Representation theory of towers of recollement: Theory, notes, and examples

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley–Lieb algebras. We demonstrate the utility of our formalism by applying it to this class

Why Do Companies Pay Dividends?

This paper presents a simple model of market equilibrium to explain why firms that maximize the value of their shares pay dividends even though the funds could instead be retained and subsequently distributed to shareholders in a way that would allow them to be taxed more favorably as capital gains. The two principal ingredients of our explanation are:(1) the conflicting preferences of shareholders in different tax brackets and (2) the shareholders' desire for portfolio diversification, we show that companies will pay a positive fraction of earnings in dividends. We also provide some comparative static analysis of dividend behavior with respect to tax parameters and to the conditions determining the riskiness of the securities.

Constructing cell data for diagram algebras

We show how the treatment of cellularity in families of algebras arising from diagram calculi, such as Jones' Temperley--Lieb wreaths, variants on Brauer's centralizer algebras, and the contour algebras of Cox et al (of which many algebras are special cases), may be unified using the theory of tabular algebras. This improves an earlier result of the first author (whose hypotheses covered only the Brauer algebra from among these families).Comment: Approximately 38 pages, AMSTeX. Revised in light of referee comments. To appear in the Journal of Pure and Applied Algebr

Extraction of black hole coalescence waveforms from noisy data

We describe an independent analysis of LIGO data for black hole coalescence events. Gravitational wave strain waveforms are extracted directly from the data using a filtering method that exploits the observed or expected time-dependent frequency content. Statistical analysis of residual noise, after filtering out spectral peaks (and considering finite bandwidth), shows no evidence of non-Gaussian behaviour. There is also no evidence of anomalous causal correlation between noise signals at the Hanford and Livingston sites. The extracted waveforms are consistent with black hole coalescence template waveforms provided by LIGO. Simulated events, with known signals injected into real noise, are used to determine uncertainties due to residual noise and demonstrate that our results are unbiased. Conceptual and numerical differences between our RMS signal-to-noise ratios (SNRs) and the published matched-filter detection SNRs are discussed.Comment: 15 pages, 11 figures. Version accepted for publicatio

Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond

The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers by inclusion, such as symplectic blob algebras (diagram algebra quotients of the type-\hati{C} Hecke algebras). By carefully reviewing the diagram algebra construction, we find a new set of functors interrelating module categories of ordinary blob algebras (diagram algebra quotients of the type-${B}$ Hecke algebras) at {\em different} values of the algebra parameters. We show that these functors generalise to determine the structure of symplectic blob algebras, and hence of certain two-boundary Temperley-Lieb algebras arising in Statistical Mechanics. We identify the diagram basis with a cellular basis for each symplectic blob algebra, and prove that these algebras are quasihereditary over a field for almost all parameter choices, and generically semisimple. (That is, we give bases for all cell and standard modules.)Comment: 61 page

Data-Driven Generalized Integer Aperture Bootstrapping for Real-Time High Integrity Applications

A new method is developed for integer ambiguity resolution in carrier-phase differential GPS (CDGPS) positioning. The method is novel in that it is (1) data-driven, (2) generalized to include partial ambiguity resolution, and (3) amenable to a full characterization of the prior and posterior distributions of the three-dimensional baseline vector that results from CDGPS. The technique is termed generalized integer aperture bootstrapping (GIAB). GIAB improves the availability of integer ambiguity resolution for high-integrity, safety-critical systems. Current high-integrity CDGPS algorithms, such as EPIC and GERAFS, evaluate the prior risk of position domain biases due to incorrect integer ambiguity resolution without further validation of the chosen solution. This model-driven approach introduces conservatism which tends to reduce solution availability. Common data-driven ambiguity validation methods, such as the ratio test, control the risk of incorrect ambiguity resolution by shrinking an integer aperture (IA), or acceptance region. The incorrect fixing risk of current IA methods is determined by functional approximations that are inappropriate for use in safety-of-life applications. Moreover, generalized IA (GIA) methods incorrectly assume that the baseline resulting from partial ambiguity resolution is zero mean. Each of these limitations is addressed by GIAB, and the claimed improvements are validated by Monte Carlo simulation. The performance of GIAB is then optimized by tuning the integer aperture size to maximize the prior probability of full ambiguity resolution. GIAB is shown to provide higher availability than EPIC for the same integrity requirements.Aerospace Engineering and Engineering Mechanic

Assessment and learning outcomes: the evaluation of deep learning in an on-line course

Using an online learning environment, students from European countries collaborated and communicated to carry out problem based learning in occupational therapy. The effectiveness of this approach was evaluated by means of the final assessments and published learning outcomes. In particular, transcripts from peer-to-peer sessions of synchronous communication were analysed. The SOLO taxonomy was used and the development of deep learning was studied week by week. This allowed the quality of the course to be appraised and showed, to a certain extent, the impact of this online international course on the learning strategies of the students. Results indicate that deep learning can be supported by synchronous communication and online meetings between course participants.</p