maxsmooth: rapid maximally smooth function fitting with applications in Global 21-cm cosmology

ABSTRACT Maximally Smooth Functions (MSFs) are a form of constrained functions in which there are no inflection points or zero crossings in high-order derivatives. Consequently, they have applications to signal recovery in experiments where signals of interest are expected to be non-smooth features masked by larger smooth signals or foregrounds. They can also act as a powerful tool for diagnosing the presence of systematics. The constrained nature of MSFs makes fitting these functions a non-trivial task. We introduce maxsmooth, an open-source package that uses quadratic programming to rapidly fit MSFs. We demonstrate the efficiency and reliability of maxsmooth by comparison to commonly used fitting routines and show that we can reduce the fitting time by approximately two orders of magnitude. We introduce and implement with maxsmooth Partially Smooth Functions, which are useful for describing elements of non-smooth structure in foregrounds. This work has been motivated by the problem of foreground modelling in 21-cm cosmology. We discuss applications of maxsmooth to 21-cm cosmology and highlight this with examples using data from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) and the Large-aperture Experiment to Detect the Dark Ages (LEDA) experiments. We demonstrate the presence of a sinusoidal systematic in the EDGES data with a log-evidence difference of 86.19 ± 0.12 when compared to a pure foreground fit. MSFs are applied to data from LEDA for the first time in this paper and we identify the presence of sinusoidal systematics. maxsmooth is pip installable and available for download at https://github.com/htjb/maxsmooth.

Integrated jerk as an indicator of affinity for artificial agent kinematics: laptop and virtual reality experiments involving index finger motion during two-digit grasping

Uncanny valley research has shown that human likeness is an important consideration when designing artificial agents. It has separately been shown that artificial agents exhibiting human-like kinematics can elicit positive perceptual responses. However the kinematic characteristics underlying that perception have not been elucidated. This paper proposes kinematic jerk amplitude as a candidate metric for kinematic human likeness, and aims to determine whether a perceptual optimum exists over a range of jerk values. We created minimum-jerk two-digit grasp kinematics in a prosthetic hand model, then added different amplitudes of temporally smooth noise to yield a variety of animations involving different total jerk levels, ranging from maximally smooth to highly jerky. Subjects indicated their perceptual affinity for these animations by simultaneously viewing two different animations side-by-side, first using a laptop, then separately within a virtual reality (VR) environment. Results suggest that (a) subjects generally preferred smoother kinematics, (b) subjects exhibited a small preference for rougher-than minimum jerk kinematics in the laptop experiment, and that (c) the preference for rougher-than minimum-jerk kinematics was amplified in the VR experiment. These results suggest that non-maximally smooth kinematics may be perceptually optimal in robots and other artificial agents.

Smooth inversion of induction logs for conductivity models with mud filtrate invasion

A robust, efficient method of inversion of induction logging data for smooth 2-D models, appropriate to an environment in which mud filtrate invades flat‐lying layers, is described. An infinite number of solutions exist to the problem of determining a conductivity structure from a finite number of imprecise induction data. Therefore, the inverse problem is regularized such that the smoothest model is sought subject to the condition that the resulting computed log agrees with the field log to a given preset level. At each iteration, the Jacobian sensitivities are approximated using the distorted Born approximation. In most cases, the algorithm converges in 3 to 4 iterations. The resulting maximally smooth models reflect the resolution power of the induction data and are unlikely to result in overinterpretation of the data. Inversion of both synthetic and field data indicates that layer boundaries are well resolved but radial boundaries are poorly resolved by conventional induction logging data.