Lusternik-Schnirelmann category of simplicial complexes and finite spaces

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of geometric category for simplicial complexes. We prove that the maximum value over the homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of category are obtained in the setting of finite topological spaces.Comment: 18 pages, 10 figures, this is a new version with some minor changes and a new exampl

Enhancing card sorting dendrograms through the holistic analysis of distance methods and linkage criteria

Card sorting has been widely used in information architecture to analyze and improve web content and navigation. This is an intuitive and cost-effective technique also useful in user research and evaluation. However, while the implementation of sorting tasks comprises a constructive and easy-toaccomplish process, the quantitative analysis of resulting card-sorting data can be a challenge for non-skilled evaluators. Several tools exist to support sorting tasks and data analysis, but still some users utilize custom spreadsheets or statistical packages in order to enhance analysis and obtain more expressive and comparable results. One of the most utilized diagrams for analyzing card-sorting results is the dendrogram, also known as a tree diagram, which is commonly based on an agglomerative clustering representation depicting groupings of related cards. However, several issues have to be considered by evaluators in order to produce meaningful dendrograms for decisionmaking. In fact, the distance method and the linkage criterion greatly influence the final dendrogram obtained. In this paper, an analysis on distance methods and linkage criteria for obtaining suitable dendrograms is proposed. The main aim is to guide evaluators and usability engineers to produce appropriate dendrograms based on available cardsorting data. In this sense, the provided clues can be widely applied to any card-sorting domain and sample size, improving card-sorting analysis by comparing different solutions through goodness indicators. Analyses applied to a publicly available dataset indicate that the results are highly dependent of the data type, so the right selection of both distance method and linkage criterion is essential for obtaining a suitable dendrogram and correctly interpreting the resultsThis work was partially supported by the Spanish Government (grant number RTI2018-095255-B-I00) and the Madrid Research Council (grant number P2018/TCS-4314

A basic reference state suitable for anomaly-coupled ocean-atmosphere climate models

AbstractA large class of ocean-atmosphere models exists in which the ocean state is coupled to the model of the atmosphere only through the anomalies of the ocean state. The sea surface temperatures are defined with respect to a mean reference state, i.e., they are the difference between the ocean state and a reference state. Due to coupled model drift, the choice of reference state is important and it can have a large impact on the variability in the model. The reference state can be calculated as an average throughout the coupled simulation and various methods of doing this (moving average, exponentially weighted moving average and accumulated mean) are compared in this note. The accumulated mean method appears to be the sole method of the three which gives both unbiased anomalies and a convergent reference state. It is recommended for use in anomaly-coupled models for improving variability and predictability

A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space-Fractional Gross-Pitaevskii Equation

The present work departs from an extended form of the classical multi-dimensional Gross-Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross-Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system. © 2019 Ahmed S. Hendy et al., published by Sciendo 2019

NIKEL_AMC: Readout electronics for the NIKA2 experiment

The New Iram Kid Arrays-2 (NIKA2) instrument has recently been installed at the IRAM 30 m telescope. NIKA2 is a state-of-art instrument dedicated to mm-wave astronomy using microwave kinetic inductance detectors (KID) as sensors. The three arrays installed in the camera, two at 1.25 mm and one at 2.05 mm, feature a total of 3300 KIDs. To instrument these large array of detectors, a specifically designed electronics, composed of 20 readout boards and hosted in three microTCA crates, has been developed. The implemented solution and the achieved performances are presented in this paper. We find that multiplexing factors of up to 400 detectors per board can be achieved with homogeneous performance across boards in real observing conditions, and a factor of more than 3 decrease in volume with respect to previous generations.Comment: 21 pages; 16 figure