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Archive for the ‘mathematics’ category

Nov 23, 2024

Quantum Computing and state-sponsored Cyber Warfare: How quantum will transform Nation-State Cyber Attacks

Posted by in categories: cybercrime/malcode, encryption, information science, mathematics, military, quantum physics

The rise of quantum computing is more than a technological advancement; it marks a profound shift in the world of cybersecurity, especially when considering the actions of state-sponsored cyber actors. Quantum technology has the power to upend the very foundations of digital security, promising to dismantle current encryption standards, enhance offensive capabilities, and recalibrate the balance of cyber power globally. As leading nations like China, Russia, and others intensify their investments in quantum research, the potential repercussions for cybersecurity and international relations are becoming alarmingly clear.

Imagine a world where encrypted communications, long thought to be secure, could be broken in mere seconds. Today, encryption standards such as RSA or ECC rely on complex mathematical problems that would take traditional computers thousands of years to solve. Quantum computing, however, changes this equation. Using quantum algorithms like Shor’s, a sufficiently powerful quantum computer could factorize these massive numbers, effectively rendering these encryption methods obsolete.

This capability could give state actors the ability to decrypt communications, access sensitive governmental data, and breach secure systems in real time, transforming cyber espionage. Instead of months spent infiltrating networks and monitoring data flow, quantum computing could provide immediate access to critical information, bypassing traditional defenses entirely.

Nov 22, 2024

Symmetry Spotted in Statistical Mechanics

Posted by in categories: mathematics, particle physics, quantum physics

The identification of a new type of symmetry in statistical mechanics could help scientists derive and interpret fundamental relationships in this branch of physics.

Symmetry is a foundational concept in physics, describing properties that remain unchanged under transformations such as rotation and translation. Recognizing these invariances, whether intuitively or through complex mathematics, has been pivotal in developing classical mechanics, the theory of relativity, and quantum mechanics. For example, the celebrated standard model of particle physics is built on such symmetry principles. Now Matthias Schmidt and colleagues at the University of Bayreuth, Germany, have identified a new type of invariance in statistical mechanics (the theoretical framework that connects the collective behavior of particles to their microscopic interactions) [1]. With this discovery, the researchers offer a unifying perspective on subtle relationships between observable properties and provide a general approach for deriving new relations.

The concept of conserved, or time-invariant, properties has roots in ancient philosophy and was crucial to the rise of modern science in the 17th century. Energy conservation became a cornerstone of thermodynamics in the 19th century, when engineers uncovered the link between heat and work. Another important type of invariance is Galilean invariance, which states that the laws of physics are identical in all reference frames moving at a constant velocity relative to each other, resulting in specific relations between positions and velocities in different frames. Its extension, Lorentz invariance, posits that the speed of light is independent of the reference frame. Einstein’s special relativity is based on Lorentz invariance, while his general relativity broadens the idea to all coordinate transformations. These final examples illustrate that invariance not only provides relations between physical observables but can shape our understanding of space, time, and other basic concepts.

Nov 20, 2024

Nanorobots move closer to clinical trials with new model that helps them navigate through the bloodstream

Posted by in categories: biotech/medical, health, mathematics, nanotechnology, robotics/AI

From repairing deadly brain bleeds to tackling tumors with precise chemotherapy, micro/nano-robots (MNRs) are a promising, up-and-coming tool that have the power to substantially advance health care. However, this tool still has difficulty navigating within the human body—a limitation that has prevented it from entering clinical trials.

Mathematical models are crucial to the optimal design and navigation of MNRs, but the are inadequate. Now, new, promising research from the University of Saskatchewan (USask) may allow MNRs to overcome the limitations that previously prevented their widespread use.

USask College of Engineering professor Dr. Chris Zhang (Ph. D.) and two Ph.D. students (Lujia Ding, N.N Hu) along with two USask alumni (Dr. Bing Zhang (Ph. D.), Dr. R. Y. Yin (Ph. D.)) are the first team to develop a highly accurate mathematical model that optimizes the design of MNRs which improves their navigation, allowing them to travel efficiently through the bloodstream. Their work was recently published in Nature Communications.

Nov 19, 2024

Math professor could help answer physics of ice buildup on planes

Posted by in categories: information science, mathematics, physics, transportation

Team develops simulation algorithms for safer, greener, and more aerodynamic aircraft.


Ice buildup on aircraft wings and fuselage occurs when atmospheric conditions conducive to ice formation are encountered during flight, presenting a critical area of focus for their research endeavors.

Ice accumulation on an aircraft during flight poses a significant risk, potentially impairing its performance and, in severe cases, leading to catastrophic consequences.

Continue reading “Math professor could help answer physics of ice buildup on planes” »

Nov 18, 2024

How Tool Used Math to Create “Lateralus”

Posted by in categories: mathematics, media & arts

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Nov 17, 2024

Our brains are vector databases — here’s why that’s helpful when using AI

Posted by in categories: mathematics, robotics/AI

The parallels between human memory and vector databases go deeper than simple retrieval. Both excel at compression, reducing complex information into manageable patterns. Both organize information hierarchically, from specific instances to general concepts. And both excel at finding similarities and patterns that might not be obvious at first glance.

This isn’t just about professional efficiency — it’s about preparing for a fundamental shift in how we interact with information and technology. Just as literacy transformed human society, these evolved communication skills will be essential for full participation in the AI-augmented economy. But unlike previous technological revolutions that sometimes replaced human capabilities, this one is about enhancement. Vector databases and AI systems, no matter how advanced, lack the uniquely human qualities of creativity, intuition, and emotional intelligence.

The future belongs to those who understand how to think and communicate in vectors — not to replace human thinking, but to enhance it. Just as vector databases combine precise mathematical representation with intuitive pattern matching, successful professionals will blend human creativity with AI’s analytical power. This isn’t about competing with AI or simply learning new tools — it’s about evolving our fundamental communication skills to work in harmony with these new cognitive technologies.

Nov 16, 2024

Proving Darwin: Making Biology Mathematical

Posted by in categories: biological, mathematics, robotics/AI

Gregory Chaitin ‘s work will limit the capability of AI.

Nov 16, 2024

A new system of logic could boost critical thinking and AI

Posted by in categories: mathematics, robotics/AI

The rigid structures of language we once clung to with certainty are cracking. Take gender, nationality or religion: these concepts no longer sit comfortably in the stiff linguistic boxes of the last century. Simultaneously, the rise of AI presses upon us the need to understand how words relate to meaning and reasoning.

A global group of philosophers, mathematicians and have come up with a new understanding of logic that addresses these concerns, dubbed “inferentialism”

One standard intuition of logic, dating back at least to Aristotle, is that a logical consequence ought to hold by virtue of the content of the propositions involved, not simply by virtue of being “true” or “false”. Recently, the Swedish logician Dag Prawitz observed that, perhaps surprisingly, the traditional treatment of logic entirely fails to capture this intuition.

Nov 14, 2024

Mathematical approach can predict crystal structure in hours instead of months

Posted by in categories: biotech/medical, mathematics, supercomputing

Researchers at New York University have devised a mathematical approach to predict the structures of crystals—a critical step in developing many medicines and electronic devices—in a matter of hours using only a laptop, a process that previously took a supercomputer weeks or months. Their novel framework is published in the journal Nature Communications.

Nov 13, 2024

Testing AI systems on hard math problems shows they still perform very poorly

Posted by in categories: mathematics, robotics/AI

A team of AI researchers and mathematicians affiliated with several institutions in the U.S. and the U.K. has developed a math benchmark that allows scientists to test the ability of AI systems to solve exceptionally difficult math problems. Their paper is posted on the arXiv preprint server.

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