Geometric k-normality of curves and applications

The notion of geometric k-normality for curves is introduced in complete generality and is investigated in the case of nodal and cuspidal curves living on several types of surfaces. We discuss and suggest some applications of this notion to the study of Severi varieties of nodal curves on surfaces of general type and on the plane.Comment: 15 page

Collision trajectories and regularisation of two-body problem on S2S^2

In this paper, we investigate collision orbits of two identical bodies placed on the surface of a two-dimensional sphere and interacting via an attracting potential of the form $V(q)=-\cot(q)$, where $q$ is the angle formed by the position vectors of the two bodies. We describe the $\omega$-limit set of the variables in the symplectically reduced system corresponding to initial data that lead to collisions. Furthermore we provide a geometric description of the dynamics. Lastly, we regularise the system and investigate its behaviour on near collision orbits. This involves the study of completely degenerate equilibria and the use of high-dimensional non-homogenous blow-ups

Open WDVV equations and Virasoro constraints

In their fundamental work, Dubrovin and Zhang, generalizing the Virasoro equations for the genus 0Gromov–Witten invariants, proved theVirasoro equations for a descendent potential in genus 0 of an arbitrary conformal Frobenius manifold. More recently, a remarkable system of partial differential equations, called the open WDVV equations, appeared in the work of Horev and Solomon. This system controls the genus 0 open Gromov–Witten invariants. In our paper, for an arbitrary solution of the open WDVV equations, satisfying a certain homogeneity condition, we construct a descendent potential in genus 0 and prove an open analog of the Virasoro equations.We also present conjectural open Virasoro equations in all genera and discuss some examples

On bi-Hamiltonian deformations of exact pencils of hydrodynamic type

In this paper we are interested in non trivial bi-Hamiltonian deformations of the Poisson pencil \omega_{\lambda}=\omega_2+\lambda \omega_1=u\delta'(x-y)+\f{1}{2}u_x\delta(x-y)+\lambda\delta'(x-y). Deformations are generated by a sequence of vector fields $\{X_2, X_4,...\}$, where each $X_{2k}$ is homogenous of degree $2k$ with respect to a grading induced by rescaling. Constructing recursively the vector fields $X_{2k}$ one obtains two types of relations involving their unknown coefficients: one set of linear relations and an other one which involves quadratic relations. We prove that the set of linear relations has a geometric meaning: using Miura-quasitriviality the set of linear relations expresses the tangency of the vector fields $X_{2k}$ to the symplectic leaves of $\omega_1$ and this tangency condition is equivalent to the exactness of the pencil $\omega_{\lambda}$. Moreover, extending the results of [17], we construct the non trivial deformations of the Poisson pencil $\omega_{\lambda}$, up to the eighth order in the deformation parameter, showing therefore that deformations are unobstructed and that both Poisson structures are polynomial in the derivatives of $u$ up to that order.Comment: 34 pages, revised version. Proof of Theorem 16 completely rewritten due to an error in the first versio

ECU-oriented models for NOx prediction. Part 1: a mean value engine model for NOx prediction

The implantation of nitrogen oxide sensors in diesel engines was proposed in order to track the emissions at the engine exhaust, with applications to the control and diagnosis of the after-treatment devices. However, the use of models is still necessary since the output from these sensors is delayed and filtered. The present paper deals with the problem of nitrogen oxide estimation in turbocharged diesel engines combining the information provided by both models and sensors. In Part 1 of this paper, a control-oriented nitrogen oxide model is designed. The model is based on the mapping of the nitrogen oxide output and a set of corrections which account for the variations in the intake and ambient conditions, and it is designed for implementation in commercial electronic control units. The model is sensitive to variations in the engine's air path, which is solved through the engine volumetric efficiency and the first-principle equations but disregards the effect of variation in the injection settings. In order to consider the effect of the thermal transients on the in-cylinder temperature, the model introduces a dynamic factor. The model behaves well in both steady-state operation and transient operation, achieving a mean average error of 7% in the steady state and lower than 10% in an exigent sportive driving mountain profile cycle. The relatively low calibration effort and the model accuracy show the feasibility of the model for exhaust gas recirculation control as well as onboard diagnosis of the nitrogen oxide emissions.Guardiola, C.; Pla Moreno, B.; Blanco-Rodriguez, D.; Calendini, PO. (2015). ECU-oriented models for NOx prediction. Part 1: a mean value engine model for NOx prediction. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. 229(8):992-1015. doi:10.1177/0954407014550191S9921015229

A New Generation of Hydrogen-Fueled Hybrid Propulsion Systems for the Urban Mobility of the Future

The H2-ICE project aims at developing, through numerical simulation, a new generation of hybrid powertrains featuring a hydrogen-fueled Internal Combustion Engine (ICE) suitable for 12 m urban buses in order to provide a reliable and cost-effective solution for the abatement of both CO2 and criteria pollutant emissions. The full exploitation of the potential of such a traction system requires a substantial enhancement of the state of the art since several issues have to be addressed. In particular, the choice of a more suitable fuel injection system and the control of the combustion process are extremely challenging. Firstly, a high-fidelity 3D-CFD model will be exploited to analyze the in-cylinder H2 fuel injection through supersonic flows. Then, after the optimization of the injection and combustion process, a 1D model of the whole engine system will be built and calibrated, allowing the identification of a “sweet spot” in the ultra-lean combustion region, characterized by extremely low NOx emissions and, at the same time, high combustion efficiencies. Moreover, to further enhance the engine efficiency well above 40%, different Waste Heat Recovery (WHR) systems will be carefully scrutinized, including both Organic Rankine Cycle (ORC)-based recovery units as well as electric turbo-compounding. A Selective Catalytic Reduction (SCR) aftertreatment system will be developed to further reduce NOx emissions to near-zero levels. Finally, a dedicated torque-based control strategy for the ICE coupled with the Energy Management Systems (EMSs) of the hybrid powertrain, both optimized by exploiting Vehicle-To-Everything (V2X) connection, allows targeting H2 consumption of 0.1 kg/km. Technologies developed in the H2-ICE project will enhance the know-how necessary to design and build engines and aftertreatment systems for the efficient exploitation of H2 as a fuel, as well as for their integration into hybrid powertrains

The Antidiabetic Effect of MSCs Is Not Impaired by Insulin Prophylaxis and Is Not Improved by a Second Dose of Cells

Type 1 diabetes mellitus (T1D) is due to autoimmune destruction of pancreatic beta-cells. Previously, we have shown that intravenously administered bone marrow-derived multipotent mesenchymal stromal cells (MSCs) allows pancreatic islet recovery, improves insulin secretion and reverts hyperglycemia in low doses streptozotocin (STZ)-induced diabetic mice. Here we evaluate whether insulin prophylaxis and the administration of a second dose of cells affect the antidiabetic therapeutic effect of MSC transplantation. Insulitis and subsequent elimination of pancreatic beta-cells was promoted in C57BL/6 mice by the injection of 40 mg/kg/day STZ for five days. Twenty-four days later, diabetic mice were distributed into experimental groups according to if they received or not insulin and/or one or two doses of healthy donor-derived MSCs. Three and half months later: glycemia, pancreatic islets number, insulinemia, glycated hemoglobin level and glucose tolerance were determined in animals that did not received exogenous insulin for the last 1.5 months. Also, we characterized MSCs isolated from mice healthy or diabetic. The therapeutic effect of MSC transplantation was observed in diabetic mice that received or not insulin prophylaxis. Improvements were similar irrespective if they received one or two doses of cells. Compared to MSCs from healthy mice, MSCs from diabetic mice had the same proliferation and adipogenic potentials, but were less abundant, with altered immunophenotype and no osteogenic potential

Mitogen-activated protein kinase activity drives cell trajectories in colorectal cancer

In colorectal cancer, oncogenic mutations transform a hierarchically organized and homeostatic epithelium into invasive cancer tissue lacking visible organization. We sought to define transcriptional states of colorectal cancer cells and signals controlling their development by performing single-cell transcriptome analysis of tumors and matched non-cancerous tissues of twelve colorectal cancer patients. We defined patient-overarching colorectal cancer cell clusters characterized by differential activities of oncogenic signaling pathways such as mitogen-activated protein kinase and oncogenic traits such as replication stress. RNA metabolic labeling and assessment of RNA velocity in patient-derived organoids revealed developmental trajectories of colorectal cancer cells organized along a mitogen-activated protein kinase activity gradient. This was in contrast to normal colon organoid cells developing along graded Wnt activity. Experimental targeting of EGFR-BRAF-MEK in cancer organoids affected signaling and gene expression contingent on predictive KRAS/BRAF mutations and induced cell plasticity overriding default developmental trajectories. Our results highlight directional cancer cell development as a driver of non-genetic cancer cell heterogeneity and re-routing of trajectories as a response to targeted therapy