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PubblicazioneSome new applications of Γ-convergence to free discontinuity problems, phase transitions, and nonlocal models(SISSA, 2026-09-25)In this thesis, we study variational models arising in three different settings: free discontinuity problems, higher-order models for phase transitions, and nonlocal variational problems. First, we study free discontinuity functionals whose surface terms are of the type commonly used in the variational theory of cohesive fracture mechanics. Since these surface terms are, generally, linear near the origin and bounded at infinity, the natural setting of the corresponding energies is that of spaces of generalised functions of bounded variation and generalised functions of bounded deformation. We investigate the fine properties of these spaces and, in particular, contribute to the general picture of generalised functions of bounded deformation by introducing a matrix-valued measure generalising the distributional symmetric gradient. We also address homogenisation problems for free discontinuity functionals. In the full gradient setting, we consider functionals with linear growth in the bulk part, a Cantor contribution, and cohesive surface terms, and prove deterministic and stochastic homogenisation results. In the framework of linearised elasticity, we study instead functionals defined on functions of bounded deformation whose bulk and surface densities have linear growth, and obtain similar deterministic and stochastic homogenisation results. Finally, we study the relaxation of energies defined on structured deformations, where the macroscopic deformation is coupled with a matrix-valued field accounting for the cumulative effect of submacroscopic slips, separations, and other disarrangements. We extend the classical integral representation theory to this cohesive setting, obtaining an explicit representation for the relaxed energies. The second part of the thesis concerns higher-order singular perturbation problems for phase transitions. We consider Modica-Mortola type energies, in which the usual first-order gradient term is replaced by a higher-order perturbation of arbitrarily prescribed order. We show that sequences with equibounded energy converge to sharp interfaces, and that the Γ-limit is given by a perimeter functional. We then study related anisotropic models involving general tensor norms and derivatives of intermediate orders, whose coefficients may be negative. For this broader class of energies, we establish equi-coercivity and Γ-convergence to an anisotropic perimeter functional, with an interfacial density determined by the orientation of the limit interface. The third and final part concerns the passage from nonlocal to local models driven by concentration phenomena. We first consider fractional quadratic energies with oscillating coefficients, and hence involving two parameters, one governing the concentration induced by the fractional kernel, while the other determining the frequency of the oscillations. We study the Γ-limit of these energies as the two parameters vary simultaneously and analyse how the interaction between these two scales influences the resulting local energy. We then turn to convolution-type functionals depending on finite differences. In this setting, the concentration of the interaction kernels produces free discontinuity energies with bulk and surface terms, whose densities we identify.
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PubblicazioneMERGE-RNA: a physics-based model to predict RNA secondary structure ensembles with chemical probing( 2026)RNA function is tied to secondary structure, operating through dynamic and heterogeneous structural ensembles. While current analysis tools typically output single static structures or averaged contact maps, chemical probing methods like DMS capture nucleotide-resolution signals representing the full structural ensemble, which remain difficult to interpret structurally. To address this, we present MERGE-RNA, a framework that describes and outputs RNA as a structural ensemble. By modeling the physics of the experimental pipeline, MERGE-RNA learns a small set of transferable and interpretable parameters, enabling the integration of measurements across different molecules, probe concentrations, and replicates in a single optimization to improve robustness. Our model employs a maximum-entropy principle to predict thermodynamic populations, with the minimal adjustments necessary to align the ensemble with experimental data. We validate MERGE-RNA on diverse RNAs, showing that it achieves structural accuracy surpassing standard pseudo-free-energy methods and yields ensembles better recapitulating measured DMS reactivity. Applied to the Vibrio vulnificus adenine riboswitch, MERGE-RNA recovers the NMR-resolved conformations and their ligand-induced rearrangement, with population shifts matching the NMR-derived $K_d$. In a designed RNA construct for which we report new DMS data, MERGE-RNA deconvolves mixed states to reveal transient intermediate populations involved in strand displacement, dynamics invisible to methods based on enumerating a small number of structures.
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PubblicazioneConstraints on Ultralight Scalar and Dark Photon Dark Matter from PPTA-DR3 and EPTA-DR2( 2026)The cold dark matter model successfully describes the Universe on large scales, yet faces challenges at subgalactic scales. Ultralight dark matter (ULDM), with particle masses around 10-22 eV, offers a promising solution to these small-scale issues. Pulsar timing arrays (PTAs), designed to detect nanohertz gravitational waves, can also provide a sensitive probe for ULDM signals. In this work, we perform a Bayesian search for ULDM using PTA datasets, focusing on two types of signals: the oscillatory gravitational potential from scalar ULDM and the fifth-force interaction mediated by dark photon dark matter (DPDM). We incorporate pulsar distances in the analysis to better model the ULDM density. No statistically significant evidence for ULDM has been found; therefore, we place 95% confidence level upper limits on the relevant parameters. For scalar ULDM, our analysis does not exclude the scenario in which ULDM constitutes all of dark matter. The constraints from PPTA-DR3 show significant improvements over the earlier PPTA-DR2 (2018 Preview) across most of the mass range, and are consistent with the recent uncorrelated limits from other PTAs. We also present for the first time the DPDM constraints using EPTA data. The obtained bounds on the DPDM from the EPTA-DR2 and PPTA-DR3 are comparable to existing constraints.
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PubblicazionepH-dependent allosteric remodeling of a bacterial riboswitch couples alkaline activation to metal sensing( 2026)The widespread yybP-ykoY riboswitches control bacterial manganese (Mn) homeostasis by activating exporter expression in response to intracellular Mn2+ levels. The Escherichia coli alx riboswitch distinctively couples Mn2+ sensing to cytoplasmic alkalinity, but the mechanism is unknown. We show that pH tunes the alx aptamer's conformational sampling to modulate Mn2+ sensitivity. Single-molecule FRET reveals that Mn2+ stabilizes a docked three-way-junction conformation, and alkaline pH shifts this equilibrium to sensitize metal-dependent folding. Molecular dynamics simulations identify a loop whose low-pH-induced base pairing perturbs the adjacent helix, predicted to allosterically disrupt the Mn2+-binding state. In vivo reporters indicate that both this loop and the Mn2+-binding core are required for optimal pH-dependent translational activation: replacing the core with the non-pH-responsive mntP sequence abolishes activation. These results define how RNA allosterically integrates orthogonal metal and proton cues to enable combinatorial environmental sensing during alkaline stress.
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PubblicazioneExact Methods for Spectral Problems via Conformal Field Theory, Supersymmetric Gauge Theory, and Topological Strings(SISSA, 2026-09-29)In this thesis, we develop and apply methods inspired by two-dimensional conformal field theory, supersymmetric gauge theory, and topological string theory to the study of spectral problems. In the first part, we investigate periodic spectral problems governed by the Lamé and Heun equations, including confluent limits of the latter. These equations arise both as classical limits of BPZ equations satisfied by degenerate Virasoro conformal blocks and as quantized Seiberg--Witten curves of four-dimensional $\mathcal N=2$ $\mathrm{SU}(2)$ gauge theories. The two descriptions are related by the AGT correspondence, under which degenerate classical conformal blocks are mapped to surface-defect partition functions in the Nekrasov--Shatashvili (NS) limit. We solve the connection problem for the Lamé equation and develop a systematic resummation procedure, based on suitable limits of blow-up equations, for bulk and defect NS functions. The resummation resolves their singular instanton expansions at resonant values of the Floquet exponent and reveals the branch structure of the accessory parameters and Floquet solutions, whose branch points determine the edges of spectral bands and gaps. For the Lamé equation, the resonant limit of the resummed accessory parameter agrees with the values obtained independently from isomonodromic and orbifold-defect constructions. The latter also provides the corresponding (anti-)periodic solutions. For the Heun equation, we extend the resummation procedure to include the Floquet solutions, obtaining at resonance both the accessory parameters and the corresponding (anti-)periodic solutions. We further construct their logarithmic companions and analyze the resonant monodromy, distinguishing the mass loci where spectral gaps close from the smaller loci where the resonant monodromy becomes semisimple. In the second part, we study finite-difference equations obtained by quantizing the mirror curves of the $Y^{N,0}$ geometries, which engineer five-dimensional $\mathcal{N}=1$ $\mathrm{SU}(N)$ gauge theories. In the framework of the open topological string/spectral theory (TS/ST) correspondence, we construct exact generalized eigenfunctions that are expected to be entire in the open and closed moduli and to become square-integrable when the spectral moduli belong to the appropriate exact quantization locus. Their four-dimensional limit gives explicit analytic solutions to the eigenvalue problem associated with $\mathsf{H}_N = 2\Lambda^N\cosh(\mathsf{p}) + V_N(\mathsf{x})$, where $V_N(x)$ is an arbitrary monic polynomial of degree $N$. These operators are solvable finite-difference deformations of the Schrödinger Hamiltonians $\mathsf{p}^{2}+V_N(\mathsf{x})$, and our solutions describe both bound states and resonances. We also identify special loci at which the eigenfunctions exhibit enhanced decay. For confining potentials, this enhancement leads to spectral degeneracies, while for potentials unbounded from below, it produces square-integrable states with real energies. We finally discuss the related operators with a $\sinh(\mathsf{p})$ kinetic term, an inverted potential $-V_N(\mathsf{x})$, or both.