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Introduction: Generative Adversarial Networks (GANs) are increasingly used to generate synthetic medical images, addressing the critical shortage of annotated data for training Artificial Intelligence (AI) systems. This study introduces a novel memory-efficient GAN architecture, incorporating Conditional Random Fields (CRFs) to generate high-resolution 3D medical images and evaluates its performance against the state-of-the-art hierarchical (HA)-GAN model. Materials and Methods: The CRF-GAN was trained using the open-source lung CT LUNA16 dataset. The architecture was compared to HA-GAN through a quantitative evaluation, using Frechet Inception Distance (FID) and Maximum Mean Discrepancy (MMD) metrics, and a qualitative evaluation, through a two-alternative forced choice (2AFC) test completed by a pool of 12 resident radiologists, in order to assess the realism of the generated images. Results: CRF-GAN outperformed HA-GAN with lower FID (0.047 vs. 0.061) and MMD (0.084 vs. 0.086) scores, indicating better image fidelity. The 2AFC test showed a significant preference for images generated by CRF-Gan over those generated by HA-GAN with a p-value of 1.93e-05. Additionally, CRF-GAN demonstrated 9.34% lower memory usage at 256 resolution and achieved up to 14.6% faster training speeds, offering substantial computational savings. Discussion: CRF-GAN model successfully generates high-resolution 3D medical images with non-inferior quality to conventional models, while being more memory-efficient and faster. Computational power and time saved can be used to improve the spatial resolution and anatomical accuracy of generated images, which is still a critical factor limiting their direct clinical applicability.

We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest compactness conditions that can be derived are already enough to obtain the convergence of the regularized functionals. This approach allows us to characterize the variational limit of the regularization even when it does not converge to the original problem. The results apply also to problems with more than two marginals.

We study barycenters of $N$ probability measures on $\mathbb{R}^d$ with respect to the $p$-Wasserstein metric ($1

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects $\infty$-cyclically monotone plans at the limit. We also present some numerical illustrations performed with Sinkhorn's algorithm.

Let $\Omega\subset\mathbb{R}^{d}$ be an open set. Given a boundary datum $g$ on $\partial\Omega$ and a function $K:\bar {\Omega} \to\mathcal{K}$, the family of all compact convex subsets of $\mathbb{R}^{d}$, we prove the existence of functions $u:\Omega\to\mathbb{R}$ such that $u=g$ on $\partial\Omega$ and $\nabla u(x)\in K(x)$ a.e. and we investigate the regularity of such solutions on the set $\mathcal{U} \subset \bar{\Omega}$ of points at which they all coincide.

An epidemiological compartmental model was used to simulate social distancing strategies to contain the COVID-19 pandemic and prevent a second wave in Sao Paulo, Brazil. Optimization using genetic algorithm was used to determine the optimal solutions. Our results suggest the best-case strategy for Sao Paulo is to maintain or increase the current magnitude of social distancing for at least 60 more days and increase the current levels of personal protection behaviors by a minimum of 10% (e.g., wearing facemasks, proper hand hygiene and avoid agglomeration). Followed by a long-term oscillatory level of social distancing with a stepping-down approach every 80 days over a period of two years with continued protective behavior., Comment: 24 pages, 4 figures, 1 table

We discover a new minimality property of the absolute minimisers of supremal functionals (also known as $L^\infty$ Calculus of Variations problems).

The COVID-19 pandemic has caused severe public health consequences in the United States. In this study, we use a hierarchical Bayesian model to estimate the age-specific COVID-19 attributable deaths over time in the United States. The model is specified by a novel non-parametric spatial approach, a low-rank Gaussian Process (GP) projected by regularised B-splines. We show that this projection defines a new GP with attractive smoothness and computational efficiency properties, derive its kernel function, and discuss the penalty terms induced by the projected GP. Simulation analyses and benchmark results show that the spatial approach performs better than standard B-splines and Bayesian P-splines and equivalently well as a standard GP, for considerably lower runtimes. The B-splines projected GP priors that we develop are likely an appealing addition to the arsenal of Bayesian regularising priors. We apply the model to weekly, age-stratified COVID-19 attributable deaths reported by the US Centers for Disease Control, which are subject to censoring and reporting biases. Using the B-splines projected GP, we can estimate longitudinal trends in COVID-19 associated deaths across the US by 1-year age bands. These estimates are instrumental to calculate age-specific mortality rates, describe variation in age-specific deaths across the US, and for fitting epidemic models. Here, we couple the model with age-specific vaccination rates to show that lower vaccination rates in younger adults aged 18-64 are associated with significantly stronger resurgences in COVID-19 deaths, especially in Florida and Texas. These results underscore the critical importance of medically able individuals of all ages to be vaccinated against COVID-19 in order to limit fatal outcomes.

We consider the $L^\infty$-optimal mass transportation problem \[ \min_{\Pi(\mu, \nu)} \gamma-\mathrm{ess\,sup\,} c(x,y), \] for a new class of costs $c(x,y)$ for which we introduce a tentative notion of twist condition. In particular we study the conditions under which the infinitely-motonone minimizers are induced by a transportation map. We also state a uniqueness result for infinitely cyclically monotone Monge minimizers that corresponds to this class of cost functions. We compare the results to previous works., Comment: 21 pages, 1 figure

Background: After a decade of a treatment as prevention (TasP) strategy based on progressive HIV testing scale-up and earlier treatment, a reduction in the estimated number of new infections in men-who-have-sex-with-men (MSM) in England had yet to be identified by 2010. To achieve internationally agreed targets for HIV control and elimination, test-and-treat prevention efforts have been dramatically intensified over the period 2010-2015, and, from 2016, further strengthened by pre-exposure prophylaxis (PrEP). Methods: Application of a novel age-stratified back-calculation approach to data on new HIV diagnoses and CD4 count-at-diagnosis, enabled age-specific estimation of HIV incidence, undiagnosed infections and mean time-to-diagnosis across both the 2010-2015 and 2016-2018 periods. Estimated incidence trends were then extrapolated, to quantify the likelihood of achieving HIV elimination by 2030. Findings: A fall in HIV incidence in MSM is estimated to have started in 2012/3, eighteen months before the observed fall in new diagnoses. A steep decrease from 2,770 annual infections (95% credible interval 2.490-3,040) in 2013 to 1,740 (1,500-2,010) in 2015 is estimated, followed by steady decline from 2016, reaching 854 (441-1,540) infections in 2018. A decline is consistently estimated in all age groups, with a fall particularly marked in the 24-35 age group, and slowest in the 45+ group. Comparable declines are estimated in the number of undiagnosed infections. Interpretation: The peak and subsequent sharp decline in HIV incidence occurred prior to the phase-in of PrEP. Definining elimination as a public health threat to be < 50 new infections (1.1 infections per 10,000 at risk), 40% of incidence projections hit this threshold by 2030. In practice, targeted policies will be required, particularly among the 45+y where STIs are increasing most rapidly., Comment: 20 pages, 5 figures

This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of Poisson-Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for Poisson-Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O'Brien's argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations., Comment: 46 pages

This document consists of a six-panel promotional brochure and a 15-page program description, both detailing the Developing a Partnership (DAP) in Early Childhood Education Program. This Los Angeles County, California, preschool/primary school training effort aims to enhance teaching and parenting skills through early childhood education. It also provides a basis for a career path for instructional assistants, associate teachers, and teachers in preschool and Head Start classrooms. The program is comprised of 12 Early Childhood Education accredited units, job-related training, support services, and job placement. Included in the presentation are descriptions of agency, parent, and educator participation criteria. The agencies participating in the program are listed, with contact information. A survey of 41 program graduates is also described. Sixty-six percent responded. Findings showed about two-thirds of the surveyed graduates had been employed in early childhood education since completing the program by non-profit delegate agencies, public delegate agencies, or private preschools. Five were employed as teachers, eight as assistant teachers, and three as instructional assistants. Over half the respondents had enrolled in some type of education program since completing their training, either a community college, 4-year college, or adult education classes. Almost all the respondents indicated that the program increased their confidence in their abilities, 90 percent stated that they had improved their parenting skills, 88 percent believed they could be successful in school, and 83 percent felt they got along better with their own children. (KB)