Symmetry Map Research Articles

Antipodal symmetry of two-loop MHV amplitudes

I present a conjecture that all two-loop MHV amplitudes in planar mathcal{N} = 4 super-Yang-Mills theory possess an antipodal symmetry when evaluated on parity-even kinematics. The symmetry acts as a change of basis on the symbol letters, followed by the antipode operation associated with the Hopf algebra structure of multiple polylogarithms. At the symbol level, I provide the symmetry map explicitly for amplitudes with up to eight external particles, and also provide evidence at all multiplicities. Intriguingly, the map acts as an isomorphism on the normal fans of the Newton polytopes of the symbol letters. The conjectured symmetry is one of the rare known cases where the antipode map shows up in physically important examples.

Large Area, High Resolution Mapping of Approximate Rotational Symmetries in a Pd77.5Cu6Si16.5 Metallic Glass Thin Film

Densely spaced four-dimensional scanning transmission electron microscopy (4D STEM) analyzed using correlation symmetry coefficients enables large area mapping of approximate rotational symmetries in amorphous materials. Here, we report the effects of Poisson noise, limited electron counts, probe coherence, reciprocal space sampling, and the probe-sample interaction volume on 4D STEM symmetry mapping experiments. These results lead to an experiment parameter envelope for high quality, high confidence 4D STEM symmetry mapping. We also establish a direct link between the symmetry coefficients and approximate rotational symmetries of nearest-neighbor atomic clusters using electron diffraction simulations from atomic models of a metallic glass. Experiments on a Pd77.5Cu6Si16.5 metallic glass thin film demonstrate the ability to image the types, sizes, volume fractions, and spatial correlations amongst local rotationally symmetry regions in the glass.

Modular control of discrete-event systems using similarity

We investigate modular supervisory control of discrete-event systems composed of several groups of components, where each group consists of similar modules. Because of the similar structures of the modules, such systems can be represented as a set of (group) templates. Supervisory control can then be performed on these templates, resulting in a set of template supervisors. We propose a modular approach to construct the template supervisors based on the local computation of supremal symmetric sublanguages and on the concept of conditional decomposability. The supremal symmetric sublanguage of a decomposable language turns out to be decomposable, and can thus be computed locally. It is proven that the local supervisors of the components of a group are similar and can thus be obtained by a symmetry map from the template supervisor of the group.

Exact Synthesis of Inline Fully Canonical Dual-Band Filters Using Dual Extracted-Pole Sections

This letter provides a new mapping function which allows us to carry out the dual extracted-pole synthesis in inline fully canonical dual-band filters for the first time. To do this, it is a necessary condition that the reflection coefficient phase takes exactly the same value at the position of the two prescribed transmission zeros (TZs), one belonging to one band and the other to the second band, involved at simultaneous extraction. This is achieved by applying an antisymmetric or odd symmetry mapping function. Two different filters, one with asymmetric and the other with symmetric prescribed TZs at each of the passbands have been synthesized which validates the proposed approach.

A fully basis invariant symmetry map of the 2HDM

We derive necessary and sufficient conditions for all global symmetries of the most general two Higgs doublet model (2HDM) scalar potential entirely in terms of reparametrization independent, i.e. basis invariant, objects. This culminates in what we call a “Symmetry Map” of the parameter space of the model and the fundamental insight that there are, in general, two algebraically distinct ways of how symmetries manifest themselves on basis invariant objects: either, basis invariant objects can be non-trivially related, or, basis covariant objects can vanish. These two options have different consequences on the resulting structure of the ring of basis invariants and on the number of remaining physical parameters. Alongside, we derive for the first time necessary and sufficient conditions for CP conservation in the 2HDM entirely in terms of CP-even quantities. This study lays the methodological foundation for analogous investigations of global symmetries in all other models that have unphysical freedom of reparametrization, most notably the Standard Model flavor sector.

Deep Learning Using Symmetry, FAST Scores, Shape-Based Filtering and Spatial Mapping Integrated with CNN for Large Scale Image Retrieval

This article presents symmetry of sampling, scoring, scaling, filtering and suppression over deep convolutional neural networks in combination with a novel content-based image retrieval scheme to retrieve highly accurate results. For this, fusion of ResNet generated signatures is performed with the innovative image features. In the first step, symmetric sampling is performed on the images from the neighborhood key points. Thereafter, the rotated sampling patterns and pairwise comparisons are performed, which return image smoothing by applying standard deviation. These values of smoothed intensity are calculated as per local gradients. Box filtering adjusts the results of approximation of Gaussian with standard deviation to the lowest scale and suppressed by non-maximal technique. The resulting feature sets are scaled at various levels with parameterized smoothened images. The principal component analysis (PCA) reduced feature vectors are combined with the ResNet generated feature. Spatial color coordinates are integrated with convolutional neural network (CNN) extracted features to comprehensively represent the color channels. The proposed method is experimentally applied on challenging datasets including Cifar-100 (10), Cifar-10 (10), ALOT (250), Corel-10000 (10), Corel-1000 (10) and Fashion (15). The presented method shows remarkable results on texture datasets ALOT with 250 categories and fashion (15). The proposed method reports significant results on Cifar-10 and Cifar-100 benchmarks. Moreover, outstanding results are obtained for the Corel-1000 dataset in comparison with state-of-the-art methods.

Electron cyclotron emission based q-profile measurement and concept for equilibrium reconstruction

Measuring the plasma equilibrium is essential for real time plasma control and for the investigation of an abundance of physics questions. However, many existing kinetic equilibria reconstruction techniques rely heavily on integrated magnetic measurements and neutron-sensitive diagnostics, which will be difficult to design and operate in ITER and DEMO. Here we present and test a conceptual design for a non-magnetic equilibrium reconstruction method using data from a radial electron cyclotron emission diagnostic and an image of the plasma boundary—diagnostics which can be robustly designed in high-neutron environments. This technique is based on the measurement of a discrete q-profile and the symmetry mapping of the electron temperature profile, both of which can be acquired with ECE.

Coarse-graining involving virtual sites: Centers of symmetry coarse-graining.

Coarse-grained (CG) models allow efficient molecular simulation by reducing the degrees of freedom in the system. To recapitulate important physical properties, including many-body correlations at the CG resolution, an appropriate mapping from the atomistic to CG level is needed. Symmetry exhibited by molecules, especially when aspherical, can be lost upon coarse-graining due to the use of spherically symmetric CG effective potentials. This mismatch can be efficiently amended by imposing symmetry using virtual CG sites. However, there has been no rigorous bottom-up approach for constructing a many-body potential of mean force that governs the distribution of virtual CG sites. Herein, we demonstrate a statistical mechanical framework that extends a mapping scheme of CG systems involving virtual sites to provide a thermodynamically consistent CG model in the spirit of the principle of maximum entropy. Utilizing the extended framework, this work defines a center of symmetry (COS) mapping and applies it to benzene and toluene systems such that the planar symmetry of the aromatic ring is preserved by constructing two virtual sites along a normal vector. Compared to typical center of mass (COM) CG models, COS CG models correctly recapitulate radial and higher order correlations, e.g., orientational and three-body correlations. Moreover, we find that COS CG interactions from bulk phases are transferable to mixture phases, whereas conventional COM models deviate between the two states. This result suggests a systematic approach to construct more transferable CG models by conserving molecular symmetry, and the new protocol is further expected to capture other many-body correlations by utilizing virtual sites.

Topological recursion, topological quantum field theory and Gromov–Witten invariants of BG

The purpose of this paper is to give a decorated version of the Eynard–Orantin topological recursion using a 2D Topological Quantum Field Theory. We define a kernel for a 2D TQFT and use an algebraic reformulation of a topological recursion to define how to decorate a standard topological recursion by a 2D TQFT. The A-model side enumerative problem consists of counting cell graphs where in addition vertices are decorated by elements in a Frobenius algebra, and which are a decorated version of the generalized Catalan numbers. We show that the function that counts these decorated graphs, which is a decoration of the counting function of the generalized Catalan numbers by a Frobenius algebra, satisfies a topological recursion with respect to the edge-contraction axioms. The path we follow to pass from the A-model side to the remodeled B-model side is to use a discrete Laplace transform as a mirror symmetry map. We show that a decorated version by a 2D TQFT of the Eynard–Orantin differentials satisfies a decorated version of the Eynard–Orantin recursion formula. We illustrate these results using a toy model for the theory arising from the orbifold cohomology of the classifying space of a finite group. In this example, the graphs are orbifold cell graphs (graphs drawn on an orbifold punctured Riemann surface) defined out of the moduli space \overline {\mathcal M}_{g,n}(BG) of stable morphisms from twisted curves to the classifying space of a finite group G . In particular we show that the cotangent class intersection numbers on the moduli space \overline {\mathcal{M}}_{g,n}(BG) satisfy a decorated Eynard–Orantin topological recursion and we derive an orbifold DVV equation as a consequence of it. This proves from a different perspective the known result which states that the \psi -class intersection numbers on \overline{\mathcal{M}}_{g,n}(BG) satisfy the Virasoro constraint condition.

Symmetric analysis, categorization, and optical spectrum of ideal pyramid quantum dots

Self-assembled quantum dots possess an intrinsic geometric symmetry. Applying group representation theory, we systematically analyze the symmetric properties of the bound states for ideal pyramid quantum dots, which neglect band mixing and strain effects. We label each bound state by its symmetry group’s corresponding irreducible representation and define a concept called the quantum dots’ symmetry category. A class of quantum dots with the same irreducible representation sequence of bound states are characterized as belonging to a specific symmetry category. This category concept generally describes the symmetric order of Hilbert space or wavefunction space. We clearly identify the connection between the symmetry category and the geometry of quantum dots by the symmetry category graph or map. The symmetry category change or transition corresponds to an accidental degeneracy of the bound states. The symmetry category and category transition are observable from the photocurrent spectroscopy or optical spectrum. For simplicity’s sake, in this paper, we only focus on inter-subband transition spectra, but the methodology can be extended to the inter-band transition cases. We predict that from the spectral measurements, the quantum dots’ geometric information may be inversely extracted.

Fast and effective quantification of symmetry in medical images for pathology detection: Application to chest radiography.

Symmetry is an important feature of human anatomy and the absence of symmetry in medical images can indicate the presence of pathology. Quantification of image symmetry can then be used to improve the automatic analysis of medical images. A method is presented that computes both local and global symmetry in 2D medical images. A symmetry axis is determined to define for each position p in the image a mirrored position p' on the contralateral side of the axis. In the neighborhood of p', an optimally corresponding position ps is determined by minimizing a cost function d that combines intensity differences in a patch around p and the mirrored patch around ps and the spatial distance between p' and ps. The optimal value of d is used as a measure of local symmetry s. The average of all values of s, indicated as S, quantifies global symmetry. Starting from an initial approximation of the symmetry axis, the optimal orientation and position of the axis is determined by greedy minimization of S. The method was evaluated in three experiments concerning abnormality detection in frontal chest radiographs. In the first experiment, global symmetry S was used to discriminate between 174 normal images and 174 images containing diffuse textural abnormalities from the publicly available CRASS database of tuberculosis suspects. Performance, measured as area under the receiver operating characteristic curve Az was 0.838. The second experiment investigated whether adding the local symmetry s as an additional feature to a set of 106 texture features resulted in improvements in classifying local patches in the same image database. We found that Az increased from 0.878 to 0.891 (P=0.001). In the third experiment, it was shown that the contrast of pulmonary nodules, obtained from the publicly available JSRT database, increased significantly in the local symmetry map compared to the original image. We conclude that the proposed algorithm for symmetry computation provides informative features which can be used to improve abnormality detection in medical images both at a local and a global level.

Hamilton–Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

In this paper, some of formulations of Hamilton–Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton–Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton–Jacobi theorems are proved and two types of Hamilton–Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie–Poisson Hamilton–Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie–Poisson Hamilton–Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

Advection-Based Function Matching on Surfaces

AbstractA tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non‐linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.

Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches.

In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.

Time symmetry of resource constrained project scheduling with general temporal constraints and take-give resources

The paper studies a lacquer production scheduling problem formulated as a resource constrained project scheduling problem with general temporal constraints (i.e., positive and negative time-lags). This real-world scheduling problem requires so-called take-give resources that are needed from the beginning of an activity to the completion of another activity of the production process. Furthermore, we consider sequence dependent changeover times on take-give resources. We formulate this problem by mixed integer linear programming and we suggest a parallel heuristic to solve the problem. This heuristic exploits a time symmetry mapping which allows an easy construction of a schedule in the backward time orientation. In the second part of the paper, it is proven that the time symmetry mapping is bijective and involutive even for the problem with general temporal constraints, changeover times, and take-give resources. The motivation to use this mapping is to improve the performance of the heuristic and to simplify its implementation. Finally, the performance of the heuristic algorithm is evaluated on a set of lacquer production benchmarks requiring take-give resources and on standard benchmarks for the resource constrained project scheduling problem with general temporal constraints where we found new better solutions in 16 and 12 instances out of 90 for UBO500 and UBO1000 respectively.

Argyres–Douglas theories, S1 reductions, and topological symmetries

In a recent paper, we proposed closed-form expressions for the superconformal indices of the and Argyres–Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S1 regime of these indices. As expected on general grounds, our study reproduces the S3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases—with the exception of the reduction of the SCFT—certain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional superconformal symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the four-dimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general SCFTs.

New Binary Hausdorff Symmetry measure based seeded region growing for retinal vessel segmentation

Automated retinal vessel segmentation plays an important role in computer-aided diagnosis of serious diseases such as glaucoma and diabetic retinopathy. This paper contributes, (1) new Binary Hausdorff Symmetry (BHS) measure based automatic seed selection, and (2) new edge distance seeded region growing (EDSRG) algorithm for retinal vessel segmentation. The proposed BHS measure directly provides a binary symmetry decision at each pixel without the computation of continuous symmetry map and image thresholding. In a multiscale mask, the BHS measure is computed using the distance sets of opposite direction angle bins with sub-pixel resolution. The computation of the BHS measure from the Hausdorff distance sets involves point set matching based geometrical interpretation of symmetry. Then, we design a new edge distance seeded region growing (EDSRG) algorithm with the acquired seeds. The performance evaluation in terms of sensitivity, specificity and accuracy is done on the publicly available DRIVE, STARE and HRF databases. The proposed method is found to achieve state-of-the-art vessel segmentation accuracy in three retinal databases; DRIVE-sensitivity (0.7337), specificity (0.9752), accuracy (0.9539); STARE-sensitivity (0.8403), specificity (0.9547), accuracy (0.9424); and HRF-sensitivity (0.8159), specificity (0.9525), accuracy (0.9420).

Quantitative symmetry determination and symmetry mapping using convergent beam electron diffraction technique

The symmetry recorded in convergent beam electron diffraction (CBED) patterns is in general determined by direct visual inspection [1], which does not provide uniform measurement. Furthermore, experimental CBED patterns are often noisy and deviate from the ideal symmetry because of the sample geometry and defects. Thus, the imperfection in experimental CBED patterns can lead to uncertainty in the symmetry determination [2]. Here, we propose a symmetry quantification method for CBED patterns using the profile R-factor (Rp) [3, 4] and the normalized cross-correlation coefficient (γ) [5]. We have also developed computer algorithms to automate these procedures. We demonstrate that the method proposed here is highly effective and provides a more precise way to determine the symmetry in CBED patterns. The symmetry quantification method can be also combined with a scanning electron diffraction technique for symmetry mapping [6]. Figure 1 shows the image processing procedures for mirror symmetry quantification. First, the symmetry related two diffraction discs (A, A’) are selected about the mirror plane (yellow line) as shown in Fig. 1(a). The template A is used as the reference motif so that the symmetry element is calculated by comparing with template A’. The template A and A’ are first aligned (Fig. 1(c)), and A’ is flipped horizontally to obtain a mirror image (A’m, Fig. 1(h)). For the rotational operation, the template A’ is simply rotated by 360/no with respect to n-fold rotation. The circular mask (Figs. 1(d) and (i)) is finally used to remove areas affected by CBED disk edge and to obtain the final templates (Figs. 1(e) and (j)). Then, we applied the profile R-factor (Rp) and the normalized cross-correlation coefficient (γ) to quantify the similarity between A (=IA(x, y)) and A’m (=IB(x, y)) as given in Eqs. (1) and (2).

The near‐symmetry of proteins

The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.

Continuous symmetry measures for complex symmetry group

Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.