Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The C60 molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Symmetry-dependent phonon renormalization in monolayer MoS2 transistor

A strong electron-phonon interaction which limits the electronic mobility of semiconductors can also have significant effects on phonon frequencies. The latter is the key to the use of Raman spectroscopy for nondestructive characterization of doping in graphene-based devices. Using in situ Raman scattering from a single-layer MoS2 electrochemically top-gated field-effect transistor (FET), we show softening and broadening of the A(1g) phonon with electron doping, whereas the other Raman-active E-2g(1) mode remains essentially inert. Confirming these results with first-principles density functional theory based calculations, we use group theoretical arguments to explain why the A(1g) mode specifically exhibits a strong sensitivity to electron doping. Our work opens up the use of Raman spectroscopy in probing the level of doping in single-layer MoS2-based FETs, which have a high on-off ratio and are of technological significance.

Direct Observation of Valley Hybridization and Universal Symmetry of Graphene with Mesoscopic Conductance Fluctuations

In graphene, the valleys represent spinlike quantities and can act as a physical resource in valley-based electronics to produce novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of 4 when valley triplet states are gapped in the presence of short-range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry class that outlines a fundamental feature arising from graphene's unique crystal structure.

Detecting symmetry in scalar fields using augmented extremum graphs

Visualizing symmetric patterns in the data often helps the domain scientists make important observations and gain insights about the underlying experiment. Detecting symmetry in scalar fields is a nascent area of research and existing methods that detect symmetry are either not robust in the presence of noise or computationally costly. We propose a data structure called the augmented extremum graph and use it to design a novel symmetry detection method based on robust estimation of distances. The augmented extremum graph captures both topological and geometric information of the scalar field and enables robust and computationally efficient detection of symmetry. We apply the proposed method to detect symmetries in cryo-electron microscopy datasets and the experiments demonstrate that the algorithm is capable of detecting symmetry even in the presence of significant noise. We describe novel applications that use the detected symmetry to enhance visualization of scalar field data and facilitate their exploration.

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si: P and Ge: P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

The complexity in visualizing volumetric data often limits the scope of direct exploration of scalar fields. Isocontour extraction is a popular method for exploring scalar fields because of its simplicity in presenting features in the data. In this paper, we present a novel representation of contours with the aim of studying the similarity relationship between the contours. The representation maps contours to points in a high-dimensional transformation-invariant descriptor space. We leverage the power of this representation to design a clustering based algorithm for detecting symmetric regions in a scalar field. Symmetry detection is a challenging problem because it demands both segmentation of the data and identification of transformation invariant segments. While the former task can be addressed using topological analysis of scalar fields, the latter requires geometry based solutions. Our approach combines the two by utilizing the contour tree for segmenting the data and the descriptor space for determining transformation invariance. We discuss two applications, query driven exploration and asymmetry visualization, that demonstrate the effectiveness of the approach.

Salts of hexamethylenetetramine with organic acids: Enhanced anomeric interactions with a lowering of molecular symmetry revealed by crystal structures

The hexamethylenetetramine (HMT) framework displays interesting stereoelectronic interactions of the anomeric type. In the highly symmetrical parent system, the nitrogen centres act as both donors and acceptors. Protonation lowers symmetry and also leads to an enhancement of the anomeric interaction around the protonated centre. X-ray diffraction crystal structures of four derivatives of HMT - with succinic, (DL)-malic, phthalic and 4-hydroxybenzoic acids - reveal significant trends. (The first three form well-defined salts, 4-hydroxybenzoic acid forming a co-crystalline compound.) Each molecular structure is essentially characterised by a major anomeric interaction involving the protonated centre as acceptor. In two cases (succinic and 4-hydroxybenzoic), secondary protonation leads to a weaker anomeric interaction site that apparently competes with the dominant one. Bond length changes indicate that the anomeric interaction decreases as malic > phthalic > succinic > 4-hydroxybenzoic, which correlates with the degree of proton transfer to the nitrogen centre. Along with other bond length and angle changes, the results offer insight into the applicability of the antiperiplanar lone pair hypothesis (ALPH) in a rigid system. (C) 2014 Elsevier B.V. All rights reserved.

Salts of hexamethylenetetramine with organic acids: Enhanced anomeric interactions with a lowering of molecular symmetry revealed by crystal structures

The hexamethylenetetramine (HMT) framework displays interesting stereoelectronic interactions of the anomeric type. In the highly symmetrical parent system, the nitrogen centres act as both donors and acceptors. Protonation lowers symmetry and also leads to an enhancement of the anomeric interaction around the protonated centre. X-ray diffraction crystal structures of four derivatives of HMT - with succinic, (DL)-malic, phthalic and 4-hydroxybenzoic acids - reveal significant trends. (The first three form well-defined salts, 4-hydroxybenzoic acid forming a co-crystalline compound.) Each molecular structure is essentially characterised by a major anomeric interaction involving the protonated centre as acceptor. In two cases (succinic and 4-hydroxybenzoic), secondary protonation leads to a weaker anomeric interaction site that apparently competes with the dominant one. Bond length changes indicate that the anomeric interaction decreases as malic > phthalic > succinic > 4-hydroxybenzoic, which correlates with the degree of proton transfer to the nitrogen centre. Along with other bond length and angle changes, the results offer insight into the applicability of the antiperiplanar lone pair hypothesis (ALPH) in a rigid system. (C) 2014 Elsevier B.V. All rights reserved.

Optimal Pulse Width Modulation of Voltage-Source Inverter fed Motor Drives with Relaxation of Quarter Wave Symmetry Condition

Optimal switching angles for minimization of total harmonic distortion of line current (I-THD) in a voltage source inverter are determined traditionally by imposing half-wave symmetry (HWS) and quarter-wave symmetry (QWS) conditions on the pulse width modulated waveform. This paper investigates optimal switching angles with QWS relaxed. Relaxing QWS expands the solution space and presents the possibility of improved solutions. The optimal solutions without QWS are shown here to outperform the optimal solutions with QWS over a range of modulation index (M) between 0.82 and 0.94 for a switching frequency to fundamental frequency ratio of 5. Theoretical and experimental results are presented on a 2.3kW induction motor drive.

Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy (eta/s) ratio corresponding to the super fluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature (T < T-c). This proves the non universality of eta/s ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling (lambda) corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the eta/s ratio seems to get modified due to the finite temperature effects.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

A hidden symmetry of AdS resonances

Recent investigations have revealed powerful selection rules for resonant energy transfer between modes of nonlinear perturbations in global anti-de Sitter (AdS) space-time. It is likely that these selection rules are due to the highly symmetric nature of the underlying AdS background, though the precise relation has remained unclear. In this article, we demonstrate that the equation satisfied by the scalar field mode functions in AdS(d+1) has a hidden SU(d) symmetry, and explicitly specify the multiplets of this SU(d) symmetry furnished by the mode functions. We also comment on the role this structure might play in explaining the selection rules.