We study phase transitions for repulsive-attractive mean-field free energies on the circle. For a $\frac{1}{n+1}$-periodic interaction whose Fourier coefficients satisfy a certain decay condition, we prove that the critical coupling strength $K_c$ coincides with the linear stability threshold $K_\#$ of the uniform distribution and that the phase transition is continuous, in the sense that the uniform distribution is the unique global minimizer at criticality. The proof is based on a sharp coercivity estimate for the free energy obtained from the constrained Lebedev--Milin inequality. We apply this result to three motivating models for which the exact value of the phase transition and its (dis)continuity in terms of the model parameters was not fully known. For the two-dimensional Doi--Onsager model $W(θ)=-|\sin(2πθ)|$, we prove that the phase transition is continuous at $K_c=K_\#=3π/4$. For the noisy transformer model $W_β(θ)=(e^{β\cos(2πθ)}-1)/β$, we identify the sharp threshold $β_*$ such that $K_c(β) = K_\#(β)$ and the phase transition is continuous for $β\leq β_*$, while $K_c(β) β_*$. We also obtain the corresponding sharp dichotomy for the noisy Hegselmann--Krause model $W_{R}(θ) = (R-2π|θ|)_{+}^2$ .

We study the sample complexity of learning an $ε$-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a worst-case SSP instance with $S$ states, $A$ actions, minimum cost $c_{\min}$, and maximum expected cost of the optimal policy over all states $B_{\star}$, where any algorithm requires at least $Ω(SAB_{\star}^3/(c_{\min}ε^2))$ samples to return an $ε$-optimal policy with high probability. Surprisingly, this implies that whenever $c_{\min} = 0$ an SSP problem may not be learnable, thus revealing that learning in SSPs is strictly harder than in the finite-horizon and discounted settings. We complement this lower bound with an algorithm that matches it, up to logarithmic factors, in the general case, and an algorithm that matches it up to logarithmic factors even when $c_{\min} = 0$, but only under the condition that the optimal policy has a bounded hitting time to the goal state.

In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce {post-hoc CS} (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by $1$, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors and persistent biases. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.

It took 120 years to figure out the forgotten fossil belonged to an extinct giant echidna. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. An illustration of what Owen's giant echidna may have looked like. The now extinct megafauna was up to three feet-long. Breakthroughs, discoveries, and DIY tips sent six days a week.

Fat is key for fudgy brownies. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. Astronauts aboard the International Space Station have brownies on their menu too . But what makes a perfect brownie?

When the Netflix anthology series "Beef" premièred, in 2023, it was a revelation in more ways than one. The show, which traced the depths into which two Angelenos descend after a road-rage incident, reintroduced Ali Wong as a dramatic lead, gave Steven Yeun a chance to go darkly comic, and shined a rare light on the issue of Asian American mental health. It also remade the career of its creator, Lee Sung Jin, a seeming overnight success who actually had nearly two decades of TV-comedy writing under his belt. Lee first pitched the show after he stalked another driver for a half hour following a parking-lot dispute; he similarly drew from life for Season 2, which stars Oscar Isaac as Josh, a country-club manager, and Carey Mulligan as his interior-designer wife, Lindsay. The couple are caught on video having a nasty fight by two members of his staff, Austin (Charles Melton) and Ashley (Cailee Spaeny). The Gen Z employees, about to embark on their own marriage, see the footage as blackmail material--and thus an opportunity to start their next chapter on secure financial footing. As in the first season, the story quickly broadens beyond the central conflict, roping in the club's new billionaire owner, Chairwoman Park (Youn Yuh-jung), her unreliable plastic-surgeon husband, and the seething resentments of both the haves and the have-nots. I met Lee earlier this month, at his new office in Hollywood. The space was sparsely decorated, but he'd already mounted posters for "Beef"; "It's Always Sunny in Philadelphia," the show that gave him his start in the industry; and "Thunderbolts," a 2025 Marvel movie directed by his creative partner, Jake Schreier. Lee, who has gone by Sonny since childhood and was credited as Sonny Lee for the first half of his career, opened up about the long road to "Beef"--a journey toward more intentional storytelling, as well as feeling "O.K. in my own skin." Perhaps surprisingly, the "Beef" character he seemed to relate to most was Josh, a congenial go-getter who mires himself in workaholism to avoid addressing his grief, as Lee did when one of his dogs died suddenly during production. We talked about his method of tailoring dialogue to his actors, the differences between Korean and American billionaires, and why class and capitalism are such inescapable themes on TV today.

Environment Animals Wildlife Birds Hawaiian forest birds are stealing each other's twigs Kleptoparasitism is a risky crime sweeping the islands' forests. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Bright red iʻiwi birds are among the offenders. Breakthroughs, discoveries, and DIY tips sent six days a week. Birds in Hawaii are stealing from each other, and this bird-on-bird crime even extends to members of the same species.

Recent studies confirm that you're better off finding a human therapist. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. Millions of people use AI systems every day, for all kinds of reasons. And it's hard to deny they can be useful at times.