Complex Symmetry Research Articles

Extreme asymmetry and chirality - A challenging quantification

Symmetry operators must be defined relatively to a space and to a metric. Complex symmetries are typically considered in the case of the cartesian product of the Euclidean space by a space whose elements are tuples of colors. While interesting open problems exist in this field, challenging ones remain in the Euclidean case, without invoking colors. We present some of these problems in the case of extreme chirality figures and of extreme asymmetrical probability distributions.

On the generalized mean transforms of complex symmetric operators

In this paper, we prove that if $$T\in {\mathcal {L}({\mathcal {H}})}$$ is complex symmetric, then its generalized mean transform $${\widehat{T}}(t)~ (t\not =0)$$ of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform $${\widehat{T}}(0)$$ of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.

Single-crystal diffraction at the high-pressure Indo-Italian beamline Xpress at Elettra, Trieste.

In this study the first in situ high-pressure single-crystal X-ray diffraction experiments at Xpress, the Indo-Italian beamline of the Elettra synchrotron, Trieste (Italy), are reported. A description of the beamline experimental setup and of the procedures for single-crystal centring, data collection and processing, using diamond anvil cells, are provided. High-pressure experiments on a synthetic crystal of clinoenstatite (MgSiO3), CaCO3 polymorphs and a natural sample of leucophoenicite [Mn7Si3O12(OH)2] validated the suitability of the beamline experimental setup to: (i) locate and characterize pressure-induced phase transitions; (ii) solve ab initio the crystal structure of high-pressure polymorphs; (iii)perform fine structural analyses at the atomic scale as a function of pressure; (iv) disclose complex symmetry and structural features undetected using conventional X-ray sources.

Evolutionary Algorithms for Community Detection in Continental-Scale High-Voltage Transmission Grids

Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively).

Does Zygomatic Complex Symmetry Differ Between Healthy Individuals and Surgically Treated Patients Using Intraoperative 3-Dimensional Cone Beam Computed Tomographic Imaging?

Reconstruction of symmetry after zygomaticomaxillary complex (ZMC) fractures is essential for esthetic appearance as well as function. Therefore, this study aimed to analyze whether bony facial symmetry in patients surgically treated for unilateral ZMC fractures via intraoperative imaging differs from that of healthy individuals. Retrospective and cross-sectional radiographic measurements of patients treated for unilateral ZMC fractures via intraoperative cone beam computed tomography (CBCT) were performed to evaluate the postoperative ZMC symmetry. The same number of healthy individuals without any history of midfacial trauma matched for age and gender served as the control group. Asymmetry of the ZMC was determined by measuring bilateral differences in the malar eminence position on CBCT. In addition, demographic statistics, etiology, and fracture type were analyzed. Analysis of 57 surgically treated patients and 57 healthy individuals with a mean age of 29years was performed. No significant difference in the symmetry of the malar eminence position was observed between healthy individuals and patients treated for a unilateral ZMC fracture (P=.890). In one third of patients, corrections were needed after intraoperative CBCT control. The results of this study indicate that, on average, a ZMC asymmetry of 1.6mm is observed in healthy individuals. Furthermore, the use of intraoperative CBCT for the treatment of dislocated ZMC fractures helps to achieve precise anatomic, symmetrical repositioning and is suggested to improve the quality of care.

Crystal Chemistry and Structural Complexity of Natural and Synthetic Uranyl Selenites

Comparison of the natural and synthetic phases allows an overview to be made and even an understanding of the crystal growth processes and mechanisms of the particular crystal structure formation. Thus, in this work, we review the crystal chemistry of the family of uranyl selenite compounds, paying special attention to the pathways of synthesis and topological analysis of the known crystal structures. Comparison of the isotypic natural and synthetic uranyl-bearing compounds suggests that uranyl selenite mineral formation requires heating, which most likely can be attributed to the radioactive decay. Structural complexity studies revealed that the majority of synthetic compounds have the topological symmetry of uranyl selenite building blocks equal to the structural symmetry, which means that the highest symmetry of uranyl complexes is preserved regardless of the interstitial filling of the structures. Whereas the real symmetry of U-Se complexes in the structures of minerals is lower than their topological symmetry, which means that interstitial cations and H2O molecules significantly affect the structural architecture of natural compounds. At the same time, structural complexity parameters for the whole structure are usually higher for the minerals than those for the synthetic compounds of a similar or close organization, which probably indicates the preferred existence of such natural-born architectures. In addition, the reexamination of the crystal structures of two uranyl selenite minerals guilleminite and demesmaekerite is reported. As a result of the single crystal X-ray diffraction analysis of demesmaekerite, Pb2Cu5[(UO2)2(SeO3)6(OH)6](H2O)2, the H atoms positions belonging to the interstitial H2O molecules were assigned. The refinement of the guilleminite crystal structure allowed the determination of an additional site arranged within the void of the interlayer space and occupied by an H2O molecule, which suggests the formula of guilleminite to be written as Ba[(UO2)3(SeO3)2O2](H2O)4 instead of Ba[(UO2)3(SeO3)2O2](H2O)3.

Intermolecular forces regulated the dimensions of CoII, CuII complexes with 2-(1H-1, 2, 4-Triazol-3-yl)pyridine

Two novel metal complexes C7H10CoN4O6S (1) and C9H8CuN4O2 (2) were synthesized by ligand 2-HTP (2-HTP = 2-(1H-1, 2, 4-triazol-3-yl)pyridine) reaction with different catalysts CoSO4·7H2O and Cu(CH3COO)2·H2O, respectively. Single crystal X-ray diffraction experiments reveal that the symmetry of complexes 1 and 2 respective belong to high centrosymmetric space group C2/c with point group C2h6 and low centrosymmetric space group P21/n with point group C2h5, however, the symmetric elements (E, C2, i, σh) remains unchanged. Meanwhile, hydrogen bonding and π-π interactions exist in structure of complex 1, while only π-π interaction exists in complex 2. In addition, Hirshfeld surface analyses, especially de, dnorm and decomposed fingerprint plots, further indicate complex 1 has stronger intermolecular interactions than complex 2, which leads to complexes 1 and 2 form a three-dimensional network and a one-dimensional chain structures, respectively.

Symmetry in protein complexes

Symmetry in protein complexes

Ultralow Thermal Conductivity and High-Temperature Thermoelectric Performance in n-Type K2.5Bi8.5Se14

We studied the narrow band-gap (0.55 eV) semiconductor K2.5Bi8.5Se14 as a potential thermoelectric material for power generation. Samples of polycrystalline K2.5Bi8.5Se14 prepared by spark plasma sintering exhibit exceptionally low lattice thermal conductivities (κlat) of 0.57–0.33 W m–1 K–1 in the temperature range of 300–873 K. The physical origin of such low κlat in K2.5Bi8.5Se14 is related to the strong anharmonicity and low phonon velocity caused by its complex low symmetry, large unit cell crystal structure, and mixed occupancy of Bi and K atoms in the lattice. High-resolution scanning transmission electron microscopy studies and microanalysis indicate that the K2.5Bi8.5Se14 sample is a single phase without intergrowth of the structurally related K2Bi8Se13 phase. The undoped material exhibits an n-type character and a figure-of-merit (ZT) value of 0.67 at 873 K. Electronic band structure calculations indicate that K2.5Bi8.5Se14 is an indirect band-gap semiconductor with multiple conduction bands clo...

Pure rotational coherent anti-Stokes Raman spectroscopy of ethylene, experiments and modelling

Rotational coherent anti-Stokes Raman spectroscopy (CARS) is an established diagnostic technique for temperature and concentration measurements in combustion-related experiments. CARS has mainly been applied on di- and tri-atomics with linear molecular symmetry, for which good agreement is achieved between experimental and theoretical spectra. Hydrocarbons have so far been less attractive for rotational CARS studies, partly because of their complex molecular symmetries making it challenging to obtain molecular parameters necessary for a successful modeling. Nevertheless, in this work we have studied the asymmetric top molecule ethylene (C2H4) using rotational CARS through experiments and theoretical modelling. Experimental spectra have been recorded at temperatures between 293 K and 804 K, and theoretical spectra have been calculated with a novel method for which the crucial temperature-dependent linewidth parameters were determined by comparison of experimental and theoretically calculated spectra. Line-mixing effects and temperature dependence of the isolated linewidths were studied using a semi-classical approach considering an exponential gap law and a scaling law. Subsequently, theoretically calculated spectra were used to evaluate the temperatures of the experimental spectra for validation of the method. The evaluated temperatures were in good agreement with thermocouple temperatures with differences up to ±7 K. Hence, this work not only investigates the potential of using rotational CARS on ethylene for diagnostic purposes, but also expands the applicability of the technique to a whole new class of molecules with asymmetric-top molecular symmetry.

Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes $k$ Majorana fermions with random all-to-all four-body interactions. We consider the SYK model in the framework of a many-body Altland-Zirnbauer classification that sees the system as belonging to one of eight (real) symmetry classes depending on the value of $k\mod 8$. We show that, depending on the symmetry class, the system may support exact many-body zero modes with the symmetries also dictating whether these may have a nonzero contribution to Majorana fermions, i.e., single-particle weight. These zero modes appear in all but two of the symmetry classes. When present, they leave clear signatures in physical observables that go beyond the threefold (Wigner-Dyson) possibilities for level spacing statistics studied earlier. Signatures we discover include a zero-energy peak or hole in the single-particle spectral function, depending on whether symmetries allow or forbid zero modes to have single-particle weight. The zero modes are also shown to influence the many-body dynamics, where signatures include a nonzero long-time limit for the out-of-time-order correlation function. Furthermore, we show that the extension of the four-body SYK model by quadratic terms can be interpreted as realizing the remaining two complex symmetry classes; we thus demonstrate how the entire tenfold Altland-Zirnbauer classification may emerge in the SYK model.

Outcomes of Zygomatic Complex Reconstruction With Patient-Specific Titanium Mesh Using Computer-Assisted Techniques

Zygomatic complex defects after extensive maxillectomy can cause severe esthetic and functional deformities. Patient-specific titanium mesh fabricated using a computer-assisted technique is a promising method for such midface reconstruction. The aim of this study was to evaluate the application and clinical outcomes of this technique. This was a retrospective study that included 9 patients with zygomatic complex defects after extensive maxillectomy from 2015 through 2017 at the authors' institution. A 3-dimensional stereo model was obtained based on mirror images of the unaffected side to fabricate a patient-specific titanium mesh using computer-assisted design and manufacturing. Titanium mesh was used to restore the contour of the zygomatic complex with free flap reconstruction after tumor resection. Anterolateral thigh flaps were used in 8 cases and a myocutaneous fibula flap was used in 1 case. Symmetry of the zygomatic complex was evaluated by measuring the zygomatic eminence on the postoperative computed tomogram, and complications were recorded during follow-up visits. Facial symmetry was self-evaluated and scored. Mean duration for follow-up was 27.3months (range, 15 to 39months). Mean deviation of the zygomatic eminence between the reconstructed and unaffected sides was 1.4±0.5mm. No significant difference was noted in the zygomatic eminence between the reconstructed and unaffected sides (P=.591). Titanium mesh exposure occurred in only 1 patient after radiotherapy. There were no other remarkable complications. All patients were satisfied with their postoperative facial symmetry. Patient-specific titanium mesh fabricated using a computer-assisted technique was an alternative option for extensive zygomatic complex reconstruction, resulting in acceptable clinical outcomes. A study with a larger sample and long-term follow-up is needed for the observation of long-term outcomes and risk of titanium mesh-related complications.

Application of modified inferior pedicle technique with inverted T pattern for severe breast hypertrophy

To explore the effectiveness of modified inferior pedicle technique with inverted T pattern for severe breast hypertrophy. Between January 2016 and May 2017, 15 patients of severe breast hypertrophy had undergone breast reduction using inferior pedicle technique with inverted T pattern combined with dermal suspension sling technique. The patients were 20 to 49 years old, with an average age of 31.6 years. Body mass index ranged from 24.9 to 32.5 kg/m 2, with an average of 30.8 kg/m 2. Among them, 11 cases had a history of childbearing. The degree of breast ptosis was rated as degree Ⅱ in 6 cases and degree Ⅲ in 9 cases. The unilateral breast reduced 615 g on average (range, 480-1 050 g). The skin flap necrosis at the "T" trilateral junction occurred in 3 cases, and healed after dressing changes. The incisions of 12 cases healed and no fat liquefaction, hematoma, or seroma occurred. The sensation of nipple and areola declined at early period after operation in 2 cases, and gradually recovered. All patients were followed up 6-18 months (mean, 13 months). The shapes of bilateral breasts and the height and symmetry of nipple-areolar complex were good, and no obvious scar was found. The effectiveness was evaluated by surgeon and showed that there were 12 cases with satisfactory breast shape and 3 cases with unsatisfactory breast shape; 3 cases with obvious scare and 12 cases with insignificant scar; 13 cases with normal nipple sensation and 2 cases with hypoesthesia; 11 cases with symmetric nipples and 4 cases with asymmetric nipples. The effectiveness was evaluated by patients and showed that the satisfactory breast shape in 10 cases, relatively satisfactory breast shape in 4 cases, and unsatisfactory breast shape in 1 case; highly acceptable scar in 9 cases, moderately acceptable scar in 4 cases, and unacceptable scar in 2 cases; overall satisfactory in 10 cases, relatively satisfactory in 4 cases, and unsatisfactory in 1 case, with the overall satisfaction rate of 93.3% (14/15). For severe breast hypertrophy, the modified inferior pedicle technique with inverted T pattern can obtain satisfactory appearance and avoid the mastoptosis.

Defecation by the ctenophore Mnemiopsis leidyi occurs with an ultradian rhythm through a single transient anal pore

AbstractDefecation in the ctenophore Mnemiopsis leidyi is a stereotyped sequence of effector responses that occur with a regular ultradian rhythm. Here I used video microscopy to describe new features and correct previous reports of the gastrovascular system during and between defecations. Contrary to the scientific literature, individuals defecated through only one of the two anal canals which possesses the only anal pore. The anal pore was not visible as a permanent structure as depicted in textbooks, but appeared at defecation and disappeared afterward. Time intervals between repeated defecations in individual animals depended on body size, ranging from ~10 min in small larvae to ~1 hr in large adults. Differential interference contrast microscopy revealed that both the opening and closing of the anal pore resembled a reversible ring of tissue fusion between apposed endodermal and ectodermal layers at the aboral end. Individuals of M. leidyi thus appear to have an intermittent anus and therefore an intermittent through‐gut that reoccur at regular intervals. The temporality of a visible anal pore in M. leidyi is novel, and may shed light on the evolution of a permanent anus and through‐gut in animals. In addition, mirror image dimorphism of the diagonal anal complex occurs in larval ctenophores but not in adults, indicating developmental flexibility in diagonal symmetry of the anal complex.

Substrate promiscuity and active site differences in gentisate 1,2-dioxygenases: electron paramagnetic resonance study.

Gentisate 1,2-dioxygenases (GDOs) are non-heme iron enzymes that catalyze the oxidation of dihydroxylated aromatic substrate, gentisate (2,5-dihydroxybenzoate). Salicylate 1,2-dioxygenase (SDO), a member of the GDO family, performs the ring scission of monohydroxylated substrates such as salicylate, thereby oxidizing a broader range of substrates compared to GDOs. Although the two types of enzymes share a high degree of sequence similarity, the origin of substrate specificity between SDO and GDOs is not understood. We present electron paramagnetic resonance (EPR) investigation of ferrous-nitrosyl complexes of SDO and a GDO from the bacterium Corynebacterium glutamicum (GDOCg). The EPR spectra of these complexes, which mimic the Fe-substrate-O2 intermediates in the catalytic cycle, show unexpected differences in the substrate binding mode and the coordination geometry of the metal cofactor in the two enzymes. Binding of substrate to the ferrous center increases the symmetry of the Fe(II)-NO complex in SDO, while a reverse trend is observed in GDOCg where substrate ligation reduces the symmetry of the nitrosyl complex. Identical EPR spectra were obtained for the NO derivatives of a variant of GDOCg(A112G), which can oxidize salicylate, and wild-type GDOCg revealing that the A112G mutation does not alter the nature of the Fe-substrate-O2 ternary complex.

Linearization criteria for two-dimensional systems of third-order ordinary differential equations by complex approach

Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex symmetry analysis. For such systems, the linearizable form, linearization criteria and symmetry group classification are presented. In this paper, we extend the complex approach to obtain a complex-linearizable form of two-dimensional systems of third-order ODEs. This form leads to a linearizable class and linearization criteria of these systems of ODEs.

Complex Symmetry of Composition Operators on Hilbert Spaces of Entire Dirichlet Series

A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class $\mathcal {H}(E, \beta _{S})$, was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibilities were not studied. In this paper, we first provide a complete characterization of boundedness of composition operators on any space $\mathcal {H}(E, \beta _{S})$, which may or may not contain constant functions. We then study complex symmetry of composition operators on $\mathcal {H}(E, \beta _{S})$, via analysis of composition conjugations.

Numerical Simulation of Stagger Spinning for D406A High-Strength Steel

Metal spinning process is widely used because of its low power requirement to producing complex symmetry components. In this paper, a modified 3D finite element(3D-FE) model is developed under the FE software environment based on characteristics of stagger spinning process. Analysis of the multi-pass spinning deformation mechanism and the effects of spinning parameters on spinning deformation is carried out. The results show that, large internal diameter of tube blank and low dimensional accuracy are caused by too little feed rate of spinning roller, especially for thin-walled tube. But if the feed rate is larger than 60mm/min, large spinning forces and instability appear. Strain rate and forming instability increase with the increase of rotational speed of mandrels, on the other hand, more obvious friction leads to bigger strain of surface of tube blank. With the radius of corner of spinning roller getting 13mm, the extensive overlaps lead to the improvement of spinning efficiency, while low forming quality accompanied by the large spinning forces occurs. Cutting phenomena leads to worse surface quality even tends to crack with the radius of corner of spinning roller being smaller than 8mm. An ideal combination of process parameters is obtained: the roller feed rate is 50mm/min, the rotational speed of mandrel is 40rad/min, the radius of corner of spinning roller is 10mm.

The feasibility and acceptability of assessing inhibitory control and working memory among adolescents via an ecological momentary assessment approach

ABSTRACTEarly adolescence is a critical period for the development of executive function (EF). EF deficits are associated with increased engagement in multiple health risk behaviors and may be influenced by momentary factors, such as state mindfulness and physical activity. Ecological momentary assessment (EMA) leverages the increasing ubiquity of smart-phones to assess moment-to-moment changes in neurocognition and behavior with minimal recall bias and high ecological validity. As such, EMA is a promising method for delivering performance-based EF tasks and assessing the degree to which EF is influenced by momentary variation in its putative antecedents (e.g. state mindfulness and PA). This study adapts the (1) State Mindfulness Attention Awareness Scale, (2) physical activity/sedentary behavior recall items, (3) complex symmetry span working memory task, and (4) the child flanker inhibitory control task into an EMA tool delivered via iPhone using Inquisit Web. This tool was piloted with a sample of 32 seventh graders over a 72 h period. Participants’ posttest survey responses indicated that they found these study activities to be enjoyable, non-burdensome, not overly difficult, and preferable to pencil-and-paper instruments. Baseline correlations between flanker task performance and both BRIEF inhibitory control (σ = .23) and working memory subscales (σ = .34) were moderate. Correlations between symmetry span working memory task performance and BRIEF inhibitory control (σabsolute = .28; σpartial = .16) and working memory subscales (σabsolute = .19; σpartial = .15) were slightly lower, demonstrating associations consistent with previous studies. This study supports the feasibility and acceptability of administering two common performance-based EF tasks to adolescents via an EMA approach.

Polarization-sensitive femtosecond mid-infrared spectrometer with a tunable Fabry–Perot filter and chirped-pulse upconversion

Femtosecond time-resolved mid-infrared (MIR) spectroscopy based on chirped-pulse upconversion is a promising method for observing molecular structure and vibrational dynamics. By using a polarized narrowband pump pulse in which center frequency is rapidly scanned with an electrically tunable Fabry-Perot filter, we have developed a femtosecond MIR spectrometer that is more sensitive to molecular structure. The pump energy and polarization dependences of transient MIR absorption spectra measured with the spectroscopic system revealed the appearance of a dark (infrared-inactive) mode due to a slight decrease in the molecular symmetry of a metal carbonyl complex, Mn2(CO)10, in solution. In addition, the rotational relaxation time of Mn2(CO)10 in solution was determined as approximately 20ps.