Symmetric Framework Research Articles

I. The isotopic Foldy-Wouthuysen representation and chiral symmetry

The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix γ5, these equations possess chiral invariance irrespective of whether fermions have mass or are massless. The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions. In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P — symmetry). This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.

Disadvantaged business enterprise goals in government procurement contracting: An analysis of bidding behavior and costs

Programs that encourage the participation of disadvantaged business enterprises (DBE) as subcontractors have been a part of government procurement auctions for over three decades. In this paper, we examine the impact of a program that requires prime contractors to subcontract out a portion of a highway procurement project to DBE firms. We study how DBE subcontracting requirements affect bidding behavior in federally funded projects. Within a symmetric independent private value framework, we use the equilibrium bidding function to obtain the cost distribution of firms undertaking projects either with or without subcontracting goals. We then use nonparametric estimation methods to uncover and compare the cost of firm bidding on a class of asphalt projects related to surface treatment in Texas. The analysis shows little differences in the cost structure between projects that have subcontracting goals and those that do not.

Symmetric Graph Regularized Constraint Propagation

This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constraint propagation is actually equivalent to solving a Lyapunov matrix equation, which is widely used in Control Theory as a standard continuous-time equation. Different from most previous constraint propagation methods that suffer from severe limitations, our method can directly be applied to multi-class problem and also can effectively exploit both must-link and cannot-link constraints. The propagated constraints are further used to adjust the similarity between data points so that they can be incorporated into subsequent clustering. The proposed method has been tested in clustering tasks on six real-life data sets and then shown to achieve significant improvements with respect to the state of the arts.

Whose Fast and Whose Feast? Intrahousehold Asymmetries in Dietary Diversity Response Among East African Pastoralists

This article explores intrahousehold dietary diversity allocation within pastoralist households in eastern Africa. We estimate income elasticities of dietary diversity for demographic cohorts allowing asymmetric behavior depending on household circumstances. We find that household heads disproportionately bear the nutritional burden when household income is below mean, while other cohorts disproportionately enjoy the nutritional gains when it is above mean. The commonly assumed symmetric framework masks this intrahousehold behavior and produces biased elasticity estimates. Stochastic dominance tests show adult daughters as better‐off than other household members in their dietary diversity, sons as worse off, and little difference between male heads and their wives.

Modeling Symmetric Macromolecular Structures in Rosetta3

Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems.

A simplified approach for solving coagulation–diffusion equation to estimate atmospheric background particle number loading factors contributed by emissions from localized sources

Abstract Coagulation and condensation/evaporation combined with atmospheric dispersion are the main processes responsible for the evolution of aerosol particle size distributions and number concentrations emitted from localized sources. A crucial question is: what fraction of freshly emitted particles survive intra-coagulation effect to persist in the atmosphere and become available for further interaction with background aerosols?. The difficulty in estimating this quantity, designated as the number survival fraction, arises due chiefly to the joint action of atmospheric diffusion with nonlinear coagulation effects which are computationally intensive to handle. We provide a simplified approach to evaluate this quantity in the context of instantaneous (puff) and continuous (plume) releases based on a reduction of the respective coagulation–diffusion equations under the assumption of a constant coagulation kernel (K). The condensation/evaporation processes, being number conserving, are not included in the study. The approach consists of constructing moment equations for the evolution of number concentration and variance of the spatial extension of puff or plume in terms of either time or downstream distance. The puff model, applicable to instantaneous releases is solved within a 3-D, spherically symmetric framework, under an additional assumption of a constant diffusion coefficient (D) which renders itself amenable to a closed form solution that provides a benchmark for developing the solution to the plume model. The latter case, corresponding to continuous releases, is discussed within a 2-D framework under the assumptions of constant advection velocity (U) and space dependent diffusion coefficient expressed in terms of turbulent energy dissipation rate (ɛ). The study brings out the special effect of the coagulation-induced flattening of the spatial concentration profiles because of which particle sizes will be larger at the centre of a Gaussian puff. For a puff of initial width b0 consisting of N0 particles, we obtain a formula for the number survival fraction as ψ puff ( ∞ ) = ( 1 + 5 A / 4 ) − 4 / 5 where, A = K N 0 / { 4 ( 2 π ) 3 / 2 D b 0 } . For plume of initial width σ0 emitting S0 particles per unit time, the formula for the survival fraction obtained by fitting the numerical solutions is obtained as ψ plume ( ∞ ) = ( 1 + 1.32 μ ) − 0.76 where, μ = K S 0 / { 6 3 U σ 0 4 / 3 ( C ɛ ) 1 / 3 } and C is a constant (∼0.8). The implication of these results such as robustness with respect to uncertainties in the choice of the initial data and applications for a few practically important problems such as vehicular emissions, forest fires, etc are discussed.

The Orbit Rigidity Matrix of a Symmetric Framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms—giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.

A fully symmetric nonlinear biorthogonal decomposition theory for random fields

We present a general approach for nonlinear biorthogonal decomposition of random fields. The mathematical theory is developed based on a fully symmetric operator framework that unifies different types of expansions and allows for a simple formulation of necessary and sufficient conditions for their completeness. The key idea of the method relies on an equivalence between nonlinear mappings of Hilbert spaces and local inner products, i.e. inner products that may be functionals of the random field being decomposed. This extends previous work on the subject and allows for an effective formulation of field-dependent and field-independent representations. The proposed new methodology can be applied in many areas of mathematical physics, for stochastic low-dimensional modelling of partial differential equations and dimensionality reduction of complex nonlinear phenomena. An application to a transient stochastic heat conduction problem in a one-dimensional infinite medium is presented and discussed.

Refinement of the crystal structure of as-schwatzite Cu6(Cu5.26Hg0.75)(As2.83Sb1.17)S13 (Aktash, Altai mountaines)

The crystal structure of As-schwatzite Cu6(Cu5.26Hg0.75)(As2.83Sb1.17)S13 (Aktash deposit, Altai mountains) is refined. Tetrahedrally shaped dark-gray single crystals of the mineral belong to the cubic crystal system: I4¯3m space group, a = 10.2890(1) A, V = 1089.2(1) A3, d = 4.99 g/cm3, Z = 2 for the composition Cu11.26Hg0.75As2.83Sb1.17S13, R = 0.0177. The structure is based on the sphalerite-like framework comprising identically oriented (Cu,Hg)S4 tetrahedra ((Cu,Hg)-S 2.3452(8) A) and (As,Sb)S3 pyramids ((As,Sb)-S 2.311(1) A) sharing their vertices. The centers of [Cu6] octahedra in the (000) and (1/2 1/2 1/2) positions coinciding with the centers of the “cluster” anionic vacancies [□]4 are occupied by the so-called “thirteenth” sulfur atom. Quantum chemical calculations of the electron density are carried out for the [As4S13Cu6]6 fragment. The calculation results confirm the presence of strain in the [As4S13Cu6]6 moiety, which exists due to the support of the surrounding symmetric framework including the external sulfur atoms of the fragment. The possibility of inclusion of mercury into the framework, which is much richer in arsenic than in antimony, is demonstrated. High stability of the framework determines significant compression of the S-centered [SCu6] octahedron in its interstices, bringing together copper atoms to 3.145(1) A and shortening the Cu-S distances to 2.224(1) A

Non-Abelian bosonic currents in cosmic strings

A non-Abelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current carrier belongs to a two-dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an Abelian current-carrying string, or the three currents are all lightlike, traveling in the same direction (only left or right movers). The third, genuinely non-Abelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.

ChemInform Abstract: The Use of C3-Symmetric Tripodal Ligands in Crystal Engineering

Abstract The use of chiral tripodal ligands in the assembly of non-centrosymmetric crystal lattice is illustrated with the triamide ligand tris[ N -( S )-(−)-(α)-methylbenzylcarbamoylmethyl]amine (H 3 1 S -mbz ). In the crystal phase, this tripodal ligand assembles into C 3 -symmetric chiral columns that are stabilized by hydrogen bonds and aryl–aryl interactions. Intercolumnar assembly is driven by the clustering of edge-to-face aryl and methyl-to-aryl interactions. Thrice deprotonation of H 3 1 S -mbz and binding of an Ni(II)–F moiety also produces a non-centrosymmetric lattice which is noteworthy for its six-fold symmetric open framework structure and the alignment of all the molecular Ni–F bonds in the lattice along the crystallographic c -axis. Crystal data: H 3 1 S -mbz crystallizes in the rhombohedral system, space group R 3 with cell dimensions a = b =22.352(5) A, c =4.882(1) A, α = β =90°, γ =120°, and Z =3; [NEt 4 ] 2 [Ni 1 S -mbz (F)] crystallizes in the hexagonal system, space group P 6 3 with cell dimensions a = b =12.0780(1) A, c =18.1231(1) A, α = β =90°, γ =120°, and Z =2.

When is a symmetric body-bar structure isostatic?

Body-bar frameworks provide a special class of frameworks which are well understood generically, with a full combinatorial theory for rigidity. Given a symmetric body-bar framework, this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. We give some initial results, and conjectures, for when these conditions are also sufficient for rigidity.

Bidding among Friends and Enemies with Symmetric Information

We consider an auction setting, in a symmetric information framework, in which bidders, even if they fail to obtain the good, care about the price paid by the winner. We prove that the outcome of the first-price auction is not affected by identity-independent price externalities, while the outcome of the second-price auction is. In contrast, identity-dependent price externalities affect the outcome of both auction formats. In any case, the second-price auction exacerbates the effects of price externalities.

Symmetry as a Sufficient Condition for a Finite Flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as “generically” as possible subject to given symmetry constraints and $(G,p)$ possesses a “fully symmetric” infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their 1978 paper “The Rigidity of Graphs” [Trans. Amer. Math. Soc., 245 (1978), pp. 279–289] and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous nonsymmetric methods.

Global collapses and expansions in star-forming clouds

Spectral molecular line profile observations of star-forming molecular clouds sometimes show distinct red asymmetric double-peaked molecular line profiles with weaker blue peaks and stronger red peaks. For some star-forming molecular clouds, such molecular transitions with red asymmetric line profiles and blue asymmetric line profiles (i.e. blue asymmetric double-peaked molecular line profiles with weaker red peaks and stronger blue peaks) may coexist in spatially resolved spectral observations, while for others, such molecular transitions with red asymmetric line profiles may completely dominate in spatially resolved spectral observations. Blue asymmetric line profiles are usually interpreted as signals of central core collapses, while red asymmetric line profiles remain unexplained. In this paper, we advance a spherically symmetric self-similar hydrodynamic model framework for envelope expansions with core collapses (EECC) of a general polytropic molecular gas cloud under self-gravity. Based on such EECC hydrodynamic cloud models, we perform tracer molecular line profile calculations using the publicly available RATRAN code for star-forming clouds with spectroscopic signatures of red asymmetric line profiles. The presence of red asymmetric line profiles from molecular cloud cores indicates that EECC processes are most likely an essential hydrodynamic process of star formation. With spatial distributions, we explore various profiles of molecular lines for several tracer molecules in different settings of EECC dynamic models with and without shocks.

A Highly Connected Porous Coordination Polymer with Unusual Channel Structure and Sorption Properties

Making connections: A hydroxy-centered trinuclear nickel cluster has been employed to construct a highly connected, highly symmetric framework with a uninodal nine-connected topology. An array of triakis tetrahedra leads to a biporous intersecting-channel system (see picture).

Secure and Efficient Multicast in Wireless Sensor Networks Allowing Ad hoc Group Formation

Multicast security is one of the most important security services in wireless sensor networks (WSNs) since it enables a sink to multicast messages to sensors in a secure manner. While multicast authentication has widely been addressed in the literature, the problem of multicast encryption still remains open in WSNs. In this paper, we propose a multicast encryption scheme called global-partition, local-diffusion (GPLD) that focuses on scheme efficiency and supports various multicast group semantics. GPLD partitions sensors into a series of elementary groups using their location and class information and accordingly builds a location-class-aware symmetric key management framework. Furthermore, the scheme leverages the fact that sensors are both end receivers and routers, which effectively minimizes global (sink-to-sensor) group key distribution and rekeying traffic while supporting various multicast group semantics. The efficiency and security properties of GPLD are justified through both analysis and simulations.

Econometrics of auctions by least squares

AbstractI investigate using the method of ordinary least squares (OLS) on auction data. I find that for parameterizations of the valuation distribution that are common in empirical practice, an adaptation of OLS provides unbiased estimators of structural parameters. Under symmetric independent private values, adapted OLS is a specialization of the method of moments strategy of Laffont, Ossard and Vuong (1995). In contrast to their estimator, here simulation is not required, leading to a computationally simpler procedure. The paper also discusses using estimation results for inference on the shape of the valuation distribution, and applicability outside the symmetric independent private values framework. Copyright © 2008 John Wiley & Sons, Ltd.

When is a symmetric pin-jointed framework isostatic?

Maxwell’s rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.

Aggregation issues in operational risk

In this paper we study copula-based models for aggregation of operational risk capital across business lines in a bank. A commonly used method of summation of the value-at-risk (VaR) measures, which relies on a hypothesis of full correlation of losses, becomes inappropriate in the presence of dependence between business lines and may lead to overestimation of the capital charge. The problem can be further aggravated by the persistence of heavy tails in operational loss data; in some cases, the subadditivity property of VaR may fail and the capital charge becomes underestimated. We use α-stable heavy-tailed distributions to model the loss data and then apply the copula approach in which the marginal distributions are consolidated in the symmetric and skewed Student t-copula framework. In our empirical study, we compare VaR and conditional VaR estimates with those obtained under the full correlation assumption. Our results demonstrate a significant reduction in capital when a t-copula is employed. However, the capital reduction is significantly smaller than in cases where a moderately heavy-tailed or thin-tailed distribution is calibrated to loss data. We also show that, when historical weekly data is used, VaR exhibits the superadditivity property for confidence levels below 94% and that, when the loss distribution approach is used, the superadditivity of VaR is observed at a higher confidence level (98%).