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- Conjugation matters. Bioctonionic veronese vectors and cayley-rosenfeld planesPublication . Corradetti, Daniele; Marrani, Alessio; Chester, David; Aschheim, Ray
Expand Motivated by the recent interest in Lie algebraic and geometric structures arising from tensor products of division algebras and their relevance to high energy theoretical physics, we analyze generalized bioctonionic projective and hyperbolic planes. After giving a Veronese representation of the complexification of the Cayley plane OP2C, we present a novel, explicit construction of the bioctonionic Cayley–Rosenfeld plane (C⊗O)P2, again by exploiting Veronese coordinates. We discuss the isometry groups of all generalized bioctonionic planes, recovering all complex and real forms of the exceptional groups F4 and E6, and characterizing such planes as symmetric and Hermitian symmetric spaces. We conclude by discussing some possible physical applications.Expand - Three Fibonacci-Chain aperiodic algebrasPublication . Corradetti, Daniele; Chester, David; Aschheim, Raymond; Irwin, Klee
Expand 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 elementary excitations that can propagate in multilayered structures and in the construction of some integrable models in quantum mechanics. Starting from the works of Patera and Twarock we present three aperiodic algebras based on Fibonacci-chain quasicrystals: a quasicrystal Lie algebra, an aperiodic Witt algebra and, finally, an aperiodic Jordan algebra. While a quasicrystal Lie algebra was already constructed from a modification of the Fibonacci chain, we here present an aperiodic algebra that matches exactly the original quasicrystal. Moreover, this is the first time to our knowledge, that an aperiodic Jordan algebra is presented leaving room for both theoretical and applicative developments.Expand - Dixon-Rosenfeld lines and the standard modelPublication . Chester, David; Marrani, Alessio; Corradetti, Daniele; Aschheim, Raymond; Irwin, Klee
Expand We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to Rosenfeld projective lines except over the Dixon algebra C⊗H⊗O. Three different Lie groups are found as isometry groups of these coset manifolds using Tits’ formula. We demonstrate how Standard Model interactions with the Dixon algebra in recent work from Furey and Hughes can be uplifted to tensor products of division algebras and Jordan algebras for a single generation of fermions. The Freudenthal–Tits construction clarifies how the three Dixon-Rosenfeld projective lines are contained within C ⊗ H ⊗ J2(O), O ⊗ J2(C ⊗ H), and C ⊗ O ⊗ J2(H). $$\mathbb {C}\otimes \mathbb {H}\otimes \mathbb {O}$$ C ⊗ H ⊗ O . Three different Lie groups are found as isometry groups of these coset manifolds using Tits’ formula. We demonstrate how Standard Model interactions with the Dixon algebra in recent work from Furey and Hughes can be uplifted to tensor products of division algebras and Jordan algebras for a single generation of fermions. The Freudenthal–Tits construction clarifies how the three Dixon-Rosenfeld projective lines are contained within $$\mathbb {C}\otimes \mathbb {H}\otimes J_{2}(\mathbb {O})$$ C ⊗ H ⊗ J 2 ( O ) , $$\mathbb {O}\otimes J_{2}(\mathbb {C}\otimes \mathbb {H})$$ O ⊗ J 2 ( C ⊗ H ) , and $$\mathbb {C}\otimes \mathbb {O}\otimes J_{2}(\mathbb {H})$$ C ⊗ O ⊗ J 2 ( H ) .Expand - A geometrical interpretation of Okubo spin groupPublication . Corradetti, Daniele; Zucconi, Francesco
Expand In this work we define, for the first time, the affine and projective plane over the real Okubo algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a flexible, composition algebra which is also a not unital division algebra. Even though Okubo algebra has been known for more than 40 years, we believe that this is the first time the algebra was used for affine and projective geometry. After showing that all axioms of affine geometry are verified, we define a projective plane over Okubo algebra as completion of the affine plane and directly through the use of Veronese coordinates. We then present a bijection between the two constructions. Finally we show a geometric interpretation of Spin(O) as the group of collineations that preserve the axis of the plane.Expand - Deep learning models for atypical serotonergic cells recognitionPublication . Corradetti, Daniele; Bernardi, Alessandro; Corradetti, Renato
Expand The serotonergic system modulates brain processes via functionally distinct subpopulations of neurons with heterogeneous properties, including their electrophysiological activity. In extracellular recordings, serotonergic neurons to be investigated for their functional properties are commonly identified on the basis of "typical"features of their activity, i.e. slow regular firing and relatively long duration of action potentials. Thus, due to the lack of equally robust criteria for discriminating serotonergic neurons with "atypical"features from non-serotonergic cells, the physiological relevance of the diversity of serotonergic neuron activities results largely understudied. New Methods : We propose deep learning models capable of discriminating typical and atypical serotonergic neurons from non-serotonergic cells with high accuracy. The research utilized electrophysiological in vitro recordings from serotonergic neurons identified by the expression of fluorescent proteins specific to the serotonergic system and non-serotonergic cells. These recordings formed the basis of the training, validation, and testing data for the deep learning models. The study employed convolutional neural networks (CNNs), known for their efficiency in pattern recognition, to classify neurons based on the specific characteristics of their action potentials. Results: The models were trained on a dataset comprising 27,108 original action potential samples, alongside an extensive set of 12 million synthetic action potential samples, designed to mitigate the risk of overfitting the background noise in the recordings, a potential source of bias. Results show that the models achieved high accuracy and were further validated on "non-homogeneous"data, i.e., data unknown to the model and collected on different days from those used for the training of the model, to confirm their robustness and reliability in real -world experimental conditions. Comparison with existing methods : Conventional methods for identifying serotonergic neurons allow recognition of serotonergic neurons defined as typical. Our model based on the analysis of the sole action potential reliably recognizes over 94% of serotonergic neurons including those with atypical features of spike and activity. Conclusion: The model is ready for use in experiments conducted with the here described recording parameters. We release the codes and procedures allowing to adapt the model to different acquisition parameters or for identification of other classes of spontaneously active neurons.Expand