Invariant Pair Research Articles

Accessing baryon to meson transition distribution amplitudes in meson production in association with a high invariant mass lepton pair at GSI-FAIR withP¯ANDA

Nucleon antinucleon annihilation into a near backward (or forward) produced meson and a high invariant mass lepton pair admits a factorized description in terms of antinucleon (or nucleon) distribution amplitudes and nucleon to meson (or antinucleon to meson) transition distribution amplitudes. We estimate the cross section of backward (and forward) pion and eta meson production in association with a high invariant mass lepton pair for the kinematical conditions of GSI-FAIR. The cross sections are found to be large enough to be measured with the PANDA detector. Interesting phenomenological applications of the approach are thus expected.

Inertial particle acceleration statistics in turbulence: Effects of filtering, biased sampling, and flow topology

In this study, we investigate the effect of “biased sampling,” i.e., the clustering of inertial particles in regions of the flow with low vorticity, and “filtering,” i.e., the tendency of inertial particles to attenuate the fluid velocity fluctuations, on the probability density function of inertial particle accelerations. In particular, we find that the concept of “biased filtering” introduced by Ayyalasomayajula et al. [“Modeling inertial particle acceleration statistics in isotropic turbulence,” Phys. Fluids 20, 0945104 (2008)10.1063/1.2976174], in which particles filter stronger acceleration events more than weaker ones, is relevant to the higher order moments of acceleration. Flow topology and its connection to acceleration is explored through invariants of the velocity-gradient, strain-rate, and rotation-rate tensors. A semi-quantitative analysis is performed where we assess the contribution of specific flow topologies to acceleration moments. Our findings show that the contributions of regions of high vorticity and low strain decrease significantly with Stokes number, a non-dimensional measure of particle inertia. The contribution from regions of low vorticity and high strain exhibits a peak at a Stokes number of approximately 0.2. Following the methodology of Ooi et al. [“A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence,” J. Fluid Mech. 381, 141 (1999)10.1017/S0022112098003681], we compute mean conditional trajectories in planes formed by pairs of tensor invariants in time. Among the interesting findings is the existence of a stable focus in the plane formed by the second invariants of the strain-rate and rotation-rate tensors. Contradicting the results of Ooi et al., we find a stable focus in the plane formed by the second and third invariants of the strain-rate tensor for fluid tracers. We confirm, at an even higher Reynolds number, the conjecture of Collins and Keswani [“Reynolds number scaling of particle clustering in turbulent aerosols,” New J. Phys. 6, 119 (2004)10.1088/1367-2630/6/1/119] that inertial particle clustering saturates at large Reynolds numbers. The result is supported by the theory presented in Chun et al. [“Clustering of aerosol particles in isotropic turbulence,” J. Fluid Mech. 536, 219 (2005)10.1017/S0022112005004568].

Lorentzian Manifolds having the Killing Property

We deal with a Lorentzian n-dimensional manifold M carrying two skew-symmetric Killing null vector fields ξ1 and ξn. They define a commutative left invariant pairing. The (n – 2)-dimensional spatial distribution orthogonal to ξ1 and ξn is involutive and its leaves are totally geodesic and pseudo-isotropic. If n = 4, then it is shown that the general space-time M is of type D in Petrov's classification and the spatial surfaces which foliate M are totally geodesic and pseudo-isotropic. Properties of the congruence of Debever are pointed-out.

Progressively weighted affine adaptive correlation matching for quasi-dense 3D reconstruction

Correlation matching has been widely accepted as a rudimentary similarity measure to obtain dense 3D reconstruction from a stereo pair. In particular, given a large overlapping area between images with minimal scale differences, the correlation results followed by a geometrically constrained global optimisation delivers adequately dense and accurate reconstruction results. In order to achieve greater reliability, however, correlation matching should correctly account for the geometrical distortion introduced by the different viewing angles of the stereo or multi-view sensors. Conventional adaptive least squares correlation (ALSC) matching addresses this by modifying the shape of a matching window iteratively, assuming that the distortion can be approximated by an affine transform. Nevertheless, since an image captured from different viewing angle is often not practically identical due to scene occlusions, the matching confidence normally deteriorates. Subsequently, it affects the density of the reconstruction results from ALSC-based stereo region growing algorithms. To address this, we propose an advanced ALSC matching method that can progressively update matching weight for each pixel in an aggregating window using a relaxation labelling technique. The experimental results show that the proposed method can improve matching performance, which consequently enhances the quality of stereo reconstruction. Also, the results demonstrate its ability to refine a scale invariant conjugate point pair to an affine and scale invariant point pair.

On the order three Brauer classes for cubic surfaces

Abstract We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.

The and -Analogs of Zagreb Indices and Coindices of Graphs

The first and second Zagreb indices were first introduced by Gutman and Trinajstić (1972). It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. Recently, the first and second Zagreb coindices, a new pair of invariants, were introduced in Došlić (2008). In this paper we introduce the and ()-analogs of the above Zagreb indices and coindices and investigate the relationship between the enhanced versions to get a unified theory.

On Dynamical Adjoint Functor

We give an explicit formula relating the dynamical adjoint functor and dynamical twist over nonalbelian base to the invariant pairing on parabolic Verma modules. As an illustration, we give explicit $U(sl(n))$- and $U_\hbar(sl(n))$-invariant star product on projective spaces.

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies. Based on the concept of invariant pairs, a theoretically sound and reliable numerical continuation procedure is developed. Particular attention is paid to the situation when the procedure approaches a singularity, that is, when eigenvalues included in the invariant pair collide with other eigenvalues. For the real generic case, it is proven that such a singularity only occurs when two eigenvalues collide on the real axis. It is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair. The viability of our continuation procedure is illustrated by a numerical example.

CUBIC SURFACES WITH A GALOIS INVARIANT PAIR OF STEINER TRIHEDRA

We present a method to construct non-singular cubic surfaces over ℚ with a Galois invariant pair of Steiner trihedra. We start with cubic surfaces in a form generalizing that of Cayley and Salmon. For these, we develop an explicit version of Galois descent.

Exclusive production of large invariant mass pion pairs in ultraperipheral ultrarelativistic heavy ion collisions

The cross section for exclusive production of π+π− and π0π0 meson pairs in ultrarelativistic heavy ion collisions is calculated for LHC energy sNN=3.5 TeV taking into account photon–photon mechanism. We concentrate on the production of large two-pion invariant masses where the mechanism of the elementary γγ→ππ process is not fully understood. In order to include a size of nuclei we perform calculation in the impact-parameter equivalent photon approximation (EPA). Realistic charge densities are used to calculate charged form factor of 208Pb nucleus and to generate photon fluxes associated with ultrarelativistic heavy ions. Sizeable cross sections are obtained that can be measured at LHC. The cross section for elementary γγ→ππ process is calculated in the framework of pQCD Brodsky–Lepage (BL) mechanism with the distribution amplitude used to describe recent data of the BaBar Collaboration on pion transition form factor, using hand-bag mechanism advocated to describe recent Belle data as well as t- and u-channel meson/reggeon exchanges. We present distributions in two-pion invariant mass as well as the pion pair rapidity for the nuclear process.

A new method for resolving combinatorial ambiguities at hadron colliders

We present a new method for resolving combinatorial ambiguities that arise in multi-particle decay chains at hadron colliders where the assignment of visible particles to the different decay chains has ambiguities. Our method, based on selection cuts favoring high transverse momentum and low invariant mass pairings, is shown to be significantly superior to the more traditional hemisphere method for a large class of decay chains, producing an increase in signal retention of up to a factor of 2. This new method can thus greatly reduce the combinatorial ambiguities of decay chain assignments.

Probing dense nuclear matter with electromagnetic and rare hadronic probes

We present preliminary results on strangeness and dilepton production in Ar+KCl reactions at 1.76 AGeV. For the first time an ω signal could be extracted in heavy-ion collisions in this energy region. Furthermore we find a strong enhancement of yield in the low invariant lepton pair mass region over an elementary reference suggesting the onset of non trivial effects of the medium. This hint is supported by a nearly complete vanishing of the OZI suppression of the ϕ to ω ratio which is characteristic for elementary reactions.

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

2-D Niblett-Bostick magnetotelluric inversion

A simple and robust imaging technique for two-dimensional magnetotelluric interpretations has been developed following the well known Niblett-Bostick transformation for one-dimensional profiles. The algorithm processes series and parallel magnetotelluric impedances and their analytical influence functions using a regularized Hopfield artificial neural network. The adaptive, weighted average approximation preserves part of the nonlinearity of the original problem, yet no initial model in the usual sense is required for the recovery of the model; rather, the built-in relationship between model and data automatically and concurrently considers many half spaces whose electrical conductivities vary according to the data. The use of series and parallel impedances, a self-contained pair of invariants of the impedance tensor, avoids the need to decide on best angles of rotation for identifying TE and TM modes. Field data from a given profile can thus be fed directly into the algorithm without much processing. The solutions offered by the regularized Hopfield neural network correspond to spatial averages computed through rectangular windows that can be chosen at will. Applications of the algorithm to simple synthetic models and to the standard COPROD2 data set illustrate the performance of the approximation.

Structural determinants of specific DNA-recognition by the THAP zinc finger

Human THAP1 is the prototype of a large family of cellular factors sharing an original THAP zinc-finger motif responsible for DNA binding. Human THAP1 regulates endothelial cell proliferation and G1/S cell-cycle progression, through modulation of pRb/E2F cell-cycle target genes including rrm1. Recently, mutations in THAP1 have been found to cause DYT6 primary torsion dystonia, a human neurological disease. We report here the first 3D structure of the complex formed by the DNA-binding domain of THAP1 and its specific DNA target (THABS) found within the rrm1 target gene. The THAP zinc finger uses its double-stranded β-sheet to fill the DNA major groove and provides a unique combination of contacts from the β-sheet, the N-terminal tail and surrounding loops toward the five invariant base pairs of the THABS sequence. Our studies reveal unprecedented insights into the specific DNA recognition mechanisms within this large family of proteins controlling cell proliferation, cell cycle and pluripotency.

On a computation of rank two Donaldson–Thomas invariants

For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which satisfy a certain stability condition. This is a rank two version of the DT-invariant of rank one, studied by Li, Behrend-Fantechi and Levine-Pandharipande. We use the wall-crossing formula of DT-invariants established by Joyce-Song, Kontsevich-Soibelman.

A block Newton method for nonlinear eigenvalue problems

We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences from the linear case is that distinct eigenvalues may have linearly dependent eigenvectors or even share the same eigenvector. This has been a severe hindrance in the development of general numerical schemes for computing several eigenvalues of a nonlinear eigenvalue problem, either simultaneously or subsequently. The purpose of this work is to show that the concept of invariant pairs offers a way of representing eigenvalues and eigenvectors that is insensitive to this phenomenon. To demonstrate the use of this concept in the development of numerical methods, we have developed a novel block Newton method for computing such invariant pairs. Algorithmic aspects of this method are considered and a few academic examples demonstrate its viability.

Nonperturbative effect in threshold resummation

We show that the conventional threshold resummation calculation cannot describe well the low energy Drell-Yan (DY) data without including the non-perturbative correction terms which are deduced from analyzing the asymptotic behavior of the resummation formalism. It is demonstrated that the non-perturbative correction is generally small for the large invariant mass DY pairs produced at the Tevatron and the LHC.

Molecular Adaptation in RNA Complexes

In this issue, Batey and colleagues show that the purine riboswitch is able to bind purine analogs by exploiting various strategies, including lateral shifts of the bases and, most importantly, changes in ligand tautomeric form.

Dark matter and sub-GeV hidden U(1) in GMSB models

Motivated by the recent PAMELA and ATIC data, one is ledto a scenario with heavy vector-like dark matter in associationwith a hidden U(1)X sector below GeV scale. Realizing this ideain the context of gauge mediated supersymmetry breaking (GMSB), aheavy scalar component charged under U(1)X is found to be agood dark matter candidate which can be searched for directscattering mediated by the Higgs boson and/or by the hidden gaugeboson. The latter turns out to put a stringent bound on thekinetic mixing parameter between U(1)X and U(1)Y: θ ≲ 10−6. For the typical range of model parameters, wefind that the decay rates of the ordinary lightest neutralino intohidden gauge boson/gaugino and photon/gravitino are comparable,and the former decay mode leaves displaced vertices of leptonpairs and missing energy with distinctive length scale larger than20 cm for invariant lepton pair mass below 0.5 GeV. Anunsatisfactory aspect of our model is that the Sommerfeld effectcannot raise the galactic dark matter annihilation by more than60 times for the dark matter mass below TeV.