random network

Imagine a large orchestra without a conductor. Each musician hears everyone else and adjusts to the collective hum. If every instrument amplifies its neighbors, the sound builds to a screech; if some occasionally dampen it, the orchestra may fall into silence or break into cacophony.

Picture a flock of birds gathering around a feeder that no one built. Each bird searches for food on its own, yet they all end up together. Usually, such behavior is explained by social instinct: birds want to be near their kin. But what if the flock is simply a side effect of greed?

In a nine-story building with a thousand rooms on each floor, some people whisper and others shout. Neighbors pass the message along, but if everyone speaks too softly, the message fades by the third floor. If too loudly, by the top floor it becomes an unintelligible roar. Between these extremes, there is a regime where a whisper makes it all the way through without distortion.

In a pot of water, microscopic spheres, colloidal particles, are floating. Each sphere is coated with long polymer chains that look like a brush and carries an electric charge. If you get the temperature and solution composition right, the spheres start arranging themselves into ordered patterns — crystals.

A cookbook without a shopping list: that's what a scientist faces when looking at a scheme of chemical reactions. The arrows and formulas on paper look neat, but once you start hunting in the lab for molecules that will actually behave that way, a real quest begins.

Holding in mind the exact position of a pen as it's slowly moved is a routine task for the brain. For artificial neural networks, it's nearly impossible. Standard recurrent networks like GRU and LSTM tend to break continuous motion into rigid steps: the pen doesn't glide smoothly but jumps from point to point.

The human mind is like a construction set that builds itself. New ideas don't die with their creators: they are passed on, mixed, and selected. This process is called cultural evolution: useful inventions stick, useless ones are forgotten. That's how a ratchet works — a mechanism that only turns forward. But what exactly happens in the head when one thought displaces another?

A neuron receives thousands of signals on its branching processes — the dendrites. Some signals push the cell toward firing (excitation), others hold it back (inhibition). For a long time, it was thought that the neuron simply adds up all the 'fors' and 'againsts.' But in real dendrites, inhibition works differently: it can not subtract but divide the excitatory signal.

A cloud of atoms cooled to near absolute zero suddenly starts behaving like a brain. One excited atom triggers a chain reaction — neighbors light up in turn, and an avalanche of activity sweeps through the gas. Physicists call this Rydberg facilitation: atoms are easier to excite when an excited one is nearby.

A city at night: lights on in some windows, dark in others. If you connect with lines the windows that light up simultaneously, you get a web of connections. Researchers studied such a web in tiny brain organoids — living clusters of nerve cells grown in the lab.

The optical sky background is a cosmic palimpsest, where light from billions of unresolved galaxies is layered, each layer corresponding to a different epoch. Until now we could only distinguish the brightest "letters"—individual stars and nearby galaxies.

Communicating with a satellite is like trying to hear a whisper in a storm: the signal drowns in noise. Engineers have created an AI algorithm that runs directly on the satellite and, with minimal power consumption, detects distortions more accurately than previous methods.

In boiling soup, molecules collide chaotically and react. But if you measure how their concentrations change, patterns emerge. This is how carbon chemical networks work — mixtures of molecules that spontaneously 'cook' information, turning each reaction into an elementary computation. Previously they were used only for modeling nature.

After a stone is thrown, the circles on water vanish, but the liquid retains microscopic oscillations. The slightest gust, and ripples appear again. Neural networks behave similarly. When electrical signals quiet down, the memory of them remains in the contact points — synapses.

In a kitchen with gas burners, each heats differently. If the cook moves the pots, food may burn. Just so in a wireless network: the antenna-burners and user-pots require precise placement. Ordinary neural networks don’t distinguish positions, treating all burners as identical. So they struggle to estimate signal quality or adjust transmission.

Evolution resembles not just a tree with diverging branches, but a woven tapestry. Threads of ancestry cross when species exchange genes — for example, bacteria pass drug resistance to each other, and plants crossbreed to produce hybrids.

A snowflake grows, an oil slick spreads, a crowd moves — each case has its own equations. But the end result is often the same: shape, speed, and pattern follow a simple scheme that repeats across scales. This is universality — when a common law hides behind the details.

Back in 1967, Jocelyn Bell Burnell caught the first 'voice' of a neutron star — the strict pulse of a pulsar.

A tiny dust particle in a supersaturated solution sprouts into a large crystal in seconds. Neighboring particles remain invisible. A similar process was recently discovered in communities of language agents.

A handful of sand falls onto a table: each grain rolls down until it rests in a hollow. That's how a potential works: the table's surface tells the grains where to go. But in a river with whirlpools, there's no single basin everything flows into. Water swirls, returns, and meanders. For such systems, the usual map of 'pits and hills' doesn't apply.

A neural network, like a sheet of graph paper, receives homogeneous signals at its input, and draws its own coordinate grid. Initially, connections between inputs and network cells form a gentle hill: the response is strongest at the center and fades toward the edges.

Population growth from a distance looks like a train picking up speed: it crawls at first, then gains momentum. But look closely at the data, and the picture blurs. One measurement shows a dozen individuals, another a hundred. Classical models wipe away this scatter like annoying smudges on a lens. They assume the noise is uniform and simply ignore it.

Picking out a single faulty microchip from a million, without any clue what the fault looks like, is a classic needle-in-a-haystack problem. A classical computer would test each chip one by one.

A city is a living system: it consumes resources, produces waste, and its 'circulatory system'—the road network — delivers people and goods to their destinations. But while engineers design transport arteries as rigid geometry of straight lines, nature has spent millions of years perfecting ideal distribution networks.

An orchestra at its first rehearsal without a conductor. Violins come in at the wrong time, brass is late, and instead of a symphony, you get cacophony. That's roughly how a computer model of the brain behaves when you remove special cells — von Economo neurons.

You can feel an unfamiliar object along its length, across its width, or diagonally: each time gaining new information. But what if one way of feeling tells you absolutely nothing about what another would reveal? That's exactly how mutually unbiased bases work in quantum mechanics: measuring in one of them leaves you completely in the dark about the outcome in another.

After a game of Scrabble, the board looks like a mosaic: tiles are scattered but form a connected pattern — islands of words in a sea of empty cells. Such a pattern can be described mathematically, but usually that requires complex rules.

Three people sit in three corners of a room. Each receives a sealed envelope from an invisible courier, but the couriers do not coordinate and have never met. The people open the envelopes and see a note with one word: "yes" or "no." They choose nothing themselves: they just read.

The brain constantly juggles tasks: it reacts to a sharp sound, solves an equation, or drifts into daydreams. Scientists have long suspected that switches between different "scenarios" of neural network activity underlie this, but extracting them from the chaos of electrical signals was difficult.

Two runners on the same track. One starts halfway down the course, the other from the starting line. Who's faster? The answer is obvious, but in brain science, such a trick went unnoticed for a long time. Neural networks that replicate the connections of a real fruit fly brain were considered better learners than random networks.

A laser that usually produces a steady beam starts to tremble near its threshold, like a string about to sound. This trembling is not a defect but quantum noise: atoms inside the laser emit light randomly, without any external cause.

Neurons in the brain and nodes in artificial neural networks don't just fire with simple yes/no signals; they also handle smoothly varying quantities, like where an object is and how big it is. But neural responses are finicky: the same stimulus triggers slightly different bursts of activity each time.

A mouse brain contains about 70 million neurons, and the connections between them are far from evenly distributed: some cells have only a couple of dozen contacts, while others have thousands. It's like a city with quiet alleys and bustling squares. But until now, it was unclear how this unevenness affects the brain's actual function.

The brain isn't one big computer: it's more like an orchestra, where different groups of musicians play their parts. Neural networks for memory, attention, or emotions are constantly talking to each other. In Alzheimer's disease, this orchestra starts to go off-key: some groups fall silent, others play out of sync.

Turbulent water flowing through a pipe and the swing of a pendulum may seem worlds apart. But they share something fundamental: both follow their own laws of motion, which can be described by numbers. A neural network trained on just one such 'dance of numbers' suddenly starts to understand another — without a single extra example.

A neural network can be compared to a dormitory where each resident gets their own room. Usually, each feature in the data occupies a separate neuron, and learning proceeds sequentially: first one feature, then another. This is slow and depends on which data you happen to get. But if you allow several features to share a room, overlap them, the picture changes.

Proteins in a cell communicate like people in a bustling city: some pass signals, others put on the brakes, and still others just hang around. A graph neural network sees the map of these connections, who's linked to whom, but to it, they're just lines.

A photo taken through frosted glass always comes out blurry. As light passes through a sample, it scatters, and the camera sees only a smudge instead of a sharp image. Scientists have long known how to recover an image from such a smudge, but old methods are finicky: they either get stuck on a wrong solution or require too many exposures, bombarding the fragile sample.

On a table lies a handful of round magnets. As long as no one touches them, they lie in disarray. But send a short current pulse through them, and each disk flips: the north pole swaps with the south. Neighboring disks push each other with their fields, like people in a crowded queue, and the whole handful arranges into a pattern that depends on which way the magnetic wind blew and how warm it is around.

A group of people searches for a lost item in a large park. Some get tired and leave, others join along the way. The number of searchers is constantly changing. How does this affect the search time? Until now, science had no clear answer. In a new study, a general model of such a process has been built. In it, independent participants randomly enter and leave the search.