Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain

We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum affine algebra of the deformed Hubbard chain has a coideal subalgebra which is consistent with the reflection (boundary Yang-Baxter) equation. We derive the corresponding reflection matrix and furthermore show that the aforementioned algebra in the rational limit specializes to the (generalized) twisted Yangian of the Y=0 giant graviton.Comment: 21 page. v2: minor correction

Secret Symmetries in AdS/CFT

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.Comment: 20 pages, pdfLaTeX; Submitted to the Proceedings of the Nordita program `Exact Results in Gauge-String Dualities'; Based on the talk presented by A.T., Nordita, 15 February 201

The Quantum Affine Origin of the AdS/CFT Secret Symmetry

We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra U_q(gl(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix.Comment: 22 page

Standard survey methods for estimating colony losses and explanatory risk factors in Apis mellifera

This chapter addresses survey methodology and questionnaire design for the collection of data pertaining to estimation of honey bee colony loss rates and identification of risk factors for colony loss. Sources of error in surveys are described. Advantages and disadvantages of different random and non-random sampling strategies and different modes of data collection are presented to enable the researcher to make an informed choice. We discuss survey and questionnaire methodology in some detail, for the purpose of raising awareness of issues to be considered during the survey design stage in order to minimise error and bias in the results. Aspects of survey design are illustrated using surveys in Scotland. Part of a standardized questionnaire is given as a further example, developed by the COLOSS working group for Monitoring and Diagnosis. Approaches to data analysis are described, focussing on estimation of loss rates. Dutch monitoring data from 2012 were used for an example of a statistical analysis with the public domain R software. We demonstrate the estimation of the overall proportion of losses and corresponding confidence interval using a quasi-binomial model to account for extra-binomial variation. We also illustrate generalized linear model fitting when incorporating a single risk factor, and derivation of relevant confidence intervals

Evaluating the Assumptions of Surface Reflectance and Aerosol Type Selection Within the MODIS Aerosol Retrieval Over Land: The Problem of Dust Type Selection

Aerosol Optical Depth (AOD) and Angstrom exponent (AE) values derived with the MODIS retrieval algorithm over land (Collection 5) are compared with ground based sun photometer measurements at eleven sites spanning the globe. Although, in general, total AOD compares well at these sites (R2 values generally over 0.8), there are cases (from 2 to 67% of the measurements depending on the site) where MODIS clearly retrieves the wrong spectral dependence, and hence, an unrealistic AE value. Some of these poor AE retrievals are due to the aerosol signal being too small (total AOD<0.3) but in other cases the AOD should have been high enough to derive accurate AE. However, in these cases, MODIS indicates AE values close to 0.6 and zero fine model weighting (FMW), i.e. dust model provides the best fitting to the MODIS observed reflectance. Yet, according to evidence from the collocated sun photometer measurements and back-trajectory analyses, there should be no dust present. This indicates that the assumptions about aerosol model and surface properties made by the MODIS algorithm may have been incorrect. Here we focus on problems related to parameterization of the land-surface optical properties in the algorithm, in particular the relationship between the surface reflectance at 660 and 2130 nm

Thermodynamics of hydrogen vacancies in MgH2 from first-principles calculations and grand-canonical statistical mechanics

Ab initio calculations and statistical mechanics are combined to elucidate the thermodynamics of H vacancies in MgH2. A general method based on a grand-canonical ensemble of defect configurations is introduced to model the exchange of hydrogen between crystalline MgH2 and gas-phase H2. We find that, at temperatures and hydrogen partial pressures of practical interest, MgH2 is capable of accommodating only very small concentrations of hydrogen vacancies, which consist mainly of isolated defects rather than vacancy clusters, contrary to what is expected from a simple energetic analysis.Comment: 13 pages, 5 figures. Paper accepted in Physical Review

Bound State Transfer Matrix for AdS5 x S5 Superstring

We apply the algebraic Bethe ansatz technique to compute the eigenvalues of the transfer matrix constructed from the general bound state S-matrix of the light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures on the quantum characteristic function, and to extend them to the general case.Comment: 36 pages, LaTeX, v2: typos corrected, ref added; v3: accepted for publication in JHEP

The existence problem for dynamics of dissipative systems in quantum probability

Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $\delta$ is densely defined in a unital $C^{\ast}$-algebra $\mathfrak{A}$. The identity element in ${\frak A}$ is also in the domain of $\delta$. Completely dissipative maps $\delta$ are defined by the requirement that the induced maps, $(a_{ij})\to (\delta (a_{ij}))$, are dissipative on the $n$ by $n$ complex matrices over ${\frak A}$ for all $n$. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of ${\frak A}$ is injective, we show the existence of an extension of $\delta$ which is the infinitesimal generator of a quantum dynamical semigroup of completely positive maps in the von Neumann algebra. If $\delta$ is a given well-behaved *-derivation, then we show that each of the maps $\delta$ and $-\delta$ is completely dissipative.Comment: 24 pages, LaTeX/REVTeX v. 4.0, submitted to J. Math. Phys.; PACS 02., 02.10.Hh, 02.30.Tb, 03.65.-w, 05.30.-

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z=0 giant graviton and the Z=0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed reflection matrices for both boundaries which in the q->1 limit specialize to the ones obtained using twisted Yangians.Comment: 36 pages. v2: minor typos corrected, references updated; v3: published versio