Physical Sciences and Mathematics Commons^™

Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, Austin J. Phillips

Honors Theses

The 3n + l Conjecture states that when the Collatz function is applied repeatedly to an initial value, the sequence of values generated always converges to 1, regardless of the starting value. This paper strengthens the claim that all such sequences are convergent by showing that certain types of nonconvergent sequences cannot exist. Specifically, no sequence with parity-periodic values can exist This eliminates all possible nontrivially periodic sequences and all divergent sequences with periodic parity. Therefore, if a counterexample to the conjecture exists, It must be a divergent sequence whose values display no parity periodicity.

A Web Of Influence: How The Msp Program Has Shaped The Thoughts Of Three Instructors, J. Reyes

Journal of Mathematics and Science: Collaborative Explorations

No abstract provided.

A Sketch-Based Language For Representing Uncertainty In The Locations Of Origin Of Herbarium Specimens, Barry J. Kronenfeld, Andrew Weeks

Faculty Research and Creative Activity

Uncertainty fields have been suggested as an appropriate model for retrospective georeferencing of herbarium specimens. Previous work has focused only on automated data capture methods, but techniques for manual data specification may be able to harness human spatial cognition skills to quickly interpret complex spatial propositions. This paper develops a formal modeling language by which location uncertainty fields can be derived from manually sketched features. The language consists of low-level specification of critical probability isolines from which a surface can be uniquely derived, and high-level specification of features and predicates from which low-level isolines can be derived. In a case …

A Sketch-Based Language For Representing Uncertainty In The Locations Of Origin Of Herbarium Specimens, Barry Kronenfeld, Andrew Weeks

Faculty Research and Creative Activity

Uncertainty fields have been suggested as an appropriate model for retrospective georeferencing of herbarium specimens. Previous work has focused only on automated data capture methods, but techniques for manual data specification may be able to harness human spatial cognition skills to quickly interpret complex spatial propositions. This paper develops a formal modeling language by which location uncertainty fields can be derived from manually sketched features. The language consists of low-level specification of critical probability isolines from which a surface can be uniquely derived, and high-level specification of features and predicates from which low-level isolines can be derived. In a case …

Cbtv: Visualising Case Bases For Similarity Measure Design And Selection, Brian Mac Namee, Sarah Jane Delany

Conference papers

In CBR the design and selection of similarity measures is paramount. Selection can benefit from the use of exploratory visualisation- based techniques in parallel with techniques such as cross-validation ac- curacy comparison. In this paper we present the Case Base Topology Viewer (CBTV) which allows the application of different similarity mea- sures to a case base to be visualised so that system designers can explore the case base and the associated decision boundary space. We show, using a range of datasets and similarity measure types, how the idiosyncrasies of particular similarity measures can be illustrated and compared in CBTV allowing …

Inside The Selection Box: Visualising Active Learning Selection Strategies, Brian Mac Namee, Rong Hu, Sarah Jane Delany

Conference papers

Visualisations can be used to provide developers with insights into the inner workings of interactive machine learning techniques. In active learning, an inherently interactive machine learning technique, the design of selection strategies is the key research question and this paper demonstrates how spring model based visualisations can be used to provide insight into the precise operation of various selection strategies. Using sample datasets, this paper provides detailed examples of the differences between a range of selection strategies.

Landscape Patterns Of Community Structure, Biomass And Net Primary Productivity Of Mangrove Forests In The Florida Coastal Everglades As A Function Of Resource, Regulators, Hydroperiod, And Hurricane Distrubance, Edward Castaneda

LSU Doctoral Dissertations

Spatial and temporal patterns of mangrove vegetation in the Florida Coastal Everglades (FCE) reflect a major interplay of resources, regulators and hydroperiod gradients. I investigated landscape patterns of community structure, biomass and NPP of mangroves along two FCE estuaries: Shark River and Taylor River. I also evaluated whether pulsing events such as Hurricane Wilma are significant to soil nutrient inventories and vertical accretion of mangroves in FCE. There was a higher forest structural complexity of mangroves in Shark River relative to Taylor River. The biomass root:shoot ratio was 17 times higher in Taylor River relative to Shark River, indicating that …

Palynological Analysis Of Tiger And Trinity Shoals, Louisiana Continental Shelf, Russell Ryan Crouch

LSU Master's Theses

Forty sediment samples taken from twenty-six vibracores collected from Holocene shoals (Tiger and Trinity) were processed for palynomorphs and analyzed to characterize the terrestrial and marine paleo-environments of southern Louisiana at the time of deposition of each shoal. Abundant and diverse pollen assemblages were recovered while marine microplankton were sparse (< 2% relative abundance). Pollen species were grouped by plants of similar environmental significances including arboreal, non-arboreal, aquatic, and shrub categories. Palynological signals were compared in detail between each core, as well as along strike and dip transects, to help determine whether or not these shoals were deposited coevally or in distinct depositional cycles. Evidence shows that Tiger and Trinity Shoals carry remarkably similar palynological profiles, indicating that sediments of these shoals areS from the same source, and that deposition extended over an interval of time such that climate change was not sufficient enough to alter the vegetation response (hence palynological signal). Pollen profiles show source sediments are predominantly from the lower Mississippi River drainage basin and exhibit species similar to those present in modern Louisiana coastal marshes and swamps (i.e., Taxodium distichum, Cyperaceae, Graminae, Chenopodiaceae, and Asteraceae), and coastal to upland hardwood forests of the Mississippi River alluvial valley (i.e., Pinus, Quercus, Carya, and Liquidambar styraciflua).

Decentralized Nearly Optimal Control Of A Class Of Interconnected Nonlinear Discrete-Time Systems By Using Online Hamilton-Bellman-Jacobi Formulation, S. Mehraeen, Sarangapani Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton Jacobi-Bellman (HJB) equation online and forward-in-time for the decentralized nearly optimal control of nonlinear interconnected discrete-time systems in affine form with unknown internal subsystem and interconnection dynamics. Only the state vector of the local subsystem is considered measurable. the decentralized optimal controller design for each subsystem consists of an action neural network (NN) that is aimed to provide a nearly optimal control signal, and a critic NN which approximates the cost function. the NN weights are tuned online for both the NNs. It is shown …

Optimal Control Of Affine Nonlinear Continuous-Time Systems Using An Online Hamilton-Jacobi-Isaacs Formulation, T. Dierks, Sarangapani Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

Solving the Hamilton-Jacobi-Isaacs (HJI) equation, commonly used in ℋ∞ optimal control, is often referred to as a two-player differential game where one player tries to minimize the cost function while the other tries to maximize it. in this paper, the HJI equation is formulated online and forward-in-time using a novel single online approximator (SOLA)-Based scheme to achieve optimal regulation and tracking control of affine nonlinear continuous-time systems. the SOLA-Based adaptive approach is designed to learn the infinite horizon HJI equation, the corresponding optimal control input, and the worst-case disturbance. a novel parameter tuning algorithm is derived which not only achieves …

Interference-Aware Multipath Routing And Link Rate Control In Multihop Wireless Networks, Maggie X. Cheng, Xuan Gong

Computer Science Faculty Research & Creative Works

In multihop wireless networks, end-to-end throughput is often hard to predict and is even harder to optimize due to the effect of interference. to date there is no precise result other than asymptotic bounds for this question: if there is no routing information given, what is the maximum throughput of a network using uncoordinated transmission such as IEEE 802.11 MAC? This paper attempts to address this question for a given network with specific traffic demand. in this paper we use a cross-layer design scheme to optimize network performance. the paper includes a basic linear programming model, from which the routing …

Cycle Life Prediction Of Battery-Supercapacitor Hybrids Using Artificial Neural Networks, Thomas Weigert, Q. Tian, K. Lian

Computer Science Faculty Research & Creative Works

The cycle life of batteries and battery-supercapacitor hybrid systems was predicted using artificial neural networks. The presented techniques are able to predict the cycle life of a device based on a short (around 4% of the average cycle life) initial segment of the discharge curve. the prediction showed good performance with a correlation coefficient above 0.95. We were able to improve the predication further by considering readily available measurements of the device and usage. ©The Electrochemical Society.

Integration Of Paleotempestology With Coastal Risk And Vulnerability Assessment: Case Studies From The Dominican Republic And Nicaragua, Devyani Kar

LSU Doctoral Dissertations

Hurricanes account for a significant portion of damages, injuries, and fatalities in the Caribbean. The Dominican Republic has had 3 major hurricane strikes in this century resulting in loss of lives for thousands of people and billions of US $ in economic loss. Major hurricanes had been relatively infrequent in north-eastern Nicaragua’s modern history until Hurricane Felix, a Category 5 storm, made landfall in the north-east in 2007. It caused 130 confirmed deaths and brought devastation to many villages. These events highlight a need for re-evaluation of hurricane risk based on a more comprehensive and long-term hurricane history. Using paleotempestological …

Using Inoceramid Bivalve Taphonomy As A Paleoenvironmental Indicator Across The Cenomanian/Turonian Horizon At The Pueblo, Colorado Gssp, Jacob Frederick Grosskopf

LSU Master's Theses

Recent paleoenvironmental and geochemical studies indicate that benthic conditions during Oceanic Anoxic Event II (OAE II) (93.5 Mya) in the Cretaceous Interior Seaway (CIS) were dysoxic rather than anoxic. In this thesis, dysoxic benthic conditions were tested for by observing patterns in taphonomic alteration of the calcite portions of inoceramid bivalve shells during and after OAE II. Inoceramid valves were extracted from beds that spanned OAE II at the Cenomanian/Turonian Global Boundary Stratotype Section and Point (GSSP) in Pueblo, Colorado: beds 62 (Hartland Shale), 72 (Bridge Creek Limestone), and 115 (Bridge Creek Limestone). Degree of alteration was tallied using categorical …

Delineation Of A Produced Water Plume In Pointe Coupee Parish, Louisiana, Matthew C. Smith

LSU Master's Theses

Three pits were excavated in the 1960’s at the Fordoche Oil Field in Lottie, Louisiana, as evaporation pits for oil well produced brines. The pits were closed and completed in the 1980’s. Previous studies indicate that produced water has leached into the subsurface within the area to the south and southeast of the pits. Ground penetrating radar (GPR) was utilized in an attempt to delineate the present location of the plume as well as test the feasibility of GPR within a clayey soil in south Louisiana. In addition to collection of GPR data, electrical conductivity logs and soil cores (including …

A Petrophysical Evaluation Of Factors That Control Cap Rock Seal Quality, Andrew Tyler Harrison

LSU Master's Theses

Textural and mineralogical variations within 33 shale samples were analyzed to provide a model for predication of hydrocarbon top-seal efficiency. Variation in mineral abundances in the subsurface influences petrophysical properties and other characteristics of hydrocarbon sealing sequences and reservoirs. In geophysical well logs, various proxies, such as gamma ray emission and neutron absorption, are used to assess changes in mineral composition. This study directly compares X-ray diffraction measurements of mineral percentages and geophysical responses from Middle Miocene cored intervals in the Santa Cruz Well; Mississippi Canyon block 519, Gulf of Mexico with those derived from well logging. Distinct textural differences …

Patterns Of Habitat Suitability And Abundance Trends Of Current And Candidate Coastal Fish Species Of Concern In Louisiana, Elin Rose Sandy

LSU Master's Theses

Louisiana’s estuaries and coastal waters play an important role in providing habitat for several estuarine-dependent species and also serve as a nursery for the juveniles of several other species. The current rate of land loss in Louisiana and the decline of estuarine-dependent species force us to improve our understanding of the recruitment of these species into Louisiana’s estuaries. Habitat suitabilities were developed for several fish species of concern (SOC) and other estuarine-dependent species across three environmental gradients, abundance patterns were developed for seasons, five-year intervals, and coastal study areas (CSAs). Chi-square analyses and ANOVAs were then used to test for …

Taphonomy And Sedimentology Of Two Miocene Vertebrate Fossil Sites On Fort Polk, Louisiana, Julie Lynn Hill

LSU Master's Theses

The discovery of a terrestrial mammalian fauna in the Miocene deposits on Fort Polk, Louisiana, fills a geographic gap in the Gulf Coast paleontological framework, but the provenance of the fossils, nature of the depositional environments, and relationships between the sites is still debated. This is especially true for the TVOR site cluster. TVOR SE has a mixture of marine and terrestrial vertebrates in association with a partly dissolved, in situ bed of articulated oyster shells, which stands in contrast to the fully terrestrial and freshwater assemblage at TVOR, and the indeterminate site TVOR S. Although limited outcrop may bias …

Estuarine Phytoplankton Response To Annual And Manipulated River Inputs, Jessica Czubakowski

LSU Master's Theses

River water entering estuaries affects the physical and chemical environment at irregular intervals creating a highly dynamic aquatic habitat. Phytoplankton are important primary producers in estuaries that respond quickly to their changing environment. Since 1991, Breton Sound estuary in southeast Louisiana has been directly influenced by Mississippi River water through the Caernarvon Freshwater Diversion structure. Over a 12 month period, the phytoplankton response was examined, in terms of biomass, abundance, community composition and potential phycotoxin production to seasonal changes in river input into the estuary. Within this 12 month period, a short pulse study was also carried out to examine …

Mahalanobis Taguchi System (Mts) As A Prognostics Tool For Rolling Element Bearing Failures, Ahmet Soylemezoglu, Sarangapani Jagannathan, Can Saygin

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, a novel Mahalanobis-Taguchi system (MTS)-Based fault detection, isolation, and prognostics scheme is presented. the proposed data-driven scheme utilizes the Mahalanobis distance (MD)-Based fault clustering and the progression of MD values over time. MD thresholds derived from the clustering analysis are used for fault detection and isolation. When a fault is detected, the prognostics scheme, which monitors the progression of the MD values, is initiated. Then, using a linear approximation, time to failure is estimated. the performance of the scheme has been validated via experiments performed on rolling element bearings inside the spindle headstock of a microcomputer numerical …

Studies Of Small Systems In Quantum Information, Sai Vinjanampathy

LSU Doctoral Dissertations

I study two topics in quantum information theory from the perspective of algebra and geometry. The first relates to exploring the geometry of unitary operators for small quantum systems, specifically three-level systems. Such an understanding of the space over which quantum systems evolve is central to understanding the detailed dynamics of quantum systems and to understand the correlation properties of subsystems that compose a given quantum system. The geometry of unitary operators also allows for the calculation of path-dependent phases called geometric phases. These geometric phases are central to understanding a variety of experiments. I present a general technique, called …

A Study Of The Interactions Of Lipid Bilayers And Dendrimers Using Small Angle X-Ray Scattering And Freeze Fracture Transmission Electron Microscopy, Derek R. Dorman

LSU Doctoral Dissertations

Lipids are fundamental to all life forms, a key component of cell walls, and essential to proper respiratory function. They are amphiphilic molecules and readily form bilayers. Dendrimers are designer molecules that can be tailored to provide a variety of endgroup moieties, sizes, and charges. The interaction of liposomes and dendrimers can provide information on how medicine interacts with cells and an array of unique structures can be imagined from their assembly into superstructures. Polypropylenimine tetraamine (DAB-Am) and 1-directional arborol dendrimers have been studied in different molar concentrations with 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayers. One-directional arborols are amphiphilic dendrimers with a hydrophilic …

Fabrication Of Receptor-Modified Microfluidic Surfaces For Applications In Glycoprotein Screening, Jennifer Macalindong De Guzman

LSU Doctoral Dissertations

Glycoproteins have long been identified to have a profound association with human pathological processes, and they are much sought after as potential biomarkers to aid in the early diagnosis and clinical prognosis of cancers and diseases. There is currently high demand for high-throughput and low–limit–of–detection techniques that can afford profiling of the glycoproteome. Micro-total analysis systems (µTAS) based on microfluidics have the potential to fulfill these requirements, but in order to reduce the complexity of the protein pool, the µTAS devices must contain a pre-isolation and enrichment component. The research project undertaken here involved derivatization of microfluidic …

Method Of Riemann Surfaces In Modelling Of Cavitating Flow, Anna Zemlyanova

LSU Doctoral Dissertations

This dissertation is concerned with the applications of the Riemann-Hilbert problem on a hyperelliptic Riemann surface to problems on supercavitating flows of a liquid around objects. For a two-dimensional steady irrotational flow of liquid it is possible to introduce a complex potential w(z) which allows to apply the powerful methods of complex analysis to the solution of fluid mechanics problems. In this work problems on supercavitating flows of a liquid around one or two wedges have been stated. The Tulin single-spiral-vortex model is employed as a cavity closure condition. The flow domain is transformed into an auxiliary domain with known …

Hamilton-Jacobi Theory For Optimal Control Problems On Stratified Domains, Richard Charles Barnard

LSU Doctoral Dissertations

This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used …

Design And Development Of Chiral And Achiral Molecularly Imprinted Stationary Phases, Jason Paul Lejeune

LSU Doctoral Dissertations

Although the cross-linker can comprise over 80% of the polymer composition, improving the nature of the cross-linker in molecularly imprinted polymers has not been studied extensively. The goal of this research is to develop novel cross-linking monomers to either use in the One MoNomer Molecularly Imprinted Polymer system (OMNiMIP) or use in conjunction with other commercially available cross-linkers and functional monomers. Chapter 2 contains research into the understanding of the performance of a new cross-linking monomer (N, O - bismethacryloyl ethanolamine, NOBE) discovered in the Spivak Research Group. The ability of this monomer to outperform traditional two monomer systems in …

Searches For Gravitational Waves From Known Pulsars With Science Run 5 Ligo Data, B. P. Abbott, R. Abbott, F. Acernese, R. Adhikari, P. Ajith, B. Allen, G. Allen, M. Alshourbagy, R. S. Amin, S. B. Anderson, W. G. Anderson, F. Antonucci, S. Aoudia, M. A. Arain, M. Araya, H. Armandula, P. Armor, K. G. Arun, Y. Aso, S. Aston, P. Astone, P. Aufmuth, C. Aulbert, S. Babak, P. Baker, G. Ballardin, S. Ballmer, C. Barker, D. Barker, F. Barone

Physics and Astronomy Faculty Publications and Presentations

We present a search for gravitational waves from 116 known millisecond and young pulsars using data from the fifth science run of the LIGO detectors. For this search, ephemerides overlapping the run period were obtained for all pulsars using radio and X-ray observations. We demonstrate an updated search method that allows for small uncertainties in the pulsar phase parameters to be included in the search. We report no signal detection from any of the targets and therefore interpret our results as upper limits on the gravitational wave signal strength. The most interesting limits are those for young pulsars. We present …

Search For Gravitational-Wave Bursts Associated With Gamma-Ray Bursts Using Data From Ligo Science Run 5 And Virgo Science Run 1, B. P. Abbott, R. Abbott, F. Acernese, R. Adhikari, P. Ajith, B. Allen, G. Allen, M. Alshourbagy, R. S. Amin, S. B. Anderson, W. G. Anderson, F. Antonucci, S. Aoudia, M. A. Arain, M. Araya, H. Armandula, P. Armor, K. G. Arun, Y. Aso, S. Aston, P. Astone, P. Aufmuth, C. Aulbert, S. Babak, P. Baker, G. Ballardin, S. Ballmer, C. Barker, D. Barker, F. Barone

Physics and Astronomy Faculty Publications and Presentations

We present the results of a search for gravitational-wave bursts (GWBs) associated with 137 gamma-ray bursts (GRBs) that were detected by satellite-based gamma-ray experiments during the fifth LIGO science run and first Virgo science run. The data used in this analysis were collected from 2005 November 4 to 2007 October 1, and most of the GRB triggers were from the Swift satellite. The search uses a coherent network analysis method that takes into account the different locations and orientations of the interferometers at the three LIGO-Virgo sites. We find no evidence for GWB signals associated with this sample of GRBs. …

Pursuing Geoengineering For Atmospheric Restoration, James Salzman, Robert B. Jackson

Faculty Scholarship

Geoengineering is fraught with problems, but research on three approaches could lead to the greatest climate benefits with the smallest chance of unintentional environmental harm. The authors propose a model for thinking about geoengineering based on the concept of restoration, suggesting the term “atmospheric restoration.” Under this model geoengineering efforts are prioritized based on three principles: to treat the cause of the disease itself, to reduce the chance of harm, and to prioritize activities with the greatest chance of public acceptance.

Based on these principles, the authors propose three forms of geoengineering that could provide the greatest climate benefits with …

Microfluidic Devices Interfaced To Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry For Proteomics, Jeonghoon Lee

LSU Doctoral Dissertations

Microfluidic interfaces were developed for off-line matrix-assisted laser desorption/ionization mass spectrometry (MALDI). Microfluidic interfaces allow samples to be manipulated on-chip and deposited onto a MALDI target plate for analysis. For this research, microfluidic culturing devices and automated digestion and deposition microfluidic chip platforms were developed for the identification of proteins. The microfluidic chip components were fabricated on a poly(methyl methacrylate), PMMA, wafer using the hot embossing method and a molding tool with structures prepared via micromilling. One of the most important components of the chip system was a trypsin microreactor. An open channel microreactor was constructed in a 100 µm …