McDonald Generalized Power Weibull Distribution: Properties, and Applications

This research introduces a novel six-parameter model called the McDonald Generalized Power Weibull distribution. The model contains several sub-models that prove highly valuable in modeling real-life scenarios, including the McDonald Weibull, McDonald exponential, McDonald Nadarajah-Haghighi, beta generalized power Weibull distribution, and Kumaraswamy generalized power distributions, among others. The proposed model demonstrates suitability in modeling survival/reliability data, accommodating various hazard failure rates such as increasing, decreasing, unimodal (upside-down bathtub), modified bathtub, and reversed J-shape. Various properties of the new model are investigated, including moments, quantiles, incomplete moments, moment-generating functions, and order statistics. The maximum likelihood estimation method is employed to estimate the model parameters. The study concludes by illustrating the flexibility of the proposed model through the use of lifetime data to demonstrate its applicability

Large N limit of SO(N) gauge theory of fermions and bosons

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(H|H )/U(H_+|H_+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H_+|H_+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in our earlier work). In the Majorana fermion case the phase space is given by O_1(H)/U(H_+), where H refers to the complex one-particle states and H_+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.Comment: 27 pages, no figure

On two dimensional coupled bosons and fermions

We study complex bosons and fermions coupled through a generalized Yukawa type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod. Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show that in this approximation we do not have boson-antiboson and fermion-antifermion bound states occuring together. There is a possibility of having only fermion-antifermion bound states. We support this claim by finding distributional solutions with energies lower than the two mass treshold in the fermion sector. This also has implications from the point of view of scattering theory to this model. We discuss some aspects of the scattering above the two mass treshold of boson pairs and fermion pairs. We also briefly present a gauged version of the same model and write down the linearized equations of motion.Comment: 25 pages, no figure

Supergrassmannian and large N limit of quantum field theory with bosons and fermions

We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.Comment: 24 pages, Latex; v.3 appendix added, typos corrected, to appear in JM

Induced vacuum condensates in the background of a singular magnetic vortex in 2+1-dimensional space-time

We show that the vacuum of the quantized massless spinor field in 2+1-dimensional space-time is polarized in the presence of a singular magnetic vortex. Depending on the choice of the boundary condition at the location of the vortex, either chiral symmetry or parity is broken; the formation of the appropriate vacuum condensates is comprehensively studied. In addition, we find that current, energy and other quantum numbers are induced in the vacuum.Comment: LaTeX2e, 27 page

Dynamical Generation of Extended Objects in a 1+11+1 Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis

We analyze the $1+1$ dimensional Nambu-Jona-Lasinio model non-perturbatively. In addition to its simple ground state saddle points, the effective action of this model has a rich collection of non-trivial saddle points in which the composite fields \sigx=\lag\bar\psi\psi\rag and \pix=\lag\bar\psi i\gam_5\psi\rag form static space dependent configurations because of non-trivial dynamics. These configurations may be viewed as one dimensional chiral bags that trap the original fermions (``quarks") into stable extended entities (``hadrons"). We provide explicit expressions for the profiles of these objects and calculate their masses. Our analysis of these saddle points is based on an explicit representation we find for the diagonal resolvent of the Dirac operator in a \{\sigx, \pix\} background which produces a prescribed number of bound states. We analyse in detail the cases of a single as well as two bound states. We find that bags that trap $N$ fermions are the most stable ones, because they release all the fermion rest mass as binding energy and become massless. Our explicit construction of the diagonal resolvent is based on elementary Sturm-Liouville theory and simple dimensional analysis and does not depend on the large $N$ approximation. These facts make it, in our view, simpler and more direct than the calculations previously done by Shei, using the inverse scattering method following Dashen, Hasslacher, and Neveu. Our method of finding such non-trivial static configurations may be applied to other $1+1$ dimensional field theories

Reliability and Validity of the HD-PRO-TriadTM, a Health-Related Quality of Life Measure Designed to Assess the Symptom Triad of Huntington\u27s Disease.

BACKGROUND: Huntington\u27s disease (HD), is a neurodegenerative disorder that is associated with cognitive, behavioral, and motor impairments that diminish health related quality of life (HRQOL). The HD-PRO-TRIADTM is a quality of life measure that assesses health concerns specific to individuals with HD. Preliminary psychometric characterization was limited to a convenience sample of HD participants who completed measures at home so clinician-ratings were unavailable. OBJECTIVES: The current study evaluates the reliability and validity of the HD-PRO-TRIADTM in a well-characterized sample of individuals with HD. METHODS: Four-hundred and eighty-two individuals with HD (n = 192 prodromal, n = 193 early, and n = 97 late) completed the HD-PRO-TRIADTM questionnaire. Clinician-rated assessments from the Unified Huntington Disease Rating Scales, the short Problem Behaviors Assessment, and three generic measures of HRQOL (WHODAS 2.0, RAND-12, and EQ-5D) were also examined. RESULTS: Internal reliability for all domains and the total HD-PRO-TRIADTM was excellent (all Cronbach\u27s α \u3e0.93). Convergent and discriminant validity were supported by significant associations between the HD-PRO-TRIADTM domains, and other patient reported outcome measures as well as clinician-rated measures. Known groups validity was supported as the HD-PRO-TRIADTM differentiated between stages of the disease. Floor and ceiling effects were generally within acceptable limits. There were small effect sizes for 12-month change over time and moderate effect sizes for 24-month change over time. CONCLUSIONS: Findings support excellent internal reliability, convergent and discriminant validity, known groups validity, and responsiveness to change over time. The current study supports the clinical efficacy of the HD-PRO-TRIADTM. Future research is needed to assess the test-retest reliability of this measure

1+1 dimensional QCD with fundamental bosons and fermions

We analyze the properties of mesons in 1+1 dimensional QCD with bosonic and fermionic ``quarks'' in the large \nc limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of ``mesons'' formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.Comment: 20 pages, harvmac, 5 figure

Boson--fermion bound states in two dimensional QCD

We derive the boson--fermion bound state equation in a two dimensional gauge theory in the large--\nc limit. We analyze the properties of this equation and in particular, find that the mass trajectory is linear with respect to the bound state level for the higher mass states.Comment: 5pp, 2 figs (as a separate file), TIT/HEP-23

Agreement Between Clinician-Rated Versus Patient-Reported Outcomes in Huntington Disease

BACKGROUND: Clinician-rated measures of functioning are often used as primary endpoints in clinical trials and other behavioral research in Huntington disease. As study costs for clinician-rated assessments are not always feasible, there is a question of whether patient self-report of commonly used clinician-rated measures may serve as acceptable alternatives in low risk behavioral trials. AIM: The purpose of this paper was to determine the level of agreement between self-report and clinician-ratings of commonly used functional assessment measures in Huntington disease. DESIGN: 486 participants with premanifest or manifest Huntington disease were examined. Total Functional Capacity, Functional Assessment, and Independence Scale assessments from the Unified Huntington Disease Rating scale were completed by clinicians; a self-report version was also completed by individuals with Huntington disease. Cronbach\u27s α was used to examine internal consistency, one-way analysis of variance was used to examine group differences, and paired t tests, kappa agreement coefficients, and intra-class correlations were calculated to determine agreement between raters. RESULTS: Internal consistency for self-reported ratings of functional capacity and ability were good. There were significant differences between those with premanifest, early-, and late-stage disease; those with later-stage disease reported less ability and independence than the other clinical groups. Although self-report ratings were not a perfect match with associated clinician-rated measures, differences were small. Cutoffs for achieving specified levels of agreement are provided. CONCLUSIONS: Depending on the acceptable margin of error in a study, self-reported administration of these functional assessments may be appropriate when clinician-related assessments are not feasible