Colour-dressed hexagon tessellations for correlation functions and non-planar corrections

We continue the study of four-point correlation functions by the hexagon tessellation approach initiated in 1611.05436 and 1611.05577. We consider planar tree-level correlation functions in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory involving two non-protected operators. We find that, in order to reproduce the field theory result, it is necessary to include $SU(N)$ colour factors in the hexagon formalism; moreover, we find that the hexagon approach as it stands is naturally tailored to the single-trace part of correlation functions, and does not account for multi-trace admixtures. We discuss how to compute correlators involving double-trace operators, as well as more general $1/N$ effects; in particular we compute the whole next-to-leading order in the large-$N$ expansion of tree-level BMN two-point functions by tessellating a torus with punctures. Finally, we turn to the issue of "wrapping", L\"uscher-like corrections. We show that $SU(N)$ colour-dressing reproduces an earlier empirical rule for incorporating single-magnon wrapping, and we provide a direct interpretation of such wrapping processes in terms of $\mathcal{N}=2$ supersymmetric Feynman diagrams.Comment: 42 pages, typos correcte

Constrained low-tubal-rank tensor recovery for hyperspectral images mixed noise removal by bilateral random projections

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and sparsity can govern the solution of the denoised tensor in the recovery procedure. To solve the constrained low-tubal-rank model, we develop an iterative algorithm based on bilateral random projections to efficiently solve the proposed model. The advantage of random projections is that the approximation of the low-tubal-rank tensor can be obtained quite accurately in an inexpensive manner. Experimental examples for hyperspectral image denoising are presented to demonstrate the effectiveness and efficiency of the proposed method.Comment: Accepted by IGARSS 201

Why Use a Hamilton Approach in QCD?

We discuss $QCD$ in the Hamiltonian frame work. We treat finite density $QCD$ in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum ($\theta$-angles) and distribution functions in $QED_{1+1}$. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian $QCD$.Comment: Proceedings of Hadrons and Strings, invited talk given by H. Kr\"{o}ger; Text (LaTeX file), 3 Figures (ps file

Modulation of the Period of the Quasi-Biennial Oscillation by the Solar Cycle

The authors examine the mechanism of solar cycle modulation of the Quasi-Biennial Oscillation (QBO) period using the Two-and-a-Half-Dimensional Interactive Isentropic Research (THINAIR) model. Previous model results (using 2D and 3D models of varying complexity) have not convincingly established the proposed link of longer QBO periods during solar minima. Observational evidence for such a modulation is also controversial because it is only found during the period from the 1960s to the early 1990s, which is contaminated by volcanic aerosols. In the model, 200- and 400-yr runs without volcano influence can be obtained, long enough to establish some statistical robustness. Both in model and observed data, there is a strong synchronization of the QBO period with integer multiples of the semiannual oscillation (SAO) in the upper stratosphere. Under the current level of wave forcing, the period of the QBO jumps from one multiple of SAO to another and back so that it averages to 28 months, never settling down to a constant period. The “decadal” variability in the QBO period takes the form of “quantum” jumps; these, however, do not appear to follow the level of the solar flux in either the observation or the model using realistic quasi-periodic solar cycle (SC) forcing. To understand the solar modulation of the QBO period, the authors perform model runs with a range of perpetual solar forcing, either lower or higher than the current level. At the current level of solar forcing, the model QBO period consists of a distribution of four and five SAO periods, similar to the observed distribution. This distribution changes as solar forcing changes. For lower (higher) solar forcing, the distribution shifts to more (less) four SAO periods than five SAO periods. The record-averaged QBO period increases with the solar forcing. However, because this effect is rather weak and is detectable only with exaggerated forcing, the authors suggest that the previous result of the anticorrelation of the QBO period with the SC seen in short observational records reflects only a chance behavior of the QBO period, which naturally jumps in a nonstationary manner even if the solar forcing is held constant, and the correlation can change as the record gets longer

Nonstationary Synchronization of Equatorial QBO with SAO in Observations and a Model

It has often been suggested that the period of the quasi-biennial oscillation (QBO) has a tendency to synchronize with the semiannual oscillation (SAO). Apparently the synchronization is better the higher up the observation extends. Using 45 yr of the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data of the equatorial stratosphere up to the stratopause, the authors confirm that this synchronization is not just a tendency but a robust phenomenon in the upper stratosphere. A QBO period starts when a westerly SAO (w-SAO) descends from the stratopause to 7 hPa and initiates the westerly phase of the QBO (w-QBO) below. It ends when another w-SAO, a few SAO periods later, descends again to 7 hPa to initiate the next w-QBO. The fact that it is the westerly but not the easterly SAO (e-SAO) that initiates the QBO is also explained by the general easterly bias of the angular momentum in the equatorial stratosphere so that the e-SAO does not create a zero-wind line, unlike the w-SAO. The currently observed average QBO period of 28 months, which is not an integer multiple of SAO periods, is a result of intermittent jumps of the QBO period from four SAO to five SAO periods. The same behavior is also found in the Two and a Half Dimensional Interactive Isentropic Research (THINAIR) model. It is found that the nonstationary behavior in both the observation and model is caused not by the 11-yr solar-cycle forcing but by the incompatibility of the QBO’s natural period (determined by its wave forcing) and the “quantized” period determined by the SAO. The wave forcing parameter for the QBO period in the current climate probably lies between four SAO and five SAO periods. If the wave forcing for the QBO is tuned so that its natural period is compatible with the SAO period above (e.g., at 24 or 30 months), nonstationary behavior disappears