Multiple Integrals Research Articles

A role for the C. elegans Argonaute protein CSR-1 in small nuclear RNA 3' processing.

The Integrator is a multi-subunit protein complex that catalyzes the maturation of snRNA transcripts via 3' cleavage, a step required for snRNA incorporation with snRNP for spliceosome biogenesis. Here we developed a GFP based in vivo snRNA misprocessing reporter as a readout of Integrator function and performed a genome-wide RNAi screen for Integrator regulators. We found that loss of the Argonaute encoding csr-1 gene resulted in widespread 3' misprocessing of snRNA transcripts that is accompanied by a significant increase in alternative splicing. Loss of the csr-1 gene down-regulates the germline expression of Integrator subunits 4 and 6 and is accompanied by a reduced protein translation efficiency of multiple Integrator catalytic and non-catalytic subunits. Through isoform and motif mutant analysis, we determined that CSR-1's effect on snRNA processing is dependent on its catalytic slicer activity but does not involve the CSR-1a isoform. Moreover, mRNA-sequencing revealed high similarity in the transcriptome profile between csr-1 and Integrator subunit knockdown via RNAi. Together, our findings reveal CSR-1 as a new regulator of the Integrator complex and implicate a novel role of this Argonaute protein in snRNA 3' processing.

Widespread occurrence and diverse origins of polintoviruses influence lineage-specific genome dynamics in stony corals.

Stony corals (Order: Scleractinia) are central to vital marine habitats known as coral reefs. Numerous stressors in the Anthropocene are contributing to the ongoing decline in coral reef health and coverage. While viruses are established modulators of marine microbial dynamics, their interactions within the coral holobiont and impact on coral health and physiology remain unclear. To address this key knowledge gap, we investigated diverse stony coral genomes for 'endogenous' viruses. Our study uncovered a remarkable number of integrated viral elements recognized as 'Polintoviruses' (Class Polintoviricetes) in thirty Scleractinia genomes; with several species harboring hundreds to thousands of polintoviruses. We reveal massive paralogous expansion of polintoviruses in stony coral genomes, alongside the presence of integrated elements closely related to Polinton-like viruses (PLVs), a group of viruses that exist as free virions. These results suggest multiple integrations of polintoviruses and PLV-relatives, along with paralogous expansions, shaped stony coral genomes. Re-analysis of existing gene expression data reveals all polintovirus structural and non-structural hallmark genes are expressed, providing support for free virion production from polintoviruses. Our results, revealing a significant diversity of polintovirus across the Scleractinia order, open a new research avenue into polintovirus and their possible roles in disease, genomic plasticity, and environmental adaptation in this key group of organisms.

On‐line machine‐learning forecast uncertainty estimation for sequential data assimilation

AbstractQuantifying forecast uncertainty is a key aspect of state‐of‐the‐art numerical weather prediction and data assimilation systems. Ensemble‐based data assimilation systems incorporate state‐dependent uncertainty quantification based on multiple model integrations. However, this approach is demanding in terms of computations and development. In this work, a machine‐learning method is presented based on convolutional neural networks that estimates the state‐dependent forecast uncertainty represented by the forecast error covariance matrix using a single dynamical model integration. This is achieved by the use of a loss function that takes into account the fact that the forecast errors are heteroscedastic. The performance of this approach is examined within a hybrid data assimilation method that combines a Kalman‐like analysis update and the machine‐learning‐based estimation of a state‐dependent forecast error covariance matrix. Observing system simulation experiments are conducted using the Lorenz'96 model as a proof‐of‐concept. The promising results show that the machine‐learning method is able to predict precise values of the forecast covariance matrix in relatively high‐dimensional states. Moreover, the hybrid data assimilation method shows similar performance to the ensemble Kalman filter, outperforming it when the ensembles are relatively small.

Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals

We firstly study ∗integrability and commutativity for multiplicative fractional integrals with exponential kernels, proposed by Peng et al. (2022). Secondly, making use of such operators, we present a symmetrical multiplicative fractional integrals identity. Based on it, and the fact that the function T∗ is multiplicatively convex or the function (lnT∗)θ is convex for θ>1, especially pondering the case of 0<θ≤1, we establish the symmetrical Hermite–Hadamard type inequalities for multiplicative convexity. We also give some applications in special means under multiplicative calculus.

Consensus of Multiple High-Order Integrator Agents With Time-Varying Connectivity and Delays: Protocols Using Only Relative States

Consensus of Multiple High-Order Integrator Agents With Time-Varying Connectivity and Delays: Protocols Using Only Relative States

The influence of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current

In the present paper, the effect of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current is studied. The wave potential and Stokes stream function are used to formulate this problem. Multiple integrals representing the free surface elevation are obtained by mathematical analysis using the Laplace transform in time and the Fourier transform in space. This is divided into various multiple integrals, using the steepest descent method to evaluate them asymptotically for a large time and distance. There are three types of ground disturbances taken into consideration: D0(x)=e(−x2/2), D0(x)=e−|x|, and D0(x)=δ(x). The effect of uniform current speed (U) and viscosity (ν) on the free surface elevation is illustrated for the three forms of ground disturbances. It is observed that the presence of current often amplifies the energy of the propagating wave and also increases its amplitude. Moreover, as viscosity increases, the amplitude of free surface elevation decreases with respect to time, and further, the period of oscillation of surface elevation becomes smaller for a large time.

Modified Nested Saturated Control for Uncertain Multiple Integrators With High-Order Nonlinear Perturbation.

This article studies the global asymptotic stability problem of multiple integrators subject to uncertain parameters and high-order nonlinear perturbation. By introducing a modified saturation function with positive tunable parameters, three types of modified nested saturated controllers with different parameter assignments are proposed to handle the uncertain integrators with high-order nonlinear perturbation. The specific mechanism of the modified nested saturated controllers with different parameter assignments, in which control parameters appear before states, saturation functions, or saturation levels, is comprehensively analyzed. With the help of a modified saturation function, the global convergence domain of each state can be kept invariable in the saturation reduction analysis. Meanwhile, a large saturation level is obtained by adjusting positive tunable parameters. Combining with derivatives calculation and M -matrix-based comparison theory, proposed saturated control schemes are utilized to handle the considered system. Finally, an active magnetic bearing (AMB) system is revisited as an uncertain mechanical system and used to verify the feasibility of the proposed control designs.

A Multiple Integration Approach to the Broken Stick Problem with Predetermined Minimum Piece Lengths

Summary Not many mathematical problems can be successfully introduced around a dinner table or in other social settings, but a quick internet search tells us that broken stick problems are among the classics that still engage. The fact that solutions may require basic knowledge of calculus, probability, and combinatorics helps demonstrate the power and necessity of mathematical formalism. In this article, the general intention has been to show how multiple integrals calculate probabilities in relation to polygons made by pieces from a randomly broken stick of unit length. Most of this article is devoted to proving a probability formula for the case where side lengths have predetermined lower bounds. This formula generalizes a well known corresponding formula without these requirements.

Heterologous Biosynthesis of Kauralexin A1 in Saccharomyces cerevisiae through Metabolic and Enzyme Engineering.

Kauralexin A1 (KA1) is a key intermediate of the kauralexin A series metabolites of maize phytoalexins. However, their application is severely limited by their low abundance in maize. In this study, an efficient biosynthetic pathway was constructed to produce KA1 in Saccharomyces cerevisiae. Also, metabolic and enzyme engineering strategies were applied to construct the high-titer strains, such as chassis modification, screening synthases, the colocalization of enzymes, and multiple genomic integrations. First, the KA1 precursor ent-kaurene was synthesized using the efficient diterpene synthase GfCPS/KS from Fusarium fujikuroi, and optimized to reach 244.36 mg/L in shake flasks, which displayed a 200-fold increase compared to the initial strain. Then, the KA1 was produced under the catalysis of ZmCYP71Z18 from Zea mays and SmCPR1 from Salvia miltiorrhiza, and the titer was further improved by integrating the fusion protein into the genome. Finally, an ent-kaurene titer of 763.23 mg/L and a KA1 titer of 42.22 mg/L were achieved through a single-stage fed-batch fermentation in a 5 L bioreactor. This is the first report of the heterologous biosynthesis of maize diterpene phytoalexins in S. cerevisiae, which lays a foundation for further pathway reconstruction and biosynthesis of the kauralexin A series maize phytoalexins.

On parameterized inequalities for fractional multiplicative integrals

Abstract In this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively s s -convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.

Abstract 6792: Investigating differential expression of Palladin isoform 3 in 2D and 3D pancreatic cancer cell cultures

Abstract Palladin (PALLD) is an actin-binding protein widely expressed in mammalian tissues that modulates cytoskeletal dynamics. Palladin is linked to the progression of breast, pancreatic, and renal cancers. There are at least 9 known isoforms of PALLD but isoforms 3 (iso3) and 4 (iso4) appear most significant in cancer cells and associated fibroblasts. Our goal is to understand iso3 in pancreatic cancer (PC) cell lines grown in various culture environments to shed light on the intricate interplay between culture conditions and gene regulation. Cell models were developed as 3D spheroids from hanging drops after optimizing culture conditions by utilizing a combination of inexpensive methylcellulose (MC) and rat tail collagen viscosity ranges across cell seeding densities. The quality of the developed spheroids was assessed using multiple parameters, like diameter, integrity, and circularity to determine ideal spheroid characteristics. Spheroids that formed at a lower MC viscosity range (350-550 mPa·s) led to peripheral loose cells and a higher viscosity range (7,000-10,000 mPa·s) resulted in elongated shapes. Moderate viscosity ranges (1,000-1,800 mPa·s and 3,500-5,600 mPa·s) consistently produced circular and compact spheroids. Optimal incubation times varied from 72 to 96 hr depending on the cell line. Invasion dynamics within collagen-MC gels revealed that PANC-1 had significantly higher invasion potential compared to BxPC-3 and a control cell line C2C12. RT-qPCR results show that PALLD iso3 was particularly overexpressed in the 3D culture environment of PANC-1, suggesting that elevated PALLD isoform 3 expression may be a characteristic of 3D culture, particularly in invasive PC types. Taken together, the study validates the importance of extracellular viscosity for influencing spheroid characteristics toward generating reproducible 3D spheroids. The investigation also highlights PALLD iso3 as a potentially valuable biomarker for aggressive forms of pancreatic cancer. Citation Format: Sonali Biswas, Jason A. Bush. Investigating differential expression of Palladin isoform 3 in 2D and 3D pancreatic cancer cell cultures [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 6792.

Effects of topographical disturbances on flexural wave motion in a viscous fluid

Main causes of ground disturbances are geological events such as earthquakes, underwater gravity mass flows, volcanic eruptions, and bottom explosions. This paper investigates the effects of transitory ground disturbance on the generation of flexural waves in the presence of a thin floating elastic plate. The problem is formulated using the Stokes stream function and wave potential boundary value problems in a viscous fluid. The expression of the plate deflection is obtained as multiple infinite integrals using the Fourier and Laplace transforms, which is further solved by the steepest descent method. Three types of ground disturbances such as H0(x)=e(−x2/2), H0(x)=e−|x|, and H0(x)=δ(x) are considered. The deflection of the floating elastic plate is investigated in connection to ground disturbances, fluid viscosity, and structural parameters such as mass per unit length of the plate and flexural rigidity. The study reveals that with higher viscosity and flexural rigidity, the amplitude of the plate deflection is reduced. Moreover, these two parameters play a great role in the reduction of plate deflection.

Stabilising control for impulsive systems

This paper is aimed at stabilising control for impulsive systems via the state feedback. Firstly, stability analysis for the closed-loop system is conducted using a Lyapunov-like functional (LLK) that is not necessarily continuous nor positive definite. Built on two subintervals of the impulsive interval being separated by the current instant, a concrete LLK is constructed by introducing multiple integrals of the state and cross terms among the integrals, the state and impulsive states. Integral equations of the impulsive system are exploited and high-order integral inequalities are taken when estimating the derivative of the LLK. New stability results with interval dwell-time, maximal dwell-time or minimal dwell-time are obtained. Secondly, based on the stability results the stabilising control problem is solved via linear matrix inequality approach. Finally, numerical examples illustrate that the stability results are less conservative and the control for impulsive systems is valid.

State of the Art Technologies for High Yield Heterologous Expression and Production of Oxidoreductase Enzymes: Glucose Oxidase, Cellobiose Dehydrogenase, Horseradish Peroxidase, and Laccases in Yeasts P. pastoris and S. cerevisiae

Oxidoreductase (OXR) enzymes are in high demand for biocatalytic applications in the food industry and cosmetics (glucose oxidase (GOx) and cellobiose dehydrogenase (CDH)), bioremediations (horseradish peroxidase (HRP) and laccase (LAC)), and medicine for biosensors and miniature biofuel cells (GOx, CDH, LAC, and HRP). They can be used in a soluble form and/or within the yeast cell walls expressed as chimeras on the surface of yeast cells (YSD), such as P. pastoris and S. cerevisiae. However, most of the current studies suffer from either low yield for soluble enzyme expression or low enzyme activity when expressed as chimeric proteins using YSD. This is always the case in studies dealing with the heterologous expression of oxidoreductase enzymes, since there is a requirement not only for multiple OXR gene integrations into the yeast genome (super transformations), and codon optimization, but also very careful design of fermentation media composition and fermentation conditions during expression due to the need for transition metals (copper and iron) and metabolic precursors of FAD and heme. Therefore, scientists are still trying to find the optimal formula using the above-mentioned approaches; most recently, researcher started using protein engineering and directed evolution to increase in the yield of recombinant enzyme production. In this review article, we will cover all the current state-of-the-art technologies and most recent advances in the field that yielded a high expression level for some of these enzymes in specially designed expression/fermentation systems. We will also tackle and discuss new possibilities for further increases in fermentation yield using cutting-edge technologies such as directed evolution, protein and strain engineering, high-throughput screening methods based on in vitro compartmentalization, flow cytometry, and microfluidics.

Rate of convergence for the Smoluchowski–Kramers approximation for distribution-dependent SDEs driven by fractional Brownian motions

In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the following distribution-dependent SDE driven by fractional Brownian motion [Formula: see text] where [Formula: see text] denotes the law of [Formula: see text], [Formula: see text] is a [Formula: see text]-dimensional fractional Brownian motion with Hurst parameter [Formula: see text]. Based on the techniques of multiple integrals and Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence.

Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results

Abstract The objective of this manuscript is to introduce the notion of multiplicative 𝔪 {\mathfrak{m}} -metric space, inspired by the concepts of multiplicative metric space and 𝔪 {\mathfrak{m}} -metric space. We propose a generalized notion of the distance function known as the multiplicative 𝔪 {\mathfrak{m}} -metric. Firstly, we present the fundamental definitions for the multiplicative 𝔪 {\mathfrak{m}} -metric space, then delve into the topological aspects, including the convergence of sequences and completeness. Additionally, we provide various illustrations to support our discussion. We also generalize some well-known contraction mappings and prove fixed point theorems on the complete multiplicative 𝔪 {\mathfrak{m}} -metric space. To complement our findings, we have included numerical results along with graphs to provide visual support for our conclusions. Furthermore, we explore the potential of utilizing the multiplicative 𝔪 {\mathfrak{m}} -metric to demonstrate the existence of the solution to a multiplicative integral equation.

The semiclassical approximation of multiple functional integrals

In this paper, we study the semiclassical approximation of multiple functional integrals. The integrals are defined through the Lagrangian and the action. Of all possible trajectories, the greatest contribution to the integral is given by the classical trajectory x̅cl for which the action S takes an extremal value. The classical trajectory is found as a solution of the multidimensional Euler – Lagrange equation. To calculate the functional integrals, the expansion of the action with respect to the classical trajectory is used, which can be interpreted as an expansion in powers of Planck’s constant. The numerical results for the semiclassical approximation of double functional integrals are given.

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

Abstract In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝ n . The main idea is to use a reducing transformation procedure obtained by using α-dense curves. First, the region Ω f whose measure represents the value of the integral, is densified by a specific curve ℓ α(t) of finite length. Therefore, the multiple integral can be approached by a simple integral corresponding to ℓ α (t). Some numerical examples are given.

Attentional Modulation in Early Visual Cortex: A Focused Reanalysis of Steady-state Visual Evoked Potential Studies.

Steady-state visual evoked potentials (SSVEPs) are a powerful tool for investigating selective attention. Here, we conducted a combined reanalysis of multiple studies employing this technique in a variety of attentional experiments to, first, establish benchmark effect sizes of attention on amplitude and phase of SSVEPs and, second, harness the power of a large data set to test more specific hypotheses. Data of eight published SSVEP studies were combined, in which human participants (n = 135 in total) attended to flickering random dot stimuli based on their defining features (e.g., location, color, luminance, or orientation) or feature conjunctions. The reanalysis established that, in all the studies, attention reliably enhanced amplitudes, with color-based attention providing the strongest effect. In addition, the latency of SSVEPs elicited by attended stimuli was reduced by ∼4 msec. Next, we investigated the modulation of SSVEP amplitudes in a subset of studies where two different features were attended concurrently. Although most models assume that attentional effects of multiple features are combined additively, our results suggest that neuronal enhancement provided by concurrent attention is better described by multiplicative integration. Finally, we used the combined data set to demonstrate that the increase in trial-averaged SSVEP amplitudes with attention cannot be explained by increased synchronization of single-trial phases. Contrary to the prediction of the phase-locking account, the variance across trials of complex Fourier coefficients increases with attention, which is more consistent with boosting of a largely phase-locked signal embedded in non-phase-locked noise.

Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals

Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals