Where does renewal collide?

A renewal process is a model of events that recur over time, where the gaps between successive events are independent of one another and drawn from one fixed probability distribution: it generalises the Poisson process, in which those gaps are exponential. Feller's 1941 On the integral equation of renewal theory fixed the term and derived the equation that governs the expected number of events by a given time, and Smith's 1958 Renewal theory and its ramifications consolidated the field. The referent is a mathematical counting process defined by a distribution of waiting times, not the rebuilding of a city district or the ongoing replacement of cells in living tissue.[1][2]

Unit

One renewal is a single recurrence of the event, with the time since the last one drawn from a fixed distribution

Recovery means

At each event the process starts afresh, so its future behaviour depends only on the fixed gap distribution and not on its past

Measured by

Estimated from observed times between events by fitting the gap distribution and computing the renewal function

Urban renewal is the publicly led clearance and redevelopment of parts of a city judged to be run down, replacing existing buildings with new housing, commercial, or public uses. Colean's 1953 book Renewing our cities introduced the term as a program of continuous rebuilding, and Anderson's 1964 The federal bulldozer analysed the United States renewal programs carried out between 1949 and 1962. The referent is a policy and physical process applied to urban land and buildings, distinct from a recurring mathematical process or the turnover of cells in a body.[3][4]

Unit

One renewal project is a single designated area cleared and redeveloped under a public program

Recovery means

Not applicable

Measured by

Tracked by land area cleared, dwelling units demolished and built, and public funds spent per project

In biology, renewal is the ongoing replacement of cells in a tissue, where dividing cells produce new cells that mature and take the place of those lost to normal turnover. Leblond and Walker's 1956 review Renewal of cell populations classified tissues by how their cells are renewed, and Weissman's 2000 Stem cells article framed self-renewal, a stem cell's capacity to divide and yield another stem cell, as central to that replacement. The referent is a continuous biological turnover within living tissue, and it is not a mathematical counting process or the redevelopment of a city.[5][6]

Unit

One renewal event is a single cell division that replaces a lost or aging cell

Recovery means

The tissue keeps its size and function as newly formed cells replace those shed or destroyed

Measured by

Quantified by cell turnover rate, labelling of dividing cells, and tracking of stem cell division