The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence is governed by the spectrum of the linearized EM map. How these two levels fit into a single dynamical picture has remained less transparent. We make explicit the latent-variable operator that connects them. Along the EM trajectory, the likelihood increment admits a global energy decomposition in terms of posterior-relative entropy. Linearization at a nondegenerate maximizer $θ^\ast$ then reveals the local operator \[ \mathcal G_{θ^\ast}=I-DT(θ^\ast), \] which coincides with both the missing-information ratio and the information-geometric Hessian of the observed likelihood. This operator provides a unified description of local contraction, posterior rigidity, and geometric curvature. Its spectrum yields a sharp characterization of local convergence and naturally leads to an optimal scalar relaxation rule for locally accelerated EM. These results place global descent, local spectral behavior, and optimal local relaxation within a common dynamical framework.

Due to health and energy concerns, the California Legislature is considering bills to prohibit data centers from being exempted from the state's stringent environmental law and impose new tariffs on new major energy users that strain power supplies.

But the only native stork found in the U.S. is not out of the woods just yet. Breakthroughs, discoveries, and DIY tips sent six days a week. After over 40 years of recovery efforts, one population of the wood stork ()is being removed from the federal list of endangered and threatened wildlife. The large birds are as tall as 45 inches with wingspans that can reach 65 inches and are the only native storks in the United States. They are primarily found in the southeastern United States, where they feed on fish.

A 2025 survey in the forests of Laos, Vietnam, and Cambodia uncovered several rare and endangered animals. A pig-tailed macaque is caught on camera in a Cambodian forest. Breakthroughs, discoveries, and DIY tips sent six days a week. The results of a new camera-trap survey in Southeast Asia is revealing a bevy of hidden biodiversity tucked within the Annamites mountain range . This largely unexplored wildlife hotspot has a forest stretching 683 miles (1,100 kilometers) across the countries of Laos, Vietnam, and Cambodia.

Before the EPA, Utah saw 100 times more lead exposure. Breakthroughs, discoveries, and DIY tips sent six days a week. The evidence is clear--and in your hair. Americans were exposed to as much as 100 times more lead in their daily lives than they are today before the Environmental Protection Agency was established in 1970. In an effort to examine the dramatic reduction in toxic heavy metal exposure, researchers turned to human hair samples dating back a century.

The achievement of the 2030 Sustainable Development Goals (SDGs) is dependent upon strategic resource distribution. We propose a causal discovery framework using Panel Vector Autoregression, along with both country-specific fixed effects and PCMCI+ conditional independence testing on 168 countries (2000-2025) to develop the first complete causal architecture of SDG dependencies. Utilizing 8 strategically chosen SDGs, we identify a distributed causal network (i.e., no single 'hub' SDG), with 10 statistically significant Granger-causal relationships identified as 11 unique direct effects. Education to Inequality is identified as the most statistically significant direct relationship (r = -0.599; p < 0.05), while effect magnitude significantly varies depending on income levels (e.g., high-income: r = -0.65; lower-middle-income: r = -0.06; non-significant). We also reject the idea that there exists a single 'keystone' SDG. Additionally, we offer a proposed tiered priority framework for the SDGs namely, identifying upstream drivers (Education, Growth), enabling goals (Institutions, Energy), and downstream outcomes (Poverty, Health). Therefore, we conclude that effective SDG acceleration can be accomplished through coordinated multi-dimensional intervention(s), and that single-goal sequential strategies are insufficient.

Activists are demanding a way to hold the memory-chip maker accountable to its promises to protect the environment and embrace communities of color in central New York. Days after Micron broke ground on a $100 billion chip factory in New York state, a coalition of environmentalists, labor unions, and civil rights groups are urging the US tech giant to sign a deal that would make a series of promises to be a good neighbor legally enforceable. Micron's megafab to make memory chips is on track to become the biggest commercial development in state history and the largest chipmaking complex in the country . Officials held a groundbreaking ceremony in the city of Clay, near Syracuse, last Friday. The first chips could arrive in five years, though the entire site won't be finished for 20 years.

Indonesia's government has filed multiple lawsuits seeking more than $200m in damages against six firms, after deadly floods wreaked havoc across Sumatra, killing more than 1,000 people last year, although environmentalists criticised the moves as inadequate. Environmentalists, experts and the government pointed the finger at deforestation for its role in last year's disaster that washed torrents of mud and wooden logs into villages across the northwestern part of the island. The sum represents both fines for damage and the proposed monetary value of recovery efforts. The suits were filed to courts on Thursday in Jakarta and North Sumatra's Medan, the ministry added. "We firmly uphold the principle of polluter pays," Environment Minister Hanif Faisol Nurofiq said in a statement.