Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Forward decay — where it appears

A decay that weights each arrival by how far it sits between a fixed landmark in the past and now, which keeps a polynomial weight in a single running sum. Its memory is a share of the time since the landmark rather than a fixed span, so a counter started at boot forgets over a quarter of its uptime.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

00.2500.5000.7501010203040age of an arrival, secondsweight it carries nowexponential, half-life 4.0 sbackward polynomial, α = 2, scale 4.0 sforward, β = 2, landmark 20 s backforward, β = 2, landmark 160 s backdotted: half weightweights at the moment of reading

A decay measured from where it started

An exponentially decayed counter is one number because its weights fade by elapsed time alone. Forward decay keeps a polynomial weight in one number too, by measuring each arrival from a fixed landmark. Its memory is then a share of the time since that landmark: at β = 2 an arrival counts half at 29% of that time. Anchored at the start of a stream, it takes 5.3 seconds to register a fourfold rise twenty seconds in and 83 seconds when the rise comes at five minutes.

streaming · Decay 010200100200seconds since the burstestimated rate, arrivals a secondthe burstexponentialexact polynomialthree exponentialsrestarted forwardfaint: the same streamswith the burst removedmatched at 5.0% spread · burst of 300 in one secondthe same event, four descents

What a heavier tail actually buys

Four decays, each tuned until it is equally quiet on a stream with nothing happening, then given one burst. At a burst of three hundred they see it for 54, 63, 68 and 104 seconds — indistinguishable. At nine thousand the exact polynomial reaches 384 seconds and the exponential 156. The shape of a tail does not decide how far back a scheme can see. It decides how fast that distance grows with the size of the event, and the exchange rate is the reciprocal of the exponent.

streaming · Decay

Named alongside it

The objects these essays reach for when they reach for this one.

Design parameterEstimatorExponential decayHalf lifeHonest limitState bitsStreaming modelTimestampVarianceArrival processFalse alarmFitting

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