We present a near-infrared (NIR) candidate star cluster catalog for the central kiloparsec of M82 based on new JWST NIRCam images. We identify star cluster candidates using the F250M filter, finding 1357 star cluster candidates with stellar masses >10⁴ M _⊙. Compared to previous optical catalogs, nearly all (87%) of the candidates we identify are new. The star cluster candidates have a median intrinsic cluster radius of ≈1 pc and stellar masses up to 10⁶ M _⊙. By comparing the color–color diagram to dust-free yggdrasil stellar population models, we estimate that the star cluster candidates have A _V ∼ 3−24 mag, corresponding to A _2.5μm ∼ 0.3−2.1 mag. There is still appreciable dust extinction toward these clusters into the NIR. We measure the stellar masses of the star cluster candidates, assuming ages of 0 and 8 Myr. The slope of the resulting cluster mass function is β = 1.9 ± 0.2, in excellent agreement with studies of star clusters in other galaxies.

We present a complete set of structural parameters for a sample of 99 intermediate-age super star cluster (SSCs) in the disc of M82, and carry out a survival analysis using the semi-analytical cluster evolution code emacss. The parameters are based on the profile-fitting analysis carried out in previous work, with the mass-related quantities derived using a mass-to-light ratio for a constant age of 100 Myr. The SSCs follow a power-law mass function with an index α = 1.5, and a lognormal size function with a typical half-light radius, Rh = 4.3 pc, which is both comparable with the values for clusters in the Magellanic Clouds, rather than in giant spirals. The majority of the SSCs follow a power-law mass−radius relation with an index of b = 0.29 ± 0.05. A dynamical analysis of M82 SSCs using emacss suggests that 23 per cent of the clusters are tidally limited, with the rest undergoing expansion at present. Forward evolution of these clusters suggests that the majority would dissolve in ∼2 Gyr. However, a group of four massive compact clusters, and another group of five SSCs at relatively large galactocentric distances, are found to survive for a Hubble time. The model-predicted mass, Rh, μV, and core radius of these surviving SSCs at 12 Gyr are comparable with the corresponding values for the sample of Galactic globular clusters.

We present the structural parameters of 99 super star clusters (SSCs) in the disc of M82. Moffat-EFF, King, and Wilson models were fitted using a χ2-minimization method to background-subtracted surface brightness profiles in the F435W (B), F555W (V), and F814W (I) bands of the Advanced Camera for Surveys (ACS) of the Hubble Space Telescope. The majority of the SSC profiles are best fitted by the Moffat-EFF profile. The scale parameter rd and the shape parameter γ in the three filters are identical within the measurement errors. The analysed sample is big enough to allow the characterization of the distributions of core radii Rc and γ. The obtained distribution of Rc follows a lognormal form, with centre and $\sigma \mathrm{ log}\big {(}\frac{R_{\rm c}}{pc}\big {)}$ being 1.73 pc and 0.25, respectively. The γ distribution is also lognormal with centre and σlog(γ) being 2.88 and 0.08, respectively. M82 is well known for the absence of current star formation in its disc, with all disc SSCs older than 50 Myr and hardly any cluster older than ∼300 Myr. The derived distributions compare very well with the distributions for intermediate-age clusters in the Large Magellanic Cloud (LMC), which is also a low-mass late-type galaxy similar to M82. On the other hand, the distributions of Rc in both these galaxies are shifted towards larger values as compared to SSCs of similar age in the giant spiral galaxy M83. M82 and LMC also span a narrower range of γ values as compared to that in M83.

We tested different optical elements placed in three different positions by applying the irradiance transport equation (ITE), obtaining the wavefront [ W ( x , y ) ] and aberration surface [ AS ( r , θ ) ]. The existing noise in the captures I as well as in the W and A S were analyzed applying several filters: first a filter based on Legendre polynomials (LP), generating the most probable points increasing the data resolution; second, a filter based on a 50 deg 2D-LP was used as a multilineal fit (multiple linear regression); and third, an ideal bandpass filter in the Fourier space after inducing a periodicity using Ronchi simulated masks with periods in x , y , x y was used to perform data scanning (similar to the four-step phase-shifting method). Signal-to-noise ratio values were obtained for each proposed filter along with the most probable image free from noise, determined from a linear combination of the original data and the applied filters.

In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs’ surface to the data in order to obtain the wavefront surface ($W(x,y)$ of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces ($\mathrm{AS}(x,y)$).

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving the inverse problem from the EEG measurements, the so-called Electroencephalographic Inverse Problem (EIP), which is ill-posed in the Hadamard sense since the problem has numerical instability. We focus on the identification of volumetric dipolar sources of the EEG by constructing and modeling a simplification to reduce the multilayer conductive medium (two layers or regions ${\Omega }_1$ and ${\Omega }_2$) to a problem of a single layer of a homogeneous medium with a null Neumann condition on the boundary. For this simplification purpose, we consider the Cauchy problem to be solved at each time. We compare the results we obtained solving the multiple layers problem with those obtained by our simplification proposal. In both cases, we solve the direct and inverse problems for two different sources, as synthetic results for dipolar sources resembling epileptic foci, and a similar case with an external stimulus (intense light, skin stimuli, sleep problems, etc). For the inverse problem, we use the Tikhonov regularization method to handle its numerical instability. Additionally, we build an algorithm to solve both models (multiple layers problem and our simplification) in time, showing optimization of the problem when considering 128 divisions in the time interval $[0,1]$ s, solving the inverse problem at each time (interval division) and comparing the recovered source with the initial one in the algorithm. We observed a significant decrease in the computation times when simplifying the numerical calculations, resulting in a decrease up to $50\%$ in the execution times, between the EIP multilayer model and our simplification proposal, to a single layer homogeneous problem of a homogeneous medium, which translates into a numerical efficiency in this type of problem.