Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

Dynamical differential equations compatible with rational qKZ equations

For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $gl_N$ Weyl group.Comment: 7 pages, AmsLaTe

Spectral triples and the super-Virasoro algebra

We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representation of the Ramond algebra with central charge c and minimal lowest weight h=c/24 is graded and gives rise to a net of even theta-summable spectral triples with non-zero Fredholm index. The irreducible unitary positive energy representations of the Neveu-Schwarz algebra give rise to nets of even theta-summable generalised spectral triples where there is no Dirac operator but only a superderivation.Comment: 27 pages; v2: a comment concerning the difficulty in defining cyclic cocycles in the NS case have been adde

Zinc-modified nanopolymers improve the quality of resin-dentin bonded interfaces

Introduction: Demineralized collagen fibers at the hybrid layer are susceptible to degradation. Remineralization may aid to improve bond longevity. Objectives: The aim of the present study was to infiltrate zinc and calcium-loaded polymeric nanoparticles into demineralized dentin to facilitate hybrid layer remineralization. Materials and methods: Zinc or calcium-loaded polymeric nanoparticles were infiltrated into etched dentin, and Single Bond Adhesive was applied. Bond strength was tested after 24 h and 6 months storage. Nanomechanical properties, dyeassisted confocal laser microscopy, and Masson’s trichrome staining evaluation were performed to assess for the hybrid layer morphology, permeability, and remineralization ability after 24 h and 3 months. Data were analyzed by ANOVA and Student–Newman–Keuls multiple comparisons tests (p < 0.05). Results: Immediate bond strength was not affected by nanoparticles infiltration (25 to 30 MPa), while after 6 months, bond strengths were maintained (22 to 24 MPa). After 3 months, permeability occurred only in specimens in which nanoparticles were not infiltrated. Dentin remineralization, at the bottom of the hybrid layer, was observed in all groups. After microscopy analysis, zinc-loaded nanoparticles were shown to facilitate calcium deposition throughout the entire hybrid layer. Young’s modulus at the hybrid layer increased from 2.09 to 3.25 GPa after 3 months, in specimens with zinc nanoparticles; meanwhile, these values were reduced from 1.66 to 0.49 GPa, in the control group. Conclusion: Infiltration of polymeric nanoparticles into demineralized dentin increased long-term bond strengths. Zinc-loaded nanoparticles facilitate dentin remineralization within the complete resin–dentin interface. Clinical relevance: Resin–dentin bond longevity and dentin remineralization at the hybrid layer were facilitated by zincloaded nanoparticles.This work was supported by a grant, MINECO/FEDER MAT2014-52036-P

Morphometric and microstructural characteristics of hippocampal subfields in mesial temporal lobe epilepsy and their correlates with mnemonic discrimination.

Pattern separation (PS) is a fundamental aspect of memory creation that defines the ability to transform similar memory representations into distinct ones, so they do not overlap when storing and retrieving them. Experimental evidence in animal models and the study of other human pathologies have demonstrated the role of the hippocampus in PS, in particular of the dentate gyrus (DG) and CA3. Patients with mesial temporal lobe epilepsy with hippocampal sclerosis (MTLE-HE) commonly report mnemonic deficits that have been associated with failures in PS. However, the link between these impairments and the integrity of the hippocampal subfields in these patients has not yet been determined. The aim of this work is to explore the association between the ability to perform mnemonic functions and the integrity of hippocampal CA1, CA3, and DG in patients with unilateral MTLE-HE. To reach this goal we evaluated the memory of patients with an improved object mnemonic similarity test. We then analyzed the hippocampal complex structural and microstructural integrity using diffusion weighted imaging. Our results indicate that patients with unilateral MTLE-HE present alterations in both volume and microstructural properties at the level of the hippocampal subfields DG, CA1, CA3, and the subiculum, that sometimes depend on the lateralization of their epileptic focus. However, none of the specific changes was found to be directly related to the performance of the patients in a pattern separation task, which might indicate a contribution of various alterations to the mnemonic deficits or the key contribution of other structures to the function. we established for the first time the alterations in both the volume and the microstructure at the level of the hippocampal subfields in a group of unilateral MTLE patients. We observed that these changes are greater in the DG and CA1 at the macrostructural level, and in CA3 and CA1 in the microstructural level. None of these changes had a direct relation to the performance of the patients in a pattern separation task, which suggests a contribution of various alterations to the loss of function

Coupling of replicate order-parameters in incommensurate multiferroics

The specific properties of incommensurate multiferroic phases resulting from the coupling of order-parameter replicates are worked out using the illustrative example of iron vanadate. The dephasing between the order-parameter copies induces an additional broken symmetry phase corresponding to the lowest symmetry of the system and varies critically at the transition to the multiferroic phase. It reflects the temperature dependence of the angle between paired spins in the antiferromagnetic spiral structure. Expressing the transition order-parameters in terms of spin-density waves allows showing that isotropic exchange interactions contribute to the stabilization of the ferroelectric phase

Inhomogeneity-induced second-order phase transitions in Potts model on hierarchical lattices

The thermodynamics of the $q$-state Potts model with arbitrary $q$ on a class of hierarchical lattices is considered. Contrary to the case of the crystal lattices, it has always the second-order phase transitions. The analytical expressions fo the critical indexes are obtained, their dependencies on the structural lattice pararmeters are studied and the scailing relations among them are establised. The structural criterion of the inhomogeneity-induced transformation of the transition order is suggested. The application of the results to a description of critical phenomena in the dilute crystals and substances confined in porous media is discussed.Comment: 9 pages, 2 figure

Universal phase transitions of B1 structured stoichiometric transition-metal carbides

The high-pressure phase transitions of B1-structured stoichiometric transition metal carbides (TMCs, TM=Ti, Zr, Hf, V, Nb, and Ta) were systematically investigated using ab initio calculations. These carbides underwent universal phase transitions along two novel phase-transition routes, namely, B1\rightarrowdistorted TlI (TlI')\rightarrowTlI and/or B1\rightarrowdistorted TiB (TiB')\rightarrowTiB, when subjected to pressures. The two routes can coexist possibly because of the tiny enthalpy differences between the new phases under corresponding pressures. Four new phases result from atomic slips of the B1-structured parent phases under pressure. After completely releasing the pressure, taking TiC as a representative of TMCs, only its new TlI'-type phase is mechanically and dynamically stable, and may be recovered.Comment: [email protected]

A 10-year characterization of the Saharan Air Layer lidar ratio in the subtropical North Atlantic

Particle extinction-to-backscatter ratio (lidar ratio) is a key parameter for a correct interpretation of elastic lidar measurements. Of particular importance is the determination of the lidar ratio of the Saharan Air Layer mineral dust transported into the free troposphere over the North Atlantic region. The location of the two sun photometer stations managed by the Izaña Atmospheric Research Centre (IARC) on the island of Tenerife and a decade of available micropulse lidar (MPL) data allow us to determine the lidar ratio under almost pure-dust conditions. This result can be considered representative of the Saharan dust transported westward over the North Atlantic in the subtropical belt. Three different methods have been used to calculate the lidar ratio in this work: (1) using the inversion of sky radiance measurements from a sun–sky photometer installed at the Izaña Observatory (2373&thinsp;m&thinsp;a.s.l.) under free-troposphere conditions; (2) the one-layer method, a joint determination using a micropulse lidar sited at the Santa Cruz de Tenerife sea-level station and photometric information considering one layer of aerosol characterized by a single lidar ratio; and (3) the two-layer method, a joint determination using the micropulse lidar and photometric information considering two layers of aerosol with two different lidar ratios. The one-layer method only uses data from a co-located photometer at Santa Cruz de Tenerife, while the two-layer conceptual approach incorporates photometric information at two heights from the observatories of Izaña and Santa Cruz de Tenerife. The almost pure-dust lidar ratio retrieval from the sun–sky photometer and from the two-layer method give similar results, with lidar ratios at 523&thinsp;nm of 49&thinsp;±&thinsp;6 and 50&thinsp;±&thinsp;11 sr. These values obtained from a decade of data records are coincident with other studies in the literature reporting campaigns in the subtropical North Atlantic region. This result shows that the two-layer method is an improved conceptual approach compared to the single-layer approach, which matches the real lower-troposphere structure well. The two-layer method is able to retrieve reliable lidar ratios and therefore aerosol extinction profiles despite the inherent limitations of the elastic lidar technique. We found a lack of correlation between lidar ratio and Ångström exponent (α), which indicates that the dust lidar ratio can be considered independent of dust size distribution in this region. This finding suggests that dust is, under most atmospheric conditions, the predominant aerosol in the North Atlantic free troposphere, which is in agreement with previous studies conducted at the Izaña Observatory.</p