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2024

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Articles 3241 - 3270 of 8259

Full-Text Articles in Physical Sciences and Mathematics

Context In Computer Vision: A Taxonomy, Multi-Stage Integration, And A General Framework, Xuan Wang Jun 2024

Context In Computer Vision: A Taxonomy, Multi-Stage Integration, And A General Framework, Xuan Wang

Dissertations, Theses, and Capstone Projects

Contextual information has been widely used in many computer vision tasks, such as object detection, video action detection, image classification, etc. Recognizing a single object or action out of context could be sometimes very challenging, and context information may help improve the understanding of a scene or an event greatly. However, existing approaches design specific contextual information mechanisms for different detection tasks.

In this research, we first present a comprehensive survey of context understanding in computer vision, with a taxonomy to describe context in different types and levels. Then we proposed MultiCLU, a new multi-stage context learning and utilization framework, …


Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe Jun 2024

Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe

Dissertations, Theses, and Capstone Projects

No abstract provided.


Towards Faster Inference Of Transformers: Strategies For Accelerating Decoding Processes, Cunxiao Du Jun 2024

Towards Faster Inference Of Transformers: Strategies For Accelerating Decoding Processes, Cunxiao Du

Dissertations and Theses Collection (Open Access)

This thesis delves into the acceleration and optimization of Transformer inference, a subject of increasing importance with the emergence of Large Language Models (LLMs). The study primarily addresses the challenges posed by two inherent properties of Transformers during inference: the quadratic complexity of the attention mechanism and the sequential nature of autoregressive inference. The research is structured into three main parts. The first part enhances the learning capabilities of non-autoregressive Transformers, achieving a remarkable 15.0x acceleration on machine translation tasks. The following section focuses on lossless acceleration through speculative decoding, where the proposed algorithm, Glide with CAPE, is shown to …


Spatial And Spectral Characterization Of The Gravitational-Wave Background With The Pta Optimal Statistic, Kyle A. Gersbach, Stephen R. Taylor, Patrick M. Meyers, Joseph D. Romano Jun 2024

Spatial And Spectral Characterization Of The Gravitational-Wave Background With The Pta Optimal Statistic, Kyle A. Gersbach, Stephen R. Taylor, Patrick M. Meyers, Joseph D. Romano

Physics and Astronomy Faculty Publications and Presentations

Pulsar timing arrays (PTAs) have made tremendous progress and are now showing strong evidence for the gravitational-wave background (GWB). Further probing the origin and characteristics of the GWB will require more generalized analysis techniques. Bayesian methods are most often used but can be computationally expensive. On the other hand, frequentist methods, like the PTA Optimal Statistic (OS), are more computationally efficient and can produce results that are complementary to Bayesian methods, allowing for stronger statistical cases to be built from a confluence of different approaches. In this work we expand the capabilities of the OS through a technique we call …


Simultaneous Chandra And Hst Observations Of The Quiescent Neutron Star Low-Mass X-Ray Binaries In 47 Tucanae, M. Van Den Berg, Liliana E. Rivera Sandoval, C O. Heinke, H. N. Cohn, P. M. Lugger, J. E. Grindlay, P. D. Edmonds, J. Anderson, A. Catuneanu Jun 2024

Simultaneous Chandra And Hst Observations Of The Quiescent Neutron Star Low-Mass X-Ray Binaries In 47 Tucanae, M. Van Den Berg, Liliana E. Rivera Sandoval, C O. Heinke, H. N. Cohn, P. M. Lugger, J. E. Grindlay, P. D. Edmonds, J. Anderson, A. Catuneanu

Physics and Astronomy Faculty Publications and Presentations

We present simultaneous Chandra X-ray Observatory and Hubble Space Telescope observations of three certain (X5, X7, W37) and two likely (X4, W17) quiescent neutron star low-mass X-ray binaries (qLMXBs) in the globular cluster 47 Tuc. We study these systems in the X-ray, optical, and near-ultraviolet (NUV) using the simultaneous data and additional non-contemporaneous HST data. We have discovered a blue and variable NUV counterpart to W17. We have not securely identified the eclipsing qLMXB W37 in the optical or NUV. Deeper high-resolution imaging is needed to further investigate the faint NUV excess near the centre of the W37 error circle. …


Spectroscopic Characterization, Dft Calculations, In Vitro Pharmacological Potentials, And Molecular Docking Studies Of N, N, O-Schiff Base And Its Trivalent Metal Complexes, Ikechukwu P. Ejidike, Amani Direm, Cemal Parlak, Adebayo A. Adeniyi, Mohammad Azam, Athar Ata, Michael O. Eze, Joshua W. Hollett, Hadley S. Clayton Jun 2024

Spectroscopic Characterization, Dft Calculations, In Vitro Pharmacological Potentials, And Molecular Docking Studies Of N, N, O-Schiff Base And Its Trivalent Metal Complexes, Ikechukwu P. Ejidike, Amani Direm, Cemal Parlak, Adebayo A. Adeniyi, Mohammad Azam, Athar Ata, Michael O. Eze, Joshua W. Hollett, Hadley S. Clayton

Michigan Tech Publications, Part 2

In this study, trivalent metal complexes of the category: [M(L)(H2O)nCly] obtained from the interaction of metal3+ ion salts with organic N, N, O-Schiff base (HL) (where: HL = 4-{(Z)-((2-{(E)-((2-hydroxyphenyl)methylidene)amino}ethyl)imino)methyl}-2-methoxyphenol; n, y = 1 or 2 and M = Ti(III), Fe(III), Ru(III), Cr(III) and Al(III)) were synthesized and characterized viz molar conductance, FT-IR, and UV–Vis spectroscopies, elemental analyses, thermal analyses (TGA and DTA), and UV–Vis spectroscopy, theoretical calculations. A distorted octahedral structure around the metal ions was proposed based on the obtained experimental and calculated data. Thermal examination of the complexes signposts the step-by-step disintegration to give the final decomposition product …


Western Kentucky University Stormwater Utility Survey 2024, Warren Campbell Jun 2024

Western Kentucky University Stormwater Utility Survey 2024, Warren Campbell

SEAS Faculty Publications

The main goal of this survey is to identify as many U.S. Stormwater Utilities (SWUs) as possible. Because many stormwater professionals do not have the time to respond to questionnaires, our primary method of identification was Internet searches. We searched key terms such as “stormwater utility,” “stormwater fee,” and “drainage fee.” We scoured online municipal codes such as Municode, AmLegal, Sterling, LexisNexis, General Code, and others. We searched through many city web websites to find utilities. We have also had many people contact me to update fees and identify new utilities. However, the data primarily comes from Internet sources and …


Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid Jun 2024

Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid

Master's Theses

Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …


Dehn's Problems And Geometric Group Theory, Noelle Labrie Jun 2024

Dehn's Problems And Geometric Group Theory, Noelle Labrie

Master's Theses

In 1911, mathematician Max Dehn posed three decision problems for finitely

presented groups that have remained central to the study of combinatorial

group theory. His work provided the foundation for geometric group theory,

which aims to analyze groups using the topological and geometric properties

of the spaces they act on. In this thesis, we study group actions on Cayley

graphs and the Farey tree. We prove that a group has a solvable word problem

if and only if its associated Cayley graph is constructible. Moreover, we prove

that a group is finitely generated if and only if it acts geometrically …


The Impact Of Video Assistant Referee (Var) On The English Premier League, Jack Kenyon Brown Jun 2024

The Impact Of Video Assistant Referee (Var) On The English Premier League, Jack Kenyon Brown

Master's Theses

The aim of this study is to examine how the introduction of the Video Assisted Referee (VAR) system influenced the English Premier League (EPL). Since its implementation in the English Premier League in 2019, VAR has been a constant source of debate and controversy. Many studies have been done on the immediate impact of VAR on other elite professional soccer leagues, but the scope of results is very limited and due to be updated. The data for the ensuing analysis consists of 3800 matches played in the English Premier League during the five seasons before (14/15, 15/16, 16/17, 17/18, and …


Accessible Real-Time Eye-Gaze Tracking For Neurocognitive Health Assessments, A Multimodal Web-Based Approach, Daniel C. Tisdale Jun 2024

Accessible Real-Time Eye-Gaze Tracking For Neurocognitive Health Assessments, A Multimodal Web-Based Approach, Daniel C. Tisdale

Master's Theses

We introduce a novel integration of real-time, predictive eye-gaze tracking models into a multimodal dialogue system tailored for remote health assessments. This system is designed to be highly accessible requiring only a conventional webcam for video input along with minimal cursor interaction and utilizes engaging gaze-based tasks that can be performed directly in a web browser. We have crafted dynamic subsystems that capture high-quality data efficiently and maintain quality through instances of user attrition and incomplete calls. Additionally, these subsystems are designed with the foresight to allow for future re-analysis using improved predictive models, as well as enable the creation …


Performance Interference Detection For Cloud-Native Applications Using Unsupervised Machine Learning Models, Eli Bakshi Jun 2024

Performance Interference Detection For Cloud-Native Applications Using Unsupervised Machine Learning Models, Eli Bakshi

Master's Theses

Contemporary cloud-native applications frequently adopt the microservice architecture, where applications are deployed within multiple containers that run on cloud virtual machines (VMs). These applications are typically hosted on public cloud platforms, where VMs from multiple cloud subscribers compete for the same physical resources on a cloud server. When a cloud subscriber application running on a VM competes for shared physical resources from other applications running on the same VM or from other VMs co-located on the same cloud server, performance interference may occur when the performance of an application degrades due to shared resource contention. Detecting such interference is crucial …


Design And Implementation Of A Vision-Based Deep-Learning Protocol For Kinematic Feature Extraction With Application To Stroke Rehabilitation, Juan Diego Luna Inga Jun 2024

Design And Implementation Of A Vision-Based Deep-Learning Protocol For Kinematic Feature Extraction With Application To Stroke Rehabilitation, Juan Diego Luna Inga

Master's Theses

Stroke is a leading cause of long-term disability, affecting thousands of individuals annually and significantly impairing their mobility, independence, and quality of life. Traditional methods for assessing motor impairments are often costly and invasive, creating substantial barriers to effective rehabilitation. This thesis explores the use of DeepLabCut (DLC), a deep-learning-based pose estimation tool, to extract clinically meaningful kinematic features from video data of stroke survivors with upper-extremity (UE) impairments.

To conduct this investigation, a specialized protocol was developed to tailor DLC for analyzing movements characteristic of UE impairments in stroke survivors. This protocol was validated through comparative analysis using peak …


Representation Theory And Its Applications In Physics, Max Varverakis Jun 2024

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …


Hyperbolic Groups And The Word Problem, David Wu Jun 2024

Hyperbolic Groups And The Word Problem, David Wu

Master's Theses

Mikhail Gromov’s work on hyperbolic groups in the late 1980s contributed to the formation of geometric group theory as a distinct branch of mathematics. The creation of hyperbolic metric spaces showed it was possible to define a large class of hyperbolic groups entirely geometrically yet still be able to derive significant algebraic properties. The objectives of this thesis are to provide an introduction to geometric group theory through the lens of quasi-isometry and show how hyperbolic groups have solvable word problem. Also included is the Stability Theorem as an intermediary result for quasi-isometry invariance of hyperbolicity.


Contrastive Filtering And Dual-Objective Supervised Learning For Novel Class Discovery In Document-Level Relation Extraction, Nicholas Hansen Jun 2024

Contrastive Filtering And Dual-Objective Supervised Learning For Novel Class Discovery In Document-Level Relation Extraction, Nicholas Hansen

Master's Theses

Relation extraction (RE) is a task within natural language processing focused on the classification of relationships between entities in a given text. Primary applications of RE can be seen in various contexts such as knowledge graph construction and question answering systems. Traditional approaches to RE tend towards the prediction of relationships between exactly two entity mentions in small text snippets. However, with the introduction of datasets such as DocRED, research in this niche has progressed into examining RE at the document-level. Document-level relation extraction (DocRE) disrupts conventional approaches as it inherently introduces the possibility of multiple mentions of each unique …


Using Plankton Edna To Estimate Whale Abundances Off The California Coast: Data Integration And Statistical Modeling, Katherine Chan Jun 2024

Using Plankton Edna To Estimate Whale Abundances Off The California Coast: Data Integration And Statistical Modeling, Katherine Chan

Master's Theses

Understanding marine mammal populations and how they are affected by human activity and ocean conditions is vital, especially in tracking population declines and monitoring endangered species. However, tracking marine mammal populations and their distribution is challenging due to difficulties in observation and costs. Using surrounding plankton environmental DNA (eDNA) has the potential to provide an indirect measure of monitoring cetacean abundances based on ecological associations. This project aims to apply statistical methods to assess the relationship of visual abundances of common species of baleen whales with amplicon sequence variants (ASV) of plankton eDNA samples from the NOAA-CalCOFI Ocean Genomics (NCOG) …


Quasi-Monte Carlo Estimation For Functional Generalized Linear Mixed Models., Ruvini Kumari Jayamaha Hitihamilage Jun 2024

Quasi-Monte Carlo Estimation For Functional Generalized Linear Mixed Models., Ruvini Kumari Jayamaha Hitihamilage

Dissertations

Functional Data Analysis (FDA) is a topic of growing interest in the statistics community and is applied in a wide range of fields such as Anthropology, Epidemiology, Meteorology, Neurology and Engineering. The data in FDA are smooth curves or surfaces in time or space which can be conceptualized as functions. Because of the smooth nature of the data and the measurements are highly correlated, making the classical methods such as univariate or multivariate analysis are infeasible for such data. Functional data Analysis (FDA) deals with these kinds of more detailed, complex, and structured data.

In this dissertation, we propose a …


On Near-Linear Cellular Automata Over Near Spaces, Abdul-Rahman M. Nasser Jun 2024

On Near-Linear Cellular Automata Over Near Spaces, Abdul-Rahman M. Nasser

Dissertations

Cellular Automata can be considered as examples of massively parallel machines. They are computational mathematical objects consisting of a grid of cells, each of which can exist in a finite number of states. These cells evolve over discrete time steps according to a set of predefined rules based on the states of neighboring cells. The notion of cellular automata was first introduced by Ulam and von Neumann and then popularized by John H. Conway in the 1970s with one of the most famous examples being The Game of Life.

This research builds on and generalizes the work of Tullio Ceccherini-Silberstein …


Enhancing Government Service Delivery: A Case Study Of Acqar Implementation And Lessons Learned From Chatgpt Integration In A Singapore Government Agency, Hui Shan Lee, Shankararaman, Venky, Eng Lieh Ouh Jun 2024

Enhancing Government Service Delivery: A Case Study Of Acqar Implementation And Lessons Learned From Chatgpt Integration In A Singapore Government Agency, Hui Shan Lee, Shankararaman, Venky, Eng Lieh Ouh

Research Collection Lee Kong Chian School Of Business

This paper presents the pilot implementation of AI Based Citizen Question-Answer Recommender (ACQAR) as an attempt to enhance citizen service delivery within a Singaporean government agency. Drawing insights from previous studies on the Empath library's use in Service Level Agreement (SLA) prediction and the implementation of the Citizen Question-Answer system (CQAS), we redesigned the pilot system, ACQAR. ACQAR integrates the outputs from Empath X SLA predictor and CQAS as essential inputs to the ChatGPT engine, creating contextually aware responses for customer service officers to use as responses to the citizens.Empath X SLA predictor anticipates the expected service response time based …


Interpretable Learning In Multivariate Big Data Analysis For Network Monitoring, José Camacho, Katarzyna Wasielewska, Rasmus Bro, David Kotz Jun 2024

Interpretable Learning In Multivariate Big Data Analysis For Network Monitoring, José Camacho, Katarzyna Wasielewska, Rasmus Bro, David Kotz

Dartmouth Scholarship

There is an increasing interest in the development of new data-driven models useful to assess the performance of communication networks. For many applications, like network monitoring and troubleshooting, a data model is of little use if it cannot be interpreted by a human operator. In this paper, we present an extension of the Multivariate Big Data Analysis (MBDA) methodology, a recently proposed interpretable data analysis tool. In this extension, we propose a solution to the automatic derivation of features, a cornerstone step for the application of MBDA when the amount of data is massive. The resulting network monitoring approach allows …


Trace Element Contamination In Urban Soils: Testing And Management, Melissa Chilinski, Melanie Stock, Paul R. Grossl, Eli Oliver Jun 2024

Trace Element Contamination In Urban Soils: Testing And Management, Melissa Chilinski, Melanie Stock, Paul R. Grossl, Eli Oliver

All Current Publications

Trace elements, often referred to as heavy metals, naturally occur in the soil at low levels. Certain land use histories can elevate the concentrations of trace elements to levels that present health risks. Understanding which elements and soil test values may impact human or crop health is an important aspect of gardening and micro-farming, particularly in urban environments that are at increased risk of soil contamination. This fact sheet provides instructions on interpreting soil test results for trace elements through the Total Element Composition EPA 3050B Soil Test (#S19) at Utah State University Analytical Laboratory.


Development And Applications Of Flexible Piezoelectric Nanogenerators Using Batio3, Pdms, And Mwcnts For Energy Harvesting And Sensory Integration In Smart Systems, Islam Uddin Shipu, Dipasree Bhowmick, Nondon Lal Dey Jun 2024

Development And Applications Of Flexible Piezoelectric Nanogenerators Using Batio3, Pdms, And Mwcnts For Energy Harvesting And Sensory Integration In Smart Systems, Islam Uddin Shipu, Dipasree Bhowmick, Nondon Lal Dey

Chemistry Faculty Publications and Presentations

Mechanical energy is a versatile and accessible green energy source, increasingly harnessed to power small-scale devices via innovative flexible piezoelectric nanogenerators (F- PNGs). These devices convert mechanical energy into electricity using lightweight materials such as Barium Titanate (BaTiO3), poly dimethyl siloxane (PDMS), and multi-walled carbon nanotubes (MWCNTs). In this design, BaTiO3 nanoparticles were embedded in a composite film with PDMS and MWCNTs, sandwiched between two copper electrodes. The BaTiO3/PDMS/MWCNT composite PENGs, synthesized for this study, produce an output voltage of ∼8 V through periodic cyclic beating. This represents an increase of about 16% compared to the PENGs without MWCNT doping. …


Predicting Rheology Of Uv-Curable Nanoparticle Ink Components And Compositions For Inkjet Additive Manufacturing, Cameron D. Lutz Jun 2024

Predicting Rheology Of Uv-Curable Nanoparticle Ink Components And Compositions For Inkjet Additive Manufacturing, Cameron D. Lutz

Master's Theses

Inkjet additive manufacturing is the next step toward ubiquitous manufacturing by enabling multi-material printing that can exhibit various mechanical, electronic, and thermal properties. These characteristics are realized in the careful formulation of the inks and their functional materials, but there are many constraints that need to be satisfied to allow optimal jetting performance and build quality when used in an inkjet 3-D printer. Previous research has addressed the desirable rheology characteristics to enable stable drop formation and how the metallic nanoparticles affect the viscosity of inks. The contending goals of increasing nanoparticle-loading to improve material deposition rates while trying to …


Semantic Structuring Of Digital Documents: Knowledge Graph Generation And Evaluation, Erik E. Luu Jun 2024

Semantic Structuring Of Digital Documents: Knowledge Graph Generation And Evaluation, Erik E. Luu

Master's Theses

In the era of total digitization of documents, navigating vast and heterogeneous data landscapes presents significant challenges for effective information retrieval, both for humans and digital agents. Traditional methods of knowledge organization often struggle to keep pace with evolving user demands, resulting in suboptimal outcomes such as information overload and disorganized data. This thesis presents a case study on a pipeline that leverages principles from cognitive science, graph theory, and semantic computing to generate semantically organized knowledge graphs. By evaluating a combination of different models, methodologies, and algorithms, the pipeline aims to enhance the organization and retrieval of digital documents. …


Morp: Monocular Orientation Regression Pipeline, Jacob Gunderson Jun 2024

Morp: Monocular Orientation Regression Pipeline, Jacob Gunderson

Master's Theses

Orientation estimation of objects plays a pivotal role in robotics, self-driving cars, and augmented reality. Beyond mere position, accurately determining the orientation of objects is essential for constructing precise models of the physical world. While 2D object detection has made significant strides, the field of orientation estimation still faces several challenges. Our research addresses these hurdles by proposing an efficient pipeline which facilitates rapid creation of labeled training data and enables direct regression of object orientation from a single image. We start by creating a digital twin of a physical object using an iPhone, followed by generating synthetic images using …


Pain Points: Cluster Analysis In Chronic Pain Networks, Iris W. Ho Jun 2024

Pain Points: Cluster Analysis In Chronic Pain Networks, Iris W. Ho

Master's Theses

Chronic pain is a pervasive health issue, affecting a significant portion of the population and posing complex challenges due to its diverse etiology and individualized impact. To address this complexity, there is a growing interest in grouping chronic pain patients based on their unique treatment needs. While various methodologies for patient grouping have emerged, leveraging graph-based approaches to produce and evaluate such groupings remains largely unexplored. Recent studies have shown promise in integrating knowledge graphs into exploring patient similarity across different biological domains, indicating potential avenues for research. Additionally, there is a growing interest in investigating patient similarity networks, highlighting …


Unraveling The History Of Deforestation In The Amazon Rainforest With Statistical Modeling, Ryan Destefano Jun 2024

Unraveling The History Of Deforestation In The Amazon Rainforest With Statistical Modeling, Ryan Destefano

Master's Theses

The Amazon rainforest, a vital ecosystem of immense biodiversity and global climate significance, faces the ongoing threat of deforestation driven by agricultural expansion. This thesis employs remote sensing techniques, focusing on the Enhanced Vegetation Index (EVI) derived from Landsat satellite imagery, to track land cover dynamics within the Amazon. The study examines historical land cover changes in current plantations in Peru and Brazil, regions where the exact timing of deforestation is uncertain. By analyzing EVI measurements dating back to 1984, inflection points indicative of deforestation events preceding plantation establishment are identified. Statistical modeling techniques, including spline fitting to analyze time …


Matrix Approximation And Image Compression, Isabella R. Padavana Jun 2024

Matrix Approximation And Image Compression, Isabella R. Padavana

Master's Theses

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some …


Phase Error Scaling Law In Two-Wavelength Adaptive Optics, Milo W. Hyde Iv, Matthew Kalensky, Michael J. Spencer Jun 2024

Phase Error Scaling Law In Two-Wavelength Adaptive Optics, Milo W. Hyde Iv, Matthew Kalensky, Michael J. Spencer

Faculty Publications

We derive a simple, physical, closed-form expression for the optical-path difference (OPD) of a two-wavelength adaptive-optics (AO) system. Starting from Hogge and Butts’ classic OPD variance integral expression, we apply Mellin transform techniques to obtain series and asymptotic solutions to the integral. For realistic two-wavelength AO systems, the former converges slowly and has limited utility. The latter, on the other hand, is a simple formula in terms of the separation between the AO sensing (i.e., the beacon) and compensation (or observation) wavelengths. We validate this formula by comparing it to the OPD variances obtained from the aforementioned series and direct …