On dynamic monopolies of graphs: the average and strict majority thresholds

Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}\cup \{0\}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a dynamic monopoly corresponding to $(G, \tau)$ if the vertices of $G$ can be partitioned into subsets $D_0, D_1,..., D_k$ such that $D_0=D$ and for any $i\in {0, ..., k-1}$, each vertex $v$ in $D_{i+1}$ has at least $\tau(v)$ neighbors in $D_0\cup ... \cup D_i$. Dynamic monopolies are in fact modeling the irreversible spread of influence in social networks. In this paper we first obtain a lower bound for the smallest size of any dynamic monopoly in terms of the average threshold and the order of graph. Also we obtain an upper bound in terms of the minimum vertex cover of graphs. Then we derive the upper bound $|G|/2$ for the smallest size of any dynamic monopoly when the graph $G$ contains at least one odd vertex, where the threshold of any vertex $v$ is set as $\lceil (deg(v)+1)/2 \rceil$ (i.e. strict majority threshold). This bound improves the best known bound for strict majority threshold. We show that the latter bound can be achieved by a polynomial time algorithm. We also show that $\alpha'(G)+1$ is an upper bound for the size of strict majority dynamic monopoly, where $\alpha'(G)$ stands for the matching number of $G$. Finally, we obtain a basic upper bound for the smallest size of any dynamic monopoly, in terms of the average threshold and vertex degrees. Using this bound we derive some other upper bounds

Organic agriculture in Iran: farmers' barriers to and factors influencing adoption

Organic agriculture is being promoted in Iran to address environmental problems resulting from the use of chemical materials in agriculture. Despite many advantages of organic agriculture, the results of several case studies show that its adoption rate is still very low among farmers. The purpose of this paper is to review previous studies that investigated the main factors influencing and challenging the adoption of organic agriculture. The review included journal articles and conference papers from 2007 to 2012. The results show that Iranian farmers have strong motives for the adoption, yet face challenges in certifying, marketing, and accessing reliable technical information and credits. Given the review of factors that govern farmers' adoption of organic agriculture, key mechanisms for promoting farmers' adoption are discussed. Further research is needed to learn how to bring these mechanisms into play in Iran

A review on medical plants affecting Staphylococcus aureus

Background and aims: Infectious diseases are among the most important causes of mortality around the world and according to the WHO report 10.5 million cases of death were happened due to infections. Staphylococcus aureus is one of the most important pathogen that its infections are varied from local infections to life threatening infections. With regard to high antibiotic resistance of this agent its control and treatment is a challenge in medicine. The aim of this study was to review the effective medicinal plants against S. aureus with special attention of native plants of Iran. Methods: A comprehensive literature review was performed on papers that have been published from 2004 till 2016 in data resources such as NCBI, Sciencedirect, Springer, Web of science and as well as local databases such as Irandoc, Islamic science citation (ISC) and magiran with special focus on those that have been reported native medicinal plants in Iran. The selected keywords were Staphylococcus aureus, medicinal plant, natural antibiotic, antibacterial plant and medicinal herbs. Results: Different studies were found that have reported effective medicinal plants against S. aureus and were able to significantly inhibit bacterial growth. As well as different parts of these plants have been investigated for antibacterial activity and found that considerable differences are present among these parts of plants. Conclusion: Based on the reported studies, there are different medicinal plants in Iran that can be regarded as effective source for discovery new antibacterial agents against S. aureus and treatment of resistant strains

Asymptotic Loss in Privacy due to Dependency in Gaussian Traces

The rapid growth of the Internet of Things (IoT) necessitates employing privacy-preserving techniques to protect users' sensitive information. Even when user traces are anonymized, statistical matching can be employed to infer sensitive information. In our previous work, we have established the privacy requirements for the case that the user traces are instantiations of discrete random variables and the adversary knows only the structure of the dependency graph, i.e., whether each pair of users is connected. In this paper, we consider the case where data traces are instantiations of Gaussian random variables and the adversary knows not only the structure of the graph but also the pairwise correlation coefficients. We establish the requirements on anonymization to thwart such statistical matching, which demonstrate the significant degree to which knowledge of the pairwise correlation coefficients further significantly aids the adversary in breaking user anonymity.Comment: IEEE Wireless Communications and Networking Conferenc

Minimum Target Sets in Non-Progressive Threshold Models: When Timing Matters

Let $G$ be a graph, which represents a social network, and suppose each node $v$ has a threshold value $\tau(v)$. Consider an initial configuration, where each node is either positive or negative. In each discrete time step, a node $v$ becomes/remains positive if at least $\tau(v)$ of its neighbors are positive and negative otherwise. A node set $\mathcal{S}$ is a Target Set (TS) whenever the following holds: if $\mathcal{S}$ is fully positive initially, all nodes in the graph become positive eventually. We focus on a generalization of TS, called Timed TS (TTS), where it is permitted to assign a positive state to a node at any step of the process, rather than just at the beginning. We provide graph structures for which the minimum TTS is significantly smaller than the minimum TS, indicating that timing is an essential aspect of successful target selection strategies. Furthermore, we prove tight bounds on the minimum size of a TTS in terms of the number of nodes and maximum degree when the thresholds are assigned based on the majority rule. We show that the problem of determining the minimum size of a TTS is NP-hard and provide an Integer Linear Programming formulation and a greedy algorithm. We evaluate the performance of our algorithm by conducting experiments on various synthetic and real-world networks. We also present a linear-time exact algorithm for trees.Comment: Accepted in ECAI-23 (26th European Conference on Artificial Intelligence