Beyond Local Minima: Certifying Solutions for Robust PCA
![Robust principal component analysis successfully recovers underlying low-rank plus sparse structure in synthetic matrices of size 100x80 with high probability, achieving a recovery success rate consistently exceeding 99.9% as quantified by a normalized reconstruction error of less than [latex]10^{-3}[/latex] across 10,000 independent trials.](https://arxiv.org/html/2601.21333v1/x4.png)
New research establishes rigorous guarantees for finding optimal solutions in robust principal component analysis, even when dealing with challenging, non-convex problems.
Time is Running Out to Claim the Free PS Plus Games for January 2026
This month’s PlayStation Plus free games have been available to download since January 6th. They are Epic Mickey: Rebrushed, Need for Speed Unbound, and Core Keeper.
The Most Perfect PlayStation Games
It’s difficult to measure the full impact, but PlayStation has undoubtedly been a major force in building the gaming community. Here’s a look at some of their most outstanding games – titles that were almost flawless when they first came out and still hold up incredibly well today, with only minor issues. We’ll focus on games published or created by Sony’s own studios.
Every Major Anime Studio’s Best Anime of 2025
As an anime fan, I’ve noticed that the major studios consistently release impressive new shows each year. With 2026 already looking promising, it’s a good moment to reflect on 2025 and pick out the standout anime from each studio. To keep things focused, I’m only considering shows that started airing in 2025 – so anything that began in 2024 and continued into 2025 won’t be included this time.
Finnegan the Fox Has Died
Almost a year before it came out, Overwatch 2 introduced Kiriko, a new support character. She’s a ninja with fox ears who can both heal teammates with protective talismans and attack enemies with throwing stars. Players quickly loved her abilities and cool design, and many especially enjoyed her special ability, a ghostly fox spirit voiced by the late Finnegan.
Matt Mercer Comments on Critical Role’s Future
Critical Role is widely considered the most impactful live-play series based on Dungeons & Dragons. Starting with popular actor Matt Mercer as Dungeon Master, the show has showcased many well-known voice actors, such as Travis Willingham, Liam O’Brien, and Laura Bailey. The latest season saw Brennan Lee Mulligan take over as DM for the fourth campaign. Now, Matt Mercer has publicly shared his feelings about stepping down from the Dungeon Master role in Critical Role.
Best Open-World Action-Adventure Games
The most popular open-world action-adventure games have a unique quality: they feel both fresh and classic. People loved them when they first came out, and they continue to draw players back in, offering years of replayability. It’s a rare achievement, but here are some of the nearly perfect action-adventure open-world games that consistently deliver.
Beyond Privacy: Designing Neural Networks for Encrypted Computation
A new architecture minimizes the performance overhead of homomorphic encryption, paving the way for faster and more practical privacy-preserving machine learning.
PlayStation Patent Reveals Wild New Controller Design
Sony files several new controller patents every year, and while they usually include traditional buttons, a recently published patent from January 27, 2026, appears to be different.
FPS Games With The Best Guns, Ranked
A great first-person shooter lets you play the way you want, but really, the guns themselves need to feel good and offer a lot of variety to keep things fun. Here are some of the best FPS games that deliver on that promise.