A Mid-infrared Study of Directly Imaged Planetary-mass Companions Using Archival Spitzer/IRAC Images

The atmospheres and accretion disks of planetary-mass and substellar companions provide an unprecedented look into planet and moon formation processes, most notably the frequency and lifetime of circumplanetary disks. In our ongoing effort to leverage the extraordinary sensitivity of the Spitzer/Infrared Array Camera (IRAC) at 3.6, 4.5, 5.8, and 8.0 μm to study wide planetary-mass and substellar companions near the diffraction limit, we present point-spread function fitting photometry of archival Spitzer/IRAC images for nine stars (G0 to M4+M7) in nearby star-forming regions or stellar associations that host companions at separations of ρ = 1.″17–12.″33. We detect all system primaries in all four IRAC channels and recover eight low-mass companions in at least one IRAC channel for our sample, five of which have not been resolved previously in IRAC images. We measure nonphotospheric [3.6]–[8.0] colors for four of the system companions (DH Tau B, 2M0441 B, SR 12 c, and ROXs 42B b), confirming or discovering the presence of circumstellar or circum(sub)stellar disks. We detect fluxes consistent with photospheric emission for four other companions (AB Pic b, CHXR 73 b, 1RXS J1609 b, and HD 203030 b) that are unlikely to host disks. Combined with past detections of accretion or disk indicators, we determine the global disk frequency of young (<15 Myr) wide companions with masses near the deuterium-burning limit to be 56% ± 12%.

A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many other fields. To find an optimal PWL function, the positioning of the breakpoints connecting adjacent linear segments must not be constrained and should be allowed to be placed freely. Although the univariate PWL fitting problem has often been approached from a global optimisation perspective, recently, two mixed-integer linear programming approaches have been presented that solve for optimal PWL functions. In this paper, we compare the two approaches: the first was presented by Rebennack and Krasko [Rebennack S, Krasko V (2020) Piecewise linear function fitting via mixed-integer linear programming. INFORMS J. Comput. 32(2):507–530] and the second by Kong and Maravelias [Kong L, Maravelias CT (2020) On the derivation of continuous piecewise linear approximating functions. INFORMS J. Comput. 32(3):531–546]. Both formulations are similar in that they use binary variables and logical implications modelled by big-[Formula: see text] constructs to ensure the continuity of the PWL function, yet the former model uses fewer binary variables. We present experimental results comparing the time taken to find optimal PWL functions with differing numbers of breakpoints across 10 data sets for three different objective functions. Although neither of the two formulations is superior on all data sets, the presented computational results suggest that the formulation presented by Rebennack and Krasko is faster. This might be explained by the fact that it contains fewer complicating binary variables and sparser constraints. Summary of Contribution: This paper presents a comparison of the mixed-integer linear programming models presented in two recent studies published in the INFORMS Journal on Computing. Because of the similarity of the formulations of the two models, it is not clear which one is preferable. We present a detailed comparison of the two formulations, including a series of comparative experimental results across 10 data sets that appeared across both papers. We hope that our results will allow readers to take an objective view as to which implementation they should use.

Temporal response modelling uncovers electrophysiological correlates of trial-by-trial error-driven learning

Humans learn from statistical regularities in the environment. We tested if prediction and prediction error may play a role in such learning in the brain. We used Error-Driven Learning (EDL) to simulate participants’ trial-by-trial learning during exposure to a bimodal distribution of non-native lexical tones. We simulated incremental trial-by-trial learning to get estimates of the degree of expectation of upcoming stimuli over the course of the experiment. The expectation estimates were combined with Temporal Response Function fitting to generate a prediction of the trial-by-trial ERP waveform. EDL simulations captured the data significantly better than chance and better than models based on either stimulus characteristics or statistical distributions. The results provide tentative evidence that trial-by-trial learning as measured in neural activity is error-driven.

A simple method to describe the COVID-19 trajectory and dynamics in any country based on Johnson cumulative density function fitting

A simple method is utilised to study and compare COVID-19 infection dynamics between countries based on curve fitting to publicly shared data of confirmed COVID-19 infections. The method was tested using data from 80 countries from 6 continents. We found that Johnson cumulative density functions (CDFs) were extremely well fitted to the data (R2 > 0.99) and that Johnson CDFs were much better fitted to the tails of the data than either the commonly used normal or lognormal CDFs. Fitted Johnson CDFs can be used to obtain basic parameters of the infection wave, such as the percentage of the population infected during an infection wave, the days of the start, peak and end of the infection wave, and the duration of the wave’s increase and decrease. These parameters can be easily interpreted biologically and used both for describing infection wave dynamics and in further statistical analysis. The usefulness of the parameters obtained was analysed with respect to the relation between the gross domestic product (GDP) per capita, the population density, the percentage of the population infected during an infection wave, the starting day and the duration of the infection wave in the 80 countries. We found that all the above parameters were significantly associated with GDP per capita, but only the percentage of the population infected was significantly associated with population density. If used with caution, this method has a limited ability to predict the future trajectory and parameters of an ongoing infection wave.

Total ozone column from Ozone Mapping and Profiler Suite Nadir Mapper (OMPS-NM) measurements using the broadband weighting function fitting approach (WFFA)

A scientific total ozone column product from Ozone Mapping and Profiler Suite Nadir Mapper (OMPS-NM) observations and the retrieval algorithm are presented. The retrieval employs the weighting function fitting approach (WFFA), a modification of the weighting function differential optical absorption spectroscopy (WFDOAS) technique. The total ozone columns retrieved with WFFA are in very good agreement with other datasets. A mean difference of 0.3 % with respect to ground-based Brewer and Dobson measurements is observed. Seasonal and latitudinal variations are well represented and in agreement with other satellite datasets. The comparison of our product with the operational product of OMPS-NM indicates a mean bias of around zero. The comparison with the Tropospheric Monitoring Instrument products (S5P/TROPOMI) OFFL and WFDOAS shows a persistent negative bias of about −0.6 % for OFFL and −2.5 % for WFDOAS. Larger differences are only observed in the polar regions. This data product is intended to be used for trend analysis and the retrieval of tropospheric ozone combined with the OMPS limb profiler data.

Combined Coulomb and Viscous Damping Estimation Using Topological Signal Processing

In this work we develop a novel time-domain approach for the simultaneous estimation of the damping parameters for a single degree of freedom oscillator with both viscous and coulomb damping. Our approach leverages zero-dimensional sublevel set persistence — a tool from Topological Signal Processing (TSP) — to analyze the ring down vibration of the signal. Sublevel set persistence is used as it alleviates the need for peak selection when analyzing the time-domain of the signal and provides an alternative noise-robust method for visualizing the damping envelope. We are able to successfully estimate the damping parameters using both a direct approach and a function fitting method. We show that the direct approach is only appropriate for low levels of additive noise, but allows for a less computationally demanding estimation of the parameters. Alternatively, the function fitting method provides accurate estimates for significantly higher levels of additive noise. The results are provided through a numerically simulated example with mixed coulomb and viscous damping. We demonstrate the robustness of our method for accurately estimating both damping parameters for various levels of additive noise, a wide range of sampling frequencies, and both high and low levels of damping. This analysis includes providing suggested limitations of the method when applied to real-world signals.

General Modulation Transfer Function Fitting Equation for Human Eye with Contact Lens

In this research, a general equation was derived to represent the modulation transfer function (MTF) of the human eye with the presence of the contact lenses (CL) and during the vision with monochrome or multi-wavelength (polychromatic) light. This equation was used to fit the MTF's curves for the eye with pupil diameters (EPD) (2.5, 4, 6, and 8 mm). The fitting equation accuracy was revealed by using the standard deviation (STD). The results indicated that the image MTF is sensitive to (EPD). Moreover, eye vision degrades as (EPD) increases due to the increased spherical and chromatic aberrations. The new equation consists of two exponential terms in addition to a correction polynomial function (H) to fit the EPD effect. The results showed that H function with power two is sufficient to give a good accuracy when the EPD is less than 4 mm, while H with power five is necessary when the EPD is larger or equal to 5 mm. The equation gives a high accuracy also in the case of vision with white light for the eye with a contact lens.