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A study on defective colouring of graphs
If different technology represent distinct colours that are to be located on some geographical region which can be represented as vertices of a graph, then the proper colouring is obtained when no two technology of same type share a common edge between the vertices they are placed on. The minimum technology required for such a colouring of a graph is the chromatic number of the graph. However, if the available technology are less than that of the minimum required, then the question arises on how to place the technology on the vertices of a graph in such a way that there is a minimum adjacency between the technology of same type. The solution for this problem can be attained by defining certain rules for the properness of colouring in which a few thresholds are tolerated. We know that, in a proper colouring every colour class is an independent set. If the available colours to colour a graph is less than that of the chromatic number of graphs, then a threshold that can be tolerated is permitting few colour classes to be non-independent set. An edge uv is said to be a monochromatic edge or bad edge if the colours assigned to both u and v are the same. -
Evaluation of personal development components in counselor education programs in India /
Journal Of Asia Pacific Counseling, Vol: 6, Issue 1, pp.1-20, ISSN: 2233-6710(Print), 2384-2121(Online). -
Identification and standardization of counsellor competencies for masters level counsellor education programs in India
Counselling psychology programs in India have been criticized for being ‘poor replicas of concepts that have originated in western cultures’. The lack of Indian models has been quoted as a drawback indicating that trainees are not necessarily competent to provide effective counselling services. The present study aimed at identifying and standardizing competenciesfor post graduate counsellor training in India based on local needs.The study employed a mixed methods design with four phases. In the first phase, a list of key occupational tasks were drawn up through a systematic review of literature and interviews with three expert practitioners. The second phase was the development of a counsellor competency list which outlined the various competencies required to fulfil the key occupational tasks determined in the previous stage. Seventy one competencies were identified and the list was then given for expert validation. In the third phase, the competency list was given to 75 practicing counsellors across India who rated the competencies on a 5-point likert scale, based on its importance for post graduate counsellor trainees. In the final stage the prioritized competencies were analyzed using a concept development approach to identify core competencies required for master level counselling psychology trainees. The resulting core competencies were three foundational competency domains which included ethical practice, personal and professional development and cultural sensitivity. -
Actualization of the educational vision of Kuriakose Elias Chavara through providing higher educational facilities in the formation of human capital in CMI and CMC higher education institutions
Kuriakose Elias Chavara, the great educational visionary of the 19th century, had opened a new path in the education field of our nation through his valuable contributions. He has soared high in the caste-ridden society and took the initial step in the field of education by starting schools with the aim of educating all irrespective of caste or creed. Understanding that education is the best tool to transform the society, he promoted the poor and the marginalized to attend school and made the high caste and the lower caste sit in the same room and on the same bench. Kuriakose Elias Chavara comprehended the immense need for education, and his work has performed a distinct function in the formation of a contemporary nation. To realize his vision, he established two indigenous congregations named Carmelites of Mary Immaculate (CMI) for men and Congregation of the Mother of Carmel (CMC) for women. Being inspired by the vision of the founder, these two Congregations started many schools and colleges all over India. The current study throws light on the Actualization of the Educational Vision of Kuriakose Elias Chavara in relation to Higher Educational Facilities and Formation of Human Capital as independent variables. -
Actulization of the educational vision of kuriakose elias chavara through providing higher educational of facilities in the formation of human capital in CMI and CMC higher education institutions
Kuriakose Elias Chavara, the great educational visionary of the 19th newlinecentury, had opened a new path in the education field of our nation through his newlinevaluable contributions. He has soared high in the caste-ridden society and took the initial step in the field of education by starting schools with the aim of educating all irrespective of caste or creed. Understanding that education is the best tool to transform the society, he promoted the poor and the marginalized to attend school and made the high caste and the lower caste sit in the same room and on the same bench. Kuriakose Elias Chavara comprehended the immense newlineneed for education, and his work has performed a distinct function in the newlineformation of a contemporary nation. To realize his vision, he established two newlineindigenous congregations named Carmelites of Mary Immaculate (CMI) for men and Congregation of the Mother of Carmel (CMC) for women. Being inspired by the vision of the founder, these two Congregations started many schools and colleges all over India. The current study throws light on the Actualization of the Educational Vision of Kuriakose Elias Chavara in relation to Higher Educational Facilities and Formation of Human Capital as independent variables. A newlineconvergent parallel mix method study was employed with a sample consisting of 190 religious faculty members of CMI and CMC higher education institutions from different parts of India. The findings of the study reveal a close positive correlation of actualization of the educational vision of Chavara with the independent variables. Educational facilities are seen to be essential in the development of quality education. Formation of Human Capital acts as significant predictor in the vision actualization. The study is based on the higher education system and religious faculty members in CMI and CMC. It is also expected that providing educational facilities and Formation of Human Capital are the newlinecombination of the vision actualization in the education field. -
Integrated intelligent framework for e-learning
E-learning is the primary method of learning for most learners after regular academics studies. Knowledge delivery through e-learning technologies increased exponentially over the years because of the advancement in internet and e-learning technologies. Knowledge delivery to some people would never have been possible without the e-learning technologies. Most of the working professionals do focused studies for carrier advancement, promotion, or for improving domain knowledge. These learners can find many E-learning is the primary method of learning for most learners after regular academics studies. Knowledge delivery through e-learning technologies increased exponentially over the years because of the advancement in internet and e-learning technologies. Knowledge delivery to some people would never have been possible without the e-learning technologies. Most of the working professionals do focused studies for carrier advancement, promotion, or for improving domain knowledge. These learners can find many free e-learning web sites from the internet easily in the domain of interest. However, it is quite difficult to find the best e-learning content suitable for their learning based on their domain knowledge level. Users spent most of the time figuring out the right content from a plethora of available content and end up learning nothing. A framework using machine learning algorithms with Random Forest Classifier is proposed to address the issue, which classifies the e-learning content based on its difficulty levels and provides the learner the best content suitable based on the knowledge level. The framework is trained with the data set collected from multiple popular e-learning web sites. The model is tested with real-time e-learning web site links and found that the e-contents in the web sites are recommended to the user based on its difficult levels as beginner level, intermediate level, and advanced level. -
A model to measure receptivity among teachers and to facilitate smooth transition of anademic trainers or teachers /
Patent Number: 202241032185, Applicant: Trixy Elizabeth John.
The invention provides a model for facilitating receptivity to change in teachers. The model provide a four-correlated factor structure. The model includes individual, organisational, bridging, and educational factors. The factors in the present invention created based on respective sub-factors provides the foundation for the model. The different sub factors comprise self-efficacy and self-regulation for individual factors; school climate, school support, principal support, professional training, communication, and participation for organisational factors. -
Model of ICT based blended education system: Productive implementation for sector skills development /
Patent Number: 202141055854, Applicant: Suplab Podder. -
Creativity and innovation in quality education and sustainability /
Patent Number: 202141034649, Applicant: Suplab Podder.
Quality education and sustainability is the interconnected aspiration for the modern society that can ensure the development of employability skills and create a sustainable society. The economists, scientists, management experts and research initiators are putting their efforts to develop a certain sustainable system in quality education through education 4.0. This is about digital equity, customised education, borderless classrooms, where the human mind is in synchronising with the technology to explore new possibilities of learning and accomplishment. -
Integrated intelligent framework for e-learning
E-learning is the primary method of learning for most learners after regular academics studies. Knowledge delivery through e-learning technologies increased exponentially over the years because of the advancement in internet and e-learning technologies. Knowledge delivery to some people would never
have been possible without the e-learning technologies. Most of the working professionals do focused studies for carrier advancement, promotion, or for improving domain knowledge. These learners can find many free e-learning web sites from the internet easily in the domain of interest. However, it is quite
difficult to find the best e-learning content suitable for their learning based on their domain knowledge level. Users spent most of the time figuring out the right content from a plethora of available content and end up learning nothing. A framework using machine learning algorithms with Random Forest Classifier
is proposed to address the issue, which classifies the e-learning content based on its difficulty levels and provides the learner the best content suitable based on the knowledge level. The framework is trained with the data set collected from
multiple popular e-learning web sites. The model is tested with real-time elearning web site links and found that the e-contents in the web sites are recommended to the user based on its difficult levels as beginner level, intermediate level, and advanced level.
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The impact of holistic education on value preference social comperence and leadership skills of engineering students
Students usually begin their academic journey in college or university during the late adolescence (17-20 years). In this dynamic period of lifespan, they are highly vulnerable to the limitations in personality development related issues of gender, self-esteem, competition, and cultural membership which may result in many challenges in life. Viewing positively, students at this age could be trained for integral growth holistically. Holistic education involves the complete and solid formation of every aspect of a student s personality. Its goal is to nurture individuals to be intellectually competent, spiritually mature, morally upright, psychologically integrated, physically healthy and socially acceptable (CMI Vision, 1991). Hence, the focus is to enable an individual to go beyond the acquisition, generation and application of knowledge but to transcend to higher realms of self-development, social integration and contribution. Thus, Holistic Education makes an attempt to take one through various aspects of personal, interpersonal and social dimensions of human life, and finally, helps individuals to understand the reality of life to live fully as human beings. This study was embarked to assess the impact of Holistic Education on the value preference, social competence, and leadership skills of engineering students. newlineThe research design was single group pre-test, post-test and delayed post-test experimental design. The researcher developed and standardised the Holistic Education curriculum with the support of the relevant literature and the subject experts. A pilot study was conducted on first year engineering students to get hands-on experience of the programme and to assess the impact of the facilitative tool. For the present intervention, 55 students from the first-year engineering class of a university in Bengaluru were selected using stratified random sampling method. -
Revolutionizing Education: Evaluating the Impact of AI and Ed Tech Tools on Learning Outcomes
The rapid evolution of artificial intelligence (AI) and educational technology (EdTech) tools is significantly transforming teaching and learning processes across the globe. This chapter seeks to critically examine the impact of Al-driven platforms and digi-tal learning tools on educational outcomes, learner engagement, and pedagogicalpractices. By exploring empirical evidence, theoretical frameworks, and real-world implementations, this chapter aims to provide a comprehensive understanding of how Al and EdTech tools are reshaping personalized learning, assessment, student support, and teacher facilitation. Particular emphasis will be given to the effectiveness of these tools in diverse educational contexts, including challenges related to accessibility, ethical considerations, and the digital divide. The chapter will also present recommendations for integrating Al and EdTech in ways that are pedagog-ically sound, inclusive, and outcome-focused. 2026 by IGI Global Scientific Publishing. All rights reserved. -
Corrected Score Estimation of Regression with Autocorrelation Under Measurement Errors
In regression models with autocorrelated errors, measurement errors in the covariates can lead to biased and inconsistent estimation of the regression coefficients. Measurement error refers to the discrepancy between the observed values of a variable and its true values. It occurs during the data collection process due to various factors such as inaccuracies in measurement instruments, limitations in the measuring process, human errors, or environmental influences. These errors can introduce bias into collected data, impacting the reliability and validity of statistical analyses and model outcomes. Recognizing the importance of time dependencies, our study extends to time series regression models in the presence of measurement error. A score function is the derivative of the log-likelihood function with respect to the parameters. In this paper, a correction for score function in regression with autocorrelated errors is considered to account for the impact of measurement errors on parameter estimation, and it attempts to provide a two-step estimation procedure to resolve the bias caused by both these challenges. Further, the efficiency of these estimates is compared with least square estimates by carrying out a simulation study for finite samples, and we conclude the proposed methodology provides more accurate results. The applicability of the proposed model has been illustrated using the Phillips Curve dataset and it was found that in the presence of measurement error, corrected score estimation gives more accurate estimates than OLS estimates. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025. -
Estimating Function Approach for Modelling Non-Gaussian Time Series
In this study, an effective technique for estimating parameters of autoregressive models with non-Gaussian errors has been presented. For non-Gaussian error distributions, classical techniques like maximum likelihood estimation (MLE) are found to be computationally intractable. To address this issue, an estimating function (EF) technique has been utilized, which effectively estimates the model parameters by taking advantage of the error structure. Specifically, AR(1) with logistic errors has been used, and the optimal estimating functions have been derived by constructing martingale-based estimating equations tailored to logistic errors. A hybrid AR(1)-ANN model has also been developed to integrate the strengths of both linear AR(1) and nonlinear ANN models. The robustness and efficiency of the pro-posed approach in parameter estimation have been investigated using simulations, comparing its mean squared error (MSE) and bias to those of MLE. The applicability of this approach has been further demonstrated using both simulated and real datasets. The results show that, in the presence of non-Gaussian errors, the EF method provides a computationally efficient and reliable alternative to classical estimation methodologies. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025. -
REGRESSION WITH VOLATILE ERRORS IN THE PRESENCE OF MEASUREMENT ERRORS
This study explores the estimation and testing of regression models with volatile errors when measurement errors are present. The presence of measurement error in models with heteroscedastic disturbances, such as those following an autoregressive conditional heteroscedasticity (ARCH) or Generalized ARCH (GARCH) structure, can lead to biased estimates and misleading inferences. To address this, we develop an estimation framework that accounts for both heteroscedasticity and mismeasured observations, ensuring consistent and asymptotically normal parameter estimates. We estimate the parameters using corrected score estimation and weighted linear regression, which effectively mitigate the impact of measurement error and hetroscedasticity. Additionally, we perform a Likelihood Ratio (LR) test to assess the significance of measurement errors in regression models with volatile errors. Through Monte Carlo simulations, we analyze the bias and efficiency of traditional estimators and demonstrate the robustness of our proposed approach. Finally, the methodology is applied to real-life economic and financial data, illustrating its practical relevance and effectiveness in empirical research. The findings contribute to improving statistical inference in models where measurement error and volatility coexist, ensuring more reliable and accurate parameter estimation. 2025, Gnedenko Forum. All rights reserved. -
Modeling of non-Gaussian time series in the presence of measurement error
Measurement error in time series refers to inaccuracies or deviations in recorded data that can distort the true underlying patterns, potentially leading to biased estimates and misleading conclusions in statistical analysis. AR models with non-Gaussian errors are crucial for accurately capturing real-world time series data with skewness, heavy tails, or outliers, leading to better forecasts and more reliable statistical inferences. Our focus in this study is on an optimal estimating function (EF) method that accounts for measurement error while estimating the parameters of AR(1) with logistic innovation. The asymptotic properties of the obtained optimal EF are also proved. The simulation study shows that incorporating measurement error into the model yields better estimates compared to ignoring its presence when measurement error exists. This shows that ignoring the measurement error leads to biased estimates. 2026 Taylor & Francis Group, LLC. -
Decision Flow Tracing and Word Impact Analysis in Hybrid Transformer-Conditioned Diffusion Models for Text-to-Image Generation
Text-to-image diffusion models have become a cornerstone of modern generative AI, offering high-quality synthesis yet remaining constrained by their black-box nature, which limits controllability and interpretability. In this work, we propose a hybrid transformer-conditioned diffusion model that integrates UNet-based denoising with multi-head cross-attention transformer blocks at critical latent stages of the diffusion process. The architecture is trained on a curated set of 50,000 samples from DiffusionDB with a 200-step latent diffusion schedule. Text prompts are encoded using a 16-token BERT encoder and mapped into a 256-dimensional latent feature space. Cross-attention layers with eight heads are interlaced within the UNet bottleneck and decoder, enabling token-to-region correspondence and fine-grained semantic propagation. To ensure interpretability, we design an explainability framework that combines hierarchical token-level attention heat maps, temporal attention rollouts, and perceptual ablation studies based on learned image patch similarity. Analysis reveals that object tokens remain spatially and temporally consistent, while attribute tokens demonstrate sharper temporal volatility. JensenShannon divergence quantifies this redistribution of attention across diffusion steps. Experimental evaluation against a standard UNet diffusion baseline demonstrates clear improvements: Frhet Inception Distance decreases by 19.6, CLIP alignment score increases by 5.4, and Inception Score improves by 18.6. Moreover, attention coherence improves by 22%, underscoring the gains in explainability. The proposed framework establishes a pathway toward accountable, high-fidelity, and interpretable text-to-image synthesis. Beyond performance, it supports critical tasks such as bias evaluation, fairness auditing, and quality assurance, offering a robust foundation for the next generation of explainable generative AI systems. The Author(s), under exclusive license to Springer Nature Switzerland AG 2026. -
Emotion-Aware Sign Language Recognition Using CNN and UNET Architectures
This paper proposes an AI-based system for the recognition of sign language with the detection of emotions for more expressive communication among speech-impaired and hearing individuals and others. Traditional sign language systems focus mainly on the aspect of hand gestures and neglect the signs for emotions that add meaning and context. In order to overcome the limitation, the project proposes a system that utilizes Convolutional Neural Nets (CNNs) for the recognition of hand signs and UNET for the segmentation of the picture so that the area of the hands can be discriminated from the background. Facial Emotion Recognition (FER) is also incorporated in order to detect signs such as happiness, sadness, or anger. Overall, the parts together constitute a multimodal recognition system that can read signs and emotions and produce more natural and expressive outputs. The paper delves into architecture, dataset challenges, and implementation concepts with publicly available databases such as RWTH-PHOENIX-Weather 2014T. The combined approach can enhance inclusivity and access in learning, communication, and assistive technology. 2025 IEEE. -
Emotion-Aware Sign Language Recognition Using CNN and UNET Architectures
This paper proposes an AI-based system for the recognition of sign language with the detection of emotions for more expressive communication among speech-impaired and hearing individuals and others. Traditional sign language systems focus mainly on the aspect of hand gestures and neglect the signs for emotions that add meaning and context. In order to overcome the limitation, the project proposes a system that utilizes Convolutional Neural Nets (CNNs) for the recognition of hand signs and UNET for the segmentation of the picture so that the area of the hands can be discriminated from the background. Facial Emotion Recognition (FER) is also incorporated in order to detect signs such as happiness, sadness, or anger. Overall, the parts together constitute a multimodal recognition system that can read signs and emotions and produce more natural and expressive outputs. The paper delves into architecture, dataset challenges, and implementation concepts with publicly available databases such as RWTH-PHOENIX-Weather 2014T. The combined approach can enhance inclusivity and access in learning, communication, and assistive technology. 2025 IEEE.