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Articles 541 - 570 of 2725
Full-Text Articles in Physical Sciences and Mathematics
Effectiveness Of Windrow Composting Methodology In Killing A Thermo-Tolerant Species Of Salmonella During Mortality Composting, Spencer Gabriel Myers
Effectiveness Of Windrow Composting Methodology In Killing A Thermo-Tolerant Species Of Salmonella During Mortality Composting, Spencer Gabriel Myers
Master's Theses
In a large agricultural operation, such as the one at Cal Poly San Luis Obispo, disposal of deceased animals is an immense issue. The cost of transporting and rendering every dead animal is inhibitory to the general function of the agricultural operations and their thin budget. Therefore, we propose that composting mortalities could be an economical alternative. Composting is a recognized method for taking animal waste products along with carbon waste and turning it into a pathogen-free, nutrient-rich topsoil. Carcass composting is in fact performed in other countries and states to varying degrees of success. However, the California EPA limits …
Combining Parts Of Speech, Term Proximity, And Query Expansion For Document Retrieval, Lubomir Stanchev, Eric Labouve
Combining Parts Of Speech, Term Proximity, And Query Expansion For Document Retrieval, Lubomir Stanchev, Eric Labouve
Computer Science and Software Engineering
Document retrieval systems recover documents from a database and order them according to their perceived relevance to a user's search query. This is a difficult task for machines to accomplish because there exists a semantic gap between the meaning of the terms in a user's literal query and a user's true intentions. The main goal of this study is to modify the Okapi BM25 document retrieval system to improve search results for textual queries and unstructured, textual corpora. This research hypothesizes that Okapi BM25 is not taking full advantage of the structure of text inside documents. This structure holds valuable …
Fabrication Of Miniaturized Paper-Based Microfluidic Devices (Micropads), E. Brandon Strong, Spencer A. Schultz, Andres Martinez, Nathaniel W. Martinez
Fabrication Of Miniaturized Paper-Based Microfluidic Devices (Micropads), E. Brandon Strong, Spencer A. Schultz, Andres Martinez, Nathaniel W. Martinez
Chemistry and Biochemistry
Microfluidic paper-based analytical devices (microPADs) are emerging as cost-effective and portable platforms for point-of-care assays. A fundamental limitation of microPAD fabrication is the imprecise nature of most methods for patterning paper. The present work demonstrates that paper patterned via wax printing can be miniaturized by treating it with periodate to produce higher-resolution, high-fidelity microPADs. The optimal miniaturization parameters were determined by immersing microPADs in various concentrations of aqueous sodium periodate (NaIO4) for varying lengths of time. This treatment miniaturized microPADs by up to 80% in surface area, depending on the concentration of periodate and length of the reaction …
Low Cost Timing System For High Precision Particle Detection, Eric Madrigal, Sasha Dolgashev, Vi Tran
Low Cost Timing System For High Precision Particle Detection, Eric Madrigal, Sasha Dolgashev, Vi Tran
STAR Program Research Presentations
The project goal was to find a way to make a low-cost high precision timing system. High precision timing systems are already on the market, however, at a high cost. Various particle research projects need a large number of timers, so a substantial budget is required. In order to bypass the need for a large enough budget, commercially available parts were used and tested. The timing system consisted of multiple parts with different low-cost microchips and counters. In order for the project to meet its goal, the timers need to work under 50 picoseconds. Although some tests showed the timers …
Ultra-Fast X-Ray Diffraction Of Metastable Structures During Hydrogen Crystallization, Andrew Pham
Ultra-Fast X-Ray Diffraction Of Metastable Structures During Hydrogen Crystallization, Andrew Pham
STAR Program Research Presentations
Big discoveries can come from small element, and hydrogen is the simplest element in the universe, but its property has been intensely studied in recent years. Hydrogen has a notably complex phase diagram, and its application is important to many scientific fields, such as fundamental physics, inertial confinement fusion, planetary sciences, etc. While sophisticated static observations have probed its structure at extremely high pressures, the higher-temperature studies applying dynamic compression is confined to optical measurement methods. In this project over the summer, I will present spectrally resolved x-ray scattering assessment from plasmons in dynamic compressed deuterium. Collaborating Compton scattering and …
Computing Homology Of Hypergraphs, Jackson Earl
Computing Homology Of Hypergraphs, Jackson Earl
STAR Program Research Presentations
In the modern age of data science, the necessity for efficient and insightful analytical tools that enable us to interpret large data structures inherently presents itself. With the increasing utility of metrics offered by the mathematics of hypergraph theory and algebraic topology, we are able to explore multi-way relational datasets and actively develop such tools. Throughout this research endeavor, one of the primary goals has been to contribute to the development of computational algorithms pertaining to the homology of hypergraphs. More specifically, coding in python to compute the homology groups of a given hypergraph, as well as their Betti numbers …
Memory In A Contact Line, Charity Lizardo, Esmeralda Orozco, Audrey Profeta, Nathan C. Keim
Memory In A Contact Line, Charity Lizardo, Esmeralda Orozco, Audrey Profeta, Nathan C. Keim
STAR Program Research Presentations
We study the behavior of the liquid-solid-vapor contact line of water held in a narrow gap between two plates. A syringe pump injects and withdraws a constant, small volume of the water, driving the contact line back and forth repeatedly and changing its shape. We take photos of the contact line after each cycle. Comparing subsequent images to each other, we find that after several cycles the contact line reaches one of two steady states: a reversible steady state, where the shape is not changing, or a fluctuating steady state, where the shape continues to change slightly. Experiments on acrylic …
The Lick Agn Monitoring Project 2011: Photometric Light Curves, Anna Pancoast, Andreas Skielboe, Liuyi Pei, Vardha Nicola Bennert, Jong-Hak Woo
The Lick Agn Monitoring Project 2011: Photometric Light Curves, Anna Pancoast, Andreas Skielboe, Liuyi Pei, Vardha Nicola Bennert, Jong-Hak Woo
Physics
In Spring 2011, the Lick AGN Monitoring Project observed a sample of 15 bright, nearby Seyfert 1 galaxies in the V band as part of a reverberation mapping campaign. The observations were taken at six ground-based telescopes, including the West Mountain Observatory 0.91 m telescope, the 0.76 m Katzman Automatic Imaging Telescope, 0.6 m Super-LOTIS at Kitt Peak, the Palomar 60 inch telescope, and the 2 m Faulkes telescopes North and South. The V-band light curves measure the continuum variability of our sample of Seyferts on an almost daily cadence for 2–3 months. We use image-subtraction software to isolate …
Polyxpress+: Using Social Networking To Enhance The User Experience Of An Interactive Location-Based Storytelling Application, Desiree Creel
Polyxpress+: Using Social Networking To Enhance The User Experience Of An Interactive Location-Based Storytelling Application, Desiree Creel
Master's Theses
There’s no denying the ever increasing presence of social networking in our daily lives. Every day, people share what they are thinking, doing, and experiencing. But even more so, they check their favorite networks to see what the people in their lives are sharing. Social networking has become so prevalent that most applications incorporate it since it keeps users engaged and beckons them back to the application again and again.
PolyXpress is an interactive, location-based storytelling mobile application that functions as a platform for creating and experiencing stories. Written as a research project at California Polytechnic State University, it allows …
Validation Of The Nonhydrostatic General Curvilinear Coastal Ocean Mode (Gccom) For Stratified Flows, Mariangel Garcia, Paul Choboter, Ryan K. Walter, Jose E. Castillo
Validation Of The Nonhydrostatic General Curvilinear Coastal Ocean Mode (Gccom) For Stratified Flows, Mariangel Garcia, Paul Choboter, Ryan K. Walter, Jose E. Castillo
Physics
While global-and basin-scale processes can be captured quite well with computationally-inexpensive hydrostatic models, smaller-scale features such as shoaling nonlinear internal waves and bores, coastal fronts, and other convective processes require the use of a nonhydrostatic model to accurately capture dynamics. Here the nonhydrostatic capabilities of the General Curvilinear Coastal Ocean Model (GCCOM) in a stratified environment are introduced. GCCOM is a three-dimensional, nonhydrostatic Large Eddy Simulation (LES), rigid lid model that has the ability to run in a fully three-dimensional general curvilinear coordinate system. This model was previously validated for unstratified flows with curvilinear coordinates. Here, recent advances of the …
Detrital Zircon Geochronology And Evolution Of The Nacimiento Block Late Mesozoic Forearc Basin, Central California Coast, Scott Johnston, Andrew R.C. Kylander-Clark, Alan D. Chapman
Detrital Zircon Geochronology And Evolution Of The Nacimiento Block Late Mesozoic Forearc Basin, Central California Coast, Scott Johnston, Andrew R.C. Kylander-Clark, Alan D. Chapman
Physics
Forearc basins are first-order products of convergent-margin tectonics, and their sedimentary deposits offer unique perspectives on coeval evolution of adjacent arcs and subduction complexes. New detrital zircon U-Pb geochronologic data from 23 sandstones and 11 individual conglomerate clasts sampled from forearc basin strata of the Nacimiento block, an enigmatic stretch of the Cordilleran forearc exposed along the central California coast, place constraints on models for forearc deformation during evolution of the archetypical Cordilleran Mesozoic margin. Deposition and provenance of the Nacimiento forearc developed in three stages: (1) Late Jurassic– Valanginian deposition of lower Nacimiento forearc strata with zircon derived from …
Geologic Map And Structural Development Of The Noerthernmost Sur-Nacimiento Fault Zone, Central California Coast, Scott M. Johnston, John S. Singleton, Alan D. Chapman, Gabriella Murray
Geologic Map And Structural Development Of The Noerthernmost Sur-Nacimiento Fault Zone, Central California Coast, Scott M. Johnston, John S. Singleton, Alan D. Chapman, Gabriella Murray
Physics
The Sur-Nacimiento fault exposed along the central California coast (United States) juxtaposes the Salinian block arc against the Nacimiento block accretionary complex, cuts out the majority of the forearc basin and western arc, and requires a minimum of 150 km of orogen-normal crustal excision within the Mesozoic California convergent margin. Despite this significant strain, the kinematic evolution of the Sur-Nacimiento fault remains poorly understood, with diverse hypotheses suggesting sinistral, dextral, thrust, or normal displacement along the fault. This Late Cretaceous–Paleogene strain history is complicated by the location of the fault within a belt of subparallel faults that have accommodated significant …
Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe
Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe
Mathematics
The invariant subspace problem asks if every bounded linear operator on a Banach space has a nontrivial closed invariant subspace. Per Enflo has shown this is false in general, however it is known that every compact operator has an invariant subspace. The purpose of this project is to explore introductory results in functional analysis. Specifically we are interested in understanding compact operators and the proof that all compact operators on a Hilbert space have an invariant subspace. In the process of doing this we build up many examples and theorems relating to operators on a Hilbert or Banach space. Continuing …
On Nonnegatively Curved Hypersurfaces In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
On Nonnegatively Curved Hypersurfaces In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Mathematics
In this paper we prove a conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily properly embedded.
Eye Pressure Monitior, Andrea Nella Levy
Eye Pressure Monitior, Andrea Nella Levy
Computer Engineering
The document describes a mobile application that takes information from an attached device which tests eye pressure. The device consists of an IOIO board connected to a custom device that measures the frequency of a given waveform. The device was designed by another student for their senior project, which I am taking over. This device is connected to an IOIO board which is a board designed by a Google employee which works with an android phone in order to create applications that work with embedded systems. The board comes with an API and connects to the phone via a micro-USB. …
Influence Of High Aspect Ratio Nanoparticle Filler Addition On Piezoelectric Nanocomposites, Jeremy A. Armas
Influence Of High Aspect Ratio Nanoparticle Filler Addition On Piezoelectric Nanocomposites, Jeremy A. Armas
Master's Theses
Piezoelectric nanogenerators (PNGs) are a new class of energy harvesting materials that show potential as a direct energy source for low powered electronics. Recently, piezoelectric polymers have been utilized for PNG technology due to low toxicity, high flexibility, and facile solution processing which provide manufacturing opportunities such as screen printing. Throughout the last decade, countless projects have focused on how to enhance the energy harvesting capabilities of these PNGs through the incorporation of nanoparticle fillers, which have been reported to enhance the piezoelectric properties of the film either directly through their intrinsic piezoelectric properties or through acting as surfaces for …
Improving Ultra-Wideband Localization By Detecting Radio Misclassification, Cory A. Mayer
Improving Ultra-Wideband Localization By Detecting Radio Misclassification, Cory A. Mayer
Master's Theses
The Global Positioning System (GPS) and other satellite-based positioning systems are often a key component in applications requiring localization. However, accurate positioning in areas with poor GPS coverage, such as inside buildings and in dense cities, is in increasing demand for many modern applications. Fortunately, recent developments in ultra-wideband (UWB) radio technology have enabled precise positioning in places where it was not previously possible by utilizing multipath-resistant wide band pulses.
Although ultra-wideband signals are less prone to multipath interference, it is still a bottleneck as increasingly ambitious projects continue to demand higher precision. Some UWB radios include on-board detection of …
Cleaver: Classification Of Everyday Activities Via Ensemble Recognizers, Samantha Hsu
Cleaver: Classification Of Everyday Activities Via Ensemble Recognizers, Samantha Hsu
Master's Theses
Physical activity can have immediate and long-term benefits on health and reduce the risk for chronic diseases. Valid measures of physical activity are needed in order to improve our understanding of the exact relationship between physical activity and health. Activity monitors have become a standard for measuring physical activity; accelerometers in particular are widely used in research and consumer products because they are objective, inexpensive, and practical. Previous studies have experimented with different monitor placements and classification methods. However, the majority of these methods were developed using data collected in controlled, laboratory-based settings, which is not reliably representative of real …
Revealing The Broad Line Region Of Ngc 1275: The Relationship To Jet Power, Brian Punsly, Paola Marziani, Vardha Nicola Bennert, Hiroshi Nagai, Mark A. Gurwell
Revealing The Broad Line Region Of Ngc 1275: The Relationship To Jet Power, Brian Punsly, Paola Marziani, Vardha Nicola Bennert, Hiroshi Nagai, Mark A. Gurwell
Physics
NGC 1275 is one of the most conspicuous active galactic nuclei (AGN) in the local universe. The radio jet currently emits a flux density of ~10 Jy at ~1 mm wavelengths, down from the historic high of ~65 Jy in 1980. Yet, the nature of the AGN in NGC 1275 is still controversial. It has been debated whether this is a broad emission line (BEL) Seyfert galaxy, an obscured Seyfert galaxy, a narrow line radio galaxy, or a BL Lac object. We clearly demonstrate a persistent Hβ BEL over the last 35 yr with a full width at half …
Validation Of The Nonhydrostatic General Curvilinear Coastal Ocean Model (Gccom) For Stratified Flows, Mariangel Garcia, Paul Choboter, Ryan K. Walter, Jose E. Castillo
Validation Of The Nonhydrostatic General Curvilinear Coastal Ocean Model (Gccom) For Stratified Flows, Mariangel Garcia, Paul Choboter, Ryan K. Walter, Jose E. Castillo
Physics
While global- and basin-scale processes can be captured quite well with computationally-inexpensive hydrostatic models, smaller-scale features such as shoaling nonlinear internal waves and bores, coastal fronts, and other convective processes require the use of a nonhydrostatic model to accurately capture dynamics. Here the nonhydrostatic capabilities of the General Curvilinear Coastal Ocean Model (GCCOM) in a stratified environment are introduced. GCCOM is a three-dimensional, nonhydrostatic Large Eddy Simulation (LES), rigid lid model that has the ability to run in a fully three-dimensional general curvilinear coordinate system. This model was previously validated for unstratified flows with curvilinear coordinates. Here, recent advances of …
Studying The [O Iii]Λ5007 Å Emission-Line Width In A Sample Of ∼ 80 Local Active Galaxies: A Surrogate For Σ⋆?, Vardha Nicola Bennert, Donald Loveland, Edward Donohue, Maren Cosens, Sean Lewis, S. Komossa, Tommaso Treu, Matthew A. Malkan, Nathan Milgram, Kelsi Flatland, Matthew W. Auger, Daesong Park, Mariana S. Lazarova
Studying The [O Iii]Λ5007 Å Emission-Line Width In A Sample Of ∼ 80 Local Active Galaxies: A Surrogate For Σ⋆?, Vardha Nicola Bennert, Donald Loveland, Edward Donohue, Maren Cosens, Sean Lewis, S. Komossa, Tommaso Treu, Matthew A. Malkan, Nathan Milgram, Kelsi Flatland, Matthew W. Auger, Daesong Park, Mariana S. Lazarova
Physics
For a sample of ∼ 80 local (0.02 ≤ z" role="presentation">z ≤ 0.1) Seyfert-1 galaxies with high-quality long-slit Keck spectra and spatially resolved stellar-velocity dispersion (σ⋆) measurements, we study the profile of the [O iii]λ5007 Å emission line to test the validity of using its width as a surrogate for σ⋆. Such an approach has often been used in the literature, since it is difficult to measure σ⋆ for type-1 active galactic nuclei (AGNs) due to the AGN continuum outshining the stellar-absorption lines. Fitting the [O iii] line with a single Gaussian or Gauss–Hermite …
Studying The Potential Of The [Oii] Emission Line As A Surrogate For Stellar Velocity Dispersion In Active Galactic Nuclei, Edward F. Donohue
Studying The Potential Of The [Oii] Emission Line As A Surrogate For Stellar Velocity Dispersion In Active Galactic Nuclei, Edward F. Donohue
Physics
We study the emission profiles of 80 active galaxies to find a surrogate for stellar velocity dispersion. We focus on the width of the emission line of once ionized oxygen, [OII], and compare our results to previous work that used [OIII]. In previous research, [OIII] was found to be a good candidate for a surrogate for stellar velocity dispersion, but analysis of the line was complicated by the presence of wings caused by gas infall and outflow in the region. Emission lines with lower ionization levels, like [OII], are known to have less artificial line-broadening from wings. The study of …
Mountaintop Neutrino Detection: A Nu(Tau) Concept, Caroline E. Paciaroni
Mountaintop Neutrino Detection: A Nu(Tau) Concept, Caroline E. Paciaroni
Physics
High-energy neutrinos traveling from the distant universe produce detectable signals at radio frequencies after interacting with the earth or its atmosphere. This is the principle behind a new experiment, the BEamforming Elevated Array for COsmogenic Neutrinos, or BEACON. BEACON will be a high altitude array of antennas that is sensitive to up-going tau neutrinos ($\nu_{\tau}$). These elementary particles serve as sources of information about the extraordinarily high energy events in the universe that create them, and also the laws of particle physics that govern their behavior. This report details the construction of a transient detector used to characterize site locations …
Assessment Of Surface Wind Datasets For Estimating Offshore Wind Energy Along The Central California Coast, Yi-Hui Wang, Ryan K. Walter, Crow White, Hayley Farr, Benjamin I. Ruttenberg
Assessment Of Surface Wind Datasets For Estimating Offshore Wind Energy Along The Central California Coast, Yi-Hui Wang, Ryan K. Walter, Crow White, Hayley Farr, Benjamin I. Ruttenberg
Physics
In the United States, Central California has gained significant interest in offshore wind energy due to its strong winds and proximity to existing grid connections. This study provides a comprehensive evaluation of near-surface wind datasets in this region, including satellite-based observations (QuikSCAT, ASCAT, and CCMP V2.0), reanalysis (NARR and MERRA), and regional atmospheric models (WRF and WIND Toolkit). This work highlights spatiotemporal variations in the performance of the respective datasets in relation to in-situ buoy measurements using error metrics over both seasonal and diurnal time scales. The two scatterometers(QuikSCAT and ASCAT) showed the best overall performance, albeit with significantly …
Adapting Cell-Free Protein Synthesis As A Platform Technology For Education, Grace W. Chu, Max Z. Levine, Nicole E. Gregorio, Javin P. Oza
Adapting Cell-Free Protein Synthesis As A Platform Technology For Education, Grace W. Chu, Max Z. Levine, Nicole E. Gregorio, Javin P. Oza
STAR Program Research Presentations
Cell-free protein synthesis (CFPS) has emerged as an enabling biotechnology for research and biomanufacturing as it allows for the production of protein without the need for a living cell. Applications of CFPS include the construction of libraries for functional genomics and structural biology, the production of personalized medicine, and the expression of virus-like particles. The absence of a cell wall provides an open platform for direct manipulation of the reaction conditions and biological machinery. This project focuses on adapting the CFPS biotechnology to the classroom, making a hands-on bioengineering approach to learning protein synthesis accessible to students grades K-16 through …
The Lick Agn Monitoring Project 2011: Dynamical Modeling Of The Broad-Line Region, Peter R. Williams, Anna Pancoast, Tommaso Treu, Brendon J. Brewer, Vardha N. Bennert, Jong-Hak Woo
The Lick Agn Monitoring Project 2011: Dynamical Modeling Of The Broad-Line Region, Peter R. Williams, Anna Pancoast, Tommaso Treu, Brendon J. Brewer, Vardha N. Bennert, Jong-Hak Woo
Physics
We present models of the Hβ-emitting broad-line region (BLR) in seven Seyfert 1 galaxies from the Lick AGN Monitoring Project 2011 sample, drawing inferences on the BLR structure and dynamics as well as the mass of the central supermassive black hole. We find that the BLR is generally a thick disk, viewed close to face-on, with preferential emission back toward the ionizing source. The dynamics in our sample range from near-circular elliptical orbits to inflowing or outflowing trajectories. We measure black hole masses of for PG 1310−108, for Mrk 50, for Mrk 141, for Mrk 279, for Mrk …
Reversible Motion In A Contact Line, Audrey Profeta, Esmeralda Orozco, Juan A. Ortiz Salazar, Dani Medina, Nathan C. Keim
Reversible Motion In A Contact Line, Audrey Profeta, Esmeralda Orozco, Juan A. Ortiz Salazar, Dani Medina, Nathan C. Keim
STAR Program Research Presentations
When a body of liquid sits on a surface, an irregular border between the wet and dry regions of the surface exists, called the contact line. Driving this contact line back and forth repeatedly can change its shape.We use a syringe pump to cyclically infuse and withdraw a predetermined volume of water, and take photos of the contact line after each cycle. Comparing these images to each other determines if the contact line is returning to the same shape. We find that below a critical value of infused volume, after many cycles the contact line reaches a steady state in …
Light Curves In X-Rays And Gamma-Rays, Daniel H. Sellers
Light Curves In X-Rays And Gamma-Rays, Daniel H. Sellers
STAR Program Research Presentations
Gamma-ray Bursts are the most luminous and energetic events in the universe. Understanding the intrinsic properties of GRBs allows for their use as standard candles (objects of known distance and luminosity) and for the study of extremely distant regions of space.
In this study we use the piecewise Willingale model to fit the X-ray flux vs. time curves (light curves) of 235 GRBs with detectable 'plateau' phase and known redshift using data from the swift repository. This sample is analyzed for consistency with a relation between the temporal decay and spectral indexes predicted by the Fireball model of GRB Emission. …
Hydrodynamics In A Shallow Seasonally Low-Inflow Estuary Following Eelgrass Collapse, Ryan K. Walter, Edwin J. Rainville, Jennifer K. O'Leary
Hydrodynamics In A Shallow Seasonally Low-Inflow Estuary Following Eelgrass Collapse, Ryan K. Walter, Edwin J. Rainville, Jennifer K. O'Leary
Physics
Hydrodynamics play a critical role in mediating biological and ecological processes and can have major impacts on the distribution of habitat-forming species. Low-inflow estuaries are widespread in arid regions and during the dry season in Mediterranean climates. There is a growing need to evaluate dynamics and exchange processes in these systems and the resultant ecological linkages. We investigate the role that hydrodynamics play in shaping environmental gradients in a short and seasonally low-inflow estuary located along the central California coast. Since 2007, eelgrass meadows in Morro Bay have declined by more than 90%, representing the collapse of the major …
Scale-Invariant Geometric Data Analysis (Sigda), Marina Girgis, Max Robinson
Scale-Invariant Geometric Data Analysis (Sigda), Marina Girgis, Max Robinson
STAR Program Research Presentations
The purpose of this research is to introduce a new data analysis method called Scale Invariant Geometric Data Analysis (SIGDA). SIGDA has been shown to be more informative than more common data analysis methods, such as Principal Component Analysis (PCA). SIGDA is used to visualize complex data sets in a way that accurately preserves data patterns and behavior. SIGDA is designed to preserve relative ratios in a numerical matrix, and the number of entries has to be more than the total number of rows and columns. Our research involved providing a simple explanation of SIGDA's mathematical process—simple enough for the …