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PubblicazioneExotic surfaces in 4-manifolds, stabilizations, and framings.(SISSA, 2025-09-09)We show that many explicit examples of exotic pairs of surfaces in a smooth 4-manifold become smoothly isotopic after one external stabilization with S^2×S^2 or CP^2#-CP^2. Our results cover surfaces produced by rim-surgery, twist-rim-surgery, annulus rim-surgery, as well as infinite families of nullhomologous surfaces and examples with non-cyclic fundamental group of the complement. A special attention is given to the identification of the stabilizing manifold and its dependence on the choices in the construction of the surface. The main idea of this thesis is given by relating internal and external stabilization, and most of the results, but not all, are proved using this relation. Moreover, we show that the 2-links in the exotic family constructed by the author of this thesis, in a joint work with Bais, Benyahia and Torres, are brunnian, i.e., they become smoothly unlinked if any of the components is removed.
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PubblicazioneTheory of polymers in binary solvent solutions: Mean-field free energy and phase behavior( 2024)We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the O(n)-vector spin model in the limit n→0, we derive an exact field-theoretic expression for the partition function of the system. The latter is then evaluated at the saddle point, providing a mean-field estimate of the free energy. The resulting expression, which conforms to the Flory-Huggins type, is then used to analyze the system's stability with respect to phase separation, complemented by a numerical approach based on convex hull evaluation. We demonstrate that this simple lattice model can effectively explain the behavior of a variety of seemingly unrelated polymer systems, which have been predominantly investigated in the past only through numerical simulations. This includes both single-chain and multichain solutions. Our findings emphasize the fundamental, mutually competing roles of solvent and cosolvent in polymer systems.
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PubblicazioneTheory of Transformers and their application to Neural Quantum States(SISSA, 2025-09-11)My PhD research focused on the Transformer architecture, a powerful deep neural network model that has emerged as a cornerstone for solving complex problems in natural language processing, image analysis, signal processing, and beyond. In particular, we studied the learning dynamics of this architecture, and its application to the representation of many-body wavefunctions, the so-called Neural Quantum States. Initially, we investigated the representational capabilities of Transformers by characterizing the statistical structures that a simplified Transformer layer, utilizing the so-called factored attention, is capable of learning. Building on these results, we utilized factored attention in deep Transformers to develop an accurate ansatz for approximating the ground states of quantum many-body Hamiltonians within the variational Monte Carlo framework. In this specific application, factored attention is crucial for achieving accurate results, demonstrating superior performance compared to the standard attention mechanism used in most of the other applications of the Transformers, and in particular in natural language processing. Alongside the development of an efficient optimization method for large-scale neural networks, we achieved state-of-the-art results on the most popular benchmark in Neural Quantum States and addressed complex physical problems that are subjects of ongoing debate. Finally, we developed a framework to train Foundation Neural Quantum States, which are versatile neural network models that approximate quantum wave functions of multiple systems simultaneously, enabling accurate estimates of challenging quantities such as disorder averages and fidelity susceptibility. We envision numerous future directions for this approach, including its extension to quantum dynamics by explicitly modeling time-dependent variational states, as well as its application to the design of novel materials in fermionic systems.
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PubblicazioneComputing canonical averages with quantum and classical optimizers: Thermodynamic reweighting for QUBO models of physical systems( 2025)We present a general method to compute canonical averages for physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO). First, we introduce a histogram reweighting scheme applicable to QUBO-based sampling constrained to specific intervals of an order parameter, e.g., physical energy. Next, we demonstrate that the scheme can accurately recover the density of states, which in turn allows for calculating expectation values in the conjugate ensemble, e.g., at a fixed temperature. The method can thus be used to advance the state-of-the-art characterization of physical systems that admit a QUBO-based representation and that are otherwise intractable with real-space sampling methods. A case in point are space-filling melts of lattice ring polymers, recently mapped in QUBO form, for which our method reveals that the ring catenation probability is nonmonotonic with the bending rigidity.
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PubblicazioneDevelopmental Trajectories Predict Dendritic Remodeling After Injury( 2025)Neurons in the adult central nervous system exhibit limited regenerative capacity, yet certain retinal ganglion cell subtypes exhibit greater resilience. We tested whether the timing of dendritic maturation shapes subtype-specific responses to injury. Reconstruction of over 1,000 retinal ganglion cells shows that ON-sustained (sONα) and ON-transient (tONα) cells follow distinct developmental trajectories: tONα cells reach peak dendritic size by postnatal day 10, while sONα cells mature by day 14. Post-injury, both subtypes undergo dendritic shrinkage; however, sONα cells remodel more rapidly and stabilize earlier. Computational modeling indicated that injury-induced morphologies resemble earlier developmental stages. Deletion of PTEN and SOCS3, which promotes axon regeneration, led to increased dendritic regression. These findings suggest that developmental timing constrains structural remodeling after injury and that axonal regeneration occurs at the expense of dendritic stability, highlighting a trade-off between axon growth and maintenance of dendritic architecture in adult retinal ganglion cells.