On Friday, US President Joe Biden on the billionaire Elon Musk's acquisition of Twitter, said that Musk had bought a social networking platform that spreads lies around the world.

"Now what worries us all, is Elon Musk's purchase of a tool that sends lies around the world...There are no more editors in America. There are no editors. How can we expect children to be risk-aware?" Biden warned.

The head of the Safety and Integrity Department at Twitter, Yoel Roth announced earlier Friday, in a tweet that the company had laid off 50 percent of its employees, while he said that there had been no change in content monitoring on Twitter.

Roth added that 15% of Twitter employees on the Safety and Integrity team, which monitors misinformation and harmful content, have been laid off. He added that company-wide layoffs affected 50 percent of employees, the first confirmation from Twitter insider about the scale of the layoffs.

"Again, to be absolutely clear, Twitter's strong commitment to content moderation remains absolutely unchanged," Musk said in a tweet shortly after Roth's tweet.

Musk had previously said Twitter had seen a "massive drop in revenue" due to civil rights groups that have raised concerns about how layoffs will affect content moderation and have pressured major advertisers to withdraw their ad spending.

As some oppose Musk’s takeover of the platform that us largely used by civil society groups and politicians, many back Musk’s new policies in the Twitter and call it a return of freedom to the platform.

A groundbreaking mathematical equation that could transform medical procedures, natural gas extraction, and plastic packaging production in the future has been discovered.

The new equation, developed by scientists at the University of Bristol, indicates that diffusive movement through permeable material can be modeled exactly for the very first time.

It comes a century after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation, and marks important progress in representing motion for a wide range of entities from microscopic particles and natural organisms to man-made devices.

Until now, scientists looking at particle motion through porous materials, such as biological tissues, polymers, various rocks and sponges have had to rely on approximations or incomplete perspectives.

The findings, published today in the journal Physical Review Research, provide a novel technique that presents exciting opportunities in a diverse range of settings including health, energy, and the food industry.

Lead author Toby Kay, who is completing a Ph.D. in Engineering Mathematics, said, "This marks a fundamental step forward since Einstein and Smoluchowski's studies on diffusion. It revolutionizes the modeling of diffusing entities through complex media of all scales, from cellular components and geological compounds to environmental habitats.

"Previously, mathematical attempts to represent movement through environments scattered with objects that hinder motion, known as permeable barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different sectors because permeable barriers are routinely encountered by animals, cellular organisms and humans."

Creativity in mathematics takes different forms and one of these is the connection between different levels of description of a phenomenon. In this instance, by representing random motion in a microscopic fashion and then subsequently zooming out to describe the process macroscopically, it was possible to find the new equation.

Further research is needed to apply this mathematical tool to experimental applications, which could improve products and services. For example, being able to model accurately the diffusion of water molecules through biological tissue will advance the interpretation of diffusion-weighted MRI (Magnetic Resonance Imaging) readings. It could also offer more accurate representation of air spreading through food packaging materials, helping to determine shelf life and contamination risk. In addition, quantifying the behavior of foraging animals interacting with macroscopic barriers, such as fences and roads, could provide better predictions on the consequence of climate change for conservation purposes.

The use of geolocators, mobile phones, and other sensors has seen the tracking revolution generate movement data of ever-increasing quantity and quality over the past 20 years. This has highlighted the need for more sophisticated modeling tools to represent the movement of wide-ranging entities in their environment, from natural organisms to man-made devices.

Senior author Dr. Luca Giuggioli, Associate Professor in Complexity Sciences at the University of Bristol, said, "This new fundamental equation is another example of the importance of constructing tools and techniques to represent diffusion when space is heterogeneous; that is, when the underlying environment changes from location to location.

"It builds on another long-awaited resolution in 2020 of a mathematical conundrum to describe random movement in confined space. This latest discovery is a further significant step forward in improving our understanding of motion in all its shapes and forms—collectively termed the mathematics of movement—which has many exciting potential applications."