We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of s-fractional perimeter, defined for 0<s<1, to the case s>=1. We show that, as the core-radius vanishes, such core-radius regularized s-fractional perimeters, suitably scaled, ?-converge to the standard Euclidean perimeter.

A prey-predator system with logistic growth of prey and hunting cooperation of predators is studied. The introduction of fractional time derivatives and the related persistent memory strongly characterize the model behavior, as many dynamical systems in the applied sciences are well described by such fractional-order models. Mathematical analysis and numerical simulations are performed to highlight the characteristics of the proposed model.

Personalized medicine (PM) moves at the same pace of data and technology and calls for important changes in healthcare. New players are participating, providing impulse to PM. We review the conceptual foundations for PM and personalized healthcare and their evolution through scientific publications where a clear definition and the features of the different formulations are identifiable. We then examined PM policy documents of the International Consortium for Personalised Medicine and related initiatives to understand how PM stakeholders have been changing.

ZBTB2 is a protein belonging to the BTB/POZ zinc-finger family whose members typically contain a BTB/POZ domain at the N-terminus and several zinc-finger domains at the C-terminus. Studies have been carried out to disclose the role of ZBTB2 in cell proliferation, in human cancers and in regulating DNA methylation. Moreover, ZBTB2 has been also described as an ARF, p53 and p21 gene repressor as well as an activator of genes modulating pluripotency. In this scenario, ZBTB2 seems to play many functions likely associated with other proteins.

We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings.

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in general relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum, and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to nontrivial identities relating the various radiative losses.

The definition of suitable generative models for synthetic yet realistic social networks is a widely studied problem in the literature. By not being tied to any real data, random graph models cannot capture all the subtleties of real networks and are inadequate for many practical contexts--including areas of research, such as computational epidemiology, which are recently high on the agenda.

Clostridium difficile is a spore-forming gram-positive bacterium, recognized as the primary cause of antibiotic-associated nosocomial diarrhoea. Clostridium difficile infection (CDI) has emerged as a major health-associated infection with increased incidence and hospitalization over the years with high mortality rates. Contamination and infection occur after ingestion of vegetative spores, which germinate in the gastro-intestinal tract.

We present a simple model describing the chemical aggression undergone by calcium carbonate rocks in presence of acid atmosphere. A large literature is available on the deterioration processes of building stones, in particular in connection with problems concerning historical buildings in the field of Cultural Heritage. It is well known that the greatest aggression is caused by sulfur dioxide and nitrate. In this paper we consider the corrosion caused by sulphur dioxide, which, reacting with calcium carbonate, produces gypsum.

Topic Modelling (TM) is a widely adopted generative model used to infer the thematic organization of text corpora. When document-level covariate information is available, so-called Structural Topic Modelling (STM) is the state-of-the-art approach to embed this information in the topic mining algorithm. Usually, TM algorithms rely on unigrams as the basic text generation unit, whereas the quality and intelligibility of the identified topics would significantly benefit from the detection and usage of topical phrasemes.