Abstract

This thesis explores and analyzes humor generation through several methods. This thesis introduces an approach to automated joke generation that leverages a novel hybrid model combining template extraction and infilling. Recognizing the inherent structure and unpredictability in humor, this work pi- oneers a method that extracts templates from existing jokes and subsequently infills these templates with new content, guided by state-of-the-art (SOTA) techniques available at the time of research. Specifically, the thesis accomplishes three main objectives: Firstly, it develops an automated system for joke genera- tion that innovatively combines template extraction with a deep learning approach for content infilling, ensuring both the preservation of joke structure and the introduction of novelty. This approach uses a rule-based method to extract a template from a joke and then infills it using BERT. Secondly, it extends the base model by incorporating advancements in language models and natural language processing to enhance the flexibility and quality of generated jokes, broadening the scope of humor that the system can produce. This approach uses a novel strategy to identify semantically salient words, and uses LLMs on top of earlier models for the infilling. Lastly, the thesis explores a distinct avenue in humor genera- tion by employing conversational prompts within a conversational AI framework with GPT-4, the SOTA at the time of presentation. This method not only diversifies the ways in which humor can be generated but also reflects on the potential of conversational AI to contribute creatively to the domain of humor. Through rigorous evaluation, this work demonstrates the efficacy of the proposed methods in generating humor that is coherent, contextually appropriate, and, most importantly, funny. This research not only contributes a novel technique to the field of computational humor but also opens up new pathways for future exploration in automated joke generation and the creative capacities of AI.

Abstract

In the realm of Natural Language Processing (NLP), enhancing knowledge graphs (KGs) with large language models (LLMs) offers a transformative approach to managing and leveraging structured information. This thesis, titled ”Leveraging Large Language Models for Knowledge Graph Enhancement: From Creation to Utilization,” explores the synergistic integration of LLMs and KGs to enhance various aspects of information extraction, entity classification, and question answering. The research is driven by the recognition of the limitations inherent in traditional KGs, which often suffer from incomplete but dynamic data, and aims to leverage the semantic capabilities of static LMs to address these gaps. The thesis presents a comprehensive study on cross-lingual fact extraction, focusing on extracting factual information from texts in low-resource Indian languages and representing it as English triples. This task is critical for capturing the rich knowledge embedded in these languages, which traditional methods often overlook. An end-to-end generative approach is employed, achieving a significant F1 score of 77.46, thereby setting a new benchmark for cross-lingual fact extraction efforts. This method is validated using the XAlign dataset, which includes multilingual data from Wikipedia articles, ensuring robust evaluation and applicability of the proposed models. Entity type classification is another focal point of this thesis. The research introduces a fine-grained entity type classification model, which is particularly effective in scenarios where KGs are being developed from scratch using only textual descriptions. This model, built upon a multilingual encoder- only language model and incorporating hierarchy-aware losses, utilizes our Wikidata Entity Type Classification (WETC) dataset. By leveraging the structure of Wikidata and the multilingual links in Wikipedia articles, the model achieves significant improvements in entity classification across various languages, attaining a performance of 0.73 Hierarchical F1. The thesis also delves into the integration of KGs with LLMs for question answering (QA). A novel approach, termed Joint Reasoning over KG and LLMs, is proposed, where the structured knowledge from KGs is combined with the generative abilities of LLMs. This hybrid architecture employs graph neural networks (GNNs) and includes modifications such as Prominent Entities for Graph Augmentation (PEGA) and QA-Context-Aware Node Pruning (CANP) to enhance the relevance and accuracy of the QA process.Experimental results demonstrate that this integrated approach significantly outperforms existing methods on various QA benchmarks, including OpenBookQA, CommonsenseQA, and MedQA-USMLE, showing notable advancements in QA accuracy over 20% points. In conclusion, this thesis makes substantial contributions to the field of knowledge graph enhancement using large language models. By addressing the challenges associated with cross-lingual fact extraction,entity classification, and QA, the research paves the way for the development of more advanced and efficient knowledge-based systems by bridging the gap between structured knowledge representation and natural language understanding.

Abstract

The Intergovernmental Panel for Climate Change (IPCC) reported that carbon dioxide (CO2) from anthropogenic emissions is the major contributor to radiative forcing in the atmosphere (IPCC, AR6). The recorded monthly average atmospheric CO2 level in the Mauna Loa Observatory (elevation of about 3397 m) was 421 ppm during March 2023, the highest level since the accurate measurements began 65 years ago. The accelerating CO2 mixing ratios were attributed to changes in land use and land cover (LU/LC). After industrialization (around 1760), CO2 emissions from fossil fuel burning started and became the most significant contributor to the global carbon budget (Ballantyne et al., 2012). Since the pre-industrial period, the burning fossil fuel and LU/LC changes have increased by 40 and 150 % for CO2 and CH4 mixing ratios, respectively (Huang et al., 2016). Recent studies suggest that the CO2 emissions from cement production exceeded global fossil fuel emissions in the past two decades (Andrew, 2018). CO2 mixing ratio levels in the atmosphere are controlled by the combined effect of sources and sinks. Only about half the amount of CO2 released remains in the atmosphere, whereas two major sinks, the terrestrial biosphere, and oceans, absorb the remaining part (Andres et al., 1996). Hence, monitoring and maintaining long-term records of atmospheric CO2 measurements are essential to understanding the carbon cycle and predicting the future behaviour of the controlling factors: photosynthesis, respiration, biomass, fossil fuel burning, and air-sea exchange processes (Machida et al., 2002). The present thesis work is aimed at understanding and assessing the CO2 variability over the Indian region using three approaches: ground-based, satellite data, and model simulations, and further integrating them to provide a comprehensive estimate of CO2 concentrations and their variability. The impact of LU/LC and its changes on CO2 emissions are quantified using ground-based observations and model simulations from 2013 to 2022. In addition, the vertical profiles of atmospheric CO2 were studied to help understand temporal variations in the vertical column, which was used to improve the satellite-based CO2 estimates. A study was conducted to understand the neighbourhood effects on atmospheric CO2 using space-based CO2 data, model simulations, and LU/LC. Further, the objective was to quantify and generate a national CO2 emission dataset as a function of climatic zones, LU/LC, satellite-derived CO2 concentration, and MIROC4-ACTM simulated inverse fluxes.Column-averaged CO2 concentrations (X) were obtained using data from a ground-based Fourier Transform Infrared (FTIR) Spectrometer that was gathered in clear sky days at the NRSC in Shadnagar, India throughout the 2016 period. Calcium Fluoride (CaF2) beam splitter and Indium Antimonide (InSb) detector are used to collect the solar absorption spectra, with the range between 1800 cm-1 to 11000 cm-1 (5.50 μm to 0.90 μm) and the spectral resolution (∆ν) of 0.01 cm-1 for this study. This study analyses spectra using a non-linear least squares Gas Fitting Spectral Analysis (GFIT) developed by the Jet Propulsion Laboratory (JPL), and licenced by California Institute of Technology (Caltech), U.S.A. With the present retrieval scheme, the precision of the FTIR achieved is 0.04 % for XCO2. During the study period, the diurnal amplitude of XCO2 was about 2 ppmv, and the present work compared FTIRretrieved XCO2 data against XCO2 observed by Orbiting Carbon Observatory-2 (OCO-2). A comparative study yields a mean relative bias of -0.78 % and -0.63 % between FTIR data and satellite data for XCO2. The Pearson correlation coefficient (R) between FTIR and satellite data is 0.96 (XCO2, N=13 co-located). In the present work, we also retrieved XCO2 using a groundbased portable EM27/SUN FTIR. The EM27/SUN spectrometers are widely used in the COllaborative Carbon Column Observing Network (COCCON). The advantages of portability of this FTIR allow experiments in a campaign mode so that data gaps in India in terms of geographical coverage can be minimized. The PROFFAST software provided by COCCON has been used to analyse the measured atmospheric solar absorption spectra. This work studied the diurnal variation and the time series of daily averaged XCO2, covering December 2020 to May 2021. The maximum value of XCO2 was observed to be 420.57 ppm. Less diurnal (XCO2~0.44 ppm), but clear seasonal changes are observed during the study period. The FTIRbased XCO2 retrievals help estimate the uncertainties in the satellite-based products and enable the highly accurate products from the satellites by adjusting the biases between ground and space-based retrievals. Thus, ground-based FTIR retrievals are decisive in validating satellite products. An airborne campaign was conducted to investigate the vertical distribution of the atmospheric CO2 using a twin-turbo prope

Abstract

Rivers are significant and low cost source of drinking, irrigation and other water demands across the world. With rising industrial and residential water demands it become essential to manage the water quality and quantity of rivers. The changes in global environmental factors have adversely affected the natural water cycle which in turn has resulted in variation of the natural inflow to river systems. While rapid urbanization, industrialization and population growth had led to rapid decline in river water quality. Without proper management and corrective plan of action for reviving the water quality of rivers there is a risk losing precious natural resources that are essential for continuance of life on earth. This study addresses these challenges within the context of altered environmental conditions that have disrupted the natural water cycle, affecting river inflows and degrading water quality. The management of water quantity in a reservoir-river system possess challenges in terms of forecasting inflows to the reservoir and regulating releases in an adequate manner so that water demands such as irrigation, industries and households can be fulfilled. Accurate predictions of reservoir inflows is critical for water management and is influenced by various climatic phenomenon indices (e.g., Arctic Oscillation, North Atlantic Oscillation, and Southern Oscillation Index) and hydroclimatic variables (e.g., precipitation, evapotranspiration). Recently the use of machine learning techniques for inflow prediction has received a lot of attention however a comprehensive approach that evaluates different algorithms combined with large-scale climate phenomenon indices, and various hydro-climatic variables is missing. To achieve this the present study implements an integrated framework of Machine Learning (ML) algorithms for short-range reservoir inflow forecasting using the climate indices and hydroclimatic data for Bhadra reservoir situated in Karnataka, India. The present study also proposes and evaluates an ensemble model using a robust weighted voting regressor (VR) method to quantify forecasting uncertainty and to improve model performances. The results of the study reveal that the LSTM approach has the greatest influence on prediction accuracy, followed comparably by each model. However, none of the four models used in the study that are Random Forest, GBR, KNN and LSTM seem to be noticeably superior to the VR method. Accessing the water quality of rivers is a challenge and requires the measurement of several water quality parameters. Also the amount of water released from the reservoir has a significant impact on the water quality parameters downstream of the river stretch. An integrated approach for water quality management which takes into account the release of water and the river flow conditions hence becomes important. This study develops and demonstrates the usefulness of such an integrated framework. The developed framework provides a holistic approach to water quantity and quality management by integrating ML algorithms for inflow predictions, numerical methods for reservoir release analysis, Global Environmental Flow Calculator for environmental flow estimations and Qual2k as river water quality model. The developed framework can be easily used to predict and simulate how individual water quality parameters change with changes in water release from the reservoir and flow conditions of the river. In order to ensure that the developed framework can be easily put to use a web application that implements the developed framework using the Bhadra river data is developed. The developed application titled Web-Based Decision Support System for Water Quantity and Quality Management of a Reservoir-River System (WQQM-RR) integrates machine learning algorithms, numerical models, and GIS visualization techniques to predict reservoir inflow, manage reservoir release, estimate downstream water quality, and interactively visualize water quality on a map using GIS. The application uses ReactJS for a responsive and modular frontend, Flask for efficient server-side operations, Open-Street Map for dynamic data visualization, and machine learning algorithms for precise inflow predictions. Additionally, integrates GEFC and Qual2K software for comprehensive water quality estimation. Majorly, the application consists of three major components: inflow prediction, reservoir release management, and water quality estimation with visualization. The inflow prediction module uses historical data on weather patterns, hydrological conditions, and other relevant factors to predict the inflow to the reservoir. The reservoir release management module uses these inflow predictions and storage data provided by the user to manage the release of water from the reservoir. The water quality estimation module uses the Global Environmental Flow Calculator (GEFC) and the QUAL2K water quality m

Abstract

In the natural course of spoken language, individuals often engage in thinking and selfcorrection during speech production. These instances of interruption or correction are commonly referred to as disfluencies. NLP models usually trained on textual data, can have difficulty while working with such data - that is, the audio transcripts from conversational speech. When performing downstream NLP tasks like Machine Translation, we must be aware of the presence of such disfluencies in the training data. These linguistic elements can be systematically removed, or handled as required, to enhance data quality, ultimately improving the output for a given task. For quite some time, disfluencies have been the subject of research. However, most of it is on English, Chinese and other European languages, and not much has been done in this direction on Indian languages. In this thesis, we present a comprehensive research on disfluencies, focussing on the following Indian languages: Hindi, Bengali, Marathi, Telugu, Kannada and Tamil. We carry out some preliminary tasks which help us understand the intricacies of disfluencies in detail - showcasing how it can affect Machine Translation, Questions Answering etc. Initially we studied this on English data, gradually expanding our research focus towards Indian languages. Unavailability of labelled data was the first challenge we encountered while working on disfluency in Indian languages. To address this, we developed some guidelines for annotating disfluencies in Indian Languages. These annotation guidelines is aimed at having a clear and uniform procedure for generating labelled data, thus improving the ‘quality’ of data. These guidelines were used to prepare manually annotated disfluency data. However, developing large amount of data manually for the task is time consuming and needs a lot of effort. To address this labelled-data scarcity problem, we worked on an algorithm to synthetically generate disfluencies. This algorithm aims to facilitate more effective model training for the identification of disfluencies in real-world conversations, thereby contributing to the advancement of disfluency research in Indian languages. The algorithm also attempts to take into account the code-mix nature in Indian Languages - English setting. We combine the manually annotated data with the synthetically generated data for conducting multiple disfluency classification experiments. We trained models for disfluency identification in all the above mentioned languages - having models trained on each language separately as well as varieties of multilingual models.

Abstract

Living organisms need to sense the environment accurately to respond to these stimuli appropriately. The accuracy of estimating the environmental input is severely limited by noise stemming from the inherent stochasticity of the chemical reactions involved in signalling pathways. Cells employ multiple strategies to improve the accuracy by tuning the reaction rates, for instance, amplifying the response, reducing the noise, etc. However, the pathway also consumes energy by incorporating ATP in phosphorylating key signalling proteins involved in the reaction pathways. In many instances, improvements in accuracy elicit extra energetic costs. For example, a higher deactivation rate suppresses the basal pathway activity, effectively amplifying the dynamic range of the response, which leads to improvement in accuracy. Higher deactivation rate also enhances the energy dissipation rate. Here, we employed a theoretical approach based on the thermodynamics of information to explore the role of accuracy and energetic cost in the performance of a Mitogen-Activated Protein Kinase signalling system. Our study shows that the accuracy-energy trade-off can explain the optimality of the reaction rates of the reaction pathways rather than accuracy alone. Our analysis elucidates the role of the interplay between accuracy and energetic cost in the evolutionary shaping of the parameter space of signalling pathways

Abstract

Persistent sadness, emotion dysregulation, and loss of pleasure are the key characteristics of depression. It is one of the most commonly reported mental disorders and is a significant contributor to the global burden of disease. However, examining depression is still challenging, especially for individuals at risk for depression. The current thesis attempts to contribute to this area by examining the impact of depression risk on specific aspects of affective experience and perceptual level processing, focusing at global/local biases in individuals vulnerable to depression. More specifically we are interested in understanding whether vulnerability to depression alters the global/local perceptual processing when experience mood congruent versus incongruent music. It was hypothesized that individuals with high compared to low risk of depression would favour local processing and show reduced global precedence effect as depression is associated with the narrow scope of attentional processing. The effect was expected to be more pronounced in negative versus positive affective states because of the mood congruency, further strengthening the narrower scope of attention processing. We address this question by performing 2 studies. We created Navon’s compound stimuli to analyse global/local perceptual processing, and Kessler-10 (in Study 1) and PHQ-9(Study-2) and GAD-7(Study2) to examine depression risks. In Study 1, we used Vastfj ¨ all’s paper, which had a small dataset of ¨ music pieces and the corresponding mood they intend to induce, and in study 2, we used the soundtrack dataset to select music tracks of varying valence and arousal for stimulating particular affective state while performing the perceptual level judgment task. In the first study, which was conducted online, participants’ task was to identify the letter “H” or “O” presented either at the global or local (G/L) perceptual level, using Navon’s method. These stimuli were presented with background music eliciting either pleasant, unpleasant or neutral mood. Each of these categories had 3 music tracks assigned to them, which were randomly assigned to a given participant. Participants were randomly assigned 1 of the 9 tracks (of lyrical music), which belonged to one of the categories, i.e., pleasant, unpleasant, and neutral. Participants were asked to play the assigned track in the background while performing the G/L task. After completing the perceptual level judgment task, participants were asked to fill out the Kessler 10 and Brief Mood Introspection Scale (BMIS) to assess their predisposed and current emotional states respectively. In the second study, which was conducted in a controlled lab setting, participants perform the same perceptual level judgment task but with a four non-lyrical music pieces varying at the valence and arousal levels. In this study, participants were also asked to report their mood after every audio-condition, i.e., high and low arousing and valence conditions, by employing BMIS. Participants were also asked to report their feeling towards the music piece after every audio. Study 1 failed to demonstrate the impact of music on immediate mood manipulation. However, study 2 showed a significant impact of background music on immediate mood, indicating successful mood manipulation. The difference in mood manipulation could be a result of consistency in the music pieces presented to every participant and or enabling the control constant, in which the music was played as soon as the instruction was over and task started. Unlike the first experiment, the music play was automated in the second experiment. Despite reporting a change in immediate mood, individuals with high risks of depression reported consistently lower mood levels than individuals with low risk of depression. The experience of lower mood levels aligns with previous findings, suggesting a negative impact of depression on immediate mood experience. The overarching effect of predisposed mood, encompassing depression or anxiety, on individuals’ transient mood experience and perceptual task performance indicates the pervasive nature of depression. Unlike previous studies, individuals with depression showed faster reaction time for both global and local stimuli in both studies, 1 2, but with reduced accuracy in the second experiment, indicating a speed-accuracy trade-off. Despite faster reaction time, individuals with a high risk of depression showed reduced global precedence than their counterparts with a low risk of depression. The findings are discussed in light of theoretical models of depression.

Abstract

High-power lasers are essential for various commercial, industrial, and military applications. In recent years, there has been a notable trend towards up-scaling laser systems for long-distance propagation. Fiber lasers have revolutionized the laser industry due to their impressive efficiency, durability, and capacity to generate highpower beams in the kilowatt range. Nevertheless, the output power of a single fiber laser is constrained by factors like non-linear effects and excessive heating. Thus, beam combination is a viable solution to generate a high-power beam by combining several low-power lasers. Various methods for combining beams can be employed, including incoherent, coherent, and spectral beam combination techniques. In incoherent beam combinations, lasers are adjusted and combined individually, without consideration of their phase. On the other hand, coherent beam combination requires precise phase matching of the beams and involves sophisticated optical and electronic circuits. Spectral beam combination combines lasers of different wavelengths using diffractive optical elements. Coherent and spectral beam combination methods often lead to increased complexity and cost of the beam combination system. Therefore, incoherent beam combinations are frequently used, especially in directed energy applications, where high intensities at longer distances are essential. Through this technique, high-power laser beams can be generated without requiring precise phase control, making them more practical and cost-effective. This thesis outlines the design and analysis of a multi-channel incoherent beam combination (IBC) system, investigating the behavior of laser beams propagating in atmospheric turbulence. It presents various initial architectures for the IBC system and devises a fiber-actuator-based optical channel design to steer high-power laser beams effectively. To improve system efficiency, this thesis optimizes the initial beam waist and power of each laser beam across different atmospheric conditions. Furthermore, to enhance the combined intensity of the IBC system, it introduces collimated, inclined, and focused-inclined directing mechanisms. Additionally, this thesis delves into the modeling and analysis of alignment errors in fiber lasers and collimating lens arrays, addressing challenges and optimizing system performance. The proposed system optimizes beam-directing channel length and minimizes heat generation, ensuring improved efficiency and suitability for scenarios with moving target locations. This thesis also introduces the incorporation of higher-order Gaussian beams into a high-power incoherent beam combination system. Various higher-order Gaussian beams like Hermite Gaussian (HG) and Laguerre Gaussian (LG) beams can be used for beam combination to generate high intensity at various distances with limited hardware requirements. It provides optimal combination efficiency with minimal hardware requirements. Theoretical modeling and detailed analysis of Hermite and Laguerre Gaussian beams in atmospheric turbulence are conducted, investigating the influence of atmospheric parameters like jitter, turbulence, wind speed, and thermal blooming on beam spreading. This thesis further investigates the impact of steadystate thermal blooming on Laguerre Gaussian beams as they propagate through the atmosphere, considering various modes of LG beams. Additionally, it analyzes how atmospheric turbulence, beam wander, residual mechanical jitter, beam quality, thermal blooming, and bore-sight error collectively influence the intensity and spot size of the beams. Our findings presented in this thesis hold significance for the design of various beam combination systems and have implications for applications in industrial, military, communication, and information transmission within atmospheric propagation scenarios.

Abstract

Early detection and effective management of medical conditions significantly enhance patient outcomes, yet challenges persist due to limited resources, particularly in achieving widespread medical expertise. While supervised deep learning excels in medical image segmentation, the scarcity of labeled data poses significant hurdles for clinical applications. In response, self-supervised learning (SSL) systems have gained traction, leveraging unlabeled medical images to extract essential properties. Among SSL methods, contrastive learning stands out, aiming to minimize the distance between similar images while maximizing it between dissimilar ones, thereby enhancing segmentation accuracy. Current SSL methods exhibit limitations, prompting the advancement of unsupervised learning techniques that leverage data’s inherent structure to learn representations without the need for labeled data. A considerable challenge with unsupervised pre-training is domain shift, which occurs when the distribution of data used for pre-training differs from that used for fine-tuning. Addressing a crucial challenge in thoracic disease diagnosis using X-ray imaging, our work in the second chapter explores the need for anatomically accurate findings and why they shouldn’t be overlooked in interpretability assessments. We propose an innovative self-supervised and weakly supervised pre-training pipeline paired with an auxiliary loss followed by supervised fine-tuning to tackle these limitations effectively. Leveraging the Chest X-ray14 dataset for pre-training and the CheXpert dataset for fine-tuning ensures model stability and generalizability across diverse data sources. Specifically, our approach demonstrates a remarkable 31% improvement in Intersection over Union on the NIH CXR dataset, enabling precise classification across 14 chest X-ray categories. While our focus lies on chest X-rays, our proposed approach extends its applicability to various imaging modalities and clinical workflows, showcasing its broad impact in medical imaging and diagnostics. In our third chapter, we expand the Swin Transformer architecture to learn from multiple medical imaging modalities, enhancing downstream performance. Our novel Swin-FUSE (Swin Multi-Modal Fusion for UnSupervised Enhancement) framework offers several advantages: utilizing CTs and MRIs for pre-training to create complementary feature representations, incorporating a domain-invariance module (DIM) to enhance domain adaptability, and demonstrating high generalizability beyond pretrained tasks. Empirical results on publicly available 3D segmentation datasets showcase a marginal 1-2% performance trade-off compared to single-modality models while achieving a remarkable 27% improvement on out-of-distribution modalities. In our fourth chapter, we introduce an attention-based model for the 2023 ISBI X-ray Projectomic Reconstruction Challenge, aimed at fostering exploration into XNH imaging challenges, particularly focusing on the white matter region of the rodent brain. Our proposed AGU-Net model demonstrates enhanced performance in merging segmented regions and producing accurate segmentations with reduced error rates, as evidenced by its higher scores in the Normalized ERL and Rand merge metrics. Our model achieved an outstanding XPRESS score of 0.8159 on the test set, securing 3 rd place. In summary, this thesis presents innovative solutions leveraging self-supervised pre-training and contrastive learning to enhance representation learning in medical imaging. These advancements extend to domain adaptation tasks, ultimately enhancing the interpretability of conventional black-box machine learning models, thus paving the way for more reliable and clinically relevant diagnostic tools

Abstract

Systems of linear equations are fundamental to numerous scientific and engineering domains, often arising from the discretization of partial differential equations (PDEs) used to model real-world phenomena. These systems can be computationally expensive to solve, especially for large-scale problems. Therefore, developing efficient solvers for linear systems is crucial for advancing scientific computing. This thesis examines the use of recursive partitioning for solving linear systems, focusing on systems derived from 3-dimensional structured grids. The research emphasizes the development of a preconditioner based on this partitioning strategy to enhance the efficiency of iterative solvers, notably the Preconditioned Conjugate Gradient (PCG) method. By decomposing the original problem into smaller, more manageable sub-problems, this approach aims to reduce the overall computational time. This strategy aligns with the principles of parallel computing, where tasks are divided and processed concurrently across multiple processors to achieve faster solutions. The effectiveness of the proposed preconditioner is assessed using Skyscraper problems with checkerboard variable jumps as test cases. These problems, known for their intricate coefficient structures, serve as relevant benchmarks for evaluating the performance gains offered by the partitioning approach.