We consider the problem of obtaining effective representations for the solutions of linear, vector-valued stochastic differential equations (SDEs) driven by non-Gaussian pure-jump Lévy processes, and we show how such representations lead to efficient simulation methods. The processes considered constitute a broad class of models that find application across the physical and biological sciences, mathematics, finance, and engineering. Motivated by important relevant problems in statistical inference, we derive new, generalised shot-noise simulation methods whenever a normal variance-mean (NVM) mixture representation exists for the driving Lévy process, including the generalised hyperbolic, normal-gamma, and normal tempered stable cases. Simple, explicit conditions are identified for the convergence of the residual of a truncated shot-noise representation to a Brownian motion in the case of the pure Lévy process, and to a Brownian-driven SDE in the case of the Lévy-driven SDE. These results provide Gaussian approximations to the small jumps of the process under the NVM representation. The resulting representations are of particular importance in state inference and parameter estimation for Lévy-driven SDE models, since the resulting conditionally Gaussian structures can be readily incorporated into latent variable inference methods such as Markov chain Monte Carlo, expectation-maximisation, and sequential Monte Carlo.

This paper presents a set of theoretical models that links a two-phase sequence of cooperative political integration and conflict to explore the reciprocal relationship between war and state formation. It compares equilibria rates of state formation and conflict using a Monte Carlo that generates comparative statics by altering the systemic distribution of ideology, population, tax rates, and war costs across polities. This approach supports three core findings. First, war-induced political integration is at least 2.5 times as likely to occur as integration to realize economic gains. Second, we identify mechanisms linking endogenous organizations to the likelihood of conflict in the system. For example, a greater domestic willingness to support public goods production facilitates the creation of buffer states that reduce the likelihood of a unique class of trilateral wars. These results suggest that the development of the modern administrative state has helped to foster peace. Third, we explore how modelling assumptions setting the number of actors in a strategic context can shape conclusions about war and state formation. We find that dyadic modelling restrictions tend to underestimate the likelihood of cooperative political integration and overestimate the likelihood of war relative to a triadic modelling context.

We report a combined experimental and theoretical study of uranyl complexes that form on the interlayer siloxane surfaces of montmorillonite. We also consider the effect of isomorphic substitution on surface complexation since our montmorillonite sample contains charge sites in both the octahedral and tetrahedral sheets. Results are given for the two-layer hydrate with a layer spacing of 14.58 Å. Polarized-dependent X-ray absorption fine structure spectra are nearly invariant with the incident angle, indicating that the uranyl ions are oriented neither perpendicular nor parallel to the basal plane of montmorillonite. The equilibrated geometry from Monte Carlo simulations suggests that uranyl ions form outer-sphere surface complexes with the [O=U=O]2+ axis tilted at an angle of ~45° to the surface normal.

We performed Monte Carlo and molecular dynamics simulations to investigate the interlayer structure of a uranyl-substituted smectite clay. Our clay model is a dioctahedral montmorillonite with negative charge sites in the octahedral sheet only. We simulated a wide range of interlayer water content (0 mg H2O/g clay — 260 mg H2O/g clay), but we were particularly interested in the two-layer hydrate that has been the focus of recent X-ray absorption experiments. Our simulation results for the two-layer hydrate of uranyl-montmorillonite yield a water content of 160 mg H2O/g clay and a layer spacing of 14.66 Å. Except at extremely low water content, uranyl cations are oriented nearly parallel to the surface normal in an outer-sphere complex. The first coordination shell consists of five water molecules with an average U-O distance of 2.45 Å, in good agreement with experimental data. At low water content, the cations can assume a perpendicular orientation to include surface oxygen atoms in the first coordination shell. Our molecular dynamics results show that ${\text{UO}}_2{\left({\text{H}}_2\text{O}\right)}_5^{2+}$ complexes translate within the clay pore through a jump diffusion process, and that first-shell water molecules are exchangeable and interchangeable.

This work presents Atomistic Topology Operations in MATLAB (atom), an open source library of modular MATLAB routines which comprise a general and flexible framework for manipulation of atomistic systems. The purpose of the atom library is simply to facilitate common operations performed for construction, manipulation, or structural analysis. Due to the data structure used, atoms and molecules can be operated upon based on different chemical names or attributes, such as atom- or molecule-ID, name, residue name, charge, positions, etc. Furthermore, the Bond Valence Method and a neighbor-distance analysis can be performed to assign many chemical properties of inorganic molecules. Apart from reading and writing common coordinate files (.pdb, .xyz, .gro, .cif) and trajectories (.dcd, .trr, .xtc; binary formats are parsed via third-party packages), the atom library can also be used to generate topology files with bonding and angle information taking the periodic boundary conditions into account, and supports basic Gromacs, NAMD, LAMMPS, and RASPA2 topology file formats. Focusing on clay-mineral systems, the library supports CLAYFF (Cygan, 2004) but can also generate topology files for the INTERFACE forcefield (Heinz, 2005, 2013) for Gromacs and NAMD.

A detailed analysis of management and performance fees for asset managers and investment funds is undertaken. While fund fees are considered as a cost of capital for investors, the structuring of such fee mechanisms in a fund can also influence a fund manager’s decisions and investment strategy, thereby also influencing the investment performance of the investors funds. The study undertaken will allow for an assessment of the effect of fee structures and the potential for asymmetric incentives to arise that may promote adverse risk-taking behaviours by the fund manager, to the detriment of the investor or retiree who places a portion of their retirement savings into such a managed fund with such fee structures. As such, understanding the mechanism of fee charging as well as pricing the fees correctly is vital. An exploration of the application of actuarial distortion pricing methods for complete and incomplete market valuation is performed on a variety of path-dependent option-like performance fee structures for various funds in the European and American markets. Furthermore, several scenario analysis and sensitivity studies are undertaken. The class of Net Asset Value models adopted are Lévy processes, and the pricing is performed via Monte Carlo techniques.

The study provides comparative risk analyses of Australia’s three Victorian dairy regions. Historical data were used to identify business risk and financial viability. Multivariate distributions were fitted to the historical price, production, and input costs using copula models, capturing non-linear dependence among the variables. Monte Carlo simulation methods were then used to generate cash flows for a decade. Factors that influenced profitability the most were identified using sensitivity analysis. The dairies in the Northern region have faced water reductions, whereas those of Gippsland and South West have more positive indicators. Our analysis summarizes long-term risks and net farm profits by utilizing survey data in a probabilistic manner.

A common tool in the practice of Markov chain Monte Carlo (MCMC) is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or is intractable. A limited set of quantitative tools exists to assess the relative accuracy and efficiency of such approximations. We derive a set of tools for such analysis based on the Hilbert space generated by the stationary distribution we intend to sample, $L_2(\pi)$. Our results apply to approximations of reversible chains which are geometrically ergodic, as is typically the case for applications to MCMC. The focus of our work is on determining whether the approximating kernel will preserve the geometric ergodicity of the exact chain, and whether the approximating stationary distribution will be close to the original stationary distribution. For reversible chains, our results extend the results of Johndrow et al. (2015) from the uniformly ergodic case to the geometrically ergodic case, under some additional regularity conditions. We then apply our results to a number of approximate MCMC algorithms.