High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method

In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability

An analytical technique to obtain higher-order approximate periods for nonlinear oscillator

ABSTRACT: This paper presents simulation results of the influence of wide range modulation index values ( ) in carrier-based PWM strategy for application in generating the stepped waveform. The waveform is tested for application in single-phase half-bridge modular multilevel converters (MMCs) topology. The results presented in this paper include a variation of the fundamental component (50 Hz) in the voltage output.  It also studies total harmonic distortion of the output voltage (THDv) and the output current (THDi) when the modulation index is changed over the linear-modulation region, 0 < < 1. It also explores the effect of a modulation index greater than 1. Moreover, different output voltage shapes, as a consequence of varied on MMCs, are also illustrated for showing the effect of varying the value of on sub-module of MMCs. ABSTRAK: Penulisan ini berkenan simulasi pengaruh pelbagai nilai indeks modulasi     ( ) dalam strategi PWM berasaskan aplikasi dalam menghasilkan bentuk gelombang yang bertingkat. Bentuk gelombang ini diuji untuk aplikasi dalam topologi MMCs. Penilaian dan hasil dari artikle ini termasuk variasi komponen asas (50 Hz) dalam voltan keluar. Ia juga meneliti jumlah penyelarasan harmonik voltan keluar (THDv) dan arus keluaran (THDi) apabila indeks modulasi ditukar dalam rantau modulasi linear, 0 < <1. Ia juga meneroka kesan indeks modulasi lebih daripada 1. Selain itu, bentuk voltan keluar yang berbeza sebagai akibat dari pelbagai  pada MMCs juga digambarkan untuk menunjukkan kesan berbeza-beza nilai  pada sub-modul MMCs

An analytical approximation technique for the duffing oscillator based on the energy balance method

In this paper, an analytical approximation technique has been presented of obtaining higher-order approximate solutions for highly nonlinear Duffing oscillator based on the energy balance method (EBM). Higher-order approximate natural frequencies have been obtained in a novel analytical way. The accuracy of the solution method is evaluated within as error analysis. It is highly remarkable that using the presented technique, the approximation solutions produces desired results even for large oscillation as compared with the exact ones. Moreover, the solution method yields much better results than existing solutions after using a suitable truncation formula. The presented technique is applied to well-known Duffing oscillator to illustrate its novelty, reliability and wider applicabilit

Sleep Problems in Children with Autism Spectrum Disorder in Bangladesh: A Case–Control Study

Background: Sleep problems in children with Autism Spectrum Disorder (ASD) are highly prevalent, but little information is available on this issue in low- to middle-income countries (LMIC) such as Bangladesh. Therefore, the present study investigated the prevalence and socio-demographic determinants of ASD sleep disturbances in a comparison with typically developing children (TDC). Methods: A cross-sectional interview study was carried out within a total of 446 Bangladeshi mothers, whose children’s mean age was 8.1±2.9 years (151 ASD [8.5±2.7 years] and 295 TDC [7.9±2.9 years]); in addition to socio-demographics, the Child Sleep Habit Questionnaire (CSHQ) was used, and a cut-off score of 41 out of 93 points considered as reflecting sleep problems. Results: About 89.7% of the children reported having problems in sleep, with ASD reporting higher frequency vs TDC (94.00% vs 87.50%; χ2=4.678, p=0.031). The overall mean CSHQ score was 48.7±7.6 in total sample, whereas ASD children reported higher scores compared to TDCs (50.9±8.1 vs 47.5±7.0, p<0.001). Similarly, subscales of CSHQ such as sleep duration (4.23±1.56 vs 3.90±1.31, p=0.017), sleep anxiety (7.23±2.05 vs 6.45 ±1.92, p<0.001), night waking (3.82±1.07 vs 3.17±1.89, p<0.001), parasomnias (8.86±2.06 vs 7.85±2.27, p<0.001), and sleep disordered breathing (4.02±2.92 vs 3.43±2.07, p=0.014) were more problematic among ASD compared to TDC. Lastly, 28.5% of ASD reported taking sleep-related medications vs 0.3% for TDC (n=1). Conclusion: Bangladeshi ASD children are highly likely to manifest sleep disturbances, which warrant urgent implementation of parental educational and support programs to mitigate the impact of sleep problems in ASD families

Analyses of Genetic Variations of Glutathione S-Transferase Mu1 and Theta1 Genes in Bangladeshi Tannery Workers and Healthy Controls

Glutathione S-transferases (GSTs) belong to a group of multigene detoxification enzymes, which defend cells against oxidative stress. Tannery workers are at risk of oxidative damage that is usually detoxified by GSTs. This study investigated the genotypic frequencies of GST Mu1 (GSTM1) and GST Theta1 (GSTT1) in Bangladeshi tannery workers and healthy controls followed by their status of oxidative stress and total GST activity. Of the 188 individuals, 50.0% had both GSTM1 and GSTT1 (+/+), 12.2% had GSTM1 (+/−), 31.4% had GSTT1 (−/+) alleles, and 6.4% had null genotypes (−/−) with respect to both GSTM1 and GSTT1 alleles. Among 109 healthy controls, 54.1% were double positive, 9.2% had GSTM1 allele, 32.1% had GSTT1 allele, and 4.6% had null genotypes. Out of 79 tannery workers, 44.3% were +/+, 16.8% were +/−, 30.5% were −/+, and 8.4% were −/−. Though the polymorphic genotypes or allelic variants of GSTM1 and GSTT1 were distributed among the study subjects with different frequencies, the differences between the study groups were not statistically significant. GST activity did not vary significantly between the two groups and also among different genotypes while level of lipid peroxidation was significantly higher in tannery workers compared to controls irrespective of their GST genotypes

Construction of copy number variation landscape and characterization of associated genes in a Bangladeshi cohort of neurodevelopmental disorders

Introduction: Copy number variations (CNVs) play a critical role in the pathogenesis of neurodevelopmental disorders (NDD) among children. In this study, we aim to identify clinically relevant CNVs, genes and their phenotypic characteristics in an ethnically underrepresented homogenous population of Bangladesh. Methods: We have conducted chromosomal microarray analysis (CMA) for 212 NDD patients with male to female ratio of 2.2:1.0 to identify rare CNVs. To identify candidate genes within the rare CNVs, gene constraint metrics [i.e., “Critical-Exon Genes (CEGs)”] were applied to the population data. Autism Diagnostic Observation Schedule-Second Edition (ADOS-2) was followed in a subset of 95 NDD patients to assess the severity of autism and all statistical tests were performed using the R package. Results: Of all the samples assayed, 12.26% (26/212) and 57.08% (121/212) patients carried pathogenic and variant of uncertain significance (VOUS) CNVs, respectively. While 2.83% (6/212) patients’ pathogenic CNVs were found to be located in the subtelomeric regions. Further burden test identified females are significant carriers of pathogenic CNVs compared to males (OR = 4.2; p = 0.0007). We have observed an increased number of Loss of heterozygosity (LOH) within cases with 23.85% (26/109) consanguineous parents. Our analyses on imprinting genes show, 36 LOH variants disrupting 69 unique imprinted genes and classified these variants as VOUS. ADOS-2 subset shows severe social communication deficit (p = 0.014) and overall ASD symptoms severity (p = 0.026) among the patients carrying duplication CNV compared to the CNV negative group. Candidate gene analysis identified 153 unique CEGs in pathogenic CNVs and 31 in VOUS. Of the unique genes, 18 genes were found to be in smaller (<1 MB) focal CNVs in our NDD cohort and we identified PSMC3 gene as a strong candidate gene for Autism Spectrum Disorder (ASD). Moreover, we hypothesized that KMT2B gene duplication might be associated with intellectual disability. Conclusion: Our results show the utility of CMA for precise genetic diagnosis and its integration into the diagnosis, therapy and management of NDD patients

Onco-Multi-OMICS Approach: A New Frontier in Cancer Research

The acquisition of cancer hallmarks requires molecular alterations at multiple levels including genome, epigenome, transcriptome, proteome, and metabolome. In the past decade, numerous attempts have been made to untangle the molecular mechanisms of carcinogenesis involving single OMICS approaches such as scanning the genome for cancer-specific mutations and identifying altered epigenetic-landscapes within cancer cells or by exploring the differential expression of mRNA and protein through transcriptomics and proteomics techniques, respectively. While these single-level OMICS approaches have contributed towards the identification of cancer-specific mutations, epigenetic alterations, and molecular subtyping of tumors based on gene/protein-expression, they lack the resolving-power to establish the casual relationship between molecular signatures and the phenotypic manifestation of cancer hallmarks. In contrast, the multi-OMICS approaches involving the interrogation of the cancer cells/tissues in multiple dimensions have the potential to uncover the intricate molecular mechanism underlying different phenotypic manifestations of cancer hallmarks such as metastasis and angiogenesis. Moreover, multi-OMICS approaches can be used to dissect the cellular response to chemo- or immunotherapy as well as discover molecular candidates with diagnostic/prognostic value. In this review, we focused on the applications of different multi-OMICS approaches in the field of cancer research and discussed how these approaches are shaping the field of personalized oncomedicine. We have highlighted pioneering studies from “The Cancer Genome Atlas (TCGA)” consortium encompassing integrated OMICS analysis of over 11,000 tumors from 33 most prevalent forms of cancer. Accumulation of huge cancer-specific multi-OMICS data in repositories like TCGA provides a unique opportunity for the systems biology approach to tackle the complexity of cancer cells through the unification of experimental data and computational/mathematical models. In future, systems biology based approach is likely to predict the phenotypic changes of cancer cells upon chemo-/immunotherapy treatment. This review is sought to encourage investigators to bring these different approaches together for interrogating cancer at molecular, cellular, and systems levels

A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator

The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method have been introduced to derive the approximate periods of strongly nonlinear Duffing-harmonic oscillator. The comparison of two methods is made to demonstrate that the rational harmonic balance method (RHBM) gives almost similar results to next higher-order approximation results of harmonic balance method (HBM). It is highly remarkable that the solution procedure in both methods are simple and takes less computational effort for determining approximate periods and shows a good agreement compared with the exact ones

A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method

In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The standard rational harmonic balance method (SRHBM) cannot be used directly; it is possible if we rewrite the nonlinear differential equations (NDEs). To overcome this previously stated issue, we offered a modified rational harmonic balance method (MRHBM). It is noticed that a MRHBM works very well for the whole range of initial amplitudes and the excellent agreement of the approximate frequencies as well as the corresponding periodic solutions with its exact ones. The method is basically illustrated by the nonlinear non-smooth oscillators, but it is additionally useful for other nonlinear oscillatory problems with mixed parity arising in recent development of nonlinear sciences and engineering

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones