#  Prediction of sunspot and plage coverage for Solar Cycle 25

Valentina Penza Dipartimento di Fisica, Università di Roma Tor Vergata, Via
della Ricerca Scientifica 1, Roma, 00133, Italy  Francesco Berrilli
Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca
Scientifica 1, Roma, 00133, Italy  Luca Bertello National Solar Observatory,
3665 Discovery Dr., Boulder, CO 80303, USA  Matteo Cantoresi Dipartimento di
Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma,
00133, Italy  Serena Criscuoli National Solar Observatory, 3665 Discovery Dr.,
Boulder, CO 80303, USA

###### Abstract

Solar variability occurs over a broad range of spatial and temporal scales,
from the Sun’s brightening over its lifetime to the fluctuations commonly
associated with magnetic activity over minutes to years. The latter activity
includes most prominently the 11-year sunspot solar cycle and its modulations.
Space weather events, in the form of solar flares, solar energetic particles,
coronal mass ejections, and geomagnetic storms, have long been known to
approximately follow the solar cycle occurring more frequently at solar
maximum than solar minimum. These events can significantly impact our advanced
technologies and critical infrastructures, making the prediction for the
strength of future solar cycles particularly important.

Several methods have been proposed to predict the strength of the next solar
cycle, cycle 25, with results that are generally not always consistent. Most
of these methods are based on the international sunspot number time series, or
other indicators of solar activity. We present here a new approach that uses
more than 100 years of measured fractional areas of the visible solar disk
covered by sunspots and plages and an empirical relationship for each of these
two indices of solar activity in even-odd cycles. We anticipate that cycle 25
will peak in 2024 and will last for about 12 years, slightly longer than cycle
24. We also found that, in terms of sunspot and plage areas coverage, the
amplitude of cycle 25 will be substantially similar or slightly higher than
cycle 24.

Sun: activity - Sun: faculae, plages - Sun: sunspots

##  1 Introduction

The variability of the Sun’s magnetic activity is the main forcing that drives
change in the near-Earth space environment, the heliosphere, and the
interplanetary medium. This variability is characterized by a large number of
phenomena that act over a wide range of temporal scales, from minutes to
centuries. A particularly important class of short-lived phenomena, up to a
few days, includes events such as solar flares and coronal mass ejections that
are responsible for the space weather. These events have a significant impact
on the functionality of satellites, communication networks, electric power
grid and technological infrastructures (e.g. Schwenn, 2006; Plainaki et al.,
2020). Instead, solar activity over longer time-scales modifies the so-called
space climate (Versteegh, 2005) that contributes to determine the conditions
of the Earth’s upper and lower atmosphere and the Earth’s climate (e.g. Bordi
et al., 2015; Matthes et al., 2017; Bigazzi et al., 2020; Lockwood & Ball,
2020) and the cosmic ray fluxes in the interplanetary space and at Earth (e.g.
Usoskin et al., 2002; Berrilli et al., 2014; Fiandrini et al., 2021).
Similarly, stellar irradiance and its variations affect exoplanets’
atmospheres and their habitability (e.g. Meadows & Barnes, 2018; Galuzzo et
al., 2021). The most evident modulation of the large-scale solar magnetic
field is its 11-year cycle, during which the Sun increases and weakens its
magnetic activity, associated with a reversal of the dominant polarities in
the polar regions. This cycle is accompanied by variations in phase of the
appearance of magnetic structures on the solar surface, such as sunspots and
plages. The dark sunspots produce a luminosity defect, while the bright plages
overcompensate with an excess (e.g. Foukal & Lean, 1988). The final result is
that the total solar irradiance varies by about $0.1\%$, in phase with the
magnetic activity (e.g. Wilson, 1978; Hudson, 1988; Kopp et al., 2016). The
strength of the different cycles is not constant, and can vary quite
significantly as indicated by the presence of grand minima periods (e.g.
Vecchio et al., 2017) such as the Maunder minimum during the years of 1645 to
1715 (e.g. Hathaway, 2015).
The capability to predict the behavior of the solar activity has become of
paramount relevance, given its enormous impact on human activities on Earth
and in space. Providing a detailed description of the literature regarding the
prediction of the next 25th solar cycle (hereafter SC25) is beyond the scope
of this paper. We therefore refer to the review of solar cycle prediction
methods, with particular focus on forecasts for SC25, given in Petrovay
(2020). The various forecasts differ in the adopted methodology (e.g., surface
flux transport models, identification of particular “termination” events,
Shannon entropy estimates, machine learning regression methods, etc.) and in
the physical observable on which the prediction is based. In particular, the
methods typically fall into three categories: precursor, model-based and
extrapolation methods. For the prediction of SC25 different studies have been
published that use the sunspot number (e.g. McIntosh et al., 2020; Singh et
al., 2021), the geomagnetic activity indices (e.g. Singh et al., 2021), the
flare number (e.g. Janssens, 2021) and the solar magnetic flux or dipole
momentum (e.g. Cameron et al., 2016; Bhowmik & Nandy, 2018; Upton & Hathaway,
2018; Labonville et al., 2019).
The aim of this work is to estimate the coverage of sunspot and plage areas
during the next SC25. We use an appropriate functional form for solar cycles
derived from the correlation between cycles for the period 1874-2019. This
approach has two important aspects: First, it is based on the observed
characteristics of the cycles and does not use sophisticated physical models
which unfortunately suffer from the difficulties connected to the complex
physical processes involved and to the inherent dynamical complexity of the
solar cycle (e.g. Bushby & Mason, 2004; Consolini et al., 2009; Charbonneau,
2020); Second, the coverage in the area of sunspots and plages can be used as
proxies to predict other activity indices important for space-climate,
including spectral and total solar irradiance variability (e.g. Foukal & Lean,
1988; Berrilli et al., 2020; Petrie et al., 2021).

##  2 Active Regions Parametrization

We characterize the shape of each solar cycle through a unique functional
form. Among those proposed in literature (e.g. Baranovski & Nollau, 2008;
Hathaway et al., 1994), we choose the following parametric fit suggested in
Volobuev (2009):

$x_{k}(t)=\left(\frac{t-T0_{k}}{Ts_{k}}\right)^{2}e^{-\left(\frac{t-T0_{k}}{Td_{k}}\right)^{2}}\quad\quad\textrm{for}\quad
T0_{k}<t<T0_{k}+\tau_{k}$ (1)

where $T0_{k}$ is the initial time of cycle $k$ (published in Hathaway et al.,
1994; Hathaway, 2015) while $Ts_{k}$ and $Td_{k}$ are two free parameters. As
discussed in Volobuev (2009), there is a strong linear correlation between
these two parameters, which reduces the fit to a single parameter ($Ts_{k}$).
This is not surprising, because the $Ts_{k}$ parameter is related to the time
of the rising phase, while the $Td_{k}$ value determines the cycle amplitude.
The relation between these two quantities is known and reported in literature:
cycles with large amplitude ($Ts_{k}$ smaller) present a shorter time of
rising to maximum (shorter $Td_{k}$). This is known as Waldmeier effect (e.g.
Hathaway et al., 1994; Hazra et al., 2015).

Figure 1:  Solar cycle-to-cycle relationship between the parameters $Td_{k}$
and $Ts_{k}$ for plage (left) and sunspot (right) areas. Two additional solar
cycle numbers, 12 and 13, have been included in the analysis of sunspot areas.
The open circles with 1-$\sigma$ error bars show the data averaged over
individual cycles. The regression lines (continuous lines) are given by Eq. 2.
Figure 2: Upper panel: reconstructed plage area (red solid line) with
confidence range (light red pattern) and observed plage composite (green solid
line) by Chatzistergos et al. (2019). Lower panel: reconstructed Sunspot area
(red solid line) with confidence range (light red pattern) and observed
sunspot area composite (green solid line) from Mandal et al. (2020). It should
be noted that our method has been developed in order to provide an estimate of
the coverage of plage and sunspot on an annual scale and therefore cannot
reproduce shorter time scale variability (e.g. months). This explains the
difference between the observed plage and sunspot coverages (green solid
lines) and the reconstructed ones (red solid line). The ability to capture
long-term behavior by the functional form is also evident.

We adopt Eq. 1 to fit, cycle by cycle, the plage and sunspots coverage data.
For this purpose we used two data sets (composites) available from the Max
Plank Institute (MPI) website (http://www2.mps.mpg.de/projects/sun-
climate/data.html). The first composite consists of plage area derived from Ca
II K spectroheliogram observations covering the period 1892 to 2019
(Chatzistergos et al., 2019). The second composite includes measurements of
daily total sunspot area for the period 1874-2019, calculated after cross-
calibration of measurements by different observers (Mandal et al., 2020). The
relation between the $Ts_{k}$ and $Td_{k}$ for plage and sunspot areas is
shown in Fig. 1. A linear fit to these data produces:

$\displaystyle Td_{k}^{plage}=(0.09\pm 0.01)Ts_{k}^{plage}+(3.27\pm
0.10)~{}~{}~{}yr$ $\displaystyle Td_{k}^{spot}=(0.022\pm
0.001)Ts_{k}^{spot}+(2.98\pm 0.04)~{}~{}~{}yr.$ (2)

The Pearson correlation coefficients are r=0.81 and r=0.72 for plage and spot
fit, respectively. A t-test was performed to determine the statistical
significance of the computed correlation coefficients. We found there is a
non-zero correlation between $Ts_{k}$ and $Td_{k}$, at a confidence level
greater than 99% for the plages and greater than 95% for the sunspots.
By inserting these relationships in Eq. 1, we obtain a one-parameter
functional form for the shape of the cycles. We repeat the fits, cycle by
cycle, and we obtain two dataset of $Ts_{k}$ values.
The active region coverages ($A(t)_{plage}$ and $A(t)_{spot}$) for the entire
analyzed period are thus reproduced as:

$A(t)=\sum_{k}x_{k}(t)$ (3)

where the cycle number k goes from the 14-th (begin data = 1902 January) to
the 23-th (begin data = 1996 August) for plage data and from the 12-th (begin
data = 1878 December) for sunspot data. The parametric reconstructions for
plage and sunspot area are shown in Fig. 2. A confidence region is estimated
by taking into account the errors on the fit parameters.

##  3 Relation between even and odd cycles

Through the fits of the observed active region coverages, we have obtained the
single parameter characterizing the last eleven cycles for the plages and the
last thirteen cycles for the sunspots.
We couple these values in pairs, i.e. as even-odd cycles, taking into account
that the complete magnetic cycle of the Sun is composed of two consecutive
cycles. By plotting the even-odd parameters, one versus the other, we obtain
the correlations shown in Fig. 3, whose fits are as follows

$\displaystyle Ts_{o}^{plage}=(0.74\pm 0.08)Ts_{e}^{plage}+(1.5\pm
1.1)~{}~{}~{}yr$ $\displaystyle Ts_{o}^{spot}=(0.69\pm
0.05)Ts_{e}^{spot}+(11\pm 3)~{}~{}~{}yr.$ (4)

where the subscript ”e” means ”even” and ”o” means ”odd”. The Pearson
correlation coefficient is 0.86 for both fits, at a confidence level greater
than 90% and 95% for the plages and sunspots respectively. We highlight the
fact that by coupling the parameters

Figure 3:  Even-odd cycle relationship between the parameters $Ts_{k}$ for
plage (left) and sunspot (right) areas. The open circles with 1-$\sigma$ error
bars in both directions show the cycle-averaged pair of data. The regression
lines (continuous lines), given by Eq. 3, were computed using the procedure
described in Press et al. (1992).  Figure 4:  Top: Observed monthly plage
coverage (green curve) during cycles 23 and 24, and prediction for cycle 25
(red curve). The shadow red area defines the lower and upper limits for the
prediction. Bottom: Same, but for sunspot coverage.

in an odd-even manner (e.g. Cycle 15 with Cycle 16) the correlation is
completely lost. This is in agreement with the well known empirically derived
Gnevyshev-Ohl rule (Gnevyshevl & Ohl, 1948), which states that the strength of
an even cycle is lower than the strength of the subsequent odd cycle.
By inserting the $Ts_{24}$ values derived from sunspot and plage observations
and $T0_{25}$ corresponding to December 2019 in Eq. 3, we are able to estimate
the $Ts_{25}$ values and therefore the shape of the variation of sunspot and
plage areas over SC25 using Eq. 1. Results are illustrated in Fig. 4. The
confidence levels shown in the figure are the envelopes of the curves computed
by varying the $T_{s_{25}}$ and $T_{d_{25}}$ values within their 1 $\sigma$
confidence level in Eq. 1. The plot shows that the maximum of plage area will
occur in April 2024, with an uncertainty of three months, and that the maximum
sunspot area coverage will occur in January 2024, with an uncertainty of two
months. The plots also show that, within the confidence level, the amplitudes
of the area coverage of sunspot and plage are similar or slightly higher to
those observed during cycle 24.

##  4 Conclusions

We have presented a prediction of the area coverage of sunspot and plages
during solar cycle 25. Our method is based on the empirical correlation
between the shapes (amplitude and duration) of even and odd cycles derived
from the analysis of more than 100 years of observations. Similar relations
between properties of subsequent cycles, in particular the even-odd cycles
relation, have been empirically derived by using solar sunspot number and
other activity proxies in numerous studies (e.g. Mursula et al., 2001; Gupta
et al., 2007; Tlatov, 2013; Takalo & Mursula, 2020; Takalo, 2021). Although
some authors suggested that the even-odd relation might be the signature of a
relic magnetic field (Mursula et al., 2001, and references therein), the
physical mechanisms responsible for the even-odd relation are not clear
(Hathaway, 2015) and it is worth noticing that the relation has been
questioned by some authors (Zolotova & Ponyavin, 2015).

The plage area maximum is predicted for April 2024, with an uncertainty of
about three months, instead the sunspot area maximum is predicted for January
2024, with an uncertainty of about two months. By combining these two results
and by assuming a perfect phase between the two quantities, we can hypothesize
the maximum intensity level of the SC25 will be in February-March 2024. By
assuming that the sunspot and plage coverage are indicative of the cycle
intensity, our prediction is a level of solar activity for the SC25 similar or
slightly higher to that of SC24. This is in agreement with most of the
forecasts presented in the literature or using the first available values of
the smoothed Solar Sunspot Number (e.g. Bhowmik & Nandy, 2018; Petrovay, 2020;
Carrasco & Vaquero, 2021) and with the conclusions of the international
NOAA/NASA co-chaired SC25 Prediction Panel.

We want to stress here that our approach is, to our knowledge, the only one
that provides a forecast for the coverage of plage and sunspot areas. These
quantities are proxies of the solar magnetic activity, can be used to derive
other activity indices important for space-climate (e.g. Mg II, F10.7, flare
indices, etc.) and are fundamental ingredients to estimate both total and
spectral irradiance variability.

The authors are grateful to Dr. Lisa Upton for providing insightful comments
on an early version of the manuscript. The National Solar Observatory is
operated by the Association of Universities for Research in Astronomy, Inc.
(AURA), under cooperative agreement with the National Science Foundation. M.
Cantoresi is supported by the Joint Research PhD Program in “Astronomy,
Astrophysics and Space Science” between the universities of Roma Tor Vergata
an Roma Sapienza, and INAF.

## References

  * Baranovski & Nollau (2008) Baranovski, A.L.and Clette1, F., & Nollau, V. 2008, Ann. Geophys., 26, 231, doi: 10.5194/angeo-26-231-2008
  * Berrilli et al. (2020) Berrilli, F., Criscuoli, S., Penza, V., & Lovric, M. 2020, Sol. Phys., 295, 38, doi: 10.1007/s11207-020-01603-5
  * Berrilli et al. (2014) Berrilli, F., Casolino, M., Del Moro, D., et al. 2014, Journal of Space Weather and Space Climate, 4, A16, doi: 10.1051/swsc/2014014
  * Bhowmik & Nandy (2018) Bhowmik, P., & Nandy, D. 2018, Nat Commun, 9, 5209, doi: https://doi.org/10.1038/s41467-018-07690-0
  * Bigazzi et al. (2020) Bigazzi, A., Cauli, C., & Berrilli, F. 2020, Annales Geophysicae, 38, 789, doi: 10.5194/angeo-38-789-2020
  * Bordi et al. (2015) Bordi, I., Berrilli, F., & Pietropaolo, E. 2015, Annales Geophysicae, 33, 267, doi: 10.5194/angeo-33-267-2015
  * Bushby & Mason (2004) Bushby, P., & Mason, J. 2004, Astronomy & Geophysics, 45, 4.7, doi: 10.1046/j.1468-4004.2003.45407.x
  * Cameron et al. (2016) Cameron, R. H., Jiang, J., & Schüssler, M. 2016, ApJ, 823, L22, doi: 10.3847/2041-8205/823/2/L22
  * Carrasco & Vaquero (2021) Carrasco, V. M. S., & Vaquero, J. M. 2021, Research Notes of the AAS, 5, 181, doi: 10.3847/2515-5172/ac19a2
  * Charbonneau (2020) Charbonneau, P. 2020, Living Reviews in Solar Physics, 17, 4, doi: 10.1007/s41116-020-00025-6
  * Chatzistergos et al. (2019) Chatzistergos, T., Ermolli, I., Krivova, N. A., & K., S. S. 2019, A&A, 625, 22, doi: 10.1051/0004-6361/201834402
  * Consolini et al. (2009) Consolini, G., Tozzi, R., & de Michelis, P. 2009, A&A, 506, 1381, doi: 10.1051/0004-6361/200811074
  * Fiandrini et al. (2021) Fiandrini, E., Tomassetti, N., Bertucci, B., et al. 2021, Phys. Rev. D, 104, 023012, doi: 10.1103/PhysRevD.104.023012
  * Foukal & Lean (1988) Foukal, P., & Lean, J. 1988, ApJ, 328, 347, doi: 10.1086/166297
  * Galuzzo et al. (2021) Galuzzo, D., Cagnazzo, C., Berrilli, F., Fierli, F., & Giovannelli, L. 2021, ApJ, 909, 191, doi: 10.3847/1538-4357/abdeb4
  * Gnevyshevl & Ohl (1948) Gnevyshevl, M., & Ohl, A. 1948, Astronomicheskii Zhurnal, 25, 18
  * Gupta et al. (2007) Gupta, M., Mishra, V. K., & Mishra, A. P. 2007, Journal of Geophysical Research (Space Physics), 112, A05105, doi: 10.1029/2006JA012076
  * Hathaway (2015) Hathaway, D. 2015, Living Reviews in Solar Physics, 12, 87, doi: 1007/lrsp-2015-4
  * Hathaway et al. (1994) Hathaway, D., Hathaway, D., & Reichmann, J. 1994, Sol. Phys., 151, 177, doi: 10.1007/BF00654090
  * Hazra et al. (2015) Hazra, G., Karak, B. B., Banerjee, D., & Choudhuri, A. R. 2015, Sol. Phys., 290, 1851, doi: 10.1007/s11207-015-0718-8
  * Hudson (1988) Hudson, H. S. 1988, ARA&A, 26, 473, doi: 10.1146/annurev.aa.26.090188.002353
  * Janssens (2021) Janssens, J. 2021, Space Weather Space Clim., 11, 3, doi: https://doi.org/10.1051/swsc/2020081
  * Kopp et al. (2016) Kopp, G., Krivova, N., Wu, C. J., & Lean, J. 2016, Sol. Phys., 291, 2951, doi: 10.1007/s11207-016-0853-x
  * Labonville et al. (2019) Labonville, F., Charbonneau, P., & Lemerle, A. 2019, Sol. Phys., 294, 82, doi: https://doi.org/10.1007/s11207-019-1480-0
  * Lockwood & Ball (2020) Lockwood, M., & Ball, W. T. 2020, Proc. R. Soc. A., 476, doi: 10.1098/rspa.2020.0077
  * Mandal et al. (2020) Mandal, S., Krivova, N. A., Solanki, S. K., Sinha, N., & Banerjee, D. 2020, A&A, 640, A78, doi: 10.1051/0004-6361/202037547
  * Matthes et al. (2017) Matthes, K., Funke, B., Andersson, M. E., et al. 2017, Geoscientific Model Development, 10, 2247, doi: 10.5194/gmd-10-2247-2017
  * McIntosh et al. (2020) McIntosh, S. W., Chapman, S., Leamon, R. J., Egeland, R., & Watkins, N. W. 2020, Sol. Phys., 295, 163, doi: 10.1007/s11207-020-01723-y
  * Meadows & Barnes (2018) Meadows, V. S., & Barnes, R. K. 2018, Factors Affecting Exoplanet Habitability, ed. H. J. Deeg & J. A. Belmonte, 57, doi: 10.1007/978-3-319-55333-7_57
  * Mursula et al. (2001) Mursula, K., Usoskin, I. G., & Kovaltsov, G. A. 2001, Sol. Phys., 198, 51, doi: 10.1023/A:1005218414790
  * Petrie et al. (2021) Petrie, G., Criscuoli, S., & Bertello, L. 2021, Solar Magnetism and Radiation (American Geophysical Union (AGU)), 83–132, doi: https://doi.org/10.1002/9781119815600.ch3
  * Petrovay (2020) Petrovay, K. 2020, Living Rev Sol Phys, 17, 2, doi: 10.1007/s41116-020-0022-z
  * Plainaki et al. (2020) Plainaki, C., Antonucci, M., Bemporad, A., et al. 2020, Journal of Space Weather and Space Climate, 10, 6, doi: 10.1051/swsc/2020003
  * Press et al. (1992) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in C, 2nd edn. (Cambridge, USA: Cambridge University Press)
  * Schwenn (2006) Schwenn, R. 2006, Living Rev. Sol. Phys., 3, 2, doi: https://doi.org/10.12942/lrsp-2006-2
  * Singh et al. (2021) Singh, P., Saad Farid, A., Singh, A., Pant, T., & A.A., A. 2021, Astrophysics and Space Science, 366, 48, doi: 10.1007/s10509-021-03953-3
  * Takalo (2021) Takalo, J. 2021, Sol. Phys., 296, 80, doi: 10.1007/s11207-021-01825-1
  * Takalo & Mursula (2020) Takalo, J., & Mursula, K. 2020, A&A, 636, A11, doi: 10.1051/0004-6361/202037488
  * Tlatov (2013) Tlatov, A. G. 2013, ApJ, 772, L30, doi: 10.1088/2041-8205/772/2/L30
  * Upton & Hathaway (2018) Upton, L. A., & Hathaway, D. H. 2018, Geophys. Res. Lett., 45, 8091, doi: 10.1029/2018GL078387
  * Usoskin et al. (2002) Usoskin, I. G., Mursula, K., Solanki, S. K., M., S., & A., K. G. 2002, J. Geophys. Res., 107, doi: 10.1029/2002JA009343
  * Vecchio et al. (2017) Vecchio, A., Lepreti, F., Laurenza, M., Alberti, T., & Carbone, V. 2017, A&A, 599, A58, doi: 10.1051/0004-6361/201629758
  * Versteegh (2005) Versteegh, G. 2005, Space Science Reviews, 120, 243, doi: 10.1007/s11214-005-7047-4
  * Volobuev (2009) Volobuev, D. 2009, Sol. Phys., 258, 319, doi: 1 10.1007/s11207-009-9429-3
  * Wilson (1978) Wilson, O. C. 1978, ApJ, 226, 379, doi: 10.1086/156618
  * Zolotova & Ponyavin (2015) Zolotova, N. V., & Ponyavin, D. I. 2015, Geomagnetism and Aeronomy, 55, 902, doi: 10.1134/S0016793215070300


# The paradox of the infinity

MOHAMED AYAD and OMAR KIHEL

##  1 Introduction

Let $(\bf P)$ be a property defined on the set of the natural numbers and
$A_{n}$ be the set of positive integers less or equal $n$, where $n$ is a
positive integer. If an integer is selected at random from $A_{n}$, then the
probability $\sigma_{n}$ that it satisfies $(\bf P)$ is the number of elements
in $A_{n}$ that satisfy $(\bf P)$ divided by $n$. If the limit of $\sigma_{n}$
when $n$ tends to infinity exists, this limit is called the natural density or
asymptotic density of the integers satisfying $(\bf P)$. Intuitively, this
density measures how frequently an integer satisfies $(\bf P)$. One can define
analogously the natural density on any infinite subset of the set of natural
numbers. Let’s consider the following situation:

Let $E$ be an infinite set on which a property $(\bf P)$ is defined. Suppose
that $E=\cup_{i\in I}E_{i}$ is a partition, where each $E_{i}$ is infinite.
Suppose also that, in each $E_{i}$, the number of elements satisfying $(\bf
P)$ is finite. Then, clearly the density of the elements satisfying $(\bf P)$
is 0 in every $E_{i}$. Is it possible that the density of the subset of $E$
containing all the elements satisfying $(\bf P)$ will be at least equal to
$1/2$?

We were first confronted with this situation while reading the paper of Arno
et al. [1]. In fact, it is in the paper [1] where it is shown that the density
of certain algebraic numbers in $\overline{\mathbb{Q}}$, which we will call
Arno et al. numbers in section 5, is equal to $1/\zeta(3)$. We have
partitioned $\overline{\mathbb{Q}}$ in a way that suggests these Arno et al.
numbers are rare. This phenomenom struck us as contradictory, which lead us to
consider the situation in greater detail. We will show in the sequel, through
two examples, that the answer to the above question may be positive. At first
glance, this problem resembles to the so called Simpson paradox in probability
and statistics. In this paper, when we say the density, we mean the natural
density.

##  2 First example

Let $E=\mathbb{N}\setminus\\{0,1\\}$. In this set the relation $(\bf P)$ will
be : $x$ is even. For any $i\geq 1$, let

$E_{i}=\\{2i\\}\cup\\{2^{i}k+1,k\geq 1\text{ odd}\\}$

The $E_{i}$ constitute a partition of $E$; each class contains a unique
element satisfying $(\bf P)$. On the other hand, the density in $E$ of the
elements satisfying $(\bf P)$ is equal to $1/2$.

Before producing the second example, we need to state, in the following
section, some results on the denominator and constant coefficient of an
algebraic number. The reader who is familiar with these notions may skip this
section.

##  3 Denominator of an algebraic number

Let $\gamma$ be an algebraic number of degree $n$,

$g(x)=c_{n}x^{n}+c_{n-1}x^{n-1}+\ldots+c_{1}x+c_{0}$

be the unique irreducible polynomial with integral coefficients such that
$g(\gamma)=0$ and $c_{n}>0$. This polynomial will be called the minimal
polynomial of $\gamma$ over $\mathbb{Z}$. Let

$I=I(\gamma)=\\{k\in\mathbb{Z},\,\,k\gamma\,\,\mbox{an algebraic integer}\\}$
(1)

Then $I(\gamma)$ is a principal ideal of $\mathbb{Z}$. Since $c_{n}\gamma$ is
an algebraic integer, then $c_{n}\in I(\gamma)$. Hence $I(\gamma)\neq(0)$. Let
$d>0$ be a generator of $I(\gamma)$, then $d$ is the smallest positive integer
such that $d\gamma$ is integral. Moreover $d\mid c_{n}$. Call this integer $d$
the denominator of $\gamma$. Let $\theta=d\gamma$, then $\theta$ is an
algebraic integer, called the numerator of $\gamma$. The leading coefficient
$c_{n}$ of $g(x)$ will be called the leading coefficient of $\gamma$. Denote
by $d(\gamma)$ and $c(\gamma)$ the denominator and the leading coefficient of
$\gamma$ respectively.

###### Proposition 1

Let $\gamma$ be an algebraic number of degree $n$,
$\gamma_{1},\ldots,\gamma_{n}$ be the list of its conjugates over
$\mathbb{Q}$. For any $i=1,\ldots,n$, let
$s_{i}(\overrightarrow{\gamma})=s_{i}(\gamma_{1},\ldots,\gamma_{n})$ be the
elementary symmetric function of degree $i$ of the $\gamma_{j}$. Let

$J=J(\gamma)=\\{k\in\mathbb{Z},\,\,ks_{i}(\vec{\gamma})\in\mathbb{Z}\,\mbox{for}\,\,i=1,\ldots,n\\},$
(2)

then $J$ is a principal ideal of $\mathbb{Z}$ generated by $c(\gamma)$.
Moreover $c(\gamma)\mid d^{n}$.

Proof. Let $c^{{}^{\prime}}$ be a generator of $J(\gamma)$ and let
$d=d(\gamma)$. Set $\gamma=\theta/d$ where $\theta$ is an algebraic integer.
Since

$d^{n}s_{k}(\gamma)=d^{n}\sum\gamma_{i_{1}}\cdots\gamma_{i_{k}}=d^{n}\sum(\theta_{i_{1}}/d)\cdots(\theta_{i_{k}}/d)$

then $d^{n}\in J(\gamma)$ thus $c^{{}^{\prime}}\mid d^{n}$. Let $c=c(\gamma)$
and let $g(x)$ be the minimal polynomial of $\gamma$ over $\mathbb{Z}$, then

$\displaystyle g(x)$ $\displaystyle=c(x-\gamma_{1})\cdots(x-\gamma_{n})$
$\displaystyle=c\big{(}x^{n}-s_{1}(\gamma)x^{n-1}+\ldots+(-1)^{n}s_{n}(\gamma)\big{)}$
$\displaystyle=cx^{n}-cs_{1}(\gamma)x^{n-1}+\ldots+(-1)^{n}cs_{n}(\gamma).$

Since $g(x)\in\mathbb{Z}[x]$ then $cs_{k}(\vec{\gamma})\in\mathbb{Z}$ for
$k=1,\ldots,n$, hence $c\in J(\gamma)$, which implies $c^{{}^{\prime}}\mid c$.
On the other hand let

$\displaystyle g_{1}(x)$
$\displaystyle=c^{{}^{\prime}}(x-\gamma_{1})\cdots(x-\gamma_{n})$
$\displaystyle=c^{{}^{\prime}}x^{n}-c^{{}^{\prime}}s_{1}(\gamma)x^{n-1}+\ldots+(-1)^{n}c^{{}^{\prime}}s_{n}(\gamma)$
$\displaystyle\in\mathbb{Z}[x].$

Since $g_{1}(\gamma)=0$, then $g(x)$ divides $g_{1}(x)$ in $\mathbb{Q}[x]$.
Set $g_{1}(x)=g(x)q$ with $q\in\mathbb{Q}$. Using the content of polynomials,
denoted by cont, We have $cont(g_{1})=qcont(g)=q$, hence $q\in\mathbb{Z}$. The
comparison of the leading coefficients leads to $c^{{}^{\prime}}=cq$, hence
$c\mid c^{{}^{\prime}}$. Finally we get $c=c^{{}^{\prime}}$.

###### Remark 2

We have shown that $d(\gamma)\mid c(\gamma)$ and $c(\gamma)\mid
d(\gamma)^{n}$, hence $d(\gamma)$ and $c(\gamma)$ have the same prime factors.

###### Example 3

In the following example we compare the denominator and the leading
coefficient. In particular we look for the condition $d(\gamma)=c(\gamma)$.

Let $\gamma=\sqrt{2}/(q2^{k})$ with $q$ positive and odd and $k\geq 0$. Here
$d(\gamma)=q2^{k}$. $\gamma$ is a root of the equation
$2^{2k}q^{2}\gamma^{2}-2=0$ which is not always irreducible over $\mathbb{Z}$.
In the different cases which follow we precise the minimal polynomial $g(x)$
of $\gamma$ over $\mathbb{Z}$.

$\bullet$ $k=0$, $g(x)=q^{2}x^{2}-2$, hence $d(\gamma)=q$ and
$c(\gamma)=q^{2}>d(\gamma)$ except if $q=1$, i.e. $\gamma=\sqrt{2}$.

$\bullet$ $k=1$ and $q=1$. Here $g(x)=2x^{2}-1$, $d(\gamma)=c(\gamma)=2$.

$\bullet$ $k=1$ and $q\geq 2$. Here $g(x)=2q^{2}x^{2}-1$, hence $d(\gamma)=2q$
and $c(\gamma)=2q^{2}>d(\gamma)$.

$\bullet$ $k\geq 2$ and $q\geq 1$. Here $g(x)=2^{2k-1}q^{2}x^{2}-1$, hence
$d(\gamma)=2^{k}q$ and $c(\gamma)=2^{2k-1}q^{2}>d(\gamma)$.

We thus get $c(\gamma)=d(\gamma)$ if and only if $\gamma=\sqrt{2}$ or
$\gamma=\sqrt{2}/2$. This example suggests that we almost always have
$c(\gamma)>d(\gamma)$.

##  4 Result of Arno-Robinson-Wheeler

These three authors have shown that the density in $\overline{\mathbb{Q}}$ of
the algebraic numbers $\gamma$ such that $c(\gamma)=d(\gamma)$ is equal to
$1/\zeta(3)=0.8319...$. These numbers will be called Arno et al. numbers. The
height of a polynomial with integral coefficients,
$P(x)=a_{k}x^{k}+\ldots+a_{0}$, is defined by $H(P)=\max_{i}|a_{i}|$. The
height of an algebraic number is the height of its minimal polynomial over
$\mathbb{Z}$. To prove their result, Arno et al. define the sets

${\cal{A}}_{d}(H)=\\{\gamma\in\overline{\mathbb{Q}},deg(\gamma)=d,\,\,\mbox{and}\,\,H(\gamma)\leq
H\\}\,\,\mbox{and}$
${\hat{\cal{A}}}_{d}(H)=\\{\gamma\in{\cal{A}}_{d}(H)\\},c(\gamma)=d(\gamma)\\},$

where $H$ is a positive integer and $H(\gamma)$ denotes the height of
$\gamma$. After obtaining an asymptotic formula of
$|{\hat{\cal{A}}}_{d}(H)|/|{\cal{A}}_{d}(H)|$, they deduce that

$\lim_{d\to\infty}\lim_{H\to\infty}|\cup_{k\leq
d}{\hat{\cal{A}}}_{k}(H)|/|\cup_{k\leq d}{\cal{A}}_{k}(H)|=1/\zeta(3).$

This result makes appear that the Arno et al. numbers are very frequent in the
set of the algebraic numbers. In the sequel we define a partition of
$\overline{\mathbb{Q}}$ which suggests that the Arno et al. numbers are rare.
With the characterizations of $d(\gamma)$ and $c(\gamma)$ given above this
result of Arno et al. seems surprising. Actually $d(\gamma)$ is the smallest
positive integer $d$ such that $d\gamma$ is an algebraic integer. In contrast,
$c(\gamma)$ is the smallest positive integer $c$ such that all the products

$c(\gamma_{1}+\ldots+\gamma_{n}),c(\gamma_{1}\gamma_{2}+\ldots+\gamma_{n-1}\gamma_{n}),\ldots,c\gamma_{1}\cdots\gamma_{n}$

are rational integers. For the first product, we clearly see that $c$ may be
replaced by $d$, but for the others? Arno’s et al. result tells us that it is
also true with a high probability.

##  5 Second example

###### Definition 4

Let $K$ be a number field of degree $n$ over $\mathbb{Q}$, $\theta$ be an
algebraic integer of $K$, and $f(x)=x^{n}+a_{n-1}x^{n-1}+\ldots+a_{1}x+a_{0}$
the characteristic polynomial of $\theta$ over $\mathbb{Q}$. The norm of
$\theta$ over $\mathbb{Q}$, denoted by
$N_{\mathbb{Q}(\theta)/\mathbb{Q}}(\theta)$, is defined by
$N_{\mathbb{Q}(\theta)/\mathbb{Q}}(\theta)=(-1)^{n}a_{0}$.

###### Proposition 5

Let $\gamma=\theta/d$ be an algebraic number of degree $n\geq 2$, where
$\theta$ is an algebraic integer and $d=d(\gamma)$. Suppose that $\gamma$ is
an Arno et al. number, then $d^{n-1}\mid
N_{\mathbb{Q}(\theta)/\mathbb{Q}}(\theta)$.

Proof. Let

$f(x)=x^{n}+a_{n-1}x^{n-1}+\ldots+a_{1}x+a_{0}$

be the minimal polynomial of $\theta$ over $\mathbb{Q}$. Since $f(d\gamma)=0$,
we have

$d\gamma^{n}+a_{n-1}\gamma^{n-1}+\cdots+(a_{1}/d^{n-2})\gamma+(a_{0}/d^{n-1})=0.$

The minimal polynomial of $\gamma$ over $\mathbb{Z}$ has the form

$g(x)=dx^{n}+c_{n-1}x^{n-1}+\ldots+c_{1}x+c_{0}.$

It follows that $g(x)$ divides the polynomial

$dx^{n}+a_{n-1}x^{n-1}+\cdots+(a_{1}/d^{n-2})x+(a_{0}/d^{n-1}).$

in $\mathbb{Q}[x]$. Let $q\in\mathbb{Q}$ such that

$dx^{n}+a_{n-1}x^{n-1}+\cdots+(a_{1}/d^{n-2})x+(a_{0}/d^{n-1})=qg(x).$

Identifying the leading coefficients, we get $q=1$ and since $c_{0}$ is an
integer, then $d^{n-1}\mid a_{0}$.

Make a partition of $\overline{\mathbb{Q}}\setminus\mathbb{Q}$ by putting in
the same class, say $C(\theta)$, all the algebraic numbers whose numerator is
equal to the algebraic integer $\theta$. The preceding proposition shows that
any class $C(\theta)$ contains a finite number (may be $0$) of Arno et al.
numbers. We thus have a second example of a set, namely
$\overline{\mathbb{Q}}\setminus\mathbb{Q}$, and the property $(\bf P)$ states:
$\gamma$ is an Arno et al. number.

We have excluded from $\overline{\mathbb{Q}}$ the rational numbers because
they are Arno et al. numbers and any corresponding class $C(\theta)$ is
infinite.

One may think that the Arno et al. numbers are mostly frequent when their
degrees are large enough. But, let $\gamma=\theta/d$ be an Arno et al.
algebraic number of degree $n$. Let $q$ be a positive integer divisible by
some prime number $p$ such that $p\not\mid
N_{\mathbb{Q}(\theta)/\mathbb{Q}}(\theta)$, then by the preceding proposition
the number $\gamma_{q}=\theta/q$ has the same degree as $\gamma$ and generates
the same field, but it is not an Arno et al. number. Obviously the number of
$\gamma_{q}$’s is infinite.

##  6 Denominator and leading coefficient in the formal case

###### Proposition 6

Let $t_{0},t_{1},\ldots,t_{n},x$ be algebraically independent variables over
$\mathbb{Z}$ and let

$G(x)=t_{n}x^{n}+\ldots+t_{1}x+t_{0}\in\mathbb{Z}[t_{0},t_{1},\ldots,t_{n}][x].$

Set $\vec{t}=(t_{0},t_{1},\ldots,t_{n})$. Let $\Gamma$ be a root of $G(x)$ in
an algebraic closure of $\mathbb{Q}(\vec{t})$. Let

$I=\\{D(\vec{t})\in\mathbb{Z}[\vec{t}],\,\,D\Gamma\,\,\mbox{is integral
over}\,\,\mathbb{Z}[\vec{t}]\\},$

then $I$ is a principal ideal of $\mathbb{Z}[\vec{t}]$ generated by $t_{n}$.

Proof. Obviously $t_{n}\in I$. Let $D(\vec{t})\in I$, then since

$t_{n}\Gamma^{n}+t_{n-1}\Gamma^{n-1}+\ldots+t_{1}\Gamma+t_{0}=0,$

we have

$\big{(}D(\vec{t})\Gamma\big{)}^{n}+\frac{t_{n-1}D(\vec{t})}{t_{n}}\big{(}D(\vec{t})\Gamma\big{)}^{n-1}+\ldots+\frac{t_{1}D(\vec{t})^{n-1}}{t_{n}}\big{(}D(\vec{t})\Gamma\big{)}+\frac{t_{0}D(\vec{t})}{t_{n}}=0,$

hence $t_{n}\mid D(\vec{t})$ thus $I=t_{n}\mathbb{Z}[\vec{t}]$.

This proposition shows that if $\Gamma$ is a root of the generic polynomial,
then its denominator and leading coefficient are equal. Since the minimal
polynomial over $\mathbb{Z}$ of any algebraic number may be obtained by
specializing the coefficients of the generic polynomial, it is tempting to
conclude that this confirms the result of Arno et al.

Question: Is it possible to find an uncountable set $E$ and a property $(\bf
P)$ satisfying the conditions stated in the introduction? Our feeling is that
the answer is negative.

## References

  * [1] S. Arno, M. L. Robinson, F. S. Wheeler, On Denominators of Algebraic Numbers and Integer Polynomials, Journal of Number Theory 57, (1996), 292-302.

Mohamed Ayad
Laboratoire de Mathématiques Pures et Appliquées
Université du Littoral, F-62228 Calais, France
<EMAIL_ADDRESS>
Omar Kihel
Department of Mathematics
Brock University, Ontario, Canada L2S 3A1
<EMAIL_ADDRESS>


#  DirectQuote: A Dataset for Direct Quotation Extraction and Attribution in
News Articles

Yuanchi Zhang1 and Yang Liu1,2,3,4,5
1Department of Computer Science and Technology, Tsinghua University, Beijing,
China
2Institute for AI Industry Research, Tsinghua University, Beijing, China
3Institute for Artificial Intelligence, Tsinghua University, Beijing, China
4Beijing National Research Center for Information Science and Technology
5Beijing Academy of Artificial Intelligence

###### Abstract

Quotation extraction and attribution are challenging tasks, aiming at
determining the spans containing quotations and attributing each quotation to
the original speaker. Applying this task to news data is highly related to
fact-checking, media monitoring and news tracking. Direct quotations are more
traceable and informative, and therefore of great significance among different
types of quotations. Therefore, this paper introduces _DirectQuote_ , a corpus
containing 19,760 paragraphs and 10,279 direct quotations manually annotated
from online news media. To the best of our knowledge, this is the largest and
most complete corpus that focuses on direct quotations in news texts. We
ensure that each speaker in the annotation can be linked to a specific named
entity on Wikidata, benefiting various downstream tasks. In addition, for the
first time, we propose several sequence labeling models as baseline methods to
extract and attribute quotations simultaneously in an end-to-end manner.111The
DirectQuote corpus is available at https://github.com/THUNLP-MT/DirectQuote

_Keywords_ Direct Quotation Extraction $\cdot$ Direct Quotation Attribution
$\cdot$ News Corpus

##  1 Introduction

A _quotation_ is a general notion that covers different kinds of speech,
thought, and writing in text (Semino and Short, 2004). It is a prominent
linguistic device for expressing opinions, statements, and assessments
attributed to the speaker (Cappelen and Lepore, 2012). Concretely, there are
three types of quotations: _direct quotations_ , _indirect quotations_ and
_mixed quotations_ (Table 1). Among all kinds of quotations, the entire
content of the _direct quotation_ (O’Keefe et al., 2013) is in quotation
marks, which means that what the speaker said is transcribed verbatim.

Direct quotations are of considerable sigificance among all types of
quotations. On the one hand, news writers attribute direct quotations to
speakers, making claims credible and authoritative, leading to more traceable
and informative news (WP et al., 2020). These direct quotations from
politicians, public figures, and other celebrities improve the authenticity
and fairness of news, making news more convincing. On the other hand, the
development of social media and advanced language generation models, such as
GPT, has led to the proliferation of fake news (Floridi and Chiriatti, 2020).
Troubled by rampant media manipulators, people are increasingly questioning
the political stance and legitimacy of the news press. Therefore, direct
quotations in the news are essential to ensure the transparency and
accountability of news.

Besides news writing, direct quotations are also actively involved in various
NLP tasks. Since direct quotations are high subjective opinions, cognitions
and assertions, they are used in opinion mining and claim detection task
(Balahur et al., 2009) to discover opinions, sentiment analysis task (Balahur
et al., 2013) to evaluate the author’s mood, fact check task to verify factual
information, statement monitoring task to track others’ speech. Many websites
apply these tasks. For example, NewsBrief is a website that automatically
extracts and attributes quotations, detects events, and updates them in real-
time. Another website, Politifact, tracks the statements of politicians for
news fact-checking to reduce misinformation. ISideWith tracks political views
on different topics to boost voter engagement and education. However, these
systems rely heavily on costly and time-consuming human labor.

In general, as shown in Figure 1, the above applications include two types of
tasks related to quotations. The first task is called _quotation extraction_
that refers to determining the span that represents the quotation in the
document. The second task, _quotation attribution_ , refers to determining the
speaker of the quotation. It is one of the primary criteria for maintaining
integrity in journalism as a primary rhetorical mechanism to promote the
veracity and correctness of reporting.

However, insufficient attention has been paid to direct quotations. Note that
several research focus on various quotations. Most of the related corpora
(Papay and Padó, 2020; Stymne and Östman, 2020; Chen et al., 2019; Zhang et
al., 2019) are based on novels. We find that literary works such as novels
usually have fixed speakers and are sophisticated grammatically and
semantically. In contrast, corpora such as PARC(Pareti, 2016) and
Polnear(Newell et al., 2018) are annotated in news text, which follows a more
straightforward grammatical style and has varying speakers. While these
pioneering work has greatly facilitated the research on the quotation, the
task of quotation extraction and attribution still faces many challenges.

On the one hand, large-scale deep learning models, such as BERT and GPT,
severely overfit on these corpora with limited size. Furthermore, corpora
generated by rule-based methods lack diversity, limiting the generalization
ability of the model. On the other hand, some corpora study broader
attribution relations that take propositional attitudes including quoting and
paraphrasing into consideration. This definition goes beyond the scope of
direct quotations, leading to inconsistencies with downstream tasks, such as
fact check and journalism supervision. Moreover, some annotated speakers are
ambiguous and adversely affect downstream tasks such as entity linking.

To alleviate the above problems, we introduce a corpus of direct quotations
called _DirectQuote_. To build the corpus, we continuously sample news from
multiple news sources to keep the text distribution in the corpus consistent
with that in actual applications. Based on the data, we select 19,706
paragraphs containing quotation marks, and annotate 10,279 quotations and
corresponding speakers. When annotating speakers, we ensure that valid
speakers should be linked to a person entity in a named entity library. Among
them, simple patterns are removed to increase the diversity of the corpus. To
the best of our knowledge, it is the largest direct quotation extraction and
attribution corpus. We hope that the corpus can assist people in understanding
and analyze quotations in the news.

Figure 1: Direct quotation extraction and attribution in news articles.

##  2 Related Work

Quotations usually contain propositional attitudes toward a third party, which
is a common form of attribution. The statements, intentions, beliefs,
knowledge, cognition, and decrees contained in the quotations belong to the
scope of event detection, discourse relations, and opinion analysis.

Many comprehensive corpora contain annotations related to quotations and
attributions; however, these corpora do not directly annotate quotations, so
quotations and attributions are studied as part of other tasks and are limited
to specific categories, resulting in a low recall. Sometimes, the speaker of
the quotation is not explicitly marked. For example, the rhetorical
annotations in PDTB (Prasad et al., 2008) potentially contain quotation
attributions; TimeBank (Pustejovsky et al., 2003) only focuses on attributions
related to events; MPQA (Deng and Wiebe, 2015) and NTCIR (Seki et al., 2008,
2010) extract quotations containing opinions, opinions, and emotions; NTCIR is
composed of quotations with explicit sources; CQSA (Elson and McKeown, 2010)
extracted the direct quotations in the novel. PolNEAR is a corpus of news
articles in English built by Newell et al. (2018). Built on a corpus sampled
from the coverage of an event of great sociological, political, and
journalistic import-campaign coverage, this corpus is an attribution corpus
that focuses on attribution relations in a very broad sense.

Some corpora are dedicated to quotation extraction and attribution. Elson et
al. (2010) assemble a corpus of more than 3000 quotations from a collection of
works by six modern authors and manually label the speakers; O’Keefe et al.
(2013) annotate 3,535 direct quotations and sources from 965 newswire texts of
Sydney Morning Herald. PARC is a corpus annotated with attribution relations
based on Wall Street Journals and can be used to analyze attribution and
validate assumptions. Fernandes et al. (2011) annotate the quotations in 685
articles based on GloboQuotes, an unlabeled Portuguese corpus obtained from
the Global.com website. Using IOB coding, the corpus is codified in a per
token basis and built with golden annotation for named entities, coreferences,
quotations, and associations between quotations and authors; however, the
scale of English news quotations in these corpora is limited.

##  3 Corpus Construction

Figure 2 shows the flowchart of constructing the corpus. In this section, we
will introduce the main steps to construct the corpus in detail.

###  3.1 Collection

Table 1: Data in the _DirectQuote_. Region | Name | URL | Numbers
---|---|---|---
U.S. | Associated Press | https://apnews.com | 438
Cable News Network | https://edition.cnn.com | 627
American Broadcasting Company | https://abcnews.go.com | 240
New York Times | https://www.nytimes.com | 5,642
| CBS Broadcasting | https://www.cbsnews.com | 4,890
UK | British Broadcasting Corporation | https://www.bbc.com | 926
Reuters | https://www.reuters.com | 5,836
The Guardian | https://www.theguardian.com | 4,302
Canada | The Globe and Mail | https://www.theglobeandmail.com | 1,955
The Star | https://www.thestar.com.my | 13,769
New Zealand | NZ Herald | https://www.nzherald.co.nz | 115
Australia | Australian Broadcasting Corporation | https://www.abc.net.au | 312
Sydney Morning Herald | https://www.smh.com.au | 93

We hope that the quotations in the corpus are diverse and can be applied in
various downstream tasks such as stance analysis and sentiment analysis.
Therefore, we select representative and multiple news sources across the
political spectrum, including 13 well-known online news media from five major
English-speaking countries, as shown in Table 1.

We start by collecting publicly available news from each publisher between
September 2020 and March 2021 from the Internet. After deduplication and
removal of unqualified news, we obtain 40,000 news articles on different
topics and genres. These texts are all downloaded from the publisher’s
official website using a web crawler. When obtaining news, we collect the
necessary metadata to ensure traceability: news title, publication time,
publisher name, and source URL.

###  3.2 Processing

Figure 2: Flowchart of corpus construction. “Q-S Pair” stands for “Quotation-
Speaker Pair”.

Considering that pre-training models such as BERT usually use fixed-size
vocabulary, we need to ensure that the input text contains only common English
letters and punctuations to facilitate training and fine-tuning. Therefore, we
extracted the plain text and related metadata from the source code of the
webpage downloaded from a website that is mixed with a large number of HTML
tags.

A single line break ("$\backslash$n") is used in the text to distinguish
different paragraphs. Rich media interspersed in the original webpage, such as
photos, video clips, audio clips, tweets, and other web pages, are deleted.
The advertisements in the article and the copyright notice placed at the end
of the article have also been removed so as not to affect the model’s
understanding of semantics. The CSS styles used by some web pages to add
punctuation marks, such as quotes to news, are converted into standard
characters. Invalid characters, such as Emoji and non-English characters, are
replaced with spaces. The title of each subsection is kept in a separate
paragraph.

###  3.3 Screening and Resampling

The news collected covers many genres. Hard news focuses on significant
current events, while soft news focuses on editorials, blogs, summaries, and
gossip. Serious news covers political and business news, while entertainment
news is about sports, fashion, and travel. These texts differ in style,
semantics, and grammar. The length of the article, the number of entities, and
the number of quotations vary greatly, so the difficulty of quotation
extraction and attribution tasks is different.

To alleviate the unbalanced distribution of news text in time, length, genre,
and content, we filter and resample the collected news. After these processes,
we obtain hard news covering global politics that is evenly distributed in
terms of publication time and the number of words; moreover, publishers such
as the New York Times tend to combine reports and opinions in the same text.
These texts are also selected into the corpus to increase the diversity of the
corpus and prevent the model from deteriorating when dealing with such news.

###  3.4 Direct Quotation Extraction

_Quotation extraction_ is defined as extracting reported speech from a third
party in the text, also known as reported speech extraction. As shown in Table
2, there are three types of quotation based on the position of the quotation
marks. The entire content of the _direct quotation_ is in quotation marks,
which means that what the speaker said is transcribed verbatim. In contrast,
quotation marks do not identify _indirect quotations_ that change the
speaker’s original words but have the same meaning. In particular, part of the
content of a _mixed quotation_ is inside the quotation marks, and part is
outside the quotation marks, which means that the critical content of the
speaker is kept verbatim, and the rest is adjusted to fit the sentence
grammatically.

The quotation marks have other usages. Some writers put quotation marks around
the words they want to distance themselves from. Quotation marks may also
indicate words used ironically or with some reservations or to signify words
used as words. In these cases, the text inside the quotation marks is not a
quotation.

First, we take direct and mixed quotations into consideration; however, mixed
quotations are often confused with other sentence components, which seriously
affects the token level agreement. The distinction between mixed speech and
unquoted speech is also vague.

To simplify the extraction task, we only consider the direct quotations
containing independent sentences, which means that there is at least one
clause in the quotation marks. This provision ensures that the extracted text
expresses something, which is conducive to applying quotations in downstream
tasks such as opinion mining and sentiment analysis. In the implementation,
simple regular expressions are used to extract all of the text inside the
quotations. Thereafter, the quotations that meet the requirements are selected
through manual annotation.

###  3.5 Direct Quotation Attribution

Table 2: Representative examples of direct quotation extraction and
attribution President Trump who made a statement that _“the growth was about
to peak”_ has been visiting China.
---
Many said: _“Release the prisoners!”_
Rothstein said she rejected “any suggestion that the public interest favors
requiring AWS to host the incendiary speech that the record shows some of
Parler’s users have engaged in.”
_“If you find it in Germany,”_ he said, _“you will find it in my bakery.”_

In this step, each quotation is attributed to an optional speaker.
Specifically, the speaker is determined by a text span in the context window
where the quotation is located.

Because the quotation attribution task mainly tracks people’s attitudes and
statements, a large number of downstream tasks, such as fact-checking, will
perform entity linking on speakers. Therefore, we hope that the speaker is a
mention of an exact person entity. Hence, every speaker can be linked to an
item in an entity library, such as Wikidata. Specifically, the legal speaker
span can be a personal pronoun or a person’s name. Allowing pronouns to act as
legitimate speakers separates the coreference resolution from the attribution
task, which improves the token-level agreement and reduces the possibility
that the speaker cannot be found in a smaller context window. Therefore, the
task is simplified, and the sequence length is shortened.

The speaker is neither a broad communicative agent, such as an artifact,
organization, website, database, or the implication of a person, such as
identity, nickname, and characteristics, because what they refer to may not be
associated with a specific person. Low traceability hinders the accuracy of
the entity-linker.

Speakers’ spans are manually annotated. The annotators from the crowdsourcing
platform determine an optional speaker for each quotation in the context
window. If the annotator fails to find a specific speaker (no speaker or no
qualified speaker) in the context window, the quotation will be assigned the
_NONE_ label. If multiple legal speakers lexically indicate the attribution
relation, the one closest to the quotation is selected. The quotation span and
speaker span must be continuous. Multiple quotations share the speaker’s span.
The annotation format is a text pair (quote, speaker). This task ignores
nested quotations.

We show some examples to demonstrate the direct quotation extraction and
attribution (Table 2). The first example is a typical pattern of direct
quotation extraction and attribution. We choose “Trump” instead of “President
Trump” as the speaker, because “President” is an identity, not part of his
name. Hence we get the most accurate speaker span. In the second example,
“many” is not a named entity or unambiguous pronoun, therefore it is not a
valid speaker. For this reason, the quotation does not has a speaker. By
adding the requirement, we ensure that all speakers are traceable and suitable
for downstream tasks such as entity linking. In the third example, content in
quotation marks is a none phrase instead of a complete clause. The premise
that quotations annotated have clear semantics is guaranteed by excluding
incomplete sentence. In the fourth example, two quotations share the same
speakers. The sequence labeling method described above is capable of handling
this pattern.

###  3.6 Validation

During annotation, we revise the annotation guidelines to improve the
consistency of the corpus. At least three crowdsourced workers view the labels
of each context window. If an annotation decision cannot be agreed upon, it
will be determined according to the annotation guidelines. For context windows
with multiple candidate speakers, the author manually check all annotations.
Finally, in 19,706 context windows, 10,279 quotations are obtained, of which
8,831 can be attributed to a specific speaker, and the remaining 1,522 have no
explicit valid speakers.

We treat quotation extraction and attribution as a sequence labeling task and
treat each token as an independent labeling decision to examine whether the
label is correct and whether the boundary of each span is accurate. After
sampling 20$\%$ of the context windows, the Krippendorff’s alpha is 0.81. The
vast majority of inconsistencies are due to the ambiguity of the speaker span.

Figure 3: Relative position of the quotation and the speaker and the
corresponding sequence.

##  4 Baseline Methods and Results

###  4.1 Methods

Although the common rule-based method is fast and performs well in the cases
of simple syntax, it cannot handle rare quotation patterns.

We decide not to adopt the pipeline design of Pareti (2016). In their work,
separate models are designed to solve quotation extraction and attribution
tasks, and additional models are introduced for named entity recognition and
dependency analysis during preprocessing. Multiple pipeline stages increase
the cumulative error and increase the time and space cost of the model, which
is not suitable for scenarios with massive amounts of data.

Instead, an end-to-end sequence annotation model is designed to perform
quotation extraction and attribution tasks simultaneously. Our model takes the
original text as input and directly predicts the quotation and speaker. As
shown in Figure 3, the model not only outputs the span of the quotation and
speaker, but also determines the correspondence between the quotation and
speaker by predicting the speaker’s direction relative to the quotation.

As shown in Figure 3, quotation extraction and attribution tasks are framed as
sequence labeling tasks, and each token is classified into one of the
following labels:

  * •

Quotation, the corresponding speaker is in the preceding text (denoted by “”)

  * •

Quotation, the corresponding speaker is in the following text (denoted by “”)

  * •

Quotation, no corresponding speaker (denoted by “”)

  * •

Speaker (denoted by “”)

  * •

Neither (denoted by “”)

All labels are in the IOB1 format. According to the type of quotation label
(left, right, no speaker), we can determine the attribution of the quotation.
In the corpus, the proportions of three types of quotations, “”“”“” , are 46%,
39% and 15% respectively.

We use the following sequence labeling methods and components:

  * •

CRF First proposed by Lafferty et al. (2001), conditional random field (CRF)
is a type of probabilistic graphical model to model sequential data such as
labels and words in sentences. During training, CRF will determine the weights
of hand-crafted feature functions to predict the labels. We adopt CRF as a
type of non-neural network method.

  * •

LSTM Long Short-Term Memory (LSTM) is a redesign of traditional recurrent
neural network architecture around its memory cell (Hochreiter and
Schmidhuber, 1997). LSTM has been shown capable of storing and accessing
information over very long timespans in varied sequence labeling tasks such as
POS tagging. We train a LSTM model as a non-pretrained neural network model.

  * •

CNN Convolutional neural network is successful in some NLP tasks using
convolution and max-pooling layer to summarize inputs (Ma and Hovy, 2016). CNN
runs in parallel to extract extracting local spatial and temporal dependence
features. Therefore, it is faster than LSTM. We add CNN layer to our model to
further enhance ability in feature extraction.

  * •

BERT Devlin et al. (2018) develop BERT, a pre-trained transformer-based
language model that achieves excellent performance through simple fine-tuning
on various natural language understanding tasks. Compared with previous
methods, BERT has stronger generalization ability, which can effectively
extract semantic and grammatical features considering long-distance
dependencies, but also involves massive parameters that occupy a lot of
storage space and take a long time to run once.

All model weights are fine-tuned to maximize the log-likelihood of the output
corresponding to the ground-truth label using the cross-entropy loss. Neither
BERT nor LSTM can handle text that is too long, so each paragraph in the
entire text is determined as a context window to be input into the model.

To prevent the model from overfitting frequently occurring names, we randomly
replace speakers with other names for data augmentation.

###  4.2 Results

Table 3: Results of quotation extraction and attribution, calculated in three categories. Method | Speaker | Quotation | Overall
---|---|---|---
Precision | Recall | F1-Measure | Precision | Recall | F1-Measure | Precision | Recall | F1-Measure
CRF | 0.7307 | 0.5296 | 0.6141 | 0.6969 | 0.6918 | 0.6943 | 0.6977 | 0.6864 | 0.6920
LSTM | 0.7368 | 0.8286 | 0.7801 | 0.7711 | 0.8534 | 0.8102 | 0.7700 | 0.8525 | 0.8092
LSTM+CRF | 0.7282 | 0.7931 | 0.7593 | 0.7816 | 0.8957 | 0.8348 | 0.7799 | 0.8922 | 0.8323
LSTM+CNN | 0.7150 | 0.8598 | 0.7808 | 0.8188 | 0.9135 | 0.8635 | 0.8150 | 0.9117 | 0.8606
LSTM+CNN+CRF | 0.7492 | 0.8409 | 0.7924 | 0.8129 | 0.9263 | 0.8659 | 0.8107 | 0.9234 | 0.8634
Bert-Base | 0.8090 | 0.9402 | 0.8697 | 0.8169 | 0.9354 | 0.8721 | 0.8164 | 0.9356 | 0.8720

The precision, recall, and F1 scores of the baseline method are shown in Table
3. 70$\%$ of the corpus is divided into training set, and the remaining 30$\%$
is divided into test set. The results are shown in three categories: speaker,
quotation, and overall. Almost all models have F1 scores of 70$\%$ or higher
in the quotation extraction and attribution tasks. This proves that it is
feasible to model the joint task of quotation extraction and attribution as a
sequence labeling task. By adding a CNN layer or a CRF layer, the feature
extraction ability of LSTM is improved, which increases the overall recall
rate by approximately 3$\%$-6$\%$. Because BERT is pre-trained on a large
number of corpora, and the Transformer model can effectively extract different
levels of semantic and grammatical features, the BERT model has stronger
accuracy and generalization capabilities, and outperforms other models by
approximately 6$\%$ absolute precision and recall of the speaker.

###  4.3 Case Study

Table 4: Examples of extraction and attribution results of the baseline models. Quotations are marked in blue, and speakers are marked in red. Input |  “We are concerned the failure to secure an adequate supply of vaccines will needlessly prolong the COVID-19 pandemic in this country, causing further loss of life and economic devastation,” a group of senators led by Patty Murray of Washington and Ron Wyden of Oregon wrote HHS.
---|---
Ground Truth |  “We are concerned the failure to secure an adequate supply of vaccines will needlessly prolong the COVID-19 pandemic in this country, causing further loss of life and economic devastation,” a group of senators led by Patty Murray of Washington and Ron Wyden of Oregon wrote HHS.
CRF |  “We are concerned the failure to secure an adequate supply of vaccines will needlessly prolong the COVID-19 pandemic in this country, causing further loss of life and economic devastation,” a group of senators led by Patty Murray of Washington and Ron Wyden of Oregon wrote HHS.
LSTM |  “We are concerned the failure to secure an adequate supply of vaccines will needlessly prolong the COVID-19 pandemic in this country, causing further loss of life and economic devastation,” a group of senators led by Patty Murray of Washington and Ron Wyden of Oregon wrote HHS.
BERT |  “We are concerned the failure to secure an adequate supply of vaccines will needlessly prolong the COVID-19 pandemic in this country, causing further loss of life and economic devastation,” a group of senators led by Patty Murray of Washington and Ron Wyden of Oregon wrote HHS.
Input |  DHS said FEMA will fund 31 high-threat, high-density urban areas that will “be required to dedicate a minimum of 30% of awards toward five priority areas: cybersecurity (7.5%); soft target and crowded places (5%); information and intelligence sharing (5%); domestic violent extremism (7.5%); and emerging threats (5%).”
Ground Truth |  DHS said FEMA will fund 31 high-threat, high-density urban areas that will “be required to dedicate a minimum of 30% of awards toward five priority areas: cybersecurity (7.5%); soft target and crowded places (5%); information and intelligence sharing (5%); domestic violent extremism (7.5%); and emerging threats (5%).”
CRF |  DHS said FEMA will fund 31 high-threat, high-density urban areas that will “be required to dedicate a minimum of 30% of awards toward five priority areas: cybersecurity (7.5%); soft target and crowded places (5%); information and intelligence sharing (5%); domestic violent extremism (7.5%); and emerging threats (5%).”
LSTM |  DHS said FEMA will fund 31 high-threat, high-density urban areas that will “be required to dedicate a minimum of 30% of awards toward five priority areas: cybersecurity (7.5%); soft target and crowded places (5%); information and intelligence sharing (5%); domestic violent extremism (7.5%); and emerging threats (5%).”
BERT |  DHS said FEMA will fund 31 high-threat, high-density urban areas that will “be required to dedicate a minimum of 30% of awards toward five priority areas: cybersecurity (7.5%); soft target and crowded places (5%); information and intelligence sharing (5%); domestic violent extremism (7.5%); and emerging threats (5%).”

Two examples are shown in Table 4. In the first instance, CRF and LSTM fail in
judging the speakers. It is quite a confusing case because “Patty Murray” and
“Ron Wyden” are actually leaders of the speakers instead of speakers
themselves. Note that BERT is more capable of understanding semantics while
other models simply extract all or part of named entities. The second example
illustrates that a quotation must not be an incomplete sentence in quotation
marks. CRF and LSTM-based models, which misjudge the content as a quotation,
may extract quotations based mainly on quotation marks. The output of BERT is
correct here probably because BERT is more sensitive to syntax.

##  5 Conclusion

This paper presents a new corpus, _DirectQuote_ , where news from 13
publishers in five countries is manually annotated to extract direct
quotations and corresponding speakers. It is helpful in solving the limitation
of insufficient resources in the quotation extraction and attribution tasks
and enable researchers to propose more sophisticated models. We apply multiple
sequence labeling models to the joint task of quotation extraction and
attribution as end-to-end baseline methods. The pre-trained BERT model
performs better in terms of accuracy and recall. By increasing the scale of
the dataset, extracting mixed quotations and indirect quotations, and applying
the dataset to large-scale automatic extraction and attribution systems will
be the future research direction.

## Acknowledgement

The authors would like to thank Xuancheng Huang and Fanzeng Xia for reviewing
and giving feedback on drafts of the paper.

## References

  * Semino and Short (2004) Elena Semino and Mick Short.  _Corpus stylistics: Speech, writing and thought presentation in a corpus of English writing_.  Routledge, 2004.
  * Cappelen and Lepore (2012) Herman Cappelen and Ernest Lepore.  Quotation.  2012\.
  * O’Keefe et al. (2013) Tim O’Keefe, James R Curran, Peter Ashwell, and Irena Koprinska.  An annotated corpus of quoted opinions in news articles.  In _Proceedings of the 51st Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)_ , pages 516–520, 2013\.
  * WP et al. (2020) Yohanes Sigit Purnomo WP, Yogan Jaya Kumar, and Nur Zareen Zulkarnain.  Understanding quotation extraction and attribution: towards automatic extraction of public figure’s statements for journalism in indonesia.  _Global Knowledge, Memory and Communication_ , 2020.
  * Floridi and Chiriatti (2020) Luciano Floridi and Massimo Chiriatti.  Gpt-3: Its nature, scope, limits, and consequences.  _Minds and Machines_ , 30(4):681–694, 2020.
  * Balahur et al. (2009) Alexandra Balahur, Ralf Steinberger, Erik Van Der Goot, Bruno Pouliquen, and Mijail Kabadjov.  Opinion mining on newspaper quotations.  In _2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology_ , volume 3, pages 523–526. IEEE, 2009.
  * Balahur et al. (2013) Alexandra Balahur, Ralf Steinberger, Mijail Kabadjov, Vanni Zavarella, Erik Van Der Goot, Matina Halkia, Bruno Pouliquen, and Jenya Belyaeva.  Sentiment analysis in the news.  _arXiv preprint arXiv:1309.6202_ , 2013.
  * Papay and Padó (2020) Sean Papay and Sebastian Padó.  Riqua: A corpus of rich quotation annotation for english literary text.  In _Proceedings of The 12th Language Resources and Evaluation Conference_ , pages 835–841, 2020.
  * Stymne and Östman (2020) Sara Stymne and Carin Östman.  Slända: An annotated corpus of narrative and dialogue in swedish literary fiction.  In _Proceedings of The 12th Language Resources and Evaluation Conference_ , pages 826–834, 2020.
  * Chen et al. (2019) Jia-Xiang Chen, Zhen-Hua Ling, and Li-Rong Dai.  A chinese dataset for identifying speakers in novels.  In _INTERSPEECH_ , pages 1561–1565. Graz, Austria, 2019.
  * Zhang et al. (2019) Hao Zhang, Frank Boons, and Riza Batista-Navarro.  Whose story is it anyway? automatic extraction of accounts from news articles.  _Information Processing & Management_, 56(5):1837–1848, 2019.
  * Pareti (2016) Silvia Pareti.  Parc 3.0: A corpus of attribution relations.  In _Proceedings of the Tenth International Conference on Language Resources and Evaluation (LREC’16)_ , pages 3914–3920, 2016.
  * Newell et al. (2018) Edward Newell, Drew Margolin, and Derek Ruths.  An attribution relations corpus for political news.  In _Proceedings of the Eleventh International Conference on Language Resources and Evaluation (LREC 2018)_ , 2018.
  * Prasad et al. (2008) Rashmi Prasad, Nikhil Dinesh, Alan Lee, Eleni Miltsakaki, Livio Robaldo, Aravind K Joshi, and Bonnie L Webber.  The penn discourse treebank 2.0.  In _LREC_. Citeseer, 2008.
  * Pustejovsky et al. (2003) James Pustejovsky, Patrick Hanks, Roser Sauri, Andrew See, Robert Gaizauskas, Andrea Setzer, Dragomir Radev, Beth Sundheim, David Day, Lisa Ferro, et al.  The timebank corpus.  In _Corpus linguistics_ , volume 2003, page 40. Lancaster, UK., 2003\.
  * Deng and Wiebe (2015) Lingjia Deng and Janyce Wiebe.  Mpqa 3.0: An entity/event-level sentiment corpus.  In _Proceedings of the 2015 conference of the North American chapter of the association for computational linguistics: human language technologies_ , pages 1323–1328, 2015.
  * Seki et al. (2008) Yohei Seki, David Kirk Evans, Lun-Wei Ku, Le Sun 0001, Hsin-Hsi Chen, and Noriko Kando.  Overview of multilingual opinion analysis task at ntcir-7.  In _NTCIR_ , pages 185–203. Citeseer, 2008.
  * Seki et al. (2010) Yohei Seki, Lun-Wei Ku, Le Sun, Hsin-His Chen, and Noriko Kando.  Overview of multilingual opinion analysis task at ntcir-8.  In _Proc. of the Seventh NTCIR Workshop_ , 2010.
  * Elson and McKeown (2010) David K Elson and Kathleen R McKeown.  Automatic attribution of quoted speech in literary narrative.  In _Twenty-Fourth AAAI Conference on Artificial Intelligence_ , 2010\.
  * Elson et al. (2010) David Elson, Nicholas Dames, and Kathleen McKeown.  Extracting social networks from literary fiction.  In _Proceedings of the 48th annual meeting of the association for computational linguistics_ , pages 138–147, 2010.
  * Fernandes et al. (2011) William Paulo Ducca Fernandes, Eduardo Motta, and Ruy Luiz Milidiú.  Quotation extraction for portuguese.  In _Proceedings of the 8th Brazilian Symposium in Information and Human Language Technology_ , 2011.
  * Lafferty et al. (2001) John Lafferty, Andrew McCallum, and Fernando CN Pereira.  Conditional random fields: Probabilistic models for segmenting and labeling sequence data.  2001\.
  * Hochreiter and Schmidhuber (1997) Sepp Hochreiter and Jürgen Schmidhuber.  Long short-term memory.  _Neural computation_ , 9(8):1735–1780, 1997.
  * Ma and Hovy (2016) Xuezhe Ma and Eduard Hovy.  End-to-end sequence labeling via bi-directional lstm-cnns-crf.  _arXiv preprint arXiv:1603.01354_ , 2016.
  * Devlin et al. (2018) Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.  Bert: Pre-training of deep bidirectional transformers for language understanding.  _arXiv preprint arXiv:1810.04805_ , 2018.