A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

The United States Supreme Court has temporarily reinstated a rule allowing an abortion pill to be prescribed through telemedicine and dispensed through the mail, lifting a judicial ban that narrowed access to the medication nationwide. Justice Samuel Alito issued an interim order on Monday, pausing for one week a decision by the New Orleans-based 5th US Circuit Court of Appeals to reimpose an older federal rule requiring an in-person clinician visit to receive mifepristone. The Supreme Court's action, called an "administrative stay", gives the justices more time to review emergency requests by two manufacturers of mifepristone to ensure that the drug can be provided via telehealth and the mail while the legal challenge plays out. Alito ordered Louisiana to respond to the drugmakers' requests by Thursday and indicated that the administrative stay would expire on May 11. The court would be expected to extend the interim stay or formally decide the requests by that time.

Landmark cases on social media's impact on children begin this week in US Two lawsuits accusing the world's largest social media companies of harming children begin this week, marking the first legal efforts to hold companies like Meta responsible for the effects their products have on young users. Opening arguments began today in a case brought by New Mexico's attorney general's office, which alleges that Meta failed to protect children from sexually explicit material. A separate case in Los Angeles, which accuses Meta and the Google-owned YouTube of deliberately designing their platforms to be addictive for children, is set to begin later this week. The New Mexico and California lawsuits are the first of a wave of 40 lawsuits filed by state attorneys general around the US against Meta, specifically, that allege that the social media giant is harming the mental health of young Americans. In the opening argument in the New Mexico case, which was first filed in 2023, prosecutors told jurors on Monday that Meta - Facebook and Instagram's parent company - had failed to disclose its platforms' harmful effects on kids.

Supreme Court transgender athletes case could reverse Title IX protections by 50 years, Jennifer Sey argues. The justices review Idaho and West Virginia laws affecting girls' sports.

The American Revolution created a lasting democracy while the French Revolution became blood-soaked tyranny. But today's armchair revolutionaries echo similar calls.

He catches nascent changes in the political weather. "During early, he kept telling me, 'Crime--there's something here,' " DeBoo told me. DeBoo studied the latest crime statistics and saw nothing unusual. He brushed off the worry. Then new numbers came out, showing a large pandemic spike in shoplifting and car theft, and concerns about crime exploded into the headlines. Last March, judging the winds, Newsom launched a podcast, "This Is Gavin Newsom."