116 resultados para Geometry of numbers


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Despite their small size, some insects, such as crickets, can produce high amplitude mating songs by rubbing their wings together. By exploiting structural resonance for sound radiation, crickets broadcast species-specific songs at a sharply tuned frequency. Such songs enhance the range of signal transmission, contain information about the signaler's quality, and allow mate choice. The production of pure tones requires elaborate structural mechanisms that control and sustain resonance at the species-specific frequency. Tree crickets differ sharply from this scheme. Although they use a resonant system to produce sound, tree crickets can produce high amplitude songs at different frequencies, varying by as much as an octave. Based on an investigation of the driving mechanism and the resonant system, using laser Doppler vibrometry and finite element modeling, we show that it is the distinctive geometry of the crickets' forewings (the resonant system) that is responsible for their capacity to vary frequency. The long, enlarged wings enable the production of high amplitude songs; however, as a mechanical consequence of the high aspect ratio, the resonant structures have multiple resonant modes that are similar in frequency. The drive produced by the singing apparatus cannot, therefore, be locked to a single frequency, and different resonant modes can easily be engaged, allowing individual males to vary the carrier frequency of their songs. Such flexibility in sound production, decoupling body size and song frequency, has important implications for conventional views of mate choice, and offers inspiration for the design of miniature, multifrequency, resonant acoustic radiators.

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Three dimensional digital model of a representative human kidney is needed for a surgical simulator that is capable of simulating a laparoscopic surgery involving kidney. Buying a three dimensional computer model of a representative human kidney, or reconstructing a human kidney from an image sequence using commercial software, both involve (sometimes significant amount of) money. In this paper, author has shown that one can obtain a three dimensional surface model of human kidney by making use of images from the Visible Human Data Set and a few free software packages (ImageJ, ITK-SNAP, and MeshLab in particular). Images from the Visible Human Data Set, and the software packages used here, both do not cost anything. Hence, the practice of extracting the geometry of a representative human kidney for free, as illustrated in the present work, could be a free alternative to the use of expensive commercial software or to the purchase of a digital model.

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Flap dynamics of HIV-1 protease (HIV-pr) controls the entry of inhibitors and substrates to the active site. Dynamical models from previous simulations are not all consistent with each other and not all are supported by the NMR results. In the present work, the er effect of force field on the dynamics of HIV-pr is investigated by MD simulations using three AMBER force fields ff99, ff99SB, and ff03. The generalized order parameters for amide backbone are calculated from the three force fields and compared with the NMR S2 values. We found that the ff99SB and ff03 force field calculated order parameters agree reasonably well with the NMR S2 values, whereas ff99 calculated values deviate most from the NMR order parameters. Stereochemical geometry of protein models from each force field also agrees well with the remarks from NMR S2 values. However, between ff99SB and ff03, there are several differences, most notably in the loop regions. It is found that these loops are, in general, more flexible in the ff03 force field. This results in a larger active site cavity in the simulation with the ff03 force field. The effect of this difference in computer-aided drug design against flexible receptors is discussed.

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The nonlinear equations for coupled elastic flapping-twisting motion of a dragonfly in- spired smart flapping wing are used for a flapping wing actuated from the root by a PZT unimorph in the piezofan configuration. Excitation by the piezoelectric harmonic force generates only the flap bending motion, which in turn, induces the elastic twist motion due to interaction between flexural and torsional vibrations modes. An unsteady aerodynamic model is used to obtain the aerodynamic forces. Numerical simulations are performed using a wing whose size is the same as the dragonfly Sympetrum Frequens wing. It is found that the value of average lift reaches to its maximum when the smart flapping wing is excited at a frequency closer to the natural frequency in torsion. Moreover, consideration of the elastic twisting of flapping wing leads to an increase in the lift force. It is also found that the flapping wing generates sufficient lift to support its own weight and carry a small pay- load. Therefore, the piezoelectrically actuated smart flapping wing based on the geometry of Sympetrum Frequens wing and undergoing flapping-twisting motions may be considered as a potential candidate for use in MAV applications.

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We describe the synthesis, crystal structures, and optical absorption spectra of transition metal substituted spiroffite derivatives, Zn2-xMxTe3O8 (M-II = Co, Ni, Cu; 0 < x <= 1.0). The oxides are readily synthesized by solid state reaction of stoichiometric mixtures of the constituent binaries at 620 degrees C. Reitveld refinement of the crystal structures from powder X-ray diffraction (XRD) data shows that the Zn/MO6 octahedra are strongly distorted, as in the parent Zn2Te3O8 structure, consisting of five relatively short Zn/M-II-O bonds (1.898-2.236 angstrom) and one longer Zn/M-II-O bond (2.356-2.519 angstrom). We have interpreted the unique colors and the optical absorption/diffuse reflectance spectra of Zn2-xMxTe3O8 in the visible, in terms of the observed/irregular coordination geometry of the Zn/M-II-O chromophores. We could not however prepare the fully substituted M2Te3O8 (M-II = Co, Ni, Cu) by the direct solid state reaction method. Density Functional Theory (DFT) modeling of the electronic structure of both the parent and the transition metal substituted derivatives provides new insights into the bonding and the role of transition metals toward the origin of color in these materials. We believe that transition metal substituted spiroffites Zn2-xMxTe3O8 reported here suggest new directions for the development of colored inorganic materials/pigments featuring irregular/distorted oxygen coordination polyhedra around transition metal ions.

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Extending the previous work of Lan et al. J. Chem. Phys., 122, 224315 (2005)], a multi-state potential model for the H atom photodissociation is presented. All three ``disappearing coordinates'' of the departing H atom have been considered. Ab initio CASSCF computations have been carried out for the linear COH geometry of C-2v symmetry, and for several COH angles with the OH group in the ring plane and also perpendicular to the ring plane. By keeping the C6H5O fragment frozen in a C-2v-constrained geometry throughout, we have been able to apply symmetry-based simplifications in the constructions of a diabatic model. This model is able to capture the overall trends of twelve adiabats at both torsional limits for a wide range of COH bend angles.

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This paper presents the design and development of a novel optical vehicle classifier system, which is based on interruption of laser beams, that is suitable for use in places with poor transportation infrastructure. The system can estimate the speed, axle count, wheelbase, tire diameter, and the lane of motion of a vehicle. The design of the system eliminates the need for careful optical alignment, whereas the proposed estimation strategies render the estimates insensitive to angular mounting errors and to unevenness of the road. Strategies to estimate vehicular parameters are described along with the optimization of the geometry of the system to minimize estimation errors due to quantization. The system is subsequently fabricated, and the proposed features of the system are experimentally demonstrated. The relative errors in the estimation of velocity and tire diameter are shown to be within 0.5% and to change by less than 17% for angular mounting errors up to 30 degrees. In the field, the classifier demonstrates accuracy better than 97.5% and 94%, respectively, in the estimation of the wheelbase and lane of motion and can classify vehicles with an average accuracy of over 89.5%.

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Conformational diversity or shapeshifting in cyclic peptide natural products can, in principle, confer a single molecular entity with the property of binding to multiple receptors. Conformational equilibria have been probed in the contryphans, which are peptides derived from Conus venom possessing a 23-membered cyclic disulfide moiety. The natural sequences derived from Conus inscriptus, GCV(D)LYPWC* (In936) and Conus loroisii, GCP(D)WDPWC* (Lo959) differ in the number of proline residues within the macrocyclic ring. Structural characterisation of distinct conformational states arising from cis-trans equilibria about Xxx-Pro bonds is reported. Isomerisation about the C2-P3 bond is observed in the case of Lo959 and about the Y5-P6 bond in In936. Evidence is presented for as many as four distinct species in the case of the synthetic analogue V3P In936. The Tyr-Pro-Trp segment in In936 is characterised by distinct sidechain orientations as a consequence of aromatic/proline interactions as evidenced by specific sidechain-sidechain nuclear Overhauser effects and ring current shifted proton chemical shifts. Molecular dynamics simulations suggest that Tyr5 and Trp7 sidechain conformations are correlated and depend on the geometry of the Xxx-Pro bond. Thermodynamic parameters are derived for the cis trans equilibrium for In936. Studies on synthetic analogues provide insights into the role of sequence effects in modulating isomerisation about Xxx-Pro bonds.

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Restriction enzyme KpnI is a HNH superfamily endonuclease requiring divalent metal ions for DNA cleavage but not for binding. The active site of KpnI can accommodate metal ions of different atomic radii for DNA cleavage. Although Mg2+ ion higher than 500 mu M mediates promiscuous activity, Ca2+ suppresses the promiscuity and induces high cleavage fidelity. Here, we report that a conservative mutation of the metal-coordinating residue D148 to Glu results in the elimination of the Ca2+-mediated cleavage but imparting high cleavage fidelity with Mg2+. High cleavage fidelity of the mutant D148E is achieved through better discrimination of the target site at the binding and cleavage steps. Biochemical experiments and molecular dynamics simulations suggest that the mutation inhibits Ca2+-mediated cleavage activity by altering the geometry of the Ca2+-bound HNH active site. Although the D148E mutant reduces the specific activity of the enzyme, we identified a suppressor mutation that increases the turnover rate to restore the specific activity of the high fidelity mutant to the wild-type level. Our results show that active site plasticity in coordinating different metal ions is related to KpnI promiscuous activity, and tinkering the metal ion coordination is a plausible way to reduce promiscuous activity of metalloenzymes.

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Thiolases are essential CoA-dependent enzymes in lipid metabolism. In the present study we report the crystal structures of trypanosomal and leishmanial SCP2 (sterol carrier protein, type-2)-thiolases. Trypanosomatidae cause various widespread devastating (sub)-tropical diseases, for which adequate treatment is lacking. The structures reveal the unique geometry of the active site of this poorly characterized subfamily of thiolases. The key catalytic residues of the classical thiolases are two cysteine residues, functioning as a nucleophile and an acid/base respectively. The latter cysteine residue is part of a CxG motif. Interestingly, this cysteine residue is not conserved in SCP2-thiolases. The structural comparisons now show that in SCP2-thiolases the catalytic acid/base is provided by the cysteine residue of the HDCF motif, which is unique for this thiolase subfamily. This HDCF cysteine residue is spatially equivalent to the CxG cysteine residue of classical thiolases. The HDCF cysteine residue is activated for acid/base catalysis by two main chain NH-atoms, instead of two water molecules, as present in the CxG active site. The structural results have been complemented with enzyme activity data, confirming the importance of the HDCF cysteine residue for catalysis. The data obtained suggest that these trypanosomatid SCP2-thiolases are biosynthetic thiolases. These findings provide promise for drug discovery as biosynthetic thiolases catalyse the first step of the sterol biosynthesis pathway that is essential in several of these parasites.

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In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.

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Synergizing graphene on silicon based nanostructures is pivotal in advancing nano-electronic device technology. A combination of molecular dynamics and density functional theory has been used to predict the electronic energy band structure and photo-emission spectrum for graphene-Si system with silicon as a substrate for graphene. The equilibrium geometry of the system after energy minimization is obtained from molecular dynamics simulations. For the stable geometry obtained, density functional theory calculations are employed to determine the energy band structure and dielectric constant of the system. Further the work function of the system which is a direct consequence of photoemission spectrum is calculated from the energy band structure using random phase approximations.

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The allowed and the ``disallowed'' regions in the celebrated Ramachandran map (phi-psi] map) was elegantly deduced by Ramachandran, Ramakrishnan and Sasisekharan even before the protein crystal structures became available. This powerful map was derived based on rigid geometry of the peptide group and later several investigations on protein crystal structures reported the occurrence of a small fraction of the phi-psi] torsion angles in the disallowed region. The question is what factors make these residues adopt disallowed conformations? Is it driven by the necessity to maintain the overall topology or is it associated with function or is it just that the disallowed conformations are extreme limits of the allowed conformations? Today, with the availability of a large number of high resolution crystal structures, we have revisited this problem. Apart from validating some of the earlier findings such as residue propensities, preferred location in the secondary structure, we have explored their spatial neighborhood preferences using the protein structure network PSN] approach developed in our lab. Finally, the structural and functional implications of the disallowed conformations are examined.

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A regular secondary structure is described by a well defined set of values for the backbone dihedral angles (phi,psi and omega) in a polypeptide chain. However in real protein structures small local variations give rise to distortions from the ideal structures, which can lead to considerable variation in higher order organization. Protein structure analysis and accurate assignment of various structural elements, especially their terminii, are important first step in protein structure prediction and design. Various algorithms are available for assigning secondary structure elements in proteins but some lacunae still exist. In this study, results of a recently developed in-house program ASSP have been compared with those from STRIDE, in identification of alpha-helical regions in both globular and membrane proteins. It is found that, while a combination of hydrogen bond patterns and backbone torsional angles (phi-psi) are generally used to define secondary structure elements, the geometry of the C-alpha atom trace by itself is sufficient to define the parameters of helical structures in proteins. It is also possible to differentiate the various helical structures by their C-alpha trace and identify the deviations occurring both at mid-positions as well as at the terminii of alpha-helices, which often lead to occurrence of 3(10) and pi-helical fragments in both globular and membrane proteins.

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Bent-core mesogens are an important class of thermotropic liquid crystals as they exhibit unusual properties as well as morphologies distinctly different from rodlike mesogens. Two bent-core mesogens with differing center rings namely benzene and thiophene are considered and investigated using high-resolution oriented solid state C-13 NMR method in their liquid crystalline phases. The mesogens exhibit different phase sequences with the benzene-based mesogen showing a B-1 phase, while the one based on thiophene showing nematic and smectic C phases. The 2-dimensional separated local field (2D-SLF) NMR method was used to obtain the C-13-H-1 dipolar couplings of carbons in the center ring as well as in the side-wing phenyl rings. Couplings, characteristic of the type of the center ring, that also provide orientational information on the molecule in the magnetic field were observed. Together with the dipolar couplings of the side-wing phenyl ring carbons from which the local order parameters of the different subunits of the core could be extracted, the bent angle of the mesogenic molecule could be obtained. Accordingly, for the benzene mesogen in its B-1 phase at 145 degrees C, the center ring methine C-13-H-1 dipolar couplings were found to be significantly larger (9.5-10.2 kHz) compared to those of the side-wing rings (1.6-2.1 kHz). From the local order parameter values of the center (0.68) as well as the side-wing rings (0.50), a bent-angle of 130.3 degrees for this mesogen was obtained. Interestingly, for the thiophene mesogen in its smectic C phase at 210 degrees C, the C-13-H-1 dipolar coupling of the center ring methine carbon (2.11 kHz) is smaller than those of the side-wing phenyl ring carbons (2.75-3.00 kHz) which is a consequence of the different structures of the thiophene and the benzene rings. These values correspond to local order parameters of 0.85 for the center thiophene ring and 0.76 for the first side-wing phenyl ring and a bent-angle of 149.2 degrees. Thus, the significant differences in the dipolar couplings and the order parameter values between different parts in the rigid core of the mesogens are a direct consequence of the nature of the center ring and the bent structure of the molecule. The present investigation thus highlights the ability of the C-13 2D-SLF technique to provide the geometry of the bent-core mesogens in a straightforward manner through the measurement of the C-13-H-1 dipolar couplings.