Granger causality (GC) [15] is a time series causal discovery framework that uses predictive modeling to identify the underlying causal structure of a time series system. Relying on the assumption that cause precedes effect, GC assesses whether including the lagged information from one time series in the autoregressive model of a second time series enhances its predictions. This improvement indicates a predictive relationship between the time series variables, where one time series provides supplemental information about the future of another time series, thereby signifying the presence of a (Granger) causal relationship. GC requires only observational data, and has been used for time series causal discovery across diverse domains, including climate science [33], political and social sciences [17], econometrics [4], and biological systems studies [13]. The original formulation of GC requires several assumptions to be satisfied for causal identifiability. In regards to the candidate time series system, it is assumed that the time series variables are stationary, and that all variables are observed (absence of latent confounders). GC was initially proposed for bivariate time series systems, but was generalised for the multivariate setting to accommodate the assumption that all relevant variables are included in the analysis [15]. Additional assumptions are made with regard to the types of causal relationships that can be identified within the time series system. GC cannot estimate a causal relationship between time series at an instantaneous time point, relying on the relationship between the lags and predicted values to determine a GC relationship.

Somber-faced Timothy Busfield appears in court for child sex abuse case as he's denied bail White House responds to Joe Rogan's warning that ICE behavior in Minneapolis resembles Hitler's Gestapo Shameless Gwyneth Paltrow, 53, pushes'miracle' $150 Goop serum... but plastic surgeon suggests she's neglected to mention a far more invasive secret behind her taut face and'TILTED' eyes Shocking truth about Minneapolis woman dragged from car by ICE while screaming that she was on her way to a doctor's appointment German troops'to touch down in Greenland in a matter of hours' as Danish leader says country is still stuck in a'fundamental disagreement' with the US over the island after'frank' meeting Benny Blanco fans left swooning after photo shows him with straight hair: 'Holy smokes' My night at America's'scariest' McDonald's that is so dangerous it does not even have a DOOR, with frightened locals renaming it'McStabby's' Progressive Portland Rep. squirms when asked about inflammatory statement she made after shooting of suspected Tren de Aragua gangsters Euphoria fans shocked over Sydney Sweeney's racy OnlyFans move: 'She's been oversexualized' Kiefer Sutherland told rideshare driver to pull over or'I'll kill you' before alleged assault in Hollywood MAGA goes wild for new scene in Landman with Glen Powell's glamorous love Michelle Randolph Six-year-old girl left all alone after ICE takes her dad away while he picked up dinner delivery: 'Where's papi?' Chicago's ultra-woke teachers' union makes glaring spelling error on flyer calling for'ultra wealthy to fund our schools' LeBron James distances himself from Rich Paul after agent pushed for Lakers to trade his client's teammates I was silenced for exposing Covid vaccine injuries in 2021... now the truth has finally come out A researcher who says she discovered that Covid vaccines could seriously injure the heart claims she was silenced during the pandemic, only to be vindicated more than four years later. Dr Jessica Rose, a Canadian researcher and expert in immunology from Memorial University of Newfoundland, said her 2021 study exposing a connection between Covid vaccines and myocarditis was mysteriously withdrawn just three weeks after it was published by the journal Current Problems in Cardiology without explanation. Myocarditis is a dangerous inflammation of the heart that can cause chest pain, shortness of breath, fatigue, irregular heartbeat, and swelling in the legs. In severe cases, it can lead to heart failure, blood clots, stroke, or sudden death. Using information from a government-run database to track vaccine side effects, Rose found a significant increase in heart damage weeks after people received the Covid vaccine.

Apple's Siri AI will be powered by Gemini The company is also blocking image generation entirely from non-subscribers. XAI logo dislpayed on a screen and Grok account on X displayed on a phone screen are seen in this illustration photo taken in London, Great Britain on July 9, 2025. X says it is changing its policies around Grok's image-editing abilities following a multi-week outcry over the chatbot repeatedly being accused of generating sexualized images of children and nonconsensual nudity. In an update shared from the @Safety account on X, the company said it has "implemented technological measures to prevent the Grok account from allowing the editing of images of real people in revealing clothing such as bikinis." The new safeguards, according to X, will apply to all users regardless of whether they pay for Grok.

The killing of George Floyd in 2020 prompted a wave of statements from tech companies and CEOs. Today, pushback against ICE is largely coming from employees, not executives. Since Donald Trump returned to the White House last January, the biggest names in tech have mostly fallen in line with the new regime, attending dinners with officials, heaping praise upon the administration, presenting the president with lavish gifts, and pleading for Trump's permission to sell their products to China . It's been mostly business as usual for Silicon Valley over the past year, even as the administration ignored a wide range of constitutional norms and attempted to slap arbitrary fees on everything from chip exports to worker visas for high-skilled immigrants employed by tech firms. But after an ICE agent shot and killed an unarmed US citizen, Renee Nicole Good, in broad daylight in Minneapolis last week, a number of tech leaders have begun publicly speaking out about the Trump administration's tactics.

Police say at least 25 kids used e-bikes and scooters to evade arrest and intimidate drivers. Breakthroughs, discoveries, and DIY tips sent six days a week. Australian police are cracking down on groups of unruly teenagers who they say are using deceptively speedy e-bikes and scooters to engage in "antisocial riding behavior." Their solution: confiscate the popular micromobility devices and crush them. The roundup, dubbed Operation Moorhead, began last week in the suburbs of Perth in southwestern Australia.

A child rights advocacy organisation in the United States is accusing Google of bypassing parental authority by allowing children to disable parental supervision over Google accounts after they turn 13. Melissa McKay, president of the Digital Childhood Institute, stated on LinkedIn that Google sent her 12-year-old an email that will unlock additional tools once he turns 13, posting screenshots of the email. Among the changes, once children turn the age of 13, they can turn off supervised experiences on YouTube and can add payment methods to Google Pay. Parents will no longer be able to block apps, turn on location sharing without the permission of the child user or block access to payment features. "Google is asserting authority over a boundary that does not belong to them. It reframes parents as a temporary inconvenience to be outgrown and positions corporate platforms as the default replacement," McKay said in a post on LinkedIn.

Apple's Siri AI will be powered by Gemini Neither company has responded to Engadget's request for comment. The two (frequently virtue-signaling) companies have inexplicably allowed Grok and X to remain in their app stores -- even as Musk's chatbot reportedly continues to produce the material. On Wednesday, a coalition of women's and progressive advocacy groups called on Tim Cook and Sundar Pichai to uphold their own rules and remove the apps. The open letters to Apple and Google were signed by 28 groups. Among them are the women's advocacy group Ultraviolet, the parents' group ParentsTogether Action and the National Organization for Women.

The scrapes and rubs the mammals leave behind shine under UV light humans can't see. Breakthroughs, discoveries, and DIY tips sent six days a week. Animals see the world around them in ways that we humans can only imagine. Arctic reindeer's eyes change color with the season to help them find food, while giant squid have eyes the size of dinner plates. Many species take advantage of seeing ultraviolet (UV) light that's invisible to humans--including deer .

You are about to hear a lot more about Claude Code. Over the holidays, Alex Lieberman had an idea: What if he could create Spotify "Wrapped" for his text messages? Without writing a single line of code, Lieberman, a co-founder of the media outlet, created "iMessage Wrapped"--a web app that analyzed statistical trends across nearly 1 million of his texts. One chart that he showed me compared his use of,,, and --he's an guy. Another listed people he had ghosted.

Apple's Siri AI will be powered by Gemini Longtime fans of the franchise were disappointed in this latest installment. The App Store is a home for many kinds of apps (including, inexplicably, one that lets users undress strangers without their consent). But hey, it also has games! And soon the store's Apple Arcade service will include one more: the not-so-highly rated . Apple announced on Wednesday that will arrive almost exactly a year after launch . The game is already available for Apple devices, but its arrival on Apple Arcade will be a first.