Open Access
Table D.1
List of commonly used symbols.
| Symbol | Description | Reference |
|---|---|---|
| λjk | interaction rate between entities j and k | Eq. (2) |
| λent(q, q′, δ) | entity interaction rate function | Eq. (2); Eq. (16) (RPMC method) |
| λj | cumulative interaction rate of entity j | Eq. (5) |
| λ | global rate of interactions | Eq. (6) |
 |
upper bound for interaction rate between buckets J and K | Eqs. (45–46) |
 |
upper bound of cumulative interaction rate for bucket J | Eq. (47) |
| λ+ | upper bound of global cumulative interaction rate | Eq. (48) |
 |
locality-aware upper bound of global cumulative interaction rate | Eq. (101) |
| v = #ℬ | number of occupied (non-empty) buckets | Eq. (41) |
| vJ | number of sub-buckets in bucket J | Sect. 5.4 |
| θx | bucket density with regard to entity property x | Eq. (36); Eqs. (42) and (43) (test kernels); Eq. (126) (Ormel’s model) |
| Bj | label of bucket currently associated with entity j | Eq. (36) |
| ℬ | set of labels of occupied (non-empty) buckets | Eq. (40) |
| B(q) | bucketing criterion | Eq. (36); Eqs. (42) and (43) (test kernels); Eq. (126) (Ormel’s model) |
| C(q) | regime classifier (RPMC method) | Eq. (44) |
| djk = d(qj, qk) | interaction distance between entities j and k | Eqs. (104), (B.8) |
| ℐ = {1,…, n} | set of all entity indices | Eq. (7) |
| ℐJ | set of entity indices in bucket J | Eq. (37) |
| lj = l(qj) | location of entity j | Sect. 5.2; Eqs. (103), (B.3) |
| ℳ | total mass (RPMC method) | Sect. 4 |
| Mk | total mass of swarm k (RPMC method) | Sect. 4 |
| mk | mass of representative particle k (RPMC method) | Sect. 4 |
| n | number of entities | Sect. 2.2 |
| nJ = #ℐJ | number of entities in bucket J | Eq. (38) |
 |
maximal number of entity pairs in buckets J, K which could possibly interact | Eqs. (101), (118) |
| Neff (q, q′, δ) | effective swarm particle count (RPMC method) | Eq. (15) |
| Nth | particle regime threshold | Sect. 1 |
| Nk | number of particles in swarm k (RPMC method) | Sect. 4 |
| Paccept = λ/λ+ | probability of acceptance of sampled event | Eq. (32) |
| Pjk = λjk/λ+ | probability of interaction between entities j and k occurring at time t + ∆t | Eq. (35) |
 |
probability of acceptance of event sampled for entities j, k from buckets J, K | Eq. (52) |
| qj ∈ ℚ | vector of properties of entity j | Sect. 2 |
| QJ | vector of property bound intervals of bucket J | Sect. 3.4; Eq. (85) |
| Rjk = R(qj, qk) | interaction radius between entities j and k | Eq. (98) |
| Rmin | smallest resolved length scale | Sect. 5 |
| sj = sJ(lj) | sub-bucket index of entity j in bucket J | Eq. (110) |
| t | current time | Sect. 3.1 |
| ∆t | event interarrival time | Eq. (4) |
| T | timescale on which changes inflicted by external operators must be considered | Sect. 3.1 |
 |
widening functions | Sect. 4.5 |
| wJ | sub-bucket width in bucket J | Eq. (108) |
| [x], [v], [𝒮] | abbreviated interval notation | Appendix A |
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.