the relative roles of individual pre-aggregative predispositions and post-aggregative position in determining cell fate? We review the literature on the subject and conclude that both factors are important. Variations in nutritional status, or in cell cycle phase at starvation, can bias the probability that an amoeba differentiates into a stalk cell or a spore. On the other hand, isolates, or slug fragments, consisting of only prestalk cells or only prespore cells can regulate so as to result in a normal range of both cell types. We identify three levels of control, each being responsible for guiding patterning in normal development: (i) 'coin tossing', whereby a cell autonomously exhibits a preference for developing along either the stalk or the spore pathway with relative probabilities that can be influenced by the environment; (ii) 'chemical kinetics', whereby prestalk and prespore cells originate from undifferentiated amoebae on a probabilistic basis but, having originated, interact (e.g. via positive and negative feedbacks), and the interaction influences the possibility of conversion of one cell type into the other, and (iii) 'positional information', in which the spatial distribution of morphogens in the slug influences the pathway of differentiation. In the case of possibilities (i) and (ii), sorting out of like cell types leads to the final spatial pattern. In the case of possibility (iii), the pattern arises in situ.

The precision of regulation in Dictyostelium discoideum: implications for cell-type proportioning in the absence of spatial pattern

We have made careful counts of the exact number of spore, stalk and basal disc cells in small fruiting bodies of Dictyostelium discoideum (undifferentiated amoebae are found only rarely and on average their fraction is 4.96 x 10(-4)). (i) Within aggregates of a given size, the relative apportioning of amoebae to the main cell types occurs with a remarkable degree of precision. In most cases the coefficient of variation (c.v.) in the mean fraction of cells that form spores is within 4.86%. The contribution of stalk and basal disc cells is highly variable when considered separately (c.v.'s upto 25% and 100%, respectively), but markedly less so when considered together. Calculations based on theoretical models indicate that purely cell-autonomous specification of cell, fate cannot account for die observed accuracy of proportioning. Cell-autonomous determination to a prestalk or prespore condition followed by cell type interconversion, and stabilised by feedbacks, suffices to explain the measured accuracy. (ii) The fraction of amoebae that differentiates into spores increases monotonically with the total number of cells. This fraction rises from an average of 73.6% for total cell numbers below 30 and reaches 86.0% for cell numbers between 170 and 200 (it remains steady thereafter at around 86%). Correspondingly, the fraction of amoebae differentiating into stalk or basal disc decreases viith total size. These trends are in accordance with evolutionary expectations and imply that a mechanism for sensing the overall size of the aggregate also plays an essential role in the determination of cell-type proportions.

TolA mediates the differential detergent resistance pattern between the Salmonella enterica subsp enterica serovars Typhi and Typhimurium

The tol-pal genes are essential for maintaining the outer membrane integrity and detergent resistance in various Gram-negative bacteria, including Salmonella. The role of TolA has been well established for the bile resistance of Salmonella enterica subsp. enterica serovar Typhimurium. We compared the bile resistance pattern between the S. enterica serovars Typhi and Typhimurium and observed that Typhi is more resistant to bile-mediated damage. A closer look revealed a significant difference in the TolA sequence between the two serovars which contributes to the differential detergent resistance. The tolA knockout of both the serovars behaves completely differently in terms of membrane organization and morphology. The role of the Pal proteins and difference in LPS organization between the two serovars were verified and were found to have no direct connection with the altered bile resistance. In normal Luria broth (LB), S. Typhi Delta tolA is filamentous while S. Typhimurium Delta tolA grows as single cells, similar to the wildtype. In low osmolarity LB, however, S. Typhimurium Delta tolA started chaining and S. Typhi Delta tolA showed no growth. Further investigation revealed that the chaining phenomenon observed was the result of failure of the outer membrane to separate in the dividing cells. Taken together, the results substantiate the evolution of a shorter TolA in S. Typhi to counteract high bile concentrations, at the cost of lower osmotic tolerance.

Off-line signature verification using genetically optimized weighted features

This paper is concerned with off-line signature verification. Four different types of pattern representation schemes have been implemented, viz., geometric features, moment-based representations, envelope characteristics and tree-structured Wavelet features. The individual feature components in a representation are weighed by their pattern characterization capability using Genetic Algorithms. The conclusions of the four subsystems teach depending on a representation scheme) are combined to form a final decision on the validity of signature. Threshold-based classifiers (including the traditional confidence-interval classifier), neighbourhood classifiers and their combinations were studied. Benefits of using forged signatures for training purposes have been assessed. Experimental results show that combination of the Feature-based classifiers increases verification accuracy. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

Vitellins and vitellogenins of Dysdercus koenigii (Heteroptera : Pyrrhocoridae) - identification, purification and temporal pattern

Two vitellins, VtA and VtB, were purified from the eggs of Dysdercus koenigii by gel filtration and ion exchange chromatography. VtA and VtB have molecular weights of 290 and 260 kDa, respectively. Both Vts are glycolipoproteinaceous in nature. VtA is composed of three polypeptides of M-r 116, 92 and 62 kDa while VtB contained an additional subunit of M-r 40 kDa. All subunits except the 116-kDa subunit are glycolipopolypeptides. Polyclonal antibody raised against VtA (anti-VtA antibody) cross-reacted with VtB and also with vitellogenic haemolymph and ovaries and pre-vitellogenic fat bodies, but not with haemolymph from either adult male, fifth instar female, or pre-vitellogenic females demonstrating sex and stage specificity of the Vts. Immunoblots in the presence of anti-VtA revealed two proteins (of 290 and 260 kDa) in both vitellogenic haemolymph and pre-vitellogenic fat bodies that are recognised as D. koenigii Vgs. In newly emerged females, Vgs appeared on day 1 in fat bodies and on day 3 in haemolymph and ovaries. Vg concentration was maximum on day 2 in fat body, day 4 in haemolymph and day 7 in ovary. Although the biochemical and temporal characteristics of these proteins show similarity to some hemipterans, they are strikingly dissimilar with those of a very closely related species. (C) 1999 Elsevier Science Inc. All rights reserved.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Direct and sensitized (energy and electron transfer) geometric isomerization of stilbene within zeolites: a comparison between solution and zeolite as reaction media

The trans- and cis-stilbenes upon inclusion in NaY zeolite are thermally stable. Direct excitation and triplet sensitization results in geometric isomerization and the excited state behavior under these conditions are similar to that in solution. Upon direct excitation, a photostationary state consisting of 65% cis and 35% trans isomers is established. Triplet sensitization with 2-acetonaphthone gave a photostationary state consisting of 63% cis and 37% trans isomers. These numbers are similar to the ones obtained in solution. Thus, the presence of cations and the confined space within the zeolite have very little influence on the overall chemistry during direct and triplet sensitization. However, upon electron transfer sensitization with N-methylacridinium (NMA) as the sensitizer within NaY, isomerization from cis-stilbene radical cation to trans-stilbene occurs and the recombination of radical ions results in triplet stilbene. Prolonged irradiation gave a photostationary state (65% cis and 35% trans) similar to triplet sensitization. This behavior is unique to the zeolite and does not take place in solution. Steady state fluorescence measurements showed that the majority of stilbene molecules are close to the N-methylacridinium sensitizer. Diffuse reflectance flash photolysis studies established that independent of the isomer being sensitized only trans radical cation is formed. Triplet stilbene is believed to be generated via recombination of stilbene radical cation and sensitizer radical anion. One should be careful in using acidic HY zeolite as a medium for photoisomerization of stilbenes. In our hands, in these acidic zeolites isomerization dominated the photoisomerization. (C) 2002 Elsevier Science B.V. All rights reserved.

Light-induced geometric isomerization of 1,2-diphenylcyclopropanes included within Y zeolites: Role of cation-guest binding

Through a systematic study of several diphenylcyclopropane derivatives, we have inferred that the cations present within a zeolite control the excited-state chemistry of these systems. In the parent 1,2-diphenylcylopropane, the cation binds to the two phenyl rings in a sandwich-type arrangement, and such a mode of binding prevents cis-to-trans isomerization. Once an ester or amide group is introduced into the system (derivatives of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid), the cation binds to the carbonyl group present in these chromophores and such a binding has no influence on the cis-trans isomerization process. Cation-reactant structures computed at density functional theory level have been very valuable in rationalizing the observed photochemical behavior of diphenylcyclopropane derivatives included in zeolites. While the parent system, 1,2-diphenyleylopropane, has been extensively investigated in the context of chiral induction in solution, owing to its failure to isomerize from cis to trans, the same could not be investigated in zeolites. However, esters of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid could be studied within zeolites in the context of chiral induction. Chiral induction as high 20% ee and 55% de has been obtained with selected systems. These numbers, although low, are much higher than what has been obtained in solution with the same system or with the parent system by other investigators (maximum similar to10% ee).

Molecular cloning and expression pattern of a Cubitus interruptus homologue from the mulberry silkworm Bombyx mori

A homologue of the segment polarity gene Cubitus interruptus from Bombyx Mori, (BmCi) has been cloned and characterized. This region harbouring Zn2+ finger motif is highly conserved across species. In B. Mori, BmCi RNA expression was first detected at stage 6 of embryogenesis, which reached maximum levels at stage 21C and was maintained until larval hatching. The segmentally reiterated striped pattern of transcript distribution in stage 21C embryos was in conformity with its predicted segment polarity nature. BmCi was expressed in the fore- and hind-wing discs, ovaries, testes and gut during fifth larval intermolt, reminiscent of its expression domains in Drosophila. Besides, BmCi expression was seen in the. anterior part of the middle silkglands in late embryonic stages, and this pattern was maintained during larval development. The transition from third to fourth and fifth larval intermolts was accompanied by an increase in the transcript levels in the middle silkglands. Our results demonstrate the presence of a novel expression domain for Ci in Bombyx. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Expression pattern of Cubitus interruptus from the mulberry silkworm Bombyx mori in late developmental stages

A partial genomic clone of Bombyx mori homologue of the segment polarity gene Cubitus interruptus (BmCi), encoding the conserved zinc finger domain and harbouring two introns, has been characterized. BmCi was expressed in the silkglands of B. mori from embryonic to the late larval stages(3rd, 4th and 5th intermoults). The expression was confined to the anterior region of the middle silkglands, overlapping with the domain of sericin-2 expression and excluding the domains of Bm invected expression, namely the middle and posterior regions of the middle silkglands. In the wing discs, the expression was restricted to the anterior compartment, which increased from 4th to 5th larval intermoults and declined later in the pupal wing buds. In gonadal tissues (both ovaries and testes) BmCi was expressed from the larval to pupal stages. The transcripts were localized to the sperm tubes containing spermatogonia in the testis of Bombyx larvae. BmCi expression, however, was not detected in any of these tissues during the moulting stages. Expression of Ci in the wing discs and gonads is evolutionarily conserved, while the silkgland represents a novel domain. Our results imply that BmCi is involved in the specification and maintenance of micro-compartment identity within the middle silkglands.