SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

Disentangling mental imagery and perceptual expectation

Mental imagery and perception are thought to rely on similar neural circuits, and many recent behavioral studies have attempted to demonstrate interactions between actual physical stimulation and sensory imagery in the corresponding sensory modality. However, there has been a lack of theoretical understanding of the nature of these interactions, and both interferential and facilitatory effects have been found. Facilitatory effects appear strikingly similar to those that arise due to experimental manipulations of expectation. Using a self-motion discrimination task, we try to disentangle the effects of mental imagery from those of expectation by using a hierarchical drift diffusion model to investigate both choice data and response times. Manipulations of expectation are reasonably well understood in terms of their selective influence on parameters of the drift diffusion model, and in this study, we make the first attempt to similarly characterize the effects of mental imagery. We investigate mental imagery within the computational framework of control theory and state estimation. • Mental imagery and perception are thought to rely on similar neural circuits; however, on more theoretical grounds, imagery seems to be closely related to the output of forward models (sensory predictions). • We reanalyzed data from a study of imagined self-motion. • Bayesian modeling of response times may allow us to disentangle the effects of mental imagery on behavior from other cognitive (top-down) effects, such as expectation.

CHEOPS Performance for Exomoons: The Detectability of Exomoons by Using Optimal Decision Algorithm

Many attempts have already been made to detect exomoons around transiting exoplanets, but the first confirmed discovery is still pending. The experiences that have been gathered so far allow us to better optimize future space telescopes for this challenge already during the development phase. In this paper we focus on the forthcoming CHaraterising ExOPlanet Satellite (CHEOPS), describing an optimized decision algorithm with step-by-step evaluation, and calculating the number of required transits for an exomoon detection for various planet moon configurations that can be observable by CHEOPS. We explore the most efficient way for such an observation to minimize the cost in observing time. Our study is based on PTV observations (photocentric transit timing variation) in simulated CHEOPS data, but the recipe does not depend on the actual detection method, and it can be substituted with, e.g., the photodynamical method for later applications. Using the current state-of-the-art level simulation of CHEOPS data we analyzed transit observation sets for different star planet moon configurations and performed a bootstrap analysis to determine their detection statistics. We have found that the detection limit is around an Earth-sized moon. In the case of favorable spatial configurations, systems with at least a large moon and a Neptune-sized planet, an 80% detection chance requires at least 5-6 transit observations on average. There is also a nonzero chance in the case of smaller moons, but the detection statistics deteriorate rapidly, while the necessary transit measurements increase quickly. After the CoRoT and Kepler spacecrafts, CHEOPS will be the next dedicated space telescope that will observe exoplanetary transits and characterize systems with known Doppler-planets. Although it has a smaller aperture than Kepler (the ratio of the mirror diameters is about 1/3) and is mounted with a CCD that is similar to Kepler's, it will observe brighter stars and operate with larger sampling rate; therefore, the detection limit for an exomoon can be the same as or better, which will make CHEOPS a competitive instruments in the quest for exomoons.