In variety testing, multi-environment trials (MET) are essential for evaluating the genotypic performance of crop plants. A persistent challenge in the statistical analysis of MET data is the estimation of variance components, which are often still inaccurately estimated or shrunk to exactly zero when using residual (restricted) maximum likelihood (REML) approaches. At the same time, institutions conducting MET typically possess extensive historical data that can, in principle, be leveraged to improve variance component estimation. However, these data are rarely incorporated sufficiently. The purpose of this paper is to address this gap by proposing a Bayesian framework that systematically integrates historical information to stabilize variance component estimation and better quantify uncertainty. Our Bayesian linear mixed model (BLMM) reformulation uses priors and Markov chain Monte Carlo (MCMC) methods to maintain the variance components as positive, yielding more realistic distributional estimates. Furthermore, our model incorporates historical prior information by managing MET data in successive historical data windows. Variance component prior and posterior distributions are shown to be conjugate and belong to the inverse gamma and inverse Wishart families. While Bayesian methodology is increasingly being used for analyzing MET data, to the best of our knowledge, this study comprises one of the first serious attempts to objectively inform priors in the context of MET data. This refers to the proposed Bayesian updating approach. To demonstrate the framework, we consider an application where posterior variance component samples are plugged into an A-optimality experimental design criterion to determine the average optimal allocations of trials to agro-ecological zones in a sub-divided target population of environments (TPE).

EVEN supervised learning is subject to the famous NoFree Lunch Theorems [1]-[3], which say that, in combinatorial optimization, there is no universal algorithm that works better than its competitors for every objective function [4]-[6]. Indeed, David Wolpert has recently proven that, on average, cross-validation performs as well as anti-crossvalidation (choosing among a set of candidate algorithms based on which has the worst out-of-sample behavior) for supervised learning. Still, he acknowledges that "it is hard to imagine any scientist who would not prefer to use [crossvalidation] to using anti-cross-validation" [7]. On the other hand, unsupervised learning has seldom been studied from the perspective of the NFLTs. This may be because the adjective "unsupervised" suggests that no human input is needed, which is misleading as many unsupervised tasks are combinatorial optimization problems that depend on the choice of the objective function. For instance, it is well known that, among the eigenvectors of the covariance matrix, Principal Components Analysis selects those with the largest variances [8]. However, mode-hunting techniques that rely on spectral manipulation aim at the opposite objective: selecting the eigenvectors of the covariance matrix with the smallest variances [9], [10]. Therefore, unlike in supervised learning, where it is difficult to identify reasons to optimize with respect to anti-cross-validation, in unsupervised learning there are strong reasons to reduce dimensionality for variance minimization. D. A. D ıaz-Pach on and T. Liu are with the Division of Biostatistics, University of Miami, Miami, FL, 33136 USA (e-mail: ddiaz3@miami.edu,

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss landscapes. We propose a lightweight curvature-aware optimization framework that augments existing first-order optimizers with an adaptive predictive correction based on secant information. Consecutive gradient differences are used as a cheap proxy for local geometric change, together with a step-normalized secant curvature indicator to control the correction strength. The framework is plug-and-play, computationally efficient, and broadly compatible with existing optimizers, without explicitly forming second-order matrices. Experiments on diverse PDE benchmarks show consistent improvements in convergence speed, training stability, and solution accuracy over standard optimizers and strong baselines, including on the high-dimensional heat equation, Gray--Scott system, Belousov--Zhabotinsky system, and 2D Kuramoto--Sivashinsky system.

In finite-width deep neural networks, the empirical kernel $G$ evolves stochastically across layers. We develop a collective kernel effective field theory (EFT) for pre-activation ResNets based on a $G$-only closure hierarchy and diagnose its finite validity window. Exploiting the exact conditional Gaussianity of residual increments, we derive an exact stochastic recursion for $G$. Applying Gaussian approximations systematically yields a continuous-depth ODE system for the mean kernel $K_0$, the kernel covariance $V_4$, and the $1/n$ mean correction $K_{1,\mathrm{EFT}}$, which emerges diagrammatically as a one-loop tadpole correction. Numerically, $K_0$ remains accurate at all depths. However, the $V_4$ equation residual accumulates to an $O(1)$ error at finite time, primarily driven by approximation errors in the $G$-only transport term. Furthermore, $K_{1,\mathrm{EFT}}$ fails due to the breakdown of the source closure, which exhibits a systematic mismatch even at initialization. These findings highlight the limitations of $G$-only state-space reduction and suggest extending the state space to incorporate the sigma-kernel.

One of the dominant paradigms in self-supervised learning (SSL), illustrated by MoCo or DINO, aims to produce robust representations by capturing features that are insensitive to certain image transformations such as illumination, or geometric changes. This strategy is appropriate when the objective is to recognize objects independently of their appearance. However, it becomes counterproductive as soon as appearance itself constitutes the discriminative signal. In weather analysis, for example, rain streaks, snow granularity, atmospheric scattering, as well as reflections and halos, are not noise: they carry the essential information. In critical applications such as autonomous driving, ignoring these cues is risky, since grip and visibility depend directly on ground conditions and atmospheric conditions. We introduce ST-STORM, a hybrid SSL framework that treats appearance (style) as a semantic modality to be disentangled from content. Our architecture explicitly separates two latent streams, regulated by gating mechanisms. The Content branch aims at a stable semantic representation through a JEPA scheme coupled with a contrastive objective, promoting invariance to appearance variations. In parallel, the Style branch is constrained to capture appearance signatures (textures, contrasts, scattering) through feature prediction and reconstruction under an adversarial constraint. We evaluate ST-STORM on several tasks, including object classification (ImageNet-1K), fine-grained weather characterization, and melanoma detection (ISIC 2024 Challenge). The results show that the Style branch effectively isolates complex appearance phenomena (F1=97% on Multi-Weather and F1=94% on ISIC 2024 with 10% labeled data), without degrading the semantic performance (F1=80% on ImageNet-1K) of the Content branch, and improves the preservation of critical appearance

Existing multi-expert learning-to-defer surrogates are statistically consistent, yet they can underfit, suppress useful experts, or degrade as the expert pool grows. We trace these failures to a shared architectural choice: casting classes and experts as actions inside one augmented prediction geometry. Consistency governs the population target; it says nothing about how the surrogate distributes gradient mass during training. We analyze five surrogates along both axes and show that each trades a fix on one for a failure on the other. We then introduce a decoupled surrogate that estimates the class posterior with a softmax and each expert utility with an independent sigmoid. It admits an $\mathcal{H}$-consistency bound whose constant is $J$-independent for fixed per-expert weight $β{=}λ/J$, and its gradients are free of the amplification, starvation, and coupling pathologies of the augmented family. Experiments on synthetic benchmarks, CIFAR-10, CIFAR-10H, and Covertype confirm that the decoupled surrogate is the only method that avoids amplification under redundancy, preserves rare specialists, and consistently improves over a standalone classifier across all settings.

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.

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.

Beijing's robot half-marathon is back for its second year with far less embarassing results The fastest time from an Honor robot came in at 50 minutes and 26 seconds. To make up for an incredibly laughable inaugural event, Beijing is running back its humanoid robot half-marathon. Fortunately, the event that pits humanoid robots made by Chinese companies against each other across 13 miles went a lot smoother this year. This year's half-marathon hosted more than 100 competitors, with first place going to Honor, better known for its smartphones, and its red-clad robot named Lightning. Living up to the name, the gold medalist finished the race in 50 minutes and 26 seconds.

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. While beautiful, Bradford pear trees also stink. Breakthroughs, discoveries, and DIY tips sent six days a week. The sun is out, the streets are humming, the days are getting longer, and the air smells like like um say, can anyone else smell that? All over America, spring is getting smellier every year, and the culprit is the Bradford pear, a tree that gained popularity in the mid-20 century for its ornamental properties.