Multi-disciplinary Pathways to Computing:A Scalable and Col aborative Approach to Capitalize on the Demand for Computer Science Education

The number of students demanding computer science(CS)education is rapidly rising,and while faculty sizes are also growing,the traditional pipeline consisting of a CS major,a CS master’s,and then a move to industry or a Ph.D.program is simply not scalable.To address this problem,the Department of Computing at the University of Illinois has introduced a multidisciplinary approach to computing,which is a scalable and collaborative approach to capitalize on the tremendous demand for computer science education.The key component of the approach is the blended major,also referred to as“CS+X”,where CS denotes computer science and X denotes a non-computing field.These CS+X blended degrees enable win-win partnerships among multiple subject areas,distributing the educational responsibilities while growing the entire university.To meet the demand from non-CS majors,another pathway that is offered is a graduate certificate program in addition to the traditional minor program.To accommodate the large number of students,scalable teaching tools,such as automatic graders,have also been developed.

Laboratory or Department?Exploration and Creation in Computer Science and Technology

In the very beginning,the Computer Laboratory of the University of Cambridge was founded to provide computing service for different disciplines across the university.As computer science developed as a discipline in its own right,boundaries necessarily arose between it and other disciplines,in a way that is now often detrimental to progress.Therefore,it is necessary to reinvigorate the relationship between computer science and other academic disciplines and celebrate exploration and creativity in research.To do this,the structures of the academic department have to act as supporting scaffolding rather than barriers.Some examples are given that show the efforts being made at the University of Cambridge to approach this problem.

Subpopulations of regulatory T cells are associated with subclinical atherosclerotic plaques,levels of LDL,and cardiorespiratory fitness in the elderly

Background:Atherosclerosis forms the pathological basis for the development of cardiovascular disease.Since pathological processes initially develop without clinically relevant symptoms,the identification of early markers in the subclinical stage plays an important role for initiating early interventions.There is evidence that regulatory T cells(Tregs)are involved in the development of atherosclerosis.Therefore,the present study aimed to identify and investigate associations with Tregs and their subsets in a cohort of healthy elderly individuals with and without subclinical atherosclerotic plaques(SAP).In addition,various lifestyle and risk factors,such as cardiorespiratory fitness,were investigated as associated signatures.Methods:A cross-sectional study was performed in 79 participants(male:n=50;age=63.6±3.7 years;body mass index=24.9±3.1 kg/m2;mean±SD)who had no previous diagnosis of chronic disease and were not taking medication.Ultrasound of the carotids to identify SAP,cardiovascular function measurement for vascular assessment and a cardiorespiratory fitness test to determine peak oxygen uptake were performed.Additionally,tests were conducted to assess blood lipids and determine glucose levels.Immunophenotyping of Tregs and their subtypes(resting(rTregs)and effector/memory(mTregs))was performed by 8-chanel flow cytometry.Participants were categorized according to atherosclerotic plaque status.Linear and logistic regression models were used to analyze associations between parameters.Results:SAP was detected in a total of 29 participants.The participants with plaque were older(64.8±3.6 years vs.62.9±3.5 years)and had higher peripheral systolic blood pressure(133.8±14.7 mmHg vs.125.8±10.9 mmHg).The participants with SAP were characterized by a lower percentage of rTregs(28.8%±10.7%vs.34.6%±10.7%)and a higher percentage of mTregs(40.3%±14.7%vs.30.0%±11.9%).Multiple logistic regression identified age(odds ratio(OR)=1.20(95%confidence interval(95%CI):1.011.42))and mTregs(OR=1.05(95%CI:1.021.10))as independent risk factors for SAP.Stepwise linear regression could reveal an association of peak oxygen uptake(β=0.441),low-density lipoprotein(LDL)(β=0.096),and SAP(β=6.733)with mTregs and LDL(β=0.104)with rTregs.Conclusion:While at an early stage of SAP,the total proportion of Tregs gives no indication of vascular changes,this is indicated by a shift in the Treg subgroups.Factors such as serum LDL or cardiopulmonary fitness may be associated with this shift and may also be additional diagnostic indicators.This could be used to initiate lifestyle-based preventive measures at an early stage,which may have a protective effect against disease progression.

Two-Stage IoT Computational Task Offloading Decision-Making in MEC with Request Holding and Dynamic Eviction

The rapid development of Internet of Things(IoT)technology has led to a significant increase in the computational task load of Terminal Devices(TDs).TDs reduce response latency and energy consumption with the support of task-offloading in Multi-access Edge Computing(MEC).However,existing task-offloading optimization methods typically assume that MEC’s computing resources are unlimited,and there is a lack of research on the optimization of task-offloading when MEC resources are exhausted.In addition,existing solutions only decide whether to accept the offloaded task request based on the single decision result of the current time slot,but lack support for multiple retry in subsequent time slots.It is resulting in TD missing potential offloading opportunities in the future.To fill this gap,we propose a Two-Stage Offloading Decision-making Framework(TSODF)with request holding and dynamic eviction.Long Short-Term Memory(LSTM)-based task-offloading request prediction and MEC resource release estimation are integrated to infer the probability of a request being accepted in the subsequent time slot.The framework learns optimized decision-making experiences continuously to increase the success rate of task offloading based on deep learning technology.Simulation results show that TSODF reduces total TD’s energy consumption and delay for task execution and improves task offloading rate and system resource utilization compared to the benchmark method.

Refinement modeling and verification of secure operating systems for communication in digital twins

In traditional digital twin communication system testing,we can apply test cases as completely as possible in order to ensure the correctness of the system implementation,and even then,there is no guarantee that the digital twin communication system implementation is completely correct.Formal verification is currently recognized as a method to ensure the correctness of software system for communication in digital twins because it uses rigorous mathematical methods to verify the correctness of systems for communication in digital twins and can effectively help system designers determine whether the system is designed and implemented correctly.In this paper,we use the interactive theorem proving tool Isabelle/HOL to construct the formal model of the X86 architecture,and to model the related assembly instructions.The verification result shows that the system states obtained after the operations of relevant assembly instructions is consistent with the expected states,indicating that the system meets the design expectations.

Monitoring and evaluation of the water quality of the Lower Neches River, Texas, USA

Increasing bacteria levels in the Lower Neches River caused by Hurricane Harvey has been of a serious concern.This study is to analyze the historical water sampling measurements and real-time water quality data collected with wireless sensors to monitor and evaluate water quality under different hydrological and hydraulic conditions.The statistical and Pearson correlation analysis on historical water samples determines that alkalinity,chloride,hardness,conductivity,and pH are highly correlated,and they decrease with increasing flow rate due to dilution.The flow rate has positive correlations with Escherichia coli,total suspended solids,and turbidity,which demonstrates that runoff is one of the causes of the elevated bacteria and sediment loadings in the river.The correlation between E.coli and turbidity indicates that turbidity greater than 45 nephelometric turbidity units in the Neches River can serve as a proxy for E.coli to indicate the bacterial outbreak.A series of statistical tools and an innovative two-layer data smoothing filter are developed to detect outliers,fill missing values,and filter spikes of the sensor measurements.The correlation analysis on the sensor data illustrates that the elevated sediment/bacteria/algae in the river is either caused by the first flush rain and heavy rain events in December to March or practices of land use and land cover.Therefore,utilizing sensor measurements along with rainfall and discharge data is recommended to monitor and evaluate water quality,then in turn to provide early alerts on water resources management decisions.

An Optimized Approach to Deep Learning for Botnet Detection and Classification for Cybersecurity in Internet of Things Environment

The recent development of the Internet of Things(IoTs)resulted in the growth of IoT-based DDoS attacks.The detection of Botnet in IoT systems implements advanced cybersecurity measures to detect and reduce malevolent botnets in interconnected devices.Anomaly detection models evaluate transmission patterns,network traffic,and device behaviour to detect deviations from usual activities.Machine learning(ML)techniques detect patterns signalling botnet activity,namely sudden traffic increase,unusual command and control patterns,or irregular device behaviour.In addition,intrusion detection systems(IDSs)and signature-based techniques are applied to recognize known malware signatures related to botnets.Various ML and deep learning(DL)techniques have been developed to detect botnet attacks in IoT systems.To overcome security issues in an IoT environment,this article designs a gorilla troops optimizer with DL-enabled botnet attack detection and classification(GTODL-BADC)technique.The GTODL-BADC technique follows feature selection(FS)with optimal DL-based classification for accomplishing security in an IoT environment.For data preprocessing,the min-max data normalization approach is primarily used.The GTODL-BADC technique uses the GTO algorithm to select features and elect optimal feature subsets.Moreover,the multi-head attention-based long short-term memory(MHA-LSTM)technique was applied for botnet detection.Finally,the tree seed algorithm(TSA)was used to select the optimum hyperparameter for the MHA-LSTM method.The experimental validation of the GTODL-BADC technique can be tested on a benchmark dataset.The simulation results highlighted that the GTODL-BADC technique demonstrates promising performance in the botnet detection process.

Structural and functional connectivity of the whole brain and subnetworks in individuals with mild traumatic brain injury:predictors of patient prognosis

Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.

3D Road Network Modeling and Road Structure Recognition in Internet of Vehicles

Internet of Vehicles (IoV) is a new system that enables individual vehicles to connect with nearby vehicles,people, transportation infrastructure, and networks, thereby realizing amore intelligent and efficient transportationsystem. The movement of vehicles and the three-dimensional (3D) nature of the road network cause the topologicalstructure of IoV to have the high space and time complexity.Network modeling and structure recognition for 3Droads can benefit the description of topological changes for IoV. This paper proposes a 3Dgeneral roadmodel basedon discrete points of roads obtained from GIS. First, the constraints imposed by 3D roads on moving vehicles areanalyzed. Then the effects of road curvature radius (Ra), longitudinal slope (Slo), and length (Len) on speed andacceleration are studied. Finally, a general 3D road network model based on road section features is established.This paper also presents intersection and road section recognition methods based on the structural features ofthe 3D road network model and the road features. Real GIS data from a specific region of Beijing is adopted tocreate the simulation scenario, and the simulation results validate the general 3D road network model and therecognitionmethod. Therefore, thiswork makes contributions to the field of intelligent transportation by providinga comprehensive approach tomodeling the 3Droad network and its topological changes in achieving efficient trafficflowand improved road safety.

Unleashing the Power of Multi-Agent Reinforcement Learning for Algorithmic Trading in the Digital Financial Frontier and Enterprise Information Systems

In the rapidly evolving landscape of today’s digital economy,Financial Technology(Fintech)emerges as a trans-formative force,propelled by the dynamic synergy between Artificial Intelligence(AI)and Algorithmic Trading.Our in-depth investigation delves into the intricacies of merging Multi-Agent Reinforcement Learning(MARL)and Explainable AI(XAI)within Fintech,aiming to refine Algorithmic Trading strategies.Through meticulous examination,we uncover the nuanced interactions of AI-driven agents as they collaborate and compete within the financial realm,employing sophisticated deep learning techniques to enhance the clarity and adaptability of trading decisions.These AI-infused Fintech platforms harness collective intelligence to unearth trends,mitigate risks,and provide tailored financial guidance,fostering benefits for individuals and enterprises navigating the digital landscape.Our research holds the potential to revolutionize finance,opening doors to fresh avenues for investment and asset management in the digital age.Additionally,our statistical evaluation yields encouraging results,with metrics such as Accuracy=0.85,Precision=0.88,and F1 Score=0.86,reaffirming the efficacy of our approach within Fintech and emphasizing its reliability and innovative prowess.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

Development of a Lightweight Model for Handwritten Dataset Recognition: Bangladeshi City Names in Bangla Script

The context of recognizing handwritten city names,this research addresses the challenges posed by the manual inscription of Bangladeshi city names in the Bangla script.In today’s technology-driven era,where precise tools for reading handwritten text are essential,this study focuses on leveraging deep learning to understand the intricacies of Bangla handwriting.The existing dearth of dedicated datasets has impeded the progress of Bangla handwritten city name recognition systems,particularly in critical areas such as postal automation and document processing.Notably,no prior research has specifically targeted the unique needs of Bangla handwritten city name recognition.To bridge this gap,the study collects real-world images from diverse sources to construct a comprehensive dataset for Bangla Hand Written City name recognition.The emphasis on practical data for system training enhances accuracy.The research further conducts a comparative analysis,pitting state-of-the-art(SOTA)deep learning models,including EfficientNetB0,VGG16,ResNet50,DenseNet201,InceptionV3,and Xception,against a custom Convolutional Neural Networks(CNN)model named“Our CNN.”The results showcase the superior performance of“Our CNN,”with a test accuracy of 99.97% and an outstanding F1 score of 99.95%.These metrics underscore its potential for automating city name recognition,particularly in postal services.The study concludes by highlighting the significance of meticulous dataset curation and the promising outlook for custom CNN architectures.It encourages future research avenues,including dataset expansion,algorithm refinement,exploration of recurrent neural networks and attention mechanisms,real-world deployment of models,and extension to other regional languages and scripts.These recommendations offer exciting possibilities for advancing the field of handwritten recognition technology and hold practical implications for enhancing global postal services.

Elevating Image Steganography:A Fusion of MSB Matching and LSB Substitution for Enhanced Concealment Capabilities

In today’s rapidly evolving landscape of communication technologies,ensuring the secure delivery of sensitive data has become an essential priority.To overcome these difficulties,different steganography and data encryption methods have been proposed by researchers to secure communications.Most of the proposed steganography techniques achieve higher embedding capacities without compromising visual imperceptibility using LSB substitution.In this work,we have an approach that utilizes a combinationofMost SignificantBit(MSB)matching andLeast Significant Bit(LSB)substitution.The proposed algorithm divides confidential messages into pairs of bits and connects them with the MSBs of individual pixels using pair matching,enabling the storage of 6 bits in one pixel by modifying a maximum of three bits.The proposed technique is evaluated using embedding capacity and Peak Signal-to-Noise Ratio(PSNR)score,we compared our work with the Zakariya scheme the results showed a significant increase in data concealment capacity.The achieved results of ourwork showthat our algorithmdemonstrates an improvement in hiding capacity from11%to 22%for different data samples while maintaining a minimumPeak Signal-to-Noise Ratio(PSNR)of 37 dB.These findings highlight the effectiveness and trustworthiness of the proposed algorithm in securing the communication process and maintaining visual integrity.

Secure and Reliable Routing in the Internet of Vehicles Network:AODV-RL with BHA Attack Defense

Wireless technology is transforming the future of transportation through the development of the Internet of Vehicles(IoV).However,intricate security challenges are intertwinedwith technological progress:Vehicular ad hoc Networks(VANETs),a core component of IoV,face security issues,particularly the Black Hole Attack(BHA).This malicious attack disrupts the seamless flow of data and threatens the network’s overall reliability;also,BHA strategically disrupts communication pathways by dropping data packets from legitimate nodes altogether.Recognizing the importance of this challenge,we have introduced a new solution called ad hoc On-Demand Distance Vector-Reputation-based mechanism Local Outlier Factor(AODV-RL).The significance of AODVRL lies in its unique approach:it verifies and confirms the trustworthiness of network components,providing robust protection against BHA.An additional safety layer is established by implementing the Local Outlier Factor(LOF),which detects and addresses abnormal network behaviors.Rigorous testing of our solution has revealed its remarkable ability to enhance communication in VANETs.Specifically,Our experimental results achieve message delivery ratios of up to 94.25%andminimal packet loss ratios of just 0.297%.Based on our experimental results,the proposedmechanismsignificantly improves VANET communication reliability and security.These results promise a more secure and dependable future for IoV,capable of transforming transportation safety and efficiency.

Automated Algorithms for Detecting and Classifying X-Ray Images of Spine Fractures

This paper emphasizes a faster digital processing time while presenting an accurate method for identifying spinefractures in X-ray pictures. The study focuses on efficiency by utilizing many methods that include picturesegmentation, feature reduction, and image classification. Two important elements are investigated to reducethe classification time: Using feature reduction software and leveraging the capabilities of sophisticated digitalprocessing hardware. The researchers use different algorithms for picture enhancement, including theWiener andKalman filters, and they look into two background correction techniques. The article presents a technique forextracting textural features and evaluates three picture segmentation algorithms and three fractured spine detectionalgorithms using transformdomain, PowerDensity Spectrum(PDS), andHigher-Order Statistics (HOS) for featureextraction.With an emphasis on reducing digital processing time, this all-encompassing method helps to create asimplified system for classifying fractured spine fractures. A feature reduction program code has been built toimprove the processing speed for picture classification. Overall, the proposed approach shows great potential forsignificantly reducing classification time in clinical settings where time is critical. In comparison to other transformdomains, the texture features’ discrete cosine transform (DCT) yielded an exceptional classification rate, and theprocess of extracting features from the transform domain took less time. More capable hardware can also result inquicker execution times for the feature extraction algorithms.

Sentiment Analysis of Low-Resource Language Literature Using Data Processing and Deep Learning

Sentiment analysis, a crucial task in discerning emotional tones within the text, plays a pivotal role in understandingpublic opinion and user sentiment across diverse languages.While numerous scholars conduct sentiment analysisin widely spoken languages such as English, Chinese, Arabic, Roman Arabic, and more, we come to grapplingwith resource-poor languages like Urdu literature which becomes a challenge. Urdu is a uniquely crafted language,characterized by a script that amalgamates elements from diverse languages, including Arabic, Parsi, Pashtu,Turkish, Punjabi, Saraiki, and more. As Urdu literature, characterized by distinct character sets and linguisticfeatures, presents an additional hurdle due to the lack of accessible datasets, rendering sentiment analysis aformidable undertaking. The limited availability of resources has fueled increased interest among researchers,prompting a deeper exploration into Urdu sentiment analysis. This research is dedicated to Urdu languagesentiment analysis, employing sophisticated deep learning models on an extensive dataset categorized into fivelabels: Positive, Negative, Neutral, Mixed, and Ambiguous. The primary objective is to discern sentiments andemotions within the Urdu language, despite the absence of well-curated datasets. To tackle this challenge, theinitial step involves the creation of a comprehensive Urdu dataset by aggregating data from various sources such asnewspapers, articles, and socialmedia comments. Subsequent to this data collection, a thorough process of cleaningand preprocessing is implemented to ensure the quality of the data. The study leverages two well-known deeplearningmodels, namely Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN), for bothtraining and evaluating sentiment analysis performance. Additionally, the study explores hyperparameter tuning tooptimize the models’ efficacy. Evaluation metrics such as precision, recall, and the F1-score are employed to assessthe effectiveness of the models. The research findings reveal that RNN surpasses CNN in Urdu sentiment analysis,gaining a significantly higher accuracy rate of 91%. This result accentuates the exceptional performance of RNN,solidifying its status as a compelling option for conducting sentiment analysis tasks in the Urdu language.

A Review of Lightweight Security and Privacy for Resource-Constrained IoT Devices

The widespread and growing interest in the Internet of Things(IoT)may be attributed to its usefulness in many different fields.Physical settings are probed for data,which is then transferred via linked networks.There are several hurdles to overcome when putting IoT into practice,from managing server infrastructure to coordinating the use of tiny sensors.When it comes to deploying IoT,everyone agrees that security is the biggest issue.This is due to the fact that a large number of IoT devices exist in the physicalworld and thatmany of themhave constrained resources such as electricity,memory,processing power,and square footage.This research intends to analyse resource-constrained IoT devices,including RFID tags,sensors,and smart cards,and the issues involved with protecting them in such restricted circumstances.Using lightweight cryptography,the information sent between these gadgets may be secured.In order to provide a holistic picture,this research evaluates and contrasts well-known algorithms based on their implementation cost,hardware/software efficiency,and attack resistance features.We also emphasised how essential lightweight encryption is for striking a good cost-to-performance-to-security ratio.

Multiple Perspective of Multipredictor Mechanism and Multihistogram Modification for High-Fidelity Reversible Data Hiding

Reversible data hiding is a confidential communication technique that takes advantage of image file characteristics,which allows us to hide sensitive data in image files.In this paper,we propose a novel high-fidelity reversible data hiding scheme.Based on the advantage of the multipredictor mechanism,we combine two effective prediction schemes to improve prediction accuracy.In addition,the multihistogram technique is utilized to further improve the image quality of the stego image.Moreover,a model of the grouped knapsack problem is used to speed up the search for the suitable embedding bin in each sub-histogram.Experimental results show that the quality of the stego image of our scheme outperforms state-of-the-art schemes in most cases.

Security Monitoring and Management for the Network Services in the Orchestration of SDN-NFV Environment Using Machine Learning Techniques

Software Defined Network(SDN)and Network Function Virtualization(NFV)technology promote several benefits to network operators,including reduced maintenance costs,increased network operational performance,simplified network lifecycle,and policies management.Network vulnerabilities try to modify services provided by Network Function Virtualization MANagement and Orchestration(NFV MANO),and malicious attacks in different scenarios disrupt the NFV Orchestrator(NFVO)and Virtualized Infrastructure Manager(VIM)lifecycle management related to network services or individual Virtualized Network Function(VNF).This paper proposes an anomaly detection mechanism that monitors threats in NFV MANO and manages promptly and adaptively to implement and handle security functions in order to enhance the quality of experience for end users.An anomaly detector investigates these identified risks and provides secure network services.It enables virtual network security functions and identifies anomalies in Kubernetes(a cloud-based platform).For training and testing purpose of the proposed approach,an intrusion-containing dataset is used that hold multiple malicious activities like a Smurf,Neptune,Teardrop,Pod,Land,IPsweep,etc.,categorized as Probing(Prob),Denial of Service(DoS),User to Root(U2R),and Remote to User(R2L)attacks.An anomaly detector is anticipated with the capabilities of a Machine Learning(ML)technique,making use of supervised learning techniques like Logistic Regression(LR),Support Vector Machine(SVM),Random Forest(RF),Naïve Bayes(NB),and Extreme Gradient Boosting(XGBoost).The proposed framework has been evaluated by deploying the identified ML algorithm on a Jupyter notebook in Kubeflow to simulate Kubernetes for validation purposes.RF classifier has shown better outcomes(99.90%accuracy)than other classifiers in detecting anomalies/intrusions in the containerized environment.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.