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Stefano Rossi

Stefano Rossi appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.OAmath.FAmath.QAmath.PRcond-mat.mtrl-sciMachine Learningmath-phmath.APmath.GRmath.MPphysics.app-phphysics.med-phphysics.opticsQuantitative MethodsTissues and Organs

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Published work

14 published item(s)

preprint2026arXiv

Kinetic theory for Transformers and the lost-in-the-middle phenomenon

We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the model, and appealing to non-hierarchical methods to estimate correlations using Glauber calculus, we prove a quantitative mean-field limit result and a next-order characterization of correlations. For iid uniformly distributed tokens, the limiting correlation equation can be solved in closed form and we obtain a rigorous explanation of the empirically observed \emph{lost-in-the-middle} phenomenon: the token retrieval profile, as a function of the source position in the prompt, is $\mathsf{U}$-shaped, with primacy, recency, and a unique interior minimum under an explicit smallness condition.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

de Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products

Local actions of $\mathbb{P}_\mathbb{N}$, the group of finite permutations on $\mathbb{N}$, on quasi-local algebras are defined and proved to be $\mathbb{P}_\mathbb{N}$-abelian. It turns out that invariant states under local actions are automatically even, and extreme invariant states are strongly clustering. Tail algebras of invariant states are shown to obey a form of the Hewitt and Savage theorem, in that they coincide with the fixed-point von Neumann algebra. Infinite graded tensor products of $C^*$-algebras, which include the CAR algebra, are then addressed as particular examples of quasi-local algebras acted upon $\mathbb{P}_\mathbb{N}$ in a natural way. Extreme invariant states are characterized as infinite products of a single even state, and a de Finetti theorem is established. Finally, infinite products of factorial even states are shown to be factorial by applying a twisted version of the tensor product commutation theorem, which is also derived here.

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preprint2022arXiv

On truncated $t$-free Fock spaces: spectrum of position operators and shift-invariant states

The ergodic properties of the shift on both full and $m$-truncated $t$-free $C^*$-algebras are analyzed. In particular, the shift is shown to be uniquely ergodic with respect to the fixed-point algebra. In addition, for every $m\geq 1$, the invariant states of the shift acting on the $m$-truncated $t$-free $C^*$-algebra are shown to yield a $m+1$-dimensional Choquet simplex, which collapses to a segment in the full case. Finally, the spectrum of the position operators on the $m$-truncated $t$-free Fock space is also determined.

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preprint2022arXiv

Tail algebras for monotone and $q$-deformed exchangeable stochastic processes

We compute the tail algebras of exchangeable monotone stochastic processes. This allows us to prove the analogue of de Finetti's theorem for this type of processes. In addition, since the vacuum state on the $q$-deformed $C^*$-algebra is the only exchangeable state when $|q|<1$, we draw our attention to its tail algebra, which turns out to obey a zero-one law.

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preprint2021arXiv

Redox-tunable structural colour images based on UV-patterned conducting polymers

Precise manipulation of light-matter interaction has enabled a wide variety of approaches to create bright and vivid structural colours. Techniques utilizing photonic crystals, Fabry-Pérot cavities, plasmonics, or high-refractive index dielectric metasurfaces have been studied for applications ranging from optical coatings to reflective displays. However, complicated fabrication procedures for sub-wavelength nanostructures, limited active areas, and inherent absence of tunability with these approaches significantly impede their further developments towards flexible, large-scale, and switchable devices compatible with facile and cost-effective production. Herein, we present a way to generate structural colours based on conducting polymer thin films prepared on metallic surfaces via vapour phase polymerization and ultraviolet (UV) light patterning. Varying the UV dose leads to synergistic variation of film absorption and thickness, which generates controllable colours from violet to red. Together with greyscale photomasks this enables fabrication of high-resolution colour images using single exposure steps. We further demonstrate spatiotemporal tuning of the structurally coloured surfaces and images via electrochemical modulation of the polymer redox state. The simple structure, facile fabrication, wide colour gamut, and dynamic colour tuning make this concept competitive for future multi-functional and smart displays.

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preprint2020arXiv

Cardiac kinematic parameters computed from video of $\textit{in situ}$ beating heart

Mechanical function of the heart during open-chest cardiac surgery is exclusively monitored by echocardiographic techniques. However, little is known about local kinematics, particularly for the reperfused regions after ischemic events. We report a novel imaging modality, which extracts local and global kinematic parameters from videos of $\textit{in situ}$ beating hearts, displaying live video cardiograms of the contraction events. A custom algorithm tracked the movement of a video marker positioned $\textit{ad hoc}$ onto a selected area and analyzed, during the entire recording, the contraction trajectory, displacement, velocity, acceleration, kinetic energy and force. Moreover, global epicardial velocity and vorticity were analyzed by means of Particle Image Velocimetry tool. We validated our new technique by i) computational modeling of cardiac ischemia, ii) video recordings of ischemic/reperfused rat hearts, iii) videos of beating human hearts before and after coronary artery bypass graft, and iv) local Frank-Starling effect. In rats, we observed a decrement of kinematic parameters during acute ischemia and a significant increment in the same region after reperfusion. We detected similar behavior in operated patients. This modality adds important functional values on cardiac outcomes and supports the intervention in a contact-free and non-invasive mode. Moreover, it does not require particular operator-dependent skills.

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preprint2020arXiv

Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory

In this paper the local iterative Lie-Schwinger block-diagonalization method, introduced in [FP], [DFPR1], and [DFPR2] for quantum chains, is extended to higher-dimensional quantum lattice systems with Hamiltonians that can be written as the sum of an unperturbed gapped operator, consisting of a sum of on-site terms, and a perturbation consisting of bounded interaction potentials of short range mutltiplied by a real coupling constant t. Our goal is to prove that the spectral gap above the ground-state energy of such Hamiltonians persists for sufficiently small values of |t|, independently of the size of the lattice. New ideas and concepts are necessary to extend our method to systems in dimension d > 1: As in our earlier work, a sequence of local block-diagonalization steps based on judiciously chosen unitary conjugations of the original Hamiltonian is introduced. The supports of effective interaction potentials generated in the course of these block-diagonalization steps can be identified with what we call minimal rectangles contained in the lattice, a concept that serves to tackle combinatorial problems that arise in the course of iterating the block-diagonalization steps. For a given minimal rectangle, control of the effective interaction potentials generated in each block-diagonalization step with support in the given rectangle is achieved by exploiting a variety of rather subtle mechanisms which include, for example, the use of weighted sums of paths consisting of overlapping rectangles and of large denominators, expressed in terms of sums of orthogonal projections, that serve to control analogous sums of projections in the numerators resulting from the unitary conjugations of the interaction potential terms involved in the local block-diagonalization step.

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preprint2019arXiv

Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebra

A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra $\mathcal{D}_2$ in the $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$, which generalizes and unifies analogous results for Cuntz and Bunce-Deddens algebras. Furthermore, the inclusion $\mathcal{O}_2\subset\mathcal{Q}_2$ is proved not to be regular. Finally, countably many novel permutative endomorphisms of $\mathcal{Q}_2$ are exhibited with prescribed images of the generator $U$.

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preprint2012arXiv

Connected components of compact matrix quantum groups and finiteness conditions

We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be profinite. We consider the problem of approximating the identity component as well as the maximal normal (in the sense of Wang) connected subgroup by introducing canonical, but possibly transfinite, sequences of subgroups. These sequences have a trivial behaviour in the classical case. We give examples, arising as free products, where the identity component is not normal and the associated sequence has length 1. We give necessary and sufficient conditions for normality of the identity component and finiteness or profiniteness of the quantum component group. Among them, we introduce an ascending chain condition on the representation ring, called Lie property, which characterizes Lie groups in the commutative case and reduces to group Noetherianity of the dual in the cocommutative case. It is weaker than ring Noetherianity but ensures existence of a generating representation. The Lie property and ring Noetherianity are inherited by quotient quantum groups. We show that A_u(F) is not of Lie type. We discuss an example arising from the compact real form of U_q(sl_2) for q<0.

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