Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

Bone-implant interface. Evaluation of osteoblastic cells behavior on nanopatterned titanium surfaces: an in vitro analysis

Protein-adsorption occurs immediately following implantation of biomaterials. It is unknown at which extent protein-adsorption impacts the cellular events at bone-implant interface. To investigate this question, we compared the in-vitro outcome of osteoblastic cells grown onto titanium substrates and glass as control, by modulating the exposure to serum-derived proteins. Substrates consisted of 1) polished titanium disks; 2) polished disks nanotextured with H2SO4/H2O2; 3) glass. In the pre-adsorption phase, substrates were treated for 1h with αMEM alone (M-noFBS) or supplemented with 10%-foetal-bovine-serum (M-FBS). MC3T3-osteoblastic-cells were cultured on the pre-treated substrates for 3h and 24h, in M-noFBS and M-FBS. Subsequently, the culture medium was replaced with M-FBS and cultures maintained for 3 and 7days. Cell-number was evaluated by: Alamar-Blue and MTT assay. Mitotic- and osteogenic-activities were evaluated through fluorescence-optical-microscope by immunolabeling for Ki-67 nuclear-protein and Osteopontin. Cellular morphology was evaluated by SEM-imaging. Data were statistically analyzed using ANOVA-test, (p<0.05). At day3 and day7, the presence or absence of serum-derived proteins during the pre-adsorption phase had not significant effect on cell-number. Only the absence of FBS during 24h of culture significantly affected cell-number (p<0.0001). Titanium surfaces performed better than glass, (p<0.01). The growth rate of cells between day3 and 7 was not affected by the initial absence of FBS. Immunolabeling for Ki-67 and Osteopontin showed that the mitotic- and osteogenic- activity were ongoing at 72h. SEM-analysis revealed that the absence of FBS had no major influence on cell-shape. • Physico-chemical interactions without mediation by proteins are sufficient to sustain the initial phase of culture and guide osteogenic-cells toward differentiation. • The challenge is avoiding adsorption of ‘undesirables’ molecules that negatively impact on the cueing cells receive from surface. This may not be a problem in healthy patients, but may have an important role in medically-compromised-individuals in whom the composition of tissue-fluids is altered.