Different Degrees Of Symmetry Research Articles

Support structure tomography using per-pixel signed shadow casting in human manikin 3D printing

This study proposes an advanced algorithm for predicting the optimal orientation in human manikin 3D printing. We can print the manikin mesh data on any scale depending on the user’s needs. Once the 3D printing scale was determined, the manikin data were dissected based on the 3D printer’s maximal printing volume using our previous work. Then, we applied the newly proposed algorithm, designated as “per-pixel signed-shadow casting,” to each dissected manikin part to calculate the volumes of the object and the support structure. Our method classified the original mesh triangles into three groups—alpha, beta, and top-covering—to eliminate the need for special hardware such as graphic cards. The result is shown as a two-dimensional bitmap file, designated as “tomograph”. This tomograph represents the local support structure distribution information on a visual and quantitative basis. Repeating this tomography method for the three rotational axes resulted in a four-dimensional (4D) box-shaped graph. The optimal orientation of any arbitrary object is easily determined from the lowest-valued pixel in the 4D box graph. We applied this proposed method to several basic primitive shapes with different degrees of symmetry and complex shapes, such as the famous “Stanford Bunny”. Finally, the algorithm was applied to human manikins using several printing scales. The theoretical values were compared with those obtained from analytical or g-code-based experimental volumes.

Structural, electronic and optoelectronic properties of asymmetric organic ligands in Dion-Jacobson phase perovskites

Dion-Jacobson (DJ) phase perovskites have attracted substantial attention in view of its showing great potential to solve the stability issue of optoelectronic devices. Herein, three organic ligands (1,3-propanediamine PDA, N-methylpropane-1,3-diammonium N-MPDA, and 3-(dimethylamino)-1-propylammonium DMPD) are selected as a spacer cation. The structural, electronic, and optoelectronic properties of organic ligands with different degrees of symmetry in n = 1 Dion-Jacobson (DJ) phase A'PbI4 (A' = PDA, N-MPDA, DMPD) perovskite are investigated by carrying out the first-principles method. The structural parameters show an increasing trend of crystal volume, octahedral distortion and stability of the crystal structure with the increase of ligand asymmetry. All three kinds of perovskites are direct bandgap semiconductors, and the bandgap values of A'PbI4 are in the order of N-MPDAPbI4 (2.711 eV) > PDAPbI4 (2.272 eV) > DMPDPbI4 (2.201 eV). The density of states (DOS) indicates that the 6p and 6s orbitals of Pb atoms and 5p orbitals of I atoms are mainly involved in conduction, while the contribution of organic ligands to electron orbitals is negligible. Additionally, the optoelectronic properties reveal that perovskite with asymmetric organic ligands has better absorption in the visible region than perovskite with symmetric organic ligands, which makes it useful as photovoltaic materials. The calculation of asymmetric organic ligands provides guidance and insights for the study of high-performance DJ phase perovskite.

Optimization of a NdFeB permanent magnet configuration for in-vivo drug delivery experiments

We propose a new concept of magnetic focusing for targeting and accumulation of functionalized superparamagnetic nanoparticles in living organs through composite configurations of different permanent magnets. The proposed setups fulfill two fundamental requirements for in vivo experiments: 1) reduced size of the magnets to best focusing on small areas representing the targeted organs of mice and rats and 2) maximization of the magnetic driving force acting on the magnetic nanoparticles dispersed in blood. To this aim, several configurations of permanent magnets organized with different degrees of symmetry have been tested. The product B·gradB proportional to the magnetic force has been experimentally measured, over a wide area (20 × 20 mm2), at a distance corresponding to the hypothetical distance of the mouse organ from the magnets. A non-symmetric configuration of mixed shape permanent magnets resulted in particularly promising to achieve the best performances for further in vivo experiments.

Controlling the Multifractal Generating Measures of Complex Networks

Mathematical modelling of real complex networks aims to characterize their architecture and decipher their underlying principles. Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph model to characterize the spatiotemporal complexity and heterogeneity encoded in the interaction weights. We provide analytical tools to verify the multifractal properties of the proposed model. By varying the parameters in the initial unit square, the model can reproduce a diverse range of multifractal spectrums with different degrees of symmetry, locations, support and shapes. We estimate and investigate the weighted multifractal graph model corresponding to two real-world complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of cognitively healthy people and patients exhibiting late mild cognitive impairment leading to Alzheimer disease. The analysis of recovered models show that the proposed random graph model provides a novel way to understand the self-similar structure of complex networks and to discriminate different network structures. Additionally, by mapping real complex networks onto multifractal generating measures, it allows us to develop new network design and control strategies, such as the minimal control of multifractal measures of real systems under different functioning conditions or states.

On the number of limit cycles in asymmetric neural networks

The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience. In this work, we investigate how the structure of recurrent connectivity influences the ability of a network to have storable patterns and in particular limit cycles, by modeling a recurrent neural network with McCulloch–Pitts neurons as a content-addressable memory system.A key role in such models is played by the connectivity matrix, which, for neural networks, corresponds to a schematic representation of the ‘connectome’: the set of chemical synapses and electrical junctions among neurons. The shape of the recurrent connectivity matrix plays a crucial role in the process of storing memories. This relation has already been exposed by the work of Tanaka and Edwards, which presents a theoretical approach to evaluate the mean number of fixed points in a fully connected model at thermodynamic limit. Interestingly, further studies on the same kind of model but with a finite number of nodes have shown how the symmetry parameter influences the types of attractors featured in the system. Our study extends the work of Tanaka and Edwards by providing a theoretical evaluation of the mean number of attractors of any given length L for different degrees of symmetry in the connectivity matrices.

Interocular Symmetry of Fixation, Optic Disc, and Corneal Astigmatism in Bilateral High Myopia: The Shanghai High Myopia Study.

PurposeWe investigate the interocular symmetry of fixation, optic disc, and corneal astigmatism in bilateral high myopia, and evaluate the predictive relationships between them.MethodsWe enrolled 202 cases with bilateral high myopia. Fixation, in terms of the bivariate contour ellipse area (BCEA), was evaluated with the Macular Integrity Assessment microperimetry. Optic disc features, including orientation, tilt, and rotation, were evaluated with ultrawide-field retinal photographs. Corneal topography was performed with Pentacam. Interocular symmetry of fixation, optic disc, and corneal astigmatism was assessed, and the predictive relationships between these parameters were investigated.ResultsAxial length differences between the two eyes were: ≥0 to ≤1 mm, 67.8%; 1 to ≤2 mm, 20.3%; 2 to ≤3 mm, 9.4%; and >3 mm, 2.5%. Axial length, 95% BCEA, and magnitude of corneal astigmatism showed good interocular symmetry, whereas the optic disc tilt, rotation, and axis of corneal astigmatism (mirror axes) showed less symmetry (all P < 0.05). No interocular symmetry was observed in the direction of the fixation ellipse. In both eyes, the corneal steep meridian more often was consistent with the optic disc orientation than inconsistent (right eye [OD], P < 0.001; left eye [OS], P = 0.029).ConclusionsAs different parameters presented different degrees of symmetry, cautions are needed when including both eyes or only one lateral eye in cases of bilateral high myopia for clinical investigations. The optic disc orientation, to some extent, may indicate the steep meridian of the cornea.Translational RelevanceOur study provided evidences for selection of eye laterality in clinical investigations of highly myopic eyes.

Polarization-independent transparent effect in windmill-like metasurface

A windmill-like metasurface featuring a polarization-independent electromagnetically induced transparency (EIT) at microwave frequencies is numerically and experimentally demonstrated. The unit cell of the metasurface consists of four rotated identical metal wires, with a 45° angle between the adjacent wires. Destructive coupling between the resonance modes of the metal wires results in the emergence of a transparent window. By combining the metal wires with different degrees of symmetry, EIT effects in the metasurface show polarization-independent properties to incident linear and circular polarization waves. In addition, it is numerically demonstrated that the metasurface possesses a low-loss slow wave property with a group index of 125 and sensing capability based on the refractive index with a figure of merit of 8.73. Such a scheme may lead to many potential applications in areas of slow light and sensing.

Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion.

Polarization-insensitive plasmonic-induced transparency in planar metamaterial consisting of a regular triangle and a ring

In this article, we demonstrate plasmonic-induced optical transparency (PIT) in a planar metamaterial consisting of a metallic regular triangle (RT) embedded in a ring nanostructure. The interference between the bright dipole mode of the RT and the dark quadrupole mode of the ring leads to the emergence of a transparent window in the visible regime. By combining nanostructures with different degrees of symmetry, the PIT transmission properties of our metamaterial remain stable with respect to the incident polarization, showing polarization-insensitivity to the incident wave. The transmission efficiency of the PIT peak for different polarizations can be maintained at greater than 95.77% with a fluctuation range of 0.01% in our calculation accuracy.

Photonic band gaps of two-dimensional phononic crystals tuned and optimized by modifying the configuration

A method is introduced to tune and optimize the photonic band gaps （PBGs） of two-dimensional photonic crystals （PCs）. PBGs between the bands at low frequency can be tuned by an additional atom rod at arbitrary positions. Moreover, fixing up the two atom rods at optimal positions and tuning the lengths of the two cylinders, the normalized gap widths of PBGs could be enlarged with a suitable configuration. The results also show that the setting up of large PBGs depends on different degrees of symmetry of the system in the case of two atom rods in a unit cell, the larger PBGs at higher frequency require lower symmetry.

Determination of ground-state properties in quantum spin systems by single-qubit unitary operations and entanglement excitation energies

CNR-INFM SMC, and Dipartimento di Fisica, Universit`a di Firenze,via G. Sansone 1, I-50019 Sesto Fiorentino, Italy(Dated: December 13, 2007)We introduce a method for analyzing ground state properties of quantum many body systems,based on the characterization of separability and entanglement by single subsystem unitary opera-tions. We apply the method to the study of the ground state structure of several interacting spin-1/2models, described by Hamiltonians with different degrees of symmetry. We show that the approachbased on single qubit unitary operations allows to introduce “entanglement excitation energies”,a set of observables that can characterize ground state properties, including the quantification ofsingle-site entanglement and the determination of quantum critical points. The formalism allowsto identify the existence and location of factorization points, and a purely quantum “transitionof entanglement” that occurs at the approach of factorization. This kind of quantum transition ischaracterized by a diverging ratio of excitation energies associated to single-qubit unitary operations.

Properties of trapped electromagnetic modes in coupled waveguides

The existence of trapped modes in coupled electromagnetic waveguides is experimentally investigated for configurations with different degrees of symmetry supporting hybrid modes. The occurrence of confined solutions in such open geometries is proven to be much more general than demonstrated so far, as predicted by Goldstone and Jaffe [J. Goldstone and R. L. Jaffe, Phys. Rev. B 45, 14100 (1992)]. The identification of the observed modes is based on the numerical modeling of the relative vector fields. The experimental results make evident that an increasing aperture of the configuration can improve the confinement of the mode instead of generating additional leakage channels. In particular, long-lived trapped modes can be easily obtained in geometries with a large aperture. Their resonance parameters can compete with those of standard close cavities working at millimeter wavelengths. The role of the symmetry on the properties of these trapped modes is discussed in detail.

Statistical thermodynamics for choice models on graphs

Formalism based on equilibrium statistical thermodynamics is applied to communication networks of decision-making individuals. It is shown that in statistical ensembles for choice models, properly defined disutility plays the same role as energy in statistical mechanics. We demonstrate additivity and extensivity of disutility and build three types of equilibrium statistical ensembles: the canonical, the grand canonical and the super-canonical. Using Boltzmann probability measure one can reproduce the logit choice model. We propose using q-distributions for temperature evolution of moments of stochastic variables. The formalism is applied to networks with fixed topologies of different degrees of symmetry, for which analytic and numerical results are presented.

Torsional analyses of trans-2-butene and propene cations: A comparative investigation of two prototypical ions with different degrees of symmetry

The mass analyzed threshold ionization spectra of trans-2-butene and propene have been obtained using single-step vacuum ultraviolet excitation. The ionization potential for trans-2-butene is 73 605±4 cm−1, while for propene it is 78 587±4 cm−1. Both species have progressions of the low frequency, torsional, normal modes. Using the torsional normal mode and first overtone from a trans-2-butene cation the torsional barrier is determined to be approximately 453 cm−1, assuming a sinusoidal potential. Normal mode analysis indicates that all low frequency normal modes of the propene cation involve substantial internal motion of the vinyl component, and the spectrum shows a very anharmonic torsional mode progression. These factors complicate direct torsional barrier analysis from the experimental lines, but through the use of various ab initio methods the propene torsional barrier is determined to be approximately 429 cm−1. Due to the anharmonicity found in propene, the correlation corrected vibrational self-consistent field method in GAMESS was used to verify the assignments of the experimental lines. The torsional barriers for both cations are found to lie approximately 275–300 cm−1 below the barrier heights of the neutral species.

Population-level compensation after loss of vegetative buds: interactions among damaged and undamaged cotton neighbours.

Population-level compensation occurs "when herbivore attack on one individual allows another individual to grow more rapidly". This form of compensation was investigated in high and low density cotton crops subjected to three treatments: (i) undisturbed controls, (ii) uniformly damaged, in which all plants were damaged, and (iii) non-uniformly damaged, in which every second plant was damaged. Damaged plants had their vegetative buds manually removed to simulate damage by Helicoverpa spp. (Lepidoptera). Removal of vegetative buds did not reduce seed cotton production per unit ground area. In uniformly damaged crops, compensation was essentially the result of profuse branching after release of apical dominance and activation of axilary buds. In non-uniformly damaged crops, population level mechanisms acted that involved strong plant-plant interactions. At both plant densities, undamaged plants grown alongside damaged neighbours accumulated more root and shoot biomass and produced more seed cotton than undamaged plants in uniform crops. Different degrees of symmetry in the relationship between damaged and undamaged neighbours lead to different degrees of compensation, viz. seed cotton production of non-uniformly damaged crops ranged from 98 to 125% of that in controls. At high plant density, neighbour status also affected flowerbud initiation and/or retention. Changes in competitive relationships as well as early detection of and response to neighbour status were likely involved in these responses.

Normal hearing thresholds for clicks.

This paper evaluates the normal hearing thresholds for clicks and assesses the effects on these thresholds of varying the duration of the listening period and the presentation rate, polarity, and symmetry of the clicks. There were no significant changes in thresholds as the listening period decreased from 2s to 300 mg. There was, however, a 2.5 dB increase in threshold at the listening period decreased from 300 to 100 ms. Increase stimulus presentation rate from 5 to 80/s decreased threshold 4.5 dB per tenfold change in rate. There were no significant differences in threshold between rarefaction and condensation clicks. The average threshold obtained from 40 normal young adults using 100-microseconds square-wave clicks presented through a TDH-49 earphone at 10/s was 36.4-dB peak SPL or 29.9 peak equivalent SPL. Neither peak SPL nor peak equivalent SPL measurements gave consistent thresholds for clicks with different degrees of symmetry. A root-mean-square measure of the pressure over the initial millisecond-SPL(1 ms)-gave a threshold of 25.6 dB. This SPL(1ms) measure of threshold proved to be far more consistent for clicks with different degrees of symmetry than either the peak SPL or the peak equivalent SPL measures.

The Determination of the Constants of Harmonic Vibrations

A general method is developed to find the relations between constants of the potential energy and the frequencies of point systems for harmonic vibrations. Useful formulas are derived (Eqs. (16) and (23)); and matrices required frequently for the solution of problems are tabulated. Relations are also found between the force constants of a molecule with a number of equivalent atoms and the vibration frequencies of an isotopic molecule of a lower degree of symmetry. This also gives the relations between the frequencies of isotopic molecules of different degrees of symmetry.