arXiv subjects

Mahdi Salehi

Publications and source records attributed to Mahdi Salehi.

8 recordsLinked to original sources

arXiv2025

Mutually equibiased bases

In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be predicted according to a predefined probability distribution $q=(q_0,\ldots,q_{d-1})$. The notion of mutual unbiasedness, however, is preserved by requiring that the extracted information is the same for any preparation and any measurement; regardless of which state from which basis is chosen to prepare the system, the outcomes of measuring the system with respect to the other basis generate the same probability distribution. In light of this, we define the notion of \emph{mutually equibiased bases} (MEBs) such that within each basis the states are equibiased with respect to the states of the other basis and that the bases are mutually equibiased with respect to each other. For $d=2,3$, we derive a set of $d+1$ MEBs. The mutual equibiasedness imposes nontrivial constraints on the distribution $q$, leading for $d=3$ to the restriction $1/3\leμ\le 1/2$ where $μ=\sum_{k=0}^{2}q_k^2$. To capture the incompatibility of the measurements in MEBs, we derive an inequality for the probabilities of projective measurements in a qudit system, which yields an associated entropic uncertainty inequality. Finally, we construct a class of positive maps and their associated entanglement witnesses based on MEBs. While an entanglement witness constructed from MUBs is generally finer than one based on MEBs when both use the same number of bases, for certain values of the index $μ$, employing a larger set of MEBs can yield a finer witness. We illustrate this behavior using isotropic states of a $3\times 3$ system. Our results reveal that not all bases in a set of $L$ MEBs can contribute to the entanglement detection. A constraint, dependent on the probability ...

quant-ph↗

arXiv2024

Wideband High Gain Metasurface-Based 4T4R MIMO antenna with Highly Isolated Ports for Sub-6 GHz 5G Applications

This study presents the design of four $178\times178$ $(mm)^{2}$ wideband, high gain, highly efficient metasurface-based 4T4R MIMO (Multiple-Input Multiple-Output) antennas with highly isolated ports, covering the middle and a portion of the upper bands of the sub 6 GHz 5G frequency spectrum for 5G-based systems, such as IoT (Internet of Things) applications, vehicular communications (e.g., rooftop antennas of cars or trains), smart industries (e.g., farms and factories). The radiating elements of these antennas use the aperture-coupled feeding technique with a dumbbell-shaped slot, a truncated square patch with two U-shaped slots, and a metasurface layer. The proposed MIMO structures place four identical radiating elements like a $2\times2$ matrix with $90^\circ$ successive rotations to produce orthogonal electromagnetic waves, improving the isolation between ports. Six-millimeter spaces are added between these elements, and two vertical and horizontal strip slots are carved on the ground as the decoupling structure to decrease the mutual coupling. Simulation results show that Antenna\_{1}, Antenna\_{2}, and Antenna\_{3} achieve gain values of 6.2 to 9.4 dBi, 8.2 to 11.6 dBi, 6.2 to 9.5 dBi, below -35, -25, and -33 isolation and almost 10 dB diversity gain from 2.8 to 4.7 GHz, 2.8 to 4.5 GHz, and 2.7 to 4.9 GHz, respectively. As a prototype, Antenna\_{4} is manufactured, and measurements are performed. It achieves 6.28 to 10.45 dBi gain values, below -23 dB isolation, and 0.001 envelope correlation coefficient over 2.7 to 4.3 GHz. The results confirm that the proposed MIMO antennas are compatible with the 5G essential requisites.

eess.SP↗

arXiv2023

A spatial analysis of COVID-19 reported cases in the Gauteng province, South Africa: Identifying wards to be targeted early in future infectious diseases outbreak

The COVID-19 pandemic caused major disruptions and contributed to the loss of livelihoods and income. The pandemic also provided public health and health systems policy shifts towards better promotion and protection in responding to such disasters and emergencies. Due to differing effects of socio-economic infectious disease vulnerabilities and pre-pandemic levels of preparedness for health emergencies, health system strengthening requires targeted and ununiform implementation. We employ spatial statistical methods on the COVID-19 confirmed cases in identifying wards that could be targeted for strengthening health security in the Gauteng Province, South Africa. In this way, the identified high-risk wards would be more effective and prepared to respond to future pandemics and emergencies.

stat.AP↗

arXiv2023

Holographic Transmitarray Antenna with linear Polarization in X band

In this paper, we present the design and demonstration of transmitarray antennas (TAs) based on the holographic technique for the first time. According to the holographic theory, the amplitudes and phases of electromagnetic waves can be recorded on a surface, and then they can be reconstructed independently. This concept is used to design single-beam and multi-beam linearly polarized holographic TAs without using any iterative optimization algorithms. Initially, a transmission impedance surface is analyzed and compared with the reflection one. Then, interferograms associated with the scalar admittance distribution are defined according to the number and direction of the radiation beams. After that, a transmission metasurface of dimensions equal to 0:26l0 is hired to design holographic TAs at 12 GHz. Several examples are provided to support the method. In the end, a linearly polarized circular aperture wideband holographic transmitarray antenna with a radius of 13.3 cm has been manufactured and tested. The antenna achieves 12.5% (11.4-12.9 GHz) 1-dB gain bandwidth and 23.8 dB maximum gain, leading to 21.46% aperture efficiency.

eess.SP↗

arXiv2021

Mutually unbiased measurements with arbitrary purity

Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the measurement operators corresponding to maximally mixed states to $1$ for the rank one projectors. In this contribution, we provide a class of MUM that encompasses the full range of purity. Similar to the MUB in which the operators corresponding to different outcomes of the same measurement commute mutually, our class of MUM possesses this sense of compatibility within each measurement. This makes the provided class more similar to the MUB, so that the main difference between them and MUB is due to the purity of the measurement operators. The spectra of these MUMs provides a way to construct a class of $d$-dimensional orthogonal matrices which leave the vector of equal components invariant. Based on this property, and by using the MUM-based entanglement witnesses, we investigate the role of purity to detect entanglement of bipartite states.

quant-ph↗

arXiv2021

Tilted Nonparametric Regression Function Estimation

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a nonparametric regression function estimator, which is obtained by minimizing the distance to an infinite order flat-top trapezoidal kernel estimator. We prove that the proposed estimator achieves a high level of accuracy. Moreover, it preserves the attractive properties of the infinite order flat-top kernel estimator. We also present an extensive numerical study for analysing the performance of two members of the tilted linear smoother class named tilted Nadaraya-Watson and tilted local linear in the finite sample. The simulation study shows that tilted Nadaraya-Watson and tilted local linear perform better than their classical analogs in some conditions in terms of Mean Integrated Squared Error (MISE). Finally, the performance of these estimators as well as the conventional estimators were illustrated by curve fitting to COVID-19 data for 12 countries and a dose-response data set.

stat.ME↗

arXiv2020

Spatial analysis and prediction of COVID-19 spread in South Africa after lockdown

What is the impact of COVID-19 on South Africa? This paper envisages assisting researchers and decision-makers in battling the COVID-19 pandemic focusing on South Africa. This paper focuses on the spread of the disease by applying heatmap retrieval of hotspot areas and spatial analysis is carried out using the Moran index. For capturing spatial autocorrelation between the provinces of South Africa, the adjacent, as well as the geographical distance measures, are used as a weight matrix for both absolute and relative counts. Furthermore, generalized logistic growth curve modeling is used for the prediction of the COVID-19 spread. We expect this data-driven modeling to provide some insights into hotspot identification and timeous action controlling the spread of the virus.

physics.soc-ph↗

arXiv2019

Some computational aspects of maximum likelihood estimation of the skew-$t$ distribution

Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high degree of flexibility of the distribution as the parameters span their admissible range, with ample variation of the associated measures of skewness and kurtosis. While this high flexibility allows to adapt a member of the parametric family to a wide range of data patterns, it also implies that parameter estimation is a more delicate operation with respect to less flexible parametric families, given that a small variation of the parameters can have a substantial effect on the selected distribution. In this context, the aim of the present contribution is to deal with some computational aspects of maximum likelihood estimation. A problem of interest is the possible presence of multiple local maxima of the log-likelihood function. Another one, to which most of our attention is dedicated, is the development of a quick and reliable initialization method for the subsequent numerical maximization of the log-likelihood function, both in the univariate and the multivariate context.

stat.CO↗