Applied Statistics stat.AP

On April 16, 2012, Washington experienced heat no one expected. The thermometer climbed 18 degrees above normal. Sixty days earlier, Bucharest and Kyiv had weather unusual for them. The link between these events was found by an algorithm that scans pairs of cities worldwide, looking for recurring coincidences.

The Paglia River behaves like a pendulum that resists being pushed. If a sudden influx of water pours in, the river does not keep gaining strength but quickly swings back to its usual level. This behavior is called antipersistence, and it was found in a twenty-two-year record of half-hourly discharge measurements near the Italian town of Orvieto.

The barometer in the port of Papeete on Tahiti and the one in Darwin, Australia, are separated by 7,400 kilometers. When one shows high pressure, the other often shows low, and this difference, called the Southern Oscillation, drives rainfall from India to Brazil. Predicting it even a month ahead is a problem with a century-long history.

Every spring, the sky over the US Great Plains starts behaving like a giant steam boiler. Warm, moist air from the Gulf of Mexico collides with dry air from the west, and in that mix, thunderstorms are born that can rip the roof off a barn in minutes. Meteorologists have long tracked the 'fuel' for such storms, but so far they have mostly looked at average values.

Winning the lottery changes the winner's life, but for the statistics of all players it means almost nothing: the probability of winning is negligible, and the average winnings per ticket remain tiny.

In 1984, the Ethiopian sky stayed silent for months. Fields cracked, livestock died, and roads were clogged with people fleeing hunger. Droughts in this country have killed hundreds of thousands, but warning of them in advance was impossible: too many threads pull the weather in different directions. The Pacific Ocean works like an invisible conductor.

A thunderstorm front is like a rubber band stretched between two fingers. The harder you pull, the wider the strip where lightning strikes. Meteorologists have long been able to measure storm intensity at a single point, but until now they didn't understand why severe weather sometimes compresses into a compact blob and sometimes covers half a continent.

A flashlight beam in fog reaches some objects and fades before touching others. So it is with El Niño forecasts: for events in the central Pacific, the light reaches almost two years ahead, but for eastern events it gets lost in random wind gusts within six months.

A fisherman in Queensland notices that in some years snapper are harder to catch, even though the nets and boat are the same. The reason hides not in the catch itself but in the water temperature several months earlier, when the fry were just hatching. A warm current arrived not for the whole year but only for a few weeks, and that short episode decided the fate of an entire fish generation.

An interpreter at a negotiation hears not only the volume of the voice but also the shift in topic. Climatologists have long listened only to volume: the average temperature. If it rises, the planet is warming. But behind the average hide events that matter more than the trend: heat waves, cold snaps, sudden changes.

In the tropical Pacific Ocean lives a giant pendulum: warm water swings from Australia to South America and back, and each swing changes weather across the entire planet. This pendulum is called El Niño–Southern Oscillation, and its behavior resembles a capricious conductor: sometimes it waves the baton sharply, sometimes slowly, and sometimes it freezes, confusing forecasters.

A fisherman casts his net into murky water, and an hour later the catch is thrashing on the deck. That's roughly how Episcanner works: it sifts through 14 years of disease records and pulls out every fever outbreak in every one of Brazil's 5,570 municipalities. From 2010 to 2023, the net caught 18,567 dengue epidemics and 2,199 chikungunya epidemics.

The chemical composition of a sample is like a soundscape. A living forest sounds polyphonic: chirping, rustles, the hum of insects. A barren desert is just the whistle of the wind.

A camera on a tripod shoots the same landscape for decades. If you don't touch the lens, the images get hazy: the landscape changes, but the focus stays put. That's roughly how climate norms work. According to World Meteorological Organization rules, they are calculated as the average over the last 30 years.

Old weather records hold surprises: the thermometer suddenly jumps by half a degree, not because of the weather, but because the station switched instruments. Such abrupt shifts in data are called changepoints, and separating them from genuine climate signals is a challenge statisticians grapple with.

Glowing spots on a dark background: that's what single-molecule images from MINFLUX look like. This microscope can reveal details smaller than five nanometers: roughly ten thousand times thinner than a human hair.

Cancer cells are like broken cars: one glitch makes them drive without stopping. In the KRAS gene, such glitches happen most often. But glitches come in different flavors: the wrong amino acid can sit in one spot of the protein, and that determines how the tumor behaves. In the new study, two such glitches were compared: G12C and G12D.

When you stir tea with a spoon, you see large whirlpools gradually break into smaller and smaller ones until the motion subsides. Physicists call this process decaying turbulence. There are two important moments: the peak of the smallest vortices (they are numerous and spin fast) and the peak of energy loss due to friction, when the fluid is most strongly decelerated.

An electrocardiogram is like a recording of an engine's hum: an experienced mechanic can hear when something's off. A heart ultrasound shows the engine itself from the inside, but the machine is pricey and specialists are scarce.

A comet hurtling through space is a mountain of ice and dust that carries itself across the Solar System. If you mount small engines on such a mountain, it becomes a ship with its own fuel: gas from the interior can be vented through nozzles to change course.

A barometer on Tahiti and one in Darwin, Australia, breathe in opposite phases. When pressure rises on one, it falls on the other, and this difference, known as the Southern Oscillation Index, serves as a pendulum for the global climate.

The Sun pulses in a slow rhythm, and that rhythm can be heard in the rains over Brazil. Sunspots on the solar disk thicken and thin roughly every eleven years, and along with them, pressure in the Pacific Ocean shifts, sea surface temperatures change, and then rainfall amounts in the northeast of the country follow suit.

Brain aging is like the wear and tear on a bridge: cracks appear unnoticed, but if you reinforce the supports in time, the structure lasts longer. Three ordinary things turned out to be such supports — handgrip strength, the ability to move for a long time without breathlessness, and lung capacity.

An orchestra without a conductor. Each musician plays their own part, and the overall volume builds, but the melody falls apart — violins rush ahead, brass lags behind. Cells behave much the same way when their DNA is modified: they may shift, but some move far, while others stay put.

Your hand rests on the table, and two short vibrations arrive at your wrist — one after the other. You need to say which is stronger. The task seems simple, but the answer depends on which vibration came first. If the first is weak and the second is strong, the difference feels larger than when they are swapped.

A rice field by the sea may look green, but the stalks are stunted and the grains are shriveled. Salt has silently poisoned the soil. In Satkhira district in southern Bangladesh, every farmer knows this scene. Salty water comes in with the tides, seeps into the ground, and the land stops yielding. To fight the problem, you first need to know where the salt is hiding beneath the roots.

The hunt for life on distant planets is like diagnosing a rare disease with a test of unknown accuracy. A single positive result means nothing: maybe it's a glitch? We search the atmospheres of exoplanets (worlds around other stars) for traces of water and other compounds, but any signal could be a false alarm.

A spectrum is like a photograph of a material's inner workings, taken with light. When a beam passes through or reflects off a sample, molecules leave characteristic dark bands, peaks, on that photograph. But if the image is overexposed or veiled in gray, making out details becomes nearly impossible.

A candle flame in a draft dances: now it flares up, now it almost goes out. Quasars behave much the same way — supermassive black holes in the centers of distant galaxies, surrounded by a scorching disk of infalling matter. Only they flicker not over seconds, but over months and years.

When you're planning a renovation, you don't buy paint by eye: you measure the wall area. In science, deciding how many samples to collect is a similar guess, but the stakes are higher. Skimp on samples, and your study becomes a lottery: you might miss a real effect, or you might mistake noise for a discovery. Overshoot, and you're wasting tubes, months, and, in animal experiments, lives.

The heart doesn't beat like a metronome: its rhythm dances to the time of day. Each of us has a moment when our pulse hits its peak. This peak is like the hand of an internal clock, and it shifts from person to person. But what moves that hand? Researchers gave people smartwatches and tracked them for nearly a month.

Every week, doctors ask AI assistants millions of questions at the bedside. But these tools are usually tested on exam-style problems, not on what clinicians actually ask in practice. A team of researchers set out to fix that. They collected 620 real questions from physicians across 30 specialties — from cardiology to oncology.

At a weather station in Brazos County, Texas, rain is recorded on magnetic tape: every day, four years straight. Nine hundred millimeters in a good season, a hundred in a bad one. Then the tape falls silent. Drought creeps in without a sound — the slow fading of the earth's pulse. The standard SPI-3 index only catches on a month or two later, once the moisture is already gone.

Look into the night sky — before you is not a scattering of lights, but a multi-layered manuscript. Under the bright ink of stars and galaxies appears a faded, almost erased text.

When a pipe bursts in the basement, a plumber acts step by step: locates the leak, measures the pressure, determines the cause, patches it up, and checks if it's dry. The same recipe — the standard model DMAIC — is being proposed against epidemics. First, they determine the scope — how many hospital beds are occupied, which industries are sagging.

Each year is a new page. From ages 9 to 13, a child's life changes rapidly, and so do their inner experiences. A team of researchers took data from the large ABCD Study survey, in which 11,864 adolescents reported over several consecutive years on their thoughts and actions — whether they had thoughts of suicide, whether they engaged in actions, and whether they harmed themselves without such thoughts.

Two photographers shoot the same mountain. One takes a hundred shots from the summit and only a couple from the base; the other does the opposite. If you try to align their images, the algorithm might decide that the summit in one photo matches the summit in the other simply because there are many similar points there, not because it's the same spot. Sampling density throws it off.

Every printed part is a lottery ticket. The prize in this lottery is not money but fatigue life: how many load cycles the metal can withstand before a crack initiates. The ticket number is set by the random arrangement of grains and pores that arise during laser powder bed fusion.