Symmetry, Volume 8, Issue 7 (July 2016) – 17 articles

Deduplication is an efficient data reduction technique, and it is used to mitigate the problem of huge data volume in big data storage systems. Content defined chunking (CDC) is the most widely used algorithm in deduplication systems. The expected chunk size is an important parameter of CDC, and it influences the duplicate elimination ratio (DER) significantly. We collected two realistic datasets to perform an experiment. The experimental results showed that the current approach of setting the expected chunk size to 4 KB or 8 KB empirically cannot optimize DER. Therefore, we present a logistic based mathematical model to reveal the hidden relationship between the expected chunk size and the DER. This model provides a theoretical basis for optimizing DER by setting the expected chunk size reasonably. We used the collected datasets to verify this model. The experimental results showed that the R² values, which describe the goodness of fit, are above 0.9, validating the correctness of this mathematic model. Based on the DER model, we discussed how to make DER close to the optimum by setting the expected chunk size reasonably. Full article

We propose an efficient image-matching method for deformable-object image matching using discrimination of deformable objects and geometric similarity clustering between feature-matching pairs. A deformable transformation maintains a particular form in the whole image, despite local and irregular deformations. Therefore, the matching information is statistically analyzed to calculate the possibility of deformable transformations, and the images can be identified using the proposed method. In addition, a method for matching deformable object images is proposed, which clusters matching pairs with similar types of geometric deformations. Discrimination of deformable images showed about 90% accuracy, and the proposed deformable image-matching method showed an average 89% success rate and 91% accuracy with various transformations. Therefore, the proposed method robustly matches images, even with various kinds of deformation that can occur in them. Full article

An efficient surface area evaluation method is introduced by using smooth surface reconstruction for three-dimensional scanned human body data. Surface area evaluations for various body parts are compared with the results from the traditional alginate-based method, and quite high similarity between the two results is obtained. We expect that our surface area evaluation method can be an alternative to measuring surface area by the cumbersome alginate method. Full article

Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D) and power spectrum decay rate (β). Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D. Full article

Both distributed healthcare systems and the Internet of Things (IoT) are currently hot topics. The latter is a new computing paradigm to enable advanced capabilities in engineering various applications, including those for healthcare. For such systems, the core social requirement is the privacy/security of the patient information along with the technical requirements (e.g., energy consumption) and capabilities for adaptability and personalization. Typically, the functionality of the systems is predefined by the patient’s data collected using sensor networks along with medical instrumentation; then, the data is transferred through the Internet for treatment and decision-making. Therefore, systems creation is indeed challenging. In this paper, we propose a model-driven framework to develop the IoT-based prototype and its reference architecture for personalized health monitoring (PHM) applications. The framework contains a multi-layered structure with feature-based modeling and feature model transformations at the top and the application software generation at the bottom. We have validated the framework using available tools and developed an experimental PHM to test some aspects of the functionality of the reference architecture in real time. The main contribution of the paper is the development of the model-driven computational framework with emphasis on the synergistic effect of security and energy issues. Full article

In this paper, a modified GrabCut algorithm is proposed using a clustering technique to reduce image noise. GrabCut is an image segmentation method based on GraphCut starting with a user-specified bounding box around the object to be segmented. In the modified version, the original image is filtered using the median filter to reduce noise and then the quantized image using K-means algorithm is used for the normal GrabCut method for object segmentation. This new process showed that it improved the object segmentation performance a lot and the extract segmentation result compared to the standard method. Full article

The paper develops applications of symmetric orbit functions, known from irreducible representations of simple Lie groups, in numerical analysis. It is shown that these functions have remarkable properties which yield to cubature formulas, approximating a weighted integral of any function by a weighted finite sum of function values, in connection with any simple Lie group. The cubature formulas are specialized for simple Lie groups of rank two. An optimal approximation of any function by multivariate polynomials arising from symmetric orbit functions is discussed. Full article

Region duplication forgery where a part of the image itself is copied and pasted onto a different part of the same image grid is becoming more popular in image manipulation. The forgers often apply geometric transformations such as rotation and scaling operations to make the forgery imperceptible. In this study, an image region duplication forgery detection algorithm is proposed based on the angular radial partitioning and Harris key-points. Two standard databases have been used: image data manipulation and MICC-F220 (Media Integration and Communication Center– of the University of Florence) for experimentation. Experiment results demonstrate that the proposed technique can detect rotated regions in multiples of 30 degrees and can detect region duplication with different scaling factors from 0.8, to 1.2. More experimental results are presented to confirm the effectiveness of detecting region duplication that has undergone other changes, such as Gaussian noise, and JPEG compression. Full article

Nowadays, several wireless location systems have been developed in the research world. The goal of these systems has always been to find the greatest accuracy as possible. However, if every node takes data from the environment, we can gather a lot of information, which may help us understand what is happening around our network in a cooperative way. In order to develop this cooperative location and tracking system, we have implemented a sensor network to capture data from user devices. From this captured data we have observed a symmetry behavior in people’s movements at a specific site. By using these data and the symmetry feature, we have developed a statistical cooperative approach to predict the new user’s location. The system has been tested in a real environment, evaluating the next location predicted by the system and comparing it with the next location in the real track, thus getting satisfactory results. Better results have been obtained when the stochastic cooperative approach uses the transition matrix with symmetry. Full article

The band structure of strongly correlated two-dimensional (2D) semimetal systems is found to be significantly affected by the spin-orbit coupling (SOC), resulting in SOC-induced Fermi surfaces. Dirac, Weyl and Majorana representations are used for the description of different semimetals, though the band structures of all these systems are very similar. We develop a theoretical approach to the band theory of two-dimensional semimetals within the Dirac–Hartree–Fock self-consistent field approximation. It reveals partially breaking symmetry of the Dirac cone affected by quasi-relativistic exchange interactions for 2D crystals with hexagonal symmetry. Fermi velocity becomes an operator within this approach, and elementary excitations have been calculated in the tight-binding approximation when taking into account the exchange interaction of $\pi ({\mathrm{p}}_z)$ -electron with its three nearest $\pi ({\mathrm{p}}_z)$ -electrons. These excitations are described by the massless Majorana equation instead of the Dirac one. The squared equation for this field is of the Klein–Gordon–Fock type. Such a feature of the band structure of 2D semimetals as the appearance of four pairs of nodes is shown to be described naturally within the developed formalism. Numerical simulation of band structure has been performed for the proposed 2D-model of graphene and a monolayer of Pb atoms. Full article

We derive a Hamiltonian version of the $\mathcal{PT}$ -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and spectral stability of breathers (time-periodic solutions localized in the lattice) supported near one pair of coupled pendula. Orbital stability or instability of breathers is proved in a subset of the existence region. Full article

In this paper, we propose a robust voice activity detection (VAD) algorithm to effectively distinguish speech from non-speech in various noisy environments. The proposed VAD utilizes power spectral deviation (PSD), using Teager energy (TE) to provide a better representation of the PSD, resulting in improved decision performance for speech segments. In addition, the TE-based likelihood ratio and speech absence probability are derived in each frame to modify the PSD for further VAD. We evaluate the performance of the proposed VAD algorithm by objective testing in various environments and obtain better results that those attained by of the conventional methods. Full article

In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss–Bonnet invariant. Examples of canonical scalar field and k-essence to support the early-time acceleration are considered. The formalism to calculate the perturbations in a Friedmann–Robertson–Walker (FRW) universe and to derive the spectral index and the tensor-to-scalar ratio is furnished. Full article

Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium-type representation of the Dark Fluid allows us to involve in its analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar element); respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of 10 models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extended; applications are considered for cosmology and space-times with spherical and pp-wave symmetries. In these applications we focused the attention on three main electromagnetic phenomena induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric Clusters; second, generation of anomalous electromagnetic responses; third, formation of Dark Epochs in the Universe history. Full article

The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of the $O(3,2)$ de Sitter group containing two $O(3,1)$ Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the $Sp\left(4\right)$ group, which serves as the basic language for two-mode squeezed states. Since the $Sp\left(4\right)$ symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified. Full article

The drastic increase of websites is one of the causes behind the recent information overload on the internet. A recommender system (RS) has been developed for helping users filter information. However, the cold-start and sparsity problems lead to low performance of the RS. In this paper, we propose methods including the visual-clustering recommendation (VCR) method, the hybrid between the VCR and user-based methods, and the hybrid between the VCR and item-based methods. The user-item clustering is based on the genetic algorithm (GA). The recommendation performance of the proposed methods was compared with that of traditional methods. The results showed that the GA-based visual clustering could properly cluster user-item binary images. They also demonstrated that the proposed recommendation methods were more efficient than the traditional methods. The proposed VCR2 method yielded an F1 score roughly three times higher than the traditional approaches. Full article

Three new classes of N-body problems of goldfish type are identified, with N an arbitrary positive integer ( $N\ge 2$ ). These models are characterized by nonlinear Newtonian (“accelerations equal forces”) equations of motion describing N equal point-particles moving in the complex z-plane. These highly nonlinear equations feature many arbitrary coupling constants, yet they can be solved by algebraic operations. Some of these N-body problems are isochronous, their generic solutions being all completely periodic with an overall period T independent of the initial data (but quite a few of these solutions are actually periodic with smaller periods $T/p$ with p a positive integer); other models are isochronous for an open region of initial data, while the motions for other initial data are not periodic, featuring instead scattering phenomena with some of the particles incoming from, or escaping to, infinity in the remote past or future. Full article