Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Skeletal muscle remodeling in response to eccentric vs. concentric loading: morphological, molecular, and metabolic adaptations

Skeletal muscle contracts either by shortening or lengthening (concentrically or eccentrically, respectively); however, the two contractions substantially differ from one another in terms of mechanisms of force generation, maximum force production and energy cost. It is generally known that eccentric action s generate greater force than isometric and concentric contractions and at a lower metabolic cost. Hence, by virtue of the greater mechanical loading involved in active lengthening, eccentric resistance training (ECC RT) is assumed to produce greater hypertrophy than concentric resistance training (CON RT). Nonetheless, prevalence of either ECC RT or CON RT in inducing gains in muscle mass is still an open issue, with some studies reporting greater hypertrophy with eccentric, some with concentric and some with similar hypertrophy within both training modes. Recent observations suggest that such hypertrophic responses to lengthening vs. shortening contractions are achieved by different adaptations in muscle architecture. Whilst the changes in muscle protein synthesis in response to acute and chronic concentric and eccentric exercise bouts seem very similar, the molecular mechanisms regulating the myogenic adaptations to the two distinct loading stimuli are still incompletely understood. Thus, the present review aims to, (a) critically discuss the literature on the contribution of eccentric vs. concentric loading to muscular hypertrophy and structural remodeling, and, (b) clarify the molecular mechanisms that may regulate such adaptations. We conclude that, when matched for either maximum load or work, similar increase in muscle size is found between ECC and CON RT. However, such hypertrophic changes appear to be achieved through distinct structural adaptations, which may be regulated by different myogenic and molecular responses observed between lengthening and shortening contractions

Using Networks To Understand Medical Data: The Case of Class III Malocclusions

A system of elements that interact or regulate each other can be represented by a mathematical object called a network. While network analysis has been successfully applied to high-throughput biological systems, less has been done regarding their application in more applied fields of medicine; here we show an application based on standard medical diagnostic data. We apply network analysis to Class III malocclusion, one of the most difficult to understand and treat orofacial anomaly. We hypothesize that different interactions of the skeletal components can contribute to pathological disequilibrium; in order to test this hypothesis, we apply network analysis to 532 Class III young female patients. The topology of the Class III malocclusion obtained by network analysis shows a strong co-occurrence of abnormal skeletal features. The pattern of these occurrences influences the vertical and horizontal balance of disharmony in skeletal form and position. Patients with more unbalanced orthodontic phenotypes show preponderance of the pathological skeletal nodes and minor relevance of adaptive dentoalveolar equilibrating nodes. Furthermore, by applying Power Graphs analysis we identify some functional modules among orthodontic nodes. These modules correspond to groups of tightly inter-related features and presumably constitute the key regulators of plasticity and the sites of unbalance of the growing dentofacial Class III system. The data of the present study show that, in their most basic abstraction level, the orofacial characteristics can be represented as graphs using nodes to represent orthodontic characteristics, and edges to represent their various types of interactions. The applications of this mathematical model could improve the interpretation of the quantitative, patient-specific information, and help to better targeting therapy. Last but not least, the methodology we have applied in analyzing orthodontic features can be applied easily to other fields of the medical science.</p

SEISMIC VULNERABILITY ASSESSMENT OF A MILITARY DRY DOCK IN MESSINA

The paper summarizes the studies conducted on the military dry dock in the Port of Messina (built in 1861), to assess the seismic vulnerability. For this work was conducted an accurate research on the historical sources of Technical Office of the Italian Civil Engineers, to know the construction methods, the operations made after the earthquake of 1908 and to increase the size on 1950. Studies have included the implementation of a finite element model for seismic analysis and with a simulation of construction stages. The analysis results are evaluated against mandatory italian design code to assess the seismic vulnerability of the structure

Equilibria, Stability, and Sensitivity for the Aerial Suspended Beam Robotic System subject to Parameter Uncertainty

This work studies how parametric uncertainties affect the cooperative manipulation of a cable-suspended beam-shaped load by means of two aerial robots not explicitly communicating with each other. In particular, the work sheds light on the impact of the uncertain knowledge of the model parameters available to an established communication-less force-based controller. First, we find the closed-loop equilibrium configurations in the presence of the aforementioned uncertainties, and then we study their stability. Hence, we show the fundamental role played in the robustness of the load attitude control by the internal force induced in the manipulated object by non-vertical cables. Furthermore, we formally study the sensitivity of the attitude error to such parametric variations, and we provide a method to act on the load position error in the presence of the uncertainties. Eventually, we validate the results through an extensive set of numerical tests in a realistic simulation environment including underactuated aerial vehicles and sagging-prone cables, and through hardware experiments

CCAAT/enhancer-binding proteins are key regulators of human type two deiodinase expression in a placenta cell line

An appropriate concentration of intracellular T(3) is a critical determinant of placenta development and function and is mainly controlled by the activity of type II deiodinase (D2). The levels of this enzyme are finely regulated in different tissues by coordinated transcriptional mechanisms, which rely on dedicated promoter sequences (e.g. cAMP response element and TATA elements) that impart inducibility and tissue specificity to Dio2 mRNA expression. Here we show that CCAAT enhancer-binding proteins α and β (C/EBPα and C/EBPβ) promote Dio2 expression in the trophoblastic cell line JEG3 through a conserved CCAAT element, which is a novel key component of the Dio2 promoter code that confers tissue-specific expression of D2 in these cells. Increased C/EBPs levels potently induce Dio2 transcription, whereas their ablation results in loss of Dio2 mRNA. By measuring the activity of several deletion and point mutant promoter constructs, we have identified the functional CCAAT element responsible for this effect, which is located in close proximity to the most 5' TATA box. Notably, this newly identified sequence is highly conserved throughout the species and binds in vivo and in vitro C/EBP, indicating the relevance of this regulatory mechanism. Together, our results unveil a novel mechanism of regulation of D2 expression in a trophoblastic cell line, which may play a relevant role during placenta development