arXiv subjects

S. Floquet

Publications and source records attributed to S. Floquet.

5 recordsLinked to original sources

arXiv2022

Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras are the natural framework for multidimensional data analysis in a quantum setting. Implementation of activation functions and unitary learning rules are discussed. In this scheme, we also provide an algebraic generalization of the quantum Fourier transform containing additional parameters that allow performing quantum machine learning. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.

quant-ph↗

arXiv2020

On the validation of Newcomb-Benford law and Weibull distribution in neuromuscular transmission

The neuromuscular junction represents a relevant substrate for revealing important biophysical mechanisms of synaptic transmission. In this context, calcium ions are important in the synapse machinery, providing the nervous impulse transmission to the muscle fiber. In this work, we carefully investigated whether intervals of spontaneous electrical activity, recorded in seven different calcium concentrations, conform Newcomb-Benford law. Our analysis revealed that electrical discharge of neuromuscular junction obeys the expected values for Newcomb-Benford law for first and second digits, while first-two digits do not perfectly follows the law. We next examined previous theoretical studies, establishing a relation between the law and lognormal and Weibull distributions. We showed that Weibull distribution is more appropriate to fit the intervals as compared to lognormal distribution. Altogether, the present findings strongly suggest that spontaneous activity is a base-scale invariant phenomenon.

q-bio.SC↗

arXiv2018

Clifford Algebras, Multipartite Systems and Gauge Theory Gravity

In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space-time algebra for gravitation developed by Lasenby and Doran (Lasenby, A. N., Doran, C. J. L, and Gull, S.F.: Gravity, gauge theories and geometric algebra. Phil. Trans. R. Soc. Lond. A, 582, 356:487 (1998)). We associate the gauge fields with description of fermionic and bosonic states using the generalized graded tensor product. Einstein's equations are deduced from the graded projections and an algebraic Hopf-like structure naturally emerges from formalism. A connection with the theory of the quantum information is performed through the minimal left ideals and entangled qubits are derived. In addition applications to black holes physics and standard model are outlined.

physics.gen-ph↗

arXiv2017

Statistical crossover and nonextensive behavior of the neuronal short-term depression

The theoretical basis of neuronal coding, associated with short term degradation in synaptic transmission, is a matter of debate in the literature. In fact, electrophysiological signals are commonly characterized as inversely proportional to stimulus intensity. Among theoretical descriptions of this phenomenon, models based on $1/f$-dependency are employed to investigate the biophysical properties of the short term synaptic depression. In this work we formulated a model based on a paradigmatic \textit{q}-differential equation to obtain a generalized formalism useful for investigation of nonextensivity in this specific type of synaptic plasticity. Our analysis reveals nonextensivity in data from electrophysiological recordings and also a statistical crossover in neurotransmission. In particular, statistical transitions providesadditional support to the hypothesis of heterogeneous release probability of neurotransmitters. On the other hand, the simple vesicle model agrees with data only at low frequency stimulations. Thus, the present work presents a method to demonstrate that short-term depression is not only governed by random mechanisms but also by a nonextensive behavior. Our findings also conciliate morphological and electrophysiological investigations into a coherent biophysical scenario.

q-bio.NC↗

arXiv2017

Lie Algebras and Generalized Thermal Coherent States

In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a Thermofield Dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on $SU(2)$ and $SU(1,1)$ symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.

math-ph↗