Search

The Wright-Fisher (W-F) diffusion model serves as a foundational framework for interpreting population evolution through allele frequency dynamics over time. Despite the known transition probability between consecutive generations, an exact analytical expression for the transition density at arbitrary time intervals remains elusive. Commonly utilized distributions such as Gaussian or Beta inadequately address the fixation issue at extreme allele frequencies (0 or 1), particularly for short periods. In this study, we introduce two alternative parametric functions, namely the Asymptotic Expansion (AE) and the Gaussian approximation (GaussA), derived through probabilistic methodologies, aiming to better approximate this density. The AE function provides a suitable density for allele frequency distributions, encompassing extreme values within the interval [0,1]. Additionally, we outline the range of validity for the GaussA approximation. While our primary focus is on W-F diffusion, we demonstrate how our findings extend to other diffusion models featuring singularities. Through simulations of allele frequencies under a W-F process and employing a recently developed adaptive density estimation method, we conduct a comparative analysis to assess the fit of the proposed densities against the Beta and Gaussian distributions., Comment: 29 pages, 4 figures

Industrial cyber-physical systems require complex distributed software to orchestrate many heterogeneous mechatronic components and control multiple physical processes. Industrial automation software is typically developed in a model-driven fashion where abstractions of physical processes called plant models are co-developed and iteratively refined along with the control code. Testing such multi-dimensional systems is extremely difficult because often models might not be accurate, do not correspond accurately with subsequent refinements, and the software must eventually be tested on the real plant, especially in safety-critical systems like nuclear plants. This paper proposes a framework wherein high-level functional requirements are used to automatically generate test cases for designs at all abstraction levels in the model-driven engineering process. Requirements are initially specified in natural language and then analyzed and specified using a formalized ontology. The requirements ontology is then refined along with controller and plant models during design and development stages such that test cases can be generated automatically at any stage. A representative industrial water process system case study illustrates the strengths of the proposed formalism. The requirements meta-model proposed by the CESAR European project is used for requirements engineering while IEC 61131-3 and model-driven concepts are used in the design and development phases. A tool resulting from the proposed framework called REBATE (Requirements Based Automatic Testing Engine) is used to generate and execute test cases for increasingly concrete controller and plant models., Comment: Conference paper, 5 pages, 5 figures

Phase imaging in electron microscopy is sensitive to the local potential, including charge redistribution from bonding. We demonstrate that electron ptychography provides the necessary sensitivity to detect this subtle effect by directly imaging the charge redistribution in single layer boron nitride. Residual aberrations can be measured and corrected post-collection, and simultaneous atomic number contrast imaging provides unambiguous sub-lattice identification. Density functional theory calculations confirm the detection of charge redistribution.

We present universal features of the topological invariant of p-wave superconducting wires after the inclusion of spatial inhomogeneities. Three classes of distributed potentials are studied, a single- impurity, a commensurate and an incommensurate model using periodic site modulations. An analytical polynomial description is achieved by splitting the topological invariant into two parts, one dependent on the chemical potential and the other not. For the homogeneous case, an elliptical region is found where the topological invariant oscillates. The zeros of these oscillations occur at points where the fermion parity switches for finite wires. The increase of these oscillations with the inhomogeneity strength leads to new non-topological phases. We characterize these new phases according to each class of spatial distributions. Such phases could also be observed in the XY model.