#  12th Workshop on the CKM Unitarity Triangle
Santiago de Compostela, 18-22 September 2023
Measurement of the CP violating phase $\phi_{s}$ and $\phi_{s}^{sq\bar{q}}$ at
LHCb

Melissa Maria Cruz Torres on behalf of the LHCb collaboration
email<EMAIL_ADDRESS>Universidad Nacional Autónoma de Honduras,
Honduras

###### Abstract

Precise measurements of the $B_{s}^{0}-\overline{B}_{s}^{0}$ mixing parameters
provide a powerful test of the Standard Model, offering potential hints to new
physics. The LHCb collaboration has performed updated measurements of the
$CP$-violating phases $\phi_{s}^{c\bar{c}s}$ and $\phi_{s}^{s\bar{s}s}$, which
supersede previous results. Also, an alternative approach to determine
$\Delta\Gamma_{s}$ is presented, bringing a new tool that may help to resolve
the tension observed between measurements made in $B_{s}^{0}\to J/\psi\phi$ by
LHC experiments.

##  1 Introduction

One of the key goals of the LHCb experiment is the measurement of the
$CP$-violating phase, $\phi_{s}$, that originates from the interference of the
mixing and direct decay of $B_{s}$ mesons to $CP$ eigenstates. Within the
Standard Model $\phi_{s}$ is predicted to be equal to $-2\beta_{s}$, where
$\beta_{s}\equiv arg[-(V_{ts}V_{tb}^{*})/(V_{cs}V_{cb}^{*})]$, ignoring
subleading penguin contributions, and where $V_{ij}$ represents the Cabibbo-
Kobayashi-Maskawa matrix elements [1]. In this sense, precise measurements of
this phase enhance the potentiality to probe physics beyond the Standard Model
[2]

##  2 Measurement of $\phi_{s}$ in $B_{s}^{0}\to J/\psi K^{+}K^{-}$ decays

The study of the time-dependent $CP$ asymmetry in decays modes with
transitions of the form $b\to c\bar{c}s$ has been performed by several
experiments. It provides insights into understanding the $CP$ violation
phenomena. The world average value of the $CP$-violating phase,
$\phi_{s}^{c\bar{c}s}$, is found to be $-0.049\pm 0.019$ rad [3], which is
dominated by the LHCb results in the decay channel $B_{s}^{0}\to J/\psi
h^{+}h^{-}$ ($h=K$ or $\pi$) [4]. An update of the phase,
$\phi_{s}^{c\bar{c}s}$, as well of the physics parameters $|\lambda|$,
$\Delta\Gamma_{s}$, $\Delta\Gamma_{s}-\Gamma_{d}$ and the $B_{s}^{0}$ mass
difference $\Delta m_{s}$, have been performed using the golden channel
$B_{s}^{0}\to J/\psi K^{+}K^{-}$ in the vicinity of $\phi(1020)$, which is
reported in this talk. These results supersede the previous ones. The dataset
used includes the full data sample from 2015 to 2018, collected by the LHCb
detector corresponding to an integrated luminosity of 6 fb-1 at $\sqrt{s}$ =
13 TeV.

The analysis strategy consists in performing a flavour-tagger time-dependent
angular analysis, where four polarization states are identified, namely
$A_{0},A_{||},A_{\perp}$ for the P-wave and $A_{s}$ for the S-wave, regarding
to the polarization states of the $K^{+}K^{-}$ system. Candidates with
$K^{+}K^{-}$ invariant masses in the range [900,1050] MeV/$c^{2}$ from
$B_{s}^{0}\to J/\psi(\to\mu^{+}\mu^{-})K^{+}K^{-}$ decays are selected
following the strategy described in reference [4]. Experimental improvements
benefit the updated measurements, as to be the flavour-tagging algorithms, the
$B_{s}^{0}$ decay-time resolution model as well as in the determination of the
particle identification. A gradient-boosted decision tree (BDT) classifier is
trained separately for each year from 2016 to 2018, improving the signal to
background ratio by a factor of 50. The Cross-feed contamination due to pion
and proton misidentification is handled by appropiate particle identification
requirements and mass constraints.

The data sample is divided into 48 independent sub samples, corresponding to
six bins in the $\phi(1020)$ region, two trigger configurations and four year
of data taking. By performing a maximum likelihood fit, a total yield of about
349 000 signal decays are extracted. The fit to the invariant mass is shown in
Fig. 1.

Figure 1: Invariant mass distribution of $B_{s}^{0}\to J/\psi K^{+}K^{-}$ for
the full data sample. The projection of the maximum likelihood fit is overlaid
[6].

To determine the phase $\phi_{s}$ in $B_{s}^{0}\to J/\psi K^{+}K^{-}$, a
weighted simultaneous fit to the distributions of decay time and decay angles
(cos$\theta_{K}$, cos$\theta_{\mu}$, $\phi_{h}$) in the helicity basis is
performed in the 48 sub samples. Along with the determination of $\phi_{s}$,
the physics parameters and the polarization amplitudes
$A_{k}=|A_{k}|e^{-i\delta_{k}}$ are also determined. The sub-index, $k$, in
the latter, stands for polarization states of the $K^{+}K^{-}$ system. The
probability density function for the signal takes into consideration the
decay-time and angular efficiencies, decay-time resolution and flavour
tagging. The results from the fit are shown in Table 1 [6]. The background
subtracted data distribution with fit projections overlaid can be seen in Fig
2.

Table 1: Physics parameters results. The first uncertainty is statistical and the second systematic [6] Parameter | Result
---|---
$\phi_{s}$ [rad] |  $-$0.039 $\pm$0.022 $\pm$0.006
$|\lambda|$ |  +1.001 $\pm$0.011 $\pm$0.005
$\Gamma_{s}-\Gamma_{d}$ [ps-1] |  $-$0.0056 ${}^{\>+0.0013}_{\>-0.0015}$ $\pm$0.0014
$\Delta\Gamma_{s}$ [ps-1] |  + 0.0845$\pm$0.0044 $\pm$0.0024
$\Delta m_{s}$ [ps-1] |  17.743 $\pm$0.033 $\pm$0.009
$|A_{\perp}|^{2}$ |  + 0.2463$\pm$0.0023 $\pm$0.0024
$|A_{0}|^{2}$ |  + 0.5179$\pm$0.0017$\pm$0.0032
$\delta_{\perp}-\delta_{0}$ [rad] |  +2.903+${}^{\>+0.075}_{\>-0.074}$ $\pm$0.048
$\delta_{||}-\delta_{0}$ [rad] |  + 3.146 $\pm$0.061 $\pm$0.052

Figure 2: Background-substracted data distribution with fit projections for
decay-time and decay-angles [6].

The results are in good agreement with LHCb Run 1 [5] and 2015+2016 [4]
measurements. The obtained values for $\phi_{s}$, $\Delta\Gamma_{s}$ and
$\Gamma_{s}-\Gamma_{d}$ represent the most precise measurements to date and
are in good agreement with SM expectations. No evidence for $CP$ violation in
found. Results also show no evidence for polarization dependence of
$\phi_{s}$. Combination of all LHCb $\phi_{s}$ measurements of $B_{s}^{0}$
decays via $b\to c\bar{c}s$ is shown in Figure 3. The combined value is
$\phi_{s}=-0.031\pm 0.018$ rad.

Figure 3: $\phi_{s}$ combination for all LHCb results [4].

##  3 $CP$ violation measurements in the penguin-mediated decay
$B_{s}^{0}\to\phi\phi$

$B$ mesons decays with Flavour-Changing Neutral Current (FCNC) transitions
provides a very sensitive ground to search for new physics. One of the
benchmark channels to study at LHCb, in FCNC decays, is the penguin-dominated
process $B_{s}^{0}\to\phi\phi$ where $\phi\to K^{+}K^{-}$ as loop
contributions could reveal new sources of $CP$ violation. A time-dependent
angular analysis, using the full Run 2 dataset, is performed on this channels
to determine the $CP$-violating parameters $\phi_{s}^{s\bar{s}s}$ and
$|\lambda|$. Any deviation of their expected values, 0 or 1 respectively,
could be an indication of new physics entering in the penguin decay or the
$B_{s}^{0}$ mixing. The analysis is performed using the full Run 2 data
sample.

The $B_{s}^{0}\to\phi\phi$ candidates are selected in the [5150,5600]
MeV/$c^{2}$ mass range, yielding about 16,000 of signal events. The three
polarization states $B_{s}^{0}$ are considered, namely $A_{0},A_{||}$ and
$A_{\perp}$ and both, polarization-dependent and polarization-independent,
scenarios are evaluated. The parameters $\phi_{s,i}$ and $|\lambda_{i}|$ are
defined by the equation

$\frac{q}{p}\cdot\frac{\overline{A}_{i}}{A_{i}}=\eta_{i}|\lambda_{i}|e^{-i\phi_{s,i}},$
(3.1)

where $\eta_{i}$ is the $CP$ eigenvalue of the polarization state $i$, $q$ and
$p$ are complex numbers relating the $B_{s}^{0}$ mass eigenstates to the
flavour eigenstates. The differential decay rate is written as

$\frac{d^{4}\Gamma(t,\vec{\Omega})}{dtd\vec{\Omega}}\varpropto\sum_{k=1}^{6}h_{k}(t)f_{s}(\vec{\Omega}),$
(3.2)

where $t$ is the decay time and $\vec{\Omega}=(\theta_{1},\theta_{2},\chi$)
refer to the helicity angles of the $K^{+}$ mesons in the $\phi$ rest frame.
$\chi$ is the angle between the $\phi\to KK$ decay planes. The angular
function $f_{k}(\vec{\Omega})$ and the time-dependent function $h_{k}(t)$ are
defined as given in references [7] and [8], respectively. After applying a
maximum-likelihood fit to the distribution of $t$, $\vec{\Omega}$ and the
initial $B_{s}^{0}$ state, the polarization-independent measurements of the
$CP$-violation parameters are reported to be $\phi_{s}^{s\bar{s}s}=-0.074\pm
0.069$ rad and $|\lambda|=1.009\pm 0.030$ in combination with Run 1 results
[4]. This is the most precise measurement of $CP$ violation in
$B_{s}^{0}\to\phi\phi$ decays to date [9] as can be seen in Fig 4. The results
solely due the Run 2 data are reported to be $\phi_{s}^{s\bar{s}s}=-0.042\pm
0.075\pm 0.009$ rad and $|\lambda|=1.004\pm 0.030\pm 0.009$, where the first
uncertainty is statistical and the second systematic [9]. The total measurable
observables can be seen in Table 2. For the polarization-dependent scenario,
no dependence of the $CP$-violation parameters in the polarization states is
found.

Figure 4: Comparison of $\phi_{s}^{s\bar{s}s}$ measurements by LHCb experiment. Results presented in this work are the denoted as Run 1 + Run 2, 9 fb-1 and Run 2, 6 fb-1 [9]. The blue vertical line represent the SM prediction. Table 2: Measured observables in the polarization-independent fit for the full Run 2 dataset [9]. Parameter | Result
---|---
$\phi_{s}^{s\overline{s}s}$ [  rad ] | $-0.042\pm 0.075\pm 0.009$
$|\lambda|$ | $\;\;\;1.004\pm 0.030\pm 0.009$
$\left|A_{0}\right|^{2}$ | $\;\;\;0.384\pm 0.007\pm 0.003$
$\left|A_{\perp}\right|^{2}$ | $\;\;\;0.310\pm 0.006\pm 0.003$
$\delta_{\parallel}-\delta_{0}$ [  rad ] | $\;\;\;2.463\pm 0.029\pm 0.009$
$\delta_{\perp}-\delta_{0}$ [  rad ] | $\;\;\;2.769\pm 0.105\pm 0.011$

##  4 A measurement of $\Delta\Gamma_{s}$ from $B_{s}^{0}\to
J/\psi\eta^{{}^{\prime}}$ and $B_{s}^{0}\to J/\psi\pi^{+}\pi^{-}$ decays

As explained before, the measurement of the $B_{s}^{0}-\overline{B}_{s}^{0}$
mixing parameters offer a powerful test of the Standard Model. Particularly,
$\Delta\Gamma_{s}$ have been determined experimentally using the golden
channel $B_{s}^{0}\to J/\psi\phi$ by ATLAS [10], CMS [11] and LHCb [6]
experiments. The results are precise but in tension with each other. In this
analysis, an alternative approach to determine $\Delta\Gamma_{s}$ that follows
closely the formalism proposed in [12], is presented.

Given that $CP$-odd modes measure the heavy mass eigenstate lifetime
($\tau_{H}=1/\Gamma_{H}$) and $CP$-even modes measure the light mass
eigenstate lifetime ($\tau_{L}=1/\Gamma_{L}$), $\Delta\Gamma_{s}$ can be
determined from the decay-width difference between a $CP$-odd and a $CP$-even
$B_{s}^{0}$ state. In this study it is used the $CP$-even decay $B_{s}^{0}\to
J/\psi\eta^{{}^{\prime}}$ and the $CP$-odd decay $B_{s}^{0}\to
J/\psi\pi^{+}\pi^{-}$, where $J/\psi\to\mu^{+}\mu^{-}$ and
$\eta^{{}^{\prime}}\to\rho^{0}\gamma$.

If $CP$ violation is considered negligible the time dependent rate can be
expressed as

$\Gamma(B_{s}^{0}(t)\to f)\varpropto
e^{-\Gamma_{s}t}[\rm{cosh}(\frac{\Delta\Gamma_{s}t}{2})+\eta_{CP}\rm{sinh}(\frac{\Delta\Gamma_{s}t}{2})],$
(4.1)

where $\eta_{CP}$ is $1$ or $-1$ for $CP$-odd or $CP$-even states,
respectively. By integrating Eq. 4.1 over a time range $[t_{1},t_{2}]$, and
performing their ratio, it is obtained the following equation

$R_{i}=\frac{N_{L}}{N_{H}}\varpropto\frac{[e^{-\Gamma_{s}t(1+y)}]_{t_{1}}^{t_{2}}}{[e^{-\Gamma_{s}t(1-y)}]_{t_{1}}^{t_{2}}}\cdot\frac{(1-y)}{(1+y)},$
(4.2)

the parameter $y$ is defined to be $\Delta\Gamma_{s}/2\Gamma_{s}$ and
experimental corrections are taken into account into; $R_{i}$ is corrected by
the relative efficiency in each decay time bin as
$R_{i}=A_{i}\frac{N_{L}^{RAW}}{N_{H}^{RAW}}$. A total of 8 time bins are
chosen, whose ranges are determined using simulation samples. Similar yields
are expected in each bin and it follows the purpose of optimizing the
sensitivity of $\Delta\Gamma_{s}$. Finally, $\Delta\Gamma_{s}$ is determined
from $\chi^{2}$ minimization of the expression above (Eq.4.2), where
$\Delta\Gamma_{s}$ and a normalization factor are free parameters.

The results are presented in Table 3. The weighted average is reported to be
$\Delta\Gamma_{s}=0.087\pm 0.012\pm 0.0009$ ps-1, where the first uncertainty
is statistical and the second systematic [13]. The study was performed using
the full data sample of proton-proton collisions collected by the LHCb between
2011 and 2018 corresponding to a integrated luminosity of 9 fb-1 in the
center-of-mass energy $\sqrt{s}$ = 7, 8 and 13 TeV. The comparison of the
results by years of datasets are shown in Fig. 5.

Figure 5: Measurements of $\Delta\Gamma_{s}$ for the sets of data taking and
the weighted average. The orange band represents $1\sigma$ error [13]

.

In summary, the value obtained for $\Delta\Gamma_{s}$ is in agreement with the
HFLAV average value, $\Delta\Gamma_{s}=0.074\pm 0.006$ ps-1 [14], obtained
from time-dependent angular analyses of $B_{s}^{0}\to J/\psi\phi$, where the
initial flavour of the state is tagged. The value reported also agrees with
the HFLAV average, $\Delta\Gamma_{s}=0.083\pm 0.005$ ps-1 [14], that includes
constraints from other untagged effective lifetime measurements.
$\Delta\Gamma_{s}$ is measured for the first time using using the decay mode
$B_{S}^{0}\to J/\psi\eta^{{}^{\prime}}$ .

Table 3: $\Delta\Gamma_{s}$ results and $\chi^{2}$ probability for the four datasets [13]. Dataset |  $\Delta\Gamma_{s}$ [$\text{\,ps}^{-1}$] | P($\chi^{2}$)
---|---|---
2011$\&$12 | 0.039 $\pm$ 0.026 | 0.83
2015$\&$16 | 0.081 $\pm$ 0.022 | 0.77
2017 | 0.117 $\pm$ 0.024 | 0.57
2018 | 0.102 $\pm$ 0.021 | 0.78

## References

  * [1] Kobayashi, M. and Maskawa, T. CP-violation in the renormalizable theory of weak interaction. Prog. Theor. Phys 1973, 49(1973), 652. Cabibbo, N. Unitary symmetry and leptonic decays. Phys. Rev. Lett. 1963, 10(1963), 531. https://doi.org/10.1143/PTP.49.652 https://doi.org/10.1103/PhysRevLett.10.531
  * [2] Buras, A. J. Flavour theory. PoS EPS-HEP2009, 024 (2009); https://doi.org/10.48550/arXiv.0910.1032
  * [3] Workman, R. L. et al. Particle Data Group. Review of particle physics. Prog. Theor. Exp. Phys. 2022, 083C01 (2022); https://pdg.lbl.gov/
https://doi.org/10.1093/ptep/ptac097

  * [4] The LHCb collaboration., Aaij, R., et al. Updated measurement of time-dependent CP-violating observables in $B_{s}^{0}\to J/\psi K^{+}K^{-}$ decays. Eur. Phys. J. 2019, C79 (2019), 706. Erratum ibid. C80 (2020), 601.; https://doi.org/10.1140/epjc/s10052-019-7159-8
https://doi.org/10.1140/epjc/s10052-020-7875-0

  * [5] The LHCb collaboration., Aaij, R., et al. Precision measurement of CP violation in $B_{s}^{0}\to J/\psi K^{+}K^{-}$ decays. Phys. Rev. Lett 2015, 114 (2015), 041801; https://doi.org/10.1103/PhysRevLett.114.041801
  * [6] The LHCb collaboration., Aaij, R., et al. Improved measurement of $CP$ violation parameters in $B_{s}^{0}\to J/\psi K^{+}K^{-}$ decays in the vicinity of the $\phi(1020)$ resonance. Phys. Rev. Lett 2024, 132 (2024), 051802; https://doi.org/10.1103/PhysRevLett.132.051802
  * [7] The LHCb collaboration., Aaij, R., et al. Measurement of $CP$ violation in the $B_{s}^{0}\to\phi\phi$ decay and search for the $B_{s}^{0}\to\phi\phi$ decay. JHEP 2019, 12 (2019), 155; https://doi.org/10.1007/JHEP12(2019)155
  * [8] Pree du, T.Search for a Strange Phase in Beautiful Oscillations, PhD thesis. Vrije U., Amsterdam, 2010.
  * [9] The LHCb collaboration., Aaij, R., et al. Precision measurement of $CP$ violation in the penguin-mediated decay $B_{s}^{0}\to\phi\phi$. Phys. Rev. Lett 2023, 131 (2019), 171802; https://doi.org/10.1103/PhysRevLett.131.171802
  * [10] The ATLAS collaboration., Aad, G., et al. Measurement of the $CP$-violating phase $\phi_{s}$ in $B_{s}^{0}\to J/\psi\phi$ decays in ATLAS at 13 TeV. Eur. Phys. J. 2021, C81 (2021), 342; https://doi.org/10.1140/epjc/s10052-021-09011-0
  * [11] The CMS collaboration., Sirunyan, A. M., et al. Measurement of the $CP$-violating phase $\phi_{s}$ in $B_{s}^{0}\to J/\psi\phi\to\mu^{+}\mu^{-}K^{+}K^{-}$ channel in proton-proton collisions at $\sqrt{s}=$ 13 TeV. Phys. Lett. 2021, B816 (2021), 136188; https://doi.org/10.1016/j.physletb.2021.136188
  * [12] Fleischer, R. and Knegjens, R. Effective lifetime of $B_{s}$ decays and $B_{s}^{0}-\overline{B}_{s}^{0}$ mixing parameter. Eur. Phys. J 2011, C71 (2022), 1789; https://doi.org/10.1140/epjc/s10052-011-1832-x
  * [13] The LHCb collaboration., Aaij, R., et al. A measurement of $\Delta\Gamma_{s}$. Phys. arXiv:2310.12649; https://doi.org/10.48550/arXiv.2310.12649
  * [14] Amhis, Y. et al. Averages of b-hadron, c-hadron, and $\tau$-lepton properties as of 2021. Phys. Rev. 2023, D107 (2023), 052008; https://doi.org/10.1103/PhysRevD.107.052008


* Nguyen et al. (2019) Ngoc Thanh Nguyen, Dosam Hwang, and Edward Szczerbicki. 2019\.  Computational collective intelligence for enterprise information systems.  _Enterp. Inf. Syst._ 13, 7-8 (2019), 933–934.  https://doi.org/10.1080/17517575.2019.1640394
  * Nguyen et al. (2009) Ngoc Thanh Nguyen, Ryszard Kowalczyk, and Shyi-Ming Chen (Eds.). 2009\.  _Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems, First International Conference, ICCCI 2009, Wroclaw, Poland, October 5-7, 2009. Proceedings_. Lecture Notes in Computer Science, Vol. 5796. Springer.  https://doi.org/10.1007/978-3-642-04441-0
  * Nicola et al. (2020) Rocco De Nicola, Stefan Jähnichen, and Martin Wirsing. 2020\.  Rigorous engineering of collective adaptive systems: special section.  _Int. J. Softw. Tools Technol. Transf._ 22, 4 (2020), 389–397.  https://doi.org/10.1007/s10009-020-00565-0
  * Nielsen et al. (2015) Claus Ballegaard Nielsen, Peter Gorm Larsen, John S. Fitzgerald, Jim Woodcock, and Jan Peleska. 2015\.  Systems of Systems Engineering: Basic Concepts, Model-Based Techniques, and Research Directions.  _ACM Comput. Surv._ 48, 2 (2015), 18:1–18:41.  https://doi.org/10.1145/2794381
  * Nolfi and Floreano (1999) Stefano Nolfi and Dario Floreano. 1999.  Learning and Evolution.  _Auton. Robots_ 7, 1 (1999), 89–113.  https://doi.org/10.1023/A:1008973931182
  * Noor et al. (2019) Joseph Noor, Hsiao-Yun Tseng, Luis Garcia, and Mani B. Srivastava. 2019.  DDFlow: visualized declarative programming for heterogeneous IoT networks. In _Proceedings of the International Conference on Internet of Things Design and Implementation, IoTDI 2019, Montreal, QC, Canada, April 15-18, 2019_ , Olaf Landsiedel and Klara Nahrstedt (Eds.). ACM, 172–177.  https://doi.org/10.1145/3302505.3310079
  * Odell (2002) James Odell. 2002\.  Objects and Agents Compared.  _J. Object Technol._ 1, 1 (2002), 41–53.  https://doi.org/10.5381/jot.2002.1.1.c4
  * Oh et al. (2017) Hyondong Oh, Ataollah Ramezan Shirazi, Chaoli Sun, and Yaochu Jin. 2017.  Bio-inspired self-organising multi-robot pattern formation: A review.  _Robotics Auton. Syst._ 91 (2017), 83–100.  https://doi.org/10.1016/j.robot.2016.12.006
  * Oliehoek and Amato (2016) Frans A. Oliehoek and Christopher Amato. 2016.  _A Concise Introduction to Decentralized POMDPs_ (1st ed.).  Springer Publishing Company, Incorporated.
  * Oliver (1993) Pamela E. Oliver. 1993\.  Formal Models of Collective Action.  _Annual Review of Sociology_ 19, 1 (Aug. 1993), 271–300.  https://doi.org/10.1146/annurev.so.19.080193.001415
  * Omicini et al. (2008) Andrea Omicini, Alessandro Ricci, and Mirko Viroli. 2008\.  Artifacts in the A&A meta-model for multi-agent systems.  _Auton. Agents Multi Agent Syst._ 17, 3 (2008), 432–456.  https://doi.org/10.1007/s10458-008-9053-x
  * O’Neill and Spector (2020) Michael O’Neill and Lee Spector. 2020.  Automatic programming: The open issue?  _Genet. Program. Evolvable Mach._ 21, 1-2 (2020), 251–262.  https://doi.org/10.1007/s10710-019-09364-2
  * Peeters et al. (2021) Marieke M. M. Peeters, Jurriaan van Diggelen, Karel van den Bosch, Adelbert W. Bronkhorst, Mark A. Neerincx, Jan Maarten Schraagen, and Stephan Raaijmakers. 2021.  Hybrid collective intelligence in a human-AI society.  _AI Soc._ 36, 1 (2021), 217–238.  https://doi.org/10.1007/s00146-020-01005-y
  * Petruzzi et al. (2015) Patricio E. Petruzzi, Dídac Busquets, and Jeremy V. Pitt. 2015.  A Generic Social Capital Framework for Optimising Self-Organised Collective Action. In _2015 IEEE 9th International Conference on Self-Adaptive and Self-Organizing Systems, Cambridge, MA, USA, September 21-25, 2015_. IEEE Computer Society, 21–30.  https://doi.org/10.1109/SASO.2015.10
  * Petticrew and Roberts (2008) Mark Petticrew and Helen Roberts. 2008.  _Systematic reviews in the social sciences: A practical guide_.  John Wiley & Sons.
  * Pianini et al. (2022a) Danilo Pianini, Roberto Casadei, and Mirko Viroli. 2022a.  Self-stabilising Priority-Based Multi-Leader Election and Network Partitioning. In _2022 IEEE International Conference on Autonomic Computing and Self-Organizing Systems (ACSOS)_. IEEE.  https://doi.org/10.1109/acsos55765.2022.00026
  * Pianini et al. (2021) Danilo Pianini, Roberto Casadei, Mirko Viroli, and Antonio Natali. 2021.  Partitioned integration and coordination via the self-organising coordination regions pattern.  _Future Gener. Comput. Syst._ 114 (2021), 44–68.  https://doi.org/10.1016/j.future.2020.07.032
  * Pianini et al. (2022b) Danilo Pianini, Federico Pettinari, Roberto Casadei, and Lukas Esterle. 2022b.  A Collective Adaptive Approach to Decentralised k-Coverage in Multi-robot Systems.  _ACM Trans. Auton. Adapt. Syst._ 17 (2022), 4:1–4:39.  https://doi.org/10.1145/3547145
  * Pinciroli and Beltrame (2016) Carlo Pinciroli and Giovanni Beltrame. 2016.  Buzz: A Programming Language for Robot Swarms.  _IEEE Softw._ 33, 4 (2016), 97–100.  https://doi.org/10.1109/MS.2016.95
  * Pournaras (2020a) Evangelos Pournaras. 2020a.  Collective Learning: A 10-Year Odyssey to Human-centered Distributed Intelligence. In _IEEE International Conference on Autonomic Computing and Self-Organizing Systems, ACSOS 2020, Washington, DC, USA, August 17-21, 2020_. IEEE, 205–214.  https://doi.org/10.1109/ACSOS49614.2020.00043
  * Pournaras (2020b) Evangelos Pournaras. 2020b.  Proof of witness presence: Blockchain consensus for augmented democracy in smart cities.  _J. Parallel Distributed Comput._ 145 (2020), 160–175.  https://doi.org/10.1016/j.jpdc.2020.06.015
  * Pournaras et al. (2018) Evangelos Pournaras, Peter Pilgerstorfer, and Thomas Asikis. 2018\.  Decentralized Collective Learning for Self-managed Sharing Economies.  _ACM Trans. Auton. Adapt. Syst._ 13, 2 (2018), 10:1–10:33.  https://doi.org/10.1145/3277668
  * Prasetyo et al. (2019) Judhi Prasetyo, Giulia De Masi, and Eliseo Ferrante. 2019\.  Collective decision making in dynamic environments.  _Swarm Intell._ 13, 3-4 (2019), 217–243.  https://doi.org/10.1007/s11721-019-00169-8
  * Psaier and Dustdar (2011) Harald Psaier and Schahram Dustdar. 2011.  A survey on self-healing systems: approaches and systems.  _Computing_ 91, 1 (2011), 43–73.  https://doi.org/10.1007/s00607-010-0107-y
  * Qiu and Zhu (2022) Wenjie Qiu and He Zhu. 2022\.  Programmatic Reinforcement Learning without Oracles. In _International Conference on Learning Representations_.  https://openreview.net/forum?id=6Tk2noBdvxt
  * Quinn and Bederson (2011) Alexander J. Quinn and Benjamin B. Bederson. 2011.  Human computation: a survey and taxonomy of a growing field. In _Proceedings of the International Conference on Human Factors in Computing Systems, CHI 2011, Vancouver, BC, Canada, May 7-12, 2011_ , Desney S. Tan, Saleema Amershi, Bo Begole, Wendy A. Kellogg, and Manas Tungare (Eds.). ACM, 1403–1412.  https://doi.org/10.1145/1978942.1979148
  * Rainey and Jamshidi (2018) Larry B. Rainey and Mo Jamshidi (Eds.). 2018.  _Engineering Emergence_.  CRC Press.  https://doi.org/10.1201/9781138046412
  * Rajasekhar et al. (2017) Anguluri Rajasekhar, Nandar Lynn, Swagatam Das, and Ponnuthurai N. Suganthan. 2017.  Computing with the collective intelligence of honey bees - A survey.  _Swarm Evol. Comput._ 32 (2017), 25–48.  https://doi.org/10.1016/j.swevo.2016.06.001
  * Reeve et al. (2011) Charlie L Reeve, Silvia Bonaccio, T Chamorro-Premuzic, A Furnham, and S von Stumm. 2011\.  The nature and structure of “intelligence”.  _The Wiley-Blackwell handbook of individual differences_ (2011), 187–216.
  * Reina et al. (2015) Andreagiovanni Reina, Roman Miletitch, Marco Dorigo, and Vito Trianni. 2015.  A quantitative micro-macro link for collective decisions: the shortest path discovery/selection example.  _Swarm Intell._ 9, 2-3 (2015), 75–102.  https://doi.org/10.1007/s11721-015-0105-y
  * Ritz et al. (2021) Fabian Ritz, Thomy Phan, Robert Müller, Thomas Gabor, Andreas Sedlmeier, Marc Zeller, Jan Wieghardt, Reiner N. Schmid, Horst Sauer, Cornel Klein, and Claudia Linnhoff-Popien. 2021\.  Specification Aware Multi-Agent Reinforcement Learning. In _Agents and Artificial Intelligence - 13th International Conference, ICAART 2021, Virtual Event, February 4-6, 2021, Revised Selected Papers_ _(Lecture Notes in Computer Science)_ , Ana Paula Rocha, Luc Steels, and H. Jaap van den Herik (Eds.), Vol. 13251. Springer, 3–21.  https://doi.org/10.1007/978-3-031-10161-8_1
  * Rizk et al. (2018) Yara Rizk, Mariette Awad, and Edward W. Tunstel. 2018.  Decision Making in Multiagent Systems: A Survey.  _IEEE Trans. Cogn. Dev. Syst._ 10, 3 (2018), 514–529.  https://doi.org/10.1109/TCDS.2018.2840971
  * Rodríguez et al. (2007) Alejandro Rodríguez, Alexander Grushin, and James A. Reggia. 2007.  Swarm Intelligence Systems Using Guided Self-Organization for Collective Problem Solving.  _Adv. Complex Syst._ 10, supp01 (2007), 5–34.  https://doi.org/10.1142/S0219525907001069
  * Rossi et al. (2018) Federico Rossi, Saptarshi Bandyopadhyay, Michael T. Wolf, and Marco Pavone. 2018.  Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy.  _CoRR_ abs/1803.05464 (2018).  arXiv:1803.05464 http://arxiv.org/abs/1803.05464
  * Rostami et al. (2018) Mohammad Rostami, Soheil Kolouri, Kyungnam Kim, and Eric Eaton. 2018.  Multi-Agent Distributed Lifelong Learning for Collective Knowledge Acquisition. In _Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS 2018, Stockholm, Sweden, July 10-15, 2018_ , Elisabeth André, Sven Koenig, Mehdi Dastani, and Gita Sukthankar (Eds.). International Foundation for Autonomous Agents and Multiagent Systems Richland, SC, USA / ACM, 712–720.  http://dl.acm.org/citation.cfm?id=3237489
  * Russell and Norvig (2020) Stuart Russell and Peter Norvig. 2020.  _Artificial Intelligence: A Modern Approach (4th Edition)_.  Pearson.  http://aima.cs.berkeley.edu/
  * Salehie and Tahvildari (2009) Mazeiar Salehie and Ladan Tahvildari. 2009.  Self-adaptive software: Landscape and research challenges.  _ACM Trans. Auton. Adapt. Syst._ 4, 2 (2009), 14:1–14:42.  https://doi.org/10.1145/1516533.1516538
  * Salminen (2012) Juho Salminen. 2012\.  Collective Intelligence in Humans: A Literature Review.  _CoRR_ abs/1204.3401 (2012).  arXiv:1204.3401 http://arxiv.org/abs/1204.3401
  * Sari et al. (2019) Asli Sari, Ayse Tosun, and Gülfem Isiklar Alptekin. 2019\.  A systematic literature review on crowdsourcing in software engineering.  _J. Syst. Softw._ 153 (2019), 200–219.  https://doi.org/10.1016/j.jss.2019.04.027
  * Scekic et al. (2020) Ognjen Scekic, Tommaso Schiavinotto, Svetoslav Videnov, Michael Rovatsos, Hong Linh Truong, Daniele Miorandi, and Schahram Dustdar. 2020\.  A Programming Model for Hybrid Collaborative Adaptive Systems.  _IEEE Trans. Emerg. Top. Comput._ 8, 1 (2020), 6–19.  https://doi.org/10.1109/TETC.2017.2702578
  * Schirner et al. (2013) Gunar Schirner, Deniz Erdogmus, Kaushik R. Chowdhury, and Taskin Padir. 2013.  The Future of Human-in-the-Loop Cyber-Physical Systems.  _Computer_ 46, 1 (2013), 36–45.  https://doi.org/10.1109/MC.2013.31
  * Schmickl et al. (2006) Thomas Schmickl, Christoph Möslinger, and Karl Crailsheim. 2006\.  Collective Perception in a Robot Swarm. In _Swarm Robotics, Second International Workshop, SAB 2006, Rome, Italy, September 30-October 1, 2006, Revised Selected Papers_ _(Lecture Notes in Computer Science)_ , Erol Sahin, William M. Spears, and Alan F. T. Winfield (Eds.), Vol. 4433. Springer, 144–157.  https://doi.org/10.1007/978-3-540-71541-2_10
  * Schranz et al. (2021) Melanie Schranz, Gianni A. Di Caro, Thomas Schmickl, Wilfried Elmenreich, Farshad Arvin, Y. Ahmet Sekercioglu, and Micha Sende. 2021\.  Swarm Intelligence and cyber-physical systems: Concepts, challenges and future trends.  _Swarm Evol. Comput._ 60 (2021), 100762.  https://doi.org/10.1016/j.swevo.2020.100762
  * Schweikard and Schmid (2013) David P. Schweikard and Hans Bernhard Schmid. 2013.  Collective Intentionality.  In _The Stanford Encyclopedia of Philosophy_ (Fall 2021 ed.), Edward N. Zalta (Ed.). Metaphysics Research Lab, Stanford University.
  * Segaran (2007) Toby Segaran. 2007\.  _Programming collective intelligence: building smart web 2.0 applications_.  O’Reilly.
  * Sene Júnior et al. (2022) Iwens Gervásio Sene Júnior, Thalia S. Santana, Renato F. Bulcão-Neto, and Barry Porter. 2022\.  The state of the art of macroprogramming in IoT: An update.  _J. Internet Serv. Appl._ 13, 1 (2022), 54–65.  https://doi.org/10.5753/jisa.2022.2372
  * Shoham (1993) Yoav Shoham. 1993\.  Agent-Oriented Programming.  _Artif. Intell._ 60, 1 (1993), 51–92.  https://doi.org/10.1016/0004-3702(93)90034-9
  * Siddique and Adeli (2015) Nazmul H. Siddique and Hojjat Adeli. 2015.  Nature Inspired Computing: An Overview and Some Future Directions.  _Cogn. Comput._ 7, 6 (2015), 706–714.  https://doi.org/10.1007/s12559-015-9370-8
  * Sieben et al. (2017) Anna Sieben, Jette Schumann, and Armin Seyfried. 2017\.  Collective phenomena in crowds—Where pedestrian dynamics need social psychology.  _PLOS ONE_ 12, 6 (06 2017), 1–19.  https://doi.org/10.1371/journal.pone.0177328
  * Sigaud (2022) Olivier Sigaud. 2022\.  Combining Evolution and Deep Reinforcement Learning for Policy Search: a Survey.  _ACM Transactions on Evolutionary Learning and Optimization_ (Oct. 2022).  https://doi.org/10.1145/3569096
  * Smirnov and Ponomarev (2019) Alexander Smirnov and Andrew Ponomarev. 2019.  Decision Support Based on Human-Machine Collective Intelligence: Major Challenges. In _Internet of Things, Smart Spaces, and Next Generation Networks and Systems_. Springer International Publishing, Cham, 113–124.
  * Smith (2010) Eric Alden Smith. 2010\.  Communication and collective action: language and the evolution of human cooperation.  _Evolution and human behavior_ 31, 4 (2010), 231–245.
  * Solar-Lezama (2009) Armando Solar-Lezama. 2009\.  The Sketching Approach to Program Synthesis. In _Programming Languages and Systems, 7th Asian Symposium, APLAS 2009, Seoul, Korea, December 14-16, 2009. Proceedings_ _(Lecture Notes in Computer Science)_ , Zhenjiang Hu (Ed.), Vol. 5904. Springer, 4–13.  https://doi.org/10.1007/978-3-642-10672-9_3
  * Sotnik (2018) Garry Sotnik. 2018\.  The SOSIEL Platform: Knowledge-based, cognitive, and multi-agent.  _Biologically Inspired Cognitive Architectures_ 26 (Oct. 2018), 103–117.  https://doi.org/10.1016/j.bica.2018.09.001
  * Stein et al. (2021) Anthony Stein, Sven Tomforde, Jean Botev, and Peter R Lewis. 2021.  Lifelike Computing Systems. In _Proceedings of the Lifelike Computing Systems Workshop (LIFELIKE)_.
  * Stradner et al. (2013) Jürgen Stradner, Ronald Thenius, Payam Zahadat, Heiko Hamann, Karl Crailsheim, and Thomas Schmickl. 2013.  Algorithmic requirements for swarm intelligence in differently coupled collective systems.  _Chaos, Solitons & Fractals_ 50 (May 2013), 100–114.  https://doi.org/10.1016/j.chaos.2013.01.011
  * Sumpter (2010) David JT Sumpter. 2010\.  _Collective animal behavior_.  Princeton University Press.
  * Suran et al. (2020) Shweta Suran, Vishwajeet Pattanaik, and Dirk Draheim. 2020\.  Frameworks for Collective Intelligence: A Systematic Literature Review.  _ACM Comput. Surv._ 53, 1, Article 14 (Feb. 2020), 36 pages.  https://doi.org/10.1145/3368986
  * Surowiecki (2005) James Surowiecki. 2005\.  _The wisdom of crowds_.  Anchor.
  * Szuba (2001) Tadeusz M Szuba. 2001\.  _Computational collective intelligence_.  John Wiley & Sons, Inc.
  * Tang and Liao (2021) Ming Tang and Huchang Liao. 2021.  From conventional group decision making to large-scale group decision making: What are the challenges and how to meet them in big data era? A state-of-the-art survey.  _Omega_ 100 (April 2021), 102141.  https://doi.org/10.1016/j.omega.2019.102141
  * Telikani et al. (2022) Akbar Telikani, Amirhessam Tahmassebi, Wolfgang Banzhaf, and Amir H. Gandomi. 2022.  Evolutionary Machine Learning: A Survey.  _ACM Comput. Surv._ 54, 8 (2022), 161:1–161:35.  https://doi.org/10.1145/3467477
  * ter Beek and Sirjani (2022) Maurice H. ter Beek and Marjan Sirjani (Eds.). 2022.  _Coordination Models and Languages - 24th IFIP WG 6.1 International Conference, COORDINATION 2022, Held as Part of the 17th International Federated Conference on Distributed Computing Techniques, DisCoTec 2022, Lucca, Italy, June 13-17, 2022, Proceedings_. Lecture Notes in Computer Science, Vol. 13271. Springer.  https://doi.org/10.1007/978-3-031-08143-9
  * Trianni (2008) Vito Trianni. 2008\.  _Evolutionary Swarm Robotics - Evolving Self-Organising Behaviours in Groups of Autonomous Robots_. Studies in Computational Intelligence, Vol. 108.  Springer.  https://doi.org/10.1007/978-3-540-77612-3
  * Tsvetkova et al. (2017) Milena Tsvetkova, Taha Yasseri, Eric T. Meyer, J. Brian Pickering, Vegard Engen, Paul Walland, Marika Lüders, Asbjørn Følstad, and George Bravos. 2017\.  Understanding Human-Machine Networks: A Cross-Disciplinary Survey.  _ACM Comput. Surv._ 50, 1 (2017), 12:1–12:35.  https://doi.org/10.1145/3039868
  * Tumer and Wolpert (2004) Kagan Tumer and David H Wolpert. 2004.  A Survey of Collectives.  In _Collectives and the design of complex systems_ , Kagan Tumer and David H Wolpert (Eds.). Springer Science & Business Media, Chapter 1.
  * Valentini et al. (2017) Gabriele Valentini, Eliseo Ferrante, and Marco Dorigo. 2017\.  The Best-of-n Problem in Robot Swarms: Formalization, State of the Art, and Novel Perspectives.  _Frontiers Robotics AI_ 4 (2017), 9.  https://doi.org/10.3389/frobt.2017.00009
  * Valentini et al. (2014) Gabriele Valentini, Heiko Hamann, and Marco Dorigo. 2014\.  Self-organized collective decision making: the weighted voter model. In _International conference on Autonomous Agents and Multi-Agent Systems, AAMAS ’14, Paris, France, May 5-9, 2014_ , Ana L. C. Bazzan, Michael N. Huhns, Alessio Lomuscio, and Paul Scerri (Eds.). IFAAMAS/ACM, 45–52.  http://dl.acm.org/citation.cfm?id=2615742
  * van der Hoek and Wooldridge (2003) Wiebe van der Hoek and Michael J. Wooldridge. 2003.  Towards a Logic of Rational Agency.  _Log. J. IGPL_ 11, 2 (2003), 135–159.  https://doi.org/10.1093/jigpal/11.2.135
  * van Gerven (2017) Marcel van Gerven. 2017\.  Computational Foundations of Natural Intelligence.  _Frontiers Comput. Neurosci._ 11 (2017), 112.  https://doi.org/10.3389/fncom.2017.00112
  * Varenne et al. (2015) Franck Varenne, Pierre Chaigneau, Jean Petitot, and René Doursat. 2015.  Programming the emergence in morphogenetically architected complex systems.  _Acta biotheoretica_ 63, 3 (2015), 295–308.  https://doi.org/10.1007/s10441-015-9262-z
  * Verbraeken et al. (2020) Joost Verbraeken, Matthijs Wolting, Jonathan Katzy, Jeroen Kloppenburg, Tim Verbelen, and Jan S. Rellermeyer. 2020.  A Survey on Distributed Machine Learning.  _ACM Comput. Surv._ 53, 2 (2020), 30:1–30:33.  https://doi.org/10.1145/3377454
  * Verma et al. (2018) Abhinav Verma, Vijayaraghavan Murali, Rishabh Singh, Pushmeet Kohli, and Swarat Chaudhuri. 2018\.  Programmatically Interpretable Reinforcement Learning. In _Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, July 10-15, 2018_ _(Proceedings of Machine Learning Research)_ , Jennifer G. Dy and Andreas Krause (Eds.), Vol. 80. PMLR, 5052–5061.  http://proceedings.mlr.press/v80/verma18a.html
  * Viroli et al. (2019) Mirko Viroli, Jacob Beal, Ferruccio Damiani, Giorgio Audrito, Roberto Casadei, and Danilo Pianini. 2019\.  From distributed coordination to field calculus and aggregate computing.  _J. Log. Algebraic Methods Program._ 109 (2019).  https://doi.org/10.1016/j.jlamp.2019.100486
  * Wang (2009) Yingxu Wang. 2009\.  On Abstract Intelligence: Toward a Unifying Theory of Natural, Artificial, Machinable, and Computational Intelligence.  _Int. J. Softw. Sci. Comput. Intell._ 1, 1 (2009), 1–17.  https://doi.org/10.4018/jssci.2009010101
  * Watson et al. (2002) Richard A. Watson, Sevan G. Ficici, and Jordan B. Pollack. 2002.  Embodied Evolution: Distributing an evolutionary algorithm in a population of robots.  _Robotics Auton. Syst._ 39, 1 (2002), 1–18.  https://doi.org/10.1016/S0921-8890(02)00170-7
  * Wechsler (1946) David Wechsler. 1946\.  _The measurement of adult intelligence (3rd ed.)_.  Williams & Wilkins Co.  https://doi.org/10.1037/11329-000
  * Weiser (1991) Mark Weiser. 1991\.  The Computer for the 21 st Century.  _Scientific american_ 265, 3 (1991), 94–105.
  * Weyns and Michel (2014) Danny Weyns and Fabien Michel. 2014.  Agent Environments for Multi-agent Systems - A Research Roadmap. In _Agent Environments for Multi-Agent Systems IV - 4th International Workshop, E4MAS 2014 - 10 Years Later, Paris, France, May 6, 2014, Revised Selected and Invited Papers_ _(Lecture Notes in Computer Science)_ , Danny Weyns and Fabien Michel (Eds.), Vol. 9068. Springer, 3–21.  https://doi.org/10.1007/978-3-319-23850-0_1
  * Weyns et al. (2010) Danny Weyns, Bradley R. Schmerl, Vincenzo Grassi, Sam Malek, Raffaela Mirandola, Christian Prehofer, Jochen Wuttke, Jesper Andersson, Holger Giese, and Karl M. Göschka. 2010.  On Patterns for Decentralized Control in Self-Adaptive Systems. In _Software Engineering for Self-Adaptive Systems II - International Seminar, Dagstuhl Castle, Germany, October 24-29, 2010 Revised Selected and Invited Papers_ _(Lecture Notes in Computer Science)_ , Rogério de Lemos, Holger Giese, Hausi A. Müller, and Mary Shaw (Eds.), Vol. 7475. Springer, 76–107.  https://doi.org/10.1007/978-3-642-35813-5_4
  * Wolf and Holvoet (2004) Tom De Wolf and Tom Holvoet. 2004.  Emergence Versus Self-Organisation: Different Concepts but Promising When Combined. In _Engineering Self-Organising Systems, Methodologies and Applications_ _(Lecture Notes in Computer Science)_ , Vol. 3464. Springer, 1–15.  https://doi.org/10.1007/11494676_1
  * Wolpert (2003) David H. Wolpert. 2003\.  _Collective Intelligence_.  Wiley, Chapter 17, 245–.  https://books.google.it/books?id=IR9__G9tRk8C
  * Wood (2016) Zena Wood. 2016\.  Considering Collectives: Roles, Members and Goals.. In _FOIS_. 359–372.
  * Wood and Galton (2009) Zena Wood and Antony Galton. 2009.  A taxonomy of collective phenomena.  _Applied Ontology_ 4, 3-4 (2009), 267–292.
  * Wooldridge (2009) Michael J. Wooldridge. 2009\.  _An Introduction to MultiAgent Systems, Second Edition_.  Wiley.
  * Woolley et al. (2015) Anita Williams Woolley, Ishani Aggarwal, and Thomas W Malone. 2015\.  Collective intelligence and group performance.  _Current Directions in Psychological Science_ 24, 6 (2015), 420–424.  https://doi.org/10.1177/0963721415599543
  * Woolley et al. (2010) Anita Williams Woolley, Christopher F. Chabris, Alex Pentland, Nada Hashmi, and Thomas W. Malone. 2010\.  Evidence for a Collective Intelligence Factor in the Performance of Human Groups.  _Science_ 330, 6004 (Oct. 2010), 686–688.  https://doi.org/10.1126/science.1193147
  * Yang et al. (2019) Tao Yang, Xinlei Yi, Junfeng Wu, Ye Yuan, Di Wu, Ziyang Meng, Yiguang Hong, Hong Wang, Zongli Lin, and Karl Henrik Johansson. 2019.  A survey of distributed optimization.  _Annu. Rev. Control._ 47 (2019), 278–305.  https://doi.org/10.1016/j.arcontrol.2019.05.006
  * Yang and He (2013) Xin-She Yang and Xingshi He. 2013.  Bat algorithm: literature review and applications.  _Int. J. Bio Inspired Comput._ 5, 3 (2013), 141–149.  https://doi.org/10.1504/IJBIC.2013.055093
  * Yang et al. (2021) Yue Yang, Yang Xiao, and Tieshan Li. 2021.  A Survey of Autonomous Underwater Vehicle Formation: Performance, Formation Control, and Communication Capability.  _IEEE Commun. Surv. Tutorials_ 23, 2 (2021), 815–841.  https://doi.org/10.1109/COMST.2021.3059998
  * Yu et al. (2018) Chao Yu, Yueting Chai, and Yi Liu. 2018.  Literature review on collective intelligence: a crowd science perspective.  _International Journal of Crowd Science_ (2018).
  * Yu et al. (2021) Zhiwen Yu, Qingyang Li, Fan Yang, and Bin Guo. 2021\.  Human-machine computing.  _CCF Trans. Pervasive Comput. Interact._ 3, 1 (2021), 1–12.  https://doi.org/10.1007/s42486-020-00051-1
  * Zambonelli et al. (2015) Franco Zambonelli, Andrea Omicini, Bernhard Anzengruber, Gabriella Castelli, Francesco L. De Angelis, Giovanna Di Marzo Serugendo, Simon A. Dobson, Jose Luis Fernandez-Marquez, Alois Ferscha, Marco Mamei, Stefano Mariani, Ambra Molesini, Sara Montagna, Jussi Nieminen, Danilo Pianini, Matteo Risoldi, Alberto Rosi, Graeme Stevenson, Mirko Viroli, and Juan Ye. 2015\.  Developing pervasive multi-agent systems with nature-inspired coordination.  _Pervasive Mob. Comput._ 17 (2015), 236–252.  https://doi.org/10.1016/j.pmcj.2014.12.002
  * Zedadra et al. (2018) Ouarda Zedadra, Antonio Guerrieri, Nicolas Jouandeau, Giandomenico Spezzano, Hamid Seridi, and Giancarlo Fortino. 2018.  Swarm intelligence-based algorithms within IoT-based systems: A review.  _J. Parallel Distributed Comput._ 122 (2018), 173–187.  https://doi.org/10.1016/j.jpdc.2018.08.007
  * Zhang et al. (2019a) Hengjie Zhang, Yucheng Dong, Francisco Chiclana, and Shui Yu. 2019a.  Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design.  _Eur. J. Oper. Res._ 275, 2 (2019), 580–598.  https://doi.org/10.1016/j.ejor.2018.11.052
  * Zhang et al. (2019b) Kaiqing Zhang, Zhuoran Yang, and Tamer Basar. 2019b.  Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms.  _CoRR_ abs/1911.10635 (2019).  arXiv:1911.10635 http://arxiv.org/abs/1911.10635
  * Zhang et al. (2015) Shuzhu Zhang, Carman K. M. Lee, Hing Kai Chan, King Lun Choy, and Zhang Wu. 2015.  Swarm intelligence applied in green logistics: A literature review.  _Eng. Appl. Artif. Intell._ 37 (2015), 154–169.  https://doi.org/10.1016/j.engappai.2014.09.007
  * Zhang et al. (2020) Tianyi Zhang, London Lowmanstone, Xinyu Wang, and Elena L. Glassman. 2020.  Interactive Program Synthesis by Augmented Examples. In _UIST ’20: The 33rd Annual ACM Symposium on User Interface Software and Technology, Virtual Event, USA, October 20-23, 2020_ , Shamsi T. Iqbal, Karon E. MacLean, Fanny Chevalier, and Stefanie Mueller (Eds.). ACM, 627–648.  https://doi.org/10.1145/3379337.3415900
  * Zhen et al. (2021) Ying Zhen, Abdullah Khan, Shah Nazir, Huiqi Zhao, Abdullah Alharbi, and Sulaiman Khan. 2021\.  Crowdsourcing usage, task assignment methods, and crowdsourcing platforms: A systematic literature review.  _J. Softw. Evol. Process._ 33, 8 (2021).  https://doi.org/10.1002/smr.2368
  * Zheng et al. (2018) Lianmin Zheng, Jiacheng Yang, Han Cai, Ming Zhou, Weinan Zhang, Jun Wang, and Yong Yu. 2018.  MAgent: A Many-Agent Reinforcement Learning Platform for Artificial Collective Intelligence. In _Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2-7, 2018_ , Sheila A. McIlraith and Kilian Q. Weinberger (Eds.). AAAI Press, 8222–8223.  https://doi.org/10.1609/aaai.v32i1.11371

  *[ICT]: information and communication technology
  *[CI]: collective intelligence
  *[ACI]: artificial collective intelligence
  *[CCI]: computational collective intelligence
  *[ ACI]: artificial collective intelligence
  *[AI]: artificial intelligence
  *[HCI]: human-computer interaction
  *[ML]: machine learning
  *[IoT]: Internet of Things
  *[MASs]: multi-agent system
  *[MAS]: multi-agent system
  *[HMCI]: human-machine collective intelligence
  *[ CI]: collective intelligence
  *[SoS]: system-of-systems
  *[AC]: aggregate computing
  *[MARL]: multi-agent reinforcement learning
  *[CAS]: collective adaptive system
  *[CPS]: cyber-physical system
  *[CASs]: collective adaptive system
  *[WSNs]: wireless sensor network
  *[ CASs]: collective adaptive system
  *[CPSs]: cyber-physical system