arXiv subjects

F. Jafari

Publications and source records attributed to F. Jafari.

6 recordsLinked to original sources

arXiv2026

Regular sets of circulant quartic graphs

For a graph $\Gamma=(V,E)$ and nonnegative integers $a$ and $b$, a nonempty proper subset $C \subset V$ is called an $(a,b)$-regular set if every vertex in $C$ has exactly $a$ neighbors in $C$, and every vertex in $V\setminus C$ has exactly $b$ neighbors in $C$. In this paper, we study the existence of such sets in connected Cayley graph $\Gamma = \operatorname{Cay}(\mathbb{Z}_n, S)$. We establish a necessary and sufficient condition for the existence of $(0, |S|)$-regular sets and identify additional conditions under which no such set can exist. We further prove that $(|S|, 0)$-regular sets do not occur in $\Gamma$, and more generally, that no connected Cayley graph $\operatorname{Cay}(G,S)$ contains a $(1, |S|)$-regular set. As a main result, we determine the existence and nonexistence of $(a,b)$-regular sets in connected circulant quartic graphs for all possible values of $a$ and $b$.

math.CO↗

arXiv2026

The Sequence Reconstruction of Permutations under Hamming Metric with Small Errors

The sequence reconstruction problem asks for the recovery of a sequence from multiple noisy copies, where each copy may contain up to $r$ errors. In the case of permutations on $n$ letters under the Hamming metric, this problem is closely related to the parameter $N(n,r)$, the maximum intersection size of two Hamming balls of radius $r$. While previous work has resolved $N(n,r)$ for small radii ($r \leq 4$) and established asymptotic bounds for larger $r$, we present new exact formulas for $r \in \{5,6,7\}$ using group action techniques. In addition, we develop a formula for $N(n,r)$ based on the irreducible characters of the symmetric group $S_n$, along with an algorithm that enables computation of $N(n,r)$ for larger parameters, including cases such as $N(43,8)$ and $N(24,14)$.

math.GR↗

arXiv2025

Detection of Vascular Leukoencephalopathy in CT Images

Artificial intelligence (AI) has seen a significant surge in popularity, particularly in its application to medicine. This study explores AI's role in diagnosing leukoencephalopathy, a small vessel disease of the brain, and a leading cause of vascular dementia and hemorrhagic strokes. We utilized a dataset of approximately 1200 patients with axial brain CT scans to train convolutional neural networks (CNNs) for binary disease classification. Addressing the challenge of varying scan dimensions due to different patient physiologies, we processed the data to a uniform size and applied three preprocessing methods to improve model accuracy. We compared four neural network architectures: ResNet50, ResNet50 3D, ConvNext, and Densenet. The ConvNext model achieved the highest accuracy of 98.5% without any preprocessing, outperforming models with 3D convolutions. To gain insights into model decision-making, we implemented Grad-CAM heatmaps, which highlighted the focus areas of the models on the scans. Our results demonstrate that AI, particularly the ConvNext architecture, can significantly enhance diagnostic accuracy for leukoencephalopathy. This study underscores AI's potential in advancing diagnostic methodologies for brain diseases and highlights the effectiveness of CNNs in medical imaging applications.

eess.IV↗

arXiv2022

New Bounds on the Size of Permutation Codes With Minimum Kendall $\tau$-distance of Three

We study $P(n,3)$, the size of the largest subset of the set of all permutations $S_n$ with minimum Kendall $\tau$-distance $3$. Using a combination of group theory and integer programming, we reduced the upper bound of $P(p,3)$ from $(p-1)!-1$ to $(p-1)!-\lceil\frac{p}{3}\rceil+2\leq (p-1)!-2$ for all primes $p\geq 11$. In special cases where $n$ is equal to $6,7,11,13,14,15$ and $17$ we reduced the upper bound of $P(n,3)$ by $3,3,9,11,1,1$ and $4$, respectively.

math.CO↗

arXiv2019

Modified Radon transform inversion using moments

Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We establish a modified Radon transform (MRT) via convolution with a mollifier and obtain its inversion formula. The relationship of the moments of the Radon transform and the moments of its modified Radon transform is derived and MRT data is used to provide a uniform approximation to the original density function. The reconstruction algorithm is implemented, and a simple density function is reconstructed from moments of its modified Radon transform. Numerical convergence of this reconstruction is shown to agree with the derived theoretical results.

math.FA↗

arXiv2011

On the range of composition operators on spaces of entire functions

The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with affine maps. After some motivation demonstrating the importance of characterization of range spaces of bandlimited functions, in this paper we identify the subspaces of $ L^2 (\mathbb{R}) $ generated by these action. Extension of these theorems where Paley-Wiener spaces are replaced by the deBranges-Rovnyak spaces are given.

math.CV↗