# Comparison of Probabilistic Deep Learning Methods for Autism Detection

Godfrin Ismail

Department of Computer Science
Dedan Kimathi University of Technology
<EMAIL_ADDRESS>Kenneth Chesoli

Department of Computer Science
Dedan Kimathi University of Technology
<EMAIL_ADDRESS>Golda Moni

Department of Computer Science
Dedan Kimathi University of Technology
<EMAIL_ADDRESS>Kinyua Gikunda
Department of Computer Science
Dedan Kimathi University of Technology
patrick.gikunda.dkut.ac.ke

###### Abstract

Autism Spectrum Disorder (ASD) is one neuro developmental disorder that is now
widespread in the world. ASD persists throughout the life of an individual,
impacting the way they behave and communicate, resulting to notable deficits
consisting of social life retardation, repeated behavioural traits and a
restriction in their interests. Early detection of the disorder helps in the
onset treatment and helps one to lead a normal life. There are clinical
approaches used in detection of autism, relying on behavioural data and in
worst cases, neuroimaging. Quantitative methods involving machine learning
have been studied and developed to overcome issues with clinical approaches.
These quantitative methods rely on machine learning, with some complex methods
based on deep learning developed to accelerate detection and diagnosis of ASD.
These literature is aimed at exploring most state-of-the-art probabilistic
methods in use today, characterizing them with the type of dataset they’re
most applied on, their accuracy according to their novel research and how well
they are suited in ASD classification. The findings will purposely serve as a
benchmark in selection of the model to use when performing ASD detection.

###### Index Terms:

Autism Spectrum Disorder, Deep Learning, Autism Detection

##  I Introduction

Autism spectrum disorder (ASD) is a term that describes a set of neuro-
developmental disorders that includes autism and Asperger’s syndrome (AS)[1].
Individuals with ASD tend to have a specific combination of deficits ranging
from social communication impairments, recurrent behavioral traits worsened by
restricted interests that begin in the early stages of their lives[2]. In a
study carried out by[3] on the prevalence of ASD since 2014, the findings were
that the disorder prevalence has risen at a high rate around the world,
bringing about the possibility of having an autism epidemic. [3] mentions that
this prevalence rate brings the need of availing ASD related services that
include training professionals and having efficient methods for identification
and diagnosis. The current diagnosis criteria for ASD are based on three main
symptoms: impaired social communication, limited interests, and repetitive
behaviors [4]. Because ASD is so complicated and varied, it can take a long
time from the time behavioral indications are noticed to the time a definitive
diagnosis is made [5]. This means that there is always a lag in treatment of
the disorder. The prevalence rate also has brought the surge in the amount of
research being carried out to aid in the detection and diagnosis of the
disorder [3].

Early diagnosis and early special education is necessary to allow a patient to
learn to perform activities and lead an almost normal life [6]. [6] found that
there are three types of data that can aid in diagnosis of ASD, these data can
either be behavioral data, data that is based on EEG (electroencephalogram)
and magnetic resonance imaging (MRI) data. A number of brain imaging
investigations have revealed functional and structural abnormalities in the
brains of people with ASD [7]. Magnetic resonance imaging (MRI)
investigations, for example, have revealed that people with ASD exhibit an
abnormal age-related brain growth trajectory in the frontal area [8] [9], this
strongly shows that functional brain imaging at a young age is critical for
detecting persistent ASD problems [10]. [11] used multimodal brain imaging
modalities [structural MRI, diffusion tensor imaging (DTI), and hydrogen
proton magnetic resonance spectrum (1H-MRS)] to explore neural structure in
the same group of people (19 adults with ASD and 18 adults with TD) and
applied the fractional anisotropy decision tree (FA), radial diffusivity (RD),
and cortical thickness as features to perform classification between ASD
patients and typically developed patients (TD). This strategy eliminates the
discrepancy that can occur when each imaging modality is used independently.
[11] Atypical brain activation in response to various cognitive activities or
diminished resting-state functional connectivity have been seen in some
functional brain investigations (RSFC).

The majority of the time, MRI characteristic features retrieved empirically
from brain scans are used to differentiate between children with ASD and those
who do not [12]. However, due to the intricacy of ASD’s pathogenic process and
our poor understanding of it, the hidden variables associated with ASD, which
can be utilized to accurately differentiate ASD from normal controls, are
difficult to notice and identify simply by looking at brain pictures [10].
Because a deep-learning artificial neural network is a data-driven method, it
can identify hidden properties in a large data set. And as the study by [13]
observes, the models based on deep learning can automatically learn complex
patterns that are hidden in a high-dimensional data and this allows the deep
learning models to achieve state-of-the-art performance in various domains,
and of most relevance in this research is the object detection for image
processing. This is the one aspect that is critical for Autism Detection and
Diagnosis as described in this paper.

This literature provides an in-depth analysis on the available state-of-the-
art probabilistic models that are used in detection and diagnosis of ASD, by a
comparison of their applicability, a review on their accuracy metrics
depending on how various literatures and research articles present them and
finally reveal what models are efficient in what circumstances. Thus, this
review is conducted to provide an answer to the following research questions:

  * •

How is deep learning used in detection and diagnosis of ASD?

  * •

What are the deep learning models used in detection and diagnosis of ASD?

  * •

What is the best model that can be applied depending on the data provided?

First section of this paper introduces machine learning and its application in
general disorder detection. The section tries to provide an insight on the
possibility of having machine learning as a next method to be applied for
early and easy disorder detection. Then we provide an introduction to deep
learning and how it has been used in neuroimaging - a type of brain images
that can be studied to analyze and reveal patterns of brain related disorders.
Lastly, we present various models that our literature has found and a most
efficient way to apply them. A conclusion of the review is presented.

##  II Methodology

We determined research questions that would direct the review process in order
to accomplish the goals in this study domain. We first collected related works
done by other scholars on Deep learning methods used in ASD detection and
diagnosis and then did a detailed review and analysis of the works. Collection
of the papers was based on an internet search from various repositories, for
researches that contained the following deep learning models; ASD-Diagnet,
VGG16, deep neural network for ASD classification, Auto-ASD Network, Xception,
Visual Geometry Group Network (VGG19) and NASNETMobile. The second criteria
search was based on ASD detection and diagnosis. An in-depth analysis of the
obtained models was done aligning to the following research questions: a)
detection or diagnosis technique addressed, b) the model being used in the
research, c) the dataset used in the model implementation and d) accuracy of
the model based on the metrics used by the researchers. The review then turns
to a comparison of the identified models, their suitability given which kind
of dataset and then finally how possibly the models could be used for better
performance.

##  III Application of Machine Learning in Disorder Detection

Machine learning is a field of research for computer scientists and
Engineering, it is a branch of artificial intelligence since it allows one to
extract meaningful patterns from examples, which is also a component when it
comes to the intelligence of humans [14]. In the recent past, machines have
demonstrated the ability to learn tasks that had previously been thought of
being too complex for machines[15]. This clearly demonstrates that machine
learning algorithms have great potential as components of computer-aided
diagnosis as well as in the area of decision support systems.

The use of machine-learning approaches in conjunction with brain imaging data
has enabled for the classification of mental states related with semantic
category representation[16]. Patients with brain activation linked with
schizophrenia have been observed in research of mental illness states [17] and
with autism [18]. Studies using ML algorithms on ASD brain imaging data
categorized patients as autistic or control based on their fMRI brain
activation with up to 97 percent accuracy [19]. A pattern of brain activation
linked to a psychological element was also discovered (self-representation).
The pattern was almost non-existent in autistic participants, but was
prevalent in typically developed (control) patients. [18]. Participants with
ASD were classified in another study. [20], In a population sample of 178 ASD
and IQ-matched typically-developing participants, the authors achieved a
classification accuracy of 76.67 percent.

Support vector machine (SVM) or Gaussian Naive Bayes (GNB) classifiers were
used in the majority of studies that combined brain imaging and machine
learning. The subjective nature of feature selection approaches for supervised
machine learning systems could make cross-study comparisons difficult. A set
of data used as the training dataset is assigned class labels in supervised
methods; the classification of other data points (test data set) is based on
the patterns observed in the training data (using the given labels). The
algorithm works by classifying labels that have already been assigned to them
(that is, they rely on feature selection, or feature engineering). The labels
and attributes chosen are based on a priori assumptions or exploratory
approaches.; As a result, they are subject to a degree of subjectivity. For
example, the number of voxels utilized for brain imaging data categorization
was empirically determined by examining sets of 100, 200, 400, and more voxels
and determining the set size that works best for classification.

##  IV Application of Deep Learning in Neuroimaging

In [21] they used Deep Neural Network to examine brain states based on
activities in the brain. They adopts task-based fMRI data from 499 patients to
train an artificial neural network with two hidden layers and a softmax output
layer to classify the data into seven categories linked to the tasks: Working
Memory, Emotion, Gambling, Language, Motor, Relational, and Social Memory.
When compared to supervised learning methods, deep models produced higher
results (mean accuracy of 50.74 percent) (mean accuracy of 47.97 percent),
supervised models such as Linear Regression and Support Vector Machine. In
[20], the researchers employed deep learning and structural T1-weighted images
to distinguish schizophrenia patients vs healthy controls; using data from the
PREDICT-HD project, the investigators also classified individuals with
Huntington’s disease versus healthy controls. First, they used data from four
studies to classify 198 schizophrenic patients and 191 controls (WPIC). [20].
trained a three-depth Deep Belief Network (50 hidden units in the first layer,
50 in the second layer, and 100 in the top layer). They were able to reach 90%
classification accuracy utilizing features extracted from three DBMs, compared
to 68 percent using raw data in a Support Vector Machine. Deep learning has a
lot of potential for clinical brain imaging applications, according to the
scientists.

##  V Review of the Deep Learning Models for Autism Detection

Use of behavioral data for detection and diagnosis of ASD has proven to be
difficult, requiring a move towards quantitative diagnosis driven by machine
learning[22]. Magnetic Resonance (MRI) and functional Magnetic Resonance
Imaging (fMRI) data is the quantitative data that has been used extensively by
most researchers to build deep learning methods for ASD diagnosis and
detection[22]. ASD-Diagnet is a deep learning based model used by [23] and
[22].

Most studies that have implemented ASD-Diagnet used fMRI data contained in the
ABIDE dataset[23]. ASD-Diagnet is a hybrid deep learning model that is used in
ASD detection based on the ABIDE dataset, containing 1035 subjects that were
studied at 17 different brain imaging centers[24]. ASD-Diagnet employs an
autoencoder and a single layer perceptron to classify ASD patients from those
that were not, called typically developed and abbreviated as TD[22]. [22] used
a cross-validation to test the accuracy of the model against other models,
ASD-Diagnet obtained a maximum classification accuracy of 82%. [22] terms this
as a better performance relative to other state of the art models[24]. [24]
criticizes the model as not having properly undertaken the effect of
structural and phenotypic information of the subjects in creation of hybrid
features. They have also noted that the model’s accuracy fluctuates when
subjected to a dataset other than ABIDE.

Figure 1: Class information in the ABIDE Dataset

VGG16 is a state-of-the-art transfer learning based deep learning model that
was pioneered by [26]. VGG16 works by applying a classification function on a
dataset consisting of facial images. [26] trains the model with two datasets;
East Asia ASD children Facial Image Dataset or otherwise East Asian Dataset
and Kaggle Autism Facial Dataset. The East Asian dataset contains 1122 images
(with 561 for TD children) of children aged between 2 and 12 years of the same
race. The Kaggle Autism Facial Dataset has 2936 images of both ASD and TD
children, evenly distributed [25].

Figure 2: The Architecture of VGG16[26]

In this feasibility and accuracy study, [26] used the East Asian dataset for
model training and verification because the ASD facial images in this dataset
are from clinically diagnosed children from a single race. The study bridges
the gap of applying computer vision in ASD screening ASD in children using
their facial images. The high classification accuracy of 95% and F1-score of
0.95 obtained by the deep learning model trained with the East Asian dataset
indicates that it is viable to use children’s facial images as a low-cost
solution to screen for ASD to achieve early intervention objectives. Suggested
that race information be provide as a prerequisite to use the model to
eliminate errors brought about from the anthropometric differences among
races.

A deep neural network was used by [27] to classify ASD children from TD
children. The data used by [27] is not the same dataset used by [26] in
detection of ASD. [27] uses Kaggle dataset that contains descriptive features
of both children with ASD and those without ASD.

The DNN developed by [27] has five layers: sequence input layer, fully
connected layer, Softmax layer, Long-Short Term Memory layer and
classification layer. Its architecture can is as below:

Figure 3: DNN structure created by[27]

The dataset used in [27] was provided by Fadi Fayez Thabtah, who used the
mobile app ASDTests to screen people of various ages for ASD, contains
different category of data. The toddler data set has 18 unique items and one
output class, whereas the child, adolescent, and adult data sets have 21
unique things and one output class. [27] A classifier model is created using
deep learning to categorise ASD and no ASD class for the purpose of diagnosing
ASD. From training data, a classifier model is created, and it is then
assessed using test data. [27] It can be shown that utilising the suggested
DNN model, 85.24 percent of toddler data is correctly classified, leaving
14.76 percent of the relevant data that did not accomplish their target class.
Additionally, [27] discovered that the accuracy rate for adolescent data was
84.21 percent, allowing 15.79 percent of the relevant data to fall outside the
target group. In the child data set, accuracy is 85.71 percent, with 14.29
percent of the data not reaching the intended class. [27] The adult data set’s
highest accuracy rate of 89.26% is finally attained, with 10.74% of the data
not meeting the target class. [27]

In [22] deep learning model, utilising only functional Magnetic Resonance
Imaging (fMRI) data, it proposes the Auto-ASD-Network model to distinguish
between people with Autism disorder and healthy subjects. A multilayer
perceptron (MLP) with two hidden layers makes up the model. [22] does data
augmentation using the Synthetic Minority OverSampling (SMOTE) algorithm to
create synthetic data and prevent overfitting, which improves classification
accuracy. The deep learning model used the ABIDE dataset.

The [22] additionally looks into how well the deep learning model worked to
extract the features. This is accomplished by using the deep learning model’s
hidden layer, which contains extracted features, as the input to an SVM
classifier in addition to performing tests on the model as a classifier. [22]
Since the best values of some SVM hyperparameters, such as the kernel function
and penalty, are not known in advance, [22] employ a technique called Auto
Tune Models (ATM) to automate the hyperparameter tuning procedure. The trials
demonstrate a considerable increase in classification accuracy when the
oversampling method and SVM are used. For four fMRI datasets, it achieves
classification accuracy of more over 70%, with the best accuracy being 80%.
[22] It enhances SVM performance by 26%, standalone MLP performance by 16%,
and the state-of-the-art ASD classification approach by 14%. [22]

[28] suggested the use of Xception, NASNETMobile, and VGG19, deep learning
models based on transfer learning, to identify autism using face traits of
autistic and typical children. Each model underwent training and testing to
identify the characteristics that, based on face features, classify youngsters
as autism or normal. [28] This study compared facial pictures of autistic and
typical kids that were taken from the publicly available online Kaggle
platform. [28] The NASNetMobile model had the lowest performance level (78%)
and the Xception model had the best testing accuracy (91%) of the three
models. [28]

The [28] employs a variety of performance evaluation metrics, including a
confusion matrix, accuracy, sensitivity, and specificity, for the three
pretrained models. A table containing the true and false values of the test
results is represented by a confusion matrix, a sort of classification
performance metric. [28] In the confusion matrix of the Xception model, the
True Positives represented 132 of the 150 autistic children, the False
Negatives represented 18, the True Negatives represented 141 of the 150
normally developing children, and the False Positives represented 9. [28] The
VGG19 model’s accuracy increased during the training phase from 56% to 85%
after 25 epochs, then it decreased to 82% during the validation phase. [28]
The performance of NASNetMobile was subpar. 70–90% of the time it was accurate
during the training phase, and 65–78% of the time during the validation phase.
[28] The accuracy of the Xception model was 100% on the training data and 91%
on the testing data. [28] Although the data generator obtained the dataset
from online sources, which made the differences in ages and photographic
quality evident, the Xception model displayed the highest level of accuracy.
[28]

##  VI Conclusion and Recommendation

There is a growing interest in autism which has propagated advancement in the
global-health know how and capacilties. Moreover, the number of autistic
children has risen in recent years, making it imperative that attention is
given to it in order to help these children get medical attention and live
fulfilling lives. This is made possible through early diagnosis to help in
deciding the best treatment and care to offer them. This paper evaluated the
performance of various deep learning models in detecting ASD: ASD-Diagnet,
VGG16, deep neural network for ASD classification, Auto-ASD Network, Xception,
Visual Geometry Group Network (VGG19) and NASNETMobile. Each model was trained
suing a different dataset and the classification accuracy recorded. Based on
the researchers findings, VGG16 achieved the highest classification accuracy
at 95%, closely followed by Xception as 91%. The results from the deep
learning models show us the possibility of deep learning being used by
specialists and families to give more accurate diagnosis of autism, especially
when they are still young. More research and future work should be undertaken
to design models that not only detect ASD, but can also diagnose the severity
of ASD.

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# Study of polysterene based scintillator ageing in the DANSS experiment

I. Alekseev11footnotetext: Corresponding author. V. Belov  A. Bystryakov  M.
Danilov  D. Filosofov  M. Fomina  P. Gorovtsov  Ye. Iusko  S. Kazartsev  A.
Kobyakin  A. Krapiva  A. Kuznetsov  N. Mashin  I. Machikhiliyan  D. Medvedev
V. Nesterov  D. Ponomarev  I. Rozova  N. Rumyantseva  V. Rusinov  A. Salamatin
E. Samigullin  Ye. Shevchik  M. Shirchenko  Yu. Shitov  N. Skrobova  D.
Svirida  E. Tarkovsky  A. Yakovleva  E. Yakushev  I. Zhitnikov  and D.
Zinatulina

###### Abstract

DANSS is a spectrometer of reactor antineutrino based on plastic scintillator.
The sensitive volume of the detector is made of 2500 polystyrene based
scintillator plates with wavelength shifting (WLS) fiber readout (strips). We
present a study of the strips light yield during 6.5 years of DANSS continuous
running. Overall ageing at the rate $0.55\pm 0.05(\mathrm{syst.})$ % per year
is observed that is considerably smaller than in other similar experiments. We
also observe the WLS fiber attenuation length shortening at the rate $0.26\pm
0.04(\mathrm{stat.})$ % per year.

##  1 Introduction

The idea of the DANSS detector [1, 2] was to have a scintillation neutrino
spectrometer on a movable platform as close as possible to the core of the
industrial nuclear reactor. The site just below the reactor body provides
several advantages like very high neutrino flux ($\sim 5\times
10^{13}\bar{\nu}_{e}/$cm${}^{2}/$s) and moderate overburden ($\sim 50$ m
w.e.), but at this site only low flammable materials are allowed due to the
fire safety reasons. This justified to assemble the sensitive volume from
polystyrene based solid state scintillator. Continuous operation of the
experiment since October 2016 in a climate controlled room provides a very
good data sample to study ageing effects of the detector.

Ageing of the plastic scintillators is already known for many years [3]. There
are several mechanisms which are usually considered. An excess mechanical
stress at a level above elastic and anelastic deformation results in
nonrecoverable damage to the scintillator structure like shear plasticity and
crazing [4], creating obstacles on the passage of the light. Humidity of the
environment can penetrate into the bulk of the scintillator and produce
fogging effect in it [5]. Atmosphere oxygen together with ultraviolet
radiation could develop photolysis of the polystyrene resulting in its
yellowing [6]. All of these effects affect transparency of the plastic and
result in smaller amount of scintillation light collected. Plastic exposition
in the DANSS experiment was very mild avoiding mechanical stresses, excessive
humidity and ultraviolet radiation.

This work was inspired by the recent study performed by T2K experiment [7].
The T2K paper covers 10 years of the operation and reports light yield
decrease in the range of $0.9\div 2.2$ % per year for different subsystems of
the detector. Measured degradation of polystyrene scintillator strips from the
MINOS experiment [8], which are similar to ours, is 2 % per year. Though
ageing as large as $7\div 10$ % per year was observed in MINERvA [9] at
$80^{\circ}$F ($27^{\circ}$C).

##  2 Experimental conditions

The DANSS experiment [1] is located at the $4^{th}$ reactor unit of the
Kalininskaya NPP about 350 km NW from Moscow. The detector is placed in a room
just below the core of the reactor. For the sake of the electronics cooling,
the room is air conditioned; thus, the temperature around 20 ∘C is maintained
all the time. The relative humidity in the room is also very low, below the
lower limit of 10% of the humidity detector used as the environment monitor.
Despite of the close vicinity of the reactor, the room is clean in terms of
radiation background and corresponds to a laboratory room environment.

The detector sensitive volume is built from scintillator plates (strips) which
were extruded from polystyrene by the Institute of Scintillating Materials,
Kharkiv, Ukraine. The strip design was developed especially for this
experiment with very specific material composition and manufacture procedure
[10]. The core plastic is doped with 1% PPO (2,5-Diphenyloxazole) and 0.03%
POPOP (1,4-bis(5-phenyloxazol-2-yl) benzene) fluors. The surface is covered by
about $\approx$0.3 mm co-extruded diffuse reflection layer. The layer consists
of polystyrene with 18%wt admixture of rutile TiO2 and 6%wt of gadolinium
oxide Gd2O3. Gadolinium has natural isotope composition and is used to capture
neutrons from the inverse beta-decay after their moderation. The final
gadolinium density is about 1.6 mg/cm2, which corresponds to $\sim$0.35%wt
with respect to the whole detector body. The layout of the strip is shown in
Figure 1. The strip has 1 m length, 40 mm width and 10 mm thickness. There are
three grooves on the top surface of the strip with wavelength shifting (WLS)
fibers Y-11(200)M by Kuraray [11]. The fibers are glued into groves with a two
component siloxane based optical gel from SUREL SUREL-SL1 (St. Petersburg,
Russia) [12]. The central fiber is read out by a SiPM S12825-050C by
Hamamatsu. Two side fibers from each of the 50 neighbor strips are collected
into 100-fiber bundles and led to a conventional PMT R7600U-300 by Hamamatsu.
The opposite ends of the fibers are polished and covered by reflective paint
“Silver shine” M415001K00250 by Manoukian Argon (Italy). The strips are put in
rows of 25 each. There are 100 rows, which form a cubic meter of the sensitive
volume of the detector. Strips in adjacent rows are perpendicular to each
other. The strips are supported by copper plates, which serve as an inner
layer of the passive shielding. The copper layer is 5 cm thick on average. The
aim during the assembly was to have most of the weight residing on the copper
frame, though there is some sag of the strips in their middle and some
touching between the strips could not be excluded. The outer part of the
shielding is assembled from 8 cm of borated polyethylene, 5 cm of lead and
another 8 cm of borated polyethylene. The shielding significantly decreases
both gamma and neutron backgrounds, making radiation doses in the strip
location well below common room conditions. Three centimeter thick
scintillator veto counters cover the detector outside the shielding on all
sides with the exception of the bottom and serve for tagging muons. The front-
end electronics are placed on two sides of the cube in a slit between copper
and borated polyethylene. The electronics are cooled by a chilled water
cooling system, providing a stable temperature for the central part of the
detector. Unfortunately, the temperature at the SiPM location varies from 18
∘C for top and bottom rows to 23 ∘C for middle rows. DANSS data acquisition
system (DAQ) is based on 64-channel, 12-bit, 125 MSPS waveform digitization
modules (WFD) [13], which sample analog signals from photodetectors in 512 ns
windows.

Figure 1: Scintillation strip layout.

The SiPM bias voltages were set once at the very beginning of the detector
operation and fixed for the rest of the running period. The setting was
carried out based on a single pixel signal with the aim of about 12 ADC units
per pixel. The voltages were fixed once, and no voltage adjustment for
temperature changes or any other reason was ever carried out. The DAQ operated
with a common trigger, fired when either an instant digital sum of all PMTs
was above a 0.5 MeV threshold or a veto system was triggered. In addition to
the common trigger, each SiPM channel was triggered individually once per
50,000 pulses in it. These individual triggers were used to collect the SiPM
thermal noise data, out of which single pixel charge and crosstalk were
extracted. Such calibration was performed for each SiPM approximately once per
half hour [14]. For the neutrino analysis stream, the energy scale of all
detectors is calibrated by atmospheric muons approximately every two days. The
present analysis does not use the energy scale from the main analysis stream
and takes SiPM data only in the form of number of photo carriers (ph.c.) per
hit. This number is corrected for SiPM saturation caused by the finite number
of pixels. SiPM S12825-050C has 667 pixels in its nearly square matrix. If
more than one photon triggers a single pixel, a signal equivalent of only one
pixel is produced. Only $511.6\pm 19.1$ of SiPM pixels are effectively
illuminated by the WLS fiber in DANSS strips [14]. This number was used for
the saturation correction. This paper is based on the statistics collected
during the period from October 10, 2016 till March 15, 2023.

##  3 Analysis

Though the detector has notable overburden, about 40 atmospheric muons pass
each second through the detector [15]. Energy deposit from close to vertical
muons is used as a standard candle. We start with selection of triggers with
vertical muons. The event should have number of hits in the above 90. This
effectively selects events with muons passing through the most of the
detector. Track coordinates in the lowest and the highest 8 planes are
calculated by averaging hits with a weight proportional to their energy
deposit. A muon track is defined as a line connecting the points with these
averaged coordinates. In order to select vertical muons only events with
distances below 20 cm in the horizontal plane between these points are
selected. So the tangent of the track zenith angle is below 0.2 and the
difference between lengths of track in a strip is less than 2%. An example of
a selected event is shown in Figure 2. A hit energy is shown by a color and
the line corresponding to the track is shown also. Dark blue rectangles show
low energy hits, produced by SiPM noise.

Figure 2: An example of selected muon event. The color scale corresponds to
strip energy deposit. A black line shows muon track position reconstructed by
its ends.

At the next stage hits are selected. Several criteria are used:

  * •

distance from muon track is less than 1.5 strip width;

  * •

there is no hit in the neighbor strips of the same layer. This is done to
avoid partial track segments shared between adjacent strips;

  * •

there are hits in the strips below and above in the same projection.

In order to have more narrow distributions the value of ph.c. is corrected for
longitudinal profile along the strip. We use average profiles extracted from
the data as described in [14]. Only strips which were alive throughout the
whole period and all the time connected to the same DAQ channel were selected.
This requirement made a significant cut over available channels leaving only
1713 out of 2500 for further analysis, but it gives a valuable simplification
of the analysis.

The whole data was splitted into 100-files chunks, which correspond to
approximately 2 days of data taking. A distribution of number of photo
carriers per hit for all hits in some data chunk is shown in Figure 3. Median
value is used in the analysis as a measure of the light yield (LY).

Figure 3: An example of number of photo carriers per hit distribution.

##  4 Results

Despite of efforts to stabilize the temperature of the detector it varies at a
level of $1^{\circ}$C. A SiPM breakdown voltage has a strong temperature
dependence [16]. As a consequence other properties like gain, crosstalk,
afterpulses probability and photon detection efficiency (PDE) also have strong
temperature dependence. The detector is equipped with 36 temperature sensors,
placed uniformly on the two sides of the copper frame close to SiPM. Readout
of the temperatures is done by an independent slow monitor system every 5
minutes and is written separately from the main DAQ data files. Graphs of the
temperatures are presented in Figure 4 (top). At the bottom part of this
figure single pixel signal dependence of the nearby SiPM is given. A clear
anticorrelation is seen.

Figure 4: Temperature dependence as a function of calendar time (the top
panel). Different colors show 3 sensors placed in the center (blue), right top
corner (red) and left bottom corner (green) of the "Y" readout plane. The
calendar time dependence of the single pixel signal (the bottom panel). The
same colors are assigned to SiPMs close to the corresponding temperature
sensors. To avoid overlap the red graph is shifted up by 5 units and the green
one by 10.

The data used in this analysis is taken in the form of ph.c., so variation in
the single pixel signal and crosstalk due to temperature is already taken into
account, but changes in PDE are still not compensated. This compensation is
done in a simple linear approximation based on the single pixel signal
measured for each SiPM in each data file. In this approximation the corrected
value of the signal is given by an equation:

$S^{ijk}_{\mathrm{corr}}=S^{ijk}(1-\alpha\frac{A^{jk}-A^{k}_{\mathrm{avg}}}{A^{k}_{\mathrm{avg}}})\>,$
(4.1)

where $S$ is a number of ph.c., upper indexes correspond to event number
($i$), file number ($j$) and strip number ($k$). $A$ is a single pixel signal
and subscript "avg" denotes its average over all files. $\alpha$ is a
correction coefficient common for all SiPM channels. The value of
$\alpha=0.85$ corresponds to the minimum of $\chi^{2}$ deviation from a linear
fit to LY over time dependence. The LY dependence over time is shown in Figure
5. The top panel shows LY without the temperature correction. The corrected
result is shown at the bottom. It is seen that some uncompensated effects are
still present. Nevertheless the LY decrease with time is clearly seen.

Figure 5: Light yield dependence over calendar time without the temperature
correction (top) and with the correction according to the equation
(4.1)(bottom). Statistical errors only.

Statistical only errors are shown in Figure 5. In order to estimate
systematical errors the detector was split into 50 sections of 50 neighbor
strips each (5 horizontally strips to 10 rows of the same direction). Annual
LY decrease was calculated in these sections. The distribution of the results
is shown in Figure 6. RMS of this distribution gives a good estimate of the
systematic error, so the ageing of the whole detector is $0.55\pm
0.05(\mathrm{syst.})$ %/year.

Figure 6: Light yield decay distribution for sections of the detector.

An observed decrease of the LY could have several reasons in addition to the
degradation of the scintillation material. They include ageing of WLS fibers,
optical gel used to glue fibers and light receivers222No ageing has been
reported for SiPM unless in severe radiation conditions [17, 18]. We can not
separate these factors with an exception of WLS fiber light attenuation length
decrease, which can be seen as a larger ageing effect for longer distance
along the strip. The LY decrease dependence over the length along the strip is
shown in Figure 7. A hint of ageing effect increase with the distance to a
SiPM is seen. At moderate distances from SiPMs the light attenuation is
described by an exponent with the attenuation length $L_{att}=3.9$ m. The
observed increase in the ageing effect with the distance could be translated
into the annual decrease of the attenuation length with a formula:

$\frac{1}{L_{att}}\frac{\partial L_{att}}{\partial
t}=L_{att}\frac{\partial}{\partial l}\left(\frac{1}{LY}\frac{\partial
LY}{\partial t}\right)\>,$ (4.2)

where $\frac{1}{LY}\frac{\partial LY}{\partial t}$ is the relative annual
decrease of the LY and $l$ is the length from muon track to SiPM. The measured
WLS attenuation length decrease, calculated from a linear fit in the range
$20\div 100$ cm shown in Figure 7, is $0.26\pm 0.04(\mathrm{stat.})$ %/year.

Figure 7: Light yield decrease dependence over the length along the strip. The
line presents the linear fit in the range $20\div 100$ cm.

##  5 Conclusions

A continuous measurement of the DANSS detector scintillator performance was
carried out for 6.5 years. An annual LY decrease $0.55\pm
0.05(\mathrm{syst.})$ %/year is clearly seen though it is smaller than in
other experiments. T2K measurement is in the range of $0.9\div 2.2$ %/year for
different detectors [7], MINOS, which was using a very similar scintillating
material, observed a decrease of about 2 %/year [8]. The small decrease of LY
at DANSS could be explained by the rather stable and mild environment of the
DANSS detector. A contrary example is the fast $7\div 10$ %/year ageing of the
MINERvA [9] scintillation detectors, which are operated at a higher
temperature ($27^{\circ}$C). Anyway ageing of DANSS scintillation strips is
small and does not require special care in the data analysis.

## Acknowledgments

DANSS collaboration is grateful to the directorates of ITEP and JINR for
constant support of this work. The collaboration appreciates the permanent
assistance of the KNPP administration and Radiation Safety Department staff.

The detector DANSS was created with the support of the State Atomic Energy
Corporation Rosatom (ROSATOM) via state contracts H.4x.44.90.13.1119 and
H.4x.44.9B.16.1006. Long time operation of the experiment and initial data
analysis were supported by the Russian Science Foundation grant 17-12-01145
(2017–2021). The presented analysis as well as current detector operation are
supported by the Russian Science Foundation grant 23-12-00085
(https://rscf.ru/project/23-12-00085/) (2023–2025).

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