arXiv subjects

Ali Zafari

Publications and source records attributed to Ali Zafari.

25 records · Page 2Linked to original sources

arXiv2023

Attention-Based Generative Neural Image Compression on Solar Dynamics Observatory

NASA's Solar Dynamics Observatory (SDO) mission gathers 1.4 terabytes of data each day from its geosynchronous orbit in space. SDO data includes images of the Sun captured at different wavelengths, with the primary scientific goal of understanding the dynamic processes governing the Sun. Recently, end-to-end optimized artificial neural networks (ANN) have shown great potential in performing image compression. ANN-based compression schemes have outperformed conventional hand-engineered algorithms for lossy and lossless image compression. We have designed an ad-hoc ANN-based image compression scheme to reduce the amount of data needed to be stored and retrieved on space missions studying solar dynamics. In this work, we propose an attention module to make use of both local and non-local attention mechanisms in an adversarially trained neural image compression network. We have also demonstrated the superior perceptual quality of this neural image compressor. Our proposed algorithm for compressing images downloaded from the SDO spacecraft performs better in rate-distortion trade-off than the popular currently-in-use image compression codecs such as JPEG and JPEG2000. In addition we have shown that the proposed method outperforms state-of-the art lossy transform coding compression codec, i.e., BPG.

eess.IV↗

arXiv2022

Metric dimension, doubly resolving set and strong metric dimension for $(C_n\Box P_k)\Box P_m$

A subset $Q = \{q_1, q_2, ..., q_l\}$ of vertices of a connected graph $G$ is a doubly resolving set of $G$ if for any various vertices $x, y \in V(G)$ we have $r(x|Q)-r(y|Q)\neqλI$, where $λ$ is an integer, and $I$ indicates the unit $l$- vector $(1,..., 1)$. A doubly resolving set of vertices of graph $G$ with the minimum size, is denoted by $ψ(G)$. In this work, we will consider the computational study of some resolving sets with the minimum size for $(C_n\Box P_k)\Box P_m$.

math.CO↗

arXiv2021

Some resolving parameters in a class of Cayley graphs

Resolving parameters is a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences. In this article, we construct a class of Toeplitz graphs, and will be denoted by $T_{2n}(W)$, so that they are Cayley graphs. First, we review some of the features of this class of graphs. In fact, this class of graphs are vertex transitive, and by calculating the spectrum of the adjacency matrix related with them, we show that this class of graphs cannot be edge transitive. Moreover, we show that this class of graphs cannot be distance regular, and since the computing resolving parameters of a class of graphs such that are not distance regular is more difficult, then we regard this as justification for our focus on some resolving parameters. In particular, we determine the minimal resolving set, doubly resolving set and strong metric dimension for this class of graphs.

math.CO↗

arXiv2021

Some algebraic properties of a class of integral graphs determined by their spectrum

Let $Γ=(V,E)$ be a graph. If all the eigenvalues of the adjacency matrix of the graph $Γ$ are integers, then we say that $Γ$ is an integral graph. A graph $Γ$ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph $Γ=Cay(\mathbb{Z}_{n}, S)$, where $n=p^m$, ($p$ is a prime integer, $m\in\mathbb{N}$) and $S=\{{a}\in\mathbb{Z}_{n}\,|\,\, (a, n)=1\}$. First, we show that $Γ$ is an integral graph. Also we determine the automorphism group of $Γ$. Moreover, we show that $Γ$ and $K_v \bigtriangledownΓ$ are determined by their spectrum.

math.CO↗

arXiv2020

Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of Layer Sun Graph

Let $G$ be a finite, connected graph of order of at least 2, with vertex set $V(G)$ and edge set $E (G)$. A set $S$ of vertices of the graph $G$ is a doubly resolving set for $G$ if every two distinct vertices of $G$ are doubly resolved by some two vertices of $S$. The minimal doubly resolving set of vertices of graph $G$ is a doubly resolving set with minimum cardinality and is denoted by $ψ(G)$. In this paper, first, we construct a class of graphs of order $2n+ Σ_{r=1}^{k-2}nm^{r}$, denoted by $LSG(n,m, k)$, and call these graphs as the layer Sun graphs with parameters $n$, $m$ and $k$. Moreover, we compute minimal doubly resolving sets and the strong metric dimension of layer Sun graph $LSG(n,m, k)$ and the line graph of the layer Sun graph $LSG(n,m, k)$.

math.CO↗

arXiv2020

Metric dimension, minimal doubly resolving sets and the strong metric dimension for jellyfish graph and cocktail party graph

Let $Γ$ be a simple connected undirected graph with vertex set $V(Γ)$ and edge set $E(Γ)$. The metric dimension of a graph $Γ$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. For an ordered subset $W = \{w_1, w_2, ..., w_k\}$ of vertices in a graph $Γ$ and a vertex $v$ of $Γ$, the metric representation of $v$ with respect to $W$ is the $k$-vector $r(v | W) = (d(v, w_1), d(v, w_2), ..., d(v, w_k ))$. If every pair of distinct vertices of $Γ$ have different metric representations then the ordered set $W$ is called a resolving set of $Γ$. It is known that the problem of computing this invariant is NP-hard. In this paper, we consider the problem of determining the cardinality $ψ(Γ)$ of minimal doubly resolving sets of $Γ$, and the strong metric dimension for jellyfish graph $JFG(n, m)$ and cocktail party graph $CP(k+1)$.

math.GM↗

arXiv2018

Some algebraic properties of bipartite Kneser graphs

Let $n$ and $k$ be integers with $n> k\geq1$ and $[n] = \{1, 2, ... , n\} $. The $bipartite \ Kneser \ graph$ $H(n, k)$ is the graph with the all $k$-element and all ($n-k$)-element subsets of $[n] $ as vertices, and there is an edge between any two vertices, when one is a subset of the other. In this paper, we show that $H(n, k)$ is an arc-transitive graph. Also, we show that $H(n,1)$ is a distance-transitive Cayley graph. Finally, we determine the automorphism group of the graph $H(n, 1)$ and show that $Aut(H(n, 1)) \cong Sym([n] )$ $\times \mathbb{Z}_2$, where $\mathbb{Z}_2$ is the cyclic group of order $2$. Moreover, we pose some open problems about the automorphism group of the bipartite Kneser graph $H(n, k)$.

math.GR↗