Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport maps, velocity fields, score fields, and guided stochastic dynamics. We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space. Within this framework, generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation. We also highlight representative theoretical guarantees, including forward-reverse convergence for iterative flow models, first-order minimax analysis in transport-map space, and error-transfer bounds for posterior sampling with generative priors. The tutorial provides a principled introduction to using generative models for scenario generation, robust decision-making, uncertainty quantification, and related problems under distributional shift.

We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symmetric matrix M. By Morse theory, the diagram has exactly n-1 finite bars, with the k-th bar living in homological dimension k-1 and having length equal to the k-th eigenvalue spacing s_k = λ_{k+1} - λ_k. This identification transfers random matrix theory (RMT) universality to persistence diagram universality: for matrices drawn from the Gaussian Orthogonal Ensemble (GOE), we derive the closed-form persistence entropy PE = log(8n/π) - 1, and verify numerically that the coefficient of variation of persistence statistics decays as n^{-0.6}. Different random matrix ensembles (GOE, GUE, Wishart) produce distinct universal persistence diagrams, providing topological fingerprints of RMT universality classes. As a practical consequence, we show that persistence entropy outperforms the standard level spacing ratio \langle r \rangle for discriminating GOE from GUE matrices (AUC 0.978 vs. 0.952 at n = 100, non-overlapping bootstrap 95% CIs), and detects global spectral perturbations in the Rosenzweig-Porter model to which \langle r \rangle is blind. These results establish persistence entropy as a new spectral diagnostic that captures complementary information to existing RMT tools.

Register now free-of-charge to explore this white paper This Whitepaper offers engineers and researchers a technical examination of the key design barriers in humanoid robotics and the component-level strategies emerging to address them, from sensing and motion control to power systems and thermal management. What you will learn about:   The core engineering challenges — complex motion control, safe human-robot interaction, and hardware cost constraints — that currently limit practical humanoid robot deployment. Sensing system architectures: how IMUs, gyroscopes, accelerometers, tactile sensors, and AMR magnetic sensors support real-time posture estimation, perception fusion, and environmental awareness. Motion and actuation design considerations including actuator-level power delivery, motor noise mitigation, PCB bend-stress resistance, and dexterous hand integration. Power and thermal system trade-offs: battery chemistry selection (LFP vs. NCA), BMS design, DC/DC converter topologies, and thermistor-based protection for operational reliability. Click 'LOOK INSIDE' to Download Now.

Things to Do in L.A. Kate Brody's 7-year-old son plays at home in North Hollywood on March 14. This is read by an automated voice. Please report any issues or inconsistencies here . Early childhood experts say excessive screen time displaces hands-on learning and peer interaction critical to development. At least 11 states have considered legislation limiting technology in the classroom this year.

Recently, learning discriminative features to improve the recognition performances gradually becomes the primary goal of deep learning, and numerous remarkable works have emerged. In this paper, we propose a novel yet extremely simple method Virtual Softmax to enhance the discriminative property of learned features by injecting a dynamic virtual negative class into the original softmax. Injecting virtual class aims to enlarge inter-class margin and compress intra-class distribution by strengthening the decision boundary constraint. Although it seems weird to optimize with this additional virtual class, we show that our method derives from an intuitive and clear motivation, and it indeed encourages the features to be more compact and separable. This paper empirically and experimentally demonstrates the superiority of Virtual Softmax, improving the performances on a variety of object classification and face verification tasks.

AI is nearly exclusively designed by men - here's how to fix it With the Trump administration's attacks on so-called woke AI it is becoming even harder to make the technology we use fairer and more diverse. It's day two of the conference at the Royal Society in London, but I'm finding it increasingly hard to concentrate on the speakers because my AI transcription software - which is supposed to make my life easier - keeps insisting on mistyping someone's name. The irony isn't lost on me: this is the session about artificial intelligence, and specifically about how women are being erased from the latest AI technologies. This is much bigger than the now-familiar idea that AI algorithms carry the biases of the datasets they are trained on, including gender bias. Instead, the focus of the conference session, chaired by computer scientist Wendy Hall, is seeking to address a more fundamental issue: the fact that new AI technologies, which will have a transformative effect on all of society, are being designed almost exclusively by men.

China's OpenClaw Boom Is a Gold Rush for AI Companies Hype around the open source agent is driving people to rent cloud servers and buy AI subscriptions just to try it, creating a windfall for tech companies. George Zhang thought OpenClaw could make him rich, even though he didn't really understand how the viral AI agent software worked. But he saw a video of a Chinese social media influencer demonstrating how it could be deployed to manage stock portfolios and make investment decisions autonomously. Zhang, who works in cross-border ecommerce in the Chinese city of Xiamen, was intrigued enough that he decided to try installing OpenClaw in late February. Zhang is one of the many people in China who got swept up in the craze over OpenClaw recently.