Computing flow pipe of embedded hybrid systems using deep group preserving scheme

In this paper, we propose a novel methodology of numerical approximation to analyze flow of a nonlinear embedded hybrid system. For proving that all trajectories of a hybrid system do not enter an unsafe region, many classic numerical approaches such as Euler, Runge–Kutta methods for ordinary differential equations (ODEs) are applied, whereas, there exist several defects, including so-called spurious solutions and ghost fixed points. Moreover, to approximate the proper solution as much as possible, step size selection becomes especially important. In comparison, integrating group preserving scheme (GPS) which calculates true circumstance getting rid of spurious solutions and ghost fixed points, with neural network model which reduces numerical errors, deep GPS (DGPS) eliminates aforementioned adverse factors and gains better numerical approximation using a large time step size. The experimental results show that the proposed method makes safety verification for an embedded hybrid system well.

     

LC–ESI-Q-TOF-MS for faster and accurate determination of microcystins and nodularins in serum

Microcystins (MC) and nodularins (Nod) are cyclic peptide hepatotoxins and tumour promoters produced by cyanobacteria. This study deals with liquid chromatography–mass spectrometry (LC–MS) analyses of 9 major cyanobacterial peptide toxins, starting with a comparison of six small particle size reversed-phase HPLC columns, from which one, Phenomenex Synergi Hydro-RP, was chosen for further chromatography with accurate mass MS studies in a complex biological fluid, serum. The instrumentation used for the serum sample analysis included a Bruker micrO-TOF-Q-MS coupled to an Agilent 1200RR LC system. Total analysis run time per sample was 8.5 min. The Q-TOF-MS instrument was operated on auto MS–MS mode to obtain fragment ions (such as the characteristic fragment m/z 135 from Adda amino acid residue) for toxin identification purposes. Detected mass errors in serum samples were in the range of from 0.3 mDa to 9.1 mDa. The narrow mass window (±20 mDa) for mass chromatograms used in quantitation gave benefits by background noise reduction. We conclude that a LC–ESI-Q-TOF-MS instrumentation is a powerful tool for identification and quantitation of cyanobacterial peptide toxins in a biological matrix.     

Purification and antibacterial activity of recombinant warnericin RK expressed in Escherichia coli

Warnericin RK is a small cationic peptide produced by Staphylococcus warneri RK. This peptide has an antimicrobial spectrum of activity almost restricted to the Legionella genus. It is a membrane-active peptide with a proposed detergent-like mechanism of action at high concentration. Moreover, the fatty acids content of Legionella was shown to modulate the peptide activity. In order to decipher the mode of action in details using solid-state NMR spectroscopy, large amount of an isotopic labeled peptide is required. Since it is less expensive to obtain such a peptide biologically, we report here methods to express warnericin RK in Escherichia coli with or without a fusion partner and to purify resulting recombinant peptides. The cDNA fragment encoding warnericin RK was synthesized and ligated into three expression vectors. Two fusion peptides, carrying polyhistidine tag in N- or C-terminal and a native peptide, without tag, were expressed in E. coli cells. Fusion peptides were purified, with a yield of 3 mg/l, by affinity chromatography and reverse-phase HPLC. The recombinant native peptide was purified using a two-step purification method consisting of a hydrophobic chromatography followed by a reverse-phase HPLC step with a yield of 1.4 mg/l. However, the anti-Legionella activity was lower for both tagged peptide probably because of structural modifications. So, the native recombinant peptide was preferentially chosen for ¹⁵N-labeling experiments. Our results suggest that the developed production and purification procedures will be useful in obtaining a large quantity of recombinant isotope-labeled warnericin RK for further studies.     

Comparative analysis of numerical integration schemes of density equation for a computational model of bone remodelling

In this study, a computational model of bone remodelling problem as proposed by Weinans et al. (1992) is described and solved by other temporal integration techniques different from the Euler scheme. This model considers three types of numerical integration schemes of the evolution of the material density during the remodelling: Euler, Heun and Runge-Kutta methods. Also the strain and the density field are obtained inside each element, at Gauss points or at the nodes of the mesh. A square plate with 1.00?m of side subjected to non-uniform pressure is simulated with two meshes of quadrilateral element with size [Formula: see text] and [Formula: see text]?m. Two increments time size: [Formula: see text] and [Formula: see text] days are used. The results show that Euler, Heun and Runge-Kutta's methods correctly approached the problem of bone remodelling and that there were no appreciable differences in the patterns obtained by the mesh and time step used. In contrast, using an element-based approach and node-based approach, substantial differences were produced in bone remodelling density pattern. 'Chess board' type discontinuities were found in the element approach near the applied pressure area, as were well-defined columns away from this. The node-based approach showed continuity in density distribution. These patterns were well represented by the methods for resolving the density equation. This study concluded that any method of time integration could be used for these meshes and time steps size.     

Detergent-Like Activity and α-Helical Structure of Warnericin RK, an Anti-Legionella Peptide

Warnericin RK is the first antimicrobial peptide known to be active against Legionella pneumophila, a pathogen bacterium that is responsible for severe pneumonia. Strikingly, this peptide displays a very narrow range of antimicrobial activity, almost limited to the Legionella genus, and a hemolytic activity. A similar activity has been described for δ-lysin, a well-known hemolytic peptide of Staphylococci that has not been described as antimicrobial. In this study we aimed to understand the mode of action of warnericin RK and to explain its particular target specificity. We found that warnericin RK permeabilizes artificial membranes in a voltage-independent manner. Osmotic protection experiments on erythrocytes showed that warnericin RK does not form well-defined pores, suggesting a detergent-like mode of action, as previously described for δ-lysin at high concentrations. Warnericin RK also permeabilized Legionella cells, and these cells displayed a high sensitivity to detergents. Depending on the detergent used, Legionella was from 10- to 1000-fold more sensitive than the other bacteria tested. Finally, the structure of warnericin RK was investigated by means of circular dichroism and NMR spectroscopy. The peptide adopted an amphiphilic α-helical structure, consistent with the proposed mode of action. We conclude that the specificity of warnericin RK toward Legionella results from both the detergent-like mode of action of the peptide and the high sensitivity of these bacteria to detergents.     

Suppression of Co1E1 replication properties by the Inc P-1 plasmid RK2 in hybrid plasmids constructed in vitro.

Hybrid plasmids were constructed in vitro by linking the Inc P-1 broad host range plasmid RK2 to the colicinogenic plasmid ColE1 at their EcoRI endonuclease cleavage sites. These plasmids were found to be immune to colicin E1, non-colicin-producing, and to exhibit all the characteristics of RK2 including self-transmissibility. These joint replicons have a copy number of 5 to 7 per chromosome which is typical of RK2, but not ColE1. Unlike ColE1, the plasmids will not replicate in the presence of chloramphenicol and are maintained in DNA polymerase I mutants of Escherichia coli. In addition, only RK2 incompatibility is expressed, although functional ColE1 can be rescued from the hybrids by EcoRI cleavage. This suppression of ColE1 copy number and incompatibility was found to be a unique effect of plasmid size on ColE1 properties. However, the inhibition of ColE1 or ColE1-like plasmid replication in chloramphenicol-treated cells is a specific effect of RK2 or segments of RK2 (Cri⁺ phenotype). This phenomenon is not a function of plasmid size and requires covalent linkage of RK2 DNA to ColE1. A specific region of RK2 (50.4 to 56.4 × 10³ base-pairs) cloned in the ColE1-like plasmid pBR313 was shown to carry the genetic determinant(s) for expression of the Cri⁺ phenotype.     

Computer simulation of rapidly responding forced exponential systems

Two common problems in computer simulations are the decisions to ignore or include a particular element of a system under study in a model and the choice of an appropriate integration algorithm. To examine aspects of these problems, a simple exponential system is considered in which a large simulation error is induced by a rather small truncation error. The effect of computational precision, step size and hardware selection on this error is examined at standard and extended precisions over a range of step sizes and on a variety of computers. For this model, simulation accuracy is an exponential function of the number of bits in the mantissa of the computer word. Optimal step size is a function of accuracy required and precision used; a trade-off between truncation and round-off errors becomes important as accuracy requirements increase. Machine selection is important primarily in economic terms if the required precision is available. We conclude that the effect on a simulation of small terms such as truncation errors can be unexpectedly large, that solutions should always be checked, and that high precision and wide dynamic range are important to the successful computer simulation of models such as that examined.     

Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.     

Robust numerical solution for the two parameter solute solvent transport model

Prediction of solute and solvent transport in cells is central to developing and testing cryopreservation protocols. As we show here, however, the models used can be difficult to accurately numerically integrate in some key cases, and thus are a challenge to implement when determining the time dependent cell state during cryoprotectant equilibration and cooling. Exact solution techniques exist for overcoming this problem, but their implementation is also challenging: inversion of a nonlinear function is required that negates much of the utility of the approach. This communication describes a simple approach for more robust numerical integration that can be implemented using any numerical differential equation solver, and can facilitate arbitrarily accurate solutions to transport models without the complication of inversion formulae or complicated numerical integration schemes. Further, a simple relevant example of red blood cell equilibration with 40% glycerol is presented with comments on extending the approach to other settings.     

Improving the local solution accuracy of large-scale digital image-based finite element analyses

Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.     

Combining geostatistical models and remotely sensed data to improve tropical tree richness mapping

Information on the spatial distribution and composition of biological communities is essential in designing effective strategies for biodiversity conservation and management. Reliable maps of species richness across the landscape can be useful tools for these purposes. Acquiring such information through traditional survey techniques is costly and logistically difficult. The kriging interpolation method has been widely used as an alternative to predict spatial distributions of species richness, as long as the data are spatially dependent. However, even when this requirement is met, researchers often have few sampled sites in relation to the area to be mapped. Remote sensing provides an inexpensive means to derive complete spatial coverage for large areas and can be extremely useful for estimating biodiversity. The aim of this study was to combine remotely sensed data with kriging estimates (hybrid procedures) to evaluate the possibility of improving the accuracy of tree species richness maps. We did this through the comparison of the predictive performance of three hybrid geostatistical procedures, based on tree species density recorded in 141 sampling quadrats: co-kriging (COK), kriging with external drift (KED), and regression kriging (RK). Reflectance values of spectral bands, computed NDVI and texture measurements of Landsat 7 TM imagery were used as ancillary variables in all methods. The R² values of the models increased from 0.35 for ordinary kriging to 0.41 for COK, and from 0.39 for simple regression estimates to 0.52 and 0.53 when using simple KED and RK, respectively. The R² values of the models also increased from 0.60 for multiple regression estimates to 0.62 and 0.66 when using multiple KED and RK, respectively. Overall, our results demonstrate that these procedures are capable of greatly improving estimation accuracy, with multivariate RK being clearly superior, because it produces the most accurate predictions, and because of its flexibility in modeling multivariate relationships between tree richness and remotely sensed data. We conclude that this is a valuable tool for guiding future efforts aimed at conservation and management of highly diverse tropical forests.     

A molecular approach to fertilization. II. Viability and artificial fertilization of Xenopus laevis gemetes

Conditions necessary for procuring, handling, and storing Xenopus laevis gametes have been investigated in order to develop a simple and reliable method for artificial fertilization. Temperature, sperm concentration, and ionic strength influence sperm and/or egg viability. Extension of the fertilizing capacity of sperm suspensions could be correlated with reversible repression of sperm motility. In the case of various salt solutions used for testes maceration, inhibition of sperm motility was primarily a function of the ionic strength. However, there was some specificity in the salt employed as KCl and CaCl₂ solutions gave anomalous results in comparison with those obtained with other salt solutions. The fertilizability of Xenopus laevis eggs could be extended by shedding the eggs in DeBoers solution. Using this information a simple reliable method for artificial fertilization of Xenopus laevis gametes has been described.     

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size.     

System Relaxation and Thermodynamic Integration

Abstract

The thermodynamic integration (TI) method for calculating free energy differences has three inherent problems: statistics, numerical integration, and relaxation. In this paper the latter is analyzed for the nonequilibrium TI method introduced by Postma which combines molecular dynamics simulation and TI in a very effective way. A nontrivial extrapolation technique is presented to remove the relaxation error and to calculate the underlying relaxation time. It is shown that the optimal choice of grid points, derived in a previous paper, for minimizing statistical errors not only removes integration errors, but also minimizes relaxation errors. The methods are applied in a calculation of the free energy of cavity formation in water.     

An optical flow-based integrated navigation system inspired by insect vision

Some insects use optic flow (OF) to perform their navigational tasks perfectly. Learning from insects' OF navigation strategies, this article proposes a bio-inspired integrated navigation system based on OF. The integrated navigation system is composed of an OF navigation system (OFNS) and an OF aided navigation system (OFAN). The OFNS uses a simple OF method to measure motion at each step along a path. The position information is then obtained by path integration. However, path integration leads to cumulative position errors which increase rapidly with time. To overcome this problem, the OFAN is employed to assist the OFNS in estimating and correcting these cumulative errors. The OFAN adopts an OF-based Kalman filter (KF) to continuously estimate the position errors. Moreover, based on the OF technique used in the OFNS, we develop a new OF method employed by the OFAN to generate the measurement input of the OF-based KF. As a result, both the OFNS and the OFAN in our integrated navigation system are derived from the same OF method so that they share input signals and some operations. The proposed integrated navigation system can provide accurate position information without interference from cumulative errors yet doing so with low computational effort. Simulations and comparisons have demonstrated its efficiency.     

Computation of molecular electrostatics with boundary element methods.

In continuum approaches to molecular electrostatics, the boundary element method (BEM) can provide accurate solutions to the Poisson-Boltzmann equation. However, the numerical aspects of this method pose significant problems. We describe our approach, applying an alpha shape-based method to generate a high-quality mesh, which represents the shape and topology of the molecule precisely. We also describe an analytical method for mapping points from the planar mesh to their exact locations on the surface of the molecule. We demonstrate that derivative boundary integral formulation has numerical advantages over the nonderivative formulation: the well-conditioned influence matrix can be maintained without deterioration of the condition number when the number of the mesh elements scales up. Singular integrand kernels are characteristics of the BEM. Their accurate integration is an important issue. We describe variable transformations that allow accurate numerical integration. The latter is the only plausible integral evaluation method when using curve-shaped boundary elements.     

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

Alpha functions are commonly used to describe different receptor channel kinetics (non-NMDA, GABA_A and GABA_B). In this paper we show that they may be represented as solutions to simple ordinary differential equations. This alternative method is compared with the commonly used direct summation of the alpha function conductances in a high-level neuronal circuit model. A parametric study shows that the differential equation method greatly speeds up the previous summation method. The forward Euler method used to solve this differential equation is shown to be accurate for this type of simulation. The modelling of NMDA receptor channel kinetics is also discussed. Received: 18 December 1992/Accepted in revised form: 28 June 1993     

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

A General Approach for Haplotype Phasing across the Full Spectrum of Relatedness

Many existing cohorts contain a range of relatedness between genotyped individuals, either by design or by chance. Haplotype estimation in such cohorts is a central step in many downstream analyses. Using genotypes from six cohorts from isolated populations and two cohorts from non-isolated populations, we have investigated the performance of different phasing methods designed for nominally ‘unrelated’ individuals. We find that SHAPEIT2 produces much lower switch error rates in all cohorts compared to other methods, including those designed specifically for isolated populations. In particular, when large amounts of IBD sharing is present, SHAPEIT2 infers close to perfect haplotypes. Based on these results we have developed a general strategy for phasing cohorts with any level of implicit or explicit relatedness between individuals. First SHAPEIT2 is run ignoring all explicit family information. We then apply a novel HMM method (duoHMM) to combine the SHAPEIT2 haplotypes with any family information to infer the inheritance pattern of each meiosis at all sites across each chromosome. This allows the correction of switch errors, detection of recombination events and genotyping errors. We show that the method detects numbers of recombination events that align very well with expectations based on genetic maps, and that it infers far fewer spurious recombination events than Merlin. The method can also detect genotyping errors and infer recombination events in otherwise uninformative families, such as trios and duos. The detected recombination events can be used in association scans for recombination phenotypes. The method provides a simple and unified approach to haplotype estimation, that will be of interest to researchers in the fields of human, animal and plant genetics.