Covariant Formulation Research Articles

Land use drives differential resource selection by African elephants in the Greater Mara Ecosystem, Kenya

Understanding drivers of space use by African elephants is critical to their conservation and management, particularly given their large home-ranges, extensive resource requirements, ecological role as ecosystem engineers, involvement in human-elephant conflict and as a target species for ivory poaching. In this study we investigated resource selection by elephants inhabiting the Greater Mara Ecosystem in Southwestern Kenya in relation to three distinct but spatially contiguous management zones: (i) the government protected Maasai Mara National Reserve (ii) community-owned wildlife conservancies, and (iii) elephant range outside any formal wildlife protected area. We combined GPS tracking data from 49 elephants with spatial covariate information to compare elephant selection across these management zones using a hierarchical Bayesian framework, providing insight regarding how human activities structure elephant spatial behavior. We also contrasted differences in selection by zone across several data strata: sex, season and time-of-day. Our results showed that the strongest selection by elephants was for closed-canopy forest and the strongest avoidance was for open-cover, but that selection behavior varied significantly by management zone and selection for cover was accentuated in human-dominated areas. When contrasting selection parameters according to strata, variability in selection parameter values reduced along a protection gradient whereby elephants tended to behave more similarly (limited plasticity) in the human dominated, unprotected zone and more variably (greater plasticity) in the protected reserve. However, avoidance of slope was consistent across all zones. Differences in selection behavior was greatest between sexes, followed by time-of-day, then management zone and finally season (where seasonal selection showed the least differentiation of the contrasts assessed). By contrasting selection coefficients across strata, our analysis quantifies behavioural switching related to human presence and impact displayed by a cognitively advanced megaherbivore. Our study broadens the knowledge base about the movement ecology of African elephants and builds our capacity for both management and conservation.

On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject.

Clustering blood donors via mixtures of product partition models with covariates.

Motivated by the problem of accurately predicting gap times between successive blood donations, we present here a general class of Bayesian nonparametric models for clustering. These models allow for the prediction of new recurrences, accommodating covariate information that describes the personal characteristics of the sample individuals. We introduce a prior for the random partition of the sample individuals, which encourages two individuals to be co-clustered if they have similar covariate values. Our prior generalizes product partition models with covariates (PPMx) models in the literature, which are defined in terms of cohesion and similarity functions. We assume cohesion functions that yield mixtures of PPMx models, while our similarity functions represent the denseness of a cluster. We show that including covariate information in the prior specification improves the posterior predictive performance and helps interpret the estimated clusters in terms of covariates in the blood donation application.

On covariant perturbations with scalar field in modified Gauss–Bonnet gravity

We investigate cosmological perturbations of f(G) gravity in the presence of a scalar field. Using the 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document} covariant formalism, we present the energy overdensity perturbation equations responsible for large scale structure formation. After applying harmonic decomposition method together with the redshift transformation technique, we obtain the fully perturbed equations in redshift space. The equations are solved to study the growth of matter overdensities contrast with redshift. For both short- and long-wavelength modes, we obtain numerical results for particular functional form f(G) models and scalar field. We find that, for this choice the energy overdensity perturbations decay with increase in redshift. However, for both short- and long-wavelength modes, the perturbations which include amplitude effects due to the f(G) models with a scalar field do differ remarkably from those in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM. The results reduce to GR results in the limit of f(G)→G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(G)\\rightarrow G$$\\end{document} and in the absence of scalar field.

Manifestly covariant variational principle for gauge theories of gravity

A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This is performed by deriving explicit manifestly covariant expressions for the Euler-Lagrange variational derivatives and Noether’s theorems for a generic action of the form typically assumed in gauge theories of gravity. The approach is illustrated by application to two scale-invariant gravitational gauge theories, namely Weyl gauge theory (WGT) and the recently proposed ‘extended’ Weyl gauge theory (eWGT), where the latter may be considered as a novel gauging of the conformal group; the method can also be straightforwardly applied to other theories with smaller or larger symmetry groups. In addition, the approach enables one easily to establish the relationship between manifestly covariant forms of variational derivatives obtained when one or more of the gauge field strengths is set to zero either before or after the variation is performed. This is illustrated explicitly for both WGT and eWGT in the case where the translational gauge field strength (or torsion) is set to zero before and after performing the variation, respectively. Published by the American Physical Society 2024

Light-front puzzles

Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

Population pharmacokinetic modeling of ilaprazole in healthy subjects and patients with duodenal ulcer in China.

Aims: This study aimed to develop a population pharmacokinetic (PopPK) model of ilaprazole in healthy subjects and patients with duodenal ulcer in Chinese and investigate the effect of potential covariates on pharmacokinetic (PK) parameters. Methods: Pharmacokinetic data from 4 phase I clinical trials and 1 phase IIa clinical trial of ilaprazole were included in PopPK analysis. Phoenix NLME 8.3 was used to establish a PopPK model and quantify the effects of covariate, such as demographic data, biochemical indicators and disease state on the PK parameters of ilaprazole. The final model was evaluated by goodness-of-fit plots, bootstrap analysis, and visual predictive check. Results: A two-compartment model with first-order elimination successfully described the pharmacokinetic properties of ilaprazole. In the final PopPK model, body weight and sex were identified as statistically significant covariates for volume of peripheral compartment (Vp) and clearance of central compartment (CL), respectively, and disease status was also screened as a significant covariate affecting both CL and Vp. The validation results demonstrated the good predictability of the model, which was accurate and reliable. Conclusion: This is the first population pharmacokinetics study of ilaprazole in the Chinese, and the PopPK model developed in this study is expected to be helpful in providing relevant PK parameters and covariates information for further studies of ilaprazole.

Hearing Loss, Hearing Aid Use, and Risk of Dementia in Older Adults

Hearing loss has been suggested as a risk factor for dementia, but there is still a need for high-quality research to better understand the association between these 2 conditions and the underlying causal mechanisms and treatment benefits using larger cohorts and detailed data. To investigate the association between hearing loss and incident dementia, as well as how hearing aid use contributes to this association. This population-based cohort study was conducted in Southern Denmark between January 2003 and December 2017 and included all residents 50 years and older. We excluded all persons with dementia before baseline as well as those who did not live in the region 5 years before baseline, with incomplete address history, or who had missing covariate information. Individual hearing status based on the Hearing Examinations in Southern Denmark database, which contains data on all pure-tone audiometry examinations performed at public hearing rehabilitation clinics in Southern Denmark. Incident cases of dementia and Alzheimer disease as identified from national registries. The study population comprised 573 088 persons (298 006 women [52%]; mean [SD] age, 60.8 [11.3] years) with 23 023 cases of dementia and mean (SD) follow-up of 8.6 (4.3) years. Having a hearing loss was associated with an increased risk of dementia, with an adjusted hazard ratio (HR) of 1.07 (95% CI, 1.04-1.11) compared with having no hearing loss. Severe hearing loss in the better and worse ear was associated with a higher dementia risk, with an HR of 1.20 (95% CI, 1.09-1.32) and 1.13 (95% CI, 1.06-1.20), respectively, compared with having no hearing loss in the corresponding ear. Compared with people without hearing loss, the risk of dementia was higher among people with hearing loss who were not using hearing aids than those who had hearing loss and were using hearing aids, with HRs of 1.20 (95% CI, 1.13-1.27) and 1.06 (95% CI, 1.01-1.10), respectively. The results of this cohort study suggest that hearing loss was associated with increased dementia risk, especially among people not using hearing aids, suggesting that hearing aids might prevent or delay the onset and progression of dementia. The risk estimates were lower than in previous studies, highlighting the need for more high-quality longitudinal studies.

Unimodular gravity in covariant formalism

In this short note we study unimodular gravity in Weyl-De Donder formalism. We find corresponding Hamiltonian and study consequence of the unimodular constraint on the conjugate covariant momenta. We also find covariant Hamiltonian for Henneaux-Teitelboim unimodular action and study corresponding equations of motion.

Proton Pump Inhibitors Use in Kidney Transplant Recipients: A Population-Based Study.

Kidney transplant recipients are commonly prescribed proton-pump inhibitors (PPIs), but due to concern for polypharmacy, chronic use should be limited. The objective was to describe PPI use in kidney transplant recipients beyond their first year of transplant to better inform and support deprescribing initiatives. We conducted a retrospective, population-based cohort study using linked health care databases. This study was conducted in Alberta, Canada. We included all prevalent adult, kidney-only transplant recipients between April 2008 and December 2017 who received their transplant between May 2002 and December 2017. The primary outcome was ongoing or new PPI use and patterns of use, including frequency and duration of therapy, and assessment of indication for PPI use. We ascertained baseline characteristics, covariate information, and outcome data from the Alberta Kidney Disease Network (AKDN). We compared recipients with evidence of a PPI prescription in the 3 months prior to study entry to those with a histamine-2-receptor antagonist (H2Ra) fill and those with neither. We identified 1823 kidney transplant recipients, of whom 868 (48%) were on a PPI, 215 (12%) were on an H2Ra, and 740 (41%) were on neither at baseline. Over a median follow-up of 5.4 years (interquartile range [IQR] = 2.6-9.3), there were almost 45 000 unique PPI prescriptions dispensed, the majority (80%) of which were filled by initial PPI users. Recipients who were on a PPI at baseline would spend 91% (IQR = 70-98) of their graft survival time on a PPI in follow-up, and nephrologists were the main prescribers. We identified an indication for ongoing PPI use in 54% of recipients with the most common indication being concurrent antiplatelet use (26%). Our kidney transplant recipients have access to universal health care coverage which may limit generalizability. We identified common gastrointestinal indications for PPI use but did not include rare conditions due to concerns about the validity of diagnostic codes. In addition, symptoms suggestive of reflux may not be well coded as the focus of follow-up visits is more likely to focus on kidney transplant. Many kidney transplant recipients are prescribed a PPI at, or beyond, the 1-year post-transplant date and are likely to stay on a PPI in follow-up. Almost half of the recipients in our study did not have an identifiable indication for ongoing PPI use. Nephrologists frequently prescribe PPIs to kidney transplant recipients and should be involved in deprescribing initiatives to reduce polypharmacy.

A validated UPLC-MS/MS method for quantification of pyrotinib and population pharmacokinetic study of pyrotinib in HER2-positive breast cancer patients.

Pyrotinb has been approved for the treatment of HER2-positive advanced or metastatic breast cancer in China. However, the plasma concentration of pyrotinb in different patients varies greatly, and in the course of treatment, if patients have intolerable adverse reactions, the drug dosage will be reduced or even stopped. This study set out to establish an ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) for the determination of pyrotinb in human plasma, analyze the population pharmacokinetics (PPK) of pyrotinib and assess the influence of patient variables on PK of pyrotinib in patients with HER2 positive breast cancer. An UPLC-MS/MS method was developed to measure pyrotinib in human plasma. Utilizing a gradient elution procedure and a Kinetex C18 column (2.1mm × 100mm, 1.7μm), sample separation was accomplished in 5.5min. Pyrotinb extraction via protein precipitation was used as a sample pre-treatment technique. In total, 50 patients provided 158 plasma samples, which were identified and used in the PPK investigation. The non-linear mixed-effects modeling (NONMEM) approach was used to assess the plasma concentrations and covariates information. For the final PPK model evaluation, external evaluation, non-parametric bootstrap, visual predictive check (VPC), and goodness-of-fit (GOF) were used. The UPLC-MS/MS method for determining plasma concentration of pyrotinib in patients had good selectivity and linearity in the range of 1-1,000ng/mL. Pyrotinib concentration profile in HER2-positive breast cancer patients was well described by a single-compartment PPK model with first-order absorption and elimination. The formulas for the final estimated values of overall parameters of CL/F and Vd/F and Ka are respectively: , , . No dosage adjustment was advised, despite the possibility that the total protein levels could have a substantial impact on the apparent distribution volume of pyrotinib with limited magnitude. In this study, an UPLC-MS/MS method was established to determine the concentration of pyrotinib in human plasma. A population pharmacokinetic model of pyrotinib in HER2 positive breast cancer patients suggested that low serum total protein reduced the clearance rate of pyrotinib in patients. Clinical medical staff should pay attention to the liver function of patients with abnormal serum total protein and be alert to the occurrence of adverse drug reactions.

Bibliographical Connections for Semiparametric Analysis in Case-Control Studies on Gene-Environment Interactions

Analyzing the gene-environment interaction (GEI) is crucial for understanding the etiology of many complex traits. Among various types of study designs, case-control studies are popular for analyzing gene-environment interactions due to their efficiency in collecting covariate information. Extensive literature explores efficient estimation under various assumptions made about the relationship between genetic and environmental variables. In this paper, we comprehensively review the methods based on or related to the retrospective likelihood, including the methods based on the hypothetical population concept, which has been largely overlooked in GEI research in the past decade. Furthermore, we establish the methodological connection between these two groups of methods by deriving a new estimator from both the retrospective likelihood and the hypothetical population perspectives. The validity of the derivation is demonstrated through numerical studies.

Estimation of Population Size Based on One-Inflated, Zero-Truncated Count Distribution with Covariate Information

In order to estimate the unknown size of the population that is difficult or hidden to enumerate, the capture-recapture method is widely used for this purpose. We propose the one-inflated, zero-truncated geometric (OIZTG) model to deal with three important characteristics of some capture–recapture data: zero-truncation, one-inflation, and observed heterogeneity. The OIZTG model is generated by two distinct processes, one from a zero-truncated geometric (ZTG) process, and the other one-count producing process. To explain heterogeneity at an individual level, the OIZTG model provides a simple way to link the covariate information. The new estimator was proposed based on the OIZTG distributions through the modified Horvitz-Thomson approach, and the parameters of the OIZTG distributions are estimated by using a maximum likelihood estimator (MLE). With regard to making inferences about the unknown size of the population, confidence interval estimations are proposed where variance estimate of population size estimator is achieved by using conditional expectation technique. All of these are assessed through simulation studies. The real data sets are provided for understanding the methodologies.

Robust Estimators for Missing Observations in Linear Discrete-Time Stochastic Systems with Uncertainties

As a first approach to estimating the signal and the state, Theorem 1 proposes recursive least-squares (RLS) Wiener fixed-point smoothing and filtering algorithms that are robust to missing measurements in linear discrete-time stochastic systems with uncertainties. The degraded quantity is given by multiplying the Bernoulli random variable by the degraded signal caused by the uncertainties in the system and observation matrices. The degraded quantity is observed with additional white observation noise. The probability that the degraded signal is present in the observation equation is assumed to be known. The design feature of the proposed robust estimators is the fitting of the degraded signal to a finite-order autoregressive (AR) model. Theorem 1 is transformed into Corollary 1, which expresses the covariance information in a semi-degenerate kernel form. The autocovariance function of the degraded state and the cross-covariance function between the nominal state and the degraded state is expressed in semi-degenerate kernel forms. Theorem 2 shows the robust RLS Wiener fixed-point and filtering algorithms for estimating the signal and state from degraded observations in the second method. The robust estimation algorithm of Theorem 2 has the advantage that, unlike Theorem 1 and the usual studies, it does not use information on the existence probability of the degraded signal. This is a unique feature of Theorem 2.

Soil permittivity estimation over vegetative fields using dual polarimetric SAR data

Soil permittivity estimation using Synthetic Aperture Radar (SAR) data under the vegetation cover has been an extensive research domain. In particular, the vegetation canopy over the soil layer complicates the interaction of microwave signals with the underneath soil layer and the vegetation canopy geometry. Nevertheless, the sensitivity of the microwave signal with the target dielectric and geometric properties makes it possible to retrieve the target permittivity from the SAR data. This work proposes a methodology for retrieving soil permittivity using dual-polarimetric (HH-HV or VV-VH) SAR data. We first derive the 2 × 2 covariance matrix (CXX-XYXB) for the extended Bragg (X-Bragg) surface scattering for both HH-HV and VV-VH configurations. The X-Bragg covariance information inherently captures the soil surface condition. Finally, we utilize the existing scattering power factorization framework to retrieve soil permittivity. We have validated the efficacy of the proposed technique using the simulated NISAR product from the L-band UAVSAR data over Manitoba, Canada, and the C- and L- band ESAR data over DEMMIN, Germany. The proposed technique achieves the soil permittivity within a Root Mean Square Error (RMSE) range of 2 to 6 for HH-HV and VV-VH configurations.

Highly magnetized quark matter in the chiral limit

AbstractWe examine the behavior of highly magnetized two‐light‐flavor quark matter within the context of a nonlocal NJL‐type model. This analysis assumes the chiral limit and incorporates the interaction between fermions and the Polyakov loop. Our calculations utilize a covariant Gaussian form factor. We present phase diagrams on the plane, illustrating different magnetic field strengths. Additionally, we examine the critical endpoint's placement and the de Haas‐Van Alphen transitions within the chiral restored phase, observing their temperature‐dependent characteristics.

Methodological derivation of the eikonal equation

Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. Understanding this derivation requires a certain number of implicit assumptions. For a better understanding of the eikonal approximation and for methodological purposes, the authors decided to repeat the derivation of the eikonal equation, explicating all possible assumptions. Methodically, the following algorithm for deriving the eikonal equation is proposed. The wave equation is derived from Maxwell’s equation. In this case, all conditions are explicitly introduced under which it is possible to do this. Further, from the wave equation, the transition to the Helmholtz equation is carried out. From the Helmholtz equation, with the application of certain assumptions, a transition is made to the eikonal equation. After analyzing all the assumptions and steps, the transition from the Maxwell’s equations to the eikonal equation is actually implemented. When deriving the eikonal equation, several formalisms are used. The standard formalism of vector analysis is used as the first formalism. Maxwell’s equations and the eikonal equation are written as three-dimensional vectors. After that, both the Maxwell’s equations and the eikonal equation use the covariant 4-dimensional formalism. The result of the work is a methodically consistent description of the eikonal equation.

The Schrödinger representation and 3D gauge theories

In this paper, we consider the Hamiltonian analysis of Yang–Mills theory and some variants of it in three space–time dimensions using the Schrödinger representation. This representation, although technically more involved than the usual covariant formulation, may be better suited for some nonperturbative issues. Specifically for the Yang–Mills theory, we explain how to set up the Hamiltonian formulation in terms of manifestly gauge-invariant variables and set up an expansion scheme for solving the Schrödinger equation. We review the calculation of the string tension, the Casimir energy and the propagator mass and compare with the results from lattice simulations. The computation of the first set of corrections to the string tension, string breaking effects, extensions to the Yang–Mills–Chern–Simons theory and to the supersymmetric cases are also discussed. We also comment on how entanglement for the vacuum state can be formulated in terms of the BFK gluing formula. This paper concludes with a discussion of the status and prospects of this approach.

Covariant canonical formulations of classical field theories

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

Classical relativistic electron-field dynamics: Hamiltonian approach to radiation reaction

Motivated by the renewed interest due to the presently available extreme light sources, the dynamics of a single classical relativistic (spinless) extended electron interacting with a classical electromagnetic field (an incoming radiation and the field radiated by the electron) is revisited. The field is treated in Lorentz gauge, with the Lorentz condition. By assumption, there is a crucial finite cut-off k max on the magnitude of any wavevector contributing to the field (preventing a point electron) and, for a simple formulation, the initial conditions for particle and fields are given in the infinitely remote past. In an infinite three-dimensional vacuum and in an inertial system, Hamilton’s dynamical equations for the particle and the complex field amplitudes acting as canonical variables (a's) yield an exact Lorentz force equation for the former, that includes the incoming radiation and an exact radiation reaction force F RR due to the field radiated by the electron. Uniform motion is obtained as a test of consistency. Based upon numerical computations, some approximations on F RR are given. A covariant formulation is also presented.