The m−m-dissimilarity map and representation theory of SLmSL_m

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $SL_m.$Comment: 11 pages, 8 figure

Crystal structure and chemistry of barium-graphite intercalation compounds

Graphite can accommodate various chemical species between graphene layers to form graphite intercalation compounds (GIC) [1]. Alkali metals can easily lead to bulk stage-1 intercalation compounds by vapor transport but for more electronegative elements, such as alkaline-earth metals or lanthanides, only a superficial intercalation is obtained and other synthesis methods have to be envisaged. Molten alloys, formed between an alkali metal and the targeted metal, have demonstrated their efficiency to prepare bulk and homogeneous GIC from these latter elements, for example the superconducting CaC6 phase [2], but some elements remain difficult to intercalate by this method. More recently, our team developed a method based on the work of Hagiwara et al., consisting in using a LiCl-KCl eutectic molten medium [3], which for example allowed to prepare for the first time a bulk SrC6 compound [4]. This work is focused on the intercalation of barium into graphite from the LiCl-KCl molten salts method. A bulk stage-1 BaC6 compound has been prepared and X-ray diffraction measurements confirmed its crystal structure [5]. Moreover, by varying the experimental conditions, two completely novel phases, denoted α and β, have been isolated. From ion beam analyses, Li0,2K0,6Ba0,35C6 and Li0,2K0,75Ba0,6C6 chemical formulae have been determined for α and β phases, respectively, showing that lithium and potassium are intercalated together with barium. X- ray diffraction led to the determination of the stacking sequence of each compound, and their planar unit cells. Lastly, a reaction mechanism is proposed, which explains the formation of the different phases observed in this study

Discrete integrable systems, positivity, and continued fraction rearrangements

In this review article, we present a unified approach to solving discrete, integrable, possibly non-commutative, dynamical systems, including the $Q$- and $T$-systems based on $A_r$. The initial data of the systems are seen as cluster variables in a suitable cluster algebra, and may evolve by local mutations. We show that the solutions are always expressed as Laurent polynomials of the initial data with non-negative integer coefficients. This is done by reformulating the mutations of initial data as local rearrangements of continued fractions generating some particular solutions, that preserve manifest positivity. We also show how these techniques apply as well to non-commutative settings.Comment: 24 pages, 2 figure

The solution of the quantum A1A_1 T-system for arbitrary boundary

We solve the quantum version of the $A_1$ $T$-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum $A_1$ $Q$-system and generalize it to the fully non-commutative case. We give the relation between the quantum $T$-system and the quantum lattice Liouville equation, which is the quantized $Y$-system.Comment: 24 pages, 18 figure

Quality of Life in Oncological Patients with Oropharyngeal Dysphagia: Validity and Reliability of the Dutch Version of the MD Anderson Dysphagia Inventory and the Deglutition Handicap Index

Quality of life is an important outcome measurement in objectifying the current health status or therapy effects in patients with oropharyngeal dysphagia. In this study, the validity and reliability of the Dutch version of the Deglutition Handicap Index (DHI) and the MD Anderson Dysphagia Inventory (MDADI) have been determined for oncological patients with oropharyngeal dysphagia. At Maastricht University Medical Center, 76 consecutive patients were selected and asked to fill in three questionnaires on quality of life related to oropharyngeal dysphagia (the SWAL-QOL, the MDADI, and the DHI) as well as a simple one-item visual analog Dysphagia Severity Scale. None of the quality-of-life questionnaires showed any floor or ceiling effect. The test-retest reliability of the MDADI and the Dysphagia Severity Scale proved to be good. The test-retest reliability of the DHI could not be determined because of insufficient data, but the intraclass correlation coefficients were rather high. The internal consistency proved to be good. However, confirmatory factor analysis could not distinguish the underlying constructs as defined by the subscales per questionnaire. When assessing criterion validity, both the MDADI and the DHI showed satisfactory associations with the SWAL-QOL (reference or gold standard) after having removed the less relevant subscales of the SWAL-QOL. In conclusion, when assessing the validity and reliability of the Dutch version of the DHI or the MDADI, not all psychometric properties have been adequately met. In general, because of difficulties in the interpretation of study results when using questionnaires lacking sufficient psychometric quality, it is recommended that researchers strive to use questionnaires with the most optimal psychometric properties

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Dust impact on surface solar irradiance assessed with model simulations, satellite observations and ground-based measurements

This study assesses the impact of dust on surface solar radiation focussing on an extreme dust event. For this purpose, we exploited the synergy of AERONET measurements and passive and active satellite remote sensing (MODIS and CALIPSO) observations, in conjunction with radiative transfer model (RTM) and chemical transport model (CTM) simulations and the 1-day forecasts from the Copernicus Atmosphere Monitoring Service (CAMS). The area of interest is the eastern Mediterranean where anomalously high aerosol loads were recorded between 30 January and 3 February 2015. The intensity of the event was extremely high, with aerosol optical depth (AOD) reaching 3.5, and optical/microphysical properties suggesting aged dust. RTM and CTM simulations were able to quantify the extent of dust impact on surface irradiances and reveal substantial reduction in solar energy exploitation capacity of PV and CSP installations under this high aerosol load. We found that such an extreme dust event can result in Global Horizontal Irradiance (GHI) attenuation by as much as 40–50 % and a much stronger Direct Normal Irradiance (DNI) decrease (80–90 %), while spectrally this attenuation is distributed to 37 % in the UV region, 33 % in the visible and around 30 % in the infrared. CAMS forecasts provided a reliable available energy assessment (accuracy within 10 % of that obtained from MODIS). Spatially, the dust plume resulted in a zonally averaged reduction of GHI and DNI of the order of 150 W/m^2 in southern Greece, and a mean increase of 20 W/m^2 in the northern Greece as a result of lower AOD values combined with local atmospheric processes. This analysis of a real-world scenario contributes to the understanding and quantification of the impact range of high aerosol loads on solar energy and the potential for forecasting power generation failures at sunshine-privileged locations where solar power plants exist, are under construction or are being planned

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Variation of health-related quality of life assessed by caregivers and patients affected by severe childhood infections.

BACKGROUND: The agreement between self-reported and proxy measures of health status in ill children is not well established. This study aimed to quantify the variation in health-related quality of life (HRQOL) derived from young patients and their carers using different instruments. METHODS: A hospital-based cross-sectional survey was conducted between August 2010 and March 2011. Children with meningitis, bacteremia, pneumonia, acute otitis media, hearing loss, chronic lung disease, epilepsy, mild mental retardation, severe mental retardation, and mental retardation combined with epilepsy, aged between five to 14 years in seven tertiary hospitals were selected for participation in this study. The Health Utilities Index Mark 2 (HUI2), and Mark 3 (HUI3), and the EuroQoL Descriptive System (EQ-5D) and Visual Analogue Scale (EQ-VAS) were applied to both paediatric patients (self-assessment) and caregivers (proxy-assessment). RESULTS: The EQ-5D scores were lowest for acute conditions such as meningitis, bacteremia, and pneumonia, whereas the HUI3 scores were lowest for most chronic conditions such as hearing loss and severe mental retardation. Comparing patient and proxy scores (n = 74), the EQ-5D exhibited high correlation (r = 0.77) while in the HUI2 and HUI3 patient and caregiver scores were moderately correlated (r = 0.58 and 0.67 respectively). The mean difference between self and proxy-assessment using the HUI2, HUI3, EQ-5D and EQ-VAS scores were 0.03, 0.05, -0.03 and -0.02, respectively. In hearing-impaired and chronic lung patients the self-rated HRQOL differed significantly from their caregivers. CONCLUSIONS: The use of caregivers as proxies for measuring HRQOL in young patients affected by pneumococcal infection and its sequelae should be employed with caution. Given the high correlation between instruments, each of the HRQOL instruments appears acceptable apart from the EQ-VAS which exhibited low correlation with the others

Baseline autoantibody profile in rheumatoid arthritis is associated with early treatment response but not long-term outcomes

Transplantation and autoimmunit