Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Large eddy simulations of solitons colliding with intrusions

The dynamics of lock-release Intrusive Gravity Currents (IGCs) generating Internal Solitary Waves (ISWs) are investigated by three-dimensional large eddy simulations. We set the numerical, laboratory-scale domain in order to release a uniform fluid in multi-layer, stratified ambient, exciting pycnocline displacements. By adopting different initial settings, we analyzed the influence of the ambient stratification on both IGCs and ISWs features. We present the main flow dynamics and the time evolution of IGC and ISW front and trough positions, respectively. During the simulations, the ISW is allowed to reach the vertical wall at the end of the domain, and it undergoes reflection. We then analyzed the interaction between the IGC and the reflected ISW: the wave is observed to accelerate as it is pushed upwards by the intrusion, which, in turns, flows below the ISW, decelerating. By analyzing instantaneous velocity fields and flow rates, we found that during this interaction, the ISW increases its celerity in response of the reduced area available for its propagation, partially occupied by the intrusion, and because the velocity field in the IGC interface surroundings acts to facilitate the ISW passage

Mixing in lock-release gravity currents propagating up a slope

Lock-exchange gravity currents propagating up a slope are investigated by large eddy simulations, focusing on the entrainment and mixing processes occurring between the dense current and the ambient fluid. Relevant parameters, such as the aspect ratio of the initial volume of dense fluid in the lock R, the angle between the bottom boundary and the horizontal direction \u3b8 and the depth aspect ratio \u3c6, are varied. The numerical results are compared with laboratory experiments and a good agreement is found. Entrainment and mixing in a lock-release gravity current are studied using different entrainment parameters and an energy budget method. The entrainment is found to depend on both Froude, Fr, and Reynolds, Re, numbers. In addition, the dependence of both entrainment and mixing on the parameters varied is discussed. The entrainment decreases with increasing steepness of the bottom and R. Irreversible mixing is not affected by the varied parameters during the slumping phase, while during the successive phases of motion, it is found to decrease with the increase of \u3b8 and R. Low entrainment and mixing occur for \u3c6 <

Bone marrow-derived cells can acquire cardiac stem cells properties in damaged heart

Experimental data suggest that cell-based therapies may be useful for cardiac regeneration following ischaemic heart disease. Bone marrow (BM) cells have been reported to contribute to tissue repair after myocardial infarction (MI) by a variety of humoural and cellular mechanisms. However, there is no direct evidence, so far, that BM cells can generate cardiac stem cells (CSCs). To investigate whether BM cells contribute to repopulate the Kit+ CSCs pool, we transplanted BM cells from transgenic mice, expressing green fluorescent protein under the control of Kit regulatory elements, into wild-type irradiated recipients. Following haematological reconstitution and MI, CSCs were cultured from cardiac explants to generate 'cardiospheres', a microtissue normally originating in vitro from CSCs. These were all green fluorescent (i.e. BM derived) and contained cells capable of initiating differentiation into cells expressing the cardiac marker Nkx2.5. These findings indicate that, at least in conditions of local acute cardiac damage, BM cells can home into the heart and give rise to cells that share properties of resident Kit+ CSCs

Arginine-Based Toothpaste Induces Calcium-Phosphates Deposits on Dentin Surface and Tubules

Objective: To test the ability of a calcium carbonate-containing toothpaste for dentinal hypersensitivity to occlude the exposed open tubules of dentin surface. Method: Dentine slices (0.9±0.1 thick) and crown segments (1.5±0.3 cm thick) from human third molars were used. Elmex Sensitive Professional toothpaste (GABA Int AG, Therwill, Switzerland) containing as main active ingredients arginine (8%), sodium monofluorophosphate (1450 ppm Fˉ) and calcium carbonate, was applied (3 min) on coronal dentin surface. Fluid flow/permeation through the dentin thickness (i.e. permeability or hydraulic conductance, Lp in microliters/min) was evaluated using a digital fluid flow-meter after smear layer formation, after EDTA treatment, after Elmex toothpaste treatment (t=0) and after soaking for 1, 7, 28 days in simulated body fluid (HBSS). Tubules occlusion, elemental analysis and mineral content were studied by ESEM-EDX. Toothpaste penetration inside dentinal tubules was analyzed by laser confocal microscopy using calcein as tracer. Result: Lp of EDTA-treated dentin significantly decreased after treatment with Elmex toothpaste (-73,32% at t=0) and after soaking in HBSS the Lp values further decreased (-77,69% at 24h, -78,18% at 7d, -83,01% at 28d). After 24h and 7d in HBSS, ESEM on Elmex-treated dentin showed the presence of precipitates on dentin surface and in the dentinal tubules; EDX revealed N (from arginine) and F (from monofluorophosphate) of the toothpaste. Lp remained significantly lower (-78,18%) than EDTA- treated control dentin. After 28d in HBSS, a calcium phosphate layer was detected on dentin surface so tubules were not visible. EDX detected F and no N. No CaP deposits were found on EDTA-treated dentin soaked in HBSS. Confocal microscopy showed an average penetration depth of the toothpaste into the dentinal tubules of ~85 microns. Conclusion: Elmex sensitive toothpaste can reduce the fluid movement into the exposed dentinal tubules and favour the formation of calcium phosphate minerals

Arginine-calcium carbonate professional treatment for tubules occlusion in hypersensitive dentin

Objective: To test the tubules occlusion of an arginine-based professional treatment for hypersensitive dentin. Method: Dentin segments/discs were prepared from erupted sound molars. Elmex sensitive professional desensitizing paste (GABA Int. by Colgate Oral Pharmaceuticals, Dallas, USA) containing arginine 8% and calcium carbonate was applied on EDTA-treated dentin for 20s at 1000rpm using a prophy cup, following the manufacturer directions. The excess was removed using a microbrush then the dentin disc was gently rinsed and immersed in 20mL of simulated body fluid (Hank\u2019s Balanced Salt Solution, HBSS) at 37\ub0C. After 24h, 7 and 28d the dentin surface was analyzed by ESEM-EDX to evaluate the tubules occlusion and the mineral content. Elmex paste mixed with calcein solution 1% was used to evaluate its penetration depth into the tubules by confocal microscopy. Result: After 24h in HBSS, ESEM-EDX analyses on Elmex-treated dentin showed the presence of precipitates on dentin surface and in the dentinal tubules, relevant amount of N(16-19 wt%, demonstrating the presence of arginine and Ca/P molar ratio 653.0. Confocal microscopy showed a penetration of the paste into the dentinal tubules to a mean depth of approx 50 microns (maximum depth penetration 100 microns). ESEM showed the presence of many tubules still obturated by material after 7d in HBSS; EDX found N (approx 19 wt%) and Ca/P molar ratio was 2.43. After 28d in HBSS a coating of calcium phosphate deposits covered the dentin surface so tubules were not visible; EDX detected N (6-7 wt%) and showed a Ca/P molar ratio of 2.14. Conclusion: Elmex sensitive professional paste can obturate the dentinal tubules and adhere to the dentin surface. Evidences of mineralizing properties have been found by the deposition of calcium and phosphate-containing minerals within the dentinal tubules and the formation of a calcium phosphate protective layer on the dentin surface

Redox Imbalance in Neurological Disorders in Adults and Children

Oxygen is a central molecule for numerous metabolic and cytophysiological processes, and, indeed, its imbalance can lead to numerous pathological consequences. In the human body, the brain is an aerobic organ and for this reason, it is very sensitive to oxygen equilibrium. The consequences of oxygen imbalance are especially devastating when occurring in this organ. Indeed, oxygen imbalance can lead to hypoxia, hyperoxia, protein misfolding, mitochondria dysfunction, alterations in heme metabolism and neuroinflammation. Consequently, these dysfunctions can cause numerous neurological alterations, both in the pediatric life and in the adult ages. These disorders share numerous common pathways, most of which are consequent to redox imbalance. In this review, we will focus on the dysfunctions present in neurodegenerative disorders (specifically Alzheimer's disease, Parkinson's disease and amyotrophic lateral sclerosis) and pediatric neurological disorders (X-adrenoleukodystrophies, spinal muscular atrophy, mucopolysaccharidoses and Pelizaeus-Merzbacher Disease), highlighting their underlining dysfunction in redox and identifying potential therapeutic strategies