arXiv subjects
Publications and source records attributed to Lorenzo Fassina.
We study a natural class of normal functions on the moduli space of pointed curves and determine their rank at every point. We prove that the rank is maximal outside the corresponding stratum of Abelian differentials, while along this stratum it drops by exactly one. As a consequence, we describe the local geometry of the associated double ramification locus.
Let $[C]$ be a general point in the moduli space of curves $M_g$ with $g > 1$. Let $G \subset J(C)$ be a connected compact subgroup of real dimension $1$ of the Jacobian, and let $L$ be an even theta characteristic on $C$. We prove that $\{ζ\in G \mid H^0(C, L \otimes ζ) \neq 0\} = \emptyset$ if and only if $L \otimes ζ_G$ is an even theta characteristic on $C$, where $ζ_G$ is the unique non-trivial point of $G$ of order two.
We study sections of the relative Picard bundle of a family of curves of genus $g \geq 2$ through the rank of the associated normal function. Using Griffiths' formula for the infinitesimal invariant and higher Schiffer variations, we establish a numerical inequality relating the rank, the minimal support of a representing divisor and the modular dimension of the family. When the modular map is dominant, we obtain a sharp classification: equality occurs only for multiples of odd theta characteristics or of the canonical section. As applications, we derive geometric consequences for plane curves, obtaining results on intersections with very general quartic curves, in the spirit of the work of Chen-Riedl-Yeong, and with quintic curves.
Heart failure (HF) affects at least 26 million people worldwide, so predicting adverse events in HF patients represents a major target of clinical data science. However, achieving large sample sizes sometimes represents a challenge due to difficulties in patient recruiting and long follow-up times, increasing the problem of missing data. To overcome the issue of a narrow dataset cardinality (in a clinical dataset, the cardinality is the number of patients in that dataset), population-enhancing algorithms are therefore crucial. The aim of this study was to design a random shuffle method to enhance the cardinality of an HF dataset while it is statistically legitimate, without the need of specific hypotheses and regression models. The cardinality enhancement was validated against an established random repeated-measures method with regard to the correctness in predicting clinical conditions and endpoints. In particular, machine learning and regression models were employed to highlight the benefits of the enhanced datasets. The proposed random shuffle method was able to enhance the HF dataset cardinality (711 patients before dataset preprocessing) circa 10 times and circa 21 times when followed by a random repeated-measures approach. We believe that the random shuffle method could be used in the cardiovascular field and in other data science problems when missing data and the narrow dataset cardinality represent an issue.
The osteoinductive property of strontium was repeatedly proven in the last decades. Compelling $\textit{in vitro}$ data demonstrated that strontium hydroxyapatite nanoparticles exert a dual action, by promoting osteoblasts-driven matrix secretion and inhibiting osteoclasts-driven matrix resorption. Recombinant human bone morphogenetic protein 2 (rhBMP2) is a powerful osteoinductive biologic, used for the treatment of vertebral fractures and critically-sized bone defects. Although effective, the use of rhBMP2 has limitations due its recombinant morphogen nature. In this study, we examined the comparison between two osteoinductive agents: rhBMP2 and the innovative strontium-substituted hydroxyapatite nanoparticles. To test their effectiveness, we independently loaded Gelfoam sponges with the two osteoinductive agents and used the sponges as agent-carriers. Gelfoam are FDA-approved biodegradable medical devices used as delivery system for musculoskeletal defects. Their porous structure and spongy morphology make them attractive in orthopedic field. The abiotic characterization of the loaded sponges, involving ion release pattern and structure investigation, was followed by $\textit{in vivo}$ implantation onto the periosteum of healthy mice and comparison of the effects induced by each implant was performed. The results demonstrated the use of sponges loaded with strontium nanoparticles as potential bone grafts might provide better outcomes for complex fractures. Strontium nanoparticles are a novel and effective non-biologic treatment for bone injuries and can be used as novel powerful therapeutics for bone regeneration.
Human bone marrow-derived mesenchymal stem cells (hBM-MSCs) are considered a great promise in the repair and regeneration of bone. Considerable efforts have been oriented towards uncovering the best strategy to promote stem cells osteogenic differentiation. In previous studies, hBM-MSCs exposed to physical stimuli such as pulsed electromagnetic fields (PEMFs) or directly seeded on nanostructured titanium surfaces ($TiO_{2}$) were shown to improve their differentiation to osteoblasts in osteogenic condition. In the present study, the effect of a daily PEMF-exposure on osteogenic differentiation of hBM-MSCs seeded onto nanostructured $TiO_{2}$ (with clusters under 100 nm of dimension) was investigated. $TiO_{2}$-seeded cells were exposed to PEMF (magnetic field intensity: 2 mT; intensity of induced electric field: 5 mV; frequency: 75 Hz) and examined in terms of cell physiology modifications and osteogenic differentiation. Results showed that PEMF exposure affected $TiO_{2}$-seeded cells osteogenesis by interfering with selective calcium-related osteogenic pathways, and greatly enhanced hBM-MSCs osteogenic features such as the expression of early/late osteogenic genes and protein production (e.g., ALP, COL-I, osteocalcin and osteopontin) and ALP activity. Finally, PEMF-treated cells resulted to secrete into conditioned media higher amounts of BMP-2, DCN and COL-I than untreated cell cultures. These findings confirm once more the osteoinductive potential of PEMF, suggesting that its combination with $TiO_{2}$ nanostructured surface might be a great option in bone tissue engineering applications.
Mechanical function of the heart during open-chest cardiac surgery is exclusively monitored by echocardiographic techniques. However, little is known about local kinematics, particularly for the reperfused regions after ischemic events. We report a novel imaging modality, which extracts local and global kinematic parameters from videos of $\textit{in situ}$ beating hearts, displaying live video cardiograms of the contraction events. A custom algorithm tracked the movement of a video marker positioned $\textit{ad hoc}$ onto a selected area and analyzed, during the entire recording, the contraction trajectory, displacement, velocity, acceleration, kinetic energy and force. Moreover, global epicardial velocity and vorticity were analyzed by means of Particle Image Velocimetry tool. We validated our new technique by i) computational modeling of cardiac ischemia, ii) video recordings of ischemic/reperfused rat hearts, iii) videos of beating human hearts before and after coronary artery bypass graft, and iv) local Frank-Starling effect. In rats, we observed a decrement of kinematic parameters during acute ischemia and a significant increment in the same region after reperfusion. We detected similar behavior in operated patients. This modality adds important functional values on cardiac outcomes and supports the intervention in a contact-free and non-invasive mode. Moreover, it does not require particular operator-dependent skills.
We have studied beating mouse cardiac syncytia $\textit{in vitro}$ in order to assess the inotropic, ergotropic, and chronotropic effects of both increasing and decreasing hydrostatic pressures. In particular, we have performed an image processing analysis to evaluate the kinematics and the dynamics of those pressure-loaded beating syncytia starting from the video registration of their contraction movement. By this analysis, we have verified the Frank-Starling law of the heart in $\textit{in vitro}$ beating cardiac syncytia and we have obtained their geometrical-functional classification.
We have implemented field models and performed a detailed numerical dosimetry inside our extremely-low-frequency electromagnetic bioreactor which has been successfully used in $\textit{in vitro}$ Biotechnology and Tissue Engineering researches. The numerical dosimetry permitted to map the magnetic induction field (maximum module equal to about 3.3 mT) and to discuss its biological effects in terms of induced electric currents and induced mechanical forces (compression and traction). So, in the frame of the tensegrity-mechanotransduction theory of Ingber, the study of these electromagnetically induced mechanical forces could be, in our opinion, a powerful tool to understand some effects of the electromagnetic stimulation whose mechanisms remain still elusive.