Multiple Integral Approach Research Articles

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.

Multiple system integration in local government asset management: A New Zealand case study

Local government in New Zealand invests in numerous Asset Management Information Systems (AMIS) in order to support their infrastructure asset operations and management decision-making. However, the silo nature of the organisational operations and proprietary constraints of AMIS have created an environment of dispersed information and systems with little or no regard to interoperability or data sharing. Adopting multiple standalone systems creates difficulties for accessing, analysing and maintaining the asset, thus compromising management efficiency and effectiveness. Consequently, there is a great desire to bring the various AMIS systems together using a Multiple System Integration (MSI) approach. This study intends to examine the MSI concept by exploring more open-sourced systems such as GIS, which is widely used in local government’s asset planning and management. In addition, being the key driver behind the technology advancement in the construction industry, BIM has created innovative applications and widened the research domains in areas such as BIM and GIS integration studies. However, the multiple system approach to further integrate the existing AMIS, is missing from both the current industry practices and academic studies. Using a case study of a BIM implementation project carried out by a local government, this research illustrates and validates the integration of BIM/GIS with the lifecycle planning specific AMIS. The novel MSI approach provides a paradigm as a solution to improve the siloed operation manner. The approach will also set the foundation for future studies in local government’s digital transformation and in the field of developing true asset Digital Twins.

Robust passivity analysis of mixed delayed neural networks with interval nondifferentiable time-varying delay based on multiple integral approach

<abstract><p>New results on robust passivity analysis of neural networks with interval nondifferentiable and distributed time-varying delays are investigated. It is assumed that the parameter uncertainties are norm-bounded. By construction an appropriate Lyapunov-Krasovskii containing single, double, triple and quadruple integrals, which fully utilize information of the neuron activation function and use refined Jensen's inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.</p></abstract>

Multiple Synchronous Tumours: A Peculiar Clinical Case

Background: Due to improvements in diagnosis, the better outcomes of oncological patients and the increase in the average age, the incidence of synchronous tumours is likely to increase. Aim: To reflect on the challenges of a case with multiple integrated diagnostic and therapeutic approaches and to bring to consideration the increasing prevalence of similar situations. Case Presentation: In this clinical case, the authors describe the evolution of an asymptomatic patient with several synchronous tumours (a GEJ primary adenocarcinoma, a low grade urothelial carcinoma in situ, a localized squamous cell lung carcinoma and 2 IPMNs). Conclusion: The challenge of this case lies in the difficult diagnostic approach, the assembly of a multidisciplinary and time-sensitive treatment plan and the individualized follow-up, due to lack of guidelines. More research is needed in this area.

Prediction and identification of transcriptional regulatory elements at the lung cancer-specific DKK1 locus.

The glycoprotein dickkopf 1 (DKK1) is highly expressed in lung cancer cell lines and tissues. Our previous study demonstrated that DKK1 promoter activity is low in lung cancer cell lines. This may be because it lacks the necessary transcriptional regulatory elements (TREs) required for higher activity levels. However, it is difficult to computationally predict functionally significant TREs, as TREs from different locations can affect large segments of distant DNA. The Encyclopedia of DNA Elements project features multiple integrated technologies and approaches for the discovery and definition of functional elements, including enhancer elements and enhancer-blocking insulators. In the present study, DNase I hypersensitive sites and histone modifications of DKK1 were investigated in the A549 lung cancer cell line using the UCSC Genome Browser. A set of cis-acting enhancer elements were identified by a dual-luciferase reporter gene assay system to increase activity of the DKK1 promoter with lung cancer specificity. To the best of our knowledge, these data provide the first insight into the role of the DKK1 locus in lung cancer, and confirm the contribution of intronic cis-acting elements to the regulation of DKK1 expression, providing a new insight into gene regulation in lung cancer, which could inform the development of targeted therapy.

Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional U+0028 LKF U+0029 with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.

Stochastic stability of fuzzy Markovian jump neural networks by multiple integral approach

PurposeThe purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.Design/methodology/approachThe authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions.FindingsIt turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results.Originality/valueThe novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks

Abstract This work studies the robust stability for a class of uncertain neutral neural networks with mixed time-varying delays. Through utilizing some novel Wirtinger-based integral inequalities and extending the convex combination technique, the upper bound on derivative of Lyapunov–Krasovskii (L–K) functional can be estimated more tightly and two mixed-delay-dependent criteria are proposed in terms of linear matrix inequalities (LMIs), in which some previously ignored information can be utilized. Different from those existent works, based on interconnected relationship between the neutral delay and neural one, some multiple integral Lyapunov terms are constructed and the conservatism can be effectively reduced. Finally, two numerical examples are given to show the benefits of the proposed criteria.

Hierarchy of stability criterion for time-delay systems based on multiple integral approach

Taking a class of time-delay systems as research object, this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free-weighting matrix technique. The hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in Lyapunov–Krasovskii functional (LKF). Together with three numerical experiments, the hierarchy of stability criterion is further shown.

Neural Circuit-Specialized Astrocytes: Transcriptomic, Proteomic, Morphological, and Functional Evidence

Astrocytes are ubiquitous in the brain and are widely held to be largely identical. However, this view has not been fully tested, and the possibility that astrocytes are neural circuit specialized remains largely unexplored. Here, we used multiple integrated approaches, including RNA sequencing (RNA-seq), mass spectrometry, electrophysiology, immunohistochemistry, serial block-face-scanning electron microscopy, morphological reconstructions, pharmacogenetics, and diffusible dye, calcium, and glutamate imaging, to directly compare adult striatal and hippocampal astrocytes under identical conditions. We found significant differences in electrophysiological properties, Ca2+ signaling, morphology, and astrocyte-synapse proximity between striatal and hippocampal astrocytes. Unbiased evaluation of actively translated RNA and proteomic data confirmed significant astrocyte diversity between hippocampal and striatal circuits. We thus report core astrocyte properties, reveal evidence for specialized astrocytes within neural circuits, and provide new, integrated database resources and approaches to explore astrocyte diversity and function throughout the adult brain. VIDEO ABSTRACT.

Hyperspectral remote sensing applied to mineral exploration in southern Peru: A multiple data integration approach in the Chapi Chiara gold prospect

Remote sensing is a strategic key tool for mineral exploration, due to its capacity of detecting hydrothermal alteration minerals or alteration mineral zones associated with different types of mineralization systems. A case study of an epithermal system located in southern Peru is presented, aimed at the characterization of mineral assemblies for discriminating potential high sulfidation epithermal targets, using hyperspectral imagery integrated with petrography, XRD and magnetic data. HyMap images were processed using the Mixture Tuned Matched Filtering (MTMF) technique for producing alteration map in the Chapi Chiara epithermal gold prospect. Extensive areas marked by advanced argillic alteration (alunite-kaolinite-dickite±topaz) were mapped in detail, as well as limited argillic (illite-smectite) and propylitic (chlorite spectral domain) alteration. The magmatic-hydrothermal processes responsible for the formation of hypogene minerals were also related to the destruction of ferrimagnetic minerals (e.g., magnetite) of host rocks such as andesite, and the remobilization/formation of paramagnetic Fe-Ti oxides (e.g., rutile, anatase). The large alteration zones of advanced argillic alteration are controlled by structures related to a regional NW-SE trend, and also by local NE-SW and ENE-WSW ones.

Wirtinger-based multiple integral inequality for stability of time-delay systems

ABSTRACTNote that the conservatism of the delay-dependent stability criteria can be reduced by increasing the integral terms in Lyapunov–Krasovskii functional (LKF). This brief revisits the stability problem for a class of linear time-delay systems via multiple integral approach. The novelty of this brief lies in that a Wirtinger-based multiple integral inequality is employed to estimate the derivative of a class of LKF with multiple integral terms. Based on these innovations, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. Two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method.

Wirtinger-based multiple integral inequality approach to synchronization of stochastic neural networks

This paper investigates the synchronization problem for a class of chaotic neural networks with discrete and unbounded distributed time delays under stochastic perturbations. Firstly, based on the Wirtinger-based double integral inequality, two novel inequalities are proposed, which are multiple integral forms of the Wirtinger-based integral inequality. Next, by applying the Jensen-type integral inequality for stochastic case and combining the Jensen integral inequality with the reciprocally convex combination approach, a delay-dependent criterion is developed to achieve the synchronization for the stochastic chaotic neural networks in the sense of mean square. In the case of no stochastic perturbations, by applying the reciprocally convex combination approach for high order case and a free-matrix-based inequality, novel delay-dependent conditions are established to achieve the synchronization for the chaotic neural networks. All the results are based on dividing the bounding of activation function into two subintervals with equal length. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Pinning sampled‐data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach

This study deals with the pinning synchronization problem for complex dynamical networks (CDNs) with Markovian jumping parameters and mixed delays under sampled‐data control technique. The mixed delays cover both discrete and distributed delays. The Markovian jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. The sufficient conditions for asymptotic synchronization of considered networks are obtained by utilizing novel Lyapunov‐Krasovskii functional and multiple integral approach. The obtained criteria is formulated in terms of LMIs, which can be checked for feasibility by making use of available softwares. Lastly, numerical simulation results are presented to validate the advantage of the propound theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 622–632, 2016

Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction---diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction---diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov---Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach

This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov–Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.

New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach

This study is concerned with the problem of stability analysis for neutral type neural networks with discrete and distributed delays. By making full use of a novel integral inequality proved to be less conservative than the celebrated Jensen׳s inequality, new stability results are established. Besides, a multiple integral inequality is also proposed firstly in neutral type neural networks with mixed delays. Based on the integral inequality, improved stability criteria in terms of linear matrix inequalities (LMIs) are derived by constructing an appropriate Lyapunov–Krasovskii functional including the multiple integral terms showed to have a great potential efficient in practice. Furthermore, less conservative stability results are obtained by dividing the distributed delay into multiple nonuniformly subinterval. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.

Integrating multiple resources to identify specific transcriptional cooperativity with a Bayesian approach

Limited cohort of transcription factors is capable to structure various gene-expression patterns. Transcriptional cooperativity (TC) is deemed to be the main mechanism of complexity and precision in regulatory programs. Although many data types generated from numerous experimental technologies are utilized in an attempt to understand combinational transcriptional regulation, complementary computational approach that can integrate diverse data resources and assimilate them into biological model is still under development. We developed a novel Bayesian approach for integrative analysis of proteomic, transcriptomic and genomic data to identify specific TC. The model evaluation demonstrated distinguishable power of features derived from distinct data sources and their essentiality to model performance. Our model outperformed other classifiers and alternative methods. The application that contextualized TC within hepatocarcinogenesis revealed carcinoma associated alterations. Derived TC networks were highly significant in capturing validated cooperativity as well as revealing novel ones. Our methodology is the first multiple data integration approach to predict dynamic nature of TC. It is promising in identifying tissue- or disease-specific TC and can further facilitate the interpretation of underlying mechanisms for various physiological conditions. tieliushi01@gmail.com Supplementary data are available at Bioinformatics online.

Discrimination, Crypticity, and Incipient Taxa in Entamoeba

Persistent difficulties in resolving clear lineages in diverging populations of prokaryotes or unicellular eukaryotes (protistan polyphyletic groups) are challenging the classical species concept. Although multiple integrated approaches would render holistic taxonomies, most phylogenetic studies are still based on single-gene or morphological traits. Such methodologies conceal natural lineages, which are considered "cryptic." The concept of species is considered artificial and inadequate to define natural populations. Social organisms display differential behaviors toward kin than to nonrelated individuals. In "social" microbes, kin discrimination has been used to help resolve crypticity. Aggregative behavior could be explored in a nonsocial protist to define phylogenetic varieties that are considered "cryptic." Two Entamoeba invadens strains, IP-1 and VK-1:NS are considered close populations of the same "species." This study demonstrates that IP-1 and VK-1:NS trophozoites aggregate only with alike members and discriminate members of different strains based on behavioral and chemical signals. Combined morphological, behavioral/chemical, and ecological studies could improve Archamoebae phylogenies and define cryptic varieties. Evolutionary processes in which selection acted continuously and cumulatively on ancestors of Entamoeba populations gave rise to chemical and behavioral signals that allowed individuals to discriminate nonpopulation members and, gradually, to the emergence of new lineages; alternative views that claim a "Designer" or "Creator" as responsible for protistan diversity are unfounded.

Examining Integrated Cell Structural Responses: Probing Cytoskeleton Behavior through a Coupled Dual-Mode Mechanical Stimulation Approach

Mechanical stimulation of cells has been shown to affect various cellular functions through the actin cytoskeleton such as cell motility, apoptosis, and proliferation. The influence of mechanics on cells is evident whether the stimulation is in the form of tension, compression, or even shear stress. In this there is a need to influence cellular function through its extracellular matrix connections with multiple integrated mechanical approaches to gain a better understanding in the field of mechanotransduction. In this study we developed a device that when utilized with an elastomeric material allows us to stimulate cells with uniaxial strip stretching, shear fluid flow or both simultaneously. This device uses a pressure regulator to induce uniaxial strip stress along the basal surface of cells and a peristaltic flow pump to induce shear stress across the apical surface. We exposed NIH/3T3 fibroblasts to uniaxial strip stretching, shear fluid flow and both simultaneously to examine the question of how the integrated inputs of mechanical stimulation are processed by the cell in terms of its structural response. We used fluorescence microscopy to examine the orientation of F-actin and G-actin structures and found alignment along the direction of force for both uniaxial strip stretching and shear fluid flow in comparison to cells exposed to both mechanical modes, which revealed an alignment out of phase between both axes of applied force. This integrated response is helping to discern the influence of the modes of stimulation in terms of overall cell behavior. These intriguing results have potential implications in a variety of fields including biophysics, mechanotransduction, and cell structure.