Quadratic Index Research Articles

New Antitrichomonal Drug-like Chemicals Selected by Bond (Edge)-Based TOMOCOMD-CARDD Descriptors

Bond-based quadratic indices, new TOMOCOMD-CARDD molecular descriptors, and linear discriminant analysis (LDA) were used to discover novel lead trichomonacidals. The obtained LDA-based quantitative structure-activity relationships (QSAR) models, using nonstochastic and stochastic indices, were able to classify correctly 87.91% (87.50%) and 89.01% (84.38%) of the chemicals in training (test) sets, respectively. They showed large Matthews correlation coefficients of 0.75 (0.71) and 0.78 (0.65) for the training (test) sets, correspondingly. Later, both models were applied to the virtual screening of 21 chemicals to find new lead antitrichomonal agents. Predictions agreed with experimental results to a great extent because a correct classification for both models of 95.24% (20 of 21) of the chemicals was obtained. Of the 21 compounds that were screened and synthesized, 2 molecules (chemicals G-1, UC-245) showed high to moderate cytocidal activity at the concentration of 10 microg/ml, another 2 compounds (G-0 and CRIS-148) showed high cytocidal activity only at the concentration of 100 microg/ml, and the remaining chemicals (from CRIS-105 to CRIS-153, except CRIS-148) were inactive at these assayed concentrations. Finally, the best candidate, G-1 (cytocidal activity of 100% at 10 microg/ml) was in vivo assayed in ovariectomized Wistar rats achieving promising results as a trichomonacidal drug-like compound.

The design of a controllable imaging device with the cold atomic medium

Under the circumstance of a Gaussian control field, the cold atomic medium with electromagnetically induced transparency (EIT) turns out to be the special medium with the quadratic index distribution which is controllable online. In our study, the optical system occupies a portion of the EIT medium which acts as an imaging device. With the help of the Collins formula, the analytic expression for the spatial distribution of the probe field in the cold atomic medium is obtained as well as the location of the imaging. The methods for improving the visibility of the imaging are proposed in this paper. Moreover, we also show that the shapes of the images on the output are strongly influenced by the intensity of the control field, which provides a potential optical processing method.

LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case

AbstractBased on the multi‐objective optimization strategy and linear matrix inequality approach, the problem of reliable guaranteed cost control with multiple criteria constraints is investigated for a class of uncertain discrete‐time systems subject to actuator faults. A fault model in actuators, which considers outage or partial degradation in independent actuators, is adopted. The quadratic stability is proved to be independent of the disturbance and the upper bound of a quadratic cost index is improved. The reliable feedback controller is designed to minimize the upper bound of the quadratic cost index, place all the closed‐loop poles in a specified disk, constrain the H∞ norm level of the disturbance attenuation into a given range and guarantee the magnitudes of control inputs less than the given bound, as well. Thus, the resulting closed‐loop system can provide satisfactory stability, transient behavior, disturbance rejection level and optimized upper bound of the quadratic cost performance despite possible actuator faults. Copyright © 2008 John Wiley & Sons, Ltd.

Virtual dielectric waveguide mode description of a high-gain free-electron laser. I. Theory

A set of mode-coupled excitation equations for the slowly growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser (FEL), including the effects of longitudinal space charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single Gaussian mode.

Response to selection from using identified genes and quadratic indices in two-traits breeding goals

Benefits from the use of optimised selection for maximising genetic gain while constraining the rate of inbreeding were evaluated through stochastic simulation for scenarios where the breeding goal includes two negatively correlated traits. One of the traits was controlled only by polygenes and had a heritability of 0.3 while the other trait was controlled by an identified additive biallelic QTL (with an initial allele frequency of 0.15) and by polygenes and had a polygenic heritability of 0.1. Optimised selection was compared to standard truncation selection both when the information on the QTL was used and when it was ignored. Extra gains in the breeding goal were observed throughout the 10 simulated generations from the combined use of optimised contributions and QTL information although, as expected, this scheme was not the most effective for improving individual traits. By generation ten, the gain in the aggregate breeding value with optimised selection was about 12% higher than with truncation selection. Optimised selection allowed extra polygenic responses in both traits but these extra responses were negative for the trait under mixed inheritance. The use of the QTL allowed not only positive gains in the trait with the lowest heritability, but also avoided the loss of the favourable allele. The effect of selecting for the QTL on each trait depended on its relative weight in the selection index and not exclusively on the inheritance model.

Regulation of a Manned Sea-Surface Vehicle via Stochastic Optimal Control.

A control system is proposed for the regulation problem of the roll-motion of a manned sea-surface vehicle. Taking into account the roll-ship equations coming from the Conolly theory, a novel stochastic model has been proposed for the uncertainties driving the total mechanical torque acting on the vehicle, deriving from the wind and/or the sea-wave action. The proposed model results in a bilinear stochastic system to which a feedback controller is applied, giving linear-optimal performance with respect to a classical quadratic index. Open loop simulations carried out on real data validate the choice of the stochastic model of the uncertainties, producing a ship-roll time evolution which resembles the real data. Closed loop simulations on a virtual ship show the effectiveness of the proposed control scheme.

Suboptimal control based on hill-climbing method for time delay systems

Recent efforts are encountered to obtain suboptimal controllers using evolutionary algorithms on control of system without delays, including proportional integral derivative (PID) controllers. However, the problem of optimisation on delay control systems has been solved through traditional techniques based on search optimal control. A numerical optimisation problem for a kind of time delay control system is presented. A suboptimal control law is synthesised using a method based on the hill-climbing algorithm, in order to minimise a quadratic index. The stability analysis for the proposed controller is proposed. Finally, experimental results using the proposed method are shown.

Double objective optimal multivariable ripple-free deadbeat control

This paper presents novel results on optimal multivariable deadbeat control. Given a discrete-time, stable, linear, time invariant plant model, we give a simple parameterization of all stabilizing ripple-free deadbeat controllers of a given order. The free parameter is then optimized in the sense that a quadratic index is kept minimal. The optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort. The proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor. Simulation results are included to illustrate the effectiveness of the proposed design algorithm.

Atom‐Based 2D Quadratic Indices in Drug Discovery of Novel Tyrosinase Inhibitors: Results of In Silico Studies Supported by Experimental Results

AbstractHerein we present results of QSAR studies of tyrosinase inhibitors employing one of the atom‐based TOMOCOMD‐CARDD (acronym of TOpological MOlecular COMputer Design‐Computer Aided “Rational” Drug Design) descriptors, molecular quadratic indices, and Linear Discriminant Analysis (LDA) as pattern recognition method. In this way, a database of 246 organic chemicals, reported as tyrosinase inhibitors having great structural variability, was analyzed and presented as a helpful tool, not only for theoretical chemists but also for other researchers in this area. In total, 12 LDA‐based QSAR models were obtained, the first six with the non‐stochastic total and local quadratic indices and the six remaining models with the stochastic molecular descriptors. The best two models for the non‐stochastic and stochastic molecular descriptors, showed an appropriate overall accuracy (92.68 and 89.10%, respectively) and a high Matthews correlation coefficient (C of 0.85 and of 0.84, correspondingly) when applied to the training set. External validation series were also used to validate the obtained models; the 91.67% (C=0.82) and 90.00% (C=0.78), were correctly classified, respectively. In order to show the possibilities of the present approach for the ligand‐based virtual screening of tyrosinase inhibitors, the developed models were used afterwards in a simulation of a virtual search for tyrosinase inhibitors. For instance, more than 93% (93.33%) and 96% (96.66%) of the screened chemicals were correctly classified by the two best LDA‐based QSAR models developed with non‐stochastic and stochastic quadratic indices, respectively. Finally, the combination of the obtained models permitted the selection/identification of new diterpenoidal alkaloid leads as tyrosinase inhibitors. The found activity is supported by observed inhibitory effects on mushroom tyrosinase enzyme, even comparable with some reference tyrosinase inhibitors. These results support a role for TOMOCOMD‐CARDD descriptors in the biosilico discovery of novel tyrosinase inhibitors from large databases of chemical structures (virtual or “in silico”), which may be used to prevent or treat pigmentation disorders.

Estadificación del cáncer de recto mediante ultrasonografía endoscópica: correlación con la estadificación histológica

our aim was to evaluate the accuracy of endosonography (EUS) in our experience, to stage rectal cancer. we prospectively included all patients with rectal cancer staged in our unit from September 2002 until February 2006 in a database. We selected those patients who had a complete EUS examination and were surgically treated without neoadjuvant therapy. Once we had the results of the histopathological staging (pTN), which was considered the gold standard, we compared the results of the previous EUS staging (uTN) with those of the pTN. We calculated the sensitivity, specificity, positive predictive value, negative predictive value and accuracy for each T stage, and for N staging considered as N positive or negative. We also calculated the global accuracy for T stage. We also calculated the agreement of uTN with pTN staging using the kappa index for N stage, and quadratic weighted kappa index for T stage. we staged 120 patients with rectal cancer during the mentioned period. Of these, 36 patients met inclusion criteria and were evaluated, 21 women and 15 men. Mean age was 68,53+/-10,15 yo (range: 48-90). Global T stage accuracy was 83%. N stage accuracy was 72%. We obtained a S, E, PPV, NPV and A of 91, 100, 100, 96 and 97% for T1; 82, 88, 75, 91 and 86% for T2; 86, 91, 86, 91 and 89% for T3; and 14, 86, 20, 80 and 72% for N stage respectively. Kappa value for T stage was 0,87 indicating a "very good" agreement between uT and pT according to the kappa index criteria. Kappa value for N stage agreement was 0,005; "poor" according to the same criteria. in our experience, the diagnostic accuracy of EUS for T and N staging of rectal cancer is 83% and 72% respectively, similar results as previously published. uT staging for rectal cancer shows a "very good" agreement with pT staging.

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but the presence of the transport delay terms complicates the solution rather more in the continuous-time case.

MOTION PLANNING AND OPTIMAL CONTROL OF AN AUTONOMOUS VTOL AIRCRAFT

This study presents a simple algorithm for motion-planning and state-to-state control of a Vertical Take-Off and Landing (VTOL) aircraft. The proposed motion-planning procedure is based on the solution of a linear algebraic equation. The resulting schemes are useful for flight control of an autonomous VTOL aircraft in case the objective is to transfer the system from a given state to a prescribed target. The proposed controller minimizes a selected quadratic index of performance. The solution to the (sub) optimal control problem is simple and reduces to the evaluation of a minimum point of a function of several variables.

Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals

The concept of atom-based quadratic indices is extended to a series of molecular descriptors (MDs) (both total and local) based on adjacency between edges. The kth edge-adjacency matrix (E ( k )) denotes the matrix of bond-based quadratic indices (non-stochastic) with respect to the canonical basis set. The kth "stochastic" edge-adjacency matrix, ES ( k ), is here proposed as a new molecular representation easily calculated from E ( k ). Then, the kth stochastic bond-based quadratic indices are calculated using ES ( k ) as operators of quadratic transformations. The study of six representative physicochemical properties of octane isomers was used to compare the ability of both series of MDs to produce significant quantitative structure-property relationship (QSPR) models. Moreover, the general performance of the new MDs in this QSPR study has been evaluated with respect to other 2D/3D well-known sets of indices and the obtained results shown a quite satisfactory behavior of the present method. The novel bond-level MDs were also used for the description and prediction of the boiling point of 28 alkyl-alcohols and to the modeling of the specific rate constant (log k) of 34 derivatives of 2-furylethylenes. These models were statistically significant and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment. The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) expose a good behavior of our method in this QSPR studies. The approach described in this report appears to be a very promising structural invariant, useful for QSPR/QSAR studies, similarity/diversity analysis, and computer-aided "rational" molecular (drug) design.

Towards a unifying approach to diversity measures: Bridging the gap between the Shannon entropy and Rao's quadratic index

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity ( Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.

Characterization of trabecular bone structure from high-resolution magnetic resonance images using fuzzy logic

The purpose of this work was to apply fuzzy logic image processing techniques to characterize the trabecular bone structure with high-resolution magnetic resonance images. Fifteen ex vivo high-resolution magnetic resonance images of specimens of human radii at 1.5 T and 12 in vivo high-resolution magnetic resonance images of the calcanei of peri- and postmenopausal women at 3 T were obtained. Soft segmentation using fuzzy clustering was applied to MR data to obtain fuzzy bone volume fraction maps, which were then analyzed with three-dimensional (3D) fuzzy geometrical parameters and measures of fuzziness. Geometrical parameters included fuzzy perimeter and fuzzy compactness, while measures of fuzziness included linear index of fuzziness, quadratic index of fuzziness, logarithmic fuzzy entropy, and exponential fuzzy entropy. Fuzzy parameters were validated at 1.5 T with 3D structural parameters computed from microcomputed tomography images, which allow the observation of true trabecular bone structure and with apparent MR structural indexes at 1.5 T and 3 T. The validation was statistically performed with the Pearson correlation coefficient as well as with the Bland-Altman method. Bone volume fraction correlation values (r) were up to .99 (P<.001) with good agreements based on Bland-Altman analysis showing that fuzzy clustering is a valid technique to quantify this parameter. Measures of fuzziness also showed consistent correlations to trabecular number parameters (r>.85; P<.001) and good agreements based on Bland-Altman analysis, suggesting that the level of fuzziness in high-resolution magnetic resonance images could be related to the trabecular bone structure.

Measurement of the thermal lens of grazing-incidence diode-pumped Nd:YVO4 laser amplifier

Abstract The thermally induced lensing effects of a diode-pumped Nd:YVO 4 laser amplifier in a grazing incidence bounce geometry are carefully measured experimentally. Measurements of the thermal effects are interpreted by considering the diode-pumped amplifier region as a thick lens. A more detailed modeling was made of a quadratic refractive index lens duct for the normal to the bounce plane distribution. Due to the asymmetric pumping the thermal lens shows significant astigmatism. The ratio between dioptric powers in the plane normal to bounce and in the bounce plane is measured to be approximately 20. A nonlinear component of the power dependence of the lens is observed and related to the nonlinear heating induced by energy transfer upconversion. Measurements made under non-lasing conditions are used to infer thermal lensing behavior under lasing conditions and this allows optimization of optical resonator design.

Non-stochastic quadratic fingerprints and LDA-based QSAR models in hit and lead generation through virtual screening: theoretical and experimental assessment of a promising method for the discovery of new antimalarial compounds

In order to explore the ability of non-stochastic quadratic indices to encode chemical information in antimalarials, four quantitative models for the discrimination of compounds having this property were generated and statistically compared. Accuracies of 90.2% and 83.3% for the training and test sets, respectively, were observed for the best of all the models, which included non-stochastic quadratic fingerprints weighted with Pauling electronegativities. With a comparative purpose and as a second validation experiment, an exercise of virtual screening of 65 already-reported antimalarials was carried out. Finally, 17 new compounds were classified as either active/inactive ones and experimentally evaluated for their potential antimalarial properties on the ferriprotoporphyrin (FP) IX biocrystallization inhibition test (FBIT). The theoretical predictions were in agreement with the experimental results. In the assayed test compound C5 resulted more active than chloroquine. The current result illustrates the usefulness of the TOMOCOMD-CARDD strategy in rational antimalarial-drug design, at the time that it introduces a new family of organic compounds as starting point for the development of promising antimalarials.

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues is proposed. It is showed that this tuning criterion is equivalent to H ∞ optimal control. Under the proposed criterion, the tuning problem is stated as an optimization problem, in which the complex/real ratio of the characteristic matrix eigenvalues, a Lyapunov quadratic index, and the spectral abscissa were simultaneously minimized. Proposed criterion was applied to the multivariate controls of a distillation column, and a non-linear chemical reactor, both reported in the literature.

Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.

Atom-based 3D-chiral quadratic indices. Part 2: Prediction of the corticosteroid-binding globulinbinding affinity of the 31 benchmark steroids data set

A quantitative structure–activity relationship (QSAR) study to predict the relative affinities of the steroid ‘benchmark’ data set to the corticosteroid-binding globulin (CBG) is described. It is shown that the 3D-chiral quadratic indices closely correlate with the measured CBG affinity values for the 31 steroids. The calculated descriptors were correlated with biological data through multiple linear regressions. Two statistically significant models were obtained when non-stochastic ( R = 0.924 and s = 0.46) as well as stochastic ( R = 0.929 and s = 0.46) 3D-chiral quadratic indices were used. A leave-one-out (LOO) approach to model validation is used here; the best results obtained in the cross-validation procedure with non-stochastic ( q 2 = 0.781) and stochastic ( q 2 = 0.735) 3D-chiral quadratic indices are better or similar to most of the 3D-QSAR approaches reported so far. These results support the idea that the 3D-chiral quadratic indices may be helpful in prediction of the corticosteroid-binding affinity for new compounds.