---

In this paper, we show how to obtain suitable differential charactristics for block ciphers with neural networks. We represent the operations of a block cipher, regarding their differential characteristics, through a directed weighted graph. In this way, the problem of finding the best differential characteristic for a block cipher reduces to the problem of finding the minimum-weight multi-path way between two known nodes in the proposed graph. We applied Hopfield network to find the minimum-weight multi-path way. In this technique, the probability of convergence to a local minimum increases when the number of rounds of the cipher increases. We also applied Boltzmann machine to avoid local minima. We applied these techniques to find 3-round, 4-round and 5-round differential characteristics of Serpent block cipher, and repeated the optimization procedures for each characteristics 100 times. With Hopfield network, we obtained suitable results 100, 20 and 1 times for 3-round, 4-round and 5-round of the Serpent respectively. With Boltzmann machine, we obtained suitable results 100, 99 and 30 times for 3-round, 4-round and 5-round of the Serpent respectively. These results show that simulated annealing help avoiding the many local minima of energy function. We compare the probabilities of our obtained differential characteristics for Serpent with the probabilities of eight differential characteristics previously reported in other papers. The comparison shows that our proposed technique obtains better results in 6 cases, and the same results in 2 cases. We also found a 7-round differential characteristic with a probability of 2-125 with Boltzmann machine. Neglecting the reported Bommerang differential characteristics of Serpent, our obtained 7-round differential characteristic is the first report on a differential characteristic for more than 6 rounds of this cipher. The results of experiments indicate the efficiency of neural networks to find suitable differential characteristics of block ciphers.

---

In statistics, Entropy is a measure of disorder of time series. Entropy is used in physiologic for signal analysis. In physiologic science, Entropy is used for performance analysis of body organs such as heart and brain. Epileptic patients have been diagnosed by this technique. In this paper for the first time, Entropy is used to determine the health condition of mechanical systems. A special kind of Entropy, namely Permutation Entropy is used for this purpose.To perform the experiment an apparatus consisting of a motor coupled with a shaft has been designed and manufactured. Vibration signals from supporting bearing of this system in different shaft states namely healthy shaft, and shafts with 3, 5 and 7 mm crack were gathered with a vibration data analyzer. The vibration were taken from sensors mounted on bearing supports of the shaft. Shaft was subjected to a constant bending moment. The vibration signals were preprocessed by permutation Entropy method. Nine different features were extracted from the Entropy signals which are fed to an Adaptive Neuro Fuzzy Inference System (ANFIS). The designed ANFIS was capable of classifying different shaft states with an overall %96 percision.

---

Computer-aided process planning (CAPP) is a bridge for integrating computer-aided design (CAD) and computer-aided manufacturing (CAM). One of the basic computer-aided process planning tasks is sequencing of machining features. Sequencing of machining features is determined based on technical and geometrical rules. In this paper, the technical rules, geometrical rules and sequencing of machining features method were discussed. At first, some of the technical rules were pointed. Then, the geometrical interactions were studied and two new geometrical rules were introduced for sequencing the machining features having geometrical interaction. These rules can yield unique results and they are identified easily by the computer systems. Also, an algorithm was introduced for automated application of these geometrical rules in computer systems. The conflict between the technical and geometrical rules that may occur in some cases was studied. This conflict must be considered in the sequencing of machining features methods. Finally, an algorithm was introduced for sequencing of machining features based on permutation. In this algorithm the technical and geometric rules were applied separately and step by step. If there is any conflict between technical and geometrical rules, this conflict could detect automatically in this algorithm. Algorithms were programmed and verified in PythonOCC.