A detection system, modeled in a graph, uses "detectors" on a subset of vertices to uniquely identify an "intruder" at any vertex. We consider two types of detection systems: open-locating-dominating (OLD) sets and identifying codes (ICs). An OLD set gives each vertex a unique, non-empty open neighborhood of detectors, while an IC provides a unique, non-empty closed neighborhood of detectors. We explore their fault-tolerant variants: redundant OLD (RED:OLD) sets and redundant ICs (RED:ICs), which ensure that removing/disabling at most one detector guarantees the properties of OLD sets and ICs, respectively. This paper focuses on constructing optimal RED:OLD sets and RED:ICs on the infinite king's grid, and presents the proof for the bounds on their minimum densities; [3/10, 1/3] for RED:OLD sets and [3/11, 1/3] for RED:ICs.

Software Defined Networking (SDN) is positioning the standard for the management of networks due to its scalability and flexibility to program the network. The SDN provides many advantages but it also involves some specific security problems take down the controller using cyber attack and in result the whole network will shut down which makes it a single point of failure. In this paper, the DDoS attacks in SDN were detected using AI-enabled, machine and deep learning, models with some specific features for data-set under normal and DDoS traffic. In our approach, initial data-set is collected from 84 features on kaggle and then the 20 top most features are selected using permutation importance algorithm. The data-set were learned and tested with AI-enabled 5 models. Our experimental results showed that the use of machine learning based random forest model has achieved the highest accuracy rate of 99.97%, in DDoS attack detection in SDN. Our contributions through this study are, first, we found highest 20 attacks that absolutely contributed to DDoS attacks. Secondly, it can reduce the time and cost of comparing various learning models and performance required for determining a learning model suitable for DDoS detection. Finally, various experimental methods for evaluating the performance of the learning model are presented so that related researchers can utilize them.

We propose that the high energy Cosmic Ray particles around the spectral turn-down commonly called the {\it knee} and up to the upturn, commonly called the {\it ankle}, mostly come from Blue Super Giant star explosions. At the upturn, i.e. the {\it ankle}, Cosmic Rays probably switch to another source class, most likely extragalactic sources. To show this we recently compiled a set of Radio Supernova data to list the magnetic field, shock speed and radius scale (Biermann et al. 2018) \cite{Biermann18}. Using particle acceleration theory at shocks, those numbers can be transformed into characteristic {\it knee} and {\it ankle} energies. Without adjusting any free parameters both of these observed energies are directly indicated by the supernova data. We now proceed to the next step in the argument, and use the Supernova Remnant data of the starburst galaxy M82. Assuming that they are Blue Supergiant star explosions, the shock will race to their outer edge with a magnetic field that follows ${B (r) \, r \, \sim \, const.}$. We argue that the shock runs through the entire magnetic plasma wind region at full speed all the way out to the wind-shell, which is of order parsec scale. The speed is observed to be $\sim \, 0.1 \, c$ at about ${10^{16} \, {\rm cm}}$ radius in the plasma wind. This demonstrates how Blue Supergiant star explosions can provide the Cosmic Ray particles across the {\it knee} and up to the {\it ankle} energy range. The data from the CREAM (Cosmic Ray Energetics and Mass Experiment) mission will test this cosmic ray concept which is reasonably well grounded in two independent radio supernova data sets. The next step in developing our understanding is to obtain accurate Cosmic Ray data near to the {\it knee}, and use unstable isotopes of Cosmic Ray nuclei at high energy to probe the "piston" driving the explosion. We plan to combine these data with the physics of the budding black hole which is probably forming in each of these stars to learn more.