Статті в журналах: "Left symmetry"

1

Rosen, S. P. "OnZ4horizontal symmetry and left-right-symmetric theories." Physical Review D 31, no. 11 (June 1, 1985): 2952–57. http://dx.doi.org/10.1103/physrevd.31.2952.

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2

Shafaq, Saba, and Mariam Saleh Khan. "Left right symmetric model with additional family symmetry." Physics Essays 30, no. 2 (June 13, 2017): 161–67. http://dx.doi.org/10.4006/0836-1398-30.2.161.

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3

Gu, Pei-Hong. "Mirror left–right symmetry." Physics Letters B 713, no. 4-5 (July 2012): 485–89. http://dx.doi.org/10.1016/j.physletb.2012.06.042.

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4

MATUTE, ERNESTO A. "RESTORATION OF PARITY SYMMETRY THROUGH PRESYMMETRY." Modern Physics Letters A 26, no. 34 (November 10, 2011): 2579–85. http://dx.doi.org/10.1142/s0217732311036917.

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Presymmetry, the hidden symmetry underlying the charge and generational patterns of quarks and leptons, is utilized for repairing the left–right asymmetry of the standard model with Dirac neutrinos. It is shown that the restoration of parity is consequent with an indispensable left–right symmetric residual presymmetry. Thus, presymmetry substantiates left–right symmetry and the experimental search for the latter is the test of the former, with the nature of neutrinos as a crucial feature that can distinguish the left–right symmetry alone and its combination with presymmetry. This phenomenological implication is in accordance with the fact that Majorana neutrinos are usually demanded in the first case, but forbidden in the second.

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5

Ferdiyan, Akmal, Apriadi Salim Adam, and Mirza Satriawan. "The Left-Right Symmetry Breaking Mechanism for the New Left-Right Symmetry Model." JPSE (Journal of Physical Science and Engineering) 5, no. 1 (August 27, 2020): 1–5. http://dx.doi.org/10.17977/um024v5i12020p001.

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6

Akhmedov, Eugeni, Manfred Lindner, Erhard Schnapka, and Jose W. F. Valle. "Dynamical left-right symmetry breaking." Physical Review D 53, no. 5 (March 1, 1996): 2752–80. http://dx.doi.org/10.1103/physrevd.53.2752.

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7

Huitu, Katri. "A minimal supersymmetric left-right model, dark matter and signals at the LHC." European Physical Journal Special Topics 229, no. 21 (December 2020): 3187–203. http://dx.doi.org/10.1140/epjst/e2020-000039-9.

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AbstractThe left-right symmetric models extend the gauge group of the Standard Model enabling treatment of the left- and right-handed fermions in the same footing. The left-right symmetry requires the existence of right-handed neutrinos, leading naturally to non-zero masses for neutrinos. Here some aspects of a supersymmetric version of the left-right symmetric models are reviewed. Such models have many virtues, including possibility for dark matter without any new additional symmetry needed in order to have a stable lightest supersymmetric particle. In the model the lightest sneutrino or the lightest neutralino can form dark matter of the universe, at the same time fulfilling all the experimental constraints. The dark matter particle in the model can be very different from the dark matter typical in the minimal supersymmetric standard model. Specific signals for this kind of models at the LHC are also discussed.

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8

Shinohara, Kyosuke, and Hiroshi Hamada. "Cilia in Left–Right Symmetry Breaking." Cold Spring Harbor Perspectives in Biology 9, no. 10 (February 17, 2017): a028282. http://dx.doi.org/10.1101/cshperspect.a028282.

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9

Ma, Ernest. "Left-right symmetry and supersymmetric unification." Physical Review D 51, no. 1 (January 1, 1995): 236–39. http://dx.doi.org/10.1103/physrevd.51.236.

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10

Akhmedov, Eugeni Kh, Anjan S. Joshipura, Stefano Ranfone, and José W.F. Valle. "Left-right symmetry and neutrino stability." Nuclear Physics B 441, no. 1-2 (May 1995): 61–75. http://dx.doi.org/10.1016/0550-3213(95)00072-z.

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11

Senjanović, Goran. "Is left–right symmetry the key?" Modern Physics Letters A 32, no. 04 (January 24, 2017): 1730004. http://dx.doi.org/10.1142/s021773231730004x.

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In collaboration with Jogesh Pati, Abdus Salam challenged the chiral gauge nature of the Standard Model by paving the road towards the left-right symmetric electro-weak theory. I describe here the logical and historical construction of this theory, by emphasising the pioneering and key role it played for neutrino mass. I show that it is a self-contained and predictive model with the Higgs origin of Majorana neutrino mass, in complete analogy with the SM situation regarding charged fermions.

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12

Hung, P. Q., and Subir Mohan. "Left-right symmetry and nonperturbative unification." Physical Review D 41, no. 1 (January 1, 1990): 253–63. http://dx.doi.org/10.1103/physrevd.41.253.

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13

Adam, Apriadi Salim, Akmal Ferdiyan, and Mirza Satriawan. "A New Left-Right Symmetry Model." Advances in High Energy Physics 2020 (January 16, 2020): 1–8. http://dx.doi.org/10.1155/2020/3090783.

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We propose a new L-R symmetry model where the L-R symmetry transformation reverses both the L-R chirality and the local quantum number. We add to the model a global quantum number F whose value is one for fermions (minus one for antifermion) and vanishes for bosons. For each standard model (SM) particle, we have the corresponding L-R dual particle whose mass is very large and which should have decayed at the current low energy level. Due to the global quantum number F, there is no Majorana neutrino in the model but a Dirac seesaw mechanism can still occur and the usual three active neutrino oscillation can still be realized. We add two leptoquarks and their L-R duals, for generating the baryon number asymmetry and for facilitating the decay of the L-R dual particles. The decay of the L-R dual particles will produce a large entropy to the SM sector and give a mechanism for avoiding the big bang nucleosynthesis constraint.

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14

Ecker, G., and W. Grimus. "CP violation and left-right symmetry." Nuclear Physics B 258 (January 1985): 328–60. http://dx.doi.org/10.1016/0550-3213(85)90616-9.

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15

CRIVEI, SEPTIMIU, and MIODRAG CRISTIAN IOVANOV. "SYMMETRY FOR COMODULE CATEGORIES." Journal of Algebra and Its Applications 11, no. 01 (February 2012): 1250009. http://dx.doi.org/10.1142/s0219498811005324.

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For coalgebras C over a field, we study when the categories [Formula: see text] of left C-comodules and [Formula: see text] of right C-comodules are symmetric categories, in the sense that there is a duality between the categories of finitely presented unitary left R-modules and finitely presented unitary left L-modules, where R and L are the functor rings associated to the finitely accessible categories [Formula: see text] and [Formula: see text].

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16

Vlieg, Elias. "Symmetry and symmetry breaking during crystal growth." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C940. http://dx.doi.org/10.1107/s2053273314090597.

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Two cases of symmetry and its breaking will be discussed in the context of crystal growth: chirality and surfaces. Chiral symmetry is a particularly interesting form of symmetry in crystal growth that may even be directly related to the homochirality that is found in Nature. About 10% of the chiral compounds crystallize as so-called racemic conglomerates, i.e. as separate crystals with only left or only right-handed molecules. The first experiments of Pasteur on a tartaric acid salt were an example of this. When crystallizing such compounds, one would expect a (symmetric) 50:50 mixture of both types of crystals, but often this is not the case. We will discuss (1) the chiral symmetry breaking in such systems [1], (2) the formation of epitaxial conglomerates that partially hide the true symmetry and (3) a phase transition from a racemic crystal (with both left- and right-handed molecules in the unit cell) to a racemic conglomerate. X-ray diffraction is often insufficient to fully characterize such systems, and solid-state NMR and computer simulations yield important additional insights. The symmetry of a bulk crystal is by definition broken at its surface, and this can manifest itself in different ways. Muscovite mica, as an example, can be made extremely flat by cleaving and therefore the bulk glide plane symmetry can be lost at the surface [2]. Charge neutrality dictates the distribution of the ions at the surface of mica and seems to be determined by local variations in the Al/Si ratio that are invisible for X-ray diffraction. By isomorphous replacement of the topmost K ions, mica can be functionalized to specifically react with other compounds.

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17

JANG, IK GYU, KYOUNG WON NAM, HONG SEONG PARK, YUNG HO JO, HYUN GUY KANG, JEONG YUN PARK, and KWANG GI KIM. "GAIT SYMMETRY ANALYSIS PROTOCOL FOR WHOLE LEG MOVEMENT SYMMETRY EVALUATION." Journal of Mechanics in Medicine and Biology 12, no. 04 (September 2012): 1250073. http://dx.doi.org/10.1142/s0219519412005010.

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Objective and accurate evaluation of patients who underwent lower limb operation is important in determining a proper rehabilitation process according to the patient's recovery status. Gait symmetry analysis is a common protocol that is used to evaluate lower limb function; however, most studies have focused only on the terminal symmetry of lower limb during gait motion and were unable to provide information about detailed motions of the whole leg. To more accurately analyze mutual symmetry of the left and right leg during gait motion, measurement of motions of the whole left and right leg including the pelvis, hip, knee, and ankle is required. Eight patients (mean [standard deviation]: age = 22.87 [6.05] years; height = 167.81 [5.86] cm; weight = 629.52 [133.63] Newtons) who underwent limbsalvage surgery and eight normal volunteers (age = 28.87 [3.79] years; height = 167 [8.36] cm; weight = 657.46 [157.02] Newtons) participated in this study. Using motion capture cameras arranged around each subject, real-time gait motion of each participant was recorded and moving trajectories of 12 submotion elements were extracted. Mutual symmetry of the motion between the left and right leg was then calculated using a Pearson correlation method, while a nonparametric Mann-Whitney test was performed for group comparison. Experimental results showed that the moving trajectories of the left and right leg were similar in the normal group (r = 0.8114[0.22]) but were critically different in the patient group (r = 0.624286[0.15]). In addition, there was statistically significant difference (p = 0.0162) in gait symmetry between the normal group and the patient group (95% confidence level). We conclude that the proposed protocol can provide a useful evaluation tool for patient recovery condition and that it could be helpful in establishing an effective postoperative treatment protocol for lower limb patients.

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18

Knox, Ethan, and P. T. Leung. "Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential." Canadian Journal of Physics 91, no. 3 (March 2013): 246–50. http://dx.doi.org/10.1139/cjp-2012-0459.

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In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.

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19

SENJANOVIĆ, GORAN. "SEESAW AT LHC THROUGH LEFT–RIGHT SYMMETRY." International Journal of Modern Physics A 26, no. 09 (April 10, 2011): 1469–91. http://dx.doi.org/10.1142/s0217751x1105302x.

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I argue that LHC may shed light on the nature of neutrino mass through the probe of the seesaw mechanism. The smoking gun signature is lepton number violation through the production of same sign lepton pairs, a collider analogy of the neutrinoless double beta decay. I discuss this in the context of left–right symmetric theories, which led originally to neutrino mass and the seesaw mechanism. A WR gauge boson with a mass in a few TeV region could easily dominate neutrinoless double beta decay, and its discovery at LHC would have spectacular signatures of parity restoration and lepton number violation. Moreover, LHC can measure the masses of the right-handed neutrinos and the right-handed leptonic mixing matrix, which could in turn be used to predict the rates for neutrinoless double decay and lepton flavor violating violating processes. The LR scale at the LHC energies offers great hope of observing these low energy processes in the present and upcoming experiments.

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20

Pérez, Pavel Fileviez. "Type III seesaw and left-right symmetry." Journal of High Energy Physics 2009, no. 03 (March 30, 2009): 142. http://dx.doi.org/10.1088/1126-6708/2009/03/142.

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21

Dupont, C., K. Agladze, and V. Krinsky. "Excitable medium with left–right symmetry breaking." Physica A: Statistical Mechanics and its Applications 249, no. 1-4 (January 1998): 47–52. http://dx.doi.org/10.1016/s0378-4371(97)00430-5.

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22

Freedman, Douglas M., George S. Edwards, Matthew J. Willems, and Roy A. Meals. "Right Versus Left Symmetry of Ulnar Variance." Clinical Orthopaedics and Related Research 354 (September 1998): 153–58. http://dx.doi.org/10.1097/00003086-199809000-00018.

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23

Mimura, Yukihiro, and S. Nandi. "Orbifold breaking of left–right gauge symmetry." Physics Letters B 538, no. 3-4 (July 2002): 406–14. http://dx.doi.org/10.1016/s0370-2693(02)02000-2.

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24

Akhmedov, Eugeni, Manfred Lindner, Erhard Schnapka, and JoséW F. Valle. "Left-right symmetry breaking in NJL approach." Physics Letters B 368, no. 4 (February 1996): 270–80. http://dx.doi.org/10.1016/0370-2693(95)01504-3.

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25

Mentus, Tatjana, and Slobodan Markovic. "Effects of symmetry and familiarity on the attractiveness of human faces." Psihologija 49, no. 3 (2016): 301–11. http://dx.doi.org/10.2298/psi1603301m.

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The effects of both symmetry (perceptual factor) and familiarity (cognitive factor) on facial attractiveness were investigated. From the photographs of original slightly asymmetric faces, symmetric left-left (LL) and right-right (RR) versions were generated. Familiarity was induced in the learning block using the repetitive presentation of original faces. In the test block participants rated the attractiveness of original, previously seen (familiar) faces, original, not previously seen faces, and both LL and RR versions of all faces. The analysis of variance showed main effects of symmetry. Post hoc tests revealed that asymmetric original faces were rated as more attractive than both LL and RR symmetric versions. Familiarity doesn?t have a significant main effect, but the symmetry-familiarity interaction was obtained. Additional post hoc tests indicated that facial attractiveness is positively associated with natural slight asymmetry rather than with perfect symmetry. Also, unfamiliar LL symmetric versions were rated as more attractive than familiar LL versions, whereas familiar RR versions were rated as more attractive than RR unfamiliar faces. These results suggested that symmetry (perceptual factor) and familiarity (cognitive or memorial factor) play differential roles in facial attractiveness, and indicate a relatively stronger effect of the perceptual compared to the cognitive factor. [Projekat Ministarstva nauke Republike Srbije, br. ON179018 i br. ON179033] This article has been corrected. Link to the correction <a href="http://dx.doi.org/10.2298/PSI1701101E">10.2298/PSI1701101E</a>

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26

Zhang Feng, Zhang Chun-Xu, and Huang Ming-Qiu. "Neutrino masses in the left-right symmetry model with a family symmetry." Acta Physica Sinica 59, no. 5 (2010): 3130. http://dx.doi.org/10.7498/aps.59.3130.

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27

Yang, Wei-Min, and Hong-Huan Liu. "The new extended left–right symmetric grand unified model with family symmetry." Nuclear Physics B 820, no. 1-2 (October 2009): 364–84. http://dx.doi.org/10.1016/j.nuclphysb.2009.05.028.

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28

Siringo, F. "Symmetry breaking of the symmetric left-right model without a scalar bidoublet." European Physical Journal C 32, no. 4 (February 2004): 555–59. http://dx.doi.org/10.1140/epjc/s2003-01442-7.

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29

Chen, J. N., F. J. van Eeden, K. S. Warren, A. Chin, C. Nusslein-Volhard, P. Haffter, and M. C. Fishman. "Left-right pattern of cardiac BMP4 may drive asymmetry of the heart in zebrafish." Development 124, no. 21 (November 1, 1997): 4373–82. http://dx.doi.org/10.1242/dev.124.21.4373.

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The first evident break in left-right symmetry of the primitive zebrafish heart tube is the shift in pattern of BMP4 expression from radially symmetric to left-predominant. The midline heart tube then ‘jogs’ to the left and subsequently loops to the right. We examined 279 mutations, affecting more than 200 genes, and found 21 mutations that perturb this process. Some cause BMP4 to remain radially symmetric. Others randomize the asymmetric BMP4 pattern. Retention of BMP4 symmetry is associated with failure to jog: right-predominance of the BMP4 pattern is associated with reversal of the direction of jogging and looping. Raising BMP4 diffusely throughout the heart, via sonic hedgehog injection, or the blocking of its action by injection of a dominant negative BMP4 receptor, prevent directional jogging or looping. The genes crucial to directing cardiac asymmetry include a subset of those needed for patterning the dorsoventral axis and for notochord and ventral spinal cord development. Thus, the pattern of cardiac BMP4 appears to be in the pathway by which the heart interprets lateralizing signals from the midline.

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30

Liu, Xiang-Shu, Han-Xiang Xu, Yan-Hong Qin, and Liang Duan. "Excitation of mirror symmetry higher-order rational soliton in modulation stability regimes on continuous wave background." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (December 2022): 123105. http://dx.doi.org/10.1063/5.0106915.

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We study the relationship between the structures of the nonlinear localized waves and the distribution characteristics of the modulation stability regime in a nonlinear fiber with both third-order and fourth-order effects. On the background frequency and background amplitude plane, the modulation stability region consists of two symmetric curves on the left and right and a point on the symmetry axis. We find that the higher-order excitation characteristics are obviously different at different positions in the modulation stability region. Their excitation characteristics are closely related to the modulation instability distribution characteristics of the system. It is shown that asymmetric high-order rational solitons are excited at the left and right stable curves, and the symmetric one is excited at the stable points. Interestingly, the asymmetric higher-order rational solitons on the left and right sides are mirror-symmetrical to each other, which coincides with the symmetry of the modulation instability distribution. These results can deepen our understanding of the relationship between nonlinear excitation and modulation instability and enrich our knowledge about higher-order nonlinear excitations.

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31

BORAH, DEBASISH. "SUPERSYMMETRIC LEFT–RIGHT MODELS WITH B-L ODD HIGGS DOUBLETS." International Journal of Modern Physics A 26, no. 07n08 (March 30, 2011): 1305–26. http://dx.doi.org/10.1142/s0217751x11052876.

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We study various possible Supersymmetric Left–Right (SUSYLR) models with Higgs doublets carrying B-L charge ±1: with single step symmetry breaking down to the Minimal Supersymmetric Standard Model (MSSM) as well as multistep symmetry breaking. Single step symmetry breaking can be achieved with the minimal field content of just Higgs doublet and bidoublets whereas multistep symmetry breaking can be realized only at the cost of including additional Higgs superfields. However, going beyond the minimal field content comes up with the exciting possibility of TeV scale intermediate symmetry which can have important implications in the ongoing collider experiments. We show that spontaneous parity violation can be achieved naturally in all these models and R-parity is spontaneously broken by the vacuum expectation value of B-L odd Higgs doublets. The tiny neutrino mass can arise from a double seesaw mechanism in the presence of additional singlet or triplet fermions. We show that gauge coupling unification can be achieved in these models with the possibility of TeV scale intermediate symmetry in some specific nonminimal versions.

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32

ASATRIAN, H. M., and A. N. IOANNISSIAN. "RARE B-MESON DECAYS IN SU(2)L × SU(2)R × U(1) MODEL." Modern Physics Letters A 05, no. 14 (June 10, 1990): 1089–96. http://dx.doi.org/10.1142/s0217732390001219.

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Rare B-meson decays are investigated in the left–right symmetric models. The scalar particle contribution to the amplitude of the b → sγ decay is calculated. It is shown that this contribution can be essential even for scalar particle masses of about several TeV. The effects due to the left–right symmetry and scalar particles can be detected by measuring photon polarization in the decay B → K*γ.

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33

Hamada, Hiroshi, and Patrick Tam. "Diversity of left-right symmetry breaking strategy in animals." F1000Research 9 (February 19, 2020): 123. http://dx.doi.org/10.12688/f1000research.21670.1.

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Left-right (L-R) asymmetry of visceral organs in animals is established during embryonic development via a stepwise process. While some steps are conserved, different strategies are employed among animals for initiating the breaking of body symmetry. In zebrafish (teleost), Xenopus (amphibian), and mice (mammal), symmetry breaking is elicited by directional fluid flow at the L-R organizer, which is generated by motile cilia and sensed by mechanoresponsive cells. In contrast, birds and reptiles do not rely on the cilia-driven fluid flow. Invertebrates such as Drosophila and snails employ another distinct mechanism, where the symmetry breaking process is underpinned by cellular chirality acquired downstream of the molecular interaction of myosin and actin. Here, we highlight the convergent entry point of actomyosin interaction and planar cell polarity to the diverse L-R symmetry breaking mechanisms among animals.

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34

Hill, Allen, and Julie Nantel. "Sensitivity of discrete symmetry metrics: Implications for metric choice." PLOS ONE 17, no. 5 (May 19, 2022): e0268581. http://dx.doi.org/10.1371/journal.pone.0268581.

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Gait asymmetry is present in several pathological populations, including those with Parkinson’s disease, Huntington’s disease, and stroke survivors. Previous studies suggest that commonly used discrete symmetry metrics, which compare single bilateral variables, may not be equally sensitive to underlying effects of asymmetry, and the use of a metric with low sensitivity could result in unnecessarily low statistical power. The purpose of this study was to provide a comprehensive assessment of the sensitivity of commonly used discrete symmetry metrics to better inform design of future studies. Monte Carlo simulations were used to estimate the statistical power of each symmetry metric at a range of asymmetry magnitudes, group/condition variabilities, and sample sizes. Power was estimated by repeated comparison of simulated symmetric and asymmetric data with a paired t-test, where the proportion of significant results is equivalent to the power. Simulation results confirmed that not all common discrete symmetry metrics are equally sensitive to reference effects of asymmetry. Multiple symmetry metrics exhibit equivalent sensitivities, but the most sensitive discrete symmetry metric in all cases is a bilateral difference (e.g. left—right). A ratio (e.g. left/right) has poor sensitivity when group/condition variability is not small, but a log-transformation produces increased sensitivity. Additionally, two metrics which included an absolute value in their definitions showed increased sensitivity when the absolute value was removed. Future studies should consider metric sensitivity when designing analyses to reduce the possibility of underpowered research.

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35

Bisgrove, B. W., J. J. Essner, and H. J. Yost. "Regulation of midline development by antagonism of lefty and nodal signaling." Development 126, no. 14 (July 15, 1999): 3253–62. http://dx.doi.org/10.1242/dev.126.14.3253.

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The embryonic midline is crucial for the development of embryonic pattern including bilateral symmetry and left-right asymmetry. In zebrafish, lefty1 (lft1) and lefty2 (lft2) have distinct midline expression domains along the anteroposterior axis that overlap with the expression patterns of the nodal-related genes cyclops and squint. Altered expression patterns of lft1 and lft2 in zebrafish mutants that affect midline development suggests different upstream pathways regulate each expression domain. Ectopic expression analysis demonstrates that a balance of lefty and cyclops signaling is required for normal mesendoderm patterning and goosecoid, no tail and pitx2 expression. In late somite-stage embryos, lft1 and lft2 are expressed asymmetrically in the left diencephalon and left lateral plate respectively, suggesting an additional role in laterality development. A model is proposed by which the vertebrate midline, and thus bilateral symmetry, is established and maintained by antagonistic interactions among co-expressed members of the lefty and nodal subfamilies of TGF-beta signaling molecules.

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36

Chacko, Zackaria, Hock-Seng Goh, and Roni Harnik. "A twin Higgs model from left-right symmetry." Journal of High Energy Physics 2006, no. 01 (January 23, 2006): 108. http://dx.doi.org/10.1088/1126-6708/2006/01/108.

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37

Ewing, T. "Genetic 'master switch' for left-right symmetry found." Science 260, no. 5108 (April 30, 1993): 624–25. http://dx.doi.org/10.1126/science.8480173.

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38

Czakon, M., J. Gluza, and M. Zrałek. "Left–right symmetry and heavy particle quantum effects." Nuclear Physics B 573, no. 1-2 (May 2000): 57–74. http://dx.doi.org/10.1016/s0550-3213(99)00717-8.

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39

Fileviez Pérez, Pavel, and Sogee Spinner. "Spontaneous R-parity breaking and left–right symmetry." Physics Letters B 673, no. 4-5 (March 2009): 251–54. http://dx.doi.org/10.1016/j.physletb.2009.02.047.

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40

Hamada, Hiroshi. "Left-right symmetry breaking in the mouse embryo." Mechanisms of Development 145 (July 2017): S1. http://dx.doi.org/10.1016/j.mod.2017.04.515.

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41

Aulakh, Charanjit S., Karim Benakli, and Goran Senjanović. "Reconciling High-Scale Left-Right Symmetry with Supersymmetry." Physical Review Letters 79, no. 12 (September 22, 1997): 2188–91. http://dx.doi.org/10.1103/physrevlett.79.2188.

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42

Bertolini, S., and J. Liu. "Small Dirac neutrino mass and left-right symmetry." Nuclear Physics B 297, no. 2 (February 1988): 401–11. http://dx.doi.org/10.1016/0550-3213(88)90026-0.

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43

Grimes, Daniel T., and Rebecca D. Burdine. "Left–Right Patterning: Breaking Symmetry to Asymmetric Morphogenesis." Trends in Genetics 33, no. 9 (September 2017): 616–28. http://dx.doi.org/10.1016/j.tig.2017.06.004.

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44

Reig, Mario, José W. F. Valle, and C. A. Vaquera-Araujo. "Unifying left–right symmetry and 331 electroweak theories." Physics Letters B 766 (March 2017): 35–40. http://dx.doi.org/10.1016/j.physletb.2016.12.049.

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45

Czyż, H., and M. Zrałek. "Left-right symmetry and the top quark mass." Physics Letters B 308, no. 3-4 (July 1993): 360–64. http://dx.doi.org/10.1016/0370-2693(93)91298-2.

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46

Gronau, M., and R. N. Mohapatra. "Maximal spontaneous CP-violation and left-right symmetry." Physics Letters B 168, no. 3 (March 1986): 248–52. http://dx.doi.org/10.1016/0370-2693(86)90973-1.

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47

Reggiani, Silvio. "The index of symmetry of three-dimensional Lie groups with a left-invariant metric." Advances in Geometry 18, no. 4 (October 25, 2018): 395–404. http://dx.doi.org/10.1515/advgeom-2017-0061.

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Abstract We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry, and we explain in what cases the group fibers over a 2-dimensional space of constant curvature.

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48

Middelkoop, Teije C., Júlia Garcia-Baucells, Porfirio Quintero-Cadena, Lokesh G. Pimpale, Shahrzad Yazdi, Paul W. Sternberg, Peter Gross, and Stephan W. Grill. "CYK-1/Formin activation in cortical RhoA signaling centers promotes organismal left–right symmetry breaking." Proceedings of the National Academy of Sciences 118, no. 20 (May 10, 2021): e2021814118. http://dx.doi.org/10.1073/pnas.2021814118.

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Proper left–right symmetry breaking is essential for animal development, and in many cases, this process is actomyosin-dependent. In Caenorhabditis elegans embryos active torque generation in the actomyosin layer promotes left–right symmetry breaking by driving chiral counterrotating cortical flows. While both Formins and Myosins have been implicated in left–right symmetry breaking and both can rotate actin filaments in vitro, it remains unclear whether active torques in the actomyosin cortex are generated by Formins, Myosins, or both. We combined the strength of C. elegans genetics with quantitative imaging and thin film, chiral active fluid theory to show that, while Non-Muscle Myosin II activity drives cortical actomyosin flows, it is permissive for chiral counterrotation and dispensable for chiral symmetry breaking of cortical flows. Instead, we find that CYK-1/Formin activation in RhoA foci is instructive for chiral counterrotation and promotes in-plane, active torque generation in the actomyosin cortex. Notably, we observe that artificially generated large active RhoA patches undergo rotations with consistent handedness in a CYK-1/Formin–dependent manner. Altogether, we conclude that CYK-1/Formin–dependent active torque generation facilitates chiral symmetry breaking of actomyosin flows and drives organismal left–right symmetry breaking in the nematode worm.

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49

Saigusa, Yusuke, Tomomasa Takada, Aki Ishii, Tomoyuki Nakagawa, and Sadao Tomizawa. "Measure of departure from cumulative local symmetry for square contingency tables having ordered categories." Biometrical Letters 57, no. 1 (June 1, 2020): 23–35. http://dx.doi.org/10.2478/bile-2020-0003.

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SummaryFor square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of symmetric cells is proposed. For ordinal square tables, the present paper proposes (1) another local symmetry model for cumulative probabilities from the upper-right and lower-left corners of the table, and (2) a measure to represent the degree of departure from the proposed model. The measure has the form of a weighted harmonic mean of the diversity index, which includes the Shannon entropy as a special case. Examples are given in which the proposed method is applied to square table data on decayed teeth in Japanese women patients.

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50

BAI, CHENGMING. "LEFT-SYMMETRIC BIALGEBRAS AND AN ANALOGUE OF THE CLASSICAL YANG–BAXTER EQUATION." Communications in Contemporary Mathematics 10, no. 02 (April 2008): 221–60. http://dx.doi.org/10.1142/s0219199708002752.

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We introduce a notion of left-symmetric bialgebra which is an analogue of the notion of Lie bialgebra. We prove that a left-symmetric bialgebra is equivalent to a symplectic Lie algebra with a decomposition into a direct sum of the underlying vector spaces of two Lagrangian subalgebras. The latter is called a parakähler Lie algebra or a phase space of a Lie algebra in mathematical physics. We introduce and study coboundary left-symmetric bialgebras and our study leads to what we call "S-equation", which is an analogue of the classical Yang–Baxter equation. In a certain sense, the S-equation associated to a left-symmetric algebra reveals the left-symmetry of the products. We show that a symmetric solution of the S-equation gives a parakähler Lie algebra. We also show that such a solution corresponds to the symmetric part of a certain operator called "[Formula: see text]-operator", whereas a skew-symmetric solution of the classical Yang–Baxter equation corresponds to the skew-symmetric part of an [Formula: see text]-operator. Thus a method to construct symmetric solutions of the S-equation (hence parakähler Lie algebras) from [Formula: see text]-operators is provided. Moreover, by comparing left-symmetric bialgebras and Lie bialgebras, we observe that there is a clear analogue between them and, in particular, parakähler Lie groups correspond to Poisson–Lie groups in this sense.

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