Symmetry Of Pattern Research Articles

Fracton critical point at a higher-order topological phase transition

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. Here we demonstrate that the existence of a two-dimensional topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $Lln(L)$. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$

Highly Integrated Multifunctional Antenna for Global Navigation Satellite System

This communication proposes a new highly integrated multifunctional global navigation satellite system (GNSS) antenna used for navigation or surveying high-precision area, the fourth-generation (4G) mobile communication, and short-distance wireless communication. The antenna consists of four elements, saying: 1) a low-profile navigation element on one substrate covering all the GNSS bands and 2) two long-term evolution multiple-input–multiple-output (LTE-MIMO) elements and one Wi-Fi element uniformly distributed on the edge of the substrate. This symmetrical configuration ensures the navigation element’s low axial ratio (AR) and radiation pattern symmetry, as well as navigation accuracy. In addition, to enhance the isolation between the GNSS element and other three elements under high integration, these three elements are designed to avoid resonating within the GNSS bands. The measured peak gains of the GNSS element are 6.0 dBi from 1.16 to 1.28 GHz and 6.5 dBi from 1.52 to 1.62 GHz. The −6 dB impedance bandwidth of the LTE-MIMO elements can cover 840–960, 1800–2200, and 2500–2700 MHz. The distance communication of the Wi-Fi element is 80 m. The experimental results indicate that the proposed multifunctional antenna features low profile, high integration, and wideband, implying potential application in the multifunctional satellite navigation system.

On Some Asymptotic Expansions for the Gamma Function

Inequalities play a fundamental role in both theoretical and applied mathematics and contain many patterns of symmetries. In many studies, inequalities have been used to provide estimates of some functions based on the properties of their symmetry. In this paper, we present the following new asymptotic expansion related to the ordinary gamma function Γ(1+w)∼2πw(w/e)ww2+760w2−120w/2exp∑r=1∞μrwr,w→∞, with the recurrence relation of coefficients μr. Furthermore, we use Padé approximants and our new asymptotic expansion to deduce the new bounds of Γ(w) better than some of its recent ones.

Finite amplitude electro-thermo convection in a cubic box

Three-dimensional electro-thermo-hydrodynamic (ETHD) flows of dielectric fluids driven by simultaneous Coulomb and buoyancy forces in a cubic box is numerically studied. The set of coupled equations associated with the ETHD phenomena are solved with the finite volume method. The code is first validated by comparing the numerically obtained linear critical values of the pure electro-convection and thermal convection with the previous studies. Then the neutral stability curve of the system is given and the finite amplitude instability thresholds with different Rayleigh numbers () are presented. It is found that along the neutral stability curve, the flow strength becomes weaker with the increase of and the decrease of electric Rayleigh number (T). Besides, the gap between the linear and nonlinear critical values expressed in terms of T decreases with the increase of . Primarily, the distributions of charge density, temperature and velocity fields with different governing parameters near neutral stability curve are presented. The temperature and charge density profiles near the linear and nonlinear critical values are given, showing that higher T results in wider charge void region and shorter distance between the charge void region’s lower boundary and injection electrode. Finally, the symmetries of the flow patterns along the neutral stability curve are also discussed briefly.

An Efficient Algorithm for Mining Stable Periodic High-Utility Sequential Patterns

Periodic high-utility sequential pattern mining (PHUSPM) is used to extract periodically occurring high-utility sequential patterns (HUSPs) from a quantitative sequence database according to a user-specified minimum utility threshold (minutil). A sequential pattern’s periodicity is determined by measuring when the frequency of its periods (the time between two consecutive happenings of the sequential pattern) exceed a user-specified maximum periodicity threshold (maxPer). However, due to the strict judgment threshold, the traditional PHUSPM method has the problem that some useful sequential patterns are discarded and the periodic values of some sequential patterns fluctuate greatly (i.e., are unstable). In frequent itemset mining (FIM), some researchers put forward some strategies to solve these problems. Because of the symmetry of frequent itemset pattern (FIPs), these strategies cannot be directly applied to PHUSPM. In order to address these issues, this work proposes the stable periodic high-utility sequential pattern mining (SPHUSPM) algorithm. The contributions made by this paper are as follows. First, we introduce the concept of stability to overcome the abovementioned problems, mine sequential patterns with stable periodic behavior, and propose the concept of stable periodic high-utility sequential patterns (SPHUSPs) for the first time. Secondly, we design a new data structure named the PUL-list to record the periodic information of sequential patterns, thereby improving the mining efficiency. Thirdly, we propose the maximum lability pruning strategy in sequential pattern (MLPS), which can prune a large number of unstable sequential patterns in advance. To assess the algorithm’s effectiveness, we perform many experiments. It turns out that the algorithm can not only mine patterns that are ignored by traditional algorithms, but also ensure that the discovered patterns have stable periodic behavior. In addition, after using the MLPS pruning strategy, the algorithm can prune 46.5% of candidates in advance on average in six datasets. Pruning a large number of candidates in advance not only speeds up the mining process, but also greatly reduces memory usage.

Correlation between Inflorescence Architecture and Floral Asymmetry-Evidence from Aberrant Flowers in Canna L. (Cannaceae).

Floral symmetry studies often focus on the development of monosymmetric and polysymmetric flowers, whereas asymmetric flowers and their position and function within the inflorescence structure are largely neglected. Cannaceae is one of the few families that possesses truly asymmetric flowers, serving as a model to study the characters and mechanisms involved in the development of floral asymmetry and its context within the developing and mature inflorescence. In this study, inflorescence structure and floral morphology of normal asymmetric flowers and 16 aberrant flower collections from Canna indica L. and C. glauca L. were photographed, analyzed, and compared with attention to stamen petaloidy, floral symmetry, and inflorescence branching patterns anterior and posterior to the aberrant flower. In comparison with normal flowers, the aberrant flowers are arranged into abnormal partial florescences, and vary in floral symmetry, orientation, and degree of androecial petaloidy. The appendage of the fertile stamen is universally located distal from the higher order bract, indicating an underlying influence of inflorescence architecture. A synthetic model is proposed to explain the relationship between floral symmetry and inflorescence structure. Data from the observation of aberrant phenotypes strongly support the hypothesis that irregular petaloidy of the stamens is correlated with an asymmetric morphogenetic field within the inflorescence that contributes to the overall floral asymmetry in Canna flowers.

A Symmetry Evaluation Method, Using Elevation Angle, for Lower Limb Movement Patterns during Sitting-to-Standing

In this paper, we propose a method that uses the femoral and tibial elevation angles to quantitatively evaluate the symmetry of lower limb movement during the transition from a sitting position to a standing position. In kinematic analysis of the transition from sitting to standing, the angles of the three joints of the lower limb are often measured. However, due to the large number of variables, it is difficult to evaluate the symmetry of the lower limb movement by comparing data from the six joints of the left and right lower limbs. In this study, therefore, we measured the femoral and tibial elevation angles of healthy participants and rehabilitation patients and visually and numerically evaluated the symmetry and asymmetry of the movement of the left and right lower limbs. We were able to identify the kinematically major lower limbs in the transition from sitting to standing and quantify the symmetry of the movement patterns of the left and right lower limbs. Furthermore, we examined the possibility that the method could be effectively used in the rehabilitation field to evaluate the motor co-ordination that constitutes the lower limb movement pattern in the transition from the sitting to standing position, such as the gait plane rule.

Six-meson amplitude in QCD-like theories

We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudoreal representations, i.e. with global symmetry and breaking patterns $\mathrm{SU}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(n)/\mathrm{SU}(n)$ (extending the QCD case), $\mathrm{SU}(2n)/\mathrm{SO}(2n)$, and $\mathrm{SU}(2n)/\mathrm{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of ten six-meson subamplitudes based on the flavor and group structures. We extend on our previous results obtained within the framework of the $\mathrm{O}(N+1)/\mathrm{O}(N)$ nonlinear sigma model, with $N$ being the number of meson flavors. This work allows for studying a number of properties of six-particle amplitudes at one-loop level.

Fibonacci Sequences, Symmetry and Order in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The physical and biological roots and role of symmetry and asymmetry appearing in biological patterns are addressed. A generalization of the Curie–Neumann principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “top-down” and “bottom-up” approaches to the explanation of symmetry in organisms are presented and discussed in detail. The “top-down” approach implies that the symmetry of the biological structure follows the symmetry of the media in which this structure is functioning; the “bottom-up” approach, in turn, accepts that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of order in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biological objects are addressed. The fine structure of the notion of “order” is discussed. Informational/algorithmic roots of order inherent in the biological systems are considered. Ordered/symmetrical patterns provide an economy of biological information, necessary for the algorithmic description of a biological entity. The application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

Comparative Study of Bilateral Symmetry in Dermatoglyphic Patterns with reference to Geographical Parameters

Introduction: The personal identification is reliable tool for both legal and societal motives in forensic discipline. The utmost conventional manner of identification of individuals is based on the fingerprints. The present study has been carried out on 200 subjects, 100 males and 100 females of different age groups belonging to range from 18-55 years of Jammu and Kashmir and Gujarat population to compare the differences in bilateral symmetry in dermatoglyphic patterns along with frequency distribution of patterns with reference to the geographical locations. The research recommends that there are significant differences in bilateral symmetry and fingerprint patterns between males and females within the two populations and significant differences are observed between the two populations. The predominant fingerprint pattern was Ulnar loop, followed by Whorl in both Jammu and Kashmir and Gujarat state. Moreover, it was observed that maximum inhabitants have 80% of Bilateral Symmetry in (40%) of the two populations followed by 100% (26%) of both Jammu and Kashmir and Gujarat populations.

Patient-led development of digital endpoints and the use of computer vision analysis in assessment of motor function in rare diseases.

Digital health technologies are transforming the way health outcomes are captured and measured. Digital biomarkers may provide more objective measurements than traditional approaches as they encompass continuous and longitudinal data collection and use of automated analysis for data interpretation. In addition, the use of digital health technology allows for home-based disease assessments, which in addition to reducing patient burden from on-site hospital visits, provides a more holistic picture of how the patient feels and functions in the real world. Tools that can robustly capture drug efficacy based on disease-specific outcomes that are meaningful to patients, are going to be key to the successful development of new treatments. This is particularly important for people living with rare and chronic complex conditions, where therapeutic options are limited and need to be developed using a patient-focused approach to achieve the biggest impact. Working in partnership with patient Organisation Duchenne UK, we co-developed a video-based approach, delivered through a new mobile health platform (DMD Home), to assess motor function in patients with Duchenne muscular dystrophy (DMD), a genetic, rare, muscular disease characterized by the progressive loss of muscle function and strength. Motor function tasks were selected to reflect the “transfer stage” of the disease, when patients are no longer able to walk independently but can stand and weight-bear to transfer. This stage is important for patients and families as it represents a significant milestone in the progression of DMD but it is not routinely captured and/or scored by standard DMD clinical and physiotherapy assessments. A total of 62 videos were submitted by eight out of eleven participants who onboarded the app and were analysed with pose estimation software (OpenPose) that led to the extraction of objective, quantitative measures, including time, pattern of movement trajectory, and smoothness and symmetry of movement. Computer vision analysis of video tasks to identify voluntary or compensatory movements within the transfer stage merits further investigation. Longitudinal studies to validate DMD home as a new methodology to predict progression to the non-ambulant stage will be pursued.

Antecedents, Continuities, and Experimental Stages in a Design System: A Symmetry Analysis of Geometric Designs of the Mimbres Tradition

Symmetry analysis characterizes ∼1300 geometric designs on bowl interiors from five sites of the Mimbres culture tradition, AD 1000–1150, of southwestern New Mexico. The analysis reveals a distinct homogeneity in pattern structure and color on three layouts (pendant, centered and band) that, classified by plane pattern symmetries, shows a preference for four finite structures (C2, C4, D2, D4) and two one-dimensional structures (p112, pmm2) and a diversity of one-color, colored, and two-color arrangements of solid and hatched motifs. The analysis reveals common shared symmetries among neighboring cultural traditions to the south in northern Mexico, to the west among the Hohokam, and to the north among the Ancestral Pueblo of central New Mexico. Classification of the designs by symmetry enables detection of experimentation in the evolution of the design system wherein finite designs were placed within banded layouts.

An Efficient Technique to Solve Time-Fractional Kawahara and Modified Kawahara Equations

In this article, we analysed the approximate solutions of the time-fractional Kawahara equation and modified Kawahara equation, which describe the propagation of signals in transmission lines and the formation of nonlinear water waves in the long wavelength region. An efficient technique, namely the natural transform decomposition method, is used in the present study. Fractional derivatives are considered in Caputo, Caputo–Fabrizio, and Atangana–Baleanu operative in the Caputo manner. We have presented numerical results graphically to demonstrate the applicability and efficiency of derivatives with fractional order to depict the water waves in long wavelength regions. The symmetry pattern is a fundamental feature of the Kawahara equation and the symmetrical aspect of the solution can be seen from the graphical representations. The obtained outcomes of the proposed method are compared to those of other well-known numerical techniques, such as the homotopy analysis method and residual power series method. Numerical solutions converge to the exact solution of the Kawahara equations, demonstrating the significance of our proposed method.

Astigmatism profile in the elderly population: Tehran Geriatric Eye Study

To determine the prevalence of astigmatism and its associated factors and examine astigmatism symmetry patterns in an elderly population. Population based cross-sectional study. The present population-based cross-sectional study was conducted on an elderly population above 60 years of age in Tehran, Iran in 2019. The sampling was done using the stratified multistage random cluster sampling method. All study participants underwent a complete optometric examination and slit-lamp biomicroscopy. The prevalence of astigmatism higher than -0.50, -1.00, and -2.00 D was 83% (95% CI: 81 -84), 52 % (95% CI: 50 -54), and 19% (95% CI: 17-20), respectively. These prevalence was 79%(95% CI: 77-81), 46(95% CI: 44-49) and 14(95% CI: 13-16) in subjects without a history of ocular surgery, respectively. Based on cylinder power worse than -1.00 D, 10% (95% CI: 9-12), 20% (95% CI: 18-22), and 21% (95% CI:19-23) of study participants had with the rule, against the rule, and oblique astigmatism, respectively. According to the results of the multiple regression model, male gender, older age, low education level, pure posterior subcapsular cataract, pseudophakia, and myopia were independent factors associated with astigmatism. The prevalence of anisorule astigmatism was 57 % (95% CI: 56-59), the most common anisorule astigmatism was against the rule-oblique type with a prevalence of 36% (95% CI: 34-38). The prevalence of astigmatism was high in the elderly population of Tehran. More than half of the participants in this study had anisorule astigmatism, and against the rule-oblique combination was more prevalent than other types. A posterior subcapsular cataract, a history of cataract surgery, and myopia were the associated factors of astigmatism in this study.

Influence of characteristic parameters on the tribological properties of vein-bionic textured cylindrical roller thrust bearings

In this research, three types of vein-bionic texture patterns inspired by five kinds of leaves (Forsythia, Clausena lansium, Ash, Pipal, and Apricot) were designed and fabricated on the raceways of the shaft washers of cylindrical roller thrust bearings (CRTBs) through a fiber laser marking system. A vertical universal wear test rig was used to obtain the coefficient of friction (COF) of bearings under starved lubrication, with a customized tribo-pair. The wear losses of the shaft washers and the worn surfaces were characterized. The influence of different veins (chief, primary, secondary) and vein-structure characteristics (pattern symmetry, number of veins) on the tribological behavior of vein-bionic textured CRTBs is investigated and discussed. The results show that the original vein-bionic (V) pattern inspired by the Ash has the best friction-reducing performance, while the texture with the no-chief vein (NC) obtained by Clausena lansium has the best wear resistance. The chief vein mainly contributes to the low friction by enhancing the secondary lubrication effect and facilitating the formation of a protective nylon film. A reasonable mechanism for improving the tribological properties of resulting textures is proposed.

Overlapping Neural Responses to Reflectional Symmetry and Glass Patterns Revealed by an ERP Priming Paradigm

The extrastriate visual cortex is activated by visual regularity and generates an ERP known as the sustained posterior negativity (SPN). Spatial filter models offer a biologically plausible account of regularity detection based on the spectral properties of an image. These models are specific to reflection and therefore imply that reflectional symmetry and Glass patterns are coded by different neural populations. We utilised the SPN priming effect to probe representational overlap between reflection and Glass patterns. For each trial, participants were presented with a rapid succession of three patterns. In the Repeated condition, three reflections or three Glass patterns were presented. In the Changing condition, patterns alternated between reflection and Glass patterns. An increase in SPN amplitude (priming) was observed in both the Repeated and Changing conditions. Results indicate a greater representational overlap in the brain between reflection and Glass patterns than predicted by spatial filter models.

Strain engineering of the magnetic anisotropy and magnetic moment in NdFeO3 epitaxial thin films

Strain engineering is a powerful mean for tuning the various functionalities of ABO3 perovskite oxide thin films. Rare-earth orthoferrite RFeO3 materials such as NdFeO3 (NFO) are of prime interest because of their intriguing magnetic properties as well as their technological potential applications especially as thin films. Here, using a large set of complementary and advanced techniques, we show that NFO epitaxial thin films, successfully grown by pulsed laser deposition on (001)-SrTiO3, show a strong magnetic anisotropy below a critical thickness tc of 54 nm, associated with the occurrence of structural modifications related to symmetry and domain pattern changes. By varying the tensile misfit strain through the decrease of film thickness below tc, the amplitudes of in and out-of-plane magnetization can be continuously tuned while their ratio stays constant. Furthermore, different low-temperature magnetic behaviors are evidenced for strained and relaxed films, suggesting that the strain-induced structural state impacts the magnetic phase stability.

Identify Patterns in Online Bin Packing Problem: An Adaptive Pattern-Based Algorithm

Bin packing is a typical optimization problem with many real-world application scenarios. In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into a bin immediately after its arrival. Inspired by duality in optimization, we proposed pattern-based adaptive heuristics for the online bin packing problem. The idea is to predict the distribution of items based on packed items, and to apply this information in packing future arrival items in order to handle uncertainty in online bin packing. A pattern in bin packing is a combination of items that can be packed into a single bin. Patterns selected according to past items are adopted and periodically updated in scheduling future items in the algorithm. Symmetry in patterns and the stability of patterns in the online bin packing problem are discussed. We have implemented the algorithm and compared it with the Best-Fit in a series of experiments with various distribution of items to show its effectiveness.

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns.

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.

Diffraction enhancement of symmetry and modular structures.

Diffraction enhancement of symmetry (DES) is the phenomenon according to which the symmetry of the diffraction pattern of a crystal can be higher than the point symmetry of the structure that has produced it. The most well known example is that of Friedel's law, which is however violated in the presence of resonant scattering. This phenomenon is addressed in monoarchetypal modular structures and it is shown that a sufficient condition for DES is that both the module and the family of stacking vectors are invariant under an isometry that is not a symmetry operation for the structure. In general, DES is still observed in the presence of significant resonant scattering. The example of SiC polytypes, where the phenomenon has been confirmed experimentally, is studied in detail but the conclusions depend only on the symmetry of the layer and on the stacking vectors: the same applies therefore to all compounds sharing these features, like ZnS.