In this paper, the notion of 2-tuples distribution matrices of the rotation symmetric orbits is proposed, by using the properties of the 2-tuples distribution matrix, a new characterization of 2-resilient rotation symmetric Boolean functions is demonstrated. Based on the new characterization of 2-resilient rotation symmetric Boolean functions, constructions of 2-resilient rotation symmetric Boolean functions (RSBFs) are further studied, and new 2-resilient rotation symmetric Boolean functions with prime variables are constructed.

In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.

This paper proposes an encryption-then-compression (EtC) system-friendly data hiding scheme for images, where an EtC system compresses images after they are encrypted. The EtC system divides an image into non-overlapping blocks and applies four block-based processes independently and randomly to the image for visual encryption of the image. The proposed scheme hides data to a plain, i.e., unencrypted image and the scheme can take hidden data out from the image encrypted by the EtC system. Furthermore, the scheme serves reversible data hiding, so it can perfectly recover the unmarked image from the marked image whereas the scheme once distorts unmarked image for hiding data to the image. The proposed scheme copes with the three of four processes in the EtC system, namely, block permutation, rotation/flipping of blocks, and inverting brightness in blocks, whereas the conventional schemes for the system do not cope with the last one. In addition, these conventional schemes have to identify the encrypted image so that image-dependent side information can be used to extract embedded data and to restore the unmarked image, but the proposed scheme does not need such identification. Moreover, whereas the data hiding process must know the block size of encryption in conventional schemes, the proposed scheme needs no prior knowledge of the block size for encryption. Experimental results show the effectiveness of the proposed scheme.

Herein, we analytically derive the effective index and field distribution of the LP01 mode of a step-index N-sided regular-polygonal-core fiber. To do this, we utilize the lowest-order non-anomalous approximation of the π/N expansion. These properties are also calculated numerically and the results are compared the with approximations.

Reproducing quadruped locomotion from an engineering viewpoint is important not only to control robot locomotion but also to clarify the nonlinear mechanism for switching between locomotion patterns. In this paper, we reproduced a quadruped locomotion pattern, gallop, using a central pattern generator (CPG) hardware network based on the abelian group Z4×Z2, originally proposed by Golubitsky et al. We have already used the network to generate three locomotion patterns, walk, trot, and bound, by controlling the voltage, EMLR, inputted to all CPGs which acts as a signal from the midbrain locomotor region (MLR). In order to generate the gallop and canter patterns, we first analyzed the network symmetry using group theory. Based on the results of the group theory analysis, we desymmetrized the contralateral couplings of the CPG network using a new parameter in addition to EMLR, because, whereas the walk, trot, and bound patterns were able to be generated from the spatio-temporal symmetry of the product group Z4×Z2, the gallop and canter patterns were not. As a result, using a constant element $hat{kappa}$ on Z2, the gallop and canter locomotion patterns were generated by the network on ${f Z}_4+hat{kappa}{f Z}_4$, and actually in this paper, the gallop locomotion pattern was generated on the actual circuit.

This paper expands Bartlett's bisection theorem. The theory of modal S-parameters and their circuit representation is constructed from a group-theoretic perspective. Criteria for the division of a circuit at a fixed node whose state is distinguished by the irreducible representation of its stabilizer subgroup are obtained, after being inductively introduced using simple circuits as examples. Because these criteria use only circuit symmetry and do not require human judgment, the distinction is reliable and implementable in a computer. With this knowledge, the entire circuit can be characterized by a finite combination of smaller circuits. Reducing the complexity of symmetric circuits contributes to improved insights into their characterization, and to savings of time and effort in calculations when applied to large-scale circuits. A three-phase filter and a branch-line coupler are analyzed as application examples of circuit and electromagnetic field analysis, respectively.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

We present a hard-wired central patter generator (CPG) hardware network that reproduces the periodic oscillations of the typical gaits, namely, walk, trot, and bound. Notably, the three gaits are generated by a single parameter, i.e., the battery voltage EMLR, which acts like a signal from the midbrain's locomotor region. One CPG is composed of two types of hardware neuron models, reproducing neuronal bursting and beating (action potentials), and three types of hardware synapse models: a gap junction, excitatory and inhibitory synapses. When four hardware CPG models were coupled into a Z4 symmetry network in a previous study [22], two neuronal oscillation patterns corresponding to four-legged animal gaits (walk and bound) were generated by manipulating a single control parameter. However, no more than two neuronal oscillation patterns have been stably observed on a hard-wired four-CPG hardware network. In the current study, we indicate that three neuronal oscillation patterns (walk, trot, and bound) can be generated by manipulating a single control parameter on a hard-wired eight-CPG (Z4 × Z2 symmetry) hardware network.

To improve immunity against process gradients, a common centroid constraint, in which every pair of capacitors should be placed symmetrically with respect to a common center point, is widely used. The pair of capacitors are derived by dividing some original capacitors into two halves. Xiao et al. proposed a method to obtain a placement which satisfies the common centroid constraints, but this method has a defect. In this paper, we propose a decoding algorithm to obtain a placement which satisfies common centroid constraints.

IEEE802.11 Wireless Local Area Networks (WLANs) are becoming more and more pervasive due to their simple channel access mechanism, Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), but this mechanism provides all nodes including Access Point and other Stations with the same channel access probability. This characteristic does not suit the infrastructure mode which has so many downlink flows to be transmitted at the Access Point that congestion at the Access Point is more likely to occur. To resolve this asymmetry traffic problem, we develop an Optimal Contention Window Adjustment method assuming the condition of erroneous channels over WLANs. This method can be easily implemented and is compatible with the original CSMA/CA mechanism. It holds the ratio of downlink and uplink flows and at the same time achieves the maximum saturation throughput in the WLANs. We use the Markov Chain analytical model to analyze its performance and validate it through the simulations.

This study investigated the relationship between social skills and facial asymmetry in facial expressions. Three-dimensional facial landmark data of facial expressions (neutral, happy, and angry) were obtained from Japanese participants (n = 62). Following a facial expression task, each participant completed KiSS-18 (Kikuchi's Scale of Social Skills; Kikuchi, 2007). Using a generalized Procrustes analysis, faces and their mirror-reversed versions were represented as points on a hyperplane. The asymmetry of each individual face was defined as Euclidian distance between the face and its mirror reversed face on this plane. Subtraction of the asymmetry level of a neutral face of each individual from the asymmetry level of a target emotion face was defined as the index of “expression asymmetry” given by a particular emotion. Correlation coefficients of KiSS-18 scores and expression asymmetry scores were computed for both happy and angry expressions. Significant negative correlations between KiSS-18 scores and expression asymmetries were found for both expressions. Results indicate that the symmetry in facial expressions increases with higher level of social skills.

This paper presents a self-clustering algorithm to detect symmetry in images. We combine correlations of orientations, scales and descriptors as a triple feature vector to evaluate each feature pair while low confidence pairs are regarded as outliers and removed. Additionally, all confident pairs are preserved to extract potential symmetries since one feature point may be shared by different pairs. Further, each feature pair forms one cluster and is merged and split iteratively based on the continuity in the Cartesian and concentration in the polar coordinates. Pseudo symmetric axes and outlier midpoints are eliminated during the process. Experiments demonstrate the robustness and accuracy of our algorithm visually and quantitatively.

Probabilistic model checking is an emerging technology for analyzing systems which exhibit stochastic behaviors. The verification of a larger system using probabilistic model checking faces the same state explosion problem as ordinary model checking. Probabilistic symmetry reduction is a technique to tackle this problem. In this paper, we study probabilistic symmetry reduction for a system with a ring buffer which can describe various applications. A key of probabilistic symmetry reduction is identifying symmetry of states with respect to the structure of the target system. We introduce two functions; Shiftδ and Reverse to clarify such symmetry. Using these functions, we also present pseudo code to construct a quotient model. Then, we show two practical case studies; the one-dimensional Ising model and the Automatic Identification System (AIS). Behaviors of them were verified, but suffered from the state explosion problem. Through the case studies, we show that probabilistic symmetry reduction takes advantage of reducing the size of state space.

In a rooted triangulated planar graph, an outer vertex and two outer edges incident to it are designated as its root, respectively. Two plane embeddings of rooted triangulated planar graphs are defined to be equivalent if they admit an isomorphism such that the designated roots correspond to each other. Given a positive integer n, we give an O(n)-space and O(1)-time delay algorithm that generates all biconnected rooted triangulated planar graphs with at most n vertices without delivering two reflectively symmetric copies.

In a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two different plane embeddings of a rooted outerplanar graphs are called symmetric copies. Given integers n ≥ 3 and g ≥ 3, we give an O(n)-space and O(1)-time delay algorithm that generates all biconnected rooted outerplanar graphs with exactly n vertices such that the size of each inner face is at most g without delivering two symmetric copies of the same graph.

This paper proposes a synthesis method of 2-channel IIR paraunitary filter banks by successive extraction of 2-port lattice sections. When a power symmetry transfer function is given, a filter bank is realized as cascade of paraunitary 2-port lattice sections. The method can synthesize both odd- and even-order filters with Butterworth or elliptic characteristics. The number of multiplications per second can also be reduced.

A metallic waveguide that has an array of dielectric rods located at a distance from the side wall of approximately one quarter the waveguide width was previously proposed for single mode propagation over a wide frequency range. In this study, the S parameters of such a waveguide were measured for the TE10 mode.

Using frictional force microscopy (FFM), the friction surface characteristics were compared between twisted nematic (TN) mode and vertical alignment (VA) mode alignment films (AFs). The friction asymmetry was detected depending on temperature conditions on TN mode AF, but not on VA mode AF. The difference between two modes was explained by leaning intermolecular repulsion caused by the pre-tilt angle uniformity and the density of side chain. No level difference according to temperature conditions appeared when the pre-tilt angle were measured after liquid crystal (LC) injection.

Symmetry constrains are the constraints that the given cells should be placed symmetrically in design of analog ICs. We use O-tree to represent placements and propose a decoding algorithm which can obtain one of the minimum placements satisfying the constraints. The decoding algorithm uses linear programming, which is too much time consuming. Therefore we propose a graph based method to recognize if there exists no placement satisfying both the given symmetry and O-tree constraints, and use the method before application of linear programming. The effectiveness of the proposed method was shown by computational experiments.

A system that has an array of dielectric rods at the center of a waveguide was previously suggested for single mode propagation with a wide frequency range. However, it is difficult to introduce the wave source from a coaxial cable, due to use of the TE10-like and TE20-like modes. In this investigation, an asymmetric setup of the dielectric rods is proposed for better coupling efficiency of the TE10 mode.