3-dimensional Λ-BMS symmetry and its deformations

In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible Lie bialgebra structures and for selected examples we explicitely construct the related Hopf algebras. Using cohomological arguments we show that this construction can always be performed by a so-called twist deformation. The resulting structures can be compared to the well-known κ-Poincaré Hopf algebras constructed on the finite dimensional Poincaré or (anti) de Sitter algebra. The dual κ Minkowski spacetime is supposed to describe a specific non-commutative geometry. Importantly, we find that some incarnations of the κ-Poincaré can not be extended consistently to the infinite dimensional algebras. Furthermore, certain deformations can have potential physical applications if subalgebras are considered. Since the conserved charges associated with asymptotic symmetries in 3-dimensional form a centrally extended algebra we also discuss briefly deformations of such algebras. The presence of the full symmetry algebra might have observable consequences that could be used to rule out these deformations.

Organosulfur Materials with High Photo- and Photo-Oxidation Stability: 10-Anthryl Sulfoxides and Sulfones and Their Photophysical Properties Dependent on the Sulfur Oxidation State

While few studies show only symmetrical and poorly mono-SOn (n = 0–2) substituted acenes, in this study, we present a synthesis of a new group of unsymmetrical, significantly substituted derivatives, which revealed unique photophysical properties. Both sulfides (S), sulfoxides (SO) and sulfones (SO2) showed very high photochemical stabilities, unusual for these groups, during UV-irradiation at 254/365 nm (air O2 and Ar), which was higher than any found in the literature. For the (S)/(SO) series (254 nm), the stabilities of 80–519 min. (air O2 and Ar) were found. At 365 nm, stabilities of 124—812 min./(air O2) for (S)/(SO) and higher for (SO2) were observed. Photoluminescence lifetimes of (SOn) of the lower anthryl symmetry remained in the following order: (SO2) < (S) < (SO); those with full symmetry were in the following order: (S) < (SO) < (SO2). The enhanced photostability was explained with DFT/MS/Hammett’s constants, which showed the leading role of the SOn groups in stabilization of HOMO/LUMO frontier orbitals. The SOn (n = 0–2) substituted acenes turned out to be tunable violet/blue/green emitters by oxidation of S atoms and the introduction of rich substitution.

Soliton Molecules and Full Symmetry Groups to the KdV-Sawada-Kotera-Ramani Equation

By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation are elastic. Then, full symmetry group is derived for the KSKR equation by the symmetry group direct method. From the full symmetry group, a general group invariant solution can be obtained from a known solution.

Probing Asymmetry in Spatial-temporal Correlations in Quantum Causal Inference

Quantum correlations in space-time encapsulate the most defining aspects of quantum physics. The dual of the spatial and temporal perspectives are bind with a one-to-one correspondence between bipartite quantum states and quantum channels. Consequently, causal relations between quantum events can sometimes be inferred solely from correlation statistics, apparently contradicting the classical \textit{credo}, `correlation does not imply causation'[1-6]. However, since the spatial-temporal duality does not imply a full symmetry of measurement statistics between the two domains[7], the extent to which correlation alone identifies quantum causality ponders inquiry vital for both fundamental and practical interests. Here, demonstrating a unified geometrical representation of spatial-temporal quantum correlation, we show that certain non-unital channels create temporal correlation without spatial analogue and break the spatial-temporal symmetry. By implementing such channels in a photonic architecture, we observe this asymmetry and classify quantum correlations using a distance criterion, thus bringing empirical insight into causal inference in quantum mechanics.

COMPRESSION OF PINWISE NUCLIDE CONCENTRATIONS IN CMS5

Pinwise nuclide number density (ND) data from the lattice physics code CASMO5 is compressed using a preconditioned truncated singular value decomposition (TSVD) to reduce storage requirements. Previously only assembly-average or single-pin NDs were optionally saved in the CMS5 few-group cross section library. However, backend analysis has prompted the desire to have pin-by-pin NDs available in the library for use by the SNF code. Adding this data set significantly increases the size of the library, particularly for lattices modeled in full assembly geometry (that is, not in half or octant symmetry). To reduce the required storage, the SVD is used to approximate the entire data with a reduced basis. In the four test cases, compression ratios of 2.7 to 8.5 were achieved for the PWR cases, with maximum errors less than 0.1%. However, the rodded BWR segment proved more difficult, with an average compression ratio of 1.6. One advantage of this technique is that the compression ratio is higher for full-symmetry cases, where the need for the compression is also highest.

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Integrable boundary states can be built up from pair annihilation amplitudes called K-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the K-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted K-matrices, respectively. We use these findings to develop a nesting procedure for K-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the K-matrices with centrally extended $$ \mathfrak{su} $$ su (2|2)c symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.

Measuring Historical and Compositional Signals in Phylogenetic Data

Most commonly-used molecular phylogenetic methods assume that the sequences evolved on a single bifurcating tree and that the evolutionary processes operating at the variable sites are Markovian. Typically, it is also assumed that these evolutionary processes were stationary, reversible and homogenous across the edges of the tree and that the multiple substitutions at variable sites occurred so infrequently that the historical signal (i.e., the signal in DNA that is due to the order and time of divergence event) in phylogenetic data has been retained, allowing for accurate phylogenetic estimates to be obtained from the data. Here, we present two metrics, λ and δCFS, to quantify the strength of the historical and compositional signals in phylogenetic data. λ quantifies loss of historical signal, with λ = 0.0 indicating evidence of a strong historical signal and λ = 1.0 indicating evidence of a fully eroded historical signal. δCFS quantifies compositional distance from full symmetry of a divergence matrix generated by comparing two sequences, with δCFS = 0.0 indicating no evidence of evolution under dissimilar conditions and δCFS > 0.0 indicating increasing evidence of lineages diverging under different conditions. The metrics are implemented in methods intended for use after multiple sequence alignment and before model selection and phylogenetic analysis. Results generated using these methods allow users of phylogenetic tools to select phylogenetic data more wisely than it previously was possible. The merits of these metrics and methods are illustrated using simulated data and multi-gene alignments obtained from 144 insect genomes.

Shock Waves Asymmetry in a Symmetric Nozzle

The results of the experimental research on the symmetry of supersonic flow in a symmetric convergent-divergent nozzle are presented. The investigations were focused on the fact that for some flow conditions the flow in a precisely symmetric nozzle becomes asymmetric. Starting from a specific value of Mach number, the flow becomes asymmetric in terms of shock wave λ-foot geometry on both sides of a symmetric nozzle. The evolution of the abovementioned asymmetry has been analysed for Mach number value ranging from M = 1.26 to M = 1.59 with the nozzle opening angle of up to 6.5° on each side. The presented results indicate that for the same flow parameters as Mach number and Reynolds number, and for the same geometry of the nozzle, different λ-foot size is formed at each wall. This unexpected behaviour is responsible for the flow asymmetry. Numerical simulations carried out earlier confirm the appearance of shock wave asymmetry. The side in which the asymmetry takes place is accidental, as the full symmetry of simulation mesh and experiment setup was secured. In numerical simulation the asymmetry follows always the same direction. In experiments the direction of asymmetry happens alternatively without any apparent reason. The explanation of the phenomena is provided in this paper.