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Category: mathematics

Mathematical modeling helps advance use of magnetic particles in targeted drug-delivery systems

A Florida State University computational scientist is paving the way for future medical breakthroughs by developing mathematical models and simulations to predict the behavior of a unique drug-delivery method, which aims to deploy treatments directly to targeted sites in the body.

Florida State University Associate Professor of Scientific Computing Bryan Quaife is part of a multi-institutional team of engineers, mathematicians and computational scientists conducting foundational research essential to the design of a drug-delivery system that could reduce medication side effects while increasing treatment efficacy. Their research expands on work proposing the use of magnetic particles to guide cell-like drug carriers toward a specific target, like a tumor.

This work, which was published in Physical Review Letters, reveals how tiny particles moving inside microscopic drug carriers can gradually stress and eventually rupture the enclosing membrane. These findings could help engineers design smarter drug-delivery systems to protect therapeutic cargo during transport and release it on demand at the desired location.

Under the Hood of Vibe Coding: A Deep Dive Into the Holographic Mathematic Miracle

If you’ve been in tech circles lately, you’ve probably heard of “Vibecoding.” Most people treat it like an industry joke—lazy developers throwing sloppy prompts at a screen until an app magically pops out. To traditional gatekeepers, it looks like dangerous, uncompilable chaos.

The “vibe” isn’t a loose, careless emotion. It’s data. Specifically, it is the human-facing interface for what advanced computer science calls Intent Orchestration.

I just published a definitive deep dive into the actual math, physics, and mechanics under the hood of this movement. We break down exactly why the traditional “Filing Cabinet” architecture of multi-agent AI is fundamentally broken, and how Holographic AI Frameworks are the solution.

We are stepping into an era of Decentralized Coherence that liberates creators from traditional development bottlenecks, transforming your role from a low-level syntax translator into a High-Dimensional Intent Architect.

The era of manual syntax is drawing to a close. The computer has finally spent enough time engineering its systems to understand our language.

But make no mistake—if your structural thinking is sloppy, your application will still fail.

The quality of your thinking is the new syntax.

Continue reading “Under the Hood of Vibe Coding: A Deep Dive Into the Holographic Mathematic Miracle” | >

Chinese AI Models Undercut OpenAI and Anthropic by Up to 9x in Pricing

And don’t assume “cheaper” means “worse.” On the SWE-bench Pro—the gold standard benchmark for coding agent capabilities—Zhipu’s GLM 5.2 scored a 62.1, beating OpenAI’s GPT-5.5 at 58.6.

Running the same AI workload through Anthropic’s Claude costs $4,811. Running it through Zhipu’s GLM model costs $544. That’s nearly a 9x price difference for equivalent work, and enterprise customers have started doing the math.

Chinese AI companies are undercutting OpenAI and Anthropic so aggressively on price that the two most prominent US AI firms are now scrambling to respond. OpenAI is reportedly considering major token price cuts, and Anthropic is expected to follow. The timing could not be worse: both companies are preparing for public market debuts.

A comparison of workload costs across leading AI models paints a stark picture. Anthropic’s Claude rings in at $4,811 per workload. OpenAI’s ChatGPT comes in lower at $3,357, but still far above the Chinese alternatives. DeepSeek prices the same workload at $1,071. Moonshot’s Kimi model does it for $948. And Zhipu’s GLM sits at just $544.

Germany’s New Photonic NPU Just Made NVIDIA’s Billion Dollar GPUs Look Like TRASH!

Photonic chips are no longer just a lab experiment, and in this video, we break down why a new photonic NPU could become one of the biggest shifts in AI hardware, data centers, and supercomputing. Instead of using electricity and transistors like a traditional GPU, this new class of processor uses light to perform computation, opening the door to dramatically faster matrix math, far lower energy use, and almost no on-chip heat. From the growing power crisis in AI infrastructure to the limits of silicon, Moore’s Law, and the memory wall, this story explores why photonic computing is suddenly becoming one of the most important technologies to watch. If you’re interested in photonic chips, optical computing, AI chips, NPUs, GPUs, data center efficiency, and the future of semiconductor technology, this video gives you the full picture. We also explore what makes these chips different from conventional silicon. The video covers photons instead of electrons, wavelength-division multiplexing, optical interference, thin-film lithium niobate, and why companies like Q.ANT are now deploying photonic processors in real supercomputing environments instead of just talking about them on research slides. We look at Q.ANT’s Native Processing Unit at the Leibniz Supercomputing Centre in Germany, the jump from first-generation to second-generation performance, and why benchmarks showing huge gains in throughput, AI inference, and energy efficiency are making people take photonic hardware much more seriously. More importantly, this is not just another faster chip story. It is about whether the AI industry can keep scaling without running straight into an energy wall. With GPUs demanding more power, more cooling, and more data movement every year, photonic co-processors may be the first real alternative that changes the economics of compute itself. The technology still has serious challenges, especially memory and optical-electrical conversion, but this may be the moment when computing with light stopped sounding like science fiction and started becoming real infrastructure.

Google Just Released What Comes After AGI — A Million Times More Powerful Than AGI!

Google DeepMind just revealed what could come after AGI, and it may be far more powerful than most people realize. In its new paper “From AGI to ASI,” DeepMind explains why human-level AI may not be the finish line, but the starting point for artificial superintelligence. In this video, we break down what AGI and ASI really mean, why Shane Legg and Marcus Hutter’s involvement matters, and how DeepMind defines superintelligence as something that can outperform massive organizations of top human experts across nearly every domain. We also explore the four possible roads from AGI to ASI: scaling, new AI architectures, recursive self-improvement, and multi-agent AI collectives. One of the most shocking ideas is that you may not need an AI smarter than a human. 100 million human-level AI agents working together could already become something far beyond us. But even superintelligence has limits. Physics, computation, mathematics, uncertainty, data, energy, and regulation could all shape what happens next. Is AGI really the end goal, or just the beginning?

#GoogleDeepMind #AGI #ASI #ArtificialIntelligence #Superintelligence #AI

Ben Goertzel Just Revealed When AGI Will ACTUALLY Happen | Ep. 38

Ben Goertzel, the godfather of AGI research and CEO of SingularityNet, just dropped some mind-blowing insights about artificial general intelligence that will change how you think about AI forever. This isn’t your typical AI hype this is raw truth from someone who’s been building AGI for decades.

In this deep dive conversation, Ben reveals the shocking reality behind current AI limitations, why decentralized AI infrastructure is crucial for humanity’s future, and his honest timeline for when we’ll actually achieve AGI. Plus, he shares what it’s like running a global AI empire while living on a remote island accessible only by ferry.

Key Topics Covered:
The real timeline for AGI development.
Why current AI models aren’t actually intelligent.
How SingularityNet is building decentralized AI infrastructure.
The ASI Alliance and the future of artificial superintelligence.
Ben’s daily routine managing hundreds of AI researchers globally.
Why math and music drive breakthrough AI thinking.

⏰ Timestamps:
0:00 — Introduction to Ben Goertzel.
2:30 — Daily life of an AGI pioneer.
8:45 — Managing a global AI empire.
15:20 — The truth about current AI limitations.
25:10 — SingularityNet and decentralized AI
35:40 — When will AGI actually happen?
45:30 — The future of artificial superintelligence.
58:15 — Closing thoughts.

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💬 What do you think about Ben’s AGI timeline? Drop your thoughts in the comments below!

Continue reading “Ben Goertzel Just Revealed When AGI Will ACTUALLY Happen | Ep. 38” | >

The Topological Lower Bound of Boltzmann Entropy: Resolving the Pure Top Boundary Condition through Proton Phase-Locking (v.01)

We establish a fundamental, non-zero lower bound for thermodynamic entropy by mapping Ludwig Boltzmann’s classical relation onto the rigid topological boundaries of GLAB chronal dynamics. In standard statistical mechanics, the number of microstates is treated as an abstract mathematical variable capable of reducing to unity , which phenomenologically implies an absolute zero entropy state . We demonstrate that this boundary condition is physically unattainable because the minimal, topologically closed space-phase cell possesses an irreversible internal structure dictated by the free proton configuration. Characterizing the stable proton as an asymmetric quantum “pure top” subject to the Janibekov instability, we prove that it inherently occupies a degenerate phase space composed of 2 intrinsic spin projections and 3 spatial rotational axes. This yields a strict, immutable minimum statistical weight of. Consequently, the absolute minimum entropy of any isolated domain in our universe is bounded by the Proton Constant:. We mathematically demonstrate that if this lower bound were violated, the phase-locking mechanism governing stellar nucleosynthesis would collapse, rendering the existence of periodic nuclear cycles and stable matter impossible.

‘Collapsible scissored surfaces’ complete trilogy of metamaterial design principles

Over the past decade, Professor L. Mahadevan’s Soft Math Lab at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) has helped establish how the ancient Japanese paper arts of folding or cutting can be used to inversely design structures that transform dramatically in shape and function. Now, the researchers have created a new class of shape-changing matter, based not on folds or cuts, but linkages—networks of interconnected scissor mechanisms that collapse into lines and deploy into curved surfaces.

The study published in the Proceedings of the National Academy of Sciences, led by physics graduate student Noah Toyonaga, establishes a mathematical and physical framework for what the authors call collapsible scissored surfaces—deployable lattices of two-bar linkages that can transform from a one-dimensional collapsed state into two-dimensional structures with prescribed geometry.

“Origami showed how folds can encode shape,” said senior author Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics. “Kirigami showed how cuts can unlock motion and functionality. This work asks a complementary question: What can be achieved when the basic building block is not a fold or a cut, but a linkage?”

Anatomically accurate digital twin of 2-year-old’s brain uncovers neural signatures linked to autism

For decades, researchers have been trying to understand the biological roots of autism spectrum disorder (ASD), a common neurodevelopmental condition that shapes how people communicate, learn and interact with the world. One of the major hurdles is that the brain’s neural networks are extraordinarily complex. Existing models still lack the detail needed to capture both the brain’s structure and its dynamic activity in a unified manner.

In a recent study published in PLOS Digital Health, researchers created a new system called FEDE (high FidElity Digital brain modEl) that builds a digital twin, a detailed computer replica or virtual copy of a real-world object. In this study, it was a virtual copy of the brain of a 2-year-old child with ASD.

To build FEDE, researchers combined maps of the child’s brain structure obtained using MRI with mathematical modeling to create a digital brain that can simulate both how the brain is built and how it functions.

Thirty years of proof: celebrating Sir Andrew Wiles and Fermat’s Last Theorem

The 23rd of June 2023 marks 30 years since Andrew Wiles delivered his first proof of Fermat’s Last Theorem, right here at INI. In this article, podcast and video interview, we celebrate this tremendous milestone for one of mathematics’ most compelling stories.

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