Multiple Integrals Research Articles

Determination of Nonstationary Stochastic Response of Linear Oscillators With Fractional Derivative Elements of Rational Order

Abstract In this paper, a technique is developed for determining the nonstationary response statistics of linear oscillators endowed with fractional derivative elements. Notably, fractional operators are particularly effective in modeling solid mechanics problems as they offer the option of influencing both the elasticity and the energy dissipation capacity of the system. In this paper, particular attention is devoted to the case of fractional derivatives of rational order that approximates reasonably well any real order model. The oscillators are subjected to stationary stochastic excitations, and the pertinent nonstationary response statistical moments are determined by first introducing a finite number of oscillator response related states; this is afforded by the rational number order of the fractional operator. Next, the technique involves proceeding to treating the problem in the Laplace transform domain. This leads to multiple convolution integrals determined by representing the transfer function of the oscillator in a partial fraction form by a pole-residue formulation. In this manner, the response evolutionary power spectral density of the fractional oscillator is derived in a closed form, while nonstationary second-order statistics can be obtained by mundane numerical integration in the frequency domain. Applications to oscillators comprising one or two fractional derivative elements are presented, considering the case of a white noise excitation and of a random process possessing the classical Kanai–Tajimi spectrum. Reliability of the developed technique is assessed by juxtaposing its analytical results with pertinent Monte Carlo simulation data.

Heterologous pulcherrimin production in Saccharomyces cerevisiae confers inhibitory activity on Botrytis conidiation.

Pulcherrimin is an iron (III) chelate of pulcherriminic acid that plays a role in antagonistic microbial interactions, iron metabolism, and stress responses. Some bacteria and yeasts produce pulcherriminic acid, but so far, pulcherrimin could not be produced in Saccharomyces cerevisiae. Here, multiple integrations of the Metschnikowia pulcherrima PUL1 and PUL2 genes in the S. cerevisiae genome resulted in red colonies, which indicated pulcherrimin formation. The coloration correlated positively and significantly with the number of PUL1 and PUL2 genes. The presence of pulcherriminic acid was confirmed by mass spectrometry. In vitro competition assays with the plant pathogenic fungus Botrytis caroliana revealed inhibitory activity on conidiation by an engineered, strong pulcherrimin-producing S. cerevisiae strain. We demonstrate that the PUL1 and PUL2 genes from M. pulcherrima, in multiple copies, are sufficient to transfer pulcherrimin production to S. cerevisiae and represent the starting point for engineering and optimizing this biosynthetic pathway in the future.

A supernumerary synthetic chromosome in Komagataella phaffii as a repository for extraneous genetic material

BackgroundKomagataella phaffii (Pichia pastoris) is a methylotrophic commercially important non-conventional species of yeast that grows in a fermentor to exceptionally high densities on simple media and secretes recombinant proteins efficiently. Genetic engineering strategies are being explored in this organism to facilitate cost-effective biomanufacturing. Small, stable artificial chromosomes in K. phaffii could offer unique advantages by accommodating multiple integrations of extraneous genes and their promoters without accumulating perturbations of native chromosomes or exhausting the availability of selection markers.ResultsHere, we describe a linear “nano”chromosome (of 15–25 kb) that, according to whole-genome sequencing, persists in K. phaffii over many generations with a copy number per cell of one, provided non-homologous end joining is compromised (by KU70-knockout). The nanochromosome includes a copy of the centromere from K. phaffii chromosome 3, a K. phaffii-derived autonomously replicating sequence on either side of the centromere, and a pair of K. phaffii-like telomeres. It contains, within its q arm, a landing zone in which genes of interest alternate with long (approx. 1-kb) non-coding DNA chosen to facilitate homologous recombination and serve as spacers. The landing zone can be extended along the nanochromosome, in an inch-worming mode of sequential gene integrations, accompanied by recycling of just two antibiotic-resistance markers. The nanochromosome was used to express PDI, a gene encoding protein disulfide isomerase. Co-expression with PDI allowed the production, from a genomically integrated gene, of secreted murine complement factor H, a plasma protein containing 40 disulfide bonds. As further proof-of-principle, we co-expressed, from a nanochromosome, both PDI and a gene for GFP-tagged human complement factor H under the control of PAOX1 and demonstrated that the secreted protein was active as a regulator of the complement system.ConclusionsWe have added K. phaffii to the list of organisms that can produce human proteins from genes carried on a stable, linear, artificial chromosome. We envisage using nanochromosomes as repositories for numerous extraneous genes, allowing intensive engineering of K. phaffii without compromising its genome or weakening the resulting strain.

A numerical technique based on multiplicative integration strategy for fractional Darboux problem

A numerical technique based on multiplicative integration strategy for fractional Darboux problem

The continuous stochastic gradient method: part II–application and numerics

In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization schemes, CSG does not discard old gradient samples from previous iterations. Instead, design dependent integration weights are calculated to form a convex combination as an approximation to the true gradient at the current design. As the approximation error vanishes in the course of the iterations, CSG represents a hybrid approach, starting off like a purely stochastic method and behaving like a full gradient scheme in the limit. In this work, the efficiency of CSG is demonstrated for practically relevant applications from topology optimization. These settings are characterized by both, a large number of optimization variables and an objective function, whose evaluation requires the numerical computation of multiple integrals concatenated in a nonlinear fashion. Such problems could not be solved by any existing optimization method before. Lastly, with regards to convergence rates, first estimates are provided and confirmed with the help of numerical experiments.

Scratch-induced surface formation mechanism in C/SiC composites

Due to the extremely complex composition of C/SiC composites, their material removal mechanisms are significantly different from those of conventional single-phase ceramic materials. Therefore, the grinding removal mechanism of C/SiC composites must be investigated so that the components based on these composites can be machined efficiently and with low damage. In this paper, nano-scratch experiments with various cutting depths are carried out along different fiber orientations to simulate the material removal process in grinding and theoretically clarify the damage failure mechanism based on different cutting thicknesses. According to the assessment of surface and subsurface morphology of the various constituents in the scratch grooves regarding different fiber orientations, the multiple brittle breakage modes and surface integrity of carbon fiber are revealed. Green’s function is applied to establish a half-space anisotropic analytic elastic stress field considering the microstructural characteristics of material, and the crack nucleation and propagation principles during micro brittle fracture regime for nano-scratch experiment are elucidated based on the fracture mechanics and the maximum principal stress criterion. The formation mechanism of machined surface morphology in macro brittle removal process is investigated under the crack deflection effect at the weak interface and based on the elastic foundation beam theory. The related findings can provide a reasonable reference framework for optimizing the grinding technology, material and tool design regarding C/SiC composites.

Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains

Evaluating a lattice path integral in terms of spectral data and matrix elements pertaining to a suitably defined quantum transfer matrix, we derive form-factor series expansions for the dynamical two-point functions of arbitrary local operators in fundamental Yang–Baxter integrable lattice models at finite temperature. The summands in the series are parameterised by solutions of the Bethe Ansatz equations associated with the eigenvalue problem of the quantum transfer matrix. We elaborate on the example of the XXZ chain for which the solutions of the Bethe Ansatz equations are sufficiently well understood in certain limiting cases. We work out in detail the case of the spin-zero operators in the antiferromagnetic massive regime at zero temperature. In this case the thermal form-factor series turn into series of multiple integrals with fully explicit integrands. These integrands factorize into an operator-dependent part, determined by the so-called Fermionic basis, and a part which we call the universal weight as it is the same for all spin-zero operators. The universal weight can be inferred from our previous work. The operator-dependent part is rather simple for the most interesting short-range operators. It is determined by two functions ρ and ω for which we obtain explicit expressions in the considered case. As an application we rederive the known explicit form-factor series for the two-point function of the magnetization operator and obtain analogous expressions for the magnetic current and the energy operators.

A Labeled RFS-Based Framework for Multiple Integrity Attackers Detection and Identification in Cyber–Physical Systems

The problem of multiple integrity attacks (attackers) detection and identification (MIADI) in cyber-physical systems (CPSs) is still a challenging problem to date. The goal of this paper is to develop a knowledge-based method capable of simultaneously detecting and identifying multiple integrity attacks aiming at different sensors in a CPS. In this paper, with the help of labeled random finite set (RFS) theory, a new solution to solve the MIADI problem is proposed. The main contributions of this paper, lie in the the following two aspects, the first is the novel formulation of the MIADI problem, in which labeled RFSs are used to model the behaviors of multiple integrity attackers for the first time, and the second is the proposed labeled RFS-based solution, which provides an elegant framework to cope with the MIADI problem. Numerical experiments are conducted and experimental results demonstrate the effectiveness of the proposed solution. This proposed solution further extends the feasibility of the labeled RFS theory in the context of CPSs cybersecurity.

CRISPR-Cas12a-integrated transgenes in genomic safe harbors retain high expression in human hematopoietic iPSC-derived lineages and primary cells

Discovery of genomic safe harbor sites (SHSs) is fundamental for multiple transgene integrations, such as reporter genes, chimeric antigen receptors (CARs), and safety switches, which are required for safe cell products for regenerative cell therapies and immunotherapies. Here we identified and characterized potential SHS in human cells. Using the CRISPR-MAD7 system, we integrated transgenes at these sites in induced pluripotent stem cells (iPSCs), primary T and natural killer (NK) cells, and Jurkat cell line, and demonstrated efficient and stable expression at these loci. Subsequently, we validated the differentiation potential of engineered iPSC toward CD34+ hematopoietic stem and progenitor cells (HSPCs), lymphoid progenitor cells (LPCs), and NK cells and showed that transgene expression was perpetuated in these lineages. Finally, we demonstrated that engineered iPSC-derived NK cells retained expression of a non-virally integrated anti-CD19 CAR, suggesting that several of the investigated SHSs can be used to engineer cells for adoptive immunotherapies.

Gaussian structure in coalescing stochastic flows

In the paper, we consider the point measure that corresponds to Arratia flow. The central limit theorem of the multiple integrals with respect to this measure was obtained.

A Multi-Fidelity Integration Method for Reliability Analysis of Industrial Robots

Abstract A multi-fidelity integration method is proposed to analyze the reliability of multiple performance indicators (MPI) for industrial robots. In order to high-fidelity mapping the performance of industrial robots, a unified multi-domain model (UMDM) is first established. The contribution-degree analysis is then used to classify the input random variables into interacting and non-interacting ones. Thus, the high-dimensional integration of reliability analysis is separated into a low-dimensional integration and multiple one-dimensional integrations in an additive form. Here, the low-dimensional integration consisting of the interacting variables is calculated using the high-precision mixed-degree cubature formula (MDCF), and the computational results are treated as high-fidelity data. The one-dimensional integration consisting of non-interacting variables is then computed by the highly efficient five-point Gaussian Hermite quadrature (FGHQ), and the computational results are named low-fidelity data. A multi-fidelity integration method is constructed by fusing the high-fidelity data and the low-fidelity data to obtain the statistical moments of the MPI. Subsequently, the probability density function and the failure probability of the MPI are estimated using the saddlepoint approximation method. Finally, some representative methods are performed to verify the superiority of the proposed method.

A novel method for global reliability sensitivity analysis by adaptive bivariate multiplicative dimensional reduction integral

The existing fractional moment-constrained maximum entropy method can efficiently analyse global reliability sensitivity (GRS). However, this method estimates the fractional moments by the univariate multiplicative dimensional reduction integral (UM-DR-I) that generates a significant error in GRS estimation, which may result from ignoring the interactions between input variables. Moreover, due to the direct bivariate decomposition of the fractional power performance function, the recently developed generalised bivariate additive dimensional reduction integral (GB-DR-I) may also result in higher computational cost and lower accuracy than that obtained with UM-DR-I regarding fractional moment and GRS estimations. To improve the efficiency of solving for GRS with an acceptable accuracy, a bivariate multiplicative dimensional reduction integral (BM-DR-I) is proposed to estimate the unconditional and conditional fractional moments required when estimating the GRS. The main innovation is that the proposed method analytically derives the BM-DR-I formulae for estimating the unconditional and conditional fractional moments; moreover, it discovers for the first time that the unconditional and conditional fractional moments can be estimated by sharing the same integral grid. Accordingly, the proposed BM-DR-I eliminates the dependence of the computational cost on the input dimensionality when estimating the GRS. In addition, to further improve the efficiency of estimating fractional moments and GRS sequentially with sufficient accuracy, an adaptive strategy for selecting effective bivariate terms was employed to construct an adaptive BM-DR-I. Four examples verify that adaptive BM-DR-I is superior to similar existing methods for estimating the GRS.

Extreme value analysis of high-dimensional Gaussian vector processes

The analysis of the extreme value pertaining to first-passage failure is a key consideration for engineering systems undergoing random vibration. Most of the literature focus on a univariate stochastic process, however for system reliability analysis, the extreme value of multiple dependent processes is required. Due to the problem complexity, analytical methods are scarce, and they are limited to low-dimensional problems (dimension refers to the number of component processes). This paper presents an analytical method for extreme analysis of multivariate stationary Gaussian processes. The method can efficiently solve high-dimensional problems, thus it has diverse applications such as analysing dynamic systems with many degrees-of-freedom, or evaluating space-time extremes of random fields by discretizing the spatial domain. A maximum process is defined, representing the maxima of the components at each time instant. The exact upcrossing rate of the maximum process is derived, and the Poisson approximation is invoked to estimate the extreme value distribution. The method is fast as it involves multiple one-dimensional integrals, which can be computed using Gaussian quadrature. Moreover, an accurate approximation is proposed that obviates the need for numerical integration. The proposed method is implemented on two examples, specifically a dynamic system and spreading ocean waves. Monte Carlo simulations, which are computationally demanding, are performed to verify the accuracy and correctness of the proposed method.

Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics

Spectral representations of iterated Itô and Stratonovich stochastic integrals of arbitrary multiplicity, including integrals from Taylor–Itô and Taylor–Stratonovich expansions, are obtained by the spectral method. They are required for the implementation of numerical methods for solving Itô and Stratonovich stochastic differential equations with high orders of mean-square and strong convergence. The purpose of such numerical methods is the modeling of nonlinear stochastic dynamics in many fields. This paper contains necessary theoretical results, as well as the results of numerical experiments.

A generalization of some integral inequalities similar to Hardy inequality on time scales

In this paper, we prove some new dynamic inequalities similar to Hardy's inequality on time scales T. The results as special cases when T=R contain continuous inequalities similar to Hardy's inequality, and when T=Z, the results contain discrete inequalities that are essentially new to the best of the authors' knowledge. R and Z denote the set of all real numbers and the set of all integers, respectively. Our main results are proved by using the Hölder inequality, Chain rule, and some properties of multiple integrals on time scales. Furthermore, some applications and examples are given to illustrate the investigated results.

Multiple parametric Marcinkiewicz integrals with mixed homogeneity along surfaces

In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.

Interplay of degeneracy and non-degeneracy in fluctuation propagation in coherent feed-forward loop motif

We present a stochastic framework to decipher fluctuation propagation in classes of coherent feed-forward loops (CFFLs). The systematic contribution of the direct (one-step) and indirect (two-step) pathways is considered to quantify fluctuations of the output node. We also consider both additive and multiplicative integration mechanisms of the two parallel pathways (one-step and two-step). Analytical expression of the output node’s coefficient of variation shows contributions of intrinsic, one-step, two-step, and cross-interaction in closed form. We observe a diverse range of degeneracy and non-degeneracy in each of the decomposed fluctuation terms and their contribution to the overall output fluctuations of each CFFL motif. The analysis of output fluctuations reveals a maximal level of fluctuations of the CFFL motif of type 1.

A Simultaneous Numerical Integration Routine for the Fast Calculation of Similar Integrations

In this paper, a fast and simultaneous integration routine that is tailored for obtaining the results of multiple numerical integrations is introduced. The routine uses the same nodes for multiple integrations defined for similar integrands. In the paper it is demonstrated by several examples that if the integrands of interest are similar on the integration path, then using the same nodes decreases the computational costs dramatically. The method is introduced by updating the popular Gauss-Kronrod quadrature rule, but the same steps given in the paper can be applied to any other numerical integration rule.

Co-Fermentation of Glucose–Xylose–Cellobiose–XOS Mixtures Using a Synthetic Consortium of Recombinant Saccharomyces cerevisiae Strains

The efficient conversion of cellulosic sugars is vital for the economically viable production of biofuels/biochemicals from lignocellulosic biomass hydrolysates. Based on comprehensive screening, Saccharomyces cerevisiae RC212 was chosen as the chassis strain for multiple integrations of heterologous β-glucosidase and β-xylosidase genes in the present study. The resulting recombinant BLN26 and LF1 form a binary synthetic consortium, and this co-culture system achieved partial fermentation of four sugars (glucose, xylose, cellobiose, and xylo-oligosaccharides). Then, we developed a ternary S. cerevisiae consortium consisting of LF1, BSGIBX, and 102SB. Almost all four sugars were efficiently fermented to ethanol within 24 h, and the ethanol yield is 0.482 g g−1 based on the consumed sugar. To our knowledge, this study represents the first exploration of the conversion of mixtures of glucose, xylose, cellobiose, and xylo-oligosaccharides by a synthetic consortium of recombinant S. cerevisiae strains. This synthetic consortium and subsequent improved ones have the potential to be used as microbial platforms to produce a wide array of biochemicals from lignocellulosic hydrolysates.

Nonlinear Integral Inequalities Involving Tempered Ψ-Hilfer Fractional Integral and Fractional Equations with Tempered Ψ-Caputo Fractional Derivative

In this paper, the nonlinear version of the Henry–Gronwall integral inequality with the tempered Ψ-Hilfer fractional integral is proved. The particular cases, including the linear one and the nonlinear integral inequality of this type with multiple tempered Ψ-Hilfer fractional integrals, are presented as corollaries. To illustrate the results, the problem of the nonexistence of blowing-up solutions of initial value problems for fractional differential equations with tempered Ψ-Caputo fractional derivative of order 0<α<1, where the right side may depend on time, the solution, or its tempered Ψ-Caputo fractional derivative of lower order, is investigated. As another application of the integral inequalities, sufficient conditions for the Ψ-exponential stability of trivial solutions are proven for these kinds of differential equations.