Comparison Principles for subelliptic equations of Monge-Ampere type

We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group

Genes and primary headaches: discovering new potential therapeutic targets

Genetic studies have clearly shown that primary headaches (migraine, tension-type headache and cluster headache) are multifactorial disorders characterized by a complex interaction between different genes and environmental factors. Genetic association studies have highlighted a potential role in the etiopathogenesis of these disorders for several genes related to vascular, neuronal and neuroendocrine functions. A potential role as a therapeutic target is now emerging for some of these genes. The main purpose of this review is to describe new advances in our knowledge regarding the role of MTHFR, KCNK18, TRPV1, TRPV3 and HCRTR genes in primary headache disorders. Involvement of these genes in primary headaches, as well as their potential role in the therapy of these disorders, will be discussed

Optimal metabolic strategies for microbial growth in stationary random environments

In order to grow in any given environment, bacteria need to collect information about the medium composition and implement suitable growth strategies by adjusting their regulatory and metabolic degrees of freedom. In the standard sense, optimal strategy selection is achieved when bacteria grow at the fastest rate possible in that medium. While this view of optimality is well suited for cells that have perfect knowledge about their surroundings (e.g. nutrient levels), things are more involved in uncertain or fluctuating conditions, especially when changes occur over timescales comparable to (or faster than) those required to organize a response. Information theory however provides recipes for how cells can choose the optimal growth strategy under uncertainty about the stress levels they will face. Here we analyse the theoretically optimal scenarios for a coarse-grained, experiment-inspired model of bacterial metabolism for growth in a medium described by the (static) probability density of a single variable (the `stress level'). We show that heterogeneity in growth rates consistently emerges as the optimal response when the environment is sufficiently complex and/or when perfect adjustment of metabolic degrees of freedom is not possible (e.g. due to limited resources). In addition, outcomes close to those achievable with unlimited resources are often attained effectively with a modest amount of fine-tuning. In other terms, heterogeneous population structures in complex media may be rather robust with respect to the amounts of cellular resources available to probe the environment and adjust reaction rates

Disentangling the Information Flood on OSNs: Finding Notable Posts and Topics

Online Social Networks (OSNs) are an integral part of modern life for sharing thoughts, stories, and news. An ecosystem of influencers generates a flood of content in the form of posts, some of which have an unusually high level of engagement with the influencer’s fan base. These posts relate to blossoming topics of discussion that generate particular interest among users: The COVID-19 pandemic is a prominent example. Studying these phenomena provides an understanding of the OSN landscape and requires appropriate methods. This paper presents a methodology to discover notable posts and group them according to their related topic. By combining anomaly detection, graph modelling and community detection techniques, we pinpoint salient events automatically, with the ability to tune the amount of them. We showcase our approach using a large Instagram dataset and extract some notable weekly topics that gained momentum from 1.4 million posts. We then illustrate some use cases ranging from the COVID-19 outbreak to sporting events

The Secondary-Tertiary Transition in Mathematics. Successful Students in Crisis

The transition from secondary school into university mathematics – also referred to as secondary-tertiary transition (STT) – is a sensitive moment for many students, also for those who have achieved high marks at the end of their schooling and are considered excellent in mathematics in the school context. The cognitive aspect has interested researchers since the late seventies, but the interest in other two aspects (social and emotional aspects) is growing. Recently we have investigated the emotional aspect further and we will report here on some of our findings underlying the necessary developments

Overview on the Link Between the Complement System and Auto-Immune Articular and Pulmonary Disease

Complement system (CS) dysregulation is a key factor in the pathogenesis of different autoimmune diseases playing a central role in many immune innate and adaptive processes. Rheumatoid arthritis (RA) is a chronic inflammatory disease characterized by ta breach of self -tolerance leading to a synovitis and extra-articular manifestations. The CS is activated in RA and seems not only to mediate direct tissue damage but also play a role in the initiation of RA pathogenetic mechanisms through interactions with citrullinated proteins. Interstitial lung disease (ILD) represents the most common extra-articular manifestation that can lead to progressive fibrosis. In this review, we focused on the evidence of CS dysregulation in RA and in ILD, and highlighted the role of the CS in both the innate and adaptive immune responses in the development of diseases, by using idiopathic pulmonary fibrosis as a model of lung disease. As a proof of concept, we dissected the evidence that several treatments used to treat RA and ILD such as glucocorticoids, pirfenidone, disease modifying antirheumatic drugs, targeted biologics such as tumor necrosis factor (TNF)-inhibitors, rituximab, tocilizumab, and nintedanib may act indirectly on the CS, suggesting that the CS might represent a potential therapeutic target in these complex diseases

Relationship between fitness and heterogeneity in exponentially growing microbial populations

Despite major environmental and genetic differences, microbial metabolic networks are known to generate consistent physiological outcomes across vastly different organisms. This remarkable robustness suggests that, at least in bacteria, metabolic activity may be guided by universal principles. The constrained optimization of evolutionarily motivated objective functions, such as the growth rate, has emerged as the key theoretical assumption for the study of bacterial metabolism. While conceptually and practically useful in many situations, the idea that certain functions are optimized is hard to validate in data. Moreover, it is not always clear how optimality can be reconciled with the high degree of single-cell variability observed in experiments within microbial populations. To shed light on these issues, we develop an inverse modeling framework that connects the fitness of a population of cells (represented by the mean single-cell growth rate) to the underlying metabolic variability through the maximum entropy inference of the distribution of metabolic phenotypes from data. While no clear objective function emerges, we find that, as the medium gets richer, the fitness and inferred variability for Escherichia coli populations follow and slowly approach the theoretically optimal bound defined by minimal reduction of variability at given fitness. These results suggest that bacterial metabolism may be crucially shaped by a population-level trade-off between growth and heterogeneity