Euclidean Correlation Research Articles

Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD

We study the fate of P wave bottomonium states in the quark-gluon plasma, using a spectral function analysis of euclidean lattice correlators. The correlators are obtained from lattice QCD simulations with two light quark flavours on highly anisotropic lattices, treating the bottom quark nonrelativistically. We find clear indications of melting immediately after the deconfinement transition.

Comparative Study on CBIR based on Color Feature

Content Based Image Retrieval (CBIR) system helps users to retrieve relevant images based on their contents. It finds images in large databases by using a unique image feature such as texture, color, intensity or shape of the object inside an image. This paper presents a comparative study between the feature extraction techniques that based on color feature. These techniques include Color Histogram, HSV Color Histogram and Color Histogram Equalization. In this study, the retrieval process is first done by measuring the similarities between the query image and the images within the WANG database using two approaches: Euclidean distance and correlation coefficients. Then, the comparison is carried out by measuring the accuracy, error rate and elapsed time of each technique.

New representation of the Adler function for lattice QCD

We address several aspects of lattice QCD calculations of the hadronic vacuum polarization and the associated Adler function. We implement a representation derived previously which allows one to access these phenomenologically important functions for a continuous set of virtualities, irrespective of the flavor structure of the current. Secondly we present a theoretical analysis of the finite-size effects on our particular representation of the Adler function, based on the operator product expansion at large momenta and on the spectral representation of the Euclidean correlator at small momenta. Finally, an analysis of the flavor structure of the electromagnetic current correlator is performed, where a recent theoretical estimate of the Wick-disconnected diagram contributions is rederived independently and confirmed.

A spectral gradient difference based approach for land cover change detection

Change detection with remotely sensed imagery plays an important role in land cover mapping, process analysis and dynamic information services. Euclidean distance, correlation and other mathematic metrics between spectral curves have been used to calculate change magnitude in most change detection methods. However, many pseudo changes would also be detected because of inter-class spectral variance, which remains a significant challenge for operational remote sensing applications. In general, different land cover types have their own spectral curves characterized by typical spectral values and shapes. These spectral values are widely used for designing change detection algorithms. However, the shape of spectral curves has not yet been fully considered. This paper proposes to use spectral gradient difference (SGD) to quantitatively describe the spectral shapes and the differences in shape between two spectra. Change magnitude calculated in the new spectral gradient space is used to detect the change/no-change areas. Then, a chain model is employed to represent the SGD pattern both qualitatively and quantitatively. Finally, the land cover change types are determined by pattern matching with the knowledgebase of reference SGD patterns. The effectiveness of this SGD-based change detection approach was verified by a simulation experiment and a case study of Landsat data. The results indicated that the SGD-based approach was superior to the traditional methods.

Perturbative S-matrix for massive scalar fields in global de Sitter space

We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays.

Lattice QCD and the two-photon decay of the neutral pion

Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wave function at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.

In-Medium Quarkonia at SPS, RHIC and LHC

A kinetic-rate equation approach in a thermally expanding medium is employed to calculate the evolution of charmonium and bottomonium distributions in heavy-ion collisions. The equilibrium properties of the quarkonia are taken from in-medium spectral functions which are schematically constrained by euclidean correlators from lattice QCD. The initial conditions for the rate equation (heavy-flavor cross sections, nuclear absorption) and the thermal evolution are constrained by light-hadron data as available. After fixing two free parameters to describe charmonium data at SPS and RHIC, the predictions for LHC are discussed in light of recent data.

A methodology to assess the intrinsic discriminative ability of a distance function and its interplay with clustering algorithms for microarray data analysis

BackgroundClustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from statistics to computer science. Following Handl et al., it can be summarized as a three step process: (1) choice of a distance function; (2) choice of a clustering algorithm; (3) choice of a validation method. Although such a purist approach to clustering is hardly seen in many areas of science, genomic data require that level of attention, if inferences made from cluster analysis have to be of some relevance to biomedical research.ResultsA procedure is proposed for the assessment of the discriminative ability of a distance function. That is, the evaluation of the ability of a distance function to capture structure in a dataset. It is based on the introduction of a new external validation index, referred to as Balanced Misclassification Index (BMI, for short) and of a nontrivial modification of the well known Receiver Operating Curve (ROC, for short), which we refer to as Corrected ROC (CROC, for short). The main results are: (a) a quantitative and qualitative method to describe the intrinsic separation ability of a distance; (b) a quantitative method to assess the performance of a clustering algorithm in conjunction with the intrinsic separation ability of a distance function. The proposed procedure is more informative than the ones available in the literature due to the adopted tools. Indeed, the first one allows to map distances and clustering solutions as graphical objects on a plane, and gives information about the bias of the clustering algorithm with respect to a distance. The second tool is a new external validity index which shows similar performances with respect to the state of the art, but with more flexibility, allowing for a broader spectrum of applications. In fact, it allows not only to quantify the merit of each clustering solution but also to quantify the agglomerative or divisive errors due to the algorithm.ConclusionsThe new methodology has been used to experimentally study three popular distance functions, namely, Euclidean distance d2, Pearson correlation dr and mutual information dMI. Based on the results of the experiments, we have that the Euclidean and Pearson correlation distances have a good intrinsic discrimination ability. Conversely, the mutual information distance does not seem to offer the same flexibility and versatility as the other two distances. Apparently, that is due to well known problems in its estimation. since it requires that a dataset must have a substantial number of features to be reliable. Nevertheless, taking into account such a fact, together with results presented in Priness et al., one receives an indication that dMI may be superior to the other distances considered in this study only in conjunction with clustering algorithms specifically designed for its use. In addition, it results that K-means, Average Link, and Complete link clustering algorithms are in most cases able to improve the discriminative ability of the distances considered in this study with respect to clustering. The methodology has a range of applicability that goes well beyond microarray data since it is independent of the nature of the input data. The only requirement is that the input data must have the same format of a "feature matrix". In particular it can be used to cluster ChIP-seq data.

OPE of the energy-momentum tensor correlator in massless QCD

We analytically calculate higher order corrections to coefficient functions of the operator product expansion (OPE) for the Euclidean correlator of two energy-momentum tensors in massless QCD. These are the three-loop contribution to the coefficient C_0 in front of the unity operator O_0=1 and the one and two-loop contributions to the coefficient C_1 in front of the gluon "condensate" operator O_1=-1/4 G^{\mu \nu} G_{\mu \nu}. For the correlator of two operators O_1 we present the coefficient C_1 at two-loop level.

Triangle anomalies, thermodynamics, and hydrodynamics

We consider 3+1-dimensional fluids with U(1)^3 anomalies. We use Ward identities to constrain low-momentum Euclidean correlation functions and obtain differential equations that relate two and three-point functions. The solution to those equations yields, among other things, the chiral magnetic conductivity. We then compute zero-frequency functions in hydrodynamics and show that the consistency of the hydrodynamic theory also fixes the anomaly-induced conductivities.

Bottomonia in the quark-gluon plasma and their production at RHIC and LHC

We study the production of bottomonium states in heavy-ion reactions at collider energies available at RHIC and LHC. We employ an earlier constructed rate equation approach which accounts for both suppression and regeneration mechanisms in the quark-gluon plasma (QGP) and hadronization phases of the evolving thermal medium. Our previous predictions utilizing two limiting cases of strong and weak bottomonium binding in the QGP are updated by i) checking the compatibility of the pertinent spectral functions with lattice-QCD results for euclidean correlators, ii) adapting the initial conditions of the rate equation by updating bottom-related input cross-sections and the charged-particle multiplicity of the fireball, and iii) converting our calculations into observables as recently measured by the STAR and CMS experiments. Our main findings are a preference for strong ϒ binding as well as a significant regeneration component at the LHC.

Classification of gasoline brand and origin by Raman spectroscopy and a novel R-weighted LSSVM algorithm

Raman spectroscopy, which is a kind of non-invasive measurement technique and the precise molecule fingerprint, has been widely applied to provide information on chemical structures and physical forms, making it possible to be used for substance classification in qualitative analysis. In this paper, we try to classify Raman spectra of 128 gasoline samples which are provided by three different refineries and belong to three different brands (90#, 93#, and 97#). Since samples are partly overlapped in the principal component space, traditional classification algorithms based on principal component analysis (PCA) cannot be effective. Least squares support vector machine (LSSVM) with the whole spectral range is introduced. Moreover, a novel local weighted LSSVM algorithm is proposed to improve the classification accuracy. The weight is constructed based on correlation coefficient R and this algorithm can be denoted as R-weighted LSSVM. In this algorithm, both of Euclidean distance and correlation coefficient are considered to select neighboring samples. LDA based on PCA, LSSVM, local LSSVM and R-weighted LSSVM are compared in the classification experiment. Experimental results show that Raman spectroscopy is an effective means to classify gasoline brand and origin, and the R-weighted LSSVM algorithm gives the best classification result.

The Hagedorn spectrum and large N c QCD in 2 + 1 and 3 + 1 dimensions

We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space correlation functions for composite operators constructed from quark and gluon fields and exploits the fact that the short time behavior of the correlators is known in QCD. The demonstration relies on one critical assumption: that perturbation theory accurately describes the trace of the logarithm of a matrix of point-to-point correlation functions in the regime where the perturbative corrections to the asymptotically free value are small.

Transport properties of the quark-gluon plasma

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.

Medium modifications and production of charmonia at LHC

A previously constructed transport approach to calculate the evolution of quarkonium yields and spectra in heavy-ion collisions is applied to PbPb (s=2.76A TeV) collisions at the Large Hadron Collider (LHC). In this approach spectral properties of charmonia are constrained by Euclidean correlators from thermal lattice QCD and subsequently implemented into a Boltzmann equation accounting for both suppression and regeneration reactions. Based on a fair description of SPS and RHIC data, we provide predictions for the centrality dependence of J/ψ yields at LHC. The main uncertainty is associated with the input charm cross section, in particular its hitherto unknown reduction due to shadowing in nuclear collisions. Incomplete charm-quark thermalization and non-equilibrium in charmonium chemistry entail a marked reduction of the regeneration yield compared to the statistical equilibrium limit.

STUDIES ON GENETIC DIVERGENCE OF SEEDED BANANA IN WEST BENGAL

Thirty four (34) types of seeded banana with B genome collected from different agroclimatic zones of West Bengal, India were characterised at the Horticultural Research Station, West Bengal, India during the years 2005-2008 by using 123 plant morphological characters with different multivariate techniques. The proximity matrix, both by squared Euclidean and cophenetic correlation, between types indicated high closeness/similarity among ‘Attiakala’, ‘Bichkela-1’, ‘Bichkela-2’ and ‘Hill Banana’. The highest proximity value of 20.62 with ‘Kalyani Local-3’ showed maximum dissimilarity with ‘Maricha’ and ‘Jhama Diara’. A dendrogram using the single linkage clustering technique on squared Euclidean distance matrix and cophenetic correlation matrix showed 13 and 14 clusters, respectively. PCA was used by considering 13 factors on the basis of variance explained, i.e. more than 3%, and total explained variation was confined to 68%. Thus considering the dominant characters with positive loading under Factor 1, such as bract scar on rachis, pollen sacs colour, leaf corrugation, general fruit shape, fruits and compound tepal, the positively loaded types were ‘Bichkela-1’, ‘Hill Banana’, ‘Attiakala’, ‘Bichkela-2’, ‘Kalyani Local-1’ and ‘Jhama Daira’. Factor 1 thus explained 14.21% of the total variance. In general, PCA results agreed with the results obtained by cluster analysis. PCA gave a better picture of the relationship between seeded banana types than cluster analysis and was useful in confirming group(s) obtained through cluster analysis. MDS group plots also clearly indicated the clustering of homogeneous types. Among the 34 seeded banana types, 32 were assessed as parthenocarpic. The two non-parthenocarpic types identified were ‘Baruipur’ and ‘Seed Banana-15’.

Research on Feature Extraction for Character Recognition of NaXi Pictograph

Character recognition is one of important applications for pattern recognition. Feature extraction is the most important problem in character recognition. In this paper, we have researched on feature extraction for character recognition of NaXi pictograph. The characteristics of NaXi pictograph are firstly analyzed. Four kinds of features, including permeability number, coarse grid, directional line element, and invariant moments, and 6 kinds of computation distances, including Lidean distance, Standardized Euclidean distance, Minkowski metric, Chebychey distance, City distance, and Correlation distance will be applied to classify characters of NaXi pictograph, based on its characteristics. We have built a sample database containing 21000 samples for 2120 NaXi characters. The results of experiments suggest that coarse grid and directional element are more suitable for character recognition of NaXi pictograph, while invariant moments is not advisable for this task.

The errant life of a heavy quark in the quark–gluon plasma

In the high-temperature phase of QCD, the heavy-quark momentum diffusion constant determines, via a fluctuation–dissipation relation, how fast a heavy quark kinetically equilibrates. This transport coefficient can be extracted from thermal correlators via a Kubo formula. We present a lattice calculation of the relevant Euclidean correlators in the gluon plasma, based on a recent formulation of the problem in heavy-quark effective field theory (HQET). We find a≈20% enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from 6Tc to 2Tc, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from 6Tc down to 2Tc, indicating a relative shift of the spectral weight to lower frequencies. A recent next-to-leading order perturbative calculation of the correlator agrees with the time dependence of the lattice data at the few-per cent level. We estimate how much additional contribution from the ω≲T region of the perturbative spectral function would be required to bring it in agreement with the lattice data at 3.1Tc.

Quarkonia and heavy-quark relaxation times in the quark-gluon plasma

A thermodynamic T-matrix approach for elastic 2-body interactions is employed to calculate spectral functions of open and hidden heavy-quark systems in the Quark-Gluon Plasma. This enables the evaluation of quarkonium bound-state properties and heavy-quark diffusion on a common basis and thus to obtain mutual constraints. The two-body interaction kernel is approximated within a potential picture for spacelike momentum transfers. An effective field-theoretical model combining color-Coulomb and confining terms is implemented with relativistic corrections and for different color channels. Four pertinent model parameters, characterizing the coupling strengths and screening, are adjusted to reproduce the color-average heavy-quark free energy as computed in thermal lattice QCD. The approach is tested against vacuum spectroscopy in the open (D, B) and hidden (Psi and Upsilon) flavor sectors, as well as in the high-energy limit of elastic perturbative QCD scattering. Theoretical uncertainties in the static reduction scheme of the 4-dimensional Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are used to calculate Euclidean correlators which are discussed in light of lattice QCD results, while heavy-quark relaxation rates and diffusion coefficients are extracted utilizing a Fokker-Planck equation.

Colour-electric spectral function at next-to-leading order

The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alpha_s^2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.