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Antisynthetase syndrome (ASSD) is a rare clinical condition that is characterized by the occurrence of a classic clinical triad, encompassing myositis, arthritis, and interstitial lung disease (ILD), along with specific autoantibodies that are addressed to different aminoacyl tRNA synthetases (ARS). Until now, it has been unknown whether the presence of a different ARS might affect the clinical presentation, evolution, and outcome of ASSD. In this study, we retrospectively recorded the time of onset, characteristics, clustering of triad findings, and survival of 828 ASSD patients (593 anti-Jo1, 95 anti-PL7, 84 anti-PL12, 38 anti-EJ, and 18 anti-OJ), referring to AENEAS (American and European NEtwork of Antisynthetase Syndrome) collaborative group’s cohort. Comparisons were performed first between all ARS cases and then, in the case of significance, while using anti-Jo1 positive patients as the reference group. The characteristics of triad findings were similar and the onset mainly began with a single triad finding in all groups despite some differences in overall prevalence. The “ex-novo” occurrence of triad findings was only reduced in the anti-PL12-positive cohort, however, it occurred in a clinically relevant percentage of patients (30%). Moreover, survival was not influenced by the underlying anti-aminoacyl tRNA synthetase antibodies’ positivity, which confirmed that antisynthetase syndrome is a heterogeneous condition and that antibody specificity only partially influences the clinical presentation and evolution of this condition.
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the true cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the true cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
During my initial days here in Frankfurt, in October 2020 amidst the pandemic crisis, all my notes revolved around three articles by Bolthausen and Kistler, which now form the starting point of this work.
The ones introduced by Bolthausen and Kistler are abstract mean field spin glass models, reminiscent of Derrida’s Generalized Random Energy Model (GREM), which generalize the GREM while remaining rigorously solvable through large deviations methods and within a classical Boltzmann-Gibbs formalism. This allows to establish, by means of a second moment method, the associated free energy at the thermodynamic limit as an orthodox, infinite-dimensional, Boltzmann-Gibbs variational principle.
Dual Parisi formulas for the limiting free energy associated with these Hamiltonians hold, and are revealed to be the finite-dimensional (”collapsed”) versions of the classical, infinite-dimensional Boltzmann-Gibbs principles.
In the 2nd chapter of this thesis, we uncover the hidden yet essential connection between real-world spin glasses, like the Sherrington-Kirkpatrick (SK) model and the random energy models. The crucial missing element is that of TAP-free energies: integrating it with the framework introduced by Bolthausen and Kistler results in a correction to the Parisi formula for the free energy, which brings it much, much closer to the ”true” Parisi solution for the SK-model. In other words, we can identify the principles that transform the classical Boltzmann-Gibbs maximization into the unorthodox (and puzzling) Parisi minimization.
This arguably stands as the primary achievement of this work.