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Background High mammographic density is associated with both risk of cancers being missed at mammography, and increased risk of developing breast cancer. Stratification of breast cancer prevention and screening requires mammographic density measures predictive of cancer. This study compares five mammographic density measures to determine the association with subsequent diagnosis of breast cancer and the presence of breast cancer at screening. Methods Women participating in the “Predicting Risk Of Cancer At Screening” (PROCAS) study, a study of cancer risk, completed questionnaires to provide personal information to enable computation of the Tyrer-Cuzick risk score. Mammographic density was assessed by visual analogue scale (VAS), thresholding (Cumulus) and fully-automated methods (Densitas, Quantra, Volpara) in contralateral breasts of 366 women with unilateral breast cancer (cases) detected at screening on entry to the study (Cumulus 311/366) and in 338 women with cancer detected subsequently. Three controls per case were matched using age, body mass index category, hormone replacement therapy use and menopausal status. Odds ratios (OR) between the highest and lowest quintile, based on the density distribution in controls, for each density measure were estimated by conditional logistic regression, adjusting for classic risk factors. Results The strongest predictor of screen-detected cancer at study entry was VAS, OR 4.37 (95% CI 2.72–7.03) in the highest vs lowest quintile of percent density after adjustment for classical risk factors. Volpara, Densitas and Cumulus gave ORs for the highest vs lowest quintile of 2.42 (95% CI 1.56–3.78), 2.17 (95% CI 1.41–3.33) and 2.12 (95% CI 1.30–3.45), respectively. Quantra was not significantly associated with breast cancer (OR 1.02, 95% CI 0.67–1.54). Similar results were found for subsequent cancers, with ORs of 4.48 (95% CI 2.79–7.18), 2.87 (95% CI 1.77–4.64) and 2.34 (95% CI 1.50–3.68) in highest vs lowest quintiles of VAS, Volpara and Densitas, respectively. Quantra gave an OR in the highest vs lowest quintile of 1.32 (95% CI 0.85–2.05). Conclusions Visual density assessment demonstrated a strong relationship with cancer, despite known inter-observer variability; however, it is impractical for population-based screening. Percentage density measured by Volpara and Densitas also had a strong association with breast cancer risk, amongst the automated measures evaluated, providing practical automated methods for risk stratification.

Recent studies show that the tunnelling radiation of vector particles has been studied successfully by WKB approximation and Hamilton-Jacobi method. In view of this, the main purpose of this paper is to study the Proca equation and the vector particles tunnelling radiation in a 4-dimensional black hole. Finally, the results here show that the temperature of the vector particle is the same as that of the Dirac particle.

Dark matter could accumulate around neutron stars in sufficient amounts to affect their global properties. In this work, we study the effect of a specific model for dark matter—a massive and self-interacting vector (spin-1) field—on neutron stars. We describe the combined systems of neutron stars and vector dark matter using Einstein–Proca theory coupled to a nuclear matter term and find scaling relations between the field and metric components in the equations of motion. We construct equilibrium solutions of the combined systems, compute their masses and radii, and also analyze their stability and higher modes. The combined systems admit dark matter (DM) core and cloud solutions. Core solutions compactify the neutron star component and tend to decrease the total mass of the combined system. Cloud solutions have the inverse effect. Electromagnetic observations of certain cloud-like configurations would appear to violate the Buchdahl limit. This could make Buchdahl-limit-violating objects smoking gun signals for dark matter in neutron stars. The self-interaction strength is found to significantly affect both mass and radius. We also compare fermion Proca stars to objects where the dark matter is modeled using a complex scalar field. We find that fermion Proca stars tend to be more massive and geometrically larger than their scalar field counterparts for equal boson masses and self-interaction strengths. Both systems can produce degenerate masses and radii for different amounts of DM and DM particle masses.

We derive conditions which are sufficient for theories consisting of multiple vector fields, which could also couple to non-dynamical external fields, to have the required structure of constraints of multi-field generalised Proca theories, so that the number of degrees of freedom is correct. The Faddeev–Jackiw constraint analysis is used and is cross-checked by Lagrangian constraint analysis. To ensure the theory is constraint, we impose a standard special form of Hessian matrix. The derivation benefits from the realisation that the theories are diffeomorphism invariance. The sufficient conditions obtained include a refinement of secondary-constraint enforcing relations derived previously in literature, as well as a condition which ensures that the iteration process of constraint analysis terminates. Some examples of theories are analysed to show whether they satisfy the sufficient conditions. Most notably, due to the obtained refinement on some of the conditions, some theories which are previously interpreted as being undesirable are in fact legitimate, and vice versa. This in turn affects the previous interpretations of cosmological implications which should later be reinvestigated.

A normal mode analysis for Proca fields in the anti-de Sitter (AdS) spacetime is given. It is found that the equations for the Proca field can be decoupled analytically. This is performed by changing the basis of the vector spherical harmonics decomposition. The normal modes and the normal mode frequencies of the Proca equation in the AdS spacetime are then analytically determined. It is also shown that the Maxwell field can be recovered by taking the massless limit of the Proca field with care so that the nonphysical gauge modes are eliminated.

We study an extended Proca model with one scalar field and one massive vector field in one space dimension and one time dimension. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE), which is the leading quantum correction to the classical energy of the soliton. For this calculation, we adopt the spectral methods approach, which heavily relies on the analytic properties of the Jost function. This function is extracted from the interaction of the quantum fluctuations with a background potential generated by the soliton. Particularly, we explore eventual non-analytical components that may be induced by mass gaps and the unconventional normalization for the longitudinal component of the vector field fluctuations. By numerical simulation, we verify that these obstacles do not actually arise and that the real and imaginary momentum formulations of the VPE yield equal results. The Born approximation to the The Jost function is crucial when implementing standard renormalization conditions. In this context, we solve problems arising from the Born approximation being imaginary for real momenta associated with energies in the mass gap.

We consider the Weyl invariant theory of gravity as an alternative approach to the problem of the origin of dark matter. According to this theory, the geometric Weyl 1-form effectively behaves as a Proca field. In this work, our starting point is to consider the existence of a gas of Weyl–Proca particles in a Bose–Einstein condensate and investigate its behavior in a cosmological context. The results obtained show that, for appropriate values of the free parameter of the model, the Weyl field behaves approximately as a dust fluid in the matter-dominated era as expected for a dark matter candidate.

We study the quantum tunneling of charged massive vector bosons from a charged static and a rotating black string. We apply the standard methods, first we use the WKB approximation and the Hamilton-Jacobi equation, and then we end up with a set of four linear equations. Finally, solving for the radial part by using the determinant of the metric equals zero, the corresponding tunneling rate and the Hawking temperature is recovered in both cases. The tunneling rate deviates from pure thermality and is consistent with an underlying unitary theory.

We revisit Weyl’s unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of the geometrization of physics started by Einstein to include the electromagnetic field, H. Weyl developed a new geometry which constitutes a kind of generalization of Riemannian geometry. In this paper, our aim is to discuss Weyl’s proposal anew and examine its consistency and completeness as a physical theory. We propose new directions and possible conceptual changes in the original work. Among these, we investigate with some detail the propagation of gravitational waves, and the new features arising in this recent modified gravity theory, in which the presence of a massive vector field appears somewhat unexpectedly. We also speculate whether the results could be examined in the context of primordial gravitational waves.

This work attempts to investigate the influence of the generalized uncertainty principle on the statistical parameters of the massive photon gases. The modified energy-momentum relations for the de Broglie Proca electrodynamics are obtained. Based on modified energy-momentum relations, we find thermodynamical characteristics such as partition function, mean energy, pressure, and entropy of the massive photon gases in the presence of a minimal length scale. Also, the upper bound on the isotropic minimal length which is close to the electroweak length scale is derived.