DAGSENS: Directed Acyclic Graph Based Direct and Adjoint Transient Sensitivity Analysis for Event-Driven Objective Functions

Adjusting for Selection Effects in Epidemiologic Studies

The transient response sensitivity analysis of the transmission line is a new hotspot problem in transmission line problems. In this paper, a sensitivity analysis method based on fast Fourier transform is proposed in the transient response sensitivity analysis of the transmission line network. The method firstly establishes the circuit equation of the whole transmission line network characteristic, and transforms the partial differential equation in the time domain into the ordinary differential equation in the frequency domain by Fourier transform. Then we find the derivative of a certain distribution parameter of the transmission line by the ordinary differential equation. The network transient response sensitivity problem is transformed into solving the transient response of the transmission line network and the partial derivative of the network parameter matrix to the circuit parameters, which greatly simplifies the analysis of the transient response sensitivity of the transmission line network, and the sensitivity analysis of the transient response of any node of the transmission line network to any network parameters is realized. The method does not need to decouple the coupled transmission line, and can accurately and quickly calculate the transient response sensitivity of any type of transmission line network. The result of the example shows that the method is correct and effective. This method provides a new reference method for the sensitivity analysis of transmission line network transient response.

Due to the popularity of Low-power and Lossy Networks (LLN), numerous low-power device applications are emerging and driving the need for an efficient routing protocol. Recently, the Internet Engineering Task Force (IETF) standardized the IPv6 Routing Protocol for Low-power and Lossy Networks (RPL). To route the packets, the RPL constructed a Directed Acyclic Graph (DAG) rooted towards the DAG root using the Objective Function (OF). However, the OF supported by the standard RPL did not yield better performance, since it used a single metric. Therefore, an OF based on Multimetrics (MMOF), which combines multiple routing metrics for Static Router Nodes (SRNs) and Mobile Nodes (MNs), has been proposed in this work. From the simulation results, it was observed that the proposed MMOF showed better performance compared with other existing OFs of the RPL.

One-step collocation methods for differential-algebraic systems of index 1

Article Figures and data Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: The risk of adult onset cardiovascular and metabolic (cardiometabolic) disease accrues from early life. Infection is ubiquitous in infancy and induces inflammation, a key cardiometabolic risk factor, but the relationship between infection, inflammation, and metabolic profiles in early childhood remains unexplored. We investigated relationships between infection and plasma metabolomic and lipidomic profiles at age 6 and 12 months, and mediation of these associations by inflammation. Methods: Matched infection, metabolomics, and lipidomics data were generated from 555 infants in a pre-birth longitudinal cohort. Infection data from birth to 12 months were parent-reported (total infections at age 1, 3, 6, 9, and 12 months), inflammation markers (high-sensitivity C-reactive protein [hsCRP]; glycoprotein acetyls [GlycA]) were quantified at 12 months. Metabolic profiles were 12-month plasma nuclear magnetic resonance metabolomics (228 metabolites) and liquid chromatography/mass spectrometry lipidomics (776 lipids). Associations were evaluated with multivariable linear regression models. In secondary analyses, corresponding inflammation and metabolic data from birth (serum) and 6-month (plasma) time points were used. Results: At 12 months, more frequent infant infections were associated with adverse metabolomic (elevated inflammation markers, triglycerides and phenylalanine, and lower high-density lipoprotein [HDL] cholesterol and apolipoprotein A1) and lipidomic profiles (elevated phosphatidylethanolamines and lower trihexosylceramides, dehydrocholesteryl esters, and plasmalogens). Similar, more marked, profiles were observed with higher GlycA, but not hsCRP. GlycA mediated a substantial proportion of the relationship between infection and metabolome/lipidome, with hsCRP generally mediating a lower proportion. Analogous relationships were observed between infection and 6-month inflammation, HDL cholesterol, and apolipoprotein A1. Conclusions: Infants with a greater infection burden in the first year of life had proinflammatory and proatherogenic plasma metabolomic/lipidomic profiles at 12 months of age that in adults are indicative of heightened risk of cardiovascular disease, obesity, and type 2 diabetes. These findings suggest potentially modifiable pathways linking early life infection and inflammation with subsequent cardiometabolic risk. Funding: The establishment work and infrastructure for the BIS was provided by the Murdoch Children's Research Institute (MCRI), Deakin University, and Barwon Health. Subsequent funding was secured from National Health and Medical Research Council of Australia (NHMRC), The Shepherd Foundation, The Jack Brockhoff Foundation, the Scobie & Claire McKinnon Trust, the Shane O'Brien Memorial Asthma Foundation, the Our Women's Our Children's Fund Raising Committee Barwon Health, the Rotary Club of Geelong, the Minderoo Foundation, the Ilhan Food Allergy Foundation, GMHBA, Vanguard Investments Australia Ltd, and the Percy Baxter Charitable Trust, Perpetual Trustees. In-kind support was provided by the Cotton On Foundation and CreativeForce. The study sponsors were not involved in the collection, analysis, and interpretation of data; writing of the report; or the decision to submit the report for publication. Research at MCRI is supported by the Victorian Government's Operational Infrastructure Support Program. This work was also supported by NHMRC Senior Research Fellowships to ALP (1008396); DB (1064629); and RS (1045161) , NHMRC Investigator Grants to ALP (1110200) and DB (1175744), NHMRC-A*STAR project grant (1149047). TM is supported by an MCRI ECR Fellowship. SB is supported by the Dutch Research Council (452173113). Editor's evaluation This paper provides data from a population-based cohort study on early life infection and proinflammatory, atherogenic metabolomic and lipidomic profiles at 12 months of age. The authors generated matched infection, metabolomics and lipidomics data from 555 infants in a pre-birth longitudinal cohort and they showed that frequent infant infections are associated with adverse metabolomic and lipidomic profiles. They also report that similar profiles are noted with higher glycoprotein acetyls (GlycA), but not hsCRP. The paper is interesting and assesses the role of infection and markers of inflammation on lipid and metabolic profile of patients. It provides a comprehensive analysis of lipids and metabolites in infants in response to infection. https://doi.org/10.7554/eLife.75170.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Infectious diseases are ubiquitous in infancy and childhood, with potential long-term impacts on health across the life course. Infection has been recognised as a potential contributor to atherosclerotic cardiovascular disease (CVD), one of the leading causes of adult morbidity and mortality, since the 19th century (Nieto, 1998). More recent adult studies link previous infection with long-term risks of disease (Bergh et al., 2017; Cowan et al., 2018; Wang et al., 2017). The mechanisms are largely unknown, but likely include immune activation and heightened inflammation (Shah, 2019), which are pathways central to CVD pathogenesis (Donath et al., 2019b; Ferrucci and Fabbri, 2018) and therefore offer potentially druggable targets in high-risk individuals (Donath et al., 2019a; Ridker et al., 2017). High-sensitivity C-reactive protein (hsCRP) has been extensively used as a marker of chronic inflammation in adult studies but is an acute phase reactant in children and may not reflect chronic inflammation in early life. Glycoprotein acetyls (GlycA) is a nuclear magnetic resonance (NMR) composite measure that is suggested to better reflect cumulative, chronic inflammation (Connelly et al., 2017). GlycA is an emerging biomarker for cardiometabolic risk (Connelly et al., 2017) that outperforms hsCRP as a predictor of CVD events and mortality (Akinkuolie et al., 2014; Duprez et al., 2016), and of infection-related morbidity and mortality (Ritchie et al., 2015). For example, in the Multi-Ethnic Study of Atherosclerosis (n = 6523), higher GlycA was associated with increased risk of incidence CVD and death, even after adjustment for hsCRP and other inflammatory markers. Conversely, prediction of these outcomes by hsCRP attenuated to null after mutual adjustment (Duprez et al., 2016). Cardiovascular and metabolic (cardiometabolic) disease pathogenesis begins in early life and accrues across the life course (Nakashima et al., 2008). Infections occur disproportionally in early childhood (Cromer et al., 2014; Grüber et al., 2008; Troeger et al., 2018; Tsagarakis et al., 2018), and there is a dose-response relationship between childhood infections, adverse cardiometabolic phenotypes (Burgner et al., 2015c), and CVD events (Burgner et al., 2015a) in adulthood. Infection is linked to proatherogenic metabolic perturbations in later childhood and adulthood (Feingold and Grunfeld, 2019; Khovidhunkit et al., 2000), including higher triglycerides and oxidised low-density lipoprotein (LDL), and lower high-density lipoprotein (HDL) cholesterol and apolipoprotein A1 (ApoA1) (Liuba et al., 2003; Pesonen et al., 1993), and to acute and chronic inflammation (Burgner et al., 2015b; Ritchie et al., 2015), but little is known about these relationships in early life, when most infections occur. We therefore aimed to characterise metabolomic and lipidomic profiles at 6 and 12 months of age and their relationship to infection burden during the first year of life. We also investigated the extent to which inflammation mediated the relationship between infection burden and metabolomic and lipidomic differences. Materials and methods Study cohort Request a detailed protocol This study used available data from 555 mother-infant dyads in the Barwon Infant Study (BIS), a population-based pre-birth longitudinal cohort (n = 1074 mother-infant dyads). The cohort details and inclusion/exclusion criteria have been detailed elsewhere (Vuillermin et al., 2015); in brief, mothers were eligible if they were residents of the Barwon region in south-east Australia and planned to give birth at the local public or private hospital. Mothers were recruited at approximately 15 weeks' gestation and provided informed consent. They were excluded if they were not a permanent Australian resident, aged <18 years, required an interpreter to complete questionnaires, or had previously participated in BIS. Infants were excluded if they were very preterm (<32 completed weeks gestation) or had a serious illness or major congenital malformation identified during the first few days of life. Ethics approval was granted by the Barwon Health Human Research Ethics Committee (HREC 10/24). Parent-reported infections Request a detailed protocol At the 4-week, 3-month, 6-month, 9-month, and 12-month time points following birth, mothers were asked to report each episode of infant illness or infection since the previous time point using standardised online questionnaires. The number of parent-reported infections from birth to 12 months was defined as the total number of respiratory tract infections, gastroenteritis, conjunctivitis, and acute otitis media episodes. In secondary analyses, numbers of parent-reported infections from birth to 6 months and from 6 to 12 months were considered. It was not possible to identify the proportion of parent-reported infections that lead to health service utilisation (Rowland et al., 2021). Other maternal and infant measures Request a detailed protocol Questionnaires during pregnancy and at birth were used to collect self-reported data on maternal age, household income, maternal education, and prenatal smoking (considered here as a dichotomous any/none exposure). Residential postcode was used to determine neighbourhood disadvantage using the Index of Relative Socio-Economic Disadvantage (IRSD) from the 2011 Socio-Economic Indexes for Areas (SEIFA) (Pink, 2013), with a lower score corresponding to greater socioeconomic disadvantage. Pre-eclampsia (based on International Association of Diabetes and Pregnancy Study Groups criteria; Tranquilli et al., 2014) and gestational diabetes (based on International Society for the Study of Hypertension in Pregnancy criteria; Nankervis et al., 2013) diagnoses were extracted from hospital records. Infant gestational age, birth weight, and mode of delivery (categorised as vaginal, planned caesarean section, or unplanned caesarean section delivery) were collected from birth records, and the age- and sex-standardised birth weight z-score was calculated using the 2009 revised British United Kingdom World Health Organisation (UK-WHO) growth charts (Cole et al., 2011). Postnatal smoking data was collected from questionnaire data, with mothers asked the average number of hours each day someone smoked near or in the same room as the child (Gray et al., 2019). This was dichotomised as any postnatal smoke exposure if >0 hr reported at any time point up to 12 months of age, or no postnatal smoke exposure. Breastfeeding duration up to 12 months of age was collected from maternal questionnaire data. As most evidence for the protective effect of breastfeeding on early life infection is from comparisons between any breastfeeding and no breastfeeding (Victora et al., 2016), and in light of previous evidence in BIS for an association between even a short duration of breastfeeding and lower odds of infection in early infancy (Rowland et al., 2021), we first looked at breastfeeding as a binary (any/none) measure in models (presented in the main text). As most infants (98.2%) were breastfed to some extent, and it is unknown the degree to which breastfeeding, and the timing of breastfeeding, might affect infant metabolomics and lipidomics, we also considered duration of breastfeeding as a continuous variable for sensitivity analyses. Metabolomic and lipidomic profiling Request a detailed protocol Venous peripheral blood was collected from infants at the 6- and 12-month time points in sodium heparin and generally processed within 4 hr, with a minority (197 of 555) of 12-month samples processed after 4 hr (median time for those 197 samples = 19.9 hr, inter-quartile range [IQR] [18.7, 21.4]). The time interval between collection and post-processing storage of samples was included as a covariate in analyses. Due to the bimodal distribution of 12-month sample collection times as samples were either processed same day of collection or the following day, sensitivity analysis excluding participants with a plasma storage time greater than 4 hr (197 out of 555 infants, predominantly processed the following day) was performed, as described in the Statistical analysis section below. Plasma was stored at –80°C, and aliquots were shipped on dry ice to Nightingale Health (Helsinki, Finland) for NMR metabolomic quantification and Baker IDI (Melbourne, Australia) for liquid chromatography/mass spectrometry (LC/MS) lipidomic quantification, as described below. For secondary analyses investigating possible 'reverse causality', that is, whether metabolomic or lipidomic profile at birth was associated with number of parent-reported infections from birth to 6 months of age, metabolomics and lipidomics data using the same platforms from venous cord blood collected at birth, as previously described (Burugupalli et al., 2022; Mansell et al., 2021), was used. The NMR-based metabolomics platform has been described in detail (Kettunen et al., 2016; Soininen et al., 2015), and quantified a broad range of metabolic measures including lipoprotein size subclasses, triglycerides, cholesterols, fatty acids, amino acids, ketone bodies, glycolysis metabolites, and GlycA. In brief, plasma samples were mixed with a sodium phosphate buffer prior to NMR measurements with Bruker AVANCE III 500 MHz and Bruker AVANCE III HD 600 MHz spectrometers (Bruker, Billerica, MA). Samples were kept at 6°C using the SampleJet sample changer (Bruker) to prevent degradation. After initial measurements, samples went through a multiple-step lipid extraction procedure using saturated sodium chloride solution, methanol, dichloromethane, and deuterochloroform. The lipid extracts were then analysed using the 600 MHz instrument (Soininen et al., 2015). The utility of this platform in epidemiological research has been detailed elsewhere (Würtz et al., 2017). Using the Nightingale Health 2016 bioinformatics protocol, 228 metabolomic measures were generated for the 12-month samples. From a subset of participants, replicate samples were quantified, and these showed a low percentage coefficient of variation (<10%). Subsequently, the Nightingale Health 2020 bioinformatics protocol was used to generate 250 metabolomic measures for the 6-month samples, with 224 of these measures also present in the 12-month data. As a large proportion of the NMR metabolomic measures are ratios and are strongly correlated with each other in children and adults (Ellul et al., 2019), an informative subset of 51 measures that captured the majority of variation in the metabolomic dataset, primarily absolute metabolite concentrations, were included in analysis presented in the main text. Analyses for excluded metabolomic measures are presented as supplementary data. To complement GlycA as a measure of inflammation, hsCRP was also quantified in 6- and 12-month plasma using enzyme-linked immunosorbent assay (ELISA) (R&D Systems, Minneapolis, MN, cat. no. DY1707), as per the manufacturer's instruction. The details of the high-performance LC/MS lipidomics platform have been described elsewhere (Beyene et al., 2020). In addition, we used medronic acid to passivate the LC/MS system to avoid peak tailing for acidic phospholipids (Hsiao et al., 2018). In brief, this platform quantified 776 lipid features in 36 lipid classes, including sphingolipids, glycerophospholipids, sterols, glycerolipids, and fatty acyls. Analysis was performed on an Agilent 6490 QQQ mass spectrometer with an Agilent 1290 series high-performance liquid chromatography system and two ZORBAX eclipse plus C18 column (2.1 × 100 mm 1.8 mm) (Agilent, Santa Clara, CA) with the thermostat set at 45°C. Mass spectrometry analysis was performed in both positive and negative ion mode with dynamic scheduled multiple reaction monitoring. Quantification of lipid species was determined by comparison to the relevant internal standard. Lipid class total concentrations were calculated as the sum of individual lipid species concentrations, except in the case of triacylglycerols (TGs) and alkyl-diacylglycerols, where we measured both neutral loss and single ion monitoring (SIM) peaks, and subsequently used the SIM species concentrations for summation purposes. Statistical analysis Request a detailed protocol Analyses were performed in R (version 3.6.3) (R Development Core Team, 2018). All metabolomic and lipidomic measures had their lowest observed non-zero value (considered the lower limit of detection) added to their value before they were natural log-transformed and scaled to a standard distribution (standard deviation units). Pearson's correlations were calculated for number of infections from birth to 12 months with 12-month GlycA and hsCRP. The estimated effect of number of parent-reported infections from birth to 12 months as an exposure on 12-month metabolomic and lipidomic profile was investigated using linear regression models for each metabolomic/lipidomic measure. Standard errors were used to calculate 95% confidence intervals for estimated effects. All models were adjusted for infant sex, exact age at 12-month time point, birth weight z-score, gestational age, maternal household income, exposure to maternal smoking during pregnancy, breastfeeding, and time from collection to storage for the plasma sample. Linear regression models adjusted for the same covariates were used to investigate 12-month GlycA and hsCRP as exposures and each metabolomic/lipidomic measure as an outcome. Two-tailed p-values were adjusted for multiple comparisons within each dataset (NMR metabolomics, LC/MS lipidomic species, and LC/MS lipidomic classes) using the Benjamini-Hochberg method (Benjamini and Hochberg, 1995). To investigate the robustness of the estimates, mean model coefficients and bias-corrected accelerated percentile bootstrap confidence intervals were calculated from nonparametric bootstrap resampling (1000 iterations) using the 'boot' package (Davison and Hinkley, 1997) (version 1.3–25) in R, included in Source Data. The assumption of linearity was investigated post hoc using plots of residual values for the top 10 metabolomic and lipidomic differences (ranked by p-value) for each of number of infections, GlycA, and hsCRP. To further investigate the other sources of potential confounding and variation that could affect findings from the primary models, several sensitivity analyses were performed. These were: (i) additional adjustment of the primary model for postnatal smoking exposure, gestational diabetes, and pre-eclampsia; (ii) analyses excluding twins (five infants); (iii) analyses excluding infants with hsCRP >5 mg/L (24 infants) as a marker of acute infection (Lemiengre et al., 2018; et al., analyses excluding plasma samples with hr from collection to storage (197 and analyses for breastfeeding duration of any Analyses of the primary models adjusted for measures of socioeconomic or maternal of household were also considered. These models are presented as supplementary plots analyses to investigate 6-month of infections were performed. The birth to 6-month models investigated the relationship between infections up to 6 months of age, 6-month inflammation, and 6-month metabolomic/lipidomic The 6- to 12-month models investigated the relationship of infections between 6 and 12 months of age, 12-month inflammation, and 12-month metabolomic/lipidomic with adjustment for the corresponding 6-month For secondary analyses to investigate regression models et al., were either for (i) each metabolomic/lipidomic measure from cord blood at birth as exposure and total number of infections from birth to 6 months of age as or (ii) each 6-month metabolomic/lipidomic measures as exposure and total number of infections from 6 to 12 months of age as the with adjustment for number of infections from birth to 6 months of age. All secondary models were adjusted for the same covariates as the primary models described that is, infant sex, gestational age, exact age 6- or 12-month time birth weight z-score, maternal household income, exposure to maternal smoking during pregnancy, and sample time between collection and post-processing with birth metabolomic/lipidomic measures as the exposure were adjusted for mode of which is associated with differences across NMR metabolomic measures in cord in this cohort et al., 2021). To investigate the potential role of inflammation in mediating associations between infection and metabolic the package et al., 2017) (version in R was then used in a to the natural effect mediated by and natural effect by of infection. 12-month GlycA or hsCRP were considered as for the effect of number of infections from birth to 12 months of age on metabolomic and lipidomic differences at 12 months, for metabolomic and lipidomic measures associated with number of infections with an adjusted from the linear regression models described mediation was calculated as the estimated natural effect by the total effect effect plus natural of the mediation model is in for model investigated in this The natural effect by glycoprotein acetyls or C-reactive protein and natural effect mediated by of parent-reported infections on metabolomic and lipidomic measures were with adjustment for were considered to for associations to exposure to and to As models investigating described suggested that 6-month GlycA or lipidomic measures may number of infections from 6 to 12 months of age, we performed mediation analyses to the percentage mediation of 12-month GlycA and hsCRP for the effect of number of infections from 6 to 12 months of age on 12-month metabolomic and lipidomic with additional adjustment for the corresponding 6-month measures of infections from birth to 6 months of age, 6-month GlycA or and the 6-month metabolomic/lipidomic Results The for the 555 infants included in this study is in and the cohort for these infants are in The number of total parent-reported infections from birth to 12 months of age was = infections from birth to 6 months of age was 2 and infections from 6 to 12 months of age was 12-month hsCRP and GlycA were mg/L and number of parent-reported infections between birth and 12 months of age was more strongly correlated with 12-month GlycA = than hsCRP = The of metabolomic and lipidomic measures at each time point for the cohort are in and (n = age at delivery smoking during pregnancy diabetes (n = (n = household to to to to (n = than year 10 of 10 of or 12 of or of birth caesarean caesarean postnatal smoke exposure to 12 months (n = of duration to weeks age weight weight at 6-month time point at 6 months z-score at 6 at 12-month time point at 12 months z-score at 12 of parent-reported infections from birth to 12 Infections from birth to 6 Infection from 6 to 12 GlycA at 6 months at 6 months at 12 months at 12 months All = 555 infants had complete covariate data for primary models, data of secondary exposures is to the relevant measure. lower value greater socioeconomic disadvantage on 2 of Barwon Infant Study participants included this study participants had complete infection data from time points between birth and 12 months of age, and 12-month plasma nuclear magnetic resonance (NMR) metabolomics data. included participants (n = out of 555) had 12-month plasma liquid chromatography/mass spectrometry (LC/MS) lipidomics data. Infection and inflammation burden and plasma NMR metabolomic profile at 12 months was evidence for higher number of infections with higher inflammatory markers per infection, 95% and hsCRP lower HDL to to and to cholesterols, lower to lower to higher and to a extent with higher triglycerides and lower to In models with GlycA as the marker of inflammation metabolomic differences observed for higher GlycA were largely similar but more those for parent-reported including HDL per in GlycA to higher and lipoprotein to higher apolipoprotein higher total fatty higher total triglycerides and amino and lower to metabolites lower to and lower to were generally similar to standard regression for models. effect were generally similar across most sensitivity analyses excluding samples with time greater than 4 hr the of estimated of parent-reported infections on HDL and hsCRP was associated with lower HDL cholesterol per in to to and to and higher to as observed for GlycA, and with lower of most other amino and to and higher triglycerides with 2 in 12-month plasma nuclear magnetic resonance (NMR) metabolomic measures for each in parent-reported infection to 12 and for each in 12-month glycoprotein acetyls (GlycA) (n = plots of the estimated 12-month metabolomic differences for each additional parent-reported infection from birth to 12 months or 12-month GlycA from adjusted linear regression models, and the

An adjoint sensitivity method is presented for parameter-dependent differential-algebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In addition, it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system.

In the article we obtained sufficient conditions of the existence of the nonlinear Noetherian boundary value problem solution for the system of differential-algebraic equations which are widely used in mechanics, economics, electrical engineering, and control theory. We studied the case of the nondegenerate system of differential algebraic equations, namely: the differential algebraic system that is solvable relatively to the derivative. In this case, the nonlinear system of differential algebraic equations is reduced to the system of ordinary differential equations with an arbitrary continuous function. The studied nonlinear differential-algebraic boundary-value problem in the article generalizes the numerous statements of the non-linear non-Gath boundary value problems considered in the monographs of А.М. Samoilenko, E.A. Grebenikov, Yu.A. Ryabov, A.A. Boichuk and S.M. Chuiko, and the obtained results can be carried over matrix boundary value problems for differential-algebraic systems. The obtained results in the article of the study of differential-algebraic boundary value problems, in contrast to the works of S. Kempbell, V.F. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and A.A. Boychuk, do not involve the use of the central canonical form, as well as perfect pairs and triples of matrices. To construct solutions of the considered boundary value problem, we proposed the iterative scheme using the method of simple iterations. The proposed solvability conditions and the scheme for finding solutions of the nonlinear Noetherian differential-algebraic boundary value problem, were illustrated with an example. To assess the accuracy of the found approximations to the solution of the nonlinear differential-algebraic boundary value problem, we found the residuals of the obtained approximations in the original equation. We also note that obtained approximations to the solution of the nonlinear differential-algebraic boundary value problem exactly satisfy the boundary condition.

Sensitivity analysis of differential-algebraic equations and partial differential equations

In this paper, an intelligent control technique is developed for improving the stability of the induction motor (IM). An intelligent technique is the adaptive neuro fuzzy inference system (ANFIS) which is proposed to improve the stability and regulate the speed of the IM. Here, the proposed technique is integrated with the phase locked loop (PLL) control. The PLL is employed to provide the slip frequency control and to provide better performance characteristics of the motor. The proposed method-based PLL technique provides an excellent speed, torque and slip frequency control of IM drives. In the proposed controller, the ANFIS is used to evaluate the error signal available from the actual speed and command speed signal. Based on the objective function, the control signals are generated for the IM. The ANFIS-based PLL technique for IM is implemented in MATLAB/Simulink platform and their performances are compared with the existing methods such as FLC and ANN techniques.

Scheduling is absolutely the resource management. A group of interdependent jobs/tasks forms the workflow application and scheduling is to map the jobs/tasks on to the collection of heterogeneous resources available in a massive geographic spread. Most complicated applications consist of interdependent jobs that coordinate to solve a problem. The completion of a particular job is the criterion function essentially to meet in order to start the execution of those jobs that depend upon it [1]. This kind of workflow application may be represented in the form of a Directed Acyclic Graph (DAG). Grid Workflow is such an application and is modeled by DAG. This paper proposes a tool that generates Directed Acyclic Graph through Randomizer, which helps in solving the scheduling problem among the dependent tasks by considering the parameters, computation cost (COMPCost) of the nodes and the communication cost (COMMCost) between the nodes. This tool is developed in Java, considering it as a platform independent and web authoring application developer. The task dependencies are made random, the computation cost and communication cost are also randomly allocated by the randomizer. The output generated by the tool includes (i) a visual component of an actual DAG,(ii) a table with complete information on task, its predecessors, COMPCost, COMMCost and (iii) detailed description about the number of levels, number of tasks at each level, identification of a tasks in a level and relationship between the nodes.

RPL is IPv6 Routing Protocol designed for Low Power and Lossy networks. RPL is a distance vector routing protocol that builds Directed Acyclic Graphs (DAGs), using implementation specific routing metrics and constraints. In the construction process of network topology, each node selects a set of potential parents towards the destination and associates itself to a preferred parent, basing on the outcome of Objective Function (OF). OF defines how one or more node and link metrics and constraints are used to compute the node rank. The purpose of this paper is to analyse, how selection of Objective Function influences network topology. The absence of published papers concerning RPL Objective Function motivates author to focus on this topic. In addition, performance evaluation of network transmission when constructed using different OF is presented. Results where obtained using simulation environment prepared for this and further planned studies on RPL.

Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which equations to be differentiated, and how many times. Both Pantelides's algorithm and Pryce's $\Sigma$-method are equivalent: if one of them finds correct structural information, the other does also. Nonsingularity of the Jacobian produced by SA indicates a success, which occurs on many problems of interest. However, these methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates $\Sigma$-method's failures and presents two conversion methods for fixing them. Both methods convert a DAE on which the $\Sigma$-method fails to an equivalent problem on which this SA is more likely to succeed.

We consider the problem of uniform allocation according to the minimax criterion of a non-renewable resource of an innovative project's activities. A lexicographic method is used for ordering these minimax criteria To solve the problem - one objective function - developed a greedy heuristic for finding the maximum path on an acyclic digraph with double weights on arcs. The greedy heuristic gives approximate solution of the problem mentioned. The obtained solution allows building a project resources plan and schedule with four types of temporary slacks with inaccurate initial data. The proposed approach allows performing an analysis of the project Risk of Performance parameter, for which has not developed the apparatus for its analysis. These include the risks that the project when complete fails to perform as intended or fails to meet the mission or business requirements that generated the justification for the project. Performance risks are estimated on the probability distribution function of a favorable/unfavorable outcome. Proposed lexicographic disintegration is a decomposition procedure and is suitable for planning and scheduling large-scale projects. Practical calculations for the convex problem in the initial statement may be performed with the help of ready-made software, and the obtained greedy solution of the problem-consequence has theoretical significance in graph theory.

The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupling induces discontinuities when inequality constraints are activated or deactivated. Two approaches for the solution of the optimization-constrained differential equations are presented. The first approach is a time splitting scheme together with a fixed-point method that alternates between the differential and optimization parts. The ordinary differential equations are approximated by the Crank-Nicolson scheme and a primal-dual interior-point method combined with a warm-start strategy is used to solve the minimization problem. The second approach considers the set of equations as a system of differential algebraic equations after replacing the minimization problem by its first order optimality conditions. An implicit 5th-order Runge-Kutta method (RADAU5) is then used. Both approaches are completed by numerical techniques for the detection and computation of the events (activation and deactivation of inequality constraints) when the system evolves in time. The computation of the events is based on continuation techniques and geometric arguments. Moreover the first approach completes the computation with extrapolation polynomials and sensitivity analysis, whereas the second approach uses dense output formulas. Numerical results for gas-aerosol system made of several chemical species are proposed for both approaches. These examples show the efficiency and accuracy of each method. They also indicate that the second approach is more efficient than the first one. Furthermore theoretical examples show that the method for the computation of the activation is of second order for the first approach and exact for the second one.

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