Metastability of the Ising model with random interaction coefficients

In this Ph.D. thesis we present results on metastability of random modifications of Ising spin systems which evolve with Glauber dynamics. Their Hamiltonians have random and possibly inhomogeneous interaction coefficients. We study these models at fixed temperature, with constant external magnetic field and in the large volume limit. The stochastic modification adds a level of randomness to the models and makes the direct study of metastability usually very difficult. Therefore, our main strategy consists in studying the model with random interaction coefficients by comparison with the model where these coefficients are replaced by their expectations. Here the latter model is called annealed model. In the first part of this thesis we summarise a joint paper with A. Bovier and E. Pulvirenti (2021). Therein we studied metastability of the Ising model on the dense Erdos-Rényi random graph with constant edge probability, also called randomly dilute Curie-Weiss model (RDCW), by comparing it with the well-known Curie-Weiss model. The main novelty in the proofs is the application of Talagrand's concentration inequality to characterise the randomness of a certain generalised partition function. In the second part we prove a simple unpublished extension to more general models of the generalised partition function methods used in the first part. The third part contains a summary of a joint paper with A. Bovier and F. den Hollander (2022), in which we studied in detail metastability of an Ising model with random interaction coefficients having a product structure. The model we analysed is the annealed version of the Ising model on a Chung-Lu-like random graph with i.i.d. weights which have finite support (ICL). We provided detailed information on the metastable regime and analysed the mean metastable exit time, proving sharp asymptotic estimates and characterising its randomness up to leading order. In the last part we give an overview on how the results of the first part were extended to a wide class of spin systems with more general random interaction coefficients, in a recent joint work with A. Bovier, F. den Hollander, E. Pulvirenti and M. Slowik. This class of models includes Ising models on various inhomogeneous dense random graphs (e.g. ICL) and randomly diluted spin models. In addition to estimates on the tails of the random mean metastable exit times (showed also in the first part for RDCW), we provided estimates on their moments and conditions on metastability, always in comparison with the annealed model. The methods used include McDiarmid's inequality and novel localisation techniques developed by Schlichting and Slowik (2019)

Helicobacter pylori Infection and Diabetes Mellitus

Helicobacter pylori colonizes the stomach and causes chronic gastritis, which most often remains asymptomatic. However, in a small proportion of infected persons, it causes peptic ulcers and gastric cancer. We reviewed recent evidence of the association between H. pylori infection and diabetes mellitus (DM). Numerous studies have shown a positive association between H. pylori infection and DM, however, findings are still conflicting. Such a link is biologically plausible, given the importance of the stomach in the homeostasis of systems outside the digestive tract; however, the mechanisms by which H. pylori might affect the risk of DM are not clear. Current knowledge indicates that H. pylori infection can affect the regulation of ghrelin and leptin, two hormones that play central roles in energy homeostasis in humans. Yet, methodological limitations are present in studies that addressed the relationships of H. pylori infection with DM and with possible risk factors for DM, including inadequate control of confounders. The important question of whether H. pylori eradication might be beneficial for glycemic control in diabetic patients is still unresolved. Future well-designed studies are needed to address these research questions, which are of clinical and great public health significance

LINGUA, IDENTITÀ E CULTURA IN ADOLESCENZA. ANTOLOGIA MULTICULTURALE PER LA SCUOLA MEDIA

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Effect of Gutta Percha on the Retention of a Post Using Different Cements

This study evaluated the effect of residual gutta percha on the retention strength of prefabricated post cemented with four different cements. Forty intact mandibular single canal canines or premolars were selected for standardized size and quality, endodontically treated, and decoronated to the cementoenamel junction. A post space was prepared to accommodate Para post XP size 4 (Coltene, Whaledent Inc., Cuy Falls, Ohio) to a depth of 8 mm. The Obtura heated gutta percha system was used to inject a very thin line of gutta percha along one lateral wall to the depth of the future post. Forty obturated teeth were randomly divided into four groups. Four different cements were used in each group to cement the posts as follows. Posts in group 1 were cemented with zinc phosphate cement (Fleck\u27s, Mizzy Inc Cherry Hill NJ). Posts in group 2 were cemented with glass ionomer cement (Ketac-Cem (Applicap capsule 3M ESPE, Dental product, ST. Paul MN). Posts in group 3 were cemented with resin modified glass ionomer cement (Rely-X, 3M ESPE, Dental Product, St. Paul MN). And posts in group 4 were cemented with Composite resin cement (Hi-X, Bisco, Irving Park Road, Schaumburg, IF). The cements were mixed according to the manufacturer\u27s instructions. The teeth were then mounted in a cylinder embedded with epoxy resin to enable subsequent post removal in a direction parallel to the long axis of the para post. The specimens were mounted on the instron machine and posts engaged by a retentive grip to perform the pull test. A constantly increasing tensile force was applied at a crosshead speed of 0.5 lbs/inch2 to the posts until failure. The force required to remove the posts were recorded in lbs/inch2. Complete removal of posts from the canals were achieved successfully in all the specimens in groups 1-3. Removal of the posts from the canals in group 4 was not achieved. Subsequently, further testing of group 4 specimens was not feasible. Specimens of groups 1 to 3 were further tested without the existence of the gutta percha on the lateral walls of the canals and were referred to as group 1B, 2B, 3B respectively. Results from these tests were recorded and compared to evaluate the effect of the remaining gutta percha on the tensile strength necessary to pull the posts from the canals. The same steps followed in the previous cementation of groups 1-3 were followed again except that post space was free from the gutta percha on the lateral walls. Following the same testing protocol described earlier the specimens were tested to failure. The forces required to remove the posts were recorded and then statistically analyzed using Mann-Whitney U and Kruskal-Wallis Ranks tests at the significance level of α = 0.05. Residual gutta percha present in the post space indicated a statistically significant difference in retention strength among the groups p \u3c 0.0001. There was also a significant difference in the retention strength among groups 1B, 2B and 3B p = 0.008. There was no statistically significant difference in retention strength between specimens cemented with resin modified glass ionomer cement (Rely-X) with or without gutta percha present p = 0.156

Metastability of Glauber dynamics with inhomogeneous coupling disorder

We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e. where spins flip with Metropolis rates at inverse temperature $\beta$. We identify conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This work provides an extension of the results known for the Ising model on the the Erd\H{o}s-R\'enyi random graph. The proofs use the potential-theoretic approach to metastability in combination with concentration inequalities.Comment: 30 page