13 citations · 41 across the 26 of their papers we have counts for
29 papers
Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones
Alessio Marrani, Daniele Corradetti
The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity alge…
Closed-Form Noise Calibration Against Membership Inference for Random-Allocation DP-SGD
Murat Bilgehan Ertan, Marten van Dijk
DP-SGD protects training data by adding Gaussian noise to clipped gradients. The amount of noise is usually chosen by running a numerical privacy accountant inside a search. We stu…
Integral Orders for the Okubo Algebra and Idempotent Geometries of the Lattice
Daniele Corradetti, Alessio Marrani
We study the Coxeter-Dickson order as a common integral support for the octonionic, para-octonionic and compact real Okubo products. The three algebra structures have the sam…
Linguistic Holonomy and Statistical Watermarks: Inner Geometry of Meaning-Preserving Transformations
Daniele Corradetti
Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by ex…
Integral Planes and Unit-Norm Polytopes
Daniele Corradetti
We introduce and study integral planes associated with crystallographic and non-crystallographic integral systems in real composition algebras. For an integral order $\Order$ in su…
Non-crystallographic systems of integers over composition algebras
Daniele Corradetti
In this work we revisit classical systems of integers inside the real normed division algebras from the point of view of finite norm shells and root systems. Building on the icosia…
Integral Shell Polytopes of Composition Algebras
Daniele Corradetti
Integral systems in real composition algebras give rise to finite metric configurations whose geometry is linked to both regular polytopes and root-systems. In this work we investi…
Integral elements of Okubo algebra and the E8-lattice
Daniele Corradetti
In this work we study the interplay between the Coxeter-Dickson -order, the para-octonions, and the real Okubo algebra. We first explain why a usual rotation presentation of…
Learning Hippo: Multi-attractor Dynamics and Stability Effects in a Biologically Detailed CA3 Extension of Hopfield Networks
Daniele Corradetti, Renato Corradetti
We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes,…
Three Dixon-Rosenfeld Planes
David Chester, Alessio Marrani, Daniele Corradetti +1
Rosenfeld postulated ``generalized'' projective planes, which exploit a correspondence between rank-one idempotents of Jordan algebras and points of pr…
RED.AI Id-Pattern: First Results of Stone Deterioration Patterns with Multi-Agent Systems
Daniele Corradetti, José Delgado Rodrigues
The Id-Pattern system within the RED.AI project (Reabilitação Estrutural Digital através da AI) consists of an agentic system designed to assist in the identification of stone dete…
Linguistic Loops and Geometric Invariants as a Way to Pre-Verbal Thought?
Daniele Corradetti, Alessio Marrani
In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define i…
A new method for structural diagnostics with muon tomography and deep learning
Lorenzo Pezzotti, Davide Cifarelli, Daniele Corradetti +7
This work investigates the production of high-resolution images of typical support elements in concrete structures by means of muon tomography (muography). By exploiting detailed M…
Synthetic Data for Discriminating Serotonergic Neurons using Convolutional Neural Networks
Daniele Corradetti, Alessandro Bernardi, Renato Corradetti
Serotonergic neurons in the raphe nuclei exhibit diverse electrophysiological properties and functional roles, yet conventional identification methods rely on restrictive criteria…
Identification of Stone Deterioration Patterns with Large Multimodal Models
Daniele Corradetti, Jose Delgado Rodrigues
The conservation of stone-based cultural heritage sites is a critical concern for preserving cultural and historical landmarks. With the advent of Large Multimodal Models, as GPT-4…
Deep Learning Models for Atypical Serotonergic Cells Recognition
Daniele Corradetti, Alessandro Bernardi, Renato Corradetti
The serotonergic system modulates brain processes via functionally distinct subpopulations of neurons with heterogeneous properties, including their electrophysiological activity.…
Recovering Composition Algebras from 3D Geometric Algebras
Daniele Corradetti
Generalized Hurwitz theorem states that there are fifteen composition algebras for any given field: seven unital, six para-unital, and two non-unital algebras. In this article we e…
Collineation groups of octonionic and split-octonionic planes
Daniele Corradetti, Alessio Marrani, Francesco Zucconi
We present a Veronese formulation of the octonionic and split-octonionic projective and hyperbolic planes. This formulation of the incidence planes highlights the relationship betw…
All Hurwitz Algebras from 3D Geometric Algebras
Daniele Corradetti, Richard Clawson, Klee Irwin
Hurwitz algebras are unital composition algebras widely known in algebra and mathematical physics for their useful applications. In this paper, inspired by works of Lesenby and Hit…
A minimal and non-alternative realisation of the Cayley plane
Daniele Corradetti, Alessio Marrani, Francesco Zucconi
The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel…
Physics with non-unital algebras? An invitation to the Okubo algebra
Alessio Marrani, Daniele Corradetti, Francesco Zucconi
This paper presents some preliminary discussion on the possible relevance of the Okubonions, i.e. the real Okubo algebra , in quantum chromodynamics (QCD). The Okubo a…
Jordan algebras over icosahedral cut-and-project quasicrystals
Daniele Corradetti, David Chester, Raymond Aschheim +1
In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a…
Dixon-Rosenfeld Lines and the Standard Model
David Chester, Alessio Marrani, Daniele Corradetti +2
We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to Rosenfeld projective lines except over the Dixon algebra $\mathbb{C}\otimes\mathbb{H}\otimes\ma…
Three Fibonacci-Chain Aperiodic Algebras
Daniele Corradetti, David Chester, Raymond Aschheim +1
Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elemen…