A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent

We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation's solution (and, in particular, of its equilibrium) in terms of an ancestral process called the killed ancestral selection graph. This representation allows one to understand the bifurcations related to the error threshold phenomenon from a genealogical point of view. Next, we characterise the ancestral type distribution by means of the pruned lookdown ancestral selection graph and study its properties at equilibrium. We also provide an alternative characterisation in terms of a piecewise-deterministic Markov process. Throughout, emphasis is on the underlying dualities as well as on explicit results.Comment: J. Math. Biol., in pres

Lines of descent in a Moran model with frequency-dependent selection and mutation

We consider the two-type Moran model with frequency-dependent selection and two-way mutation, where selection follows either the nonlinear dominance or the fittest-type-wins scheme, which will turn out as two sides of the same coin. The ancestral selection graph (ASG) of the fittest-type-wins model contains multiple branching events in addition to the binary branching and coalescence events of the classical ASG. We establish both the \emph{killed ASG} and the \emph{pruned lookdown ASG} in this setting by using the information contained in the mutation events to reduce the ASG to those parts that are informative with respect to the types of an individual from the present population, or the type of the ancestor of such an individual, respectively. The killed ASG and the pruned lookdown ASG are in factorial moment duality with the Moran model and a relative thereof, respectively

How Object Information Improves Skeleton-based Human Action Recognition in Assembly Tasks

As the use of collaborative robots (cobots) in industrial manufacturing continues to grow, human action recognition for effective human-robot collaboration becomes increasingly important. This ability is crucial for cobots to act autonomously and assist in assembly tasks. Recently, skeleton-based approaches are often used as they tend to generalize better to different people and environments. However, when processing skeletons alone, information about the objects a human interacts with is lost. Therefore, we present a novel approach of integrating object information into skeleton-based action recognition. We enhance two state-of-the-art methods by treating object centers as further skeleton joints. Our experiments on the assembly dataset IKEA ASM show that our approach improves the performance of these state-of-the-art methods to a large extent when combining skeleton joints with objects predicted by a state-of-the-art instance segmentation model. Our research sheds light on the benefits of combining skeleton joints with object information for human action recognition in assembly tasks. We analyze the effect of the object detector on the combination for action classification and discuss the important factors that must be taken into account.Comment: IEEE International Joint Conference on Neural Networks (IJCNN) 202

Lines of descent in the deterministic mutation–selection model with pairwise interaction

Baake E, Cordero F, Hummel S. Lines of descent in the deterministic mutation–selection model with pairwise interaction. Annals of Applied Probability. 2022;32(4):2400-2447.We consider the mutation-selection differential equation with pairwise interaction (or, equivalently, the diploid mutation-selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph. The formal relation to the forward model is given via duality. To make the tree tractable, we prune branches upon mutations, thus reducing it to its informative parts. The hierarchies inherent in the tree are encoded systematically via tripod trees with weighted leaves; this leads to the stratified ancestral selection graph. The latter also satisfies a duality relation with the mutation-selection equation. Each of the dualities provides a stochastic representation of the solution of the differential equation. This allows us to connect the equilibria and their bifurcations to the long-term behaviour of the ancestral process. Furthermore, with the help of the stratified ancestral selection graph, we obtain explicit results about the ancestral type distribution in the case of unidirectional mutation

Partitioning, duality, and linkage disequilibria in the Moran model with recombination

Esser M, Probst S, Baake E. Partitioning, duality, and linkage disequilibria in the Moran model with recombination. JOURNAL OF MATHEMATICAL BIOLOGY. 2016;73(1):161-197.The multilocus Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. We investigate a marginal ancestral recombination process, where each site is sampled only in one individual and we do not make any scaling assumptions in the first place. Following the ancestry of these loci backward in time yields a partition-valued Markov process, which experiences splitting and coalescence. In the diffusion limit, this process turns into a marginalised version of the multilocus ancestral recombination graph. With the help of an inclusion-exclusion principle and so-called recombinators we show that the type distribution corresponding to a given partition may be represented in a systematic way by a sampling function. The same is true of correlation functions (known as linkage disequilibria in genetics) of all orders. We prove that the partitioning process (backward in time) is dual to the Moran population process (forward in time), where the sampling function plays the role of the duality function. This sheds new light on the work of Bobrowski et al. (J Math Biol 61:455-473, 2010). The result also leads to a closed system of ordinary differential equations for the expectations of the sampling functions, which can be translated into expected type distributions and expected linkage disequilibria

Synthesis and Characterization of (Na0.5K0.5)NbO3 (NKN) Thin Films Formed by a Diol-based Sol-gel Process

Lead-free (Na0.5K0.5)NbO3 (NKN) thin films were fabricated by spin coating on Pt/Ti/SiO2/Si substrates by a diol-based sol-gel process. Na-acetate, K-acetate, Nb-pentaethoxide and 1,3 propanediol were used to prepare the NKN precursor solution. Thermal analysis showed two characteristic temperatures of 360 and 600 °C. Based on these temperatures, a heat treatment program with pyrolysis at 360 °C and calcination at 600 °C after every layer was used. To avoid inhomogeneities and secondary phases, an excess of sodium and potassium was necessary. To evaluate the proper excess amount of sodium and potassium secondary ion mass spectrometry (SIMS) lateral element maps and X-ray diffraction (XRD) patterns were recorded. An excess amount of 20% led to homogeneous distribution of the elements and to single phase perovskite NKN films with random crystal orientation. Scanning electron microscopy (SEM) images showed a pore free surface with 100 nm grains. The leakage current measurements showed a current of 1x10-3 A/cm2 at 150 kV/cm

Effect of Different Calcination Temperatures and Post Annealing on the Properties of Acetic Acid Based Sol-Gel (Na0.5K0.5)NbO3 (NKN) Thin Films

(Na0.5K0.5)NbO3 (NKN) lead free thin films were synthesized by means of an acetic acid based sol-gel process on Pt/Ti/SiO2/Si substrates. Na-acetate, K-acetate and Nb-pentaethoxide were used as metal precursors and acetic acid as the solvent. The effect of different calcination temperatures on the properties of the NKN films was investigated by X-ray diffraction, scanning electron microscopy, leakage current and hysteresis measurements. Low calcination temperatures led to low currents at high electric fields whereas high calcination temperatures led to low currents at low electric fields. Based on these findings calcination at low temperature was combined with a post annealing treatment. Low leakage currents of 4×10−4 A/cm² at 150 kV/cm and 2Pr and 2Ec values of 28 μC/cm² and 150 kV/cm, respectively, could be obtained. All films were single phase NKN with random crystal orientations and no crack or pore formation was visible on the surface