The Lanczos potential for Weyl-candidate tensors exists only in four dimensions

We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L_abc and W_abcd, then this system's integrability conditions should be checked; and so on. When we find a non-trivial condition involving only W_abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200

On Effective Constraints for the Riemann-Lanczos System of Equations

There have been conflicting points of view concerning the Riemann--Lanczos problem in 3 and 4 dimensions. Using direct differentiation on the defining partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar (in dimensions n > 2) have argued that there are effective constraints so that not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of integrability of ideals of differential forms Bampi and Caviglia have argued that there are no such constraints in dimensions n < 5, and that, in these dimensions, all Riemann tensors can have Lanczos potentials. In this paper we give a simple direct derivation of a constraint equation, confirm explicitly that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue that the Bampi and Caviglia conclusion must therefore be flawed. In support of this, we refer to the recent work of Dolan and Gerber on the three dimensional problem; by a method closely related to that of Bampi and Caviglia, they have found an 'internal identity' which we demonstrate is precisely the three dimensional version of the effective constraint originally found by Massa and Pagani, and Edgar.Comment: 9pages, Te

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

Generalized hydrodynamics and extended irreversible thermodynamics

The thermodynamic implications of the first deviations with respect to the classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. The constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities in the space of state variables are compared with those used in generalized hydrodynamics. The so-called exponential model for the memory function of the transverse-velocity correlation function is derived under the assumptions of extended irreversible thermodynamics only. Furthermore, it is also shown how more complicated memory functions can be derived. The results are carefully analyzed and compared with some microscopic derivations

A digital health intervention for cardiovascular disease management in primary care (CONNECT) randomized controlled trial

Digital health applications (apps) have the potential to improve health behaviors and outcomes. We aimed to examine the effectiveness of a consumer web-based app linked to primary care electronic health records (EHRs). CONNECT was a multicenter randomized controlled trial involving patients with or at risk of cardiovascular disease (CVD) recruited from primary care (Clinical Trial registration ACTRN12613000715774). Intervention participants received an interactive app which was pre-populated and refreshed with EHR risk factor data, diagnoses and, medications. Interactive risk calculators, motivational messages and lifestyle goal tracking were also included. Control group received usual health care. Primary outcome was adherence to guideline-recommended medications (≥80% of days covered for blood pressure (BP) and statin medications). Secondary outcomes included attainment of risk factor targets and eHealth literacy. In total, 934 patients were recruited; mean age 67.6 (±8.1) years. At 12 months, the proportion with >80% days covered with recommended medicines was low overall and there was no difference between the groups (32.8% vs. 29.9%; relative risk [RR] 1.07 [95% CI, 0.88–1.20] p = 0.49). There was borderline improvement in the proportion meeting BP and LDL targets in intervention vs. control (17.1% vs. 12.1% RR 1.40 [95% CI, 0.97–2.03] p = 0.07). The intervention was associated with increased attainment of physical activity targets (87.0% intervention vs. 79.7% control, p = 0.02) and e-health literacy scores (72.6% intervention vs. 64.0% control, p = 0.02). In conclusion, a consumer app integrated with primary health care EHRs was not effective in increasing medication adherence. Borderline improvements in risk factors and modest behavior changes were observed

A digital health intervention for cardiovascular disease management in primary care (CONNECT) randomized controlled trial

Digital health applications (apps) have the potential to improve health behaviors and outcomes. We aimed to examine the effectiveness of a consumer web-based app linked to primary care electronic health records (EHRs). CONNECT was a multicenter randomized controlled trial involving patients with or at risk of cardiovascular disease (CVD) recruited from primary care (Clinical Trial registration ACTRN12613000715774). Intervention participants received an interactive app which was pre-populated and refreshed with EHR risk factor data, diagnoses and, medications. Interactive risk calculators, motivational messages and lifestyle goal tracking were also included. Control group received usual health care. Primary outcome was adherence to guideline-recommended medications (≥80% of days covered for blood pressure (BP) and statin medications). Secondary outcomes included attainment of risk factor targets and eHealth literacy. In total, 934 patients were recruited; mean age 67.6 (±8.1) years. At 12 months, the proportion with >80% days covered with recommended medicines was low overall and there was no difference between the groups (32.8% vs. 29.9%; relative risk [RR] 1.07 [95% CI, 0.88–1.20] p = 0.49). There was borderline improvement in the proportion meeting BP and LDL targets in intervention vs. control (17.1% vs. 12.1% RR 1.40 [95% CI, 0.97–2.03] p = 0.07). The intervention was associated with increased attainment of physical activity targets (87.0% intervention vs. 79.7% control, p = 0.02) and e-health literacy scores (72.6% intervention vs. 64.0% control, p = 0.02). In conclusion, a consumer app integrated with primary health care EHRs was not effective in increasing medication adherence. Borderline improvements in risk factors and modest behavior changes were observed