An Easy Construction of Generalized Neighbor Designs in Minimal Circular Blocks

Neighbor designs are used in the experiments where neighbor effects may arise. Neighbor designs neutralize these effects and are, therefore, considered to be robust against neighbor effects. Minimal neighbor designs are always most economical among the neighbor designs and are, therefore, preferred by the experimenters. Method of cyclic shifts provides these designs in circular blocks only for odd v (number of treatments). For v even, minimal circular generalized neighbor designs in which only v 2 unordered pairs of distinct treatments do not appear as neighbors will be the better alternate to the minimal neighbor designs. In this article, such minimal generalized neighbor designs are constructed in circular blocks for v even.

Application of Convolution with Periodic Boundary Condition for Processing Data from Cylindrical Electrode Arrays

In this paper, modification of convolutional neural networks for purposes of processing electromyographic data obtained from cylindrical arrays of electrodes was proposed. Taking into account the spatial symmetry of the array, convolution operation was redefined using periodic boundary conditions, which allowed to construct a neural network that is invariant to rotations of electrodes array around its axis. Applicability of the proposed approach was evaluated by constructing a neural network containing a new type of convolutional layer and training it on the open UC2018 DualMyo dataset in order to classify gestures basing on data from a single myobracelet. The network based on the new type of convolution performed better compared to common convolutions when trained on data without augmentation, which indicates that such a network is invari­able to cyclic shifts in the input data. Neural networks with modified convolutional layers and common convolutional layers achieved f-1 scores of 0.96 and 0.65 respectively with no augmentation for input data and f-1 scores of 0.98 and 0.96 in case when train-time augmentation was applied. Test data was augmented in both cases. Potentially, proposed convolution can be applied in processing any data with the same connectivity in such a way that allows to adapt time-tested architectural solutions for networks by replacing common convolutions with modified ones.

A Public Key Cryptosystem Using a Group of Permutation Polynomials

In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field Fqm. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m2+3m – 4 left cyclic shifts, 5m2 +3m + 4 xor operations and 7 permutations on bits for decryption.