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Category: mathematics

Probability theorem gets quantum makeover after 250 years

How likely you think something is to happen depends on what you already believe about the circumstances. That is the simple concept behind Bayes’ rule, an approach to calculating probabilities, first proposed in 1763. Now, an international team of researchers has shown how Bayes’ rule operates in the quantum world.

“I would say it is a breakthrough in ,” said Professor Valerio Scarani, Deputy Director and Principal Investigator at the Center for Quantum Technologies, and member of the team. His co-authors on the work published on 28 August 2025 in Physical Review Letters are Assistant Professor Ge Bai at the Hong Kong University of Science and Technology in China, and Professor Francesco Buscemi at Nagoya University in Japan.

“Bayes’ rule has been helping us make smarter guesses for 250 years. Now we have taught it some quantum tricks,” said Prof Buscemi.

Scientists create realistic brain-wide connection maps through digital modeling

EPFL researchers have developed a powerful method to generate brain-wide, biologically realistic wiring maps of the mouse brain. Their approach bridges experimental data with mathematical and computational modeling to simulate how neurons connect across the entire brain.

The study is published in the journal Nature Communications.

One of neuroscience’s greatest challenges is understanding how the brain is wired. Even with modern imaging tools, it has been a challenge to create detailed maps that show how the brain’s billions of cells () connect, not just with their local “neighbors” but also to other, more distant cells in the brain.

A New Understanding of Einstein-Rosen Bridges

The formulation of quantum field theory in Minkowski spacetime, which emerges from the unification of special relativity and quantum mechanics, is based on treating time as a parameter, assuming a fixed arrow of time, and requiring that field operators commute for spacelike separations. This procedure is questioned in the context of quantum field theory in curved spacetime (QFTCS). In 1935, Einstein and Rosen (ER), in their seminal paper [1] proposed that “a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime” which involved two arrows of time. We further establish that the quantum effects at gravitational horizons aesthetically involve the physics of quantum inverted harmonic oscillators that have phase space horizons. Recently proposed direct-sum quantum theory reconciles the ER’s vision by introducing geometric superselection sectors associated with the regions of spacetime related by discrete transformations. This new understanding of the ER bridges promises a unitary description of QFTCS, along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background, which is statistically 650 times stronger than the standard scale-invariant power spectrum from the typical understanding of inflationary quantum fluctuations when compared with the posterior probabilities associated with the model given the data. We finally discuss the implications of this new understanding in combining gravity and quantum mechanics.

Gravity and quantum mechanics.

NASA Astronauts to Answer Questions from Students in Ohio

NASA astronauts Michael Fincke and Zena Cardman will connect with students in Ohio as they answer prerecorded science, technology, engineering, and mathematics (STEM) questions aboard the International Space Station.

The Earth-to-space call will begin at 10:15 a.m. EDT on Wednesday, Aug. 27, and will stream live on the agency’s Learn With NASA YouTube channel.

Media interested in covering the event must RSVP by 5 p.m., Monday, Aug. 25, to Mary Beddell at: 330−492−3500 or at [email protected].

A new perspective on how cosmological correlations change based on kinematic parameters

To study the origin and evolution of the universe, physicists rely on theories that describe the statistical relationships between different events or fields in spacetime, broadly referred to as cosmological correlations. Kinematic parameters are essentially the data that specify a cosmological correlation—the positions of particles, or the wavenumbers of cosmological fluctuations.

Changes in cosmological correlations influenced by variations in parameters can be described using so-called differential equations. These are a type of mathematical equation that connect a function (i.e., a relationship between an input and an output) to its rate of change. In physics, these equations are used extensively as they are well-suited for capturing the universe’s highly dynamic nature.

Researchers at Princeton’s Institute for Advanced Study, the Leung Center for Cosmology and Particle Astrophysics in Taipei, Caltech’s Walter Burke Institute for Theoretical Physics, the University of Chicago, and the Scuola Normale Superiore in Pisa recently introduced a new perspective to approach equations describing how cosmological correlations are affected by smooth changes in kinematic parameters.

New formula improves accuracy of particle concentration measurements in diverse samples

Researchers can use a metric called the particle number concentration (PNC) to calculate the number of particles in a sample, such as the number of marbles in a jar.

Researchers at the National Institute of Standards and Technology (NIST) have developed a new mathematical formula to calculate the concentration of particles suspended in a solution. The new approach, which yields more accurate results than current methods, can be used to deliver the correct drug dosage to patients, measure the amount of nanoplastics in , and help ensure the correct level of additives in , among other applications.

The researchers have published their findings in Analytical Chemistry.

Falling water forms beautiful fluted films

When water drains from the bottom of a vertical tube, it is followed by a thin film of liquid that can adopt complex and beautiful shapes. KAUST researchers have now studied exactly how these “fluted films” form and break up, developing a mathematical model of their behavior that could help improve the performance, safety, and efficiency of industrial processes.

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