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Full-Text Articles in Physical Sciences and Mathematics

Carbon And Nitrogen Isotopic Investigations Of The Late Pleistocene Paleoecology Of Eastern Beringia, Yukon Territory, Using Soils, Plants And Rodent Bones, Farnoush Tahmasebi Sep 2015

Carbon And Nitrogen Isotopic Investigations Of The Late Pleistocene Paleoecology Of Eastern Beringia, Yukon Territory, Using Soils, Plants And Rodent Bones, Farnoush Tahmasebi

Electronic Thesis and Dissertation Repository

During the late Pleistocene (130-12 ka), Beringia, a largely ice-free land located in the Mammoth Steppe Ecosystem, was home to a large grazing community of megafauna. Many of these animals, including the woolly mammoth, became extinct at the terminal Pleistocene. Assessment of the paleoenvironment, nutrient cycling and foraging ecology in Beringia should help to understand the role of climate change in their extirpation. Such information might also help to explain the curiously higher δ15N of woolly mammoths relative to other coeval herbivores.

This study assessed eastern Beringian paleoecology using stable nitrogen (N) and carbon (C) isotopic analyses of …


Optimization Of Cu2znsns4 Nanocrystal Composition And Thin Film Fabrication For Photovoltaic Applications, Saghar Khoshmashrab Sep 2015

Optimization Of Cu2znsns4 Nanocrystal Composition And Thin Film Fabrication For Photovoltaic Applications, Saghar Khoshmashrab

Electronic Thesis and Dissertation Repository

In this work Cu2ZnSnS4 (CZTS) nanocrystals (NCs) were prepared via a solvothermal, one-pot method. Given that the composition affects the electronic properties of this p-type semiconductor, comparative compositional analysis was done from various designed and synthesized analogues. EXAFS studies indicated that the stoichiometries with lower Cu-contents (Cu Sn+Zn

The effects of Cu were further studied, using Cu-poor and Cu-stoichiometric NCs.This time the precursor content of Zn was also increased to yield samples with Zn rich compositions. NCs in which the Cu concentration was below stoichiometric (Cu1.8Zn1.1Sn1.0S4.8) were more crystalline and yielded a higher photoresponse (~53 μA/cm2).

The compositionally optimized CZTS …


Transmission Of Light In Nano-Hole Metamaterial, Shankaranandh Balakrishnan . Sep 2015

Transmission Of Light In Nano-Hole Metamaterial, Shankaranandh Balakrishnan .

Electronic Thesis and Dissertation Repository

The interaction of light with metallic nano-hole array structures enable excitation of surface plasmon polaritons at any angle of incidence. Nano-hole array structure can transmit more radiation than incident light due to the presence of surface plasmon polaritons. This phenomenon has opened up possibilities for a wide range of applications such as Surface Plasmon Resonance sensing and Surface Enhanced Raman spectroscopy. In this thesis, quantum scattering theory and quantum density matrix method are employed to assess optical transmission of metallic nano-hole array structures. The scattering cross section spectrum is calculated for nano-hole array structures with different nano-hole radii and periodicities …


Computing In Algebraic Closures Of Finite Fields, Javad Doliskani Sep 2015

Computing In Algebraic Closures Of Finite Fields, Javad Doliskani

Electronic Thesis and Dissertation Repository

We present algorithms to construct and perform computations in algebraic closures of finite fields. Inspired by algorithms for constructing irreducible polynomials, our approach for constructing closures consists of two phases; First, extension towers of prime power degree are built, and then they are glued together using composita techniques. To be able to move elements around in the closure we give efficient algorithms for computing isomorphisms and embeddings. In most cases, our algorithms which are based on polynomial arithmetic, rather than linear algebra, have quasi-linear complexity.


Charging Level And Deposition Of Droplets In Electrostatic Painting, Husam Osman Sep 2015

Charging Level And Deposition Of Droplets In Electrostatic Painting, Husam Osman

Electronic Thesis and Dissertation Repository

The process of electrostatic painting has become a very important method of coating in a wide range of industrial applications including those used in the automobile industry. The general principle of spray coating is to deposit liquid droplets or solid powder particles on coated targets having various shapes. The electrostatic coating process consists of three main stages: droplet formation and charging, transportation and deposition. The complication of this process is caused by various factors, such as the physical properties of the material to be used, the appropriate electrical and mechanical conditions and the target surface to be coated, which affects …


Probabilistic Reasoning In Cosmology, Yann Benétreau-Dupin Sep 2015

Probabilistic Reasoning In Cosmology, Yann Benétreau-Dupin

Electronic Thesis and Dissertation Repository

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology.

The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments …


Dynamic Studies Of Guest Molecules In Metal-Organic Frameworks Using Solid-State Nmr, Yuanjun Lu Sep 2015

Dynamic Studies Of Guest Molecules In Metal-Organic Frameworks Using Solid-State Nmr, Yuanjun Lu

Electronic Thesis and Dissertation Repository

Metal-organic frameworks (MOFs) are a new class of porous materials that possess large three-dimensional voids in their structures. In this work, Solid-state NMR (SSNMR) is used to examine the dynamics of guest molecules at various temperatures in MOFs that possess different types of channels. Chapter 2 introduces the 13CO2 adsorption behavior in α-Mg formate studied by 13C SSNMR in conjunction with molecular dynamic simulation. 1H-13C cross polarization technique has successfully determined the adsorption sites of CO2 in this type of MOF to be hydrogen atoms. The dynamic analysis detects that at low temperature, …


Implementation Techniques For The Truncated Fourier Transform, Li Zhang Sep 2015

Implementation Techniques For The Truncated Fourier Transform, Li Zhang

Electronic Thesis and Dissertation Repository

We study various algorithms for the Truncated Fourier Transform (TFT) which is a variation of the Discrete Fourier Transform (DFT) that allows one to work with an input vector of arbitrary size without zero padding. After a review of the original algorithms for the forward and inverse TFT introduced by J. van der Hoeven, we consider the variation of D. Harvey as well as that of J. Johnson and L.C. Meng. Both variations are based on Cooley-Tukey like formulas. The former is called strict general radix as it strictly follows the specifications proposed by J. van der Hoeven, while the …


Secondary Electrohydrodynamic Flow Generated By Corona And Dielectric Barrier Discharges, Mohammadreza Ghazanchaei Sep 2015

Secondary Electrohydrodynamic Flow Generated By Corona And Dielectric Barrier Discharges, Mohammadreza Ghazanchaei

Electronic Thesis and Dissertation Repository

One of the main goals of applied electrostatics engineering is to discover new perspectives in a wide range of research areas. Controlling the fluid media through electrostatic forces has brought new important scientific and industrial applications. Electric field induced flows, or electrohydrodynamics (EHD), have shown promise in the field of fluid dynamics. Although numerous EHD applications have been explored and extensively studied so far, most of the works are either experimental studies, which are not capable to explain the in depth physics of the phenomena, or detailed analytical studies, which are not time effective. The focus of this study is …


Reactions Between Zinc Metallothionein And Carbonic Anhydrase, Tyler B. J. Pinter Sep 2015

Reactions Between Zinc Metallothionein And Carbonic Anhydrase, Tyler B. J. Pinter

Electronic Thesis and Dissertation Repository

More than 25% of proteins require metal ion cofactors for structure or function. The interactions between metalloproteins have largely been overlooked, though these interactions ultimately govern metal localization and control metal ion homeostasis. Mammalian metallothionein (MT) is a small, cysteine-rich metalloprotein that binds numerous metal ions per protein strand. Up to seven divalent metals, such as zinc or cadmium, are wrapped into a clustered two-domain structure. This unusually high metal content places MT as an attractive candidate for studying interactions with other metal-binding proteins. This present study investigates the metal transfer reactions between MTs and other metalloproteins, using carbonic anhydrase …


Clustering-Based Personalization, Seyed Nima Mirbakhsh Sep 2015

Clustering-Based Personalization, Seyed Nima Mirbakhsh

Electronic Thesis and Dissertation Repository

Recommendation systems have been the most emerging technology in the last decade as one of the key parts in e-commerce ecosystem. Businesses offer a wide variety of items and contents through different channels such as Internet, Smart TVs, Digital Screens, etc. The number of these items sometimes goes over millions for some businesses. Therefore, users can have trouble finding the products that they are looking for. Recommendation systems address this problem by providing powerful methods which enable users to filter through large information and product space based on their preferences. Moreover, users have different preferences. Thus, businesses can employ recommendation …


A Study Of Pseudo-Periodic And Pseudo-Bordered Words For Functions Beyond Identity And Involution, Manasi Kulkarni Aug 2015

A Study Of Pseudo-Periodic And Pseudo-Bordered Words For Functions Beyond Identity And Involution, Manasi Kulkarni

Electronic Thesis and Dissertation Repository

Periodicity, primitivity and borderedness are some of the fundamental notions in combinatorics on words. Motivated by the Watson-Crick complementarity of DNA strands wherein a word (strand) over the DNA alphabet \{A, G, C, T\} and its Watson-Crick complement are informationally ``identical", these notions have been extended to consider pseudo-periodicity and pseudo-borderedness obtained by replacing the ``identity" function with ``pseudo-identity" functions (antimorphic involution in case of Watson-Crick complementarity). For a given alphabet $\Sigma$, an antimorphic involution $\theta$ is an antimorphism, i.e., $\theta(uv)=\theta(v) \theta(u)$ for all $u,v \in \Sigma^{*}$ and an involution, i.e., $\theta(\theta(u))=u$ for all $u \in \Sigma^{*}$. In this thesis, …


Functional –Esime3 Containing Reagents: From Organo-Polychalcogenolates To Nhc Ligated M-E-Sime3, Mahmood Azizpoor Fard Aug 2015

Functional –Esime3 Containing Reagents: From Organo-Polychalcogenolates To Nhc Ligated M-E-Sime3, Mahmood Azizpoor Fard

Electronic Thesis and Dissertation Repository

The reaction of M[ESiMe3] (M = Li/Na; E = S, Se) with polyorganobromides, has afforded polychalcogenotrimethylsilane complexes Ar(CH2ESiMe3)n: 1,4-(Me3SiECH2)2(C6Me4) (E = S, 1; E = Se, 2), 1,3,5-(Me3SiECH2)3(C6Me3) (E = S, 3; E = Se, 4) and 1,2,4,5-(Me3SiECH2)4(C6H2)(E = S, 5; E = Se, 6). The powerful potential of these complexes as precursor to combine with …


Generalized Inclusion-Exclusion, Mike W. Ghesquiere Aug 2015

Generalized Inclusion-Exclusion, Mike W. Ghesquiere

Electronic Thesis and Dissertation Repository

Sets are a foundational structure within mathematics and are commonly used as a building block for more complex structures. Just above this we have functions and sequences before an explosion of increasingly specialized structures. We propose a re-hanging of the tree with hybrid sets (that is, signed multi-sets), as well hybrid functions (functions with hybrid set domains) joining the ranks of sequences and functions. More than just an aesthetic change, this allows symbolic manipulation of structures in ways that might otherwise be cumbersome or inefficient. In particular, we will consider simplifying the product and sum of two piecewise functions or …


On The Estimation Of Intracluster Correlation For Time-To-Event Outcomes In Cluster Randomized Trials, Sumeet Kalia Aug 2015

On The Estimation Of Intracluster Correlation For Time-To-Event Outcomes In Cluster Randomized Trials, Sumeet Kalia

Electronic Thesis and Dissertation Repository

Cluster randomized trials (CRTs) involve the random assignment of intact social units rather than independent subjects to intervention groups. Time-to-event outcomes often are endpoints in CRTs where the intracluster correlation coefficient (ICC) serves as a descriptive parameter to assess the similarity among outcomes in a cluster. However, estimating the ICC in CRTs with time-to-event outcomes is a challenge due to the presence of censored observations. The ICC is estimated for two CRTs using the censoring indicators and observed outcomes.

A simulation study explores the effect of administrative censoring on estimating the ICC. Results show that the ICC estimators derived from …


Morphology And Morphometry Of Double Layered Ejecta Craters On Mars, Ryan Schwegman Aug 2015

Morphology And Morphometry Of Double Layered Ejecta Craters On Mars, Ryan Schwegman

Electronic Thesis and Dissertation Repository

Double layered ejecta (DLE) craters display two distinct layers of ejecta that appear to have been emplaced as a mobile, ground-hugging flow. While volatile content within the target, atmosphere, or some combination of the two is generally considered a major variable enhancing the mobility of ejecta, the presence of unconsolidated surface materials may also have some effect. This statement is studied further here, aiming to determine whether bulk target lithology and/or attributes of the surface have any effect on morphometric properties between DLEs situated on sedimentary targets to those on volcanic ones. Results suggest that ejecta mobility (the distance ejecta …


Algorithms For Peptide Identification From Mixture Tandem Mass Spectra, Yi Liu Aug 2015

Algorithms For Peptide Identification From Mixture Tandem Mass Spectra, Yi Liu

Electronic Thesis and Dissertation Repository

The large amount of data collected in an mass spectrometry experiment requires effective computational approaches for the automated analysis of those data. Though extensive research has been conducted for such purpose by the proteomics community, there are still remaining challenges, among which, one particular challenge is that the identification rate of the MS/MS spectra collected is rather low. One significant reason that contributes to this situation is the frequently observed mixture spectra, which result from the concurrent fragmentation of multiple precursors in a single MS/MS spectrum. However, nearly all the mainstream computational methods still take the assumption that the acquired …


Investigating Potential Climatic Cycles In Glacially-Influenced Rhythmites Of The Upper Gowganda Formation Using Geochemical, Sedimentological And Spectral Analyses, Timothy S. Howe Aug 2015

Investigating Potential Climatic Cycles In Glacially-Influenced Rhythmites Of The Upper Gowganda Formation Using Geochemical, Sedimentological And Spectral Analyses, Timothy S. Howe

Electronic Thesis and Dissertation Repository

The upper Gowganda Formation of the Huronian Supergroup contains glacially-induced, varve-like rhythmites composed of turbiditic micro-laminae that potentially preserve a detailed record of climatic conditions during the Paleoproterozoic Era. A sedimentological analysis of upper Gowganda Formation deposits enabled identification of eight lithofacies comprising a glaciogenic depositional environment: 1) diamictite, 2) contorted argillite, 3) interlaminated siltstone and sandstone, 4) interbedded siltstone and claystone, 5) sandstone, 6) siltstone, 7) interbedded coarse-grained and fine-grained siltstone, and 8) wavy argillite. Major, trace, and rare earth element analyses indicate that the rhythmites have undergone limited recycling and chemical alteration. Whole-rock δ18O values are …


The Development Of Cyclic Rgd Peptides Stabilized Through 99mtc/Re(Co)3+, Aagam Patel Aug 2015

The Development Of Cyclic Rgd Peptides Stabilized Through 99mtc/Re(Co)3+, Aagam Patel

Electronic Thesis and Dissertation Repository

Protein secondary structure can be mimicked by incorporating structural constraints into peptides and this can be facilitated by metal coordination. The objective of this project is to establish a chelation system with a cancer targeting peptide sequence, where the coordination to a metal centre results in a cyclic metallopeptide. Cyclic RGD peptides are antagonists for αvβ3 and other integrins, which are present during tumour angiogenesis. Arg-Gly-Asp (RGD) sequence is employed in the peptide backbone, with an un-natural amino acid (3-Pal) and a chelating molecule (pyridyl-triazole, pyta) present on opposite ends of the peptide sequence to form a …


Dielectric Spectroscopy Of Polyvinyl Alcohol Hydrogels And Nanocomposites, Nuwansiri N.K. Getangama Aug 2015

Dielectric Spectroscopy Of Polyvinyl Alcohol Hydrogels And Nanocomposites, Nuwansiri N.K. Getangama

Electronic Thesis and Dissertation Repository

Gels based on polyvinyl alcohol (PVA) can be formed by repeated freezing and thawing of a solution of the polymer. PVA cryogels have applications as biomaterials, including artificial tissue and drug delivery systems. The mechanical and electrical properties of polymeric materials can be changed significantly by adding a small amount of nanometer-sized particles. In this work, the dielectric properties of PVA solutions and gels were studied in the frequency range from 10 micro Hz to 1 MHz as a function of temperature, using a dielectric spectrometer. Comparison of the dielectric constant of a PVA solution to that of water indicates …


Design And Fabrication Of Integrated Plasmonic Platforms For Ultra-Sensitive Molecular And Biomolecular Detections, Mohammadali Tabatabaei Aug 2015

Design And Fabrication Of Integrated Plasmonic Platforms For Ultra-Sensitive Molecular And Biomolecular Detections, Mohammadali Tabatabaei

Electronic Thesis and Dissertation Repository

One of the major challenges in analytical and biological sciences is to develop a device to obtain unambiguous chemical and structural properties of a material or a probe biomolecule with high reproducibility and ultra-high sensitivity. Moreover, in addition to such a high sensitivity, other cases such as minimum intrusiveness, small amounts of analyte, and short acquisition time and high reproducibility are key parameters that can be valued in any analytical measurements. Among the promising methods to achieve such endeavor, plasmon-mediated surface-enhanced spectroscopic techniques, such as surface-enhanced Raman spectroscopy (SERS), are considered as suitable options. Such techniques take advantage of the …


X-Ray Absorption Fine Structure Studies Of Calcium Silicate Hydrate Biomaterials In Drug Delivery, Xiaoxuan Guo Aug 2015

X-Ray Absorption Fine Structure Studies Of Calcium Silicate Hydrate Biomaterials In Drug Delivery, Xiaoxuan Guo

Electronic Thesis and Dissertation Repository

Calcium silicate hydrate (CSH), a new type of bioceramics, has gained significant attention in hard tissue restoration because of their impressive role in the stimulation of osteoblast proliferation and differentiation in vitro. The further development of mesoporous bioceramics opens up new opportunities for drug delivery in hard tissue therapies. In this thesis, interaction mechanisms of drug molecules with CSH of different morphologies and CSH/polymer composites, imaging of drug distributions in CSH carriers in nanoscale, and the biomineralization mechanisms of CSH in vitro during drug release are extensively investigated using X-ray absorption near edge structure (XANES) and scanning transmission X-ray …


Completely Monotone And Bernstein Functions With Convexity Properties On Their Measures, Shen Shan Aug 2015

Completely Monotone And Bernstein Functions With Convexity Properties On Their Measures, Shen Shan

Electronic Thesis and Dissertation Repository

The concepts of completely monotone and Bernstein functions have been introduced near one hundred years ago. They find wide applications in areas ranging from stochastic L\'{e}vy processes and complex analysis to monotone operator theory. They have well-known Bernstein and L\'{e}vy-Khintchine integral representations through which there are one-to-one correspondences between them and Radon measures on $[0,\infty)$ or $(0,\infty)$, respectively. In this thesis, we investigate subclasses of completely monotone and Bernstein functions with various convexity properties on their measures. These subclasses have intriguing applications in probability theories and convex analysis.

The convexity properties we investigate include convexity, harmonic convexity and $\beta$-convexity of …


Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li Aug 2015

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

Electronic Thesis and Dissertation Repository

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used …


Characterization Of Cd93 Diffusion In Human Monocytes And Chinese Hamster Ovary Cells., Maria Goiko Aug 2015

Characterization Of Cd93 Diffusion In Human Monocytes And Chinese Hamster Ovary Cells., Maria Goiko

Electronic Thesis and Dissertation Repository

The diffusion of CD93, a putative efferocytic receptor, was studied in the membrane of human monocytes and CHO cells using single particle tracking. We found that of CD93 molecules were confined in compartments consistent with actin corrals, while moved freely. Cage effect analysis showed short-lived caging of free CD93 and longer-lasting caging of confined CD93, with smaller corrals resulting in stronger caging. The motion of both free and confined CD93 was found to be consistent with a subdiffusive continuous time random walk, suggesting that CD93 diffusion is affected by several processes. We also sought to develop a total internal reflection …


Study Of The Secondary Metabolites Of Black Aspergilli From Canadian Vineyards, Tianyu Qi Aug 2015

Study Of The Secondary Metabolites Of Black Aspergilli From Canadian Vineyards, Tianyu Qi

Electronic Thesis and Dissertation Repository

Ochratoxin A (OTA) and fumonisin are mycotoxins produced by black Aspergilli that contaminate wine in many countries around the world. Both OTA and fumonisins are possible carcinogens to humans. There is limited data about the occurrence of OTA and fumonisins in Canadian vineyards. Therefore, a survey of the black Aspergilli from 2012-2014 has been conducted. In the mycotoxin study, high performance liquid chromatography-mass spectrometry was used to screen and quantify OTA and fumonisins from both black Aspergilli isolated on artificial media and grape samples. OTA was only detected from one fungal isolate and not on any grapes. Fumonisin B2 …


In Situ High-Pressure Study Of Metal-Organic Frameworks And Their Performance For Co2 Storage Probed By Vibrational Spectroscopy, Yue Hu Aug 2015

In Situ High-Pressure Study Of Metal-Organic Frameworks And Their Performance For Co2 Storage Probed By Vibrational Spectroscopy, Yue Hu

Electronic Thesis and Dissertation Repository

Metal-organic frameworks (MOFs) are an important class of porous materials, owing to their potential applications in a variety of areas, including gas storage, molecular separations, catalysis, sensors and so on. Most importantly, their extraordinary surface areas, tunable pore properties and potential for industrial scale production have made MOFs a promising material for clean energy applications, such as CO2 storage. The chemical and mechanical stabilities of MOFs play a crucial role in their CO2 storage performance, which require extreme loading pressures that are far beyond ambient pressure at times. Application of high external pressure (e.g., in gigapascal range) on …


On The Dual Risk Models, Chen Yang Aug 2015

On The Dual Risk Models, Chen Yang

Electronic Thesis and Dissertation Repository

Abstract This thesis focuses on developing and computing ruin-related quantities that are potentially measurements for the dual risk models which was proposed to describe the annuity-type businesses from the perspective of the collective risk theory in 1950’s. In recent years, the dual risk models are revisited by many researchers to quantify the risk of the similar businesses as the annuity-type businesses. The major extensions included in this thesis consist of two aspects: the first is to search for new ruin-related quantities that are potentially indices of the risk for well-established dual models; the other aspect is to generalize the settings …


High Resolution Stratigraphy And Paleoenvironmental Reconstruction Of The Upper Devonian Kettle Point Formation, Southwestern Ontario, Canada, Nikole E. Bingham-Koslowski Aug 2015

High Resolution Stratigraphy And Paleoenvironmental Reconstruction Of The Upper Devonian Kettle Point Formation, Southwestern Ontario, Canada, Nikole E. Bingham-Koslowski

Electronic Thesis and Dissertation Repository

The Upper Devonian Kettle Point Formation of southwestern Ontario consists of interbedded organic-rich black shales and organic-poor greyish green mudstones and red beds, the distribution of which were controlled by water depth, primary productivity, paleoclimate, and tectonism associated with the concurrent Acadian orogeny. Black shales were deposited under anoxic conditions and represent the background deposition. Less abundant organic-poor lithologies were formed under dysoxic to oxic conditions caused by a drop in relative sea level (either eustatic or related to subsidence or uplift). Sulphur isotope data shows a largely consistent background value for the black shales around -20‰ δ34S, …


Generating Invalid Input Strings For Software Testing, Benjamin D. Revington Aug 2015

Generating Invalid Input Strings For Software Testing, Benjamin D. Revington

Electronic Thesis and Dissertation Repository

Grammar-based testing has interested the academic community for decades, but little work has been done with regards to testing with invalid input strings. For our research, we generated LR parse tables from grammars. We then generated valid and invalid strings based on coverage of these tables. We evaluated the effectiveness of these strings in terms of code coverage and fault detection by inputting them to subject programs which accept input based on the grammars. For a baseline, we then compared the effectiveness of these strings to a more general approach where the tokens making up each string are chosen randomly. …