This paper rigorously demonstrates the existence of Abelian Lie group structures on punctured spheres, with a particular focus on the \(2\)-sphere. We establish that the \(2\)-sphere with the removal of the North and South poles, denoted \(S^2 \setminus \{N, S\}\), admits an Abelian Lie group structure. We explicitly construct this structure by employing the stereographic projection to transfer complex multiplication from the punctured complex plane \((\mathbb{C}^*, \cdot)\) to \(S^2 \setminus \{N, S\}\). Through detailed proofs, we rigorously affirm that the induced binary operation is well-defined, smooth, and satisfies the axioms of an Abelian group. Consequently, we confirm that \((S^2 \setminus \{N, S\}, \star)\) is Lie group isomorphic to \((\mathbb{C}^*, \cdot)\). Furthermore, we provide an explicit construction of a global frame for the tangent bundle of \(S^2 \setminus \{N, S\}\), thereby illustrating its parallelizability, a property inherent to Lie groups. This construction serves as a concrete example of circumventing the constraints imposed by Adams' Theorem, which restricts parallelizability and Lie group structures on closed spheres. By considering the open submanifold \(S^2 \setminus \{N, S\}\), our work highlights the significant role of manifold topology in determining the existence of Lie group structures. We extend our investigation to the singly punctured \(n\)-sphere \(S^n \setminus \{N\}\), demonstrating that it can also be endowed with an Abelian Lie group structure isomorphic to the additive Lie group \((\mathbb{R}^n, +)\), induced by vector addition via stereographic projection. The Abelian Lie group structure \((S^n \setminus \{N\}, \oplus)\) offers an alternative perspective on representing a form of quantum superposition where normalization is implicitly embedded within the geometric mapping. This comprehensive analysis illustrates the method of inducing Lie group structures through diffeomorphisms and underscores the topological flexibility of open manifolds in supporting such structures.

This work presents an analysis of the influence of connector repeatability in three different methods for estimating the propagation constant of transmission lines from twoport measurements. For this purpose, the repeatability of 16 transitions using 1.85 mm coaxial-to-microstrip end-launcher connectors has been tested. It has shown that using the same pair of connectors instead of the whole set significantly reduces the standard deviation of the transition S-parameters that affects the final estimation of the propagation constant, and especially the attenuation constant. In addition, the hypothesis that the measured data have a normal probability distribution has been validated by performing an Anderson-Darling test on the estimated S-parameters of the transition. The obtained standard deviation has been included in a sensitivity analysis, generating S-parameters from normal distribution and performing a Monte Carlo simulation. The objective is to study the standard deviation of the propagation constant obtained using the proposed methods when there are errors related to connector repeatability. In this case, unlike random errors of the analyzer, it has been found that all the compared strategies for the estimation of the propagation constant (traces, eigenvalues, and determinants) work in the same way concerning launcher repeatability errors. Furthermore, it has been seen that the propagation constant obtained also follows a normal distribution. Finally, to validate the presented theory, methods have been applied to several measurements of two lines in the 0.01-to 67-GHz frequency range, using the same kit and different combinations of different connectors. Results show that higher accuracy is obtained when using the same pair of connectors, considerably reducing attenuation constant ripple, which assesses the suitability of the proposed error analysis.

The increasing integration of renewable energy sources and energy storage systems into the electrical grid demands the development of high-performance power conversion technologies. In this context, the design of efficient and reliable power conversion systems (PCS) is crucial for the integration of these energy sources. The use of optimization tools facilitates the selection of power conversion architectures and converter topologies that enhance overall efficiency and reliability while reducing development time. This paper presents an advanced optimization tool developed for designing the dc-ac PCS of HESS, which integrates a lithium-titanate-oxide (LTO) battery and an aqueous-organicredox-flow (AORF) battery for grid connection. Four conversion architectures are explored with different degrees of dc-dc and dc-ac module parallelization. A set of optimization problems is defined to obtain the Pareto front of solutions for each architecture, resulting in different trade-offs between the system's performance metrics.

Accurate opponent trajectory prediction remains a significant challenge in autonomous racing, where vehicles often execute aggressive maneuvers and sudden acceleration changes. Transformer-based architectures like Motion Transformer (MTR) have shown promise for vehicle trajectory prediction in structured environments such as highways and urban roads. However, they, along with LSTM-enhanced methods like MixNet, face limitations in predicting trajectories under the extreme dynamics of autonomous racing, often leading to increased errors and computational inefficiencies. To address these challenges, we propose two novel methods. First, BézierMixNet extends MixNet by utilizing Bézier curves to more accurately represent trajectories through a combination of reference paths. Second, we introduce BARTé, which employs Composite Bézier Curves to achieve both computational efficiency and high prediction accuracy in dynamic racing scenarios. Our methods are evaluated on extensive datasets from the DeepRacing Formula One simulation and real-world data from the Indy Autonomous Challenge. Compared to state-of-the-art models, BARTé reduces average displacement error by approximately 4%, longitudinal error by 48% while reducing computation time by 90%, demonstrating significant advantages for high-speed autonomous racing.

Electricity service interruptions compromise households' ability to meet energy demand, and thus increase energy insecurity. Interruptions can take the form of power outages, or involuntary disconnections due to nonpayment. To achieve equitable electricity access, it is crucial to understand how electricity loss varies across demographics. However, utilities often report outages at the system or county level and face few incentives to report disconnection metrics, making spatially granular analysis of interruptions challenging. This paper presents a new method of quantifying electricity reliability by classifying unlabeled advanced metering infrastructure (AMI) data, hence disaggregating power outages from disconnections in residential electricity consumption data. We use the Commonwealth Edison utility service territory in Illinois as a case study and evaluate how the duration and frequency of power outages (outage burden) change across ZIP codes. We find that the most outage-burdened regions are concentrated in rural counties, and regions with a higher percentage of low-income residents and people of color often carry higher outage burdens than the rest of the service territory. Our proposed method is the first to disaggregate AMI data into outages and disconnections, enabling more granular metrics for electricity reliability, highlighting gaps in energy accessibility and informing the identification of energy-insecure communities.

A document by G K Wardhana. Click on the document to view its contents.

One of the fundamental requirements of democracy is trust in elections. Still, many elections around the world have been marred by allegations of fraud, undermining public confidence. One common concern is the lack of transparency at different points of the election process, which can lead to (valid or invalid) accusations involving tally manipulation or evidence tampering. To address this issue, we propose Election Transparency, an ecosystem that facilitates the registration, publication, and collaborative verification of electoral data and results. Essentially, the system allows all election data to be stored in transparency logs, so voters can more easily verify individual entries and interested organizations can analyze large data sets and ensure their integrity. Election Transparency is expected to reduce the costs of auditing procedures, such as verifying the authenticity of individual documents and recalculating election results. We have deployed a prototype with data from recent, national-scale elections in Brazil, and evaluated its performance. Although we present Election Transparency in the context of Brazilian elections, it is adaptable to similar scenarios involving electronic voting.

This paper presents a parametric family of curves that can smoothly morph from a circle (shape parameter s = 0) to any polygon circumscribed to that circle (s = 1). A fully closed solution r(φ; s, ψ) in polar coordinates is derived for the diamircle that seamlessly evolves between a diamond with interior angles ψ and 180°−ψ and its inscribed circle. Curvygons, closed curves with continuous derivative (class C1) that are intermediate to a circle of radius R and any given N-sided polygon circumscribed to that circle, are then immediately obtained by simply joining N scaled and suitably rotated diamircle segments. Conceptually related 3D curvyhedra, which smoothly morph between spheres and circumscribed polyhedra, are demonstrated. This work extends the Fernández-Guasti squircle (special case ψ = 90° of the diamircle) and the Fong sphube to much broader families of morphing 2D and 3D shapes. Application examples are showcased for computer animations, UI and industrial design, mechanical engineering, and heat diffusion physics.

In this work, an optimized broadband method using multilayer transmission lines to characterize dielectric permittivity and loss tangent of material samples is presented. For this purpose, a microstrip line loaded with a piece of the selected dielectric to be characterized is used. From two-port measurements, and using different length lines, the propagation constant can be obtained. To minimize random errors and to improve the accuracy, an over determination of the method increasing the number of lines measured and a criteria to choose the optimal line lengths is considered. Firstly, the measurement method itself is applied to uncovered microstrip lines and an accurate model of the substrate is obtained. Secondly, the lines are covered with several materials, made by FDM additive manufacturing technique, such as Acrylonitrile Butadiene Styrene (ABS), Polylactic Acid (PLA), High Impact Polystyrene (HIPS), Thermoplastic Polyurethane (TPU), Copolyester (CPE), FLEX, Polyethylene Terephthalate Glycol (PETG) and Nylon. A model of the transmission line considering the cover is developed and an electromagnetic simulator is used to indirectly determine the cover material electrical parameters. Results show excellent agreement with electromagnetic simulations in the 0.1-to 67-GHz frequency band, so they assess the suitability of the proposed method.

We present a new algorithm to automatically convert 3-dimensional left atrium surface meshes into a standard 2-dimensional space: a Left Atrial Positioning System (LAPS). Methods: Forty-five contrast-enhanced 4-dimensional computed tomography datasets were collected from 30 subjects. The left atrium volume was segmented using a trained neural network and converted into a surface mesh. LAPS coordinates were calculated on each mesh by computing lines of longitude and latitude on the surface of the mesh with reference to the center of the posterior wall and the mitral valve. LAPS accuracy was evaluated with one-way transfer of coordinates from a template mesh to a synthetic ground truth, which was created by registering the template mesh and pre-calculated LAPS coordinates to a target mesh. The Euclidian distance error was measured between each test node and its ground truth location. Results: The median point transfer error was 2.13 mm between follow-up scans of the same subject (n=15) and 3.99 mm between different subjects (n=30). The left atrium was divided into 24 anatomic regions and represented on a 2D square diagram. Conclusion: The Left Atrial Positioning System is fully automatic, accurate, robust to anatomic variation, and has flexible visualization for mapping data in the left atrium. Significance: This provides a framework for comparing regional LA surface data values in both follow-up and cohort studies.

The emergence of large language models (LLM) has driven a significant increase of AI workload in data center power demand. Renewable-powered solutions to decarbonizing LLM workload and reducing electricity costs are faced with the combined volatility of stochastic user requests and renewable energy. The key to removing the barriers in sustainable AI development lies in the adjustable capability of LLM power profiles. Therefore, this paper focuses on exploring the potential load flexibility of LLM workload and proposes a coordinated performance-safe scheduling framework. Driven by the existence of the most energy-efficient GPU core frequency that is smaller than the default maximum one, the framework slows down the fine-tuning cluster and utilizes idle GPU resources from the inference cluster to maintain the computing performance of fine-tuning tasks. Consequently, the power consumption of the total cluster is reduced, which provides a fresh source of load flexibility. Furthermore, the framework employs dynamic frequency scaling to more flexibly modify the power profile of the expanded fine-tuning cluster. The computing performance is particularly guaranteed through temporal coupling constraints. In a simulated study supported by real-world data, the results prove a 6% power-saving ability and 9% cost-saving gains at utmost.

Doppler Weather Radars (DWRs) play a crucial role in atmospheric monitoring by providing high-resolution precipitation and wind data. However, electromagnetic interference (EMI) can compromise signal quality, reducing accuracy. Traditional band-pass filters used in DWRs often have a wide frequency range, allowing unwanted signals to pass through and degrading performance. The increasing demand for compact, high-performance filters in telecommunications and radar systems necessitates innovative design approaches.

In response to the evolving landscape of commercial electric vehicles (EVs), we are pioneering the integration of a Power TakeOff (PTO) design and assembly on the e-axle of Commercial Vehicles (CVs).This innovative concept addresses the significant challenges faced by commercial EV manufacturers "The need for auxiliary hydraulic operations without the use of additional motors or external power sources". This study explores the integration of a PTO unit on the rear axle carrier housing of vehicle, which harnesses power directly from the transmission unit. By powering a hydraulic pump, this solution enables seamless operation of auxiliary hydraulic functions crucial for various commercial applications, like tipping and lifting functions. As leaders in this emerging field, our ongoing development efforts are focused on advancing this concept to market readiness.

This paper introduces a reinforcement learning framework designed to optimize energy distribution in smart grids. By using Proximal Policy Optimization (PPO) and Graph Neural Networks (GNNs), the framework effectively manages the grid's complex topology to enhance decision-making. It addresses critical challenges, including minimizing energy loss, improving reliability, and reducing operational costs. The model was trained and evaluated using the Grid2Op simulation environment and its associated L2RPN dataset, which encompasses realistic scenarios such as load fluctuations, renewable energy variability, and grid faults. The proposed method demonstrated significant advancements, achieving a reduction in energy loss to 6.8%, a reliability improvement with a SAIDI score of 3.2, and a 32% decrease in operational costs. These outcomes outperform recent methods such as GCN-SAC and rule-based systems. Furthermore, the model exhibited faster computation times, making it highly suitable for real-time grid applications. The integration of curriculum learning enabled the agent to adapt to complex and unseen scenarios effectively. This study presents a robust and scalable solution for smart grid optimization, offering significant potential for managing modern power systems and integrating renewable energy sources efficiently.

The rapid advancements in deep learning have led to the widespread adoption of Transformer-based models, which now power a variety of natural language processing (NLP) applications, from search engines to conversational AI. While these models deliver state-of-the-art performance, their high computational cost presents challenges for real-time inference, mobile deployment, and large-scale applications. As a result, numerous model compression techniques have been explored to enhance efficiency without compromising accuracy. Among these, token pruning has gained attention as a promising strategy that selectively removes less informative tokens during inference, reducing computational complexity while preserving model effectiveness. This survey provides a comprehensive review of token pruning methods, categorizing them into static and dynamic approaches and analyzing their underlying principles. We examine key evaluation metrics used to measure pruning effectiveness, explore its impact across various NLP tasks, and compare different pruning strategies in terms of efficiency, accuracy trade-offs, and generalization. Additionally, we highlight critical challenges, including maintaining long-range dependencies, ensuring robustness to distribution shifts, and scaling pruning techniques to large language models. Finally, we outline open research directions and discuss potential integrations with other efficiency-driven techniques, such as quantization and knowledge distillation. By consolidating recent progress in token pruning, this survey aims to serve as a valuable resource for researchers and practitioners striving to develop more efficient NLP models.

Black-box attacks play a crucial role in identifying vulnerabilities in deep neural networks by generating adversarial examples that remain imperceptible to human observers. Transfer-based attacks, which leverage surrogate models to craft adversarial examples for attacking victim models, have become a dominant technique in black-box settings due to their practicality and high effectiveness. However, as deep learning models continue to grow in complexity, the resulting disparities between different architectures make generating adversarial examples with strong transferability increasingly difficult. To address this challenge, we propose a novel hybrid query-transfer method called Dual Generalization Attack (DGA). Specifically, DGA enhances model generalization by incorporating a Model Filter (MF) that injects posterior information from the victim model through a limited number of queries, thereby reducing the gap between the surrogate and victim models. Additionally, DGA introduces a Multi-granularity Local Shuffle (MLS) technique to improve input generalization, enhancing input diversity while preserving consistency with the original images. This dual approach reduces the dependency of adversarial examples on both surrogate models and input configurations, thereby enhancing transferability and attack performance on unknown victim models. Extensive experiments demonstrate that DGA significantly outperforms existing black-box attacks, achieving a substantial improvement in adversarial transferability.

The growing reliance on digital systems for learning has led to an abundance of data that captures both the learning contexts and underlying processes. Learning Analytics (LA), an emerging field, utilizes innovative tools to extract meaningful insights from this data. Digital platforms like Massive Open Online Courses (MOOCs) and Free/Libre Open-Source Software (FLOSS) repositories offer unique perspectives on individual and collaborative learning. This paper explores personal constructivism in MOOCs by analyzing students' learning behaviors and their impact on performance, while also examining social constructivism in FLOSS repositories to better understand collaborative learning dynamics. By applying process mining techniques, specifically conformance alignments, and cluster analysis, we investigate how patterns of student engagement in MOOCs correlate with their learning outcomes. Our findings show that consistent engagement with videos, following a specific sequence, and minimizing time gaps between video views leads to higher performance, while irregular engagement often results in suboptimal outcomes. Additionally, we explore FLOSS repositories to examine how community interactions-such as discussions and collaborative contributions-foster knowledge construction and social learning. This study integrates insights from both personal and social constructivism to provide a comprehensive understanding of learning behaviors in MOOCs and FLOSS environments. The findings offer valuable implications for course design and community management strategies aimed at optimizing learning experiences and addressing diverse needs in digital education.

This work employs a new approach to analyze coupled-resonator circuits to design and manufacture a fully metallic dual polarization frequency selective surface (FSS). The proposed filtering structure is composed of a series of unit cells with resonators fundamentally coupled along the z-direction and then repeated periodically in the xy-plane. The fully metallic cascaded unit cell is rigorously analyzed within an infinite periodic environment as a coupled-resonator electromagnetic (EM) circuit. The convenient design of the EM resonators makes it possible to push the evanescent EM field through the metallic structure in the desired frequency band for both polarizations. An FSS prototype is manufactured and measured, and good agreement is found between the simulation results and the final prototype.