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Category: mathematics

What Is Superposition and Why Is It Important?

Imagine touching the surface of a pond at two different points at the same time. Waves would spread outward from each point, eventually overlapping to form a more complex pattern. This is a superposition of waves. Similarly, in quantum science, objects such as electrons and photons have wavelike properties that can combine and become what is called superposed.

While waves on the surface of a pond are formed by the movement of water, quantum waves are mathematical. They are expressed as equations that describe the probabilities of an object existing in a given state or having a particular property. The equations might provide information on the probability of an electron moving at a specific speed or residing in a certain location. When an electron is in superposition, its different states can be thought of as separate outcomes, each with a particular probability of being observed. An electron might be said to be in a superposition of two different velocities or in two places at once. Understanding superposition may help to advance quantum technology such as quantum computers.

One of the fundamental principles of quantum mechanics, superposition explains how a quantum state can be represented as the sum of two or more states.

Physicists demonstrate controlled expansion of quantum wavepacket in a levitated nanoparticle

Quantum mechanics theory predicts that, in addition to exhibiting particle-like behavior, particles of all sizes can also have wave-like properties. These properties can be represented using the wave function, a mathematical description of quantum systems that delineates a particle’s movements and the probability that it is in a specific position.

Fat microscopy to image lipids in cells

Lipid molecules, or fats, are crucial to all forms of life. Cells need lipids to build membranes, separate and organize biochemical reactions, store energy, and transmit information. Every cell can create thousands of different lipids, and when they are out of balance, metabolic and neurodegenerative diseases can arise. It is still not well understood how cells sort different types of lipids between cell organelles to maintain the composition of each membrane. A major reason is that lipids are difficult to study, since microscopy techniques to precisely trace their location inside cells have so far been missing.

The researchers developed a method that enables visualizing lipids in cells using standard fluorescence microscopy. After the first successful proof of concept, the authors brought mass-spectrometry expert on board to study how lipids are transported between cellular organelles.

“We started our project with synthesizing a set of minimally modified lipids that represent the main lipids present in organelle membranes. These modified lipids are essentially the same as their native counterparts, with just a few different atoms that allowed us to track them under the microscope,” explains a PhD student in the group.

The modified lipids mimic natural lipids and are “bifunctional,” which means they can be activated by UV light, causing the lipid to bind or crosslink with nearby proteins. The modified lipids were loaded in the membrane of living cells and, over time, transported into the membranes of organelles. The researchers worked with human cells in cell culture, such as bone or intestinal cells, as they are ideal for imaging.

“After the treatment with UV light, we were able to monitor the lipids with fluorescence microscopy and capture their location over time. This gave us a comprehensive picture of lipid exchange between cell membrane and organelle membranes,” concludes the author.

In order to understand the microscopy data, the team needed a custom image analysis pipeline. “To address our specific needs, I developed an image analysis pipeline with automated image segmentation assisted by artificial intelligence to quantify the lipid flow through the cellular organelle system,” says another author.

By combining the image analysis with mathematical modeling, the research team discovered that between 85% and 95% of the lipid transport between the membranes of cell organelles is organized by carrier proteins that move the lipids, rather than by vesicles. This non-vesicular transport is much more specific with regard to individual lipid species and their sorting to the different organelles in the cell. The researchers also found that the lipid transport by proteins is ten times faster than by vesicles. These results imply that the lipid compositions of organelle membranes are primarily maintained through fast, species-specific, non-vesicular lipid transport.

Continue reading “Fat microscopy to image lipids in cells” | >

Srinivasa Ramanujan

Srinivasa Ramanujan Aiyangar [ a ] FRS (22 December 1887 – 26 April 1920) was an Indian mathematician. He is widely regarded as one of the greatest mathematicians of all time, despite having almost no formal training in pure mathematics. He made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.

Ramanujan initially developed his own mathematical research in isolation. According to Hans Eysenck, “he tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered”. [ 4 ] Seeking mathematicians who could better understand his work, in 1913 he began a mail correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognising Ramanujan’s work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that “defeated me completely; I had never seen anything in the least like them before”, [ 5 ] and some recently proven but highly advanced results.

During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). [ 6 ] Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired further research. [ 7 ] Of his thousands of results, most have been proven correct. [ 8 ] The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan, [ 9 ] and his notebooks—containing summaries of his published and unpublished results—have been analysed and studied for decades since his death as a source of new mathematical ideas.

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.

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