On exceptional groups of order p^5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p^5. For an odd prime p, we classify all pairs (G,Q) where G has order p^5 and Q is a distinguished quotient. (The case p=2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p^5 with at least one exceptional quotient tends to 1/2.Comment: 23 page

On exceptional groups of order p⁵

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p5. For an odd prime p, we classify all pairs (G, Q)where G has order p5 and Q is a distinguished quotient. (The case p = 2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p5 with at least one exceptional quotient tends to 1/2

Die Zukunft des usbekischen Reformprozesses in unsteten Zeiten: eine makroökonomische Analyse der aktuellen Herausforderungen

Seit dem Beginn der Reformen unter Präsident Schawkat Mirsijojew vor sechs Jahren hat Usbekistan beachtliche Fortschritte bei der wirtschaftlichen Entwicklung gemacht. Bisherige Erfolge der Reformen zeigen sich zum Beispiel in der Einführung eines flexiblen Wechselkurses, einer verbesserten Unternehmensführung oder einem gestärkten System der öffentlichen Fürsorge. Auch haben die Reformen zur Herausbildung relativer makroökonomischer Stabilität beigetragen, dank der Usbekistan den wirtschaftlichen Schock nach dem russischen Überfall auf die Ukraine weitgehend absorbieren konnte. Trotz der erreichten Fortschritte hat sich die Umsetzung von Reformen zuletzt verlangsamt, weshalb in Bereichen wie dem der staatlichen Unternehmen noch immer strukturelle Anpassungen ausstehen. Herausforderungen für den weiteren Reformprozess bestehen vor allem in der anhaltend hohen Inflation, dem wachsenden Investitionsbedarf, der Entwicklung eines inländischen Finanzmarktes mit robustem Privatbankensektor, der geographisch bedingten Hemmung außenwirtschaftlicher Beziehungen sowie im geplanten Umstieg auf Green Economy

Solo Duck Linear Analysis

The motion of a single duck wave energy converter in the presence of waves is described by a linear matrix equation, formulated in the frequency domain. An equation for the extracted power in spectra is derived for any linear controller. The parameters in the equation of motion, namely, the radiation impedance and wave force coefficients, are found from a model by experiment in a wave tank. Predictions for the absorbed power are compared against further measurements made in the tank when the duck's motion is governed by a simple linear controller, implemented on a digital computer

Hydrate crystal structures, radial distribution functions, and computing solubility

Solubility prediction usually refers to prediction of the intrinsic aqueous solubility, which is the concentration of an unionised molecule in a saturated aqueous solution at thermodynamic equilibrium at a given temperature. Solubility is determined by structural and energetic components emanating from solid-phase structure and packing interactions, solute–solvent interactions, and structural reorganisation in solution. An overview of the most commonly used methods for solubility prediction is given in Chapter 1. In this thesis, we investigate various approaches to solubility prediction and solvation model development, based on informatics and incorporation of empirical and experimental data. These are of a knowledge-based nature, and specifically incorporate information from the Cambridge Structural Database (CSD). A common problem for solubility prediction is the computational cost associated with accurate models. This issue is usually addressed by use of machine learning and regression models, such as the General Solubility Equation (GSE). These types of models are investigated and discussed in Chapter 3, where we evaluate the reliability of the GSE for a set of structures covering a large area of chemical space. We find that molecular descriptors relating to specific atom or functional group counts in the solute molecule almost always appear in improved regression models. In accordance with the findings of Chapter 3, in Chapter 4 we investigate whether radial distribution functions (RDFs) calculated for atoms (defined according to their immediate chemical environment) with water from organic hydrate crystal structures may give a good indication of interactions applicable to the solution phase, and justify this by comparison of our own RDFs to neutron diffraction data for water and ice. We then apply our RDFs to the theory of the Reference Interaction Site Model (RISM) in Chapter 5, and produce novel models for the calculation of Hydration Free Energies (HFEs)

Learnt representations of proteins can be used for accurate prediction of small molecule binding sites on experimentally determined and predicted protein structures

Protein-ligand binding site prediction is a useful tool for understanding the functional behaviour and potential drug-target interactions of a novel protein of interest. However, most binding site prediction methods are tested by providing crystallised ligand-bound (holo) structures as input. This testing regime is insufficient to understand the performance on novel protein targets where experimental structures are not available. An alternative option is to provide computationally predicted protein structures, but this is not commonly tested. However, due to the training data used, computationally-predicted protein structures tend to be extremely accurate, and are often biased toward a holo conformation. In this study we describe and benchmark IF-SitePred, a protein-ligand binding site prediction method which is based on the labelling of ESM-IF1 protein language model embeddings combined with point cloud annotation and clustering. We show that not only is IF-SitePred competitive with state-of-the-art methods when predicting binding sites on experimental structures, but it performs better on proxies for novel proteins where low accuracy has been simulated by molecular dynamics. Finally, IF-SitePred outperforms other methods if ensembles of predicted protein structures are generated

Probing the average distribution of water in organic hydrate crystal structures with radial distribution functions (RDFs)

The authors thank the University of St Andrews, EPSRC (grant EP/L505079/1).The abundance of crystal structures of solvated organic molecules reflects the common role of solvent in the crystallisation process. An understanding of solvation is therefore important for crystal engineering, with solvent choice often affecting polymorphism as well as influencing the crystal structure. Of particular importance is the role of water, and a number of approaches have previously been considered in the analysis of large datasets of organic hydrates. In this work we attempt to develop a method suitable for application to organic hydrate crystal structures, in order to better understand the distribution of water molecules in such systems. We present a model aimed at combining the distribution functions of multiple atom pairs from a number of crystal structures. From this, we can comment qualitatively on the average distribution of water in organic hydrates.PostprintPeer reviewe

QALE-FEM for modelling 3D overturning waves

A further development of the QALE-FEM (quasi-arbitrary Lagrangian–Eulerian finite element method) based on a fully nonlinear potential theory is presented in this paper. This development enables the QALE-FEM to deal with three-dimensional (3D) overturning waves over complex seabeds, which have not been considered since the method was devised by the authors of this paper in their previous works (J. Comput. Phys. 2006; 212:52–72; J. Numer. Meth. Engng 2009; 78:713–756). In order to tackle challenges associated with 3D overturning waves, two new numerical techniques are suggested. They are the techniques for moving the mesh and for calculating the fluid velocity near overturning jets, respectively. The developed method is validated by comparing its numerical results with experimental data and results from other numerical methods available in the literature. Good agreement is achieved. The computational efficiency of this method is also investigated for this kind of wave, which shows that the QALE-FEM can be many times faster than other methods based on the same theory. Furthermore, 3D overturning waves propagating over a non-symmetrical seabed or multiple reefs are simulated using the method. Some of these results have not been found elsewhere to the best of our knowledge

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page