Generalised sifting in black-box groups

We present a generalisation of the sifting procedure introduced originally by Sims for computation with finite permutation groups, and now used for many computational procedures for groups, such as membership testing and finding group orders. Our procedure is a Monte Carlo algorithm, and is presented and analysed in the context of black-box groups. It is based on a chain of subsets instead of a subgroup chain. Two general versions of the procedure are worked out in detail, and applications are given for membership tests for several of the sporadic simple groups. Our major objective was that the procedures could be proved to be Monte Carlo algorithms, and their costs computed. In addition we explicitly determined suitable subset chains for six of the sporadic groups, and we implemented the algorithms involving these chains in the {\sf GAP} computational algebra system. It turns out that sample implementations perform well in practice. The implementations will be made available publicly in the form of a {\sf GAP} package

Suspicion of respiratory tract infection with multidrug-resistant Enterobacteriaceae: epidemiology and risk factors from a Paediatric Intensive Care Unit

Enterobacteriaceae distribution. Distribution of Enterobacteriaceae isolates (n = 167) in lower respiratory tract material, MDR (n = 51) vs susceptible (n = 116) organisms during the study period. (XLSX 14 kb

Formulas for primitive Idempotents in Frobenius Algebras and an Application to Decomposition maps

In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice of basis. The proofs use a generalisation of the well known Frobenius-Schur relations for semisimple algebras. The second part of this paper considers \Oh-free \Oh-algebras of finite \Oh-rank over a discrete valuation ring \Oh and their decomposition maps under modular reduction modulo the maximal ideal of \Oh, thereby studying the modular representation theory of such algebras. Using the formulas from the first part we derive general criteria for such a decomposition map to be an isomorphism that preserves the classes of simple modules involving explicitly known matrix representations on projective indecomposable modules. Finally we show how this approach could eventually be used to attack a conjecture by Gordon James in the formulation of Meinolf Geck for Iwahori-Hecke-Algebras, provided the necessary matrix representations on projective indecomposable modules could be constructed explicitly.Comment: 16 page

The role of hyperparameters in machine learning models and how to tune them

Hyperparameters critically influence how well machine learning models perform on unseen, out-of-sample data. Systematically comparing the performance of different hyperparameter settings will often go a long way in building confidence about a model's performance. However, analyzing 64 machine learning related manuscripts published in three leading political science journals (APSR, PA, and PSRM) between 2016 and 2021, we find that only 13 publications (20.31 percent) report the hyperparameters and also how they tuned them in either the paper or the appendix. We illustrate the dangers of cursory attention to model and tuning transparency in comparing machine learning models’ capability to predict electoral violence from tweets. The tuning of hyperparameters and their documentation should become a standard component of robustness checks for machine learning models.Published versio

Accelerated swell testing of artificial sulfate bearing lime stabilised cohesive soils

This paper reports on the physico-chemical response of two lime stabilised sulfate bearing artificial soils subject to the European Accelerated Volumetric Swell Test (EN13286-49). At various intervals during the test, a specimen was removed and subject to compositional and microstructural analysis. Ettringite was formed by both soils types, but with significant differences in crystal morphology. Ettringite crystals formed from kaolin based soils were very small, colloidal in size and tended to form on the surface of other particles. Conversely, those formed from montmorillonite were relatively large and typically formed away from the surface in the pore solution. It was concluded that the mechanism by which ettringite forms is determined by the hydroxide ion concentration in the pore solution and the fundamental structure of the bulk clay. In the kaolin soil, ettringite forms by a topochemical mechanism and expands by crystal swelling. In the montmorillonite soil, it forms by a through-solution mechanism and crystal growth

Continual Release of Differentially Private Synthetic Data from Longitudinal Data Collections

Motivated by privacy concerns in long-term longitudinal studies in medical and social science research, we study the problem of continually releasing differentially private synthetic data from longitudinal data collections. We introduce a model where, in every time step, each individual reports a new data element, and the goal of the synthesizer is to incrementally update a synthetic dataset in a consistent way to capture a rich class of statistical properties. We give continual synthetic data generation algorithms that preserve two basic types of queries: fixed time window queries and cumulative time queries. We show nearly tight upper bounds on the error rates of these algorithms and demonstrate their empirical performance on realistically sized datasets from the U.S. Census Bureau's Survey of Income and Program Participation