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This work deals with the consumption chemotaxis problem \begin{equation*} \begin{cases*} u_t = \Delta u - \chi \nabla \cdot u\nabla v + \lambda u - \mu u^2 - c \lvert \nabla u \rvert^\gamma, & \text{in $\Omega\times(0,\tmax)$}, v_t = \Delta v - uv, & \text{in $\Omega\times(0,\tmax)$}, \end{cases*} \end{equation*} in a bounded and smooth domain $\Omega\subset\R^n$, $n\geq 3$, under Neumann boundary conditions, for $\chi,\lambda,\mu,c>0$, $\tmax\in(0,\infty]$ and for $u_0,v_0$ positive initial data with a certain regularity. We will show that the problem has a unique and uniformly bounded classical solution for $\gamma\in\bigl(\frac{2n}{n+1},2\bigr]$. Moreover, we have the same result for $\gamma=\frac{2n}{n+1}$ and a condition that involves the parameters $c,\mu,n,\chi$ and the initial data.

We study some attraction repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density, and for the chemosensitivities and the production rates of the chemoattractant and the chemorepellent. Additionally, a source also involving some expression of the gradient of the species is incorporated.

This paper investigates the properties of classical solutions to a class of chemotaxis systems that model interactions between tumor and immune cells. Our focus is on examining the global existence and explosion of such solutions in bounded domains of $\mathbb{R}^n$, $n\geq3$, under Neumann boundary conditions. We distinguish between two scenarios: one where all equations are parabolic and another where only one equation is parabolic while the rest are elliptic. Boundedness is demonstrated under smallness assumptions on the initial data in the former scenario, while no such constraints are necessary in the latter. Additionally, we provide estimates for the blow-up time of unbounded solutions in three dimensions, supported by numerical simulations.

This article deals with a class of chemotaxis systems describing mechanisms from mathematical biology. In the specific, for a rather general class of attraction-repulsion models, with nonlinear productions, diffusion, sensitivities and logistic term, we are interested in deriving interplays on the parameters involved in the problem capable to ensure globality and boundedness of related solutions. This project is precisely contextualized in the frame of a series of results dealing with local and nonlocal, and linear and nonlinear, attraction-repulsion chemotaxis systems. For these problems, rooms of improvements are still open; in this sense, this research exactly enhances and extends already known analyses in the literature. More specifically, a direct comparison with [Jiao, Jadlovsk\'a, Li, Nonlinear Anal. Real World Appl., 2023; Ren, Liu, Math. Models Methods Appl. Sci., 2020; Chiyo, Yokota, Z. Angew. Math. Phys., 2022; Columbu, Frassu, Viglialoro, Appl. Anal., 2023] is carried out.

The spread of the Sars-COV-2 pandemic in 2020 had a huge impact on the life course of all of us. This rapid spread has also caused an increase in the research production in topics related to COVID-19 with regard to different aspects. Italy has, unfortunately, been one of the first countries to be massively involved in the outbreak of the disease. In this paper we present an extensive scientometric analysis of the research production both at global (entire literature produced in the first 2 years after the beginning of the pandemic) and local level (COVID-19 literature produced by authors with an Italian affiliation). Our results showed that US and China are the most active countries in terms of number of publications and that the number of collaborations between institutions varies according to geographical distance. Moreover, we identified the medical-biological as the fields with the greatest growth in terms of literature production. Furthermore, we also better explored the relationship between the number of citations and variables obtained from the data set (e.g. number of authors per article). Using multiple correspondence analysis and quantile regression we shed light on the role of journal topics and impact factor, the type of article, the field of study and how these elements affect citations.

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces where given unbounded solutions blow-up also in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved.

We study some zero-flux attraction-repulsion chemotaxis models, with nonlinear production rates for the chemorepellent and the chemoattractant. This paper partially improves some known results in the literature and moreover solves an open question. The research is also complemented with numerical simulations in bi-dimensional domains.

The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of variation from two independent populations. In order to do this we rely on the Bayesian Discrepancy Measure recently introduced in the literature. Computing this Bayesian measure of evidence is straightforward when the coefficient of variation is a function of a single parameter of the distribution. In contrast, it becomes difficult when it is a function of more parameters, often requiring the use of MCMC methods. We calculate the Bayesian Discrepancy Measure by considering a variety of distributions whose coefficients of variation depend on more than one parameter. We consider also applications to real data. As far as we know, some of the examined problems have not yet been covered in the literature.

Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the first step, quantile regression is applied to each response separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional definition of quantiles, and can be used to capture important features of a multivariate response and assess the effects of covariates on the correlation structure. We apply the proposed method to analyze two different datasets.

Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national evaluation agencies, is to assess the research quality by the evaluation of a limited number of publications in a way that each publication is rated among $n$ classes. This method produces, for each institution, a distribution of the publications in the $n$ classes. In this paper we introduce a natural geometric way to compare these assessments by introducing an ad hoc distance from the performance of an institution to the best possible achievable assessment. Moreover, to avoid the methodological error of comparing non-homogeneous institutions, we introduce a {\em geometric score} based on such a distance. The latter represents the probability that an ideal institution, with the same configuration as the one under evaluation, performs worst. We apply our method, based on the geometric score, to rank, in two specific scientific areas, the Italian universities using the results of the evaluation exercise VQR 2011-2014.