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For a graph $G$, a $k$-coloring $c:V(G)\to \{1,2,\ldots, k\}$ is called distinguishing, if the only automorphism $f$ of $G$ with the property $c(v)=c(f(v))$ for every vertex $v\in G$ (color-preserving automorphism), is the identity. In this paper, we show that the number of distinguishing $k$-colorings of $G$ is a monic polynomial in $k$, calling it the distinguishing polynomial of $G$. Furthermore, we compute the distinguishing polynomials of cycles and complete multipartite graphs. We also show that the multiplicity of zero as a root of the distinguishing polynomial of $G$ is at least the number of orbits of $G$., Comment: 13 pages, 1 figure

The emergence of supermassive black holes (SMBHs) in the early universe remains a topic of profound interest and debate. In this paper, we investigate the formation and growth of the first SMBHs within the framework of Modified Gravity (MOG), where gravity exhibits increased strength. We explore how MOG, as an alternative to the standard model, may offer novel insights into the emergence of SMBHs and potentially reconcile the discrepancies observed in the accretion and growth processes. We examine the dynamics of gas and matter in this modified gravitational framework, shedding light on the unique interplay between gravity and the formation of SMBHs., Comment: It has been accepted for publication by European Physical Journal C

With the current progress of quantum computing, quantum annealing is being introduced as a powerful method to solve hard computational problems. In this paper, we study the potential capability of quantum annealing in solving the phase unwrapping problem, an instance of hard computational problems. To solve the phase unwrapping problem using quantum annealing, we deploy the D-Wave Advantage machine which is currently the largest available quantum annealer. The structure of this machine, however, is not compatible with our problem graph structure. Consequently, the problem graph needs to be mapped onto the target (Pegasus) graph, and this embedding significantly affects the quality of the results. Based on our experiment and also D-Wave's reports, the lower chain lengths can result in a better performance of quantum annealing. In this paper, we propose a new embedding algorithm that has the lowest possible chain length for embedding the graph of the phase unwrapping problem onto the Pegasus graph. The obtained results using this embedding strongly outperform the results of Auto-embedding provided by D-Wave. Besides the phase unwrapping problem, this embedding can be used to embed any subset of our problem graph to the Pegasus graph.

Security of Intelligent Transportation Systems (ITS) heavily depends on the security of the underlying components that create such a smart ecosystem. Adaptive Cruise Control (ACC) is embedded into most modern vehicles. In this report, we study the situations that the two vehicles involved in a cruise control scenario create. More precisely, after breaking down the phases the two vehicle go through (especially the ego one), we show how a simple formula can be used to predict collisions in hard brake cruise control scenarios.

Classification is a popular task in the field of Machine Learning (ML) and Artificial Intelligence (AI), and it happens when outputs are categorical variables. There are a wide variety of models that attempts to draw some conclusions from observed values, so classification algorithms predict categorical class labels and use them in classifying new data. Popular classification models including logistic regression, decision tree, random forest, Support Vector Machine (SVM), multilayer perceptron, Naive Bayes, and neural networks have proven to be efficient and accurate applied to many industrial and scientific problems. Particularly, the application of ML to astronomy has shown to be very useful for classification, clustering, and data cleaning. It is because after learning computers, these tasks can be done automatically by them in a more precise and more rapid way than human operators. In view of this, in this paper, we will review some of these popular classification algorithms, and then we apply some of them to the observational data of nonvariable and the RR Lyrae variable stars that come from the SDSS survey. For the sake of comparison, we calculate the accuracy and F1-score of the applied models., Comment: Proceedings based on the lectures given at the hands-on workshop of the ICRANet-ISFAHAN Astronomy Meeting, to be published in Astronomical and Astrophysical Transactions

This article is based on the tutorial we gave at the hands-on workshop of the ICRANet-ISFAHAN Astronomy Meeting. We first introduce the basic theory of machine learning and sort out the whole process of training a neural network. We then demonstrate this process with an example of inferring redshifts from SDSS spectra. To emphasize that machine learning for astronomy is easy to get started, we demonstrate that the most basic CNN network can be used to obtain high accuracy, we also show that with simple modifications, the network can be converted for classification problems and also to processing gravitational wave data., Comment: Proceedings based on the lectures given at the hands-on workshop of the ICRANet-ISFAHAN Astronomy Meeting, to be published in Astronomical and Astrophysical Transactions

A vertex coloring of a graph $G$ is distinguishing if non-identity automorphisms do not preserve it. The distinguishing number, $D(G)$, is the minimum number of colors required for such a coloring and the distinguishing threshold, $\theta(G)$, is the minimum number of colors~$k$ such that any arbitrary $k$-coloring is distinguishing. Moreover, $\Phi_k (G)$ is the number of distinguishing coloring of $G$ using at most $k$ colors. In this paper, for some graph operations, namely, vertex-sum, rooted product, corona product and lexicographic product, we find formulae of the distinguishing number and threshold using $\Phi_k (G)$., Comment: 20 pages, 5 figures

A vertex coloring of a graph $G$ is called distinguishing if no non-identity automorphisms of $G$ can preserve it. The distinguishing number of $G$, denoted by $D(G)$, is the minimum number of colors required for such a coloring, and the distinguishing threshold of $G$, denoted by $\theta(G)$, is the minimum number $k$ such that every $k$-coloring of $G$ is distinguishing. As an alternative definition, $\theta(G)$ is one more than the maximum number of cycles in the cycle decomposition of automorphisms of $G$. In this paper, we characterize $\theta (G)$ when $G$ is disconnected. Afterwards, we prove that, although for every positive integer $k\neq 2$ there are infinitely many graphs whose distinguishing thresholds are equal to $k$, we have $\theta(G)=2$ if and only if $\vert V(G)\vert =2$. Moreover, we show that if $\theta(G)=3$, then either $G$ is isomorphic to one of the four graphs on~3 vertices or it is of order $2p$, where $p\neq 3,5$ is a prime number. Furthermore, we prove that $\theta(G)=D(G)$ if and only if $G$ is asymmetric, $K_n$ or $\overline{K_n}$. Finally, we consider all generalized Johnson graphs, $J(n,k,i)$, which are the graphs on all $k$-subsets of $\{1,\ldots , n\}$ where two vertices $A$ and $B$ are adjacent if $|A\cap B|=k-i$. After studying their automorphism groups and distinguishing numbers, we calculate their distinguishing thresholds as $\theta(J(n,k,i))={n\choose k} - {n-2\choose k-1}+1$, unless $ k=\frac{n}{2}$ and $i\in\{ \frac{k}{2} , k\}$ in which case we have $\theta(J(n,k,i))={n\choose k}$., Comment: 20 pages, 7 figures

Bitcoin uses blockchain technology to maintain transactions order and provides probabilistic guarantee to prevent double-spending, assuming that an attacker's computational power does not exceed %50 of the network power. In this paper, we design a novel bribery attack and show that this guarantee can be hugely undermined. Miners are assumed to be rational in this setup and they are given incentives that are dynamically calculated. In this attack, the adversary misuses the Bitcoin protocol to bribe miners and maximize their gained advantage. We will reformulate the bribery attack to propose a general mathematical foundation upon which we build multiple strategies. We show that, unlike Whale Attack, these strategies are practical. If the rationality assumption holds, this shows how vulnerable blockchain-based systems like Bitcoin are. We suggest a soft fork on Bitcoin to fix this issue at the end., Comment: This work is under review for formal publication

We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of physical parameters of the binary system., Comment: 14 pages, 5 figures

We characterize the relaxation state of galaxy systems by providing an assessment of the reliability of the photometric and spectroscopic probe via the semi-analytic galaxy evolution model. We quantify the correlations between the dynamical age of simulated galaxy groups and popular proxies of halo relaxation in observation, which are mainly either spectroscopic or photometric. We find the photometric indicators demonstrate a stronger correlation with the dynamical relaxation of galaxy groups compared to the spectroscopic probes. We take advantage of the Anderson Darling statistic ($A^2$) and the velocity-segregation ($\bar{\Delta V}$) as our spectroscopic indicators, and use the luminosity gap ($\Delta m_{12}$) and the luminosity de-centring ($D_{\mathrm{off-set}}$) as photometric ones. Firstly, we find that a combination of $\Delta m_{12}$ and $D_{\mathrm{off-set}}$ evaluated by a bivariant relation ($\mathrm{B} = 0.04 \times \Delta m_{12} - 0.11 \times Log(D_{off-set}) + 0.28$), shows a good correlation with the dynamical age compared to all other indicators. Secondly, by using the observational X-ray surface brightness map, we show that the bivariant relation brings about some acceptable correlations with X-ray proxies. These correlations are as well as the correlations between $A^2$ and X-ray proxies, offering reliable yet fast and economical method of quantifying the relaxation of galaxy systems. This study demonstrates that using photometric data to determine the relaxation status of a group will lead to some promising results that are comparable with the more expensive spectroscopic counterpart., Comment: Accepted for publication in Astronomical Journal (ApJ)

Industry 4.0 will make manufacturing processes smarter but this smartness requires more environmental awareness, which in case of Industrial Internet of Things, is realized by the help of sensors. This article is about industrial pharmaceutical systems and more specifically, water purification systems. Purified water which has certain conductivity is an important ingredient in many pharmaceutical products. Almost every pharmaceutical company has a water purifying unit as a part of its interdependent systems. Early detection of faults right at the edge can significantly decrease maintenance costs and improve safety and output quality, and as a result, lead to the production of better medicines. In this paper, with the help of a few sensors and data mining approaches, an anomaly detection system is built for CHRIST Osmotron water purifier. This is a practical research with real-world data collected from SinaDarou Labs Co. Data collection was done by using six sensors over two-week intervals before and after system overhaul. This gave us normal and faulty operation samples. Given the data, we propose two anomaly detection approaches to build up our edge fault detection system. The first approach is based on supervised learning and data mining e.g. by support vector machines. However, since we cannot collect all possible faults data, an anomaly detection approach is proposed based on normal system identification which models the system components by artificial neural networks. Extensive experiments are conducted with the dataset generated in this study to show the accuracy of the data-driven and model-based anomaly detection methods., Comment: this paper is under review in IEEE IoTJ

Our high expectations from Internet of Things (IoT) and how it will positively influence our lifestyles depend on a secure and trusted implementation of it, especially in the sensitive sectors such as health or financial. IoT platforms and solutions must provide Confidentiality, Integrity and Availability (CIA) in a secure and transparent way. Due to the extremely large scales of IoT, traditional centralized solutions for security provisioning cannot be employed in their original form. This article discusses the authentication problem in IoT, which is fundamental to providing CIA. We propose a hierarchical security architecture for this problem and focus on computationally lightweight authentication protocols which can intelligently distribute the computational load across multiple levels and effectively push the load towards upper layers., Comment: This paper is to appear in IEEE Internet of Things Magazine

With the benefits of Internet of Vehicles (IoV) paradigm, come along unprecedented security challenges. Among many applications of inter-connected systems, vehicular networks and smart cars are examples that are already rolled out. Smart vehicles not only have networks connecting their internal components e.g. via Controller Area Network (CAN) bus, but also are connected to the outside world through road side units and other vehicles. In some cases, the internal and external network packets pass through the same hardware and are merely isolated by software defined rules. Any misconfiguration opens a window for the hackers to intrude into vehicles' internal components e.g. central lock system, Engine Control Unit (ECU), Anti-lock Braking System (ABS) or Adaptive Cruise Control (ACC) system. Compromise of any of these can lead to disastrous outcomes. In this paper, we study the security of smart vehicles' adaptive cruise control systems in the presence of covert attacks. We define two covert/stealth attacks in the context of cruise control and propose a novel intrusion detection and compensation method to disclose and respond to such attacks. More precisely, we focus on the covert cyber attacks that compromise the integrity of cruise controller and employ a neural network identifier in the IDS engine to estimate the system output dynamically and compare it against the ACC output. If any anomaly is detected, an embedded substitute controller kicks in and takes over the control. We conducted extensive experiments in MATLAB to evaluate the effectiveness of the proposed scheme in a simulated environment., Comment: This paper has been accepted and is to appear in IEEE Transactions on Intelligent Transportation Systems

Intrusion Prevention Systems (IPS), have long been the first layer of defense against malicious attacks. Most sensitive systems employ instances of them (e.g. Firewalls) to secure the network perimeter and filter out attacks or unwanted traffic. A firewall, similar to classifiers, has a boundary to decide which traffic sample is normal and which one is not. This boundary is defined by configuration and is managed by a set of rules which occasionally might also filter normal traffic by mistake. However, for some applications, any interruption of the normal operation is not tolerable e.g. in power plants, water distribution systems, gas or oil pipelines, etc. In this paper, we design a learning firewall that receives labelled samples and configures itself automatically by writing preventive rules in a conservative way that avoids false alarms. We design a new family of classifiers, called $\mathfrak{z}$-classifiers, that unlike the traditional ones which merely target accuracy, rely on zero false-positive as the metric for decision making. First, we analytically show why naive modification of current classifiers like SVM does not yield acceptable results and then, propose a generic iterative algorithm to accomplish this goal. We use the proposed classifier with CART at its heart to build a firewall for a Power Grid Monitoring System. To further evaluate the algorithm, we additionally test it on KDD CUP'99 dataset. The results confirm the effectiveness of our approach.

The transient non-stationary nature of network reaction to batch arrivals has led to complex models in order to estimate the network quantities of interest. In this report we focus on the IEEE 802.15.4 standard MAC layer and try to deeply study the current approaches in modeling the network reaction to one-shot data arrivals. In addition to the general description of models, we mention the positive and negative points in each case proposing possible alternations which could improve the accuracy of the models., Comment: This is a lightly updated version of a technical report published in 2013

Cyber-Physical Systems (CPSs) are vastly used in today's cities critical infrastructure. The cyber part of these systems usually has a network component through which cyber attacks can be launched. In this paper, we first design an intrusion detection system (IDS) by identifying the plant. We assume the initial operation period of the CPS is attack-free and learn the plant model. Then, we compare the expected output found via the identifier with the real one coming through the feedback link. Any difference greater than a threshold is deemed to be an anomaly. To compensate, once the IDS flags a change in the loop, we restart the system identification to find the new transfer function. With the estimation of the new transfer function at hand, a new controller is designed to keep the system stable. To test the idea, we took a DC motor as the plant and employed ARX identifier. MATLAB Simulink environment was used to test the proposed intrusion detection and compensation framework. We applied a set of deception attacks to the forward channel in our experiments. The obtained results prove that our detection strategy works well and timely reacts to anomalies. Moreover, they show that the compensation strategy is also effective and keeps the system stable under such attacks., Comment: 9 figures, conference

Let $R$ be a finite commutative ring with $1\ne 0$. In this article, we study the total graph of $R$, denoted by $\tau (R)$, determine some of its basic graph-theoretical properties, determine when it is Eulerian, and find some conditions under which this graph is isomorphic to $Cay(R,Z(R)\backslash\lbrace 0\rbrace)$. We shall also compute the domination number of $\tau (R).