There is a worldwide effort of the research community to explore the medical, economic and sociologic impact of the COVID-19 pandemic. Many different disciplines try to find solutions and drive strategies to a great variety of different very crucial problems. The present study presents a novel analysis which results to clustering countries with respect to active cases, active cases per population and active cases per population and per area based on Johns Hopkins epidemiological data. The presented cluster results could be useful to a variety of different policy makers, such as physicians and managers of the health sector, economy/finance experts, politicians and even to sociologists. In addition, our work suggests a new specially designed clustering algorithm adapted to the request for comparison of the various COVID time-series of different countries.

General nonsingular accelerating cosmological solutions for an initial cosmic period of pure vacuum birth era are derived. This vacuum era is described by a varying cosmological “constant” suggested by the renormalization group flow of asymptotic safety scenario near the ultraviolet fixed point. In this scenario, a natural exit from inflation to the standard decelerating cosmology occurs when the energy scale lowers and the cosmological constant becomes insignificant. In the following period where matter is also present, cosmological solutions with characteristics similar to the vacuum case are generated. Remarkably the set of equations allows for particle production and entropy generation. Alternatively, in the case of nonzero bulk viscosity, entropy production and reheating is found. As for the equations of motion, they modify Einstein equations by adding covariant kinetic terms of the cosmological constant which respect the Bianchi identities. An advance of the proposed framework is that it ensures a consistent description of both a quantum vacuum birth of the universe and a subsequent cosmic era in the presence of matter.

New general spherically symmetric solutions have been derived with a cosmological ``constant'' Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.

Aim of the study: To evaluate the ability of VEMP to disclose spatial dissemination of Multiple Sclerosis. Materials and methods: Forty-six MS patients with auditory and /or vestibular symptoms were studied. Patients were divided in two groups. Group 1 included 24 patients with brainstem MRI findings, and Group 2 included 22 patients without MRI findings. VEMP and BAEP have been recorded and assessed. Results: Abnormal p13n23 wave was observed in 50%, while unilateral absence or bilateral delay of the n34p44 in 43% of the patients. The overall diagnostic value considering abnormal cases suggested by both first and second VEMP waves was increased to 71%. Statistically significant differences revealed between patients and controls for p13 latency (p=0.018). The p13n23 was abnormal in 7 patients, although MRI scanning did not reveal brainstem lesions. In 9 out of 18 MS patients suffering from unilateral hearing loss, n34p44 was present in the unaffected ears and absent in the affected side, although p13n23 was normal. Conclusion: Abnormal VEMP imply the presence of lesions undetected by MRI neuroimaging, which verifies the diagnostic value of the method. Unilateral absence of n34p44 complex was related with sensorineural hearing loss, supporting the hypothesis that n34p44 is of cochlear origin.