Meghan unveils new As Ever line with Lilibet... amid claims Netflix has been left with huge $10m surplus of her unsold products amid'split' with streamer Outrageous full story of scandalous affair that's the talk of Manhattan's exclusive private schools: Family insiders reveal humiliating sex secrets... shock'confession' letter... and the furious relative who exposed it all Sinister truth about explosive resignation of Trump's top counter-terror chief Joe Kent... and his shock claim Israel is manipulating the president: MARK HALPERIN Canada's ultimate revenge on Trump over tariffs gathers pace Ugly new Nicole Kidman and Keith Urban divorce fight ERUPTS: Her friends share humiliating details of'midlife crisis'... and reveal brutal REAL reason daughter Sunday Rose'snubbed' him Kim Kardashian takes a VERY dramatic tumble in towering $80 'stripper heels' and accidentally grabs an'old lady' as she falls on her way out of Vanity Fair Oscars party USA baseball stars slammed over'disgraceful' national anthem gesture before WBC final vs Venezuela Israel says Iran's intelligence chief has been killed in overnight airstrike in latest attack on regime: Live updates Presidential hopeful JB Pritzker's bold defiant bet against black caucus pays off Supreme Court's top judge issues chilling warning as Trump targets his own appointees Heath Ledger's lookalike daughter Matilda steps out days after 17 year anniversary of late actor's Oscar win Fox News anchor issues blistering takedown of liberal media's delusional take on Iran: 'A stalemate? I ditched my realtor and used ChatGPT to sell my Florida house instead. Here's my exact prompts and steps for you to do it too Hollywood's top insider makes VERY catty observation about Kaitlan Collins Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with Mamdani forces New York beloved preschool to hike annual fee to $36,000... and parents are fuming Alix Earle stuns in white bikini in first glimpse at 2026 Sports Illustrated Swimsuit edition... after turning heads with Tom Brady and Joe Burrow Scientists reveal what a '30% chance of rain' REALLY means Are you always getting caught in the rain without an umbrella? If so, you might be reading your weather forecast app wrong. When many people see a '30% chance of rain' on their app, they think this corresponds to the heaviness of the downpour, or the area of land that will experience it.

This paper introduces a distillation framework for an ensemble of entropy-optimal Sparse Probabilistic Approximation (eSPA) models, trained exclusively on satellite-era observational and reanalysis data to predict ENSO phase up to 24 months in advance. While eSPA ensembles yield state-of-the-art forecast skill, they are harder to interpret than individual eSPA models. We show how to compress the ensemble into a compact set of "distilled" models by aggregating the structure of only those ensemble members that make correct predictions. This process yields a single, diagnostically tractable model for each forecast lead time that preserves forecast performance while also enabling diagnostics that are impractical to implement on the full ensemble. An analysis of the regime persistence of the distilled model "superclusters", as well as cross-lead clustering consistency, shows that the discretised system accurately captures the spatiotemporal dynamics of ENSO. By considering the effective dimension of the feature importance vectors, the complexity of the input space required for correct ENSO phase prediction is shown to peak when forecasts must cross the boreal spring predictability barrier. Spatial importance maps derived from the feature importance vectors are introduced to identify where predictive information resides in each field and are shown to include known physical precursors at certain lead times. Case studies of key events are also presented, showing how fields reconstructed from distilled model centroids trace the evolution from extratropical and inter-basin precursors to the mature ENSO state. Overall, the distillation framework enables a rigorous investigation of long-range ENSO predictability that complements real-time data-driven operational forecasts.

In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games (CSGs) .

In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games (CSGs) .

Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success.

In this section, we show that Cold Sampling is an approximation of the Euler method for (5). The intuition is as follows. B.2 Why is cold sampling better than naive sampling? Naive sampling does not have this property. The proof relied on applying definitions of Lipschitz functions twice.

Dynamics forecasting refers to the task of predicting the future behavior of a dynamic system, involving learning the underlying dynamics governing the system's evolution to make accurate predictions