Abstract. We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with dust FRW background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance.

The discovery of a void of size ∼200h −1 Mpc and average density contrast of ∼ − 0.1 aligned with the cold spot direction has been recently reported. It has been argued that, although the first-order integrated Sachs-Wolfe (ISW) effect of such a void on the cosmic microwave background is small, the second-order Rees-Sciama (RS) contribution exceeds this by an order of magnitude and can entirely explain the observed cold spot temperature profile. In this paper we examine this surprising claim using both an exact calculation with the spherically symmetric Lemaître-Tolman-Bondi metric, and perturbation theory about a background Friedmann-Robertson-Walker metric. We show that both approaches agree well with each other, and both show that the dominant temperature contribution of the postulated void is an unobservable dipole anisotropy. If this dipole is subtracted, we find that the remaining temperature anisotropy is dominated by the linear ISW signal, which is orders of magnitude larger than the second-order RS effect, and that the total magnitude is too small to explain the observed cold spot profile. We calculate the density and size of a void that would be required to explain the cold spot, and show that the probability of existence of such a void is essentially zero in ΛCDM. We identify the importance of a posteriori selection effects in the identification of the cold spot, but argue that even after accounting for them, a supervoid explanation of the cold spot is always disfavored relative to a random statistical fluctuation on the last scattering surface.

Abstract. We consider a Swiss Cheese model with a random arrangement of Lemaître-Tolman-Bondi holes in ΛCDM cheese. We study two kinds of holes with radius r b = 50 h −1 Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra.In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95% limit |∆D A /D A | 10 −4 .We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1σ, whereas in the open case the probability is only 1.4%.

Objective:In medical imaging, a limited number of trained deep learning algorithms have been externally validated and released publicly. We hypothesized that a deep learning algorithm can be trained to identify and localize subarachnoid haemorrhage (SAH) on head computed tomography (CT) scans, and that the trained model performs satisfactorily when tested using external and real-world data.Methods:We used non-contrast head CT images of patients admitted Helsinki University Hospital between 2012 and 2017. We manually segmented (i.e. delineated) SAH on 90 head CT scans, and used the segmented CT scans together with 22 negative (no SAH) control CT scans in training an open-source convolutional neural network (U-Net) to identify and localize SAH. We then tested the performance of the trained algorithm by using external datasets (137 SAH and 1242 control cases) collected in two foreign countries, and also by creating a dataset of consecutive emergency head CT scans (8 SAH and 511 control cases) performed during on call hours in 5 different domestic hospitals in September 2021. We assessed the algorithm’s capability to identify SAH by calculating patient- and slice-level performance metrics, such as sensitivity and specificity.Results:In the external validation set of 1379 cases, the algorithm identified 136 out of 137 SAH cases correctly (sensitivity 99.3%, specificity 63.2%). Of the 49064 axial head CT slices, the algorithm identified and localized SAH in 1845 out of 2110 slices with SAH (sensitivity 87.4%, specificity 95.3%). Of 519 consecutive emergency head CT scans imaged in September 2021, the algorithm identified all 8 SAH cases correctly (sensitivity 100.0%, specificity 75.3%). The slice-level (27167 axial slices in total) sensitivity and specificity were 87.3% and 98.8%, as the algorithm identified and localized SAH in 58 out of 77 slices with SAH. The performance of the algorithm can be tested on through a webservice.Conclusions:We show that the shared algorithm identifies SAH cases with a high sensitivity, and that the slice-level specificity is high. In addition to openly sharing a high-performing deep learning algorithm, our work presents infrequently used approaches in designing, training, testing and reporting deep learning algorithms developed for medical imaging diagnostics.Classification of Evidence:This study provides Class III evidence a deep learning algorithm correctly identifies the presence of subarachnoid hemorrhage on CT scan.