# Making the Most Out of the Limited Context Length:
Predictive Power Varies with Clinical Note Type and Note Section

Hongyi Zheng1 Yixin Tracy Zhu1 Lavender Yao Jiang1, 2
Kyunghyun Cho1 Eric Karl Oermann1, 2
NYU Center for Data Science1 NYU Langone Health2
{hz2212, yz5880, lyj2002<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Recent advances in large language models have led to renewed interest in
natural language processing in healthcare using the free text of clinical
notes. One distinguishing characteristic of clinical notes is their long time
span over multiple long documents. The unique structure of clinical notes
creates a new design choice: when the context length for a language model
predictor is limited, which part of clinical notes should we choose as the
input? Existing studies either choose the inputs with domain knowledge or
simply truncate them. We propose a framework to analyze the sections with high
predictive power. Using MIMIC-III, we show that: 1) predictive power
distribution is different between nursing notes and discharge notes and 2)
combining different types of notes could improve performance when the context
length is large. Our findings suggest that a carefully selected sampling
function could enable more efficient information extraction from clinical
notes.

##  1 Introduction

Electronic Health Records (EHR) enable the development of language model based
clinical predictor, which takes in clinical notes to predict patient outcomes.
Clinical notes in EHR exhibit two unique characteristics. 1) Clinical notes
cover a long time span (from a few weeks to over a year), which results in
their sparsity of information-rich sections. 2) Clinical notes also tend to be
long: many discharge notes could take up to $10,000$ tokens, which makes using
the entire note as model input computationally expensive. 3) The strong noise
level in the medical notes (usually due to the domain-specific abbreviations
and typos) also poses a challenge to extract information effectively.

These distinguishing characteristics of clinical notes lead to a new design
choice: when the context length is limited due to the constrained compute or
model architecture, what parts of clinical notes should we sample to maximize
the model’s performance? We propose a framework to subsample text sections
with high predictive power.

Empirically, we explore the distribution of predictive power over clinical
note types and sections by searching over these variables. We found that 1)
the predictive power distribution is different between nursing notes and
discharge notes: the predictive power is stronger at the beginning and end of
discharge notes, while uniform within nursing notes. 2) The effect of
combining sections from different types of notes improves the performance when
the context size is large, but harms the performance when the context size is
small. More details of task formulation can be found at section 3. Our code is
publicly available on
GitHub111https://github.com/nyuolab/EfficientTransformer.

##  2 Related Work

Existing methods for subsampling clinical notes for the BERT-based model are
mostly based on domain knowledge. For instance, Yang et al. (2022) and Darabi
et al. (2020) choose discharge notes as they summarize patients’ visits. Thapa
et al. (2022) chooses the notes within three days before a cutoff time in
consideration of timeliness. While these assumptions are based on domain
knowledge, they require human input and may not generalize. Thus, we are
interested in exploring a data-driven sampling choice without assumptions of
expert inputs.

Another related, but orthogonal approach to the limited context length problem
is note aggregation. Instead of subsampling notes, Huang et al. (2019) propose
to feed everything to the model, one maximum context length at a time, and
aggregate the outputs for the final prediction. In their work, notes of one
patient are split into a partition of subsequences, and the patient’s re-
admission risk is obtained by taking a weighted average of probabilities
computed from each subsequence. This method’s compute cost scales with the
aggregated sequence length, which can be expensive for records with long
clinical notes. In contrast, our method aims to find one single information-
rich segment as input.

##  3 Method

We formalize our prediction task as follows: given a set of clinical notes $x$
associated with an admission record, we want to predict the class label $y$
which is our patient outcome of interest. Ideally, we want to train a
classifier $f_{w^{*}}$ to approximate $p(y\mid x)$. The optimal parameter is

$w^{*}=\arg\max_{w}~{}m(f_{w}(x),y),$

where $m$ is a metric function of interest. Nevertheless, due to the
computational constraint, we need to reduce the input size via a sampling
function $s_{\theta}$ so that $s_{\theta}(x)$ fits the input length limit and
preserves information. Empirically, the optimal parameters are

$w^{*},\theta^{*}=\arg\max_{w,\theta}~{}m(f_{w}(s_{\theta}(x),y)).$

We say a sample function $s_{\theta}$ has a higher predictive power if
$m(f_{w^{*}}(s_{\theta}(x),y))$ is larger.

While current works chose $s_{\theta}$ based on prior medical knowledge or
simply fix it as a truncation function, we propose to explore different
sampling functions $s_{\theta}$ to make the most out of the limited context
length with the highest predictive power. Notice that in our work, $s$ and
$\theta$ are searched manually, instead of using learning algorithms.

##  4 Experimental Setup

We hypothesize that for 30-day all-cause readmission prediction, there exists
an alternative sampling function that enables similar or better performance
than the commonly used “truncated discharge notes". More formally, we focus on
a parameterized sampling function with 2 variables: 1) which section of tokens
to include, 2) what type(s) of clinical notes to use.

#### Model

We finetuned two clinical language models in our experiments. The first is
Clinical-BERT (Alsentzer et al., 2019), which continued to pretrain BERT using
approximately 2 million notes from MIMIC-III and has a maximum sequence length
of 512. The second is the ClinicalLongformer (Li et al., 2022), which
continued to pretrain Longformer (Beltagy et al., 2020) with MIMIC-III notes
and enables input of up to $4096$ tokens. Both models are finetuned to predict
the probability of 30-day all-cause readmission: that is, whether the patient
will be re-admitted to the hospital within 30 days of their discharge dates.

#### Dataset

We use the discharge notes and nursing notes in the noteevent table of the
MIMIC-III database Johnson et al. (2016). There are $~{}40,000$ de-identified
admission records available to use after filtering out all admission records
without nursing notes and discharge notes. The admission records are split
into 75% train, 12.5% validation, and 12.5% test sets. Other types of medical
notes such as physician notes are excluded from consideration in our
experiments due to their scarcity in the database. See Appendix A for data
preprocessing.

#### Sliding Window

To extract different sections of the clinical notes, we use a sliding window
technique. Let $n$ be the window’s width. Let $l$ be the total number of
tokens of the text. The window is placed based on an input parameter
$p\in[0,1]$ indicating the location of the midpoint of the window, where the
window interval is

$[lp-n/2,lp+n/2].$

In case where $lp-n/2<0$, we shifted the window backward so that the front of
the window aligns with the beginning of the input tokens. In the case where
$lp+n/2>l$ we shifted the window forward to let the back of the window match
the end of the tokens. Also, when $l<n$, we ignore the input $p$ and pad the
tokens to maximum input length $n$.

We try $11$ different values of $p$ ($0.0,0.1,\cdots 1.0$) for ClinicalBERT
and $2$ values of $p$ ($0.0$ and $1.0$) for ClincialLongformer along with an
additional fragmented window trial $p=\mathrm{both}$ which looks into the
first $n/2$ and last $n/2$ tokens of the input text. Similarly, when $l<n$, we
simply pad the sequence to the window’s length.

#### Mixing Notes

To control different types of clinical notes, we experimented with the
following options: 1) first nursing note, 2) last nursing note, 3) discharge
note, 4) first nursing notes + discharge note, 5) last nursing notes +
discharge notes. For options with two types of notes, $n/2$ tokens are
allocated to each type, and three values for $p_{1}$ and $p_{2}$ each
($0.0,1.0$ and $\mathrm{both}$) are used to select $n/2$ tokens from each type
of note, resulting in $9$ possible input parameter combinations.

Figure 1:  Performance of ClinicalBERT on Different Text Sections and
Different Types of Notes,
Error Bars Represent 95% Confidence Intervals

##  5 Results

###  5.1 Different Sections in Nursing Notes and Discharge Notes

We finetune ClinicalBERT and ClinicalLongformer on different sections of
nursing and discharge notes. We used sliding windows to extract a sequence of
tokens that meets the model’s maximum sequence length. We have three key
observations.

Different Types of Clinical Notes Show Disparate Predictive Power
Distributions Over Text Sections. As shown in Figure 1, the discharge notes
(blue line) show quite uneven predictive power distribution, where the
beginning ($p=0.0$) and end ($p=1.0)$ sections of the text provide strong
predictive power while the middle sector ($0.2\leq p\leq 0.5$) shows a
significant dip in predictive power. In contrast, the predictive power of the
nursing notes (orange and green line) turns out to be uniformly distributed:
using different sections of the nursing notes ($0.0\leq p\leq 1.0$) does not
make a significant difference. We speculate that this discrepancy may stem
from the domain knowledge that discharge notes are more structured than
nursing notes: they often start with basic descriptions of the patient
information and ends with suggestions for the patients, whereas nursing notes
often have multiple types of information mixed together throughout the text.

Nursing Notes Provide Modest Predictive Power. Nursing notes produce decent
re-admission prediction results: according to Figure 1 and Figure 2, although
their predictive power is not as strong as discharge notes (which are
typically written right before patients leave the hospital), they consistently
achieve AUC ROC scores of over $0.7$ which indicates modest predictability
Schneeweiss et al. (2001). Moreover, the first nursing notes (orange line in
Figure 1, second group of bars in Figure 2) of each admission provide similar
predictive power as compared to the last nursing notes (green line in Figure
1, third group of bars in Figure 2), indicating the possibility of re-
admission risk evaluation at the early stage of the admission. This finding is
especially valuable from the perspective of intervention, as it is more
practical to decide whether the patient should be discharged at the time
before the discharge note is written. Also, the abundance of nursing notes
makes them a suitable alternative for re-admission risk evaluation tasks when
discharge notes are unavailable.

Figure 2: Performance of ClinicalLongformer on Different Text Sections and
Different Types of Notes,
Error Bars Represent 95% Confidence Intervals Figure 3: Performance of
ClinicalBERT and ClinicalLongformer on Clinical Note Combinations,
Error Bars Represent 95% Confidence Intervals

Preserving the Beginning Tokens Is Not the Only Option. It is generally
assumed that when the available input tokens are limited, the leading tokens
of each clinical note should be used. Nevertheless, our experiments show that
for discharge notes, spending half of the available tokens on the beginning
section and spending the remaining half on the end section ($p=\mathrm{both}$)
achieves slightly better performance (AUC ROC of $0.849$ versus $0.845$ for
ClinicalBERT, $0.869$ versus $0.864$ for ClinicalLongformer) as compared to
using the leading token only ($p=0.0$). We speculate that this helps as it
avoids the weakly predictive middle sector of the clinical notes.

###  5.2 Combining Sections from Different Types

We combine text sections from two different types of clinical notes and
finetune ClinicalBERT and ClinicalLongformer. This experiment helps us
investigate the question: when the amount of available tokens is fixed, does
combining information from different clinical notes work better than using
discharge notes only? Since discharge notes are shown to provide strong
predictive power in our prior experiments, we only investigate the note type
combinations that include discharge notes (first nursing + discharge, last
nursing + discharge).

The Effect of Allocating Tokens to Different Types of Clinical Notes Depends
on the Context Size. When the context size is relatively large
(ClinicalLongformer, as shown in the right side of figure 3), allocating the
available tokens to different types of clinical notes (blue, orange, and green
bars) leads to improvements in performance. The baseline (dashed red line)
uses discharge notes only and has a lower AUC ROC ($0.013$ to $0.019$) than
models finetuned with combined notes. However, when the context is small
(Clinical BERT, as shown in the left side of figure 3), distributing the
already limited number of tokens to different clinical notes hurts the
performance: the AUC ROC of ClinicalBERT finetuned with mixed notes falls
below the baseline performance by $-0.009$ to $-0.001$. We speculate that this
may be related to the uneven predictive power distribution in discharge notes:
if there are already a sufficient number of tokens covering the most
informative sections of the discharge notes, the rest of the discharge notes
might not be as informative as the prior nursing notes.

##  6 Discussion and Future Works

Our findings suggest that when the input size is constrained, a carefully
selected sampling function that chooses the text with high predictive power
could benefit model performance. Specifically on the task of readmission
prediction from MIMIC-III notes, we show that the predictive power varies
across note types and note sections. This insight enables more efficient
information extraction from long and noisy clinical notes, which is beneficial
when the computing resource is limited and the context length needs to be
controlled.

Our findings call for two future directions. First, the performance
disparities between ClinicalBERT and ClinicalLongformer (subsection 5.2)
indicate that the best strategy to allocate the input context is related to
the maximum sequence length, and more work should be done to determine their
exact relationship. Another direction is investigating the predictive power
pattern based on the authorship of the clinical note. We showed (subsection
5.1) that discharge notes (written by doctors) have a more uneven predictive
power pattern as compared to nursing notes (written by nurses). How the domain
knowledge of the author would affect the clinical note quality is worth
investigating.

## Limitations

We acknowledge three limitations in our experiments. First, in our second
experiment, we fixed the window size for each type of note to be $n/2$. A more
comprehensive investigation could also search for the optimal window size for
each note type. Second, although we explored one fragmented window
configuration $p=\mathrm{both}$, we did not explore other fragmented window
configurations due to resource constraints. Lastly, we did not investigate
more types of clinical notes (e.g., physician notes and ECG notes) because
MIMIC-III has limited examples for other note types. We expect it to be
resolved in future works with MIMIC-IV’s publication Johnson et al. (2023).

## References

  * Alsentzer et al. (2019) Emily Alsentzer, John R. Murphy, Willie Boag, Wei-Hung Weng, Di Jin, Tristan Naumann, and Matthew B. A. McDermott. 2019.  Publicly available clinical bert embeddings.
  * Beltagy et al. (2020) Iz Beltagy, Matthew E. Peters, and Arman Cohan. 2020.  Longformer: The long-document transformer.  _CoRR_ , abs/2004.05150.
  * Darabi et al. (2020) Sajad Darabi, Mohammad Kachuee, Shayan Fazeli, and Majid Sarrafzadeh. 2020.  Taper: Time-aware patient ehr representation.  _IEEE Journal of Biomedical and Health Informatics_ , 24(11):3268–3275.
  * Huang et al. (2019) Kexin Huang, Jaan Altosaar, and Rajesh Ranganath. 2019.  Clinicalbert: Modeling clinical notes and predicting hospital readmission.  _arXiv preprint arXiv:1904.05342_.
  * Johnson et al. (2023) Alistair Johnson, Lucas Bulgarelli, Lu Shen, Alvin Gayles, Ayad Shammout, Steven Horng, Tom Pollard, Sicheng Hao, Benjamin Moody, Brian Gow, Li-wei Lehman, Leo Celi, and Roger Mark. 2023.  Mimic-iv, a freely accessible electronic health record dataset.  _Scientific Data_ , 10:1.
  * Johnson et al. (2016) Alistair E.W. Johnson, Tom J. Pollard, Lu Shen, Li wei H. Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G. Mark. 2016.  Mimic-iii, a freely accessible critical care database.  _Nature_.
  * Li et al. (2022) Yikuan Li, Ramsey M. Wehbe, Faraz S. Ahmad, Hanyin Wang, and Yuan Luo. 2022.  Clinical-longformer and clinical-bigbird: Transformers for long clinical sequences.  _CoRR_ , abs/2201.11838.
  * Schneeweiss et al. (2001) Sebastian Schneeweiss, John D Seeger, Malcolm Maclure, Philip S Wang, Jerry Avorn, and Robert J Glynn. 2001.  Performance of comorbidity scores to control for confounding in epidemiologic studies using claims data.  _American journal of epidemiology_ , 154(9):854–864.
  * Thapa et al. (2022) Nischay Bikram Thapa, Sattar Seifollahi, and Sona Taheri. 2022.  Hospital readmission prediction using clinical admission notes.  In _Australasian Computer Science Week 2022_ , pages 193–199.
  * Yang et al. (2022) Grace Yang, Ming Cao, Lavender Y Jiang, Xujin C Liu, Alexander Cheung, Hannah Weiss, Davied Kurland, Kyunghyun Cho, and Eric K Oermann. 2022.  Language model classifier aligns better with physician word sensitivity than xgboost on readmission prediction.  _arXiv preprint arXiv:2211.07047_.

## Appendices

##  Appendix A Preprocessing

We preprocessed the dataset with the following approach: First of all,
admission records with missing discharge notes or missing nursing notes are
eliminated. Then, for each remaining admission record, the nursing notes
associated with that record are sorted according to their timestamp. The first
and last created nursing notes for each admission are selected and
concatenated with the discharge notes of the same admission record to produce
the clinical note set for every admission. Lastly, we clean the datasets by
removing the de-identification patterns (’[** de-identified info **]’) in the
clinical notes, which usually occupy a lot of tokens.


# A search for ultra high energy neutrinos from TXS 0506+056 using the Pierre
Auger Observatory

###### Abstract

Results of a search for ultra-high-energy neutrinos with the Pierre Auger
Observatory from the direction of the blazar TXS 0506+056 are presented. They
were obtained as part of the follow-up that stemmed from the detection of
high-energy neutrinos and gamma rays with IceCube, Fermi-LAT, MAGIC, and other
detectors of electromagnetic radiation in several bands. The Pierre Auger
Observatory is sensitive to neutrinos in the energy range from 100 PeV to 100
EeV and in the zenith angle range from $\theta=60^{\circ}$ to
$\theta=95^{\circ}$, where the zenith angle is measured from the vertical
direction. No neutrinos from the direction of TXS 0506+056 have been found.
The results were analyzed in three periods: One of 6 months around the
detection of IceCube-170922A, coinciding with a flare period of TXS 0506+056,
a second one of 110 days during which the IceCube collaboration found an
excess of 13 neutrinos from a direction compatible with TXS 0506+056, and a
third one from 2004 January 1 up to 2018 August 31, over which the Pierre
Auger Observatory has been taking data. The sensitivity of the Observatory is
addressed for different spectral indices by considering the fluxes that would
induce a single expected event during the observation period. For indices
compatible with those measured by the IceCube collaboration the expected
number of neutrinos at the Observatory is well- below one. Spectral indices as
hard as 1.5 would have to apply in this energy range to expect a single event
to have been detected.

neutrinos — multi-messenger — blazar

††journal: ApJ

##  1 Introduction

On 2017 September 22, a through-going muon that deposited 23.7 TeV was
detected at the IceCube telescope (Aartsen et al., 2017) in Antarctica, likely
to be produced by a neutrino. The most probable energy for the neutrino is 290
TeV (Aartsen et al., 2018a) assuming a spectrum compatible with the measured
diffuse flux (Aartsen et al., 2015, 2016). Within a minute, the arrival
direction and energy estimates were reported through the Gamma-ray Coordinates
Network Circular (Kopper et al., 2017) as part of the routine of the multi-
messenger that is being established in high-energy astrophysics. Six days
later, flaring activity in the $\gamma$-ray band was observed in the Fermi
Large Area Telescope (Fermi-LAT), from TXS 0506+056 (RA= 9h 55.6m, Dec= +5∘
41.6’), a powerful blazar at relatively high redshift of $0.3365\pm 0.0010$
(Paiano et al., 2018) and only $0.1^{\circ}$ away from the deduced neutrino
direction (Tanaka et al., 2017). The chance possibility of this correlation
was estimated to be $\sim 0.3\%$ (3$\sigma$ level) which motivated further
scrutinizing of this object in practically all bands of the electromagnetic
spectrum and in neutrinos (Aartsen et al., 2018a; Padovani et al., 2018).

The remarkable multi-messenger effort that followed revealed a complex
variable activity. Most notably, the search of archival IceCube data for
signal correlations from the same direction also revealed an excess flux of
$13\pm 5$ through-going muons between December 2014 and February 2105,
dominating the background neutrino flux from this region, which was
interpreted as a burst of neutrinos over a time window of about 110 days from
the same object (Aartsen et al., 2018b). The significance of such an excess
localized in the reported time window being due to background atmospheric
neutrinos is estimated to be at the $3.5\sigma$ level. A Very-High-Energy
(VHE) signal between 80 and 400 GeV was detected in the MAGIC telescope when
integrating observation between 2017 September 24 and 2017 October 4,
confirming the flaring activity observed by Fermi-LAT (Ansoldi et al., 2018).

The detection of neutrinos from the direction of TXS 0506+056 illustrates the
potential of multi-messenger observations (Aartsen et al., 2018a). The follow-
up studies have attracted a lot of attention since the detection of neutrinos
from blazars would provide the first robust evidence of hadronic acceleration
in astrophysical jets, potentially explaining the diffuse high-energy neutrino
excess detected by IceCube over the atmospheric background, and providing much
insight into the modeling of these powerful objects. While the energy of the
gamma rays that can reach us from such an extragalactic source is limited by
pair production in the background radiation fields, neutrinos are not prone to
similar interactions and will travel unimpeded up to the highest energies.
Moreover, TXS 0506+056 is listed among the 50 brightest objects in the third
catalog of active galactic nuclei detected by Fermi-LAT (Ackermann et al.,
2015), suggesting that neutrino emission may be highly non-uniform within the
blazar population (Halzen et al., 2019). Naturally, other neutrino searches
have followed with other facilities spanning different energy bands, such as
ANTARES (Dornic & Coleiro, 2017) and Kamiokande (Hagiwara et al., 2019). These
searches have reported no signals.

Ultra-High-Energy (UHE) neutrinos have been searched for with the Pierre Auger
Observatory since 2004 (Abraham et al., 2008) by looking for inclined showers
that develop deep in the atmosphere. The Observatory has been shown to have a
similar sensitivity to that of IceCube for UHE neutrinos of energies above 100
PeV (Aab et al., 2019a). Moreover, it has been shown to have a distinctive
directional sensitivity which can have a unique potential to search for
transient events from point sources that are at preferred declinations (Aab et
al., 2019b). This is partly due to the enhanced capability of the Observatory
to trigger on air showers produced by the decay of tau leptons originating
from Earth-skimming tau neutrino interactions near the surface of the Earth.
The search for correlated neutrinos from the direction of TXS 0506+056 with
the Pierre Auger Observatory has lead to a negative result (Pedreira, 2019).
In this article we describe the search made and the implications for the
possible neutrino flux that could be emitted from this object in the UHE band.

##  2 The search of neutrinos with the Pierre Auger Observatory

Ultra-high-energy neutrinos arriving with high zenith-angles can induce air
showers deep in the atmosphere. These can be detected with arrays of particle
detectors, such as those operated within the Pierre Auger Observatory located
in the Mendoza province, Argentina. This Observatory is the largest and
highest-precision detector available to measure cosmic rays of EeV energies
and above (Aab et al., 2015a). It consists of a 3000 km2 array of water-
Cherenkov detectors, the Surface Detector (SD), at ground level arranged on a
triangular grid with 1600 detectors 1.5 km apart. The SD samples the front of
the extensive air- showers that develop when UHE cosmic rays interact in the
upper layers of the atmosphere. The Pierre Auger Observatory also includes a
Fluorescence Detector (FD) comprising 27 telescopes that are used to view the
atmosphere over the array and capture the fluorescence light that is emitted
as the shower passes through the atmosphere. The Observatory was designed to
detect cosmic-ray showers, produced by nuclei or protons interacting in the
upper layers of the atmosphere.

When regular cosmic-rays (i.e. protons, nuclei, photons) arrive with zenith
angles exceeding about $60^{\circ}$, their induced showers are largely
absorbed in the atmosphere, well-before reaching ground level. As a result,
the shower front at observation level is mostly composed of ultra-relativistic
muons that have small time spreads, giving characteristic sharp signals in the
particle detectors of the array. Neutrinos, on the other hand, can interact
deeper in the atmosphere so that when the neutrino-induced shower front
reaches ground level it still has a large fraction of electrons, positrons,
and photons (the electromagnetic component), which gives a signal in the
detectors which is typically distributed over a larger time interval (Capelle
et al., 1998). For instance, while an $80^{\circ}$ proton shower has a signal
spread of $\sim 100$ ns about 1 km from the shower axis, a neutrino shower can
reach over $1~{}\mu$s.

The identification of the electromagnetic signals in the SD stations provides
the basis for the discrimination between neutrino-induced showers and those
from the background of hadronic cosmic-rays. This is basically done using
variables related to the ratio of the integrated signal to its peak value in
selected stations which provide a measure of the time-width of the signal. For
optimization purposes the search is carried out using three distinct groups of
events. Each group is selected from the data with its own set of criteria,
based on variables that relate to the zenith angle and broadly correspond to
zenith angles between $60^{\circ}$ and $75^{\circ}$, “Downward-Going Low”
(DGL), those between $75^{\circ}$ and $90^{\circ}$, “Downward-Going High”
(DGH), and those between $90^{\circ}$ and $95^{\circ}$, “Earth-Skimming” (ES).
The method devised for each group, in addition to the selection of events,
includes the search for neutrino candidates within, as explained in detail in
(Aab et al., 2015b, 2019a). The ES search provided the most competitive limit
for diffuse flux of UHE neutrinos in the 100 PeV to 10 EeV range in 2008
(Abraham et al., 2008), before IceCube had been fully completed. Later updates
including the DGH and DGL searches have set limits (Aab et al., 2015b, 2019a)
comparable to contemporary bounds from IceCube in the same energy range
(Aartsen et al., 2018c).

For the bounds reported here, we make the implicit assumption that the fluxes
of all neutrino flavors are equal because of flavor oscillations as they
travel to Earth (Learned & Pakvasa, 1995), corresponding to a flavor ratio of
$\nu_{e}:\nu_{\mu}:\nu_{\tau}$ of 1:2:0 at the source. It is however possible
that the actual flavor ratios at the source are significantly different, as
has been for instance argued in case of acceleration of secondaries in flares
(Klein et al., 2013; Winter et al., 2014). These could result in modified
flavor ratios at Earth that would require reevaluation. The remarkable
sensitivity of the Observatory to UHE neutrinos is in part due to the Earth-
skimming channel (Bertou et al., 2002), in which tau neutrinos traveling
through the Earth interact just below the surface, producing a tau lepton that
exits to the atmosphere and induces an upcoming air shower. Because of this
channel, the Pierre Auger Observatory provides complementary information to
IceCube relative to the tau flavor.

Figure 1: Effective area of the Pierre Auger Observatory as a function of
neutrino energy for each search channel. The shaded bands bound the
instantaneous effective area for each neutrino detection channel and indicate
the variation with zenith angle in the corresponding range. TXS 0506+056 at a
declination $\delta\simeq 5.7^{\circ}$ is viewed at the SD of Auger for a
limited amount of time (see Fig. 2) and with a range of zenith angles from
$\theta=60^{\circ}$ to $\theta=95^{\circ}$, the sensitivity being largest
below the horizon ($\theta>90^{\circ}$). The full lines represent the
effective area for the different detection channels when averaging over a full
day, i.e. when including the periods during a day, when the source cannot be
seen. The instantaneous effective area of IceCube for the declination of TXS
0506+056 is also shown for comparison. For IceCube at the South Pole the
zenith angle of TXS 0506+056 is practically constant over time and given by
$\theta=90^{\circ}+\delta$. The width of the grey band corresponds in this
case to different stages of IceCube construction and configuration which
depend on the period under consideration.

There are a number of coincidences that make this channel most effective. The
matter depth of the Earth’s chord is a rapidly varying function as the nadir
angle of the upcoming tau neutrino, $180^{\circ}-\theta$, approaches the
horizontal ($\theta=90^{\circ}$). Depending on this angle there is a
characteristic neutrino energy, $E_{\mathrm{ch}}(\theta)$, at which the matter
depth matches the neutrino mean free path. This angle roughly optimizes the
search for neutrinos of energy $\sim E_{\mathrm{ch}}(\theta)$. On the other
hand, for the SD to detect these showers, they must be nearly horizontal so
that the shower develops at a very low altitude and the shower front reaches
the ground as it extends laterally. It turns out that for nadir angles between
$85^{\circ}$ and $90^{\circ}$, the values of $E_{\mathrm{ch}}(\theta)$ are in
the 100 PeV to 10 EeV range, large enough to induce showers that can be
detected by such a sparse array. Moreover, at about 1 EeV, there is a sweet-
spot in which the probability for the tau neutrino to convert and for the tau
lepton to exit the Earth and to be detected in the SD is maximal (Alvarez-
Muñiz et al., 2019). This is because of a combination of different effects: Up
to about 1 EeV, the matter depth the tau lepton is able to traverse before
exiting the Earth is mainly governed by the tau decay length, which increases
linearly with energy, enhancing the effective detector volume. Above about 1
EeV, energy losses in the Earth start to dominate in the exit path of the tau
lepton so that its range only rises logarithmically with energy. In addition,
because of the increased tau decay length in the atmosphere, showers more
often start developing at higher altitudes making the detection of the shower
front by the surface detector array less likely (Zas, 2005).

As a result, for the Earth-skimming detection, the neutrino arrival directions
must be within a very small angular range of few degrees below the horizon.
For these directions, the effective area of the Observatory for detecting tau-
flavor neutrinos is very much enhanced relative to the search method for
downward-going neutrinos (DGH and DGL). This is the reason why the Pierre
Auger Collaboration could set the best limit to UHE neutrinos from GW170817
(Albert et al., 2017), the binary neutron star merger event detected in
gravitational waves and followed up in most bands of the electromagnetic
spectrum (Abbott et al., 2017). The instantaneous effective area is highly
dependent on the arrival zenith-angle which is a function of the source
declination and the hour-angle, so that the sensitivity of the Observatory is
highly directional and time-dependent (Aab et al., 2019b). This can be
appreciated in Fig. 1 where the three wide coloured bands span the
instantaneous effective area of the Observatory within the zenith angle
intervals corresponding to the three search channels. For the Earth-skimming
channel the width is largest, reflecting the rapid variation of effective area
as the zenith angle changes by only 5 degrees from $90^{\circ}$ to
$95^{\circ}$ reaching a maximum at $\sim 91^{\circ}$.

Figure 2: Hours per day a source is visible in each of the search channels as
a function of declination. The declination of TXS 0506+056 is marked with an
arrow.

The search for neutrinos from the direction of TXS 0506+056 will be considered
for periods much longer than a day. Thus, the effective area for neutrino
detection must be integrated over time as the source position transits over
different zenith angles. In Fig. 1 we have also shown the daily average of the
effective area for the Observatory in each of the three search channels for
the blazar declination of $5.7^{\circ}$ (full colored lines), where they are
compared to the effective area of IceCube detector for the same source
(Aartsen et al., 2018b). Due to the location of the IceCube detector, the
effective area for a fixed position in space depends only on its declination
and is otherwise independent of time for each configuration. The width of the
IceCube band here is due to the different configurations achieved after
different construction stages (Aartsen et al., 2018b). The effective exposure
can be approximately calculated by multiplying the daily average of the
effective area for the corresponding declination, by the length of the time
period under consideration (Aab et al., 2019b). The daily average depends
strongly on declination and this is partly because the source is only
“visible” in neutrinos during a varying fraction of the day in each zenith
angle range. This fraction is displayed in Fig. 2 as a function of the
declination for each of the three types of searches. The black arrow marks the
declination of TX0506+056, indicating that the source is not at a declination
that maximizes the observation time. This effect also contributes to the large
variations in effective area as a function of the source declination. For
periods much larger than a sidereal day the approximation is very accurate
because variations in effective area with time have been relatively small
since the Observatory was completed in 2008 June.

##  3 Results and discussion

Figure 3: UHE flux reference that would give one expected neutrino event at
the Pierre Auger Observatory over a period of half a year (2017 March 22 -
September 22) for a spectrum $dN/dE\propto E^{-2}$ in comparison to the flux
that would produce on average one detection like the IceCube-170922A event
over the same period (solid red and black lines). Flux references are also
shown for the Pierre Auger Observatory for a period of $\sim$15 years during
which it has taken data (2004 January 1 - 2018 August 31) and for a period of
7.5 years for IceCube (Aartsen et al., 2018a) (dashed red and black lines).
The average VHE and UHE photon fluxes measured with Fermi-LAT, and MAGIC
around 2017 September 22 (Aartsen et al., 2018a), and the archival photon
measurement from Fermi-LAT (Acero et al., 2015), as well as the UHE photon
flux from this direction that would give one expected photon event in half a
year at the Pierre Auger Observatory, are also shown for comparison.

All the data collected with the Pierre Auger Observatory were searched for
candidate neutrino events in the direction of TXS 0506+056 with negative
results. Instead of providing a flux limit we calculate the expected flux that
would have been deduced if a single neutrino had been observed, assuming a
steady flux over a given period of time. This illustrates the expected
sensitivity to a given flux and can be easily converted to a flux limit at
$90\%$ confidence multiplying it by a factor $2.39$ (Feldman & Cousins, 1998).
The results naturally depend on the assumptions that are made with respect to
the time period over which the search is integrated. Two benchmark scenarios
have been discussed in the original article addressing the correlated
detection in neutrinos and in the HE and VHE gamma-ray bands (Aartsen et al.,
2018a). The first is of half a year and it is motivated by the time window
that gave the largest significance to a search for an excess of neutrino-
compatible events in the archival data of IceCube, interpreted as a neutrino
flare (Aartsen et al., 2018b). The second period corresponds to 7.5 years, the
whole observation time that the IceCube detector had been in operation at the
time of detection. We here address similar scenarios of half a year and the
whole observation period of the Pierre Auger Observatory which is 15 years
from 2004 January 1 to 2018 August 31. We note that periods over which the SD
was unstable have been removed from the analysis and that during the first
four years of operation the effective area was a rapidly growing function of
time because the Observatory was under construction until 2008 June.

The average spectral fluxes of UHE neutrinos with a fixed spectral index
($\sim E^{-\gamma}$) that would produce a single event at the Observatory for
these two periods are displayed in Fig. 3 for a spectral index of
$\gamma=2.0$, assumed to hold in the energy range between 100 PeV and 10 EeV
and to be constant in time during the corresponding time period. In this plot
they are compared to the fluxes obtained from the neutrino detected in 2017
September 22 and inferred to have energy of order few hundred TeV, considering
a period of half a year and 7.5 years. The plot also displays the average VHE
gamma-ray flux detected with Fermi-LAT and MAGIC over periods within a couple
of weeks around the neutrino detection date of 2017 September 22 (Aartsen et
al., 2018a). These gamma-ray fluxes correspond to the reported flaring
activity and have not been corrected for absorption in the extragalactic
background light. They are considerably larger than the average gamma-ray
fluxes that had been recorded to date from this source, and which are also
illustrated for comparison (Acero et al., 2015). The sensitivity of the Auger
Observatory to UHE neutrinos is about an order of magnitude below
extrapolations with $E^{-2}$ spectra, partly due to the non optimal position
of the source.

Figure 4: UHE neutrino flux sensitivities for the Pierre Auger Observatory
(one event expected) assuming a constant flux during a period of 110 days from
19 October 2014 to 6 February 2015 in comparison to the measured photon flux
(Padovani et al., 2018) and to the neutrino flux inferred with IceCube during
the same period with a spectral index of $\gamma=2.1\pm 0.2$ (Aartsen et al.,
2018b). The band shown for IceCube is obtained using the extreme values of
$\gamma$ ($\sim$1.75, $\sim$2.45) from the given one-sigma contour plot and
($\sim 1.5$ and $\sim 2.7$) from the two-sigma contour.

We have also compared the sensitivity of the Observatory to the neutrino flux
observed by IceCube between 19 October 2014 and 6 February 2015\. The analysis
of this period resulted in constraints for the normalization and spectral
index of the observed fluence (Aartsen et al., 2018b). This period of
increased neutrino flux in IceCube was not coincident with a VHE gamma-ray
flare from the same source, although a hardening of the spectrum in the GeV
region was reported (Padovani et al., 2018). In Fig. 4 we display the
$1\sigma$ and $2\sigma$ bands of the average flux obtained from the fluence
reported assuming an activity period of 110 days as obtained from the IceCube
data analysis using a Gaussian window. The bands are calculated using the
whole parameter space allowed at $68\%$ and $95\%$ confidence levels in the
IceCube analysis. The extreme values of the spectral index are $\gamma\sim
1.75$ and $\gamma\sim 2.45$ ($\sim 1.5$ and $\sim 2.7$) for the $68\%$
($95\%$) CL contour plot (Aartsen et al., 2018b). The figure also displays the
average gamma-ray flux obtained for this period illustrating the reported
hardening (Padovani et al., 2018). The results obtained indicate that the
Pierre Auger Observatory could only be expected to have detected a signal if
the flux extrapolated to the EeV regime with spectral indices harder than
$\gamma\sim 1.5$.

With the Pierre Auger Observatory it is also possible to search for UHE
photons (Aab et al., 2016; Niechciol, 2017; Aab et al., 2019c). For a source
as distant as TXS 0506+056, any UHE photon flux that could have been produced
is expected to be strongly attenuated through interactions with the cosmic
photon-background fields, unless new physics would occur. The data have been
searched for UHE photons between 10 and 300 EeV in coincidence with
IceCube-170922A over a period of half a year and also in coincidence with the
110 day interval interpreted by (Aartsen et al., 2018b) as burst of neutrinos.
No event has been found with an angular distance to the source below
$2^{\circ}$. The shower with closest angular distance to the source
($2.1^{\circ}$) was observed for the latter period and the corresponding value
of the Principal Component (PC) for photon discrimination (Rautenberg, 2019)
is very low, so that less than $0.1\%$ of the simulated photons have a smaller
PC value. As a result, the probability of this event to be a correlating
photon is less than $6\times 10^{-5}$. Assuming an $E^{-2}$ spectrum, the
photon energy flux that would give one expected photon event at the
Observatory is $1.8\times 10^{-12}$ erg cm-2 s-1. For the half a year period
in 2017 the closest event, at an angular distance of $3.0^{\circ}$, has an
even lower probability to be a photon, and the reference energy flux for one
detected photon becomes $1.0\times 10^{-12}$ erg cm-2 s-1.

In summary, we have studied the implications of the non-observation of UHE
neutrinos with the Pierre Auger Observatory. The source is not located at one
of the preferential declinations for observation so the flux constraints that
can be obtained are rather limited. The neutrino flux from TXS 0506+056 at
100s of TeV sampled by IceCube with event IceCube-170922 was converted to a
flux using a half a year period (Aartsen et al., 2018a). If the flux from the
source had an $E^{-2}$ spectrum extending to the EeV and if it had remained
constant over the lifetime of the Observatory with the same normalization, one
neutrino event could be expected to have been observed at the Pierre Auger
Observatory. We have also shown that the Observatory could have a chance to
detect UHE neutrinos produced between October 2014 and February 2015 only in
case the spectrum extended to the EeV range with a spectral index harder than
$\gamma\sim 1.5$ (Aartsen et al., 2018b).

## Acknowledgments

The successful installation, commissioning, and operation of the Pierre Auger
Observatory would not have been possible without the strong commitment and
effort from the technical and administrative staff in Malargüe. We are very
grateful to the following agencies and organizations for financial support:

Argentina – Comisión Nacional de Energía Atómica; Agencia Nacional de
Promoción Científica y Tecnológica (ANPCyT); Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET); Gobierno de la Provincia de
Mendoza; Municipalidad de Malargüe; NDM Holdings and Valle Las Leñas; in
gratitude for their continuing cooperation over land access; Australia – the
Australian Research Council; Brazil – Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq); Financiadora de Estudos e Projetos (FINEP);
Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ); São Paulo
Research Foundation (FAPESP) Grants No. 2019/10151-2, No. 2010/07359-6 and No.
1999/05404-3; Ministério da Ciência, Tecnologia, Inovações e Comunicações
(MCTIC); Czech Republic – Grant No. MSMT CR LTT18004, LM2015038, LM2018102,
CZ.02.1.01/0.0/0.0/16_013/0001402, CZ.02.1.01/0.0/0.0/18_046/0016010 and
CZ.02.1.01/0.0/0.0/17_049/0008422; France – Centre de Calcul IN2P3/CNRS;
Centre National de la Recherche Scientifique (CNRS); Conseil Régional Ile-de-
France; Département Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS);
Département Sciences de l’Univers (SDU-INSU/CNRS); Institut Lagrange de Paris
(ILP) Grant No. LABEX ANR-10-LABX-63 within the Investissements d’Avenir
Programme Grant No. ANR-11-IDEX-0004-02; Germany – Bundesministerium für
Bildung und Forschung (BMBF); Deutsche Forschungsgemeinschaft (DFG);
Finanzministerium Baden-Württemberg; Helmholtz Alliance for Astroparticle
Physics (HAP); Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF);
Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-
Westfalen; Ministerium für Wissenschaft, Forschung und Kunst des Landes Baden-
Württemberg; Italy – Istituto Nazionale di Fisica Nucleare (INFN); Istituto
Nazionale di Astrofisica (INAF); Ministero dell’Istruzione, dell’Universitá e
della Ricerca (MIUR); CETEMPS Center of Excellence; Ministero degli Affari
Esteri (MAE); México – Consejo Nacional de Ciencia y Tecnología (CONACYT) No.
167733; Universidad Nacional Autónoma de México (UNAM); PAPIIT DGAPA-UNAM; The
Netherlands – Ministry of Education, Culture and Science; Netherlands
Organisation for Scientific Research (NWO); Dutch national e-infrastructure
with the support of SURF Cooperative; Poland -Ministry of Science and Higher
Education, grant No. DIR/WK/2018/11; National Science Centre, Grants No.
2013/08/M/ST9/00322, No. 2016/23/B/ST9/01635 and No. HARMONIA
5–2013/10/M/ST9/00062, UMO-2016/22/M/ST9/00198; Portugal – Portuguese national
funds and FEDER funds within Programa Operacional Factores de Competitividade
through Fundação para a Ciência e a Tecnologia (COMPETE); Romania – Romanian
Ministry of Education and Research, the Program Nucleu within MCI
(PN19150201/16N/2019 and PN19060102) and project PN-
III-P1-1.2-PCCDI-2017-0839/19PCCDI/2018 within PNCDI III; Slovenia – Slovenian
Research Agency, grants P1-0031, P1-0385, I0-0033, N1-0111; Spain – Ministerio
de Economía, Industria y Competitividad (FPA2017-85114-P and FPA2017-85197-P),
Xunta de Galicia (ED431C 2017/07), Junta de Andalucía (SOMM17/6104/UGR), Feder
Funds, RENATA Red Nacional Temática de Astropartículas (FPA2015-68783-REDT)
and María de Maeztu Unit of Excellence (MDM-2016-0692); USA – Department of
Energy, Contracts No. DE-AC02-07CH11359, No. DE-FR02-04ER41300, No. DE-
FG02-99ER41107 and No. DE-SC0011689; National Science Foundation, Grant No.
0450696; The Grainger Foundation; Marie Curie-IRSES/EPLANET; European Particle
Physics Latin American Network; and UNESCO.

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=3000 The Pierre Auger Collaboration

A. Aab75, P. Abreu67, M. Aglietta50,49, J.M. Albury12, I. Allekotte1, A.
Almela8,11, J. Alvarez-Muñiz74, R. Alves Batista75, G.A. Anastasi58,49, L.
Anchordoqui82, B. Andrada8, S. Andringa67, C. Aramo47, P.R. Araújo Ferreira39,
H. Asorey8, P. Assis67, G. Avila10, A.M. Badescu70, A. Bakalova30, A.
Balaceanu68, F. Barbato56,47, R.J. Barreira Luz67, K.H. Becker35, J.A.
Bellido12, C. Berat34, M.E. Bertaina58,49, X. Bertou1, P.L. Biermannb, T.
Bister39, J. Biteau32, J. Blazek30, C. Bleve34, M. Boháčová30, D.
Boncioli53,43, C. Bonifazi24, L. Bonneau Arbeletche19, N. Borodai64, A.M.
Botti8, J. Bracke, T. Bretz39, F.L. Briechle39, P. Buchholz41, A. Bueno73, S.
Buitink14, M. Buscemi54,44, K.S. Caballero-Mora62, L. Caccianiga55,46, L.
Calcagni4, A. Cancio11,8, F. Canfora75,77, I. Caracas35, J.M. Carceller73, R.
Caruso54,44, A. Castellina50,49, F. Catalani17, G. Cataldi45, L. Cazon67, M.
Cerda9, J.A. Chinellato20, K. Choi74, J. Chudoba30, L. Chytka31, R.W. Clay12,
A.C. Cobos Cerutti7, R. Colalillo56,47, A. Coleman88, M.R. Coluccia52,45, R.
Conceição67, A. Condorelli42,43, G. Consolati46,51, F. Contreras10, F.
Convenga52,45, C.E. Covault80,h, S. Dasso5,3, K. Daumiller37, B.R. Dawson12,
J.A. Day12, R.M. de Almeida26, J. de Jesús8,37, S.J. de Jong75,77, G. De
Mauro75,77, J.R.T. de Mello Neto24,25, I. De Mitri42,43, J. de Oliveira26, D.
de Oliveira Franco20, V. de Souza18, E. De Vito52,45, J. Debatin36, M. del
Río10, O. Deligny32, N. Dhital64, A. Di Matteo49, C. Dobrigkeit20, J.C.
D’Olivo63, Q. Dorosti41, R.C. dos Anjos23, M.T. Dova4, J. Ebr30, R.
Engel36,37, I. Epicoco52,45, M. Erdmann39, C.O. Escobarc, A. Etchegoyen8,11,
H. Falcke75,78,77, J. Farmer87, G. Farrar85, A.C. Fauth20, N. Fazzinic, F.
Feldbusch38, F. Fenu58,49, B. Fick84, J.M. Figueira8, A. Filipčič72,71, T.
Fodran75, M.M. Freire6, T. Fujii87,f, A. Fuster8,11, C. Galea75, C.
Galelli55,46, B. García7, A.L. Garcia Vegas39, H. Gemmeke38, F. Gesualdi8,37,
A. Gherghel-Lascu68, P.L. Ghia32, U. Giaccari75, M. Giammarchi46, M. Giller65,
J. Glombitza39, F. Gobbi9, F. Gollan8, G. Golup1, M. Gómez Berisso1, P.F.
Gómez Vitale10, J.P. Gongora10, N. González8, I. Goos1,37, D. Góra64, A.
Gorgi50,49, M. Gottowik35, T.D. Grubb12, F. Guarino56,47, G.P. Guedes21, E.
Guido49,58, S. Hahn37,8, R. Halliday80, M.R. Hampel8, P. Hansen4, D. Harari1,
V.M. Harvey12, A. Haungs37, T. Hebbeker39, D. Heck37, G.C. Hill12, C. Hojvatc,
J.R. Hörandel75,77, P. Horvath31, M. Hrabovský31, T. Huege37,14, J.
Hulsman8,37, A. Insolia54,44, P.G. Isar69, J.A. Johnsen81, J. Jurysek30, A.
Kääpä35, K.H. Kampert35, B. Keilhauer37, J. Kemp39, H.O. Klages37, M.
Kleifges38, J. Kleinfeller9, M. Köpke36, G. Kukec Mezek71, B.L. Lago16, D.
LaHurd80, R.G. Lang18, N. Langner39, M.A. Leigui de Oliveira22, V. Lenok37, A.
Letessier-Selvon33, I. Lhenry-Yvon32, D. Lo Presti54,44, L. Lopes67, R.
López59, R. Lorek80, Q. Luce36, A. Lucero8, A. Machado Payeras20, G.
Mancarella52,45, D. Mandat30, B.C. Manning12, J. Manshanden40, P. Mantschc, S.
Marafico32, A.G. Mariazzi4, I.C. Mariş13, G. Marsella52,45, D. Martello52,45,
H. Martinez18, O. Martínez Bravo59, M. Mastrodicasa53,43, H.J. Mathes37, J.
Matthews83, G. Matthiae57,48, E. Mayotte35, P.O. Mazurc, G. Medina-Tanco63, D.
Melo8, A. Menshikov38, K.-D. Merenda81, S. Michal31, M.I. Micheletti6, L.
Miramonti55,46, D. Mockler13, S. Mollerach1, F. Montanet34, C. Morello50,49,
M. Mostafá86, A.L. Müller8,37, M.A. Muller20,d,24, K. Mulrey14, R. Mussa49, M.
Muzio85, W.M. Namasaka35, L. Nellen63, M. Niculescu-Oglinzanu68, M.
Niechciol41, D. Nitz84,g, D. Nosek29, V. Novotny29, L. Nožka31, A Nucita52,45,
L.A. Núñez28, M. Palatka30, J. Pallotta2, P. Papenbreer35, G. Parente74, A.
Parra59, M. Pech30, F. Pedreira74, J. Pȩkala64, R. Pelayo61, J. Peña-
Rodriguez28, J. Perez Armand19, M. Perlin8,37, L. Perrone52,45, S.
Petrera42,43, T. Pierog37, M. Pimenta67, V. Pirronello54,44, M. Platino8, B.
Pont75, M. Pothast77,75, P. Privitera87, M. Prouza30, A. Puyleart84, S.
Querchfeld35, J. Rautenberg35, D. Ravignani8, M. Reininghaus37,8, J. Ridky30,
F. Riehn67, M. Risse41, P. Ristori2, V. Rizi53,43, W. Rodrigues de Carvalho19,
J. Rodriguez Rojo10, M.J. Roncoroni8, M. Roth37, E. Roulet1, A.C. Rovero5, P.
Ruehl41, S.J. Saffi12, A. Saftoiu68, F. Salamida53,43, H. Salazar59, G.
Salina48, J.D. Sanabria Gomez28, F. Sánchez8, E.M. Santos19, E. Santos30, F.
Sarazin81, R. Sarmento67, C. Sarmiento-Cano8, R. Sato10, P. Savina52,45,32,
C.M. Schäfer37, V. Scherini45, H. Schieler37, M. Schimassek36,8, M. Schimp35,
F. Schlüter37,8, D. Schmidt36, O. Scholten76,14, P. Schovánek30, F.G.
Schröder88,37, S. Schröder35, J. Schulte39, S.J. Sciutto4, M.
Scornavacche8,37, R.C. Shellard15, G. Sigl40, G. Silli8,37, O. Sima68,h, R.
Šmída87, P. Sommers86, J.F. Soriano82, J. Souchard34, R. Squartini9, M.
Stadelmaier37,8, D. Stanca68, S. Stanič71, J. Stasielak64, P. Stassi34, A.
Streich36,8, M. Suárez-Durán28, T. Sudholz12, T. Suomijärvi32, A.D.
Supanitsky8, J. Šupík31, Z. Szadkowski66, A. Taboada36, A. Tapia27, C.
Timmermans77,75, O. Tkachenko37, P. Tobiska30, C.J. Todero Peixoto17, B.
Tomé67, A. Travaini9, P. Travnicek30, C. Trimarelli53,43, M. Trini71, M.
Tueros4, R. Ulrich37, M. Unger37, L. Vaclavek31, M. Vacula31, J.F. Valdés
Galicia63, L. Valore56,47, E. Varela59, A. Vásquez-Ramírez28, D. Veberič37, C.
Ventura25, I.D. Vergara Quispe4, V. Verzi48, J. Vicha30, J. Vink79, S.
Vorobiov71, H. Wahlberg4, A.A. Watsona, M. Weber38, A. Weindl37, L. Wiencke81,
H. Wilczyński64, T. Winchen14, M. Wirtz39, D. Wittkowski35, B. Wundheiler8, A.
Yushkov30, O. Zapparrata13, E. Zas74, D. Zavrtanik71,72, M. Zavrtanik72,71, L.
Zehrer71, A. Zepeda60, M. Ziolkowski41

1

Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San
Carlos de Bariloche, Argentina

2

Centro de Investigaciones en Láseres y Aplicaciones, CITEDEF and CONICET,
Villa Martelli, Argentina

3

Departamento de Física and Departamento de Ciencias de la Atmósfera y los
Océanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires,
Argentina

4

IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina

5

Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos
Aires, Argentina

6

Instituto de Física de Rosario (IFIR) – CONICET/U.N.R. and Facultad de
Ciencias Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina

7

Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), and Universidad Tecnológica Nacional – Facultad Regional Mendoza
(CONICET/CNEA), Mendoza, Argentina

8

Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina

9

Observatorio Pierre Auger, Malargüe, Argentina

10

Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe,
Argentina

11

Universidad Tecnológica Nacional – Facultad Regional Buenos Aires, Buenos
Aires, Argentina

12

University of Adelaide, Adelaide, S.A., Australia

13

Université Libre de Bruxelles (ULB), Brussels, Belgium

14

Vrije Universiteit Brussels, Brussels, Belgium

15

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil

16

Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Nova Friburgo,
Brazil

17

Universidade de São Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil

18

Universidade de São Paulo, Instituto de Física de São Carlos, São Carlos, SP,
Brazil

19

Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil

20

Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil

21

Universidade Estadual de Feira de Santana, Feira de Santana, Brazil

22

Universidade Federal do ABC, Santo André, SP, Brazil

23

Universidade Federal do Paraná, Setor Palotina, Palotina, Brazil

24

Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro,
RJ, Brazil

25

Universidade Federal do Rio de Janeiro (UFRJ), Observatório do Valongo, Rio de
Janeiro, RJ, Brazil

26

Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil

27

Universidad de Medellín, Medellín, Colombia

28

Universidad Industrial de Santander, Bucaramanga, Colombia

29

Charles University, Faculty of Mathematics and Physics, Institute of Particle
and Nuclear Physics, Prague, Czech Republic

30

Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

31

Palacky University, RCPTM, Olomouc, Czech Republic

32

Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France, France

33

Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités
Paris 6 et Paris 7, CNRS-IN2P3, Paris, France

34

Univ. Grenoble Alpes, CNRS, Grenoble Institute of Engineering Univ. Grenoble
Alpes, LPSC-IN2P3, 38000 Grenoble, France, France

35

Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany

36

Karlsruhe Institute of Technology, Institute for Experimental Particle Physics
(ETP), Karlsruhe, Germany

37

Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany

38

Karlsruhe Institute of Technology, Institut für Prozessdatenverarbeitung und
Elektronik, Karlsruhe, Germany

39

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

40

Universität Hamburg, II. Institut für Theoretische Physik, Hamburg, Germany

41

Universität Siegen, Fachbereich 7 Physik – Experimentelle Teilchenphysik,
Siegen, Germany

42

Gran Sasso Science Institute, L’Aquila, Italy

43

INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy

44

INFN, Sezione di Catania, Catania, Italy

45

INFN, Sezione di Lecce, Lecce, Italy

46

INFN, Sezione di Milano, Milano, Italy

47

INFN, Sezione di Napoli, Napoli, Italy

48

INFN, Sezione di Roma “Tor Vergata”, Roma, Italy

49

INFN, Sezione di Torino, Torino, Italy

50

Osservatorio Astrofisico di Torino (INAF), Torino, Italy

51

Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali ,
Milano, Italy

52

Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”,
Lecce, Italy

53

Università dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila,
Italy

54

Università di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy

55

Università di Milano, Dipartimento di Fisica, Milano, Italy

56

Università di Napoli “Federico II”, Dipartimento di Fisica “Ettore Pancini”,
Napoli, Italy

57

Università di Roma “Tor Vergata”, Dipartimento di Fisica, Roma, Italy

58

Università Torino, Dipartimento di Fisica, Torino, Italy

59

Benemérita Universidad Autónoma de Puebla, Puebla, México

60

Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), México,
D.F., México

61

Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas
del Instituto Politécnico Nacional (UPIITA-IPN), México, D.F., México

62

Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, México

63

Universidad Nacional Autónoma de México, México, D.F., México

64

Institute of Nuclear Physics PAN, Krakow, Poland

65

University of Łódź, Faculty of Astrophysics, Łódź, Poland

66

University of Łódź, Faculty of High-Energy Astrophysics,Łódź, Poland

67

Laboratório de Instrumentação e Física Experimental de Partículas – LIP and
Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa,
Portugal

68

“Horia Hulubei” National Institute for Physics and Nuclear Engineering,
Bucharest-Magurele, Romania

69

Institute of Space Science, Bucharest-Magurele, Romania

70

University Politehnica of Bucharest, Bucharest, Romania

71

Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova
Gorica, Slovenia

72

Experimental Particle Physics Department, J. Stefan Institute, Ljubljana,
Slovenia

73

Universidad de Granada and C.A.F.P.E., Granada, Spain

74

Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago
de Compostela, Santiago de Compostela, Spain

75

IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

76

KVI – Center for Advanced Radiation Technology, University of Groningen,
Groningen, The Netherlands

77

Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science
Park, Amsterdam, The Netherlands

78

Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, The
Netherlands

79

Universiteit van Amsterdam, Faculty of Science, Amsterdam, The Netherlands

80

Case Western Reserve University, Cleveland, OH, USA

81

Colorado School of Mines, Golden, CO, USA

82

Department of Physics and Astronomy, Lehman College, City University of New
York, Bronx, NY, USA

83

Louisiana State University, Baton Rouge, LA, USA

84

Michigan Technological University, Houghton, MI, USA

85

New York University, New York, NY, USA

86

Pennsylvania State University, University Park, PA, USA

87

University of Chicago, Enrico Fermi Institute, Chicago, IL, USA

88

University of Delaware, Department of Physics and Astronomy, Bartol Research
Institute, Newark, DE, USA

—–

a

School of Physics and Astronomy, University of Leeds, Leeds, United Kingdom

b

Max-Planck-Institut für Radioastronomie, Bonn, Germany

c

Fermi National Accelerator Laboratory, USA

d

also at Universidade Federal de Alfenas, Poços de Caldas, Brazil

e

Colorado State University, Fort Collins, CO, USA

f

now at Hakubi Center for Advanced Research and Graduate School of Science,
Kyoto University, Kyoto, Japan

g

also at Karlsruhe Institute of Technology, Karlsruhe, Germany

h

also at University of Bucharest, Bucharest, Romania