In June 2015, Caitlyn Jenner created waves of excitement with her coming out announcement on the cover of Vanity Fair: “Call me Caitlyn.” From the perspective of critical trans politics, however, the heightened visibility of trans people in mainstream media does not call for unequivocal celebration. Though trans women of color, such as Laverne Cox and Janet Mock, are more visible in mainstream media than ever before, mainstream media still largely depicts trans people through white constructs of what it means to be trans, namely medicalized binary transitions. Many trans people who deviate from mainstream media’s depiction of trans people are creating their own media on YouTube to voice their lived experiences. I argue that while YouTube is a particularly accessible platform for trans people to challenge transnormativity, the reach of trans YouTubers’ messages are highly limited by the medium’s design and genre conventions.

Spectrofluorometric probe methods are developed and examined regarding their ability to model preferential solvation around probe molecules in binary solvents. The first method assumes that each fluorophore is solvated by only one type of solvent molecule and that each fluorophore contributes to the emission intensity. Expressions for this model are illustrated using fluorescence behavior of pyrene, benzo[e]pyrene, benzo[ghi]perylene, and coronene dissolved in binary n-heptane + 1,4-dioxane and n-heptane + tetrahydrofuran mixtures. The second method treats the solvational sphere as a binary solvent microsphere, with the fluorophore's energy in both the ground and the excited states mathematically expressed using the "nearly ideal binary solvent" (NIBS) model. Expressions derived from this model are illustrated using fluorescence behavior of 9,9'-bianthracene and 9,9*-bianthracene-10-carboxaldehyde in binary toluene + acetonitrile and dibutyl ether + acetonitrile.

"Experts in information theory have long been interested in the maximal size, A(n, d), of a binary error-correcting code of length n and minimum distance d, The problem of determining A(n, d) involves both the construction of good codes and the search for good upper bounds. For quite some time now, Delsarte's linear programming approach has been the dominant approach to obtaining the strongest general purpose upper bounds on the efficiency of error-correcting codes. From 1973 forward, the linear programming bound found many applications, but there were few significant theoretical advances until Schrijver proposed a new code upper bound via semidefinite programming in 2003. Using the Terwilliger algebra, a recently introduced extension of the Bose-Mesner algebra, Schrijver formulated a new SDP strengthening of the LP approach. In this project we look at the dual solutions of the semidefinite programming bound for binary error-correcting codes. We explore the combinatorial meaning of these variables for small n and d, such as n = 4 and d = 2. To obtain information like this, we wrote a computer program with both Matlab and CVX modules to get solution of our primal SDP formulation. Our program efficiently generates the primal solutions with corresponding constraints for any n and d. We also wrote a program in C++ to parse the output of the primal SDP problem, and another Matlab script to generate the dual SDP problem, which could be used in assigning combinatorial meaning to the values given in the dual optimal solution. Our code not only computes both the primal and dual optimal variable values, but allows the researcher to display them in meaningful ways and to explore their relationship and dependence on arameters. These values are expected to be useful for later study of the combinatorial meaning of such solutions."

The present research seeks to characterization of an additively manufactured and heat-treated Ti-xMn gradient alloy, a binary system that has largely been unexplored. In order to rapidly assess this binary system, compositionally graded Ti-xMn (0<x<15 wt%) specimens were fabricated using the LENS (Laser Engineered Net Shaping) and were subsequently heat-treated and characterized using a wide range of techniques. Microstructural changes with respect to the change in thermal treatments, hardness and chemical composition were observed and will be presented. These include assessments of both continuous cooling, leading to observations of both equilibrium and metastable phases, including the titanium martensites, and to direct aging studies looking for composition regimes that produce highly refined alpha precipitates – a subject of great interest given recent understandings of non-classical nucleation and growth mechanisms. The samples were characterized using SEM, EDS, TEM, and XRD and the properties probed using a Vickers Microhardness tester.

The purpose of this thesis is to explore methodology concerning Markov Chain Monte Carlo (MCMC), a powerful technique in the Bayesian framework, on binary variables. The primary application of interest in this thesis is applying this methodology to phase haplotypes, a type of categorical variable. Haplotypes are the combination of variants present in an individual’s genome. Phasing refers to estimating the true haplotype. By considering only biallelic and heterozygous variants, the haplotype can be expressed as a vector of binary variables. Accounting for differences in haplotypes is essential for the study of associations between genotype and disease. MCMC is an extremely popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. Techniques for sampling categorical variables in MCMC have been developed in a variety of disparate settings. Samplers include Gibbs, Metropolis-Hastings, and exact Hamiltonian based samplers. A review of these techniques is presented and their relevance to the genetic model discussed. An important consideration in using simulated MCMC draws for inference is that they have converged to the distribution of interest. Since the distribution is typically of a non-standard form, convergence cannot generally be proven and, instead, is assessed with convergence diagnostics. The convergence diagnostics developed so far focus on continuous variables and may be inappropriate for binary variables or categorical variables in general. Two convergence diagnostics are proposed that are tailor-made for categorical variables by modeling the data using categorical time series models. Performance of the convergence diagnostics is evaluated under various simulations. The methodology developed in the thesis is applied to estimate haplotypes. There are two main challenges involved in accounting for haplotype differences. One is estimating the true combination of genetic variants on a single chromosome, known as haplotype phasing. The other is the phenomenon of allele-specific expression (ASE) in which haplotypes can be expressed non-equally. No existing method addresses these two intrinsically linked challenges together. Rather, current strategies rely on known haplotypes or family trio data, i.e. having data on subject of interest and their parents. A novel method is presented, named IDP-ASE, which is capable of phasing haplotypes and quantifying ASE using only RNA-seq data. This model leverages the strengths of both Second Generation Sequencing (SGS) data and Third Generation Sequencing (TGS) data. The long read length of TGS data facilitates phasing, while the accuracy and depth of SGS data facilitates estimation of ASE. Moreover, IDP-ASE is capable of estimating ASE at both the gene and isoform level.

The class of groups generated by automata have been a source of many counterexamples in group theory. At the same time it is connected to other branches of mathematics, such as analysis, holomorphic dynamics, combinatorics, etc. A question that naturally arises is finding the ways to classify these groups. The task of a complete classification and understanding at the moment seems to be too ambitious, but it is reasonable to concentrate on some smaller subclasses of this class. One approach is to consider groups generated by small automata: the automata with k states over d-letter alphabet (so called, (k,d)-automata) with small values of k and d. Certain steps in this directions have been made already: All groups generated by (2,2)-automata have been classified, and groups generated by (3,2)-automata were studied. In this work we study the class of groups generated by (4,2)-automata. More specifically, we partition all such automata into equivalence classes up to symmetry and minimal symmetry (symmetric and minimally symmetric automata naturally generate isomorphic groups) and classify completely all finite groups generated by automata in this class. We also list all classes generating abelian groups. Another important result of the project is developing a database of (4,2)-automata and computational routines that represent a new effective tool for the search for (4,2)-automata generating groups with specific properties, which hopefully will lead to finding counterexamples of certain conjectures.

The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency.

The original intent of this pro ject was to perform real time digital communications between a personal computer (PC) as the transmitter and a digital signal processor (DSP) as the receiver using the audio band analog channel. Although transmitter and receiver were both designed with baseband binary Pulse Amplitude Modulation (PAM), a low data rate and a sampling rate of 8 kilohertz, it was not possible to achieve communication between the two with traditional synchronization algorithms because of large differences in sampling clock frequencies. This thesis explores the theory and results of implementing digital communications between systems with different sampling frequencies. The receiver structure has no a priori knowledge of the transmitter’s sampling rate, although it is assumed to be approximately equal to that of the receiver. Therefore, a receiver structure that can correct this clock frequency offset is developed. Similar sampling frequencies at the transmitter and receiver are assumed in most derivations in the literature. A search of the literature found no cases of a large difference in the sampling frequencies. In general, if the receiver knows the transmitter’s sampling rate, a resampling filter at the receiver converts the signal to one compatible with the transmitters sampling rate. However, here it is assumed that the receiver does not know the transmitter’s exact sampling frequency and must be estimated. The mathematical expressions for the signals in the system are derived. The sampling frequency offset introduces errors in the correct detection of the signal when it is done through traditional synchronization algorithms. Therefore, a receiver structure that corrects the sampling frequency offset based on the interpolation concept is proposed. This structure will be shown to work when the correct sampling frequency ratio is known. Later, an approach to estimate the sampling frequency ratio is explored. A feedback estimator structure is derived from the Maximum Likelihood optimum criteria. A feed forward estimator that assumes the clock frequency of the transmitter and uses a synchronization sequence is explored as well.

This thesis presents new methods for finding optimal and near-optimal constant weight binary codes with distance d and weight w such that d=2(w-1). These methods have led to the discovery of a number of new codes which are being submitted for publication. Improvements in methods for generating lexicographic codes are also discussed, with suggestions for further research in this area.

In the standard theory of pulsar spin-up, a neutron star (NS) in a binary system accretes matter from its companion star; this serves to transfer angular momentum to the NS, increasing the spin frequency of the pulsar. Measurement of the orbital parameters and system geometry, and in particular the final system masses, thus provide important constraints for theories regarding binary evolution. We present results from an investigation of three binary pulsar systems. PSR J1802-2124 is in an intermediate-mass pulsar binary system with a massive white dwarf companion in a compact orbit with a period of 16.8 hours. We have per-formed timing analysis on almost five years of data in order to determine the amount of Shapiro delay experienced by the incoming pulsar signal as it traverses the potential well of the companion star on its way to Earth. We find the pulsar in this system to have a relatively low mass at 1.24 ± 0.11 M®, and the companion mass to be 0.79 ± 0.04111.).We argue that the full set of system properties indicates that the system underwent a common-envelope phase in its evolutionary history. The double pulsar system PSR 0737-3039A/B is a highly relativistic double neutron star (DNS) binary, with a 2.4-hour orbital period. The low mass of the second-formed NS, as well the low system eccentricity and proper motion, have suggested a different evolutionary scenario compared to other known DNS systems. We describe analysis of the pulse profile shape over six years of observations, and present the constraints this provides on the system geometry. We find the recycled pulsar in this system, PSR 0737-3039A,to have a low misalignment angle between its spin and orbital angular momentum axes, with a 95.4% upper limit of 14 °, assuming emission from both magnetic poles. This tight constraint lends credence to the idea that the supernova that formed the second pulsar was relatively symmetric, possibly involving electron captures onto an 0-Ne-Mg core. We have also conducted timing analysis of PSR J1756-2251 using four years of data, and have obtained tight constraints on the component masses and orbital parameters in this DNS system. We have measured four post-Keplerian timing parameters for this pulsar; the Shapiro delay s parameter, with a 5% measured uncertainty, is consistent at just above the la level with the predictions of general relativity. The pulsar in this system has a fairly typical NS mass of 1.312 ± O.017M®, and the companion NS to be relatively light, with a mass of 1.2581017 Mo. This, together with the somewhat low orbital eccentricity of this system (e 0.18), suggests a similar evolution to that of the double pulsar. We investigate this further, through a similar pulse profile analysis to that performed with PSR J0737-3039A, with the goal of constraining the geometry of this system.