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

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

Substrate Type and Concentration Differently Affect Colon Cancer Cells Ultrastructural Morphology, EMT Markers, and Matrix Degrading Enzymes

: Aim of the study was to understand the behavior of colon cancer LoVo-R cells (doxorubicin-resistant) vs. LoVo-S (doxorubicin sensitive) in the initial steps of extracellular matrix (ECM) invasion. We investigated how the matrix substrates Matrigel and type I collagen-mimicking the basement membrane (BM) and the normal or desmoplastic lamina propria, respectively-could affect the expression of epithelial-to-mesenchymal transition (EMT) markers, matrix-degrading enzymes, and phenotypes. Gene expression with RT-qPCR, E-cadherin protein expression using Western blot, and phenotypes using scanning electron microscopy (SEM) were analyzed. The type and different concentrations of matrix substrates differently affected colon cancer cells. In LoVo-S cells, the higher concentrated collagen, mimicking the desmoplastic lamina propria, strongly induced EMT, as also confirmed by the expression of Snail, metalloproteases (MMPs)-2, -9, -14 and heparanase (HPSE), as well as mesenchymal phenotypes. Stimulation in E-cadherin expression in LoVo-S groups suggests that these cells develop a hybrid EMT phenotype. Differently, LoVo-R cells did not increase their aggressiveness: no changes in EMT markers, matrix effectors, and phenotypes were evident. The low influence of ECM components in LoVo-R cells might be related to their intrinsic aggressiveness related to chemoresistance. These results improve understanding of the critical role of tumor microenvironment in colon cancer cell invasion, driving the development of new therapeutic approaches

Early treatment of Class III malocclusion with RME and facial mask: evaluation of dentoalveolar effects on digital dental casts

Aim: To analyse the dental effects on digital dental casts in subjects with Class III malocclusion treated with bonded Rapid Maxillary Expansion and Facial Mask (RME/FM). Materials and methods: A study group sample (SG) of 29 subjects (13 females and 16 males) and mean age of 7.4 years (SD 1.2 years) was selected. A bonded RME was placed and activated 1/4 of a turn per day until overcorrection of the transverse width. At the end of expansion, patients were given FMs and treated at least to a positive overjet. The SG was compared with a control group (CG) of 21 prepubertal subjects (9 females; 12 males) presenting with normal occlusion and mean age of 7.9 years (SD 1.6 years). For each subject of the SG and CG initial (pretreatment, T1) and final (post-treatment, T2) digital dental casts were available. Significant in between-group differences were tested with the Student's t-test. Results: The transverse dimension of the upper arch was significantly greater in SG vs. CG (IMAW: +2.6 mm; ICAW: +3.1 mm). Anterior arch length and arch depth were significantly smaller in SG when compared with CG (AAL: -3.2 mm, AD: -3.4 mm) at the end of therapy. Conclusion: The orthopaedic treatment with bonded RME/FM produced in subjects treated in the deciduous or early mixed dentition a significant expansion of the maxillary arch and mesialisation of the posterior teeth with a reduction of the arch depth