arXiv subjects

F. Ahmadi

Publications and source records attributed to F. Ahmadi.

13 recordsLinked to original sources

arXiv2025

Entropy-Enhanced Conformal Features from Ricci Flow for Robust Alzheimer's Disease Classification

Background and Objective: In brain imaging, geometric surface models are essential for analyzing the 3D shapes of anatomical structures. Alzheimer's disease (AD) is associated with significant cortical atrophy, making such shape analysis a valuable diagnostic tool. The objective of this study is to introduce and validate a novel local surface representation method for the automated and accurate diagnosis of AD. Methods: The study utilizes T1-weighted MRI scans from 160 participants (80 AD patients and 80 healthy controls) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Cortical surface models were reconstructed from the MRI data using Freesurfer. Key geometric attributes were computed from the 3D meshes. Area distortion and conformal factor were derived using Ricci flow for conformal parameterization, while Gaussian curvature was calculated directly from the mesh geometry. Shannon entropy was applied to these three features to create compact and informative feature vectors. The feature vectors were used to train and evaluate a suite of classifiers (e.g. XGBoost, MLP, Logistic Regression, etc.). Results: Statistical significance of performance differences between classifiers was evaluated using paired Welch's t-test. The method proved highly effective in distinguishing AD patients from healthy controls. The Multi-Layer Perceptron (MLP) and Logistic Regression classifiers outperformed all others, achieving an accuracy and F$_1$ Score of 98.62%. Conclusions: This study confirms that the entropy of conformally-derived geometric features provides a powerful and robust metric for cortical morphometry. The high classification accuracy underscores the method's potential to enhance the study and diagnosis of Alzheimer's disease, offering a straightforward yet powerful tool for clinical research applications.

cs.CV↗

arXiv2024

The modulated soliton fields in the Goldstone boson model

It is well known that massless Goldstone bosons have not yet been observed. In the Goldstone boson model, after the spontaneous symmetry breaking under $U(1)$, two coupled nonlinear equations are obtained for which we present the exact solitonic solutions. These solutions completely localize the energy density of the model and show the existence of two boson fields, one massive and the other massless. Also, it is seen that the solitonic waves are modulated and the massless wave rides on the massive wave. Finally, we calculate the charge density of the model, which again confirms the neutrality of these boson fields. Since massive bosons can be observed in the laboratory, these solitonic waves may be useful in tracking and detecting Goldstone bosons.

hep-th↗

arXiv2022

Effect of RGUP on the nonlinear Klein-Gordon model with spontaneous symmetry breaking

In the framework of the relativistic generalized uncertainty principle (RGUP), we study the nonlinear Klein-Gordon field with $ϕ^4$ self-interaction. This generalization comes from the quantum gravity theories that predict the existence of a minimal measurable length scale. The quantum gravity effects slightly modify the momentum and change the Lagrangian density of the field. This model, specifically in the context of spontaneous symmetry breaking, is so fruitful and leads us to many interesting phenomena. Due to the complexity of the consequent equations, the model is normally studied via perturbation mechanisms. However, here, we apply a generalized $tanh$-method which supposed that the field solutions should be $sech$-functions of segments of space and time. By this extended method, we find some more general solutions with respect to our previous work \cite{Mir1}. Several solutions can be found but we select only the normalizable and bounded solitary fields. The energy spectrum of each field solution is obtained in an analytical form and discussed. The modification parameter of the corresponding RGUP is estimated by using the rest energy of the mass of the Higgs boson.

hep-th↗

arXiv2021

The solitary solutions of nonlinear Klein-Gordon field with minimal length

The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study the implications of the presence of the minimal length on the Klein-Gordon filed with ϕ4self-interaction. Considering the process of spontaneous symmetry breaking, the potential also includes the ϕ3term. The consequent field equation is a fourth-order differential equation and is considered to have solitary solutions. The sech method is applied and the normalized solutions are obtained in closed forms and the energy spectrum of the solitary fields is determined. The modification parameter of the theory is estimated by the width and the energy of the obtained solitary fields.

hep-th↗

arXiv2020

Deflation of Vacuum Energy During Inflation Due to Bulk-Brane Interaction

We consider a brane world inflationary model in which inflation is driven by dynamics of a self-interacting scalar field living in the five-dimensional bulk. The scalar field is non-minimally coupled to matter fields on the brane and acts as an inflaton which induces a slow-roll inflation. We show that although the Friedmann equation is modified at early times due to effects of the extra dimension, the slow-roll condition is the same as that of the four-dimensional case. Due to the non-minimal coupling of matter with the bulk scalar, there is an energy transfer between the two components. We investigate the conditions under which the direction of this energy transfer can be from matter onto the bulk scalar. There are at least two advantages in this case: 1) It establishes a mechanism by which a large effective cosmological term on the brane is deflated during the inflation period. 2) The energy flow onto the bulk inflaton gives a more strongly damped evolution of the scalar field in the slow-roll region for a given potential. We then show that our results are supported by numerical estimations with quadratic and exponential potentials.

gr-qc↗

arXiv2019

Protecting the entropic uncertainty lower bound in Markovian and non-Markovian environment via additional qubits

The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is expressed in terms of the standard deviation of the measured observables. In quantum information theory, it is shown that the uncertainty principle can be expressed by Shannon's entropy. The entopic uncertainty lower bound can be altered by considering a particle as the quantum memory which is correlated with the measured particle. We assume that the quantum memory is an open system. We also select the quantum memory from $N$ qubit which interact with common reservoir. In this work we investigate the effects of the number of additional qubits in reservoir on entropic uncertainty lower bound. We conclude that the entropic uncertainty lower bound can be protected from decoherence by increasing the number of additional qubit in reservoir.

quant-ph↗

arXiv2018

Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems

The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information theory, this principle is expressed in terms of entropic measures. Entropic uncertainty bound can be altered by considering a particle as a quantum memory. In this work we investigate the entropic uncertainty relation under the relativistic motion. In relativistic uncertainty game Alice and Bob agree on two observables, $\hat{Q}$ and $\hat{R}$, Bob prepares a particle constructed from the free fermionic mode in the quantum state and sends it to Alice, after sending, Bob begins to move with an acceleration $a$, then Alice does a measurement on her particle $A$ and announces her choice to Bob, whose task is then to minimize the uncertainty about the measurement outcomes. we will have an inevitable increase in the uncertainty of the Alic's measurement outcome due to information loss which was stored initially in B. In this work we look at the Unruh effect as a quantum noise and we will characterize it as a quantum channel.

quant-ph↗

arXiv2018

Particle creation in the framework of f(G) gravity

In this paper, we study the problem of massless particle creation in a flat, homogeneous and isotropic universe in the framework of $f(G)$ gravity. The Bogolyubov coefficients are calculated for the accelerating power-law solutions of the model in a matter dominated universe, from which the total number of created particle per unit volume of space can be obtained. It is proved that the total particle density always has a finite value. Therefore, the Bogolyubov transformations are well-defined and the Hilbert spaces spanned by the vacuum states at different times are unitarily equivalent. We find that the particles with small values of the mode $k$ are produced in the past and particles with large values of $k$ are produced only in the future. The negative pressure resulting from the gravitational particle creation is also determined. It is then argued that this pressure even in the presence of energy density and thermal pressure may affect significantly the cosmic expansion.

gr-qc↗

arXiv2017

Effect of the Chameleon Scalar Field on Brane Cosmological Evolution

We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain both the direction of energy transfer and dynamics of the extra dimension.

gr-qc↗

arXiv2007

Lorentz violation and the speed of gravitational waves in brane-worlds

Lorentz violation in a brane-world scenario is presented and used to obtain a relationship between the speed of gravitational waves in the bulk and that on the brane. Lorentz violating effects would manifest themselves in gravitational waves travelling with a greater speed in the bulk than on the brane and this effect is independent of the signature of the extra dimension.

gr-qc↗

arXiv2006

Stabilization of test particles in Induced Matter Kaluza-Klein theory

The stability conditions for the motion of classical test particles in an $% n $-dimensional Induced Matter Kaluza-Klein theory is studied. We show that stabilization requires a variance of the strong energy condition for the induced matter to hold and that it is related to the hierarchy problem. Stabilization of test particles in a FRW universe is also discussed.

gr-qc↗

arXiv2006

Lorentz violation in brane cosmology, accelerated expansion and fundamental constants

The notion of Lorentz violation in four dimensions is extended to a 5-dimensional brane-world scenario by utilizing a dynamical vector field assumed to point in the bulk direction, with Lorentz invariance holding on the brane. The cosmological consequences of this theory consisting of the time variation in the gravitational coupling $G$ and cosmological term $Λ_4$ are explored. The brane evolution is addressed by studying the generalized Friedmann and Raychaudhuri equations. The behavior of the expansion scale factor is then considered for different possible scenarios where the bulk cosmological constant is zero, positive or negative.

gr-qc↗

arXiv2003

Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization

We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.

hep-th↗