Open Access. Powered by Scholars. Published by Universities.®

Electrical and Computer Engineering Commons

Open Access. Powered by Scholars. Published by Universities.®

Electronic Theses and Dissertations

Discipline
Institution
Keyword
Publication Year

Articles 31 - 60 of 1176

Full-Text Articles in Electrical and Computer Engineering

Distributed Energy Resources (Der) Capacity Estimation With Spatiotemporal Downscaling For Transmission And Distribution Coordination, Abhilasha Suvedi Jan 2025

Distributed Energy Resources (Der) Capacity Estimation With Spatiotemporal Downscaling For Transmission And Distribution Coordination, Abhilasha Suvedi

Electronic Theses and Dissertations

The primary objective of this thesis is to accurately estimate the capacity of distributed energy resources (DERs) using the spatiotemporally downscaled local solar irradiance for their efficient integration into transmission-level grid operations. Accurate estimation of DER capacity is crucial for their enhanced integration into real-time electricity markets. Different methods of spatiotemporally downscaling the solar irradiance are presented in this thesis, followed by their integration into the 12 house distribution network – a low voltage residential distribution system. Grid support functions (GSFs) like Volt-Watt Control, Volt-VAR control, and Frequency-Watt Control are applied to effectively regulate the frequency and maintain the voltage …


Spectrum Optimization For Advanced Air Mobility Communications Using Deep Reinforcement Learning., Rafael D. Apaza Dec 2024

Spectrum Optimization For Advanced Air Mobility Communications Using Deep Reinforcement Learning., Rafael D. Apaza

Electronic Theses and Dissertations

As aviation operations expand and new participants enter the National Airspace System (NAS), the demand for aeronautical communications will experience a significant rise. This surge is propelled by increased air travel and the emergence of Urban Air Mobility (UAM) operations, a subset of Advanced Air Mobility (AAM). UAM aims to facilitate intra-city transportation of people and cargo utilizing remotely piloted aircraft capable of electric vertical takeoff and landing operations. The growing dependence on efficient wireless communication systems underscores the critical importance of intelligent spectrum allocation and effective airspace management to ensure safe, seamless, and technologically advanced air operations. However, the …


Development Of A Square Wave Voltage Field-Oriented Controller For A Linear Vapor Compressor., Thomas Everson Dec 2024

Development Of A Square Wave Voltage Field-Oriented Controller For A Linear Vapor Compressor., Thomas Everson

Electronic Theses and Dissertations

In this thesis, a novel control strategy for an inverter-driven linear compressor system is proposed in which the overall electrical losses of a coupled inverter-linear motor system are reduced through the use of a modified square wave inverter modulation scheme to minimize inverter switching losses at the expense of a modest increase in conduction losses. The controller is based on a single-phase field-oriented control strategy, and to achieve the FOC control objectives, the fundamental and dc components of the applied square wave voltage are matched to the corresponding values requested by the current controller. To validate the efficiency improvements offered …


Co-Emulation Of Robotics And Software-Defined Radio Based 5g Wireless Communications., Bhaskara Venkata Raju Garuda Dec 2024

Co-Emulation Of Robotics And Software-Defined Radio Based 5g Wireless Communications., Bhaskara Venkata Raju Garuda

Electronic Theses and Dissertations

The convergence of robotics and 5G wireless communication technologies has opened new avenues for real-time, dynamic robotic applications. This dissertation introduces a novel framework that integrates the Robot Operating System (ROS), Software-Defined Radios (SDRs), and 5G wireless networks to achieve seamless coemulation of robotic systems. The research emphasizes the unique features of 5G, such as ultra-low latency and high throughput, which enable critical applications like remote surgery, industrial automation, and autonomous vehicles. The methodology combines ROS for robotic control, SDRs for programmable communication channels, and 5G testbeds for high-speed, reliable data transmission. The experimental evaluation focuses on both position-based and …


Model-Based Navigation And Control Of Multirotor Uavs: A Machine Learning Approach, Serhat Sönmez Nov 2024

Model-Based Navigation And Control Of Multirotor Uavs: A Machine Learning Approach, Serhat Sönmez

Electronic Theses and Dissertations

In recent decades, unmanned systems, particularly Unmanned Aerial Vehicles (UAVs), have seen significant advancement and unprecedented growth in military, civilian and public domain applications. Scientists have focused on enhancing UAV navigation and control through cutting-edge technologies and support tools. UAVs find applications in many fields, except military, such as agriculture, infrastructure inspection, wildlife monitoring, search and rescue, emergency response, border protection, to name but a few relevant civilian applications. Given the faster-than-exponential increase of available computational power, learning-based algorithms have emerged as a prominent tool for (real-time) multirotor UAV navigation and control. This dissertation centers around the fusion of conventional …


Koopman-Based Modeling For Nonlinear Control Of Multirotor Uavs, Simone Martini Aug 2024

Koopman-Based Modeling For Nonlinear Control Of Multirotor Uavs, Simone Martini

Electronic Theses and Dissertations

This PhD dissertation focuses on adopting the emerging Koopman Operator theory for modeling and nonlinear control of multirotor UAVs, focusing specifically on quadrotors for proof-of-concept demonstration purposes.

The Koopman Operator theory is based on the foundation that nonlinear dynamics in the state space may be represented as a linear evolution of some functions in the state space. Thus, using appropriately defined and possibly nonlinear functions of the state variables, called observables, as a new and maybe infinite set of coordinates that are referred to as lifted space, the original nonlinear dynamics appear to be linear. The implications of this theory …


Denoising And Super-Resolution Of In-Vitro 4e Flow Mri In A Stenotic Phantom Model Using Physics-Informed Neural Networks., Shrouk M. Wally Aug 2024

Denoising And Super-Resolution Of In-Vitro 4e Flow Mri In A Stenotic Phantom Model Using Physics-Informed Neural Networks., Shrouk M. Wally

Electronic Theses and Dissertations

In recent years, the use of 4D flow MRI has revolutionized cardiovascular imag- ing by providing comprehensive data on blood flow dynamics over time. However, the limited spatial and temporal resolution of this imaging modality can hinder the accurate assessment of complex hemodynamic phenomena. This thesis explores the application of Physics-Informed Neural Networks (PINNs) to enhance the resolution of 4D flow MRI data, thereby improving its clinical utility. PINNs are a class of neural networks that integrate physical laws into their training process. By embedding these physics equations, PINNs can discover the underlying physics of fluid dynamics to produce more …


Novel Sensors, Algorithms And Metrics For Human-Robot Interaction., Henry Lee Reynolds Aug 2024

Novel Sensors, Algorithms And Metrics For Human-Robot Interaction., Henry Lee Reynolds

Electronic Theses and Dissertations

The increased presence and deployment of robotics in sectors such as the medical field results in the demand for robots to, directly and indirectly, interface with people and their environment, making human-robot interaction (HRI) a vital thrust of robotics research. Assistive robots, for example, aid humans in accomplishing tasks or by providing support in the workforce. As the demand for nurses and the aging population increases, the assistive robots deployed will be deeply rooted in environments that require constant interaction with humans. This work contributed to improving aspects of HRI through 1) Expanding accessibility of the methods used for interfacing …


Reinforcement Learning Assisted Communication Resources Optimization In Advanced Air Mobility., Ruixuan Han Aug 2024

Reinforcement Learning Assisted Communication Resources Optimization In Advanced Air Mobility., Ruixuan Han

Electronic Theses and Dissertations

Advanced air mobility (AAM), which envisages a safe and efficient aviation transportation system, has drawn significant attention to support the increasing mobility demand in metropolitan areas. Communication services for AAM aerial vehicles (AVs) are crucial for ensuring flight safety. This dissertation explores three research topics on communication resource allocation problems in AAM applications. The first topic, addressed in Chapter II, investigates the joint velocity selection and spectrum allocation problem for AAM applications to enhance spectrum utilization efficiency (SUE). In the AAM scenario, multiple AVs travel along predefined paths for passenger and cargo deliveries. Given that AAM aims to provide fast …


Deep Reinforcement Learning-Based Dynamic Routing And Spectrum Access In Aeronautical Networks., Zhe Wang Aug 2024

Deep Reinforcement Learning-Based Dynamic Routing And Spectrum Access In Aeronautical Networks., Zhe Wang

Electronic Theses and Dissertations

As the airspace is experiencing an increasing number of aircraft, spectrum sharing among Air Vehicles (AVs) and Terrestrial Users (TUs) emerges as a compelling solution to improve spectrum utilization efficiency. I investigated three types of aeronautical communication including the single-hop Air-Air Communication Network (AACN), the multi-hop Air-Air Ad-hoc Network (AAAN), and the Aerial and Terrestrial Hybrid Network (ATHN). I assume a spectrum-limited scenario through all communication networks. Thus, the number of communication pairs is greater than that of the available channels, resulting in co-channel interference due to the reuse of the same channel among communication links. In a single-hop AACN, …


Development And Processing Of Shape Memory Polymer Composites (Smpcs) For Application In Structural Robotics And Robotic Sensors., Kavish Sudan Aug 2024

Development And Processing Of Shape Memory Polymer Composites (Smpcs) For Application In Structural Robotics And Robotic Sensors., Kavish Sudan

Electronic Theses and Dissertations

Shape Memory Polymers (SMPs) have attracted significant attention since their introduction in the 1980s due to their remarkable ability to regain their original shape from a temporarily deformed state when exposed to an external stimulus, typically heat. This shape memory effect, driven by thermal transitions such as the glass transition temperature (Tg) or melting temperature (Tm), has made SMPs highly attractive for applications in soft robotics, aerospace, and biomedical devices. However, SMPs face challenges such as limited mechanical strength, thermal stability, and electrical conductivity, which hinder their broader adoption in advanced applications. To address these challenges, …


Incremental Quantities Based Permissive Overreaching Transfer Trip Scheme For Protecting Inverter-Based Renewable Resources, Osama Zangoti Jun 2024

Incremental Quantities Based Permissive Overreaching Transfer Trip Scheme For Protecting Inverter-Based Renewable Resources, Osama Zangoti

Electronic Theses and Dissertations

The power generation landscape evolves, with the increase of inverter-based resources (IBRs) such as solar photovoltaics and wind turbines, providing sustainable and clean energy sources. The shift towards IBRs mitigates climate change, creating considerable challenges to traditional power system protection due to their low fault current. Conventional protection schemes are designed around the internal dynamic of synchronous generators where they can supply an elevated fault current. This thesis explores a protection scheme designed to enhance the security of IBRs. The incremental characteristics of voltage and current coupled with the Permissive Overreaching Transfer Trip scheme (POTT) provide a remarkable ability to …


Mems Optical Cavities For Low Power Communication., Jacob Schopp May 2024

Mems Optical Cavities For Low Power Communication., Jacob Schopp

Electronic Theses and Dissertations

This thesis discusses the use of MEMS (microelectromechanical systems) optical cavities for use in low power communication. MEMS optical cavities are thin air gaps between an actuated MEMS mirror and a fixed glass encapsulation. By moving the MEMS mirror the reflectivity of the MEMS optical cavity can be changed. This change in reflectivity can be used to transmit information passively by modulating reflected light intensity instead of generating new light using a light source. These MEMS optical cavities are demonstrated using optical fibers for illumination delivery and reflected light collection. In addition to being reflected for communication, the illuminating light …


Quantum-Powered Battery Scheduling In Modern Distribution Grids, Diba Ehsani Mar 2024

Quantum-Powered Battery Scheduling In Modern Distribution Grids, Diba Ehsani

Electronic Theses and Dissertations

The rising need for exploiting a novel and evolved computation is an increasing concern in the power distribution system to address the exponential growth of distribution-connected devices. Scheduling numerous battery energy storage systems in an optimal way is one of the emerging challenges that will be more noticeable as the number of batteries, including residential, community, and vehicle batteries, increases in the grid. This thesis focuses on this topic and offers a necessary component in building the quantum-compatible distribution system of the future. Using a constrained quadratic model (CQM) on D-Wave’s hybrid solver as well as a binary quadratic model …


Data-Driven Approaches For Enhancing Power Grid Reliability, Behrouz Sohrabi Mar 2024

Data-Driven Approaches For Enhancing Power Grid Reliability, Behrouz Sohrabi

Electronic Theses and Dissertations

This thesis explores the transformative potential of data-driven approaches in addressing key operational and reliability issues in power systems. The first part of this thesis addresses a prevalent problem in power distribution networks: the accurate identification of load phases. This study develops a data-driven model leveraging consumption measurements from smart meters and corresponding substation data to reconstruct topology information in low-voltage distribution networks. The proposed model is extensively tested using a dataset with more than 5,000 real load profiles, demonstrating satisfactory performance for large-scale networks. The second part of the thesis pivots to a crucial safety concern: the risk and …


Parameter Identifiability Analysis And Calibration For Power System Dynamic Models, Lei Wang Jan 2024

Parameter Identifiability Analysis And Calibration For Power System Dynamic Models, Lei Wang

Electronic Theses and Dissertations

Accurate dynamic models are crucial for stable and reliable power system operation, making their validation essential. The accuracy of parameter estimation is influenced by several factors, including available observables, model structure, and estimation methods. However, in dynamic models, estimating parameters can be difficult when some of them are unidentifiable, meaning their values cannot be uniquely determined from the available data. This challenge may stem from limited impact of parameters on the measured outputs, parameter interactions, or poor data quality. Therefore, an identifiability analysis should be conducted prior to parameter estimation or model calibration. This preliminary step helps to determine which …


Optimizing Large Language Models And Multimodal Approaches For Biomedical Publication And Satellite Imagery, Youngsun Jang Jan 2024

Optimizing Large Language Models And Multimodal Approaches For Biomedical Publication And Satellite Imagery, Youngsun Jang

Electronic Theses and Dissertations

This dissertation comprises two main sections: the first focuses on natural language processing (NLP) for extracting key information from scientific literature using large language models (LLMs), and the second addresses remote sensing for detecting natural disasters, such as floods, from satellite imagery using a multimodal approach. The first section investigates methods to enhance Transformer-based models in classifying and extracting information from biomedical scientific publications. Key contributions include the development of a custom dataset for classification and Question and Answering (Q&A) tasks, fine-tuning Transformer models like the Bidirectional Encoder Representations from Transformers (BERT) and addressing multi-span answer issues with the TAg-based …


Structural Construction And Surface Modification Of Copper Current Collectors For Lithium Metal Batteries, Yaohua Liang Jan 2024

Structural Construction And Surface Modification Of Copper Current Collectors For Lithium Metal Batteries, Yaohua Liang

Electronic Theses and Dissertations

Graphene, a prevalent anode material in commercial lithium-ion batteries, has reached its theoretical capacity limit. The imperative is to develop high-capacity anode materials to meet the growing demand for energy density. Lithium metal, renowned for its exceptionally high theoretical specific capacity density (3680 mAh g-1) and low reduction potential (-3.04 V, relative to the standard hydrogen electrode), is commonly dubbed the "Holy Grail" for negative electrode materials in high-energy-density batteries. However, practical advancements in lithium metal anodes face obstacles like low Coulombic efficiency, limited cycle life, and heightened reactivity to the electrolyte and internal short circuits resulting from lithium dendrite …


Evaluating The Impact Of Perceptual Loss In Generative Adversarial Models And Diffusion Models For Document Image Enhancement, Farzaneh Karimpour Jan 2024

Evaluating The Impact Of Perceptual Loss In Generative Adversarial Models And Diffusion Models For Document Image Enhancement, Farzaneh Karimpour

Electronic Theses and Dissertations

Documents often suffer from various types of degradation which make them difficult to read and restrict OCR performance. This study investigates the effectiveness of perceptual loss in enhancing document image cleanup by comparing a GAN-based model and a diffusion model. In our experiments, we utilized the DE-GAN model as a GAN-based model and the NAF-DPM model as a diffusion model, both enhanced by incorporating perceptual loss. We then compared the results of both models and evaluated them by using the DIBCO 2013, DIBCO 2017, and H-DIBCO 2018 datasets revealed that our approach consistently outperforms existing state-of-the-art methods. Results showed that …


Comparative Analysis Of Deep Learning-Based Anomaly Detection Models For Gps Spoofing Detection, Hasan Mirzakhaninafchi Jan 2024

Comparative Analysis Of Deep Learning-Based Anomaly Detection Models For Gps Spoofing Detection, Hasan Mirzakhaninafchi

Electronic Theses and Dissertations

As autonomous vehicles (AVs) become integral to modern transportation, their susceptibility to cyber-attacks, particularly GPS spoofing, presents a serious security threat. This study addresses these challenges by applying a suite of deep learning models to enhance the detection of anomalous GPS signals. Focusing on autoencoder-based architectures, the proposed models such as long short-term memory-based variational autoencoder (LSTM-VAE), LSTM-based autoencoder (LSTM-AE), multilayer perceptron-based variational autoencoder (MLP-VAE), MLP-based Autoencoder (MLPAE), Stacked LSTM-based variational autoencoder (Stacked-LSTM-VAE), stacked LSTM-based autoencoder (Stacked-LSTM-AE), memory-augmented-LSTM-VAE (Mem-LSTM-VAE), and time-series-anomaly-detection-generative-adversarial-networks (TadGAN) were trained exclusively on authentic GPS data. This unsupervised learning approach which used for the above-mentioned models enables …


An Integrated Hybrid P2p-Dr Networks For A Transactive Energy Market Platform Considering Electricity Network Constraints, Sheroze Liaquat Jan 2024

An Integrated Hybrid P2p-Dr Networks For A Transactive Energy Market Platform Considering Electricity Network Constraints, Sheroze Liaquat

Electronic Theses and Dissertations

No abstract provided.


A Modular Framework For Surface-Embedded Actuation And Optical Sensing In Soft Robots., Paul Bupe Jr Dec 2023

A Modular Framework For Surface-Embedded Actuation And Optical Sensing In Soft Robots., Paul Bupe Jr

Electronic Theses and Dissertations

This dissertation explores the development and integration of modular technologies in soft robotics, with a focus on the OptiGap sensor system. OptiGap serves as a simple, flexible, cost-effective solution for real-time sensing of bending and deformation, validated through simulation and experimentation. Working as part of an emerging category of soft robotics called Soft, Curved, Reconfigurable, Anisotropic Mechanisms, or SCRAMs, this research also introduces the Thermally-Activated SCRAM Limb (TASL) technology, which employs shape-memory alloy (SMA) wire embedded in curved sheets for surface actuation and served as the initial inspiration for OptiGap. In addition, the EneGate system is presented as a complementary …


Investigating Mems Devices In Flow Conditions Relevant To Flow-Through Systems., Mohammad Shafquatul Islam Dec 2023

Investigating Mems Devices In Flow Conditions Relevant To Flow-Through Systems., Mohammad Shafquatul Islam

Electronic Theses and Dissertations

Advancements in microscale actuating technologies has substantially expanded the possibilities of interacting with the surrounding environment. Microstructures that deflect in response to mechanical forces are one of the largest application areas of microelectromechanical systems (MEMS). MEMS devices, functioning as sensors, actuators, and support structures, find applications in inertial sensors, pressure sensors, chemical sensors, and robotics, among others. Driven by the critical role of catalytic membrane reactors, this dissertation aims to evaluate enzyme activity on polymeric membranes and explore how fabrication methods from the field of Electrical and Computer Engineering (ECE) can incorporate sensing and actuation into these porous surfaces. Toward …


Adaptive Personalized Drug Delivery Method For Warfarin And Anemia Management: Modeling And Control., Affan Affan Dec 2023

Adaptive Personalized Drug Delivery Method For Warfarin And Anemia Management: Modeling And Control., Affan Affan

Electronic Theses and Dissertations

Personalized precision medicine aims to develop the appropriate treatments for suitable patients at the right time to obtain optimal results. Personalized medicine is challenging due to inter- and intra-patient variability, narrow therapeutic window, the effect of other medications, comorbidity (more than one disease at a time), nonlinear patient dynamics, and time-varying patient dose response characteristics which include bleeding (internal and external). This research aims to develop a framework for an adaptive personalized modeling and control method with minimum clinical patient specific dose response data for optimal drug dosing. The proposed methodology is applied to anemia and warfarin management. It is …


Design, Fabrication, And Integration Of Robotic Skin Sensors For Human Robot Interaction., Olalekan Olakitan Olowo Dec 2023

Design, Fabrication, And Integration Of Robotic Skin Sensors For Human Robot Interaction., Olalekan Olakitan Olowo

Electronic Theses and Dissertations

Enhancing physical human-robot interaction in modern robotics relies on refining the tactile perception of robot skin sensors. This research focuses on crucial aspects of the development process, including fabrication techniques, miniaturization, and integration for a more efficient collaborative human-robot interface. The fabrication process of robot skin sensors, designed to mimic human skin, is explored both within and outside cleanroom environments. An enhanced technique is presented to increase fabrication yield and create more miniaturized sensor designs with feature sizes in the tens of microns. These sensors function as piezoresistive arrays using organic polymers like PEDOT: PSS as the pressure-sensing medium. Various …


Molecular Dynamics Study Of Characterization In Metal-Free Friction Materials, Yizhan Zhang Nov 2023

Molecular Dynamics Study Of Characterization In Metal-Free Friction Materials, Yizhan Zhang

Electronic Theses and Dissertations

Metallic friction materials currently used in industry may adversely impact the environment. Substitutions for metals in friction materials, on the other hand, can introduce operational safety issues and other unforeseeable issues such as thermal-mechanical instabilities and insufficient strength. In view of it, this dissertation focuses on developing different kinds of materials from simple structure to complex structure and evaluating the material properties with the assistance of molecular dynamics (MD) tools at the nano scale.

First, the concept of the contacted surfaces in friction at the atomic scale was introduced in order to get accurate understanding of the friction process compared …


Frequency Stability Constrained Grid Operation With High Penetration Of Renewables, Ningchao Gao Nov 2023

Frequency Stability Constrained Grid Operation With High Penetration Of Renewables, Ningchao Gao

Electronic Theses and Dissertations

Achieving carbon neutrality necessitates a significant integration of renewable energy into power systems. However, the swift implementation of fluctuating renewable energy (VRE) sources such as solar photovoltaics (PV) exacerbates real time power imbalances due to the randomness and uncertainty associated with VRE power generation. Further, the declining reliance on conventional synchronous generators (SGs) for system inertia presents considerable challenges in maintaining frequency stability, especially following disturbances.

Two possible solutions are proposed to address the first issue. Firstly, a speedy real time generation dispatch can be scheduled to allocate generation resources within short time intervals to effectively respond to changes in …


Consensus-Based Active And Reactive Power Control And Management Of Microgrids, Shruti Singh Aug 2023

Consensus-Based Active And Reactive Power Control And Management Of Microgrids, Shruti Singh

Electronic Theses and Dissertations

Microgrids incorporating distributed generation and renewable energy sources offer potential solutions to the energy crisis while modernizing traditional grids. Despite cost-effectiveness in some technologies, financial support remains crucial for expensive ones like PV, fuel cells, and storage technologies. Microgrids bring economic benefits, efficiency, reduced emissions, and improved power quality. Their success hinges on cost reductions in renewables, storage, reliability, and energy management systems, enabling operation both with and without the utility grid.

Economic Dispatch optimizes system costs, considering all constraints. Various methods tackle this problem, including quadratic convex functions, Lagrangian relaxation, and quadratic programming. For microgrids with distributed generators, seamless …


Characteristics Of Refractivity And Sea State In The Marine Atmospheric Surface Layer And Their Influence On X-Band Propagation, Douglas Matthew Pastore Aug 2023

Characteristics Of Refractivity And Sea State In The Marine Atmospheric Surface Layer And Their Influence On X-Band Propagation, Douglas Matthew Pastore

Electronic Theses and Dissertations

Predictions of environmental conditions within the marine atmospheric surface layer (MASL) are important to X-band radar system performance. Anomalous propagation occurs in conditions of non-standard atmospheric refractivity, driven by the virtually permanent presence of evaporation ducts (ED) in marine environments. Evaporation ducts are commonly characterized by the evaporation duct height (EDH), evaporation duct strength, and the gradients below the EDH, known as the evaporation duct curvature. Refractivity, and subsequent features, are estimated in the MASL primarily using four methods: in-situ measurements, numerical weather and surface layer modeling, boundary layer theory, and inversion methods.

The existing refractivity estimation techniques often assume …


The Modernization Of Large Power Transformer Tanks, Babajide O. Williams Jun 2023

The Modernization Of Large Power Transformer Tanks, Babajide O. Williams

Electronic Theses and Dissertations

Due to the current demands placed on the power grid in terms of climate change, increasing urbanization, and terrorist attacks, the U.S. government in response to these demands, mandated that all the grid components be modernized in order to increase their reliability. As a critical component of the grid, Large Power Transformers (LPTs) play a key role in ensuring sustainable power generation and distribution. A literature search performed in this work and the analysis of data retrieved from the search showed that the tanks of these LPTs are critical to their durability, longevity, and reliability. Therefore, the reliability of LPTs …