Penalty Shootouts: Is the Team That Kicks First More Likely to Win? Penalty kicks are already proving critical to big wins at this year's World Cup. But the advantage in penalty kicks has more to do with psychological effects than who kicks first. A penalty kick during the Netherlands' round of 32 match against Morocco. In a World Cup, some of the most important matches are decided by a penalty shootout. When that moment comes, the captains want to win the coin toss to decide the order of the kicks.

Who will control Africa's AI infrastructure, and at what cost? In April, African Union ministers gathered in Tangier, Morocco, to discuss artificial intelligence at a moment when governments across the continent are racing to develop AI strategies, attract investment and expand digital infrastructure. Beneath the enthusiasm, however, sits a more fundamental question. As foreign technology companies invest in data centres, cloud services and AI systems across Africa, how much control will African countries ultimately have over the infrastructure on which those technologies depend? The debate reflects a broader shift in how policymakers are thinking about AI.

We propose a Koopman-enhanced physics-informed neural network (K--PINN) framework for parameter inference and forecasting in nonlinear epidemic models. This method combines Koopman operator theory and physics-informed learning. It maps epidemic states into a latent observable space where the dynamics evolve approximately linearly while satisfying the governing epidemic equations through automatic differentiation. This integration improves interpretability, parameter identifiability, and long-term predictive stability. We apply the proposed framework to a normalized SEIRSD epidemic model and evaluate it using synthetic monkeypox (Mpox) data and real-world datasets from Germany, Morocco, and Sweden for the SARS-CoV-2 virus. Synthetic trajectories are generated using a structure-preserving, nonstandard finite difference scheme to ensure reliable training data. Numerical results demonstrate that K--PINN achieves more accurate parameter estimation, trajectory reconstruction, and long-term forecasting than classical PINNs and Koopman-EDMD approaches. These results suggest that K--PINN is an effective machine learning framework for epidemic modeling that can be extended to more complex systems.

Pat McAfee wages war on Omaha's famous Jell-o shot bar after crew gets cold reception at College World Series NASCAR legend Tony Stewart calls mourning fans'a--holes' in tone-deaf rant about Kyle Busch Brewers' Jacob Misiorowski breaks brains and radar guns with hardest pitch ever by a starting pitcher US fans were out in full force ahead of the USMNT's first match of the 2026 FIFA World Cup MLB announces drive-in theater screenings of'The Sandlot' with live games and fireworks for July 4th California Democratic Party under fire for'you're not allowed to watch' World Cup post Victor Wembanyama isn't good or mature enough to be the face of the NBA -- at least not yet Trump praised for having'lots of energy' ahead of 80th birthday Trump calls Maine Democratic Senate candidate Graham Platner a'thug' Charter Space founder responds to critics' worries about SpaceX impact on market Rep. Byron Donalds shares his faith redemption story amid Florida gubernatorial run Iran's foreign minister says peace with US'has never been closer' GOP lawmaker says it's'really important' that US continues cartel crackdown Spencer Pratt's use of AI to boost campaign sparks debate FBI arrests first suspect on'most wanted fraudsters' list Brazil favored at -145 with the over at 2.5 +115, while Japan's tactical play could neutralize Haaland INSTANT REACTION FIFA World Cup Now reacts to USA's 4-1 dominant win over Paraguay Melissa Ortiz, Peter Crouch, Sacha Kljestan, Bob Bradley, Stu Holden, Brad Guzan and Mo Edu react to USA's 4-1 win over Paraguay. We are all jazzed up about the World Cup, right? I mean it is in our own backyard this year and the USA Men's National Team just won their first game with a dominant 4-1 victory over Paraguay. More importantly to me, we just won 1.35 units on the game because we took the over for it. I'm headed back to the pitch today for a couple of different plays.

NASCAR legend Tony Stewart calls mourning fans'a--holes' in tone-deaf rant about Kyle Busch Brewers' Jacob Misiorowski breaks brains and radar guns with hardest pitch ever by a starting pitcher US fans were out in full force ahead of the USMNT's first match of the 2026 FIFA World Cup MLB announces drive-in theater screenings of'The Sandlot' with live games and fireworks for July 4th California Democratic Party under fire for'you're not allowed to watch' World Cup post Victor Wembanyama isn't good or mature enough to be the face of the NBA -- at least not yet Rep. Byron Donalds shares his faith redemption story amid Florida gubernatorial run Iran's foreign minister says peace with US'has never been closer' GOP lawmaker says it's'really important' that US continues cartel crackdown Spencer Pratt's use of AI to boost campaign sparks debate FBI arrests first suspect on'most wanted fraudsters' list Accused Charlie Kirk killer's attorneys seek to BLOCK death penalty Kayleigh McEnany: Capitalism isn't the big evil Bernie Sanders would have you believe OutKick Sports Pat McAfee wages war on Omaha's famous Jell-o shot bar after crew gets cold reception at College World Series McAfee says the general manager was unhappy he didn't call ahead and mocked his ability to pay for shots Dan Dakich asks how ESPN's relevance has changed since adding Pat McAfee. We've got drama at the College World Series, and it has nothing to do with baseball. Pat McAfee has waged war with Rocco's -- the famous Omaha-based bar known for its Jell-O shot challenge during the 12-day tournament. And by war, I mean McAfee stuffed the GM in a locker during a heated segment on his ESPN and YouTube show Friday afternoon. It was nowhere near what I thought it was going to be like, McAfee said of the crew's experience at the bar earlier this week.

Bayesian Deep Ensembles (BDEs) represent a powerful approach for uncertainty quantification in deep learning, combining the robustness of Deep Ensembles (DEs) with flexible multi-chain MCMC. While DEs are affordable in most deep learning settings, (long) sampling of Bayesian neural networks can be prohibitively costly. Yet, adding sampling after optimizing the DEs has been shown to yield significant improvements. This leaves a critical practical question: How long should the sequential sampling process continue to yield significant improvements over the initial optimized DE baseline? To tackle this question, we propose a stopping rule based on E-values. We formulate the ensemble construction as a sequential anytime-valid hypothesis test, providing a principled way to decide whether or not to reject the null hypothesis that MCMC offers no improvement over a strong baseline, to early stop the sampling. Empirically, we study this approach for diverse settings. Our results demonstrate the efficacy of our approach and reveal that only a fraction of the full-chain budget is often required.

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as is the case with text data. Sequential Monte Carlo (SMC) methods give a natural way of representing and updating this uncertainty over time, but have prohibitive memory requirements for large-scale problems. We propose a novel SMC algorithm that decomposes clustering problems into approximately independent subproblems, allowing a more compact representation of the algorithm state. Our approach is motivated by the knowledge base construction problem, and we show that our method is able to accurately and efficiently solve clustering problems in this setting and others where traditional SMC struggles.

Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our `plug-and-play' framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.

Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.