# Effective exploitation of a geyser bubble-chamber equipment as a background-
free fast neutron detector

###### Abstract

MOSCAB equipment, a geyser-concept bubble-chamber originally thought for the
search of dark matter in the form of WIMPs, is employed for the detection of
fast neutrons. Once the background-free operating conditions are determined
such that the detector is sensitive only to neutrons, which occurs when the
neutron energy threshold required for nucleation is higher than approximately
2.5 MeV, the detector response to fast neutrons is investigated using a
241AmBe neutron source.

Sets of detection efficiency functions are then produced via Monte Carlo
simulations and post-processing, their validation being performed
experimentally and discussed. Finally, the use of the detector to measure the
fast neutron activity of very weak n-sources in clean environments, as well as
to monitor the cosmic ray variations through the neutron component of the
Extensive Air Showers, is considered.

R. Bertoni1, G. Bruno2,6, N. Burgio3,4,5, M. Corcione4,5,b, L. Cretara4, M.
Frullini4,
W. Fulgione6,7,a, G. Palmerini8, A. Quintino4,5, N. Redaelli1, A.
Santagata3,4,5,
D. Sorrenti1,9, L. Zanotti1,10.

1) INFN, Sezione di Milano Bicocca, P.za della Scienza 3, I-20126 Milano,
Italy

2) New York University Abu Dhabi, United Arab Emirates

3) ENEA, Centro Ricerche Casaccia, (Roma), Italy

4) DIAEE, Sapienza Università di Roma, Via Eudossiana 18, I-00184 Roma, Italy

5) INFN, Sezione di Roma La Sapienza, P.le Aldo Moro 2, I-00185 Roma, Italy

6) INFN, LNGS, Via G. Acitelli 22, I-67100 Assergi (L’Aquila), Italy

7) INAF, Osservatorio Astrofisico di Torino, I-10025 Pino Torinese (Torino),
Italy

8) SIA, Sapienza Università di Roma, Via Salaria 851, I-00138 Roma, Italy

9) Dip.Inform., Sist. e Comunic., Università di Milano Bicocca, Italy

10) DISAT, Università di Milano Bicocca, P.za della Scienza 3, I-20126 Milano,
Italy

$\mathrm{a)}$<EMAIL_ADDRESS>
$\mathrm{b)}$<EMAIL_ADDRESS>
##  1 Introduction

The MOSCAB bubble-chamber detector relies on the geyser technique, a variant
of the superheated liquid technique of extreme simplicity originally
introduced by Hahn and Reist to detect fissions fragments [1]. It was thought,
designed, built and developed by Antonino Pullia and his team, to search for
dark matter in the form of WIMPs through a possible spin-dependent interaction
occurring with fluorine nuclei, as illustrated and discussed by Bertoni et al.
[2] and Antonicci et al. [3]. On the other hand, the same equipment, or a
simplified version of the same device, can be effectively operated to detect
fast neutrons, which is the topic of the present paper.

MOSCAB detector has been firstly tested above ground at Milano-Bicocca
University using, as a target liquid, 0.7L of octafluoropropane
($\mathrm{C_{3}F_{8}}$) kept at different metastability conditions. Later, the
apparatus was moved underground to the INFN Gran Sasso National Laboratories
(LNGS), repeating both background and neutron sensitivity measurements, which
were performed for two different configurations of the detector, equipped with
either a 2L vessel filled with 1.2L of $\mathrm{C_{3}F_{8}}$ or a 18L vessel
filled with 13L of $\mathrm{C_{3}F_{8}}$.

The operation principles of MOSCAB detector, exactly as for any traditional
bubble chamber, are based on the theoretical model originally proposed by
Seitz [4], according to which pressure and temperature of the metastable
liquid determine the minimum recoil energy required for bubble nucleation,
also called the critical energy. On the other hand, since the critical energy
must be released within a sufficiently small volume of the sensitive liquid,
bubble nucleation depends also on the stopping power of the ionizing particle,
which makes the detector entirely unaffected by the backgrounds due to
recoiling electrons and minimum ionizing radiation, provided that the critical
energy is not too low. This means that, besides neutrons, the only residual
particle-induced background is represented by $\alpha$-decay events, yet, as
it will be shown, such a source of background can be completely muted by
operating the detector above specific recoil energy thresholds.

In this general framework, thanks to the extremely low neutron flux typical of
the environmental background of LNGS underground laboratories, as well
described by Wulandari et al.[5], we could easily conduct measurements of the
residual internal background of the detector. Subsequently, the bubble
nucleation model describing the behaviour of the detector operated in
different configurations and exposed to a neutron source is presented, and the
related detection efficiency functions for fast neutrons with energies up to
20 MeV are employed to compare the experimental data with the numerical
results of Monte Carlo simulations and post-processing. Finally, the detector
sensitivity and its possible applications in measuring and monitoring low
fluxes of fast neutrons in the absence of background are also discussed.

##  2 Basic outlines of the detector

The MOSCAB detector basically consists of a closed quartz vessel filled with a
target liquid, i.e., $\mathrm{C_{3}F_{8}}$, and its saturated vapour. The
bottom of the vessel contains the sensitive liquid kept at a constant
temperature $\mathnormal{T_{L}}$ by an external thermal bath, whereas the
saturated vapour located on top of it is maintained at a lower constant
temperature $\mathnormal{T_{V}}$. Considering that the pressure exerted inside
the vessel is the saturation pressure ${\mathnormal{p_{s}(T_{V})}}$ imposed by
the vapour, which is lower than the equilibrium saturation pressure
$\mathnormal{p_{s}(T_{L})}$, the target liquid is in underpressure, and then
in a superheated state, whose degree of metastability can be identified using
the reduced superheat parameter $\mathnormal{SH}$ introduced by d’Errico [6]

$\mathnormal{SH}=\frac{\mathnormal{T_{L}}-\mathnormal{T_{V}}}{\mathnormal{T_{c}}-\mathnormal{T_{V}}}$
(1)

where $\mathnormal{T_{c}}$ is the critical temperature of the target liquid,
i.e., $\mathnormal{T_{c}}$ $\mathnormal{\mathrm{=71.87~{}^{o}C}}$.

The degree of metastability is continuously monitored by measuring both the
liquid temperature $\mathnormal{T_{L}}$ and the saturated vapour pressure
$\mathnormal{p_{s}(T_{V})}$ with a sampling time interval of 6 seconds, then
calculating the vapour temperature $\mathnormal{T_{V}}$ using the fluid
properties at saturation extracted from the NIST Chemistry Web Book [7].

A schematic view of the MOSCAB bubble chamber is displayed in Figure 1, in
which the two different configurations of the detector discussed in the
present work, one equipped with a 2L vessel and the other with a 18L vessel,
are shown superimposed. A detailed description of the apparatus can be found
in the study performed by Antonicci et al. [3].

Figure 1: The MOSCAB bubble chamber. Both the 2L and 18L vessels are reported.

As far as the response to ionizing particles is concerned, bubble nucleation
requires that the locally deposited energy of a traversing particle exceeds a
defined critical energy necessitated to create a vapour bubble of critical
radius $\mathnormal{R_{c}}$, i.e., ${\mathnormal{E_{dep}\geq E_{c}}}$, and
that the stopping power of the particle is large enough to release this energy
as heat over a critical deposition length ${\mathnormal{L_{c}}}$ such to be
effective to produce a stable vapour bubble of radius $\mathnormal{R_{c}}$,
the subsequent growth of the newborn bubble being ensured by the energy
supplied by the surrounding liquid, as described by Archambault et al. [8],
which means

$\mathnormal{E_{dep}=\int^{L_{c}}_{0}S(E)~{}dx\geq E_{c}},$ (2)

where $S(E)=-dE/dx$ is the stopping power of the ionizing particle of energy
$E$, whose values can be calculated using the SRIM package [9].

The critical energy $\mathnormal{E_{c}}$ is given by the sum of the energy
required to vaporize the mass of liquid involved in the phase change and the
energy required to form the vapour bubble surface

$\mathnormal{E_{c}}=\frac{4}{3}\pi\mathnormal{R_{c}}^{3}\mathnormal{\rho_{V}}\mathnormal{\lambda}+4\pi\mathnormal{R_{c}}^{2}\
(\mathnormal{\sigma}-\mathnormal{T_{L}}\frac{\mathrm{d}\mathnormal{\sigma}}{\mathrm{d}\mathnormal{T}}\
),$ (3)

where $\mathnormal{\rho_{V}}$ is the mass density of the saturated vapour and
$\mathnormal{\lambda}$ is the latent heat of vaporization, both evaluated at
the vapour temperature $\mathnormal{T_{V}}$, while $\mathnormal{\sigma}$ is
the surface tension of the liquid calculated at the liquid temperature
$\mathnormal{T_{L}}$.

The critical radius $\mathnormal{R_{c}}$, consistent with the condition of
mechanical equilibrium between the surface tension and the pressure difference
at the bubble surface, can be calculated as the radius of the vapour bubble
corresponding to the maximum of the free enthalpy variation associated with
the phase change

$\mathnormal{R_{c}}=\frac{2\mathnormal{\sigma}}{\mathnormal{\rho_{V}}\mathnormal{\lambda}\frac{\mathnormal{T_{L}}-\mathnormal{T_{V}}}{\mathnormal{T_{V}}}}.$
(4)

In the present investigation, the detector has been operated at a stable
nominal liquid temperature $\mathnormal{T_{L}\mathrm{=25~{}^{o}C}}$ with a
maximum liquid-vapour temperature difference around $\mathrm{5~{}^{o}C}$,
which corresponds to a maximum liquid underpressure of about 1 bar.
Accordingly, the superheat parameter $\mathnormal{SH}$ ranges approximately
between 0.05 and 0.1, while the related critical energy $\mathnormal{E_{c}}$
spans from about 100 keV to nearly 500 keV and the critical radius
$\mathnormal{R_{c}}$ from 80 nm to 140 nm.

Indeed, as thoroughly discussed in a recent study performed by Bruno et al.
[10], a number of equations are available in the literature for the
calculation of $\mathnormal{R_{c}}$ and $\mathnormal{E_{c}}$, see e.g. Bugg
[11] and Tenner [12], to name a few. However, in the critical energy range of
interest for the current study the use of equations (3) and (4) or alternative
equations proposed by other authors is essentially equivalent, leading to
values of $\mathnormal{E_{c}}$ well in agreement within 5 percent.
Additionally, it seems worth pointing out that, due to the relatively small
temperature differences imposed between the target liquid and its vapour, the
critical radius $\mathnormal{R_{c}}$ can be reasonably assumed to be
proportional to 1/$SH$ — see equations (1) and (4) — which implies that, since
the volume term in the critical energy equation is largely predominant with
respect to the surface term, the critical energy $\mathnormal{E_{c}}$ can be
regarded to be proportional to $R_{c}\mathrm{{}^{3}}$, and then to 1/$SH^{3}$.

On the other hand, since $\mathnormal{R_{c}}$ is the natural length scale of
the process, the critical deposition length ${\mathnormal{L_{c}}}$ can be
expressed in units of the critical diameter of the vapour bubble

$L_{c}=k_{D}\cdot(2R_{c})$ (5)

where ${\mathnormal{k_{D}}}$ represents the so-called nucleation parameter,
whose value, as well as its possible dependence on ${\mathnormal{SH}}$ or
${\mathnormal{E_{c}}}$, are not known a priori, but have to be estimated by
comparing the experimental counting rates at several operating conditions with
the corresponding predictions of Monte Carlo simulations combined with the
application of the nucleation model. Indeed, different possible values of the
nucleation parameter are reported in the literature ranging from 1 to 10 or
more, yet, a value of the order of 3, regardless of the nature of the
sensitive liquid, seems to find possible theoretical justifications, as e.g.
discussed by Norman and Spiegel [13], and Bell [14]. Moreover, according to
Archambault et al. [8], the value of ${\mathnormal{k_{D}}}$ should be expected
to increase as the critical energy is increased.

##  3  Background measurements and detector response to
$\alpha$-decay events

Figure 2: Stopping power in $\mathrm{C_{3}F_{8}}$ at $\mathrm{25^{o}C}$ for
carbon, fluorine and alpha particles (from SRIM package). The region of the
parameter space in which nucleation is permitted is highlighted.

The main strength of bubble-chamber detectors using superheated liquids is
that they can be operated in such thermodynamic conditions to make them
insensitive to electron recoils and minimum ionizing particles, which is the
case of the aforementioned operating conditions of the MOSCAB detector. This
means that the only remaining sources available for bubble nucleation are
neutrons and $\alpha-$decays occurring inside the liquid. However, it must be
pointed out that $\alpha-$particles have a stopping power always lower than
that of fluorine and carbon ions, as recently discussed by Ardid et al. [15].
This implies that it is possible to find a region in the parameter space
${(E,dE/dx)}$ where the detector maintains its sensitivity to nuclear recoils
of fluorine and carbon ions, becoming at the same time insensitive to
$\alpha-$particles, whose stopping power, even at the Bragg peak, is lower
than that required for bubble nucleation, as displayed in Figure 2, in which
the stopping powers in $\mathrm{C_{3}F_{8}}$ at $\mathrm{25~{}^{o}C}$ for
fluorine and carbon ions are compared with the stopping power typical for an
$\alpha-$particle.

Additionally, it must be considered that, although the daughter nuclei emitted
in the $\alpha-$decay process, namely $\mathrm{{}^{218}Po}$,
$\mathrm{{}^{214}Pb}$ and $\mathrm{{}^{210}Pb}$ in the case of the
$\mathrm{{}^{222}Rn}$ decay chain, have a remarkable stopping power, much
higher than $\mathrm{{}^{12}C}$ and $\mathrm{{}^{19}F}$, their kinetic energy
is rather limited. In fact, the highest energy of a naturally emitted
$\alpha-$particle is 8.79 MeV, from the decay of $\mathrm{{}^{212}Po}$ in the
$\mathrm{{}^{232}Th}$ cascade, which implies a kinetic energy of the
corresponding recoiling nucleus lower than 170 keV. Considering that the
energy released by the recoiling nucleus and some amount of the energy
deposited by the $\alpha-$particle along its track can add up, it is expected
that at a critical energy around 200 keV the detector starts becoming
insensitive to $\alpha-$decay processes.

Figure 3: Background counting rates of the MOSCAB detector equipped with the
18L vessel filled with 13L of $\mathrm{C_{3}F_{8}}$ plotted versus both the
critical energy $\mathnormal{E_{c}}$ and the superheat parameter
$\mathnormal{SH}$.

A detailed study of this behaviour has been conducted with the MOSCAB detector
located in Hall C of LNGS underground laboratories. The detector was equipped
with both the 2L and the 18L vessels, filled with 1.2L and 13L of
$\mathrm{C_{3}F_{8}}$, respectively, and, as said earlier, operated in
thermodynamic conditions tuned to obtain a superheat parameter
$\mathnormal{SH}$ ranging roughly between 0.05 and 0.1, which corresponds to
an approximate critical energy range between 100 keV and 500 keV. In
particular, a campaign of measurements more than 1800 hours long has been
performed from February 2020 to February 2021 to characterize the background
of the detector equipped with the 18L vessel, whose results are shown in
Figure 3, confirming the results previously obtained using the 2L vessel. It
is apparent that the background counting rate dramatically decreases as
$\mathnormal{E_{c}}$ increases from 100 keV to 200 keV, i.e., as
$\mathnormal{SH}$ decreases from 0.09 to about 0.07, reaching values lower
than one event per ten days, full in line with the neutron flux at the Gran
Sasso underground Laboratory, which confirms that the main intrinsic
background source of the detector is represented by $\alpha-$decays mostly due
to the $\mathrm{{}^{222}Rn}$ chain and that when the detector is operated at
$\mathrm{SH\leq 0.07}$ its internal background rate becomes lower than or at
least of the same magnitude of the extremely low environmental neutron flux.

##  4 Detector response to fast neutrons

###  4.1 Data taking

To measure the detector sensitivity, the bottom of the MOSCAB bubble chamber
includes a vertical sleeve allowing to locate a calibration source just below
the quartz vessel to minimize the amount of water between the source and the
target liquid. Therefore, the response to neutrons of the detector operated in
the same thermodynamic conditions as those indicated before was measured using
a 241AmBe neutron source, with an integral neutron strength of nearly 1 n/s.

Figure 4: Event rates of the MOSCAB detector equipped with the 18L vessel,
plotted versus both $\mathnormal{E_{c}}$ and $\mathnormal{SH}$. Full down
triangles (black) represent the background counting rate, while the red dots
represent the event rate recorded using the 241AmBe n-source.

The measurements of the detector response to neutron-induced ion recoils have
been performed from December 2019 to April 2021, during more than 2000 hours
of data taking. The 241AmBe source has been used with the detector equipped
with the 2L and the 18L vessels. The results related to the 18L vessel filled
with 13L of $\mathrm{C_{3}F_{8}}$ are reported in Figure 4, where the
distributions of the recorded event rate are plotted versus the critical
energy $\mathnormal{E_{c}}$ and the superheat parameter $\mathnormal{SH}$. In
the same figure, the background counting rates already shown in Figure 3 are
also displayed for comparison purposes. The horizontal error bars represent
the standard deviations of $\mathnormal{E_{c}}$ or $\mathnormal{SH}$, which is
mainly due to the instrumental uncertainties and hence constant with respect
to $\mathnormal{SH}$, whereas the vertical error bars represent the
uncertainty of the mean counting rate.

It is apparent that, even for superheat conditions such that the background
counting rate is negligible, i.e., lower than one event per 10 days, the
detector maintains its sensitivity to neutron-induced ion recoils.

###  4.2 Detector response simulation

The modelling of the detector response is based on the bubble nucleation
process described earlier and summarized by equation (5), which defines the
nucleation parameter $k_{D}$, whose values have been determined by the
comparison between each experimental bubble rate detected using the mentioned
241AmBe neutron source located beneath the 2L vessel or the 18L vessel and the
numerical results of the Monte Carlo simulations and post-processing carried
out in the same thermodynamic conditions. The effects of the neutron transport
and elastic and inelastic interactions with the fluorine and carbon nuclei of
the sensitive liquid are evaluated by the way of the MCNP 6.2 code [16] and
the SPECTRA-PKA code [17]. The energy distributions of the recoiled ions, in
conjunction with the stopping power data for $\mathrm{{}^{19}F}$ and
$\mathrm{{}^{12}C}$ in $\mathrm{C_{3}F_{8}}$ at temperature $T_{L}$ calculated
by the way of the SRIM code, are then used to determine the critical
deposition length $L_{c}$ along which, in the continuous slowing-down
approximation, a recoiled ion deposits an average energy $E_{dep}$ at least
equal to the critical energy $E_{c}$, such that the simulated and experimental
counting rates are the same.

Accordingly, denoting as $(d\dot{N}_{r}/dE)_{C}$ and $(d\dot{N}_{r}/dE)_{F}$
the rate of carbon and fluorine recoiled ions per unit energy, respectively, a
pair of threshold recoil energies $E_{th}^{C}$ and $E_{th}^{F}$ can be
determined for each value of $\mathnormal{E_{c}}$ such that the nucleation
rate $\dot{N}_{ev}(E_{c},k_{D})$ is

$\dot{N}_{ev}(E_{c},k_{D})=\int^{\infty}_{E_{th}^{C}}\left(\frac{d\dot{N}_{r}}{dE}\right)_{C}~{}dE+\int^{\infty}_{E_{th}^{F}}\left(\frac{d\dot{N}_{r}}{dE}\right)_{F}~{}dE.$
(6)

Thus, once the numerical counting rate is imposed to be the same as the
experimental one and the critical deposition length $L_{c}$ is assumed to be
the same for any ionizing particle, the value of $k_{D}$ can be calculated by
integrating the reciprocal of the stopping power for either 12C or 19F

$\mathnormal{k_{D}(E_{c})=\frac{\mathrm{1}}{\mathrm{2}R_{c}(E_{c})}\int^{E_{th}^{F}}_{E_{th}^{F}-E_{c}}\frac{{dE}}{S_{F}(E)}=\frac{\mathrm{1}}{\mathrm{2}R_{c}(E_{c})}\int^{E_{th}^{C}}_{E_{th}^{C}-E_{c}}\frac{{dE}}{S_{C}(E)}}.$
(7)

Figure 5: The nucleation parameter $k_{D}$ as a function of the critical
energy $\mathnormal{E_{c}}$ and the superheat parameter $\mathnormal{SH}$. The
red dots and blue triangles are obtained by the measurements with the 18L
vessel and the 2L vessel respectively. The best fit curve is shown with the
1$\sigma$ region shaded in grey.

The distribution of the values obtained for the nucleation parameter $k_{D}$
is displayed in Figure 5 versus the critical energy $E_{c}$ and the superheat
parameter $\mathnormal{SH}$, showing that the critical deposition length is
practically independent of the volume of the sensitive liquid, which means
that $k_{D}$ can be considered to be a characteristic of the target liquid and
its degree of metastability. As far as the interpolation curve is concerned,
it must be noticed that within the investigated energy range the electronic
stopping power for both fluorine and carbon ions is largely dominant with
respect to the nuclear counterpart and, since its value is directly
proportional to the ion speed, as described by Lindhard [19], the solution of
each integral in equation (7) can be assumed to be proportional to
$E_{c}^{1/2}$. Therefore, taking into account the afore-mentioned
proportionality relation $R_{c}\propto E_{c}^{1/3}$, the nucleation parameter
$k_{D}$ is expected to be proportional to $E_{c}^{1/6}$, which can be
expressed using the general form:

$\mathnormal{k_{D}(E_{c})=a\cdot\sqrt[6]{E_{c}}+b}.$ (8)

Actually, a satisfactory best fit of the data is obtained when the values of
the two empirical constants $a$ and $b$ are assumed to be 0.42 and 1.70, as
shown in Figure 5 where the 1$\sigma$ region is shaded in grey.

Figure 6: The neutron energy threshold as a function of $\mathnormal{E_{c}}$
and $SH$. The red dots and blue triangles are obtained by the measurements
with the 18L vessel and the 2L vessel respectively. Small for F nuclei and
large for C nuclei.

The procedure described above allows to determine a direct relationship
between the metastability degree at which the equipment is operated,
identified by the reduced superheat parameter $SH$, and the neutron energy
threshold $E_{th}^{n}$. In fact, the recoil energy thresholds $E_{th}^{C}$ and
$E_{th}^{F}$ establish the minimum amount of kinetic energy needed to the
recoiled ion to produce a bubble nucleation and then, taking into account the
kinematic factor, the corresponding neutron energy threshold $E_{th}^{n}$.
Indeed, in the entire investigated energy range such a neutron energy
threshold is determined by carbon, as displayed in Figure 6, where the
distributions of $E_{th}^{n}$, due to recoiling $\mathrm{{}^{12}C}$ and
$\mathrm{{}^{19}F}$ nuclei, are plotted versus both $E_{c}$ and the
$\mathnormal{SH}$. According to the data, the relationships existing between
the neutron threshold $E_{th}^{n}$ and both the critical energy and the
superheat parameter are well approximated by the following equations

$\displaystyle\mathnormal{E_{th}^{n}(E_{c})}=(12.5\pm 0.2)E_{c}+(7.5\pm 70)$
(9) $\displaystyle\mathnormal{E_{th}^{n}(SH)=\mathrm{\frac{(1.036\pm
0.016)}{\mathnormal{SH}^{2.95}}+(7.5\pm 70)}}$ (10)

##  5 Efficiency curves

Figure 7: Efficiency functions of the MOSCAB detector versus the neutron
energy. The efficiencies curves are calculated for an isotropic point-like
source located at the bottom of the 18L vessel filled with 13L of
$\mathrm{C_{3}F_{8}}$ and different value of the critical energy
$\mathnormal{E_{c}}$.

The bubble nucleation model based on equations (2)-(5) and (8) exhaustively
describes the behaviour of MOSCAB detector, at least in the critical energy
range $\mathrm{100~{}keV\leq\mathnormal{E_{c}}}$
$\mathrm{\mathnormal{E_{c}}\leq 500~{}keV}$, thus allowing to generate, via
MCNP simulations and subsequent data processing, sets of response functions
using mono-energetic neutron sources.

The detection efficiency curves computed for an isotropic point-like source
located just below the bottom of the 18L vessel filled with 13L of
$\mathrm{C_{3}F_{8}}$ are displayed in Figure 7, where the distributions of
the expected number of nucleation events per emitted neutron are plotted
against the neutron energy, using the critical energy $\mathnormal{E_{c}}$ as
a parameter. Similar response functions have also been obtained using the 2L
vessel filled with 1.2L of $\mathrm{C_{3}F_{8}}$. Notice that, due to the
location of the source and its isotropic emission, the maximum reachable
detection efficiency is of about 35% for the 18L vessel, and about 20% for the
2L vessel due to the different geometry of the two jars.

The obtained efficiency curves have then been employed to determine the rates
of nucleation events consequent to the emission by the 241AmBe neutron source
used in the experimental campaign. The comparison between the simulated
counting rates and the experimental data is reported in Figure 8 for the 2L
and the 18L vessels. The excellent agreement proves the reliability of the
developed nucleation model, which proves to be effective regardless of the
amount of the target liquid and the geometry of the vessel.

Figure 8: Event rate response of the MOSCAB detector to the 241AmBe neutron
source equipped with the 18L and the 2L vessels filled with
$\mathrm{C_{3}F_{8}}$, plotted versus both $\mathnormal{E_{c}}$ and
$\mathnormal{SH}$. The red dots and blue triangles represent the counting rate
detected inside the 18L and the 2L vessels respectively. The black dots
represent the corresponding results from the Monte Carlo simulations.

Thus, using this bubble-chamber detector, placed in a clean environment, i.e.,
an underground laboratory, it is possible to characterize a neutron source
and, if the energy spectrum is known, determine its activity with very high
sensitivity in a reasonable time. In fact, if the rate of neutrons emitted by
the source per unit energy is written as

$\frac{d\dot{N}_{n}}{dE}=A\cdot g_{n}(E)$ (11)

where A is the source activity and $g_{n}(E)$ is the normalized spectrum of
the neutron source, then the nucleation rate detected when the critical energy
is set to $\mathnormal{E_{c}}$ can be expressed as

$\dot{N}_{ev}(E_{c})=\int^{\infty}_{0}{G(E_{c},E)\cdot A\cdot g_{n}(E)dE}$
(12)

in which $G(E_{c},E)$ is the efficiency function describing the response of
the detector to neutrons emitted by a point-like source located in the source-
housing of the equipment. Accordingly, the minimum detectable source activity
can be evaluated as:

$A_{min}(E_{c})=\frac{\dot{N}_{s}(E_{c})}{\int^{\infty}_{0}{G(E_{c},E)\cdot
g_{n}(E)dE}}$ (13)

in which $\dot{N}_{s}$ represents the 99% c.l. upper limit of the background
counting rate, or the lower discernible counting rate due to a neutron source.

If the external background conditions are the same as those of the LNGS
underground laboratory, the results achieved for an isotropic point-like
neutron source located inside the detector source-housing, for example a 252Cf
source, are listed in Table 1 for different values of the critical energy
$\mathnormal{E_{c}}$. Thus, a 252Cf source with an activity of $\mathrm{1\cdot
10^{-3}}$ neutrons per second could be disentangled from the background at 99%
c.l. by a measurement having a duration of the order of ten days. Of course,
should both the activity and the energy spectrum of the source be unknown, the
coupling of the procedure discussed above with an unfolding technique can
effectively be used to fully characterize the neutron source emission.

Table 1: Minimum detectable source activity, $\mathrm{A_{min}}$, for a 252Cf source placed inside the detector source-housing, if the external background conditions are the same as those of the LNGS underground laboratory. $\mathnormal{E_{c}}~{}[keV]$ | $\mathrm{\dot{N}_{s}~{}[{ev}\cdot sec^{-1}]}$ | $\int^{\infty}_{0}{G(E_{c},E)g_{n}(E)dE}$ | $\mathrm{A_{min}~{}[n\cdot sec^{-1}]}$
---|---|---|---
100 | $~{}~{}~{}\mathrm{1.91\cdot 10^{-4}}$ | $\mathrm{7.80\cdot 10^{-2}}$ | $\mathrm{2.45\cdot 10^{-3}}$
200 | $~{}~{}~{}\mathrm{1.44\cdot 10^{-5}}$ | $\mathrm{1.78\cdot 10^{-2}}$ | $\mathrm{8.09\cdot 10^{-4}}$
300 | $~{}~{}~{}\mathrm{9.00\cdot 10^{-6}}$ | $\mathrm{4.42\cdot 10^{-3}}$ | $\mathrm{2.04\cdot 10^{-3}}$
400 | $~{}~{}~{}\mathrm{5.33\cdot 10^{-6}}$ | $\mathrm{9.08\cdot 10^{-4}}$ | $\mathrm{5.87\cdot 10^{-3}}$
500 | $~{}~{}~{}\mathrm{5.33\cdot 10^{-6}}$ | $\mathrm{2.64\cdot 10^{-4}}$ | $\mathrm{2.02\cdot 10^{-2}}$

Figure 9: Event rates of the MOSCAB detector equipped with the 18L vessels,
plotted versus both $\mathnormal{E_{c}}$ and $\mathnormal{SH}$. The red dots
represent the detector counting rate when the 241AmBe source is located inside
the source-housing, while the blue stars represent the counting when the same
source is placed in contact with the outer surface of the detector. The black
dots reports the corresponding results from the simulations. The background
counting rate, represented using black down triangles, is also reported and
compared with the counting rate expected from the environmental fast neutron
flux as calculated by Wulandari et al. [5] for the Hall C of the Gran Sasso
Laboratory (gray line).

The validation of the simulation of the detector behaviour, which the
efficiency curves are derived from, has been carried out by changing the
experimental conditions, i.e., by moving the 241AmBe source from the source-
housing at the bottom of the quartz vessel to the outside of the detector, in
direct contact with its external surface, again using the 18L vessel filled
with 13L of $\mathrm{C_{3}F_{8}}$. The new counting rates plotted versus both
$\mathnormal{E_{c}}$ and $\mathnormal{SH}$ are displayed in Figure 9, where
the data previously obtained with the same neutron source located inside the
source-housing of the detector are also reported for comparison, revealing
that the presence of the water thermal bath surrounding the quartz vessel
containing the target liquid, as well as the stainless-steel boundary wall of
the detector, give rise to an attenuation of the neutron flux emitted by the
241AmBe source of the order of $\mathrm{10^{2}}$. In the same figure, the
expected rates obtained by the Monte Carlo simulations and subsequent post-
processing are also represented using black dots, whose satisfactory degree of
agreement with the experimental data makes us confident enough in the
reliability of both the nucleation model and the detector simulation
procedure.

##  6 Detector sensitivity

Figure 10: Efficiency functions of the MOSCAB detector versus the neutron
energy, calculated for a spherical (3m diameter) isotropic neutron source
surrounding the detector equipped with the 18L vessel filled with 13L of
$\mathrm{C_{3}F_{8}}$ and different value of the critical energy
$\mathnormal{E_{c}}$.

The efficiency functions $G^{\prime}(E_{c},E)$ of the MOSCAB detector affected
by a diffuse flux of neutrons, obtained by simulating a neutron emission by a
spherical surface having a diameter of 3m inside which the detector is
enclosed, are reported in Figure 10, the change in slope occurring around E
=10 MeV being due to the rise of the n-capture cross sections of the oxygen
contained into the water of the thermal bath. Following the same procedure
employed for a neutron source located inside the source-housing, the minimum
detectable diffuse neutron flux at 99% c.l. can be calculated as:

$\Phi_{min}(E_{c})=\frac{\dot{N}_{s}(E_{c})}{S\cdot\int^{\infty}_{0}{G^{\prime}(E_{c},E)\cdot
g_{n}(E)dE}}$ (14)

where $S$ is the surface area of the sphere surrounding the detector, from
which the incoming simulated neutrons take origin.

As an example of application of equation (14) the contribution of the
environmental background of LNGS to the background counting rate of the
detector has been calculated. A detailed discussion on the low energy
component of the neutron flux inside LNGS underground laboratories can be
found in the study executed on this topic by Wulandari et al. [5], according
to which the flux is dominated by neutrons produced in the concrete layer,
thus implying that the neutron flux is practically independent of the specific
location considered. Fission and ($\mathrm{\alpha,n}$) reactions contribute to
the total production rates but, while the spontaneous fission of
$\mathrm{{}^{238}U}$ mainly produces neutrons having energies below 4 MeV, the
($\mathrm{\alpha,n}$) reactions are substantially responsible for the
production of neutrons with higher energies. Of course, an increase in the
water content of the rock or the concrete layer can determine a neutron flux
decrease due to the higher hydrogen content and a consequently higher
moderation efficiency. Thus, based on the neutron spectrum calculated by
Wulandary and co-workers for the Hall C of LNGS, the efficiency curves
displayed in Figure 10 are used to determine the nucleation event rate
$\mathrm{\dot{N}_{W}}$ expected inside the detector equipped with the 18L
vessel filled with 13L of $\mathrm{C_{3}F_{8}}$, as listed in Table 2, in
which the measured background rate $\mathrm{\dot{N}_{bk}}$ is also reported
for comparison.

It is worth noticing that for $\mathnormal{E_{c}}\leq$ 100 keV the event rate
of the detector due to internal $\alpha$-decay events exceeds the
environmental background, while for $\mathnormal{E_{c}}\geq$ 300 keV both the
calculated and measured event rates, become lower than one event per ten days.
In the energy region between these two values, the experimental counting rate
can be ascribed to be due to the environmental background, as shown in Figure
9 and reported in Table 2.

Table 2:  MOSCAB 18L background counting rate as a function of the critical energy, $\mathnormal{E_{c}}$ in comparison with the counting rate expected from the environmental fast neutron flux as calculated by Wulandari et al. [5] for the Hall C of the Gran Sasso Laboratory.  $\mathnormal{E_{c}}~{}[keV]$ | $\mathrm{\dot{N}_{bk}~{}[{ev}\cdot h^{-1}]}$ | $\mathrm{\dot{N}_{W}~{}[{ev}\cdot h^{-1}]}$
---|---|---
$\mathrm{152\pm 5}$ | $\mathrm{~{}(3.0\pm 1.7)\cdot 10^{-2}}$ | $\mathrm{3.71\cdot 10^{-2}}$
$\mathrm{162\pm 5}$ | $\mathrm{~{}(4.1\pm 2.1)\cdot 10^{-2}}$ | $\mathrm{3.24\cdot 10^{-2}}$
$\mathrm{183\pm 6}$ | $\mathrm{~{}(3.0\pm 1.1)\cdot 10^{-2}}$ | $\mathrm{2.50\cdot 10^{-2}}$
$\mathrm{206\pm 15}$ | $\mathrm{~{}(8.0\pm 5.0)\cdot 10^{-3}}$ | $\mathrm{1.90\cdot 10^{-2}}$
$\mathrm{219\pm 7}$ | $\mathrm{~{}(4.0\pm 4.0)\cdot 10^{-3}}$ | $\mathrm{1.58\cdot 10^{-2}}$
$\mathrm{286\pm 11}$ | $\mathrm{~{}(4.0\pm 4.0)\cdot 10^{-3}}$ | $\mathrm{6.11\cdot 10^{-3}}$
$\mathrm{398\pm 21}$ | $<\mathrm{4.2\cdot 10^{-3}}$ | $\mathrm{1.20\cdot 10^{-3}}$
$\mathrm{514\pm 23}$ | $<\mathrm{4.2\cdot 10^{-3}}$ | $\mathrm{2.39\cdot 10^{-4}}$

Surely, both the size and design main features of the MOSCAB detector do not
make this detector suitable for monitoring the varying flux of background
neutrons in the very extreme conditions existing inside LNGS underground
laboratories. Nevertheless the general agreement between the detector counting
rates and the expectations due to the environmental background corroborates
the use of this detector to measure very low fluxes of fast neutrons in what
we could define intrinsic background-free conditions.

##  7 Conclusions

MOSCAB bubble-chamber, originally designed for the direct observation of WIMPs
in the spin-dependent channel, has been employed for the detection of fast
neutrons using different configurations of the equipment and different amounts
of sensitive liquid.

First of all, it has been shown that the detector can be operated at
metastability degrees such that the target liquid is sensitive only to
neutrons. Actually, this occurs when the reduced superheat parameter SH is
kept lower than 0.07, or the critical energy $\mathnormal{E_{c}}$ is kept
higher than nearly 200 keV, which approximately corresponds to a 2.5 MeV
neutron energy threshold required for nucleation. In these conditions the
residual internal background rate of the detector is lower than one event
occurring every ten days and the steadiness of operation of the detector for
long times of observation are extremely enhanced, as we demonstrated by
running MOSCAB bubble-chamber during more than 4000 hours in the very clean
environment of LNGS underground laboratories.

Subsequently, the detector response to fast neutrons, described through a
bubble nucleation model assuming the existence of a critical deposition length
of the energy released by the recoiled ions, has been investigated using a
weak 241AmBe neutron source, which has allowed us to generate detection
efficiency functions via Monte Carlo simulation and post-processing, whose
validation has been performed experimentally.

Finally, thanks to the demonstrated reliability of the simulation procedure of
the apparatus, we have displayed that MOSCAB bubble-chamber can be effectively
used to measure the fast neutron activity of very weak n-sources, provided
that the external background is almost negligible, as it happens inside the
LNGS underground laboratories. On the other hand, placed above ground without
any additional shield, the same equipment could be exploited to monitor the
cosmic ray variations through the neutron component of the Extensive Air
Showers, as well as to detect the presence of any signal on top of the cosmic
ray background. In particular, to study variations of the cosmic ray neutron
flux whose energy spectrum extends to high energies, high neutron energy
thresholds have to be set, which means that any other neutron source but
cosmic rays will be practically absent, the information brought by the cosmic
radiation being uncontaminated. Further investigations on this topic are
scheduled to be conducted in the very next future.

##  8 acknowledgements

The authors wish to thank all the staff of the National Gran Sasso Laboratory
for their constant support and cooperation during these years. Some of the
scientists who imagined and realized the MOSCAB detector, Pietro Negri and
Antonino Pullia, are not with us anymore. We are left with their memory and
their teachings.

## References

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# Analyzing Gender Polarity in Short Social Media Texts with BERT: The Role of
Emojis and Emoticons

Saba Yousefian Jazi  Departmet of Computer Science and
Engineering
University of North Texas
Denton, Texas 76205
Email<EMAIL_ADDRESS>Amir Mirzaeinia  Departmet of Computer
Science and
Engineering
University of North Texas
Denton, Texas 76205
Email<EMAIL_ADDRESS>Sina Yousefian Jazi  Independent Researcher
Santa Clara, California 95051
Email<EMAIL_ADDRESS>
###### Abstract

In this effort we fine tuned different models based on BERT to detect the
gender polarity of twitter accounts. We specially focused on analysing the
effect of using emojis and emoticons in performance of our model in
classifying task. We were able to demonstrate that the use of these none word
inputs alongside the mention of other accounts in a short text format like
tweet has an impact in detecting the account holder’s gender.

##  I Introduction

One of the public and big size data source for textual data is tweeter. This
platform initially was designed to gives users the opportunity to send a short
textual input in the platform. Although the platform has evolved into much
more input types, and increased the limit of tweets to 280 character, the main
functionality for the users still stays as short texts.Along with the
popularity of this platform, the developed API’s provides the opportunity to
scrap and analyze this textual data. Even though after February 2023, access
to such data is not free, there are some available dataset collected from
tweeter that still could be useful. One of the main concerns that comes with
every public social media platform, is the security and privacy of such
platforms. In 2020, around 130 high profile tweeter accounts were hacked.
While some were immediately disabled, others were used to tweet unauthorized
notes. One of the motivations of this effort is to help the security teams in
detecting such incidents. If a model can successfully detects that the input
text does not match the authors style, it can flag such activity and proceed
further actions. One of the main indications and simplest step in such
process, could be detecting if the gender of author matches the users gender.
Aside from the security purposes, there are interests in marketing and
financial sectors regarding social analysis of social media users, including
tweeter. Detecting a simple but private information such as gender of users
from texts may seem trivial at first, but most of the developments in Large
language models are focused on large texts. In contrast to large texts with
high word count, short texts may not provide as much context for pretrained
models such as BERT. That is why we hypothesize that in such scenarios we need
to use style parameters as much as possible. Specifically, inn this paper we
investigate the answer to this question: given a short text document, can we
identify if the author is a man or a woman based on their style of tweeting?

##  II Background

Not much research delves into analyzing the diverse styles found in short
texts from different users. Some researchers have tackled similar tasks, like
digging into profiles, as seen in studies [1], [2], and [3]. They sifted
through thousands of profiles, studying how people described themselves using
various subjects, word choices, and qualifications. While these studies
provided valuable insights into a wide range of users, including non-binary
ones, they often overlooked the nuances of text styles. Profiles, being
usually short and lacking full sentences, sometimes relied on profile pictures
for predictions.

One of the closest attempts at detecting gender from tweets was done in [4].
They tried different methods, like bag-of-words and traditional machine
learning, to understand short texts better. But they missed out on emojis and
emoticons, which we think could be crucial in understanding how users
communicate. Another attempt in Twitter author profiling was [5], one of the
few to consider both text styles and elements like mentions and emoticons,
though their main focus was on telling apart robot and non-robot profiles and
they used different methods. In 2023, researchers in [6] published another
approach to incorporate a user’s profile description on Twitter to their
tweets to identify the gender. However, they applied more classical machine
learning methods in their experiments. These days, more recent transformer-
based models (such as BERT. [7]) have been shown to be more effective than
classical approaches in these applications. We mostly focused on how
parameters tied to style, such as mentions and emojis can improve pretrained
models such as BERT to quickly adapt to new tasks on short texts.

As social media grows, so does the issue of virtual aggression. There have
been limited efforts to detect gender based on profanity or hate speech in
tweets, like the works shown in [8] and [9]. While these studies mostly aimed
to find out which types of users engaged in negative communication, they also
tried to define and analyze their target groups. However, like previous
efforts, they often simplified initial data, leaving out details such as
emoticons, connections, and mentions among different users.

TABLE I: Distribution of career categories in dataset Career | Female | Male
---|---|---
`Singer` | `13` | `9`
`Actor/Actress` | `5` | `1`
`Media personality` | `3` | `4`
`Athlete/sport analyst` | `0` | `2`

##  III Pretrained Model

For the purpose of this effort, we used a Bidirectional Encoder
Representations from Transformers (BERT) architecture. BERT is one of the
advanced models that is developed for large language model applications
published in 2018 [7]. The BERT model excels in tasks such as text
classification, question answering, sentiment analysis, and language
translation. BERT is pre-trained on vast amounts of text data using
unsupervised learning techniques that helps BERT to learn rich and
comprehensive representations of words and sentences, enabling it to
understand language nuances, semantics, and relationships effectively. The
model we selected is a BERT Base uncased model, pre-trained with 110 million
parameters for different tasks including classification. We also used the BERT
tokenizer and BERT embedding to feed our input into the model. We then added a
drop out layer with the rate of 0.1% as drop out percentage. We then added the
dense layer with the sigmoid function to perform the binary classification on
our dataset. for the training process, we achieved the best results with
learning rate of 2e-5. In each experiment, we trained the classifier for 10
epochs on Tesla T4 GPU with each of them taking 25 minutes to run on our
dataset.

##  IV Experiments

Although we used the BERT preprocessing layer for our input, we did some
preprocessing before feeding the data to the first layer. We first removed the
retweets from the tweet dataset. These samples are easily recognized since
they start with ”b\RT”. Removing these tweets decreased the number of tweet
samples significantly. We also shuffled the dataset to make sure that before
sampling dataset for validation portion, samples are mixed properly. We
selected 25% of our dataset for validation. We checked both training and
validation set to have similar distribution as original dataset, regarding the
male and female percentage, mean tweet length and max tweet length. After the
initial cleaning, we applied our functions to turn emojis and emoticons into
representing texts. Since the data is collected and read as UTF-8, the emojis
will follow this pattern: a 4 character- sub-string starting with backslash
and a lower case alphabet, then an upper case alphabet and then 1 digit. Table
II showcases a few samples of these emojis. In total 842 emoji codes were
recognizable and we ran the function to replace them with their equivalent
text that defines the emoji.

###  IV-A Data

Before february 2023, there were multiple ways one could use to scrap twitter
data. The first approach could be using the available python libraries such as
Tweepy to access the standard Twitter API. Although the Twitter API was easily
accessible via a simple registration, there were still some limitation
regarding scrapping the Twitter data. The first limitation, comes to the
timeline of tweets. Using this method, one could only scrap the tweets up to 7
days ago. This limitation made it very hard to gather a large deadset in a
short amount of time. Another limitation of such library is that one can only
scrap the last 3200 of an account. After 2023, gathering data was made even
more cumbersome, as one needs to pay for such access added to the other
limitations. Considering these limitations and many more, we decided to go
with one of the big twitter detests that is gathered and shared with public.
This dataset is called ” 1000 celebrity tweets” and is available in kaggle
dataset section. This dataset that is updated monthly, consists of tweets from
the top 1000 most followed celebrity accounts in twitter. The number of tweets
for each account is very different and can goes from twenty to four thousands
tweets per an account. Also the timeline of tweets varies depending on how
frequent the account holders tweet and how old their account is. Another
important attribution about this dataset is that it does not separate English
or non-English speaker and the dataset contains many different language
speaker accounts.

For our project, we separated 21 female English speaker accounts and 16 male
English speaker accounts. The gender of these accounts were confirmed from the
biography of them or Wikipedia information. The reason for different number of
male and female account holders is that we wanted to make sure that the
distribution of tweets in the combined dataset will remain as 50% for each
gender. As the career distribution of our dataset accounts is shown in Table
I, we can see that most of these accounts belong to singers and this type of
accounts disproportionately effects the type of tweets that we have at our
disposal.

Figure 1:  Confusion matrix of original experiment: replacing the emojis with
text and including mentions.

###  IV-B Experiment with mentions

After analysing the results and some of the wrong labeled samples, we noticed
that the presence of mentioning of other accounts, which starts with ”$@$”, be
it a person or not, would cause the model to change its prediction. To test
our hypothesis, we altered the same training dataset to be free of mentions
and run the same process of fine tuning and validation. As it is shown in
table III, we can see that our hypothesis regarding presence of mentions
effecting the performance of model was correct.

###  IV-C Sentiment analyses

After running the model on validation set, we analysed some of the mistakes
and correct labeled samples. We noticed that there is a small difference
between the male tweets wrongfully labeled from the female tweets wrongfully
labeled. We noticed that the female tweets that have been wrongfully labeled
as male, had relatively shorter distribution than the correct labeled ones. It
is not worthy to mention that we also noticed that male tweets that were
labeled correctly as male had also shorter length.

TABLE II: Emojis and their UTF-8 codes in tweet samples. code | text replacement
---|---
`\xF0\x9F\x98\xA0` | ANGRY FACE
`\xF0\x9F\x98\x89` | WINKING FACE
`\xF0\x9F\x98\xA2` | CRYING FACE
`\xF0\x9F\x98\xAB` | TIRED FACE
`\xF0\x9F\x98\xB5` | DIZZY FACE

Since most of the emojis and emoticons are replaced with words with high
intensity in emotions, we decided to analyse our validation samples from the
sentiment view. To achieve that goal, we used “text2emotion” library to
analyse the test samples to see if there is a correlation between the emotions
perceived from tweet after replacing the emojis and the prediction or not.
This library is able to categorize text into 5 classes of: Angry, Fear, Happy,
Sad and Surprise. The results showed that the tweets that were not categorized
as any emotion, or neutral emotion were mostly labeled as male and tweets that
were categorized as fear or happy were mostly categorized as female.

Figure 2:  Confusion matrix of second experiment: replacing the emojis with
text and removing mentions.

##  V Discussion of results

Although we were able to replace more than 800 emojis, there were still some
emojis that were not replaced with text. That is because new emojis are
developed and added to the collection of available emojis everyday and it is
hard to keep track of every new developed emojis and their code and textual
meaning. We also think that the text that is used as replacement may have an
effect in giving the whole sample a positive or negative sentiment, even
though the intensity of the original text without emoji is not comparable with
it. Another challenging factor that we have to keep in mind is that since
these celebrities mostly have a person or a team responsible for public
relations, there may be a good chance that many of their tweets are not
entered by themselves or being checked, controlled or filtered before sending
to the public. Because of that, the personality of a person may not fully be
portrayed in their tweets. Also, a good portion of tweets from the TV
celebrities, are not specifically representative of the celebrity in that show
and mostly about the show. That also happens when the account belongs to a
band or any team effort. Similar Case happens for singers or actors that tweet
about their new album or movie. Although they may be tweeting themselves, but
since these tweets mostly have an advertisement schema, they do not provide
any useful information and that could be some sort of redundant data.

##  VI Conclusion

TABLE III: Comparison of results in different model code | Accuracy | Precision | Recall
---|---|---|---
`With mention+no emoji` | 0.7764 | 0.7841 | 0.7728
`With mention+with emoji` | 0.7807 | 0.7571 | 0.8370
`No mention+no emoji` | 0.7813 | 0.7600 | 0.7904
`No mention+with emoji` | 0.7901 | 0.7663 | 0.8001

Tweeter is one of the semi-free available textual sources that could be used
for many language analyses and NLP modelings. We believe that there is a lot
to be done regarding processing the short text. Although recent developments
in attention based models such as BERT has hugely improved the results in many
tasks, these models are mostly not as great when it comes to shorter texts.
With all that being said, we believe that there is a need to analyse how big
is the impact of replacement text in sentiment of texts. There is also a need
to gather the samples from accounts that may tweet more freely and are able to
express their thoughts and feelings more uncensored. Also, it is better to
focus on diversifying the authors type of activities or career since that has
a huge impact on what they tweet about too.

## References

  * [1] Z. M. Nia, A. Ahmadi, B. Mellado, J. Wu, J. Orbinski, A. Agary, and J. D. Kong, “Twitter-based gender recognition using transformers,” 2022.
  * [2] M. Thelwall, S. Thelwall, and R. Fairclough, “Male, female, and nonbinary differences in uk twitter self-descriptions: A fine-grained systematic exploration,” Journal of Data and Information Science, vol. 6, no. 2, pp. 1–27, 2021.
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  * [4] P. Vashisth and K. Meehan, “Gender classification using twitter text data,” in 2020 31st Irish Signals and Systems Conference (ISSC), pp. 1–6, 2020.
  * [5] S. Ouni, F. Fkih, and M. N. Omri, “Bots and gender detection on twitter using stylistic features,” in International Conference on Computational Collective Intelligence, pp. 650–660, Springer, 2022.
  * [6] B. Onikoyi, N. Nnamoko, and I. Korkontzelos, “Gender prediction with descriptive textual data using a machine learning approach,” Natural Language Processing Journal, vol. 4, p. 100018, 2023.
  * [7] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, “Bert: Pre-training of deep bidirectional transformers for language understanding,” arXiv preprint arXiv:1810.04805, 2018.
  * [8] S. C. Wong, P. L. Teh, and C.-B. Cheng, “How different genders use profanity on twitter?,” in Proceedings of the 2020 4th International Conference on Compute and Data Analysis, pp. 1–9, 2020.
  * [9] D. Ortega-Sánchez, J. P. Blanch, J. I. Quintana, E. S. d. l. Cal, and R. de la Fuente-Anuncibay, “Hate speech, emotions, and gender identities: A study of social narratives on twitter with trainee teachers,” International Journal of Environmental Research and Public Health, vol. 18, no. 8, 2021.


# Graph Representation of the Magnetic Field Topology in High-Fidelity Plasma
Simulations for Machine Learning Applications

Ioanna Bouri  Fanni Franssila  Markku Alho  Giulia Cozzani  Ivan Zaitsev
Minna Palmroth  Teemu Roos

###### Abstract

Topological analysis of the magnetic field in simulated plasmas allows the
study of various physical phenomena in a wide range of settings. One such
application is magnetic reconnection, a phenomenon related to the dynamics of
the magnetic field topology, which is difficult to detect and characterize in
three dimensions. We propose a scalable pipeline for topological data analysis
and spatiotemporal graph representation of three-dimensional magnetic vector
fields. We demonstrate our methods on simulations of the Earth’s magnetosphere
produced by Vlasiator, a supercomputer-scale Vlasov theory-based simulation
for near-Earth space. The purpose of this work is to challenge the machine
learning community to explore graph-based machine learning approaches to
address a largely open scientific problem with wide-ranging potential impact.

Machine Learning, ICML

##  1 Introduction

Magnetic reconnection is a fundamental plasma physical process characterized
by a topological reconfiguration of the magnetic field and energy conversion
from magnetic to kinetic and thermal energy, leading to plasma heating,
particle acceleration, and mixing of plasmas (Priest & Forbes, 2000; Li et
al., 2021). The phenomenon is encountered in different settings and plays a
key role in the eruption of solar flares and coronal mass ejections (CMEs) in
the solar corona (Mei et al., 2012), in the Earth’s magnetosphere and its
interaction with the solar wind (Angelopoulos et al., 2008; Palmroth et al.,
2017; Li et al., 2022), in astrophysical plasmas (Parker, 1979; Yamada et al.,
2010), as well as in fusion plasma during major and minor tokamak disruptions
(Taylor, 1986; Yamada, 1999).

Magnetic reconnection is linked to _space weather_ conditions that can
potentially damage terrestrial technological infrastructure, satellites, and
manned space missions (Odenwald et al., 2006). CMEs cause magnetospheric
magnetic storms (Schwenn et al., 2005), during which the terrestrial power
grids may suffer from Geomagnetically Induced Currents (GICs) and even fail
(Pulkkinen et al., 2005). Solar flares accelerate particles into relativistic
energies, which propagate to the Earth’s upper atmosphere and affect satellite
and radar signals that can be significantly altered or lost during active
space weather conditions (Baker et al., 2004).

The nature of the phenomenon is well-understood in two-dimensional (2D)
settings, and quasi-2D models have been successful at reproducing many
features of reconnection in the solar corona and the Earth’s magnetosphere
(Cassak & Shay, 2007; Liu et al., 2022). However, magnetic reconnection is
intrinsically a three-dimensional (3D) process. This becomes especially
evident when considering reconnection in the solar corona, where the magnetic
field forms twisted coronal loops with complex topologies (Lee, 2022). Despite
considerable progress, the additional complexity introduced in 3D settings
continues to pose many open questions regarding the nature of 3D magnetic
reconnections in the solar and the Earth’s magnetospheric environment
(Daughton et al., 2011).

We present a scalable pipeline for topological data analysis and graph
representation of 3D magnetic vector fields. First, we introduce spatial null
graphs, a graph representation that can be used to characterize the topology
of a magnetic field. In addition, to encode the temporal evolution of the
magnetic field, we extend this concept with spatiotemporal null graphs.
Finally, we present the spatial and spatiotemporal null graphs produced by the
topological analysis of the magnetic vector field in the Earth’s magnetotail.
For this purpose, we use 3D global simulations produced by Vlasiator, a
supercomputer-scale Vlasov theory-based model that incorporates the solar wind
– magnetosphere – ionosphere system (Palmroth et al., 2018). The constructed
graphs enable the use of topological information as input for machine learning
methods such as (spatiotemporal) graph neural networks (GNNs) (Reinhart, 2018;
Ma & Tang, 2021).

##  2 Magnetic Field Topology

This section introduces some concepts of vector field topology. For a general
introduction, see (Günther & Baeza Rojo, 2020); for reviews focused on
magnetic fields and magnetic reconnection in particular, see (Longcope, 2005;
Parnell et al., 2010).

The magnetic field on a location with spatial coordinates
$\vec{x}=~{}(x,y,z)\in~{}\mathbb{R}^{3}$ can be represented as a vector field
$\vec{B}(\vec{x})=~{}(B_{x}(\vec{x}),B_{y}(\vec{x}),B_{z}(\vec{x}))$.
According to Gauss’s law for magnetism, the field has zero divergence
everywhere

$\nabla\cdot\vec{B}=\left(\frac{\partial B_{x}}{\partial x}+\frac{\partial
B_{y}}{\partial y}+\frac{\partial B_{z}}{\partial z}\right)\equiv 0.$ (1)

From a topological perspective, _magnetic nulls_ , points where the magnetic
field vanishes $\|\vec{B}(\vec{x}_{0})\|_{2}=0$, are of special interest. At
such points, the structure of the local field can be characterized by forming
a first-order Taylor approximation around $\vec{x}_{0}$:

$\vec{B}(\vec{x})=J(\vec{x}_{0})(\vec{x}-\vec{x}_{0})+o(\|\vec{x}-\vec{x}_{0}\|_{2}),$

where $J=\nabla\vec{B}$ is the Jacobian of the magnetic field. The topology of
the field is characterized by the magnetic skeleton, which comprises of the
magnetic nulls, separatrix surfaces delineating distinct magnetic domains, and
separator curves formed on the intersections of separatrix surfaces (Bungey et
al., 1996; Longcope & Klapper, 2002; Longcope, 2005; Parnell et al., 2010).

To extract the magnetic skeleton of a field, we use the Visualization Toolkit
(VTK) (Schroeder et al., 2006) – an open source software package for
scientific data analysis and visualization. The VTK vector field topology
filter (Bujack et al., 2021) is a later extension to the package that adds the
functionality for computing the main elements of the topological skeletons of
2D and 3D vector fields.

###  2.1 Magnetic nulls

Magnetic nulls can be classified into different types that characterize their
topology, according to the eigenvalues of the Jacobian matrix $J$ of the
vector field (Lau & Finn, 1990; Günther & Baeza Rojo, 2020).

Given the three eigenvalues of the Jacobian,
$(\lambda_{1},\lambda_{2},\lambda_{3})\in\mathbb{C}^{3}$, it follows from Eq.
(1) that their sum is equal to zero: $\lambda_{1}+\lambda_{2}+\lambda_{3}=0$,
and, therefore, two of the eigenvalues must have the same sign while the third
one is of the opposite sign111We do not consider _degenerate nulls_ where one
or more of the eigenvalues is exactly zero. Such points are physically
unstable (Priest & Titov, 1996) and can be handled as special cases of one or
more of the four types we introduce here.. Moreover, while the eigenvalues can
be complex-valued, the eigenvalues with non-zero imaginary parts always come
in pairs of complex conjugates, so that their real parts are the same, and the
third eigenvalue is a real number of the opposite sign.

Due to the above constraints, each null can be classified in terms of its
_polarity_ ; if the two same-sign eigenvalues are negative, the null is
classified as a _negative null_ , otherwise it is a _positive null_ (Parnell
et al., 2010). Furthermore, magnetic nulls with complex eigenvalues exhibit a
_spiraling_ topology (Longcope, 2005). Figure 1 illustrates the resulting
classification into four types, where types A and B represent (non-spiraling)
topologies of negative and positive magnetic nulls, while types As and Bs
encode spiraling topologies of negative and positive magnetic nulls,
respectively.

Type A

Type B

Type As

Type Bs

Figure 1: Classification of magnetic nulls – Type A: real eigenvalues with
signs (-,-,+); Type B: real eigenvalues with signs (+,+,-); Type As: two
complex and one real eigenvalues with signs of real parts (-,-,+); Type Bs:
two complex and one real eigenvalues with signs of real parts (+,+,-). Figure
from (Franssila, 2023).

###  2.2 Separatrices and separators

Figure 2: _Left:_ Detected proper and 2D null points. _Right:_ The resulting
spatial graph at the same time-step of the simulation. The spatial edges
represent different types of separators in blue (As $\leftrightarrow$ Bs), red
(A $\leftrightarrow$ B), green (A $\leftrightarrow$ Bs, B $\leftrightarrow$
As), pink (A $\leftrightarrow$ As, B $\leftrightarrow$ Bs) and yellow (A
$\leftrightarrow$ A, B $\leftrightarrow$ B, As $\leftrightarrow$ As, Bs
$\leftrightarrow$ Bs).

The eigenvectors of the Jacobian can be used to define the so-called
_separatrices_ that are associated with the magnetic nulls (Longcope, 2005;
Günther & Baeza Rojo, 2020). Each non-degenerate null has one 2D separatrix or
_fan surface_ and two one-dimensional virtual separatrices or _spines_
(Longcope, 2005). The fan surface is defined by the infinitely many magnetic
field lines within the plane spanned by the two eigenvectors corresponding to
the same-sign eigenvalues. The two spine field lines end in the magnetic null
point, entering along the directions parallel and antiparallel to the third
eigenvector, normal to the fan plane (Longcope, 2005).

In physical simulations, magnetic nulls connect via _separator curves_ (or
reconnection lines) formed by the intersection of the fan surfaces of two
connected nulls (Palmroth et al., 2006). However, the process of integrating
the separatrices to find their intersection can be computationally very
expensive, which is why separators are usually approximated (Haynes & Parnell,
2010).

In order to approximate the separators, we choose to follow the _2D null
lines_ : curves along which two of the magnetic field components are zero,
while the third can vary. Zeiler et al. (2002) found that with a small guide-
field, 3D reconnection is well-approximated by a 2D system. Specifically in
the magnetotail environment, we ignore the East-West component of the magnetic
field, $B_{y}$, since it tends to exhibit the least variation as the guide-
field component, and we require that the other two components are zero,
$B_{x}=B_{z}=0$. We call such points _2D nulls_ and use the term _proper null_
to refer to points where $\|\vec{B}\|_{2}=0$, which are clearly a subset of
the 2D nulls. We provide a modification of the existing VTK vector field
topology filter to detect such 2D nulls.

##  3 Graph Representations

Originally introduced by Longcope & Klapper (2002), _null graphs_ are graph
representations that characterize the topology of a magnetic field by encoding
the connectivity between proper nulls (vertices) via separators (edges).

We extend their definition to construct a graph representation that can be
useful for different machine learning tasks and downstream applications, such
as spatiotemporal GNNs (Reinhart, 2018). We propose two computationally
efficient heuristics to trace the connectivity between proper nulls both
spatially and temporally.

###  3.1 Spatial Null Graphs

After modifying the VTK vector field topology filter to detect the 2D magnetic
nulls where $B_{x}=B_{z}=0$ (sec. 2.2), we construct the 2D null lines by
connecting the 2D nulls to each other based on spatial proximity.

In practice, the 2D null lines can be traced by initializing at most two paths
from each proper null based on a cut-off value on the maximum Euclidean
distance from the proper null. Each of the paths is then iteratively expanded
by finding – within the same cut-off distance – the nearest 2D null that is
not already included in any of the already traced paths. Paths terminating
without reaching a proper null are considered a dead end and are discarded,
while paths ending at a proper null become edges in the null graph. The type
of each proper null (A / B / As / Bs) is encoded as a node feature in the
graph.

###  3.2 Spatiotemporal Null Graphs

Consider a bipartite graph
$\mathcal{G}=(\mathcal{V}_{i},\mathcal{V}_{i+1},\mathcal{E})$, where the
vertex sets $\mathcal{V}_{i}$ and $\mathcal{V}_{i+1}$ are defined by proper
nulls detected at times $t_{i}$ and $t_{i+1}$, respectively. The set of edges
$\mathcal{E}$ represents a (partial) matching between the magnetic nulls with
the interpretation that vertices $v\in\mathcal{V}_{i}$ and
$v^{\prime}\in\mathcal{V}_{i+1}$ are connected by an edge
$e=(v,v^{\prime})\in\mathcal{E}$ if they correspond to the same proper null.
The problem can be cast as an _unbalanced assignment problem_ defined by the
following maximization problem

$\max_{\mathcal{E}\in\mathfrak{M}}\sum_{(v,v^{\prime})\in\mathcal{E}}1/w(v,v^{\prime}),$

where the set of allowed matchings $\mathfrak{M}$ is defined by requiring that
each vertex appears in at most one edge, and the weight
$w(v,v^{\prime})=\|\vec{x}(v)-\vec{x}(v^{\prime})\|_{2}$ is defined by the
Euclidean distance between the respective coordinates of the proper nulls $v$
and $v^{\prime}$. Additional constraints including $(i)$ a maximum distance
constraint $w_{\max}$, or $(ii)$ matching only the same type nulls, can be
incorporated by letting $w(v,v^{\prime})=-1$, for any edge that does not
satisfy them. We apply both constraints to get an initial matching, and, for
some of the unmatched magnetic nulls, we need to run a subsequent matching
without constraint $(ii)$ to account for type switches.

All vertices in $\mathcal{V}_{i}$ that remain unmatched are considered to have
disappeared after step $t_{i}$. Likewise, all vertices in $\mathcal{V}_{i+1}$
that remain unmatched are considered to have appeared before step $t_{i+1}$.
According to Murphy et al. (2015), proper nulls can either appear by entering
the simulation domain across a boundary, or as a result of a bifurcation, in
which case they appear in pairs of opposite polarity. These two cases can be
distinguished based on the coordinates and types of the unmatched vertices in
$\mathcal{V}_{i+1}$.

##  4 Results and discussion

The supercomputer-generated simulations from Vlasiator provide large-scale,
high-fidelity data – some of which is openly available (Palmroth, 2023). To
give an idea of the scale of available data, the example of the published
Vlasiator dataset provides 170 time-steps $\times$ 1,723,328 grid points at
each time-step, i.e., the time series consists of a total of $\sim$ 293
million grid points. Working with such scales requires efficient and scalable
methods, and the spatiotemporal graph representation of the data can allow for
less resource-intensive machine learning approaches.

The magnetotail simulations used to produce the results presented here,
consist of a grid with resolution $50\times 127\times 108$ in the $x$
(tailward–Earthward), $y$ (East–West), and $z$ (North–South) directions of the
magnetic field, respectively. A step of one unit in any direction of the grid
corresponds to 1000 km, and the time series used to generate the
spatiotemporal null graphs has 1 s cadence (Franssila, 2023).

First, the modified VTK topology filter is used to detect 2D and proper nulls,
and to classify the latter in types (sec. 2.1). The 2D nulls are detected
using $B_{y}$ as the guide-field component (sec. 2.2). The results obtained
from the first stage of the process are illustrated on the left side of Figure
2.

The result of the spatial tracing method (sec. 3.1), is presented on the right
of Figure 2. The 3D null points are colored according to their type. Different
types of spatial connectivity are also color-encoded, using different colors
of spatial edges depending on the type of the connection.

Figure 3 shows an example of a spatiotemporal graph, where for each time-step
$t_{i}$ for $i\in\\{0,1,2\\}$, a 2D projection (X-Y plane) of the spatial
graph is presented. The temporal edges trace the temporal evolution of each
proper null across all time-steps. The colors of the temporal edges represent
the type of the proper null traced over time, with the exception of the pink
temporal edges which denote a type switch scenario (e.g., $t_{0}\rightarrow
t_{1}$: B $\rightarrow$ Bs). Finally, the green circle at $t_{2}$ is used to
mark a pair of proper nulls of opposite polarity that appear together before
$t_{2}$ due to a bifurcation.

Figure 3: Spatiotemporal null graph. At each time-step a 2D projection (X-Y
plane) of the corresponding spatial graph is illustrated. The proper nulls are
colored based on their type, and the color of each temporal edge represents
the type of the traced proper null, with the exception of the pink edge which
denotes a type switch. The green circle at $t_{2}$ marks a pair of proper
nulls of opposite polarity that appear together after a bifurcation.

We have presented a scalable data analysis pipeline for the detection and
spatiotemporal tracing of proper magnetic nulls. These methods allow us to
characterize the topology a 3D magnetic field using graph representations. The
resulting spatiotemporal null graphs can be useful in various downstream
learning tasks, especially in GNN applications (Reinhart, 2018; Zhou et al.,
2020; Wu et al., 2020).

In the process of formulating 3D magnetic reconnection detection as a machine
learning task, two potential limitations arise. If we formulate the problem as
a supervised learning task, there is a severe difficulty in reliably labeling
a sufficient amount of training data, as 3D magnetic reconnection remains
difficult to detect and characterize. Similarly, if we were to formulate the
problem as an unsupervised learning task, questions arise regarding the
interpretability of results and the model performance evaluation.

Currently, we are working on a GNN approach that aims to circumvent these
issues by formulating the learning task as a plasmoid222Outflows of plasma
driven by the magnetic tension force of newly reconnected field lines (Liu et
al., 2013). formation forecast, as their generation is linked to reconnecting
plasmas (Samtaney et al., 2009). The location of a plasmoid can be
characterized using the magnetic skeleton (Birn et al., 1997), which allows us
to use spatiotemporal null graphs to learn when and where a plasmoid is
formed. Next, in order to detect the magnetic reconnection, we can examine the
reconnection rate and energy conversion rate at the possible reconnection
sites located in close proximity to the newly-formed plasmoid. This work can
then be extended to facilitate the study of magnetized plasmas in different
settings, which is linked to a variety of open questions that can be
interesting to both the astrophysics and machine learning research
communities.

## Acknowledgements

Funding in direct support of this work: Research Council of Finland grants
#345635 (DAISY) and #339327 (Carrington). The authors thank the Finnish
Computing Competence Infrastructure (FCCI) for supporting this work with
computational and data storage resources.

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