Resetting a stochastic process has been shown to expedite the completion time of some complex task, such as finding a target for the first time. Here we consider the cost of resetting by associating a cost to each reset, which is a function of the distance travelled during the reset event. We compute the Laplace transform of the joint probability of first passage time $t_f$, number of resets $N$ and resetting cost $C$, and use this to study the statistics of the total cost. We show that in the limit of zero resetting rate the mean cost is finite for a linear cost function, vanishes for a sub-linear cost function and diverges for a super-linear cost function. This result contrasts with the case of no resetting where the cost is always zero. For the case of an exponentially increasing cost function we show that the mean cost diverges at a finite resetting rate. We explain this by showing that the distribution of the cost has a power-law tail with continuously varying exponent that depends on the resetting rate. The dataset is related to the upcoming paper John C. Sunil, Richard A. Blythe, Martin R. Evans and Satya N. Majumdar (in submission), 'The Cost of Stochastic Resetting'.

HadUK-Grid is a collection of gridded climate variables derived from the network of UK land surface observations. The data have been interpolated from meteorological station data onto a uniform grid to provide complete and consistent coverage across the UK. The datasets cover the UK at 1 km x 1 km resolution. These 1 km x 1 km data have been used to provide a range of other resolutions and across countries, administrative regions and river basins to allow for comparison to data from UKCP18 climate projections. The dataset spans the period from 1836 to 2024, but the start time is dependent on climate variable and temporal resolution.

The gridded data are produced for daily, monthly, seasonal and annual timescales, as well as long term averages for a set of climatological reference periods. Variables include air temperature (maximum, minimum and mean), precipitation, sunshine, mean sea level pressure, wind speed, relative humidity, vapour pressure, days of snow lying, and days of ground frost.

This data set supersedes the previous versions of this dataset which also superseded UKCP09 gridded observations. Subsequent versions may be released in due course and will follow the version numbering as outlined by Hollis et al. (2019, see linked documentation).

The changes for v1.3.1.ceda HadUK-Grid datasets are as follows:

Changes to the dataset * Added data for calendar year 2024 * Extended the daily temperature grids back to 1931

Changes to the input data * Incorporated additional daily rainfall data for 60 sites in Scotland, 1922-45 * Incorporated additional monthly rainfall data for two sites - Westonbirt (1880-1951) & Ackworth School (1852-53) * Fixed a 1-day offset for sunshine duration values for six stations between 1971 and 1993 * Corrected the daily rainfall data for Macclesfield, 1958-60 (the values had been stored in the wrong units) * Improved the quality control of the most recent three months of rainfall data (Oct-Dec 2024) * Removed Corpach from the wind speed grids (the station is poorly modelled - this only affects 14 months) * Reviewed the quality control flags that had been applied automatically to historical air and grass minimum temperature data. In many cases it was possible to remove the flags and this has allowed us to incorporate additional data into the grids for 1961-1997 for these variables. * Improved the business logic relating to data completeness. This affects monthly wind speed and has allowed us to re-introduce some of the data that were excluded in the previous release.

• Net changes to the input station data:
  • Total of 131314637 observations
  • 126821432 (96.6%) unchanged
  • 105327 (0.08%) modified for this version
  • 4387878 (3.34%) added in this version
  • 44224 (0.03%) deleted from this version

The primary purpose of these data are to facilitate monitoring of UK climate and research into climate change, impacts and adaptation. The datasets have been created by the Met Office with financial support from the Department for Business, Energy and Industrial Strategy (BEIS) and Department for Environment, Food and Rural Affairs (DEFRA) in order to support the Public Weather Service Customer Group (PWSCG), the Hadley Centre Climate Programme, and the UK Climate Projections (UKCP18) project. The output from a number of data recovery activities relating to 19th and early 20th Century data have been used in the creation of this dataset, these activities were supported by: the Met Office Hadley Centre Climate Programme; the Natural Environment Research Council project "Analysis of historic drought and water scarcity in the UK"; the UK Research & Innovation (UKRI) Strategic Priorities Fund UK Climate Resilience programme; The UK Natural Environment Research Council (NERC) Public Engagement programme; the National Centre for Atmospheric Science; National Centre for Atmospheric Science and the NERC GloSAT project; and the contribution of many thousands of public volunteers. The dataset is provided under Open Government Licence.

This dataset (Table S1) contains a total of 163 single-grain analytical data of apatite (U-Th)/He (AHe) measurements from 49 of the newly collected bedrock samples. Furthermore, the data table contains weighted mean AHe ages for reset samples. Data were acquired between 2018 and 2020 at the University of Tübingen, Germany, using standard heavy mineral separation techniques to obtain apatite concentrates, a Leica binocular for apatite selection, a Patterson helium line for single-grain helium measurements, and a Thermo Fisher Scientific iCAP Qc and Agilent 7900 ICP-MS for uranium, thorium, and samarium measurements via isotope dilution inductively coupled plasma mass spectrometry.

This dataset (Table S2) contains a total of 79 single-grain analytical data of zircon (U-Th)/He (ZHe) measurements from 23 of the newly collected bedrock samples. Furthermore, the data table contains weighted mean ZHe ages for reset samples. Data were acquired between 2019 and 2021 at the University of Tübingen, Germany, using standard heavy mineral separation techniques to obtain zircon concentrates, a Leica binocular for zircon selection, a Patterson helium line for single-grain helium measurements, and a Thermo Fisher Scientific iCAP Qc and Agilent 7900 ICP-MS for uranium and thorium measurements via isotope dilution inductively coupled plasma mass spectrometry.