# Estimating Personal Model Parameters from Utterances in Model-based
Reminiscence

Shoki Sakai, Kazuki Itabashi, Junya Morita  Department of Informatics,
Graduated School of Integrated Science and Technology, Shizuoka University
3-5-1 Johoku, Naka-ku, Hamamatsu, Japan
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Reminiscence therapy is mental health care based on the recollection of
memories. However, the effectiveness of this method varies amongst
individuals. To solve this problem, it is necessary to provide more
personalized support; therefore, this study utilized a computational model of
personal memory recollection based on a cognitive architecture adaptive
control of thought-rational (ACT-R). An ACT-R memory model reflecting the
state of users is expected to facilitate personal recollection. In this study,
we proposed a method for estimating the internal states of users through
repeated interactions with the memory model. The model, which contains the
lifelog of the user, presents a memory item (stimulus) to the user, and
receives the response of the user to the stimulus, based on which it adjusts
the internal parameters of the model. Through the repetition of these
processes, the parameters of the model will reflect the internal states of the
user. To confirm the feasibility of the proposed method, we analyzed
utterances of users when using a system that incorporates this model. The
results confirmed the ability of the method to estimate the memory retrieval
parameters of the model from the utterances of the user. In addition, the
ability of the method to estimate changes in the mood of the user caused by
using the system was confirmed. These results support the feasibility of the
interactive method for estimating human internal states, which will eventually
contribute to the ability to induce memory and emotions recall for our well-
being.

###### Index Terms:

model-based reminiscence, cognitive modeling, cognitive architecture, ACT-R,
interactive system, parameter estimation

††This work was supported by JSPS KAKENHI Grant Numbers 20H05560 and 22H04861.

##  I Introduction

Happiness or health is one of our universal and constant desires. According to
the WHO Charter, “health is a state of complete physical, mental, and social
well-being and not merely the absence of disease or infirmity [1].” This
definition suggests the importance of being mentally and socially, as well as
physically fit. One of the ways to improve one’s mental well-being is by
recollecting pleasant memories from the past. The emotion that arises from
recalling pleasant memories of the past is known as nostalgia across various
cultures [2], and has been reported to principally be a positive emotion,
although it also includes bittersweet feelings [3].

The effect of nostalgia has been applied to mental health care. For example,
Butler proposed the use of psychotherapies, in which people discuss their old
experiences and memories from past photographs, music, and other media related
to them, for mental health care [4]. Such memory-based therapies include life
review and reminiscence. The former aims to reevaluate one’s life by
reflecting on the past, whereas the latter aims to achieve psychological
stability by evoking nostalgic memories. Reminiscence therapy has been
demonstrated to promote positive emotions and suppress negative emotions for
all age groups [5, 6] not only to improve cognitive function in the elderly
and patients with dementia [7, 8].

Among several types of reminiscence therapies, this study mainly focused on
the use of personal recollections, rather than group recollection [9], to
resolve large individual differences in emotional factors involved in memory
contents. In addition, we assumed two axes of core affect (arousal and
valence) [10] as the internal factors affecting the memory recollection of an
individual [11]. This assumption suggests that encouraging memory recollection
based on the state of these internal variables should provide appropriate
support for the reminiscence of an individual.

To achieve this personalized support, this study utilized a computational
model that represents the recollection process of personal memory. There is
considerable research on the simulation of human cognitive processes using
cognitive architectures [12, 13], which is a modeling approach that employs a
standardized structure to represent an individual process occurring during a
specific task. In addition, these structures can interact with humans by
providing a stimulus to the user and receiving a response to it. Accordingly,
the model reflects the internal state of the user by adjusting the parameters
of the cognitive model through repeated interactions.

We believe that building a cognitive model that simulates the memory
recollection of the user can provide support for personalized reminiscence. To
date, the authors have explored the method of tracing the user’s internal
state during memory recall. Based on these previous studies, this study
proposed an interaction design for a cognitive model that can trace the human
internal state. To confirm the feasibility of the proposed design, we analyzed
the utterance data obtained when a reminiscence support system equipped with
the cognitive model was used.

##  II Related Works

This section reviews previous research relating to the memory recollection
support method investigated in this study. Section II-A describes the
framework of the cognitive architecture. Section II-B introduces research on
systems that support individual memory recollections as the precedents of this
study. Following this review, Section II-C clarifies the limitations of the
previous studies, which necessitated the goal of this study.

###  II-A Cognitive Architecture and Memory Models

As mentioned previously, cognitive architecture is a structure that represents
general human cognitive processes. This structure can simulate diverse
cognitive functions for various tasks and individuals by constructing
cognitive models on a common foundation. Among the various cognitive
architectures (see [14] as a review), adaptive control of thought-rational
(ACT-R) has been employed in various studies [15]. The essential components of
ACT-R have been implemented as a production system, and are composed of
various modules for vision, motor movements, memory storage, and goal
management. The system can capture various aspects of human cognition by
communicating information between the modules that correspond to each part of
the human brain, indicating the ability of ACT-R to reproduce the human
internal process.

Some studies have modeled individual humans using the ACT-R. For example,
Somer et al proposed the concept of the “Cognitive Twin” [16] and demonstrated
the efficacy of ACT-R for personalized decision support by constructing and
using a decision-making model of an individual. Such individualization of
cognitive functions in the ACT-R was realized by the knowledge (memory) and
the parameters involved in the use of knowledge. By manipulating these
factors, the ACT-R model generates a variety of behaviors related to the same
task. The knowledge incorporated in the ACT-R consists of declarative and
procedural knowledge. Declarative knowledge comprises units known as “chunk”,
and individual chunks are linked to form a semantic network through
attributes. Production rules, which involve procedural knowledge, are
necessary for serially exploring such semantic networks. Accordingly, the
ACT-R model selects one of the attributes linked to the currently recalled
knowledge, and induces its to the next unit of knowledge.

This memory retrieval process can be diversified by manipulating the numerical
parameters attached to the knowledge. Chunks and production rules have
parameters called the activation and the utility, respectively. The
activations are affected by the frequency of memory recall and memory decay,
whereas the utilities are affected by rewards and the learning rate. When
invoking declarative knowledge using a semantic network, the utility of the
production rule is used in selecting attributes, and the activation determines
the chunk to be retrieved when there are multiple available candidates among
the selected attributes.

###  II-B Memory Support Systems Using Cognitive Models

This study follows a series of ACT-R based memory support systems developed by
the authors’ group. First, Morita et al [17] developed a photo slideshow
system that supports reminiscence therapy and utilized the memory mechanism of
the ACT-R described in Section II-A. This slide-show system includes a
collection of private photos of users as a lifelog, and these photos are
connected to each other via semantic links classified into four attributes:
Who (person appearing in the photos), What (results of image recognition),
When (timestamp), and Where (GPS information). The ACT-R model sequentially
recollects photos by following these semantic links based on the utilities of
each attribute and the activation of each memory item. The authors asserted
that such memory transitions simulate mental time travel, which is vivid
recalling of experiences in a time that is not the current time, as if
experiencing time travel [18]. Based on this assumption, they proposed a
model-based reminiscence using visualizations generated by this mental time
travel model.

The model-based reminiscence involves the recollection of past memory based on
dynamically changing photos in the form of a slideshow. This method is
considered to learn the cognitive and emotional states of the user, and
present photos based on the learning (personalized) results. To utilize a
user’s reaction for such learning, Itabashi et al developed an interactive
method based on an emotional model for monitoring the state of the user [19].
In this system, the authors assembled time-series data based on heart rate
variability (HRV) and online subjective mood rating111The users rate their
mood state for the currently displayed photo using the interface attached to
the display of slideshow as interactive parameters. The feedback from the HRV
(arousal) was directly mapped to a noise assigned to the activation of the
photo, whereas the online subjective mood rating (valence) was mapped to the
reward related to the rule for retrieving the photo.

ACT-R theoretically assumes that activation-based memory retrieval causes a
concentration of retrieval on the most recent memory [20, 21]. Therefore, the
activation is considered to reflect the physiological arousal [22]. By
applying this assumption and utilizing HRV, the photo retrieval of the system
proposed by Itabashi et al concentrates on a specific photo when the user is
in a stress state (i.e., small HRV). Contrary, retrieval is not limited to
recent photos but also older photos when arousal is low and a relaxed state is
induced (i.e., high HRV).

In addition, the interactive memory retrieval proposed by Itabashi et al has
been applied in other contexts beyond a photo slideshow. For example, Morita
et al [23] developed a web extension that mitigates negative emotions when
using the Internet by building a model of memory and emotion using the ACT-R.
They focused on web advertising, including behavioral targeting, to naturally
apply memory models in a web environment. Their system displays regularly
changing images on web pages, and these images affect the implicit memory
process of the user. They confirmed inhibition of negative memory recall
during web use using a memory and emotion model, as well as physiological
sensing to modulate memory retrieval.

###  II-C Limitations of the Past Studies

As discussed above, cognitive model-based personalized memory supports have
been developed. However, the reliance of previous systems on physiological
data (i.e., HRV) that can only be measured using dedicated equipment has
limited its application in various fields. In addition, the mood state rating
used by Itabashi et al [19] requires the user to intentionally operate the
interface every time a picture is changed, which may inhibit natural
reminiscence. To solve these limitations, this study proposed and tested an
interaction design that indirectly estimates the internal states of the user
by applying the machine-learning method to naturally produced user responses
measured using a conventional device.

##  III Interactive Estimation of User Model Parameters

Figure 1: Scheme of the Human-Model interaction. The model provides a stimulus
to a user. The user receives a stimulus and responds to it. The model updates
its internal parameters based on the received response and determines a new
stimulus.

The general framework of the human-model interaction adopted in this study is
described in Fig. 1. In this framework, the model consists of several
parameters for simulating memory recall as the internal states ($I^{\prime}$).
Based on the current $I^{\prime}$, the model provides stimuli ($S$) to humans
and receives their responses ($R$). Subsequently, based on the human response,
the model updates its internal state $I^{\prime}$ and determines the next
stimulus $S$ based on the updated $I^{\prime}$. By repeating this interaction,
we expect that the internal state of the model ($I^{\prime}$) will eventually
reflect the human internal state ($I$).

This framework is applied to the model-based reminiscence described in the
previous section: the stimulus ($S$) corresponds to the display photo, and the
human response ($R$) corresponds to verbal/nonverbal reactions to the photo.
Although a human internal state ($I$) cannot be directly observed, the self-
rating of the mood state by the user can be obtained. In contrast, the
internal state of the model ($I^{\prime}$) is considered a parameter that can
be observed by the modeler. The parameters consisted in the model-based
reminiscence include the activation $A_{i}$ and the utility $U_{i}$, which are
defined as follows:

  * •

Utility: As mentioned in Section II-B, each of the photos in the declarative
knowledge of the model consists of four types of attributes, Who (p: person),
What (o: object), Where (l: location), and When (t: time). Fig. 2 shows an
example of a network created from the attributes attached to photos. As shown
in the image, the photos form a network connected by common attributes, and
attributes to be used to move to the next photos are determined by the utility
of the rule $i$ corresponding to the attribute. The utility for the rule $i$
can be expressed as:

${U_{i}}^{n}={U_{i}}^{n-1}+\alpha[{R_{i}}^{n}-{U_{i}}^{n-1}]\mid
i\in\\{p,o,l,t\\}$ (1)

where ${U_{i}}^{n}$ is calculated from the previous utility ${U_{i}}^{n-1}$,
the learning rate $\alpha$, and the reward ${R_{i}}^{n}$ provided by the self-
rating of mood by the user.

  * •

Activation: Based on the original ACT-R setting [15], the activation $A_{i}$
in this study is calculated as:

${A_{i}}=\ln(\sum^{n}_{j=1}{t^{-d}_{j}})+{Sa_{i}}+{\epsilon_{i}}$ (2)

where $n$, $t_{j}$, and $d$ are the frequency of the recollection of chunk
$i$, the time passed since the $j$th recall, and the decay rate, respectively.
These parameters induce the concentration on a specific photo [21], whereas
$Sa_{i}$ indicates a term representing the effects of contexts (see [17] for
details). $\epsilon_{i}$ is a transient noise parameter that mitigates the
concentration on a specific photo, which was mapped to the HRV of the user in
the previous studies [19, 23].

Figure 2: Example of photos network. The number A given to each photo means
the activation. The photos are connected to each other via a network of
attributes. Each attribute has a utility $U_{i}$ that is assigned to the
corresponding production rule.

In this study, we assumed that the stimulus ($S$) provided by the model is
determined according to the internal state of the model ($I^{\prime}$), which
indirectly affects the human internal state ($I$). Based on this relationship,
this study assumed that the estimation of the internal state of the model
($I^{\prime}$) using the human response ($R$) is a means of estimating the
human internal state ($I$). Thus, this study proposed a method that
interactively estimates the human internal states based on the model’s
internal states and human responses to stimuli. To verify the practicability
of this proposed method, we investigated the possibility of estimating the two
internal states (i.e., the human and model internal states) from the human
response ($R$). To achieve this, we set two research questions (RQs):

  1. RQ 1

($R\rightarrow I^{\prime}$) Is it possible to estimate the internal state of
the model from human responses to stimuli?

  2. RQ 2

($R\rightarrow I$) Is it possible to estimate the human internal state
(obtained by self-reports) from human responses?

These questions were examined based on the verbal utterances as $R$ obtained
during the experiment where the ACT-R memory model presented lifelog photos
($S$) to participants.

##  IV Method

This section presents the investigation method for the feasibility of the
proposed estimation method. First, the experiment using the model-based
reminiscence system is described. Next, the dataset constructed from the
experiment is presented. Lastly, the analytical methods are explained.

###  IV-A Experiment

To examine the effect of the different internal states of the model on the
human internal states, we compared the behavior of participants under four
conditions (within participants): 1) no activation and no reward, 2) no
activation with reward, 3) activation with no reward, 4) activation with
reward.

As described in Section II-A, the activation of ACT-R is affected by the
frequency of memory recall and by memory decay. Therefore, under the condition
in which the activation was calculated, intensive retrieval of recent and
frequently retrieved photos is expected to occur owing to the characteristics
of the memories simulated by ACT-R. In contrast, when the activation was not
calculated, not only recent but also older photos are retrieved. In addition,
as described in Section II-A and II-B, the utility value determines which
attributes are used to retrieve the photos. Therefore, the condition with the
reward induces the retrieval of photos that reflect the mood towards the
currently displayed photo. From the combination of the effects of these
parameters, the model can be assumed to exhibit the behavior listed in Table
I, where each factor corresponds to the two axes of core affect [10].

TABLE I: Experimental Conditions | Reward (Valence)
---|---
| Not calculated | Calculated
Activation | Calculated |  | Biased search toward some photos.
---
Not react to participants’ moods
| Biased search toward some photos.
---
React to participants’ moods
(Arousal) | Not calculated |  | Wide search reaching to a variety of photos.
---
Not react to participants’ moods.
| Wide search reaching to a variety of photos.
---
React to participants’ moods.
Figure 3: Interface for mood state rating. Users rate their mood state using
the interface in the red square.

For the experiment, twenty-four participants aged $2161$ consisting of $13$
males and $11$ females were recruited through the crowdsourcing service
Lancers222https://www.lancers.jp, and the experiment was conducted using the
video chat tool Zoom333https://zoom.us/. Before participating in the
experiment, they provided their personal photos, whose minimum number of
photos required to participate in the experiment was 200.

Participants watched all four conditions of the slideshow in the experiment.
As there were four experimental conditions, 24 possible patterns of viewing
orders existed. The 24 participants were assigned to each pattern in order to
counterbalance the viewing order of the experimental conditions. The viewing
duration for each condition was 5 min.

To evaluate the changes in the mood state caused by viewing the photo
slideshow, a mood state survey was conducted using the Japanese version of the
Profile of Mood States 2nd Edition (POMS-2) [24] before and after viewing each
photo slideshow condition. The participants were also asked to verbalize their
thoughts while viewing the photos [25] and rate their current mood on a
6-point scale in response to the photos displayed on the user interface, as
indicated by the red boxed position in Fig. 3.

###  IV-B Data Set

Both the text and voice data of the participants’ utterances were used for the
analysis. The text data was constructed using the software tool
Vrew444https://vrew.voyagerx.com/ja/, which enables the automatic
transcription of recorded audio through voice recognition. After the automatic
transcription, typographical errors were corrected manually, and tags
indicating the start and end of the experiment and the time the photos were
switched were inserted.

Referring to the photo switching time tag, the recorded audio data was
segmented. Following this first segmentation, segments longer than 11 s were
further divided into collections of 11 s segments (11 s is the approximate
unit time to switch the display photos). The ACT-R model used in this
experiment is programmed to retrieve a photo every 11 s. If the model failed
in retrieving an image or retrieved the same photo as the previous trial, the
displayed photos were not switched.

To estimate the internal states of the model and participants, we extracted
prosodic features from the divided audio files using openSMILE, which is an
open-source toolkit that can automatically extract features from audio signals
and is primarily used for automatic emotion recognition [26]. Particularly, we
utilized a feature vector known as the eGeMAPS feature set, which consists of
a total of 88 features: 62 minimalistic parameter sets and 26 extended
parameter sets [27]. Subsequently, a score obtained from the sentiments
analysis using Google’s Cloud Natural Language
API555https://cloud.google.com/natural-language applied to the transcribed
texts was added to the features and an 89-dimensional feature vector was
constructed for the analysis.

The total number of utterance feature vectors created by the aforementioned
procedure was 2403 (an average of 100.125 for the 24 participants). These
feature vectors were standardized before analysis.

###  IV-C Analysis Method

Using the as-obtained feature vectors, the internal states of both the model
and the participants were classified, and RQs described in Section III were
addressed using the results as follows:

  * •

Analysis for RQ 1: The experimental conditions were classified according to
the utterances of the participants. As the parameters of the internal state of
the model were manipulated as the experimental condition, which involves the
activation and the reward, we assumed that RQ 1 answered “yes” if this
classification is successful.

  * •

Analysis for RQ 2: Compared to that of the model, the human internal state
cannot be directly observed. Therefore, we classified the data obtained by
indirect means (i.e., the self-reports and the self-rating of their moods
using the user interface). This analysis was composed of two types of
analyses: the first analysis is on the change in the mood ratings measured
after the end of each condition, and the other is on the change in the mood
ratings for each photo assigned as a task during the photo viewing. The latter
analysis is expected to better reflect the real-time changes in the mood of
participants.

For this analysis, a support vector machine (SVM) was used with the parameters
optimized by the grid search. The kernel and parameter ranges are shown in
Table II. The evaluation was based on the accuracy and F-measure of the 5-fold
cross-validation. According to the classification results shown in Table III,
the accuracy was calculated using: $\frac{TP+TN}{TP+FP+FN+TN}$. The F-measure
was calculated $\frac{2\cdot Precision\cdot Recall}{Precision+Recall}$ using
Precision ($\frac{TP}{TP+FP}$) and Recall ($\frac{TP}{TP+FN}$).

TABLE II: Kernels and Parameters Used During the Grid Search.

Kernel | C | Gamma
---|---|---
Linear | $0.0010.010.1110100$ | –
RBF | $0.0010.010.1110100$ | $0.00010.0010.010.1110$

TABLE III: Available Classification Result | True Value
---|---
| True | False
Classification Result | True |  | TP
---
(True Positive)
| FP
---
(False Positive)
| False |  | FN
---
(False Negative)
| TF
---
(True Negative)

##  V Result

This section presents the results of our analysis regarding the two RQs.
Sections V-B and V-C present the results of the analyses of RQ 1 (i.e.,
estimating the model’s internal state from human responses) and RQ 2 (i.e.,
estimating the human internal state from his / her reactions), respectively.
Before presenting these analyses, Section V-A presents the basic data on the
model and human behavior obtained in the experiment.

###  V-A Basic Results of the Experiment

####  V-A1 Model behavior

Fig. 5 shows the results of the number of photos (types) for each of the
experimental conditions. In this graph, the photos that were displayed more
than once were counted as one to eliminate duplicates, implying that a smaller
value indicates that the model focused on smaller photo sets. A two-way (the
activation vs. the reward) analysis of variance (ANOVA) was conducted using
the number of photos presented as the dependent variable. The analysis
revealed that there was a significant difference in the activation
($F(1,23)=95.48,p<.01$). This result confirmed the effect of activation
explained in Section III. The analysis in Section V-B presents the examination
of the detectability of such model difference from the utterance during the
task.

Figure 4: Number of photos presented (Error bars are standard deviation).
Figure 5: TMD scores for POMS-2 (error bars are standard error).
---

####  V-A2 Mood changes of the participants

Fig. 5 shows the total mood disturbance (TMD) scores, which is a measure of
the overall mood state in POMS-2. The dashed line in the figure corresponds to
the TMD score when measured prior to the start of the experiment. A two-way
(the activation vs.the reward) ANOVA with the TMD scores as the dependent
variable indicated a significant main effect in the reward
($F(1,23)=4.59,p<.05$). As the TMD score indicates that the negativity of a
mood increases with an increase in the score, these results suggest that the
participants were induced to feel more positive under the reward calculation
condition than under the no reward condition by reflecting the mood of the
participants to the model. The possibility of detecting such mood changes from
the utterance during the task is explored in Section V-C.

###  V-B Classification of the Internal States of the Model

####  V-B1 Combination of the two parameters

To address RQ 1, the four conditions, which involve the presence or absence of
activation and rewards, were classified. The result revealed that the
classification performance exceeded chance level
($Accuracy_{conditions}=0.456$, $F_{conditions}=0.457$). These results and the
heat map shown in Fig. 6 suggest the possibility of estimating differences in
the internal state of the model using utterances from the user.

Figure 6: Classification results of the experimental conditions. (A:
Activation, R: Reward)

####  V-B2 Independent parameters

Next, we further examined how well each of the internal states of the model
(activation and reward) can be classified from the response of the
participants. Thus, the analysis consisted of two classifications:
classification of the “calculated” or ”not calculated” activation, and
classification of the “calculated” or “not calculated” the reward. The
confusion matrices of these classifications are shown in Figs. 8 and 8. Both
matrices exhibited moderate classification results ($Accuracy_{A}=0.640$,
$F_{A}=0.640$, $Accuracy_{R}=0.680$, $F_{R}=0.679$). From these results and
the relationships discussed in Section III, the differences in the stimuli
provided by the model were considered to affect the human internal state, and
those differences in the internal state were reflected in the responses
(utterance).

Figure 7: Activation classified result. Figure 8: Reward classified result.
---

###  V-C Classification of Human Internal States

####  V-C1 Classification based on post-hoc self-report

This analysis investigated the feasibility of estimating the human internal
state from their utterances (RQ2). In this analysis, we classified whether the
TMD scores of the POMS-2, which were answered after viewing the photos, were
higher or lower than those before viewing or after viewing one of the previous
conditions. However, two participants whose scores kept decreasing during the
experiment were excluded from this analysis. The results are shown in Fig. 10,
and they indicate that the classification performance for the human internal
state was better than that for the internal state of the model
($Accuracy_{TMD}=0.738$, $F_{TMD}=0.738$). This result suggests the
possibility of estimating changes in the mood of users from their utterances.

Figure 9: Classification of changes in TMD scores on the POS-2. Figure 10:
Classification of changes in mood rating.
---

####  V-C2 Classification based on real-time self-report

Next, we examined the possibility of the real-time estimation of the human
internal state. This analysis classified the changes in the mood rating during
the photo presentation. Each utterance segment was labeled with “up” and
“down” direction tags to indicate whether the participants reported that their
feeling moved positively or negatively, respectively. Data segments in which
there was no change were excluded. The resulting confusion matrix is shown in
Fig. 10. The classification performance was not better than that of chance
($Accuracy_{MoodRating}=0.511$, $F_{MoodRating}=0.505$). This result may be
partly attributed to the fact that some participants made few moves on the
user interface during the experiment.

###  V-D Classification for Individual Participants

The previous classification included all utterance segments without
distinguishing participants. Considering the characteristics of prosody and
emotion change, it is reasonable to assume that individual differences
distorted the classification results. Therefore, in this section, we presented
the classification results for each participant. Table IV summarizes the
results of the model and human internal states for all participants. As
indicated in the mean scores, although there was no difference in the general
patterns of the performance, there were improvements in the classification
results in this analysis. The classification results for POMS-2 (post-hoc
self-reports) were higher than those for the two model parameters (activation
and reward). The classification for the real-time human internal states
exhibited the worst classification performance.

TABLE IV: Individual Classification Result

ID | Activation | Reward | POMS-2 | Mood Rating
---|---|---|---|---
| Accuracy | F-measure | Accuracy | F-measure | Accuracy | F-measure | Accuracy | F-measure
1 | 0.64 | 0.71 | 0.57 | 0.68 | 0.64 | 0.74 | 0.78 | 0.75
2 | 0.87 | 0.84 | 0.89 | 0.76 | 0.77 | 0.81 | 0.67 | 0.58
3 | 0.89 | 0.87 | 0.76 | 0.74 | 0.67 | 0.73 | 0.49 | 0.52
4 | 0.75 | 0.74 | 0.58 | 0.52 | – | – | 0.40 | 0.45
5 | 0.74 | 0.75 | 0.80 | 0.87 | 1.00 | 1.00 | 0.51 | 0.56
6 | 0.68 | 0.61 | 0.66 | 0.61 | 0.63 | 0.57 | 0.44 | 0.33
7 | 0.71 | 0.56 | 0.94 | 0.96 | 0.70 | 0.66 | 0.39 | 0.40
8 | 0.94 | 0.97 | 0.77 | 0.78 | 0.80 | 0.74 | 0.56 | 0.41
9 | 0.88 | 0.86 | 0.72 | 0.70 | 0.75 | 0.76 | 0.57 | 0.46
10 | 0.73 | 0.71 | 0.76 | 0.76 | 0.70 | 0.71 | 0.51 | 0.42
11 | 0.84 | 0.74 | 0.76 | 0.78 | 0.79 | 0.67 | 0.66 | 0.56
12 | 0.67 | 0.59 | 0.70 | 0.69 | 0.74 | 0.63 | 0.86 | 0.73
13 | 0.60 | 0.67 | 0.89 | 0.86 | 0.87 | 0.89 | 0.40 | 0.30
14 | 0.64 | 0.59 | 0.66 | 0.71 | 0.72 | 0.80 | 0.43 | 0.42
15 | 0.80 | 0.80 | 0.74 | 0.74 | 0.59 | 0.59 | 0.43 | 0.43
16 | 0.64 | 0.64 | 0.67 | 0.67 | 0.77 | 0.77 | 0.44 | 0.44
17 | 0.60 | 0.60 | 0.76 | 0.76 | 0.71 | 0.71 | 0.39 | 0.39
18 | 0.63 | 0.63 | 0.74 | 0.74 | 0.79 | 0.79 | 0.46 | 0.46
19 | 0.71 | 0.71 | 0.56 | 0.56 | 0.69 | 0.69 | 0.41 | 0.41
20 | 0.78 | 0.78 | 0.70 | 0.70 | 0.85 | 0.85 | 0.48 | 0.48
21 | 0.72 | 0.72 | 0.75 | 0.75 | 0.96 | 0.96 | 0.56 | 0.56
22 | 0.71 | 0.71 | 0.69 | 0.69 | 0.77 | 0.77 | 0.53 | 0.53
23 | 0.53 | 0.53 | 0.73 | 0.73 | – | – | 0.44 | 0.44
24 | 0.75 | 0.75 | 0.60 | 0.60 | 0.77 | 0.77 | 0.65 | 0.65
Mean | 0.73 | 0.71 | 0.72 | 0.72 | 0.76 | 0.75 | 0.52 | 0.49

##  VI Conclusion

In the first section, we discussed the importance of providing support matched
to the human internal state to obtain the appropriate effect of reminiscence
therapy. In this study, we employed a model-based reminiscence with a
cognitive architecture to support personalized reminiscence. To personalize
the model, the parameters of the model should be mapped to the human internal
state during memory recollection. Although previous studies have directly
mapped physiological indices to corresponding model parameters, the
application of these methods under various settings is limited. Therefore, to
estimate the human internal state when using model-based reminiscence, we
proposed a machine-learning based method, in which the model interactively
estimates the human internal state using naturally produced user response
(utterance).

To verify the feasibility of the proposed method, we classified internal
states using the utterances of participants during photo observation. In this
analysis, we attempted to classify the internal state of the model
(experimental conditions) and the human internal state (POMS-2, mood rating).
The first classification revealed that although the performance was not high,
the internal states of the model can be estimated from human reactions
($R\rightarrow I^{\prime}$ in Fig. 1). The second analysis revealed that the
POMS-2 classification results exhibited better classification than the
classification of the internal states of the model. This result suggests that
it is possible to estimate changes in the human mood state from prosodic
features, and indicates the possibility of estimating human internal states
from the human responses ($R\rightarrow I$ in Fig. 1).

These results indicate that the two RQs described in this study can be
answered. In addition, these classification results also support the
effectiveness of the model-based reminiscence. Particularly, the fact that we
were able to classify differences in the internal state of the model from the
human responses indicates that different internal states of the model caused
differences in the human responses. This implies that differences in the
internal parameters of the model affected the human internal state. Thus, this
study successfully advanced the interactive memory support approach based on
cognitive models. We believe that this approach will contribute to the control
of memory recall accompanied with emotions.

However, some limitations should be noted. This study did not consider how the
estimation of the internal state of humans and models can be utilized to
improve the human-model interaction. Particularly, although the fact that the
success of this classification reflects the effectiveness of the model
parameter in stimulating the human internal state was considered, the use of
the estimation of the internal state of the model was not described. In the
future study, a design for implementing the indices in the framework of
interactive memory support should be developed.

Finally, it should also be noted that the classification of the human internal
state is based on indirect indicators. Regarding the means of observing human
internal states, post-hoc measurements cannot address changes in the internal
state depending on the situation, and real-time rating is problematic in terms
of user load. Although these limitations are some of our motivations to
utilize natural user response (verbalization), as an experimental study, it is
better to collect more accurate user responses in real-time. Future studies
should collect physiological data to support the result obtained in this
study.

## Ethical Impact Statement

The experiment was reviewed and approved by Shizuoka University Research
Ethics Committee. In the experiments of this study, we informed the
participants fully about the handling of their personal data in advance, and
collected the data after obtaining their free-will consent. If participants
request that all photos uploaded to the server be deleted, they are informed
that they can be completely deleted from the server.

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# A giant glitch from the magnetar SGR J1935+2154 before FRB 200428

M.Y. Ge  Key Laboratory of Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  Yuan-Pei Yang
South-Western Institute For Astronomy Research, Yunnan University, Kunming
650504, China  Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  Fangjun Lu  Key Laboratory of Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049,
China  Key Laboratory of Stellar and Interstellar Physics and School of
Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China
Shiqi Zhou  School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai
519082, China  Long Ji  School of Physics and Astronomy, Sun Yat-Sen
University, Zhuhai 519082, China  S.N. Zhang  Key Laboratory of Particle
Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China  University of Chinese Academy of Sciences, Chinese
Academy of Sciences, Beijing 100049, China  Bing Zhang  Nevada Center for
Astrophysics, University of Nevada, Las Vegas, NV 89154, USA  Department of
Physics and Astronomy, University of Nevada, Las Vegas, NV 89154, USA  Liang
Zhang  Key Laboratory of Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  Pei Wang
National Astronomical Observatories, Chinese Academy of Sciences, Beijing
100101, China  Kejia Lee  Department of Astronomy, Peking University, Beijing
100871, China  National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, China  Weiwei Zhu  National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China  Jian Li
CAS Key Laboratory for Research in Galaxies and Cosmology, Department of
Astronomy, University of Science and Technology of China, Hefei 230026, China
School of Astronomy and Space Science, University of Science and Technology of
China, Hefei 230026, Chin  Xian Hou  Yunnan Observatories, Chinese Academy of
Sciences, Kunming 650216, China  Qiao-Chu Li  School of Astronomy and Space
Science, Nanjing University, Nanjing 210023, China  Key laboratory of Modern
Astronomy and Astrophysics, Nanjing University, Nanjing 210023, China

###### Abstract

Fast radio bursts (FRBs) are short pulses observed in radio frequencies
usually originating from cosmological distances. The discovery of FRB 200428
and its X-ray counterpart from the Galactic magnetar SGR J1935+2154 suggests
that at least some FRBs can be generated by magnetars. However, the majority
of X-ray bursts from magnetars are not associated with radio emission. The
fact that only in rare cases can an FRB be generated raises the question
regarding the special triggering mechanism of FRBs. Here we report a giant
glitch from SGR J1935+2154, which occurred approximately $3.1\pm 2.5$ day
before FRB 200428, with $\Delta\nu=19.8\pm 1.4$ $\mu$Hz and
$\Delta\dot{\nu}=6.3\pm 1.1$ pHz s-1. The corresponding spin-down power change
rate $\Delta\dot{\nu}/\dot{\nu}$ is among the largest in all the detected
pulsar glitches. The glitch contains a delayed spin-up process that is only
detected in the Crab pulsar and the magnetar 1E 2259+586, a large persistent
offset of the spin-down rate, and a recovery component which is about one
order of magnitude smaller than the persistent one. The temporal coincidence
between the glitch and FRB 200428 suggests a physical connection between the
two. The internally triggered giant glitch of the magnetar likely altered the
magnetosphere structure dramatically in favour of FRB generation, which
subsequently triggered many X-ray bursts and eventually FRB 200428 through
additional crustal cracking and Alfvén wave excitation and propagation.

FRB — stars: neutron — magnetars: general — X-rays: individual (SGR
J1935+2154)

##  1 Introduction

SGR J1935+2154 was discovered when it entered an outburst phase in 2014, which
was followed by four major activity episodes in February 2015, May to July
2016, and November 2019 (Israel et al., 2016; Kozlova et al., 2016; Younes et
al., 2017; Lin et al., 2020a, b). Starting from April 27 2020, multiple short
bursts and a burst forest including hundreds of bursts from SGR J1935+2154
were detected by multiple space X-ray and Gamma-ray instruments (Younes et
al., 2020; Kaneko et al., 2021). Surprisingly, during the outburst, a double-
peaked low-luminosity fast radio burst (FRB) from the direction of SGR
J1935+2154 was observed by CHIME (CHIME/FRB Collaboration et al., 2020) and
STARE2 (Bochenek et al., 2020) at April 28 UTC 14:34:24, which was
subsequently named as FRB 200428. The fluence of FRB 200428 recorded by STARE2
(Bochenek et al., 2020) is $\sim$1.5 MJy ms, making the brightness record of
radio bursts from Galactic magnetars. At the same time, its X-ray counterpart,
a bright X-ray burst, was detected by orbital high energy instruments such as
Insight-HXMT, INTEGRAL, Konus-wind and AGILE (Li et al., 2021; Mereghetti et
al., 2020; Ridnaia et al., 2021; Tavani et al., 2021). Insight-HXMT discovered
the double X-ray peaks corresponding to the double radio peaks (Li et al.,
2021), and both Insight-HXMT and INTEGRAL localized the X-ray burst as coming
from SGR J1935+2154 (Li et al., 2021; Mereghetti et al., 2020). This is the
first time that a counterpart of an FRB was detected at other wavelengths,
which allowed the identification of the origin of an FRB.

However, the mechanism triggering FRB 200428 is not well understood yet. It is
widely suggested that FRBs are generated by the magnetospheric activities of
magnetars, either triggered internally (Yang & Zhang, 2018; Lyubarsky, 2020a;
Lu et al., 2020; Yang & Zhang, 2021; Wang et al., 2021; Li et al., 2022) or
externally (Zhang, 2017, 2020; Geng et al., 2021; Dai, 2020). Recently, Younes
et al. (2022) report that SGR J1935+2154 experienced one spin-down glitch,
followed by FRB-like bursts and a pulsed radio episode. So the timing
properties of SGR J1935+2154 around the epoch of FRB 200428 may provide
crucial clues to unveil the physical process that triggered the FRB. This
work, we only focus the timing properties around FRB 200428 considering Younes
et al. (2022) have published their results.

##  2 Observations and data analysis

###  2.1 Observations and data reduction

In this work, the observations from NICER, NuSTAR, Chandra and XMM-Newton are
utilized to study the spin evolution of SGR J1935+2154 as listed in Appendix
Table 1.

NICER is a payload onboard the International Space Station devoted to the
study of neutron stars through soft X-ray timing (Gendreau et al., 2016). Its
X-ray Timing Instrument (XTI) is an aligned collection of 56 X-ray
concentrator optics (XRC) and silicon drift detector (SDD) pairs, which
records individual photons with good spectral resolution and time resolution
to $\sim 0.1$ $\mu$s relative to the Universal Time. The cleaned events data
in 0.8-4.0 keV are used for profile and timing analyses by using the standard
nicerl2 command with “$\rm underonly\\_range=0-200$”. The arrival time of each
event to barycentre is corrected via barycorr with coordinates $\alpha=19^{\rm
h}34^{\rm m}55^{\rm s}.68$ and $\delta$=21∘53′48′′.2 (Israel et al., 2016).
The solar ephemeris for Solar System Barycentre (SSB) correction is DE405.

SGR J935+2154 was observed by NuSTAR around May 02 and 11 (OBSID 80602313002,
80602313004), 2020, with corresponding exposure times of 38 and 31 ks
(Harrison et al., 2013). In this work, we analyze data from two telescopes on
NuSTAR (usually labeled by their focal plane modules, FPMA and FPMB) using
HEASoft (version 6.29). We utilize nupipline with NuSTAR CALDB v20180312 to
create GTIs and select a circular region of radius $180^{\prime\prime}$
centred on the pulsar position to extract the source spectrum. The arrival
time of each photon is corrected to SSB with the same solar ephemeris.

We processed the data collected by PN of XMM-Newton from 2014 to May, 2020
(Jansen et al., 2001) using the Science Analysis System (SAS) (v14.0.01)
software. The time intervals contaminated by flaring particle background are
discarded. Events in a circular region with a radius of $50^{\prime\prime}$
centred on the pulsar position are selected to ensure that all the source
events are included. Only PN data are utilized to perform the timing analysis
considering the time resolution. The arrival time of each photon is corrected
to SSB with the same solar ephemeris.

Chandra observed SGR J1935+2154 four times in 2014 and 2016, with the ObsIDs
of 15874, 15875, 17314, and 18884, respectively. The corresponding time
resolutions in these observations are, 0.44 s, 2.85 ms, 2.85 ms, and 2.85 ms.
Therefore, these four observations are used for timing analyses, as listed in
Table LABEL:table:obs. The data were reprocessed with the Chandra Interactive
Analysis of Observations software (CIAO, version 4.14) using the calibration
files available in the Chandra CALDB 4.9.6 data base. The scientific products
were extracted following the standard procedures, but adopting extraction
regions with different sizes in order to properly subtract the underlying
diffuse component. For 15874, we extract the events from a circular region
with radius of 1.5′′ for the timing analysis. While for observations 15875,
17314 and 18884 at continuous clocking (CC) mode, events in rectangular boxes
of 3′′ x 2′′ sides aligned to the CCD readout direction are used to perform
timing analysis. For the timing analysis, we applied the Solar system
barycentre correction to the photon arrival times with AXBARY.

###  2.2 Timing analysis

We perform both partially phase-coherent timing (PPCT) analysis and fully
phase-coherent timing (FPCT) analysis for SGR J1935+2154 to study its timing
behaviors using TEMPO2 (Hobbs et al., 2006). The PPCT analysis can mitigate
the pronounced effects of timing noise on the long term evolution and show
spin evolution clearly (Ferdman et al., 2015), while the FPCT analysis can get
more accurate spin parameters of the pulsar, because the timing noise such as
glitches revealed by PPCT analysis can be included in the new timing model. To
perform PPCT analysis, we need to have spin frequencies and times of arrival
(ToAs) in different epochs, which are obtained with $Z^{2}_{1}$ searching,
i.e., the frequency making the folded profile deviating the most from a
uniform distribution as represented by the $Z^{2}_{1}$ value is taken as the
spin frequency at the time of each observation, and the phase of the minimum
point in each profile is then taken as the TOA of that observation (Ge et al.,
2012; Younes et al., 2020).

The data used for timing analysis span in about 2300 days from MJD 56853 to
59172. Two obvious abnormalities of SGR J1935+2154 are recognised since the
frequencies obtained with $Z^{2}_{1}$ searching in two epochs deviate
obviously from the extrapolation of the earlier data. In order to show the
spin evolution clearly, as discussed above, the PPCT analysis is performed
(Ferdman et al., 2015; Ge et al., 2019), and the resulted spin parameters in
different epochs are given in Table 1. The spin parameters obtained from the
above mentioned time spans are then fitted with equation (1) in TEMPO2.

$\nu(t)=\nu_{0}+\dot{\nu}_{0}{(t-t_{0})}$ (1)

where $\nu_{0}$, $\dot{\nu}_{0}$ are frequency and frequency derivative at the
reference time $t_{\rm 0}$, and $t$ corresponds to the center of each sub-data
set.

Based on the above preliminary timing results of SGR J1935+2154, we can
further perform FPCT analysis to get more accurate timing solutions using the
data around G1 and G2 respectively, with equation (2) shown below.

$\nu(t)=\nu_{0}+\dot{\nu}_{0}{(t-t_{0})}+\Delta{\nu}_{\rm
p}+\Delta\dot{\nu}_{\rm p}{(t-t_{\rm g})}+\Delta{\nu_{\rm d1}}{\rm
e}^{-\frac{(t-t_{\rm g})}{\tau_{\rm d1}}}+\Delta{\nu_{\rm d2}}{\rm
e}^{-\frac{(t-t_{\rm g})}{\tau_{\rm d2}}}$ (2)

where $\nu_{0}$, $\dot{\nu}_{0}$ are frequency and frequency derivative at
epoch $t_{\rm 0}$, $\Delta\nu_{\rm p}$ and $\Delta\dot{\nu}_{\rm p}$ are the
persistent offsets of frequency and frequency derivative at the glitch epoch
$t_{\rm g}$, $\Delta\nu_{\rm d1}$, $\Delta\nu_{\rm d2}$, $\tau_{\rm d1}$ and
$\tau_{\rm d2}$ are the parameters of the two exponential components. The
overall amplitudes of the glitches can be then inferred with
$\Delta\nu=\Delta\nu_{\rm p}+\Delta\nu_{\rm d1}+\Delta\nu_{\rm d2}$ and
$\Delta\dot{\nu}=\Delta\dot{\nu}_{\rm p}-\Delta\nu_{\rm d1}/\tau_{\rm
d1}-\Delta\nu_{\rm d2}/\tau_{\rm d2}$. Furthermore, the recover factor
$Q=\Delta\nu_{\rm d2}/\Delta\nu$ can be calculated as usually defined (Dib &
Kaspi, 2014; Lower et al., 2021). The detailed timing parameters for the two
glitches are listed in Table 2. The errors of spin parameters are obtained
from TEMPO2 software.

For SGR J1935+2154, the timing results have not been affected by the timing
accuracy of different telescopes. For NICER and NuSTAR, their time resolutions
are 0.1 $\mu$s and 0.1 ms, respectively Gendreau et al. (2016); Bachetti et
al. (2021), which much shorted the spin period of SGR J1935+2154. The time
resolutions of XMM-Newton and Chandra observations are not as good as NICER
and NuSTAR but they do not show differences on the timing results as reported
in Israel et al. (2016).

##  3 Results

###  3.1 The spin evolution

The long time evolution and short time variations of $\nu$ and $\dot{\nu}$
could be illustrated directly as in Figure 1, which shows two spin-up glitches
on MJD 57822 and 58964.5, which are named G1 and G2. The information about the
first glitch (G1) is quite limited due to the incomplete time coverage and not
concerned in this work. Unfortunately, as no timing information about SGR
J1935+2154 is available between MJD 58110 and 58965, we do not know the exact
rotation state of SGR J1935+2154 before the burst forest and FRB 200428.
However, as shown in Figures 1 and 2, the timing behaviors around FRB 200428,
which are obtained with both PPCT and FPCT analysis from the observations, are
very typical for a glitch, which has three components, the persistent, the
delayed spin-up and the recovering components, similar to the big glitches in
the Crab pulsar (Ge et al., 2020). The fitting parameters as listed in Table 2
show that G2 is a giant glitch happened on MJD 58964.5(2.5) with
$\Delta\nu/\nu=(6.4\pm 0.4)\times{10}^{-5}$ and
$\Delta\dot{\nu}/\dot{\nu}=-4.4\pm 0.7$, where both $\Delta\nu$ and
$\Delta\dot{\nu}$ include the delayed spin-up component that will be discussed
later. There are two exponential components following G2. The first
exponential component with $\tau_{\rm d1}=8\pm 1$ day represents the delayed
spin-up process that was previously only detected in large glitches of the
Crab pulsar and magnetar 1E 2259+586 (Ge et al., 2020; Woods et al., 2004).
The second one is a slow recovery process with $\tau_{\rm d2}=131\pm 6$ day
and $\Delta\nu_{\rm d2}=2.50\pm 0.16{\rm{\mu}Hz}$. Remarkably, in the
evolution of the spin-down rate, a large persistent offset
($\Delta\dot{\nu}_{p}$) of $-2.031\pm 0.019$ pHz s-1 is present, which is 1.4
times of the spin-down rate $\dot{\nu}$ before the glitch and is about one
order of magnitude larger than the slow recovery component. Such a persistent
offset should be due to an increase in the external torque caused by a
rearrangement of the magnetosphere (Link et al., 1992; Zhang et al., 2022),
and the large value implies that the magnetosphere changes dramatically at the
glitch, consistent with the large pulse profile changes after G2 (Younes et
al., 2020) (Figure 3).

###  3.2 Tight constraint on on the epoch of G2

The overall timing analyses have not given a very tight constraint on the
occurrence time of G2. We therefore discuss whether it happened before FRB
200428 or not with detailed studies on timing behaviors and profiles, since it
is crucial for understanding the possible causal connection between the glitch
and FRB 200428. The data are divided into two part according to the epoch of
FRB 200428 as plotted in Figure 4. In Figure 5, we give the $Z_{1}^{2}$
variations with spin frequency for the pre-FRB data, the post-FRB data and the
whole dataset, respectively. The $Z_{1}^{2}$ values for the three datasets all
reach their respective maxima at frequency around $0.3079468(12)$ Hz, and the
value of the whole dataset is the highest, which is also consistent with the
results from Younes et al. (2020) and Borghese et al. (2020). The difference
of peak frequencies is smaller than $1.2\,\mu$Hz, much smaller than
$19\,\mu$Hz, the frequency jump of G2, meaning that G2 must happened in
advance, i.e., before FRB 200428. We also fold the pre- and post-FRB pulse
profiles of this magnetar with the same set of spin parameters obtained above.
As shown in Figure 6, the two profiles are not different from each other
significantly and share the same minimum phase, supporting the previous
conclusion from another aspect. Therefore, G2 happened at least before MJD
58967.2, which is 0.4 day before FRB 200428. From these two aspects, G2
occurred at least 0.4 days before FRB 200428 and probably occurred at $3.1\pm
2.5$ day earlier than FRB 200428.

###  3.3 Delayed spin-up components

We compare the delayed spin-up component of G2 with that of the glitches in
the Crab pulsar and 1E 2259+586, as presented in Figure 7. Interestingly, in
the $\Delta\nu/\nu$ -$\tau_{\rm d1}$ diagram, where $\tau_{\rm d1}$ is the
timescale of the spin-up component, all the spin-up events can be roughly
fitted with a power-law function ($\alpha=2.0$). This indicates that the
mechanisms for angular momentum transfer of the glitches in the Crab pulsar,
1E 2259+586 and SGR J1935+2154 are similar. The existence of the rather long
timescale spin-up components in the Crab pulsar and the non-detection of such
components from the Vela pulsar and PSR J0537-6910 are suggested to be due to
the different states of their crusts and interiors (Ge et al., 2020), i.e.,
the Crab pulsar is younger and hence less solidified. The existence of the
delayed spin-up component of SGR J1935+2154 thus implies that it is young. It
is worth noting here that the delayed spin-up components may have been
detected from several other magnetars even though their timing properties are
not well resolved (Woods et al., 2004; Dib & Kaspi, 2014), indicating that
they are also young as widely believed.

###  3.4 Comparison with other glitch samples

From the known glitch sample of isolated pulsars, this event of SGR J1935+2154
is among the largest two in terms of the relative glitch amplitudes in the
$\Delta\nu/\nu$-$\Delta\dot{\nu}/\dot{\nu}$ diagram (Dib & Kaspi, 2014;
Espinoza et al., 2011; Lower et al., 2021) as shown in Figure 8. The other
glitch-like event in magnetars with a comparable relative amplitude is
associated with the super burst of SGR 1900+14 around MJD 51050 (Woods et al.,
1999). Although the $\Delta\nu$ and $\Delta\dot{\nu}$ values of the large
glitches in the Crab pulsar, Vela pulsar, PSR J0205+6449 and PSR J0537-6910
are comparable with those of G2 in SGR J1935+2154 (as shown in Figure 8 (b)),
the relative change of the rotation frequency is much greater than those of
the pulsars considering that this magnetar rotates much more slowly than the
pulsars. Moreover, among the magnetar glitch sample, G2 has the largest
$\Delta\nu$ value while SGR 1900+14 has the largest $\Delta\nu<0$ value (Woods
et al., 1999).

##  4 Discussion

For the physical connection between FRBs and glitches, we suggest the
following scenario based on the previous theoretical framework and the
observational properties of SGR J1935+2154 around the glitch. After the
glitch, the motion of the core superfluid neutron vortices in the direction
perpendicular to the spin axis during the spin-down relaxation phase of the
glitch would alter the core magnetic field, which would result in the movement
of the neutron star crust and the change in the surface magnetic field
(Ruderman et al., 1998). Crustquakes are expected if the solid crust does not
plastically adjust to the less-oblate equilibrium shape required by the
pulsar’s spin-down or if the magnetic stress exceeds the shear modulus (Baym &
Pines, 1971; Thompson & Duncan, 1995; Perna & Pons, 2011; Li et al., 2022).
Crustal fracturing produces Alfvén waves and then generates X-ray bursts
(Thompson & Duncan, 1995). On the other hand, some FRB emission models
proposed that FRB are associated with magnetar activity, such as FRBs produced
in the charge starvation region triggered by Alfvén waves or crust plate
motions (Kumar & Bošnjak, 2020; Lu et al., 2020; Wadiasingh et al., 2020; Yang
& Zhang, 2021), FRB produced by relativistic plasmoids/outflows lunched by
Alfvén waves (Metzger et al., 2019; Yuan et al., 2020), FRB generated by
magnetic reconnection near the light-cylinder (Lyubarsky, 2020b), etc.
Immediately after the glitch, frequent magnetic activities generate plenty of
energetic charged particles in the form of electron-positron pairs, which
easily power X-ray bursts. However, if FRBs are produced in the magnetosphere
as proposed by some models (e.g., Kumar & Bošnjak, 2020; Lu et al., 2020;
Wadiasingh et al., 2020; Yang & Zhang, 2021), they would be difficult to be
generated in such a pair-rich environment due to the following two reasons: 1)
the abundant pairs would shield the charge starvation region necessary for FRB
generation; 2) even if an FRB is generated under some specific conditions, it
is difficult to escape from a pair-rich magnetosphere due to a large
scattering optical depth in the magnetosphere. Some time later, the magnetic
field configuration becomes less irregular, as represented by the decrease of
X-ray burst frequency (Cai et al., 2022). Particles can escape easily from the
magnetosphere in the form of a pulsar wind like that in PSR B0540–69 after a
spin-down rate transition (Ge et al., 2019). FRBs and weak radio bursts may be
then generated due to the formation of the charge starvation region in the
magnetosphere. This explains why FRB 200428 occurred a few days after G2
(Zhang et al., 2020; Kirsten et al., 2021) . Long after the glitch, as the
crust plate is recovered and magnetic field rearrangement is finished,
magnetic activities become less frequent and FRBs become more difficult to be
generated. In short, FRBs preferably occur some time after the most active
episodes triggered by giant glitches in magnetars. It is therefore essential
to closely monitor the spin evolution of magnetars in X-rays and coordinate
radio follow-up observations when a major glitch is detected in order to
further test this FRB generation scenario.

##  5 Summary

We utilize the observations from NICER, NuSTAR, Chandra and XMM-Newton to
study the timing behaviour of SGR J1835+2154 and the possible trigger
mechanism of FRB 200428. From the timing result, we find a giant glitch from
SGR J1935+2154, which occurred approximately $3.1\pm 2.5$ day before FRB
200428, with $\Delta\nu=19.8\pm 1.4$ $\mu$Hz and $\Delta\dot{\nu}=6.3\pm 1.1$
pHz s-1. The corresponding spin-down power change rate
$\Delta\dot{\nu}/\dot{\nu}$ is among the largest in all the detected pulsar
glitches. The glitch contains a delayed spin-up process that is only detected
in the Crab pulsar and the magnetar 1E 2259+586, a large persistent offset of
the spin-down rate, and a recovery component which is about one order of
magnitude smaller than the persistent one. The temporal coincidence between
the glitch and FRB 200428 suggests a physical connection between the two,
which supplies more constraint on the trigger mechanism of FRB 200428.

Figure 1: The spin evolution of SGR J1935+2154. Panel (a): The evolution of
spin frequency $\nu$ by subtracting the polynomial component as parameterized
in Table 2 by PPCT method. Panel (b): The evolution of spin-down rate
$\dot{\nu}$. The values of $\nu$ and $\dot{\nu}$ are obtained according to
PPCT analysis and listed in Table 1. Panel (c): Timing residuals of the model
fitting with parameters listed in Table 2 by FPCT method. Panels (d), (e) and
(f) illustrate the corresponding zoomed in structures of (a), (b) and (c)
around FRB 200428. The solid and dashed red lines represent the fitted spin
evolution including and not including the delayed spin-up components. The
vertical dot-dashed green line represents the epoch of FRB 200428 while the
vertical thin dotted lines represent the epochs of G1 and G2. The dotted blue
and magenta lines represent the occurrence time of the two weak radio bursts
detected by FAST and Westerbork (Zhang et al., 2020; Kirsten et al., 2021),
respectively. The confidence level for all the data points are 1-$\sigma$
level in this paper.

Figure 2: The timing residuals of SGR J1935+2154 with timing parameters
pre-G2. Panel (a): the residuals before glitch epoch of G2. Panel (b):
residuals with the timing parameters pre G2. The dot dashed line represents
the glitch epoch of G2. Figure 3: The X-ray pulse profiles of SGR J1935+2154
normalised by the mean count rate in different epoches. The red squares and
line represent the pulse profile between MJD 58053 and 58110 (2017.10.27-29)
obtained with NICER. The green squares and line represent the pulse profile
obtained with NICER between MJD 58967 and 58970 (2020.04.28-05.01), which
covers FRB 200428 (Borghese et al., 2020). The blue squares and line represent
the pulse profile obtained with NuSTAR at MJD 58971 and 58979 (2020.05.02 and
05.10) (Borghese et al., 2020, 2022). The magenta squares and line are the
pulse profile obtained with XMM-Newton at MJD 58972 (2020.05.03) (Borghese et
al., 2022). The cyan squares and line represent the pulse profile between MJD
58986 and 59010 (2020.05.17-06.10) obtained with NICER. The pulse profiles are
moved upward with a step size of 0.3 to show them more clearly. Figure 4: The
lightcurve of NICER ObsID 3020560101. The light curve of burst forest is
removed. The dashed line represents the time of FRB 200428. Figure 5:
$Z_{1}^{2}$ variation with rotation frequency of SGR J1935+2154 around FRB
200428 using the NICER data. The red, green and blue lines represent the
$Z_{1}^{2}$ values versus frequency for the pre-FRB data (35000 to 40000 s
ahead of ObsID 3020560101 as shown in Figure 4), the post-FRB data (5500 to
7000 s of ObsID 3020560101 and ObsIDs 3020560102, 3020560103, 3655010101 and
3655010102) and the whole dataset. The curves show that the frequency remains
quite stable in this duration.  Figure 6: The pulse profiles of SGR J1935+2154
obtained with the NICER data before and after FRB 200428. The blue points
represent the pulse profile before FRB 200428, and the red points represent
the pulse profile after FRB 200428. The data selection is the same as in
Figure 5. Figure 7: The correlation between $\Delta{\nu}/\nu$ and time scale
$\tau_{d1}$ of the delayed spin-up components of glitches in the Crab pulsar,
SGR J1935+2154 and 1E 2259+586. The blue squares, red circle and magenta
square represent those of the Crab pulsar, SGR J1935+2154 and 1E 2259+586
(Woods et al., 2004; Ge et al., 2020; Shaw et al., 2021), respectively. The
green triangle denotes the detected duration upper limit (12.4 s) of the spin
frequency jump for glitches of the Vela pulsar (Palfreyman et al., 2018),
which is the first for more constraint on the rise time of glitch. The dashed
line represents a power-law fit with $\alpha=2.0$.

Figure 8: Panel (a): Comparison of glitch G2 in SGR J1935+2154 with other
glitches of rotation powered pulsars in the
$\Delta{\nu}/\nu-\Delta{\dot{\nu}}/\dot{\nu}$ diagram. Panel (b): The
$\Delta{\nu}-\Delta{\dot{\nu}}$ diagram. The red circles, green circle, blue
squares and grey dots represent the two glitches of SGR J1935+2154, the anti-
glitch of SGR 1900+14 (Woods et al., 1999), glitches of other known magnetars,
and glitches of normal rotation-powered pulsars (Dib & Kaspi, 2014; Espinoza
et al., 2011; Lower et al., 2021), respectively. The empty blue squares
represent the anti-glitches of 1E 2259+586 (Archibald et al., 2013). The black
circles, squares, triangles and stars in panel (b) represent the glitches of
the Crab pulsar, the Vela pulsar, PSR J0537-6910 and PSR J0205+6449 (Dib &
Kaspi, 2014; Lower et al., 2021), respectively. The glitch catalog also be
obtained from website: http://www.jb.man.ac.uk/pulsar/glitches/gTable.html and
https://www.atnf.csiro.au/people/pulsar/psrcat/glitchTbl.html.

Table 1: The spin parameters of SGR J1935+2154 obtained with partially phase-coherent timing analysis. No. | Start | Finish | PEPOCH | $\nu$ | $\dot{\nu}$
---|---|---|---|---|---
| MJD | MJD | MJD | Hz | ${\rm pHzs^{-1}}$
1 | 56822 | 56950 | 56899 | 0.308163446(2) | -1.359(2)
2 | 56892 | 57335 | 57101 | 0.3081397240(3) | -1.35892(7)
3 | 56926 | 57605 | 57251 | 0.3081221081(3) | -1.35923(5)
4 | 58046 | 58086 | 58068 | 0.30803445(2) | -1.42(9)
5 | 58067 | 58130 | 58088 | 0.30803204(3) | -1.44(5)
6 | 58966 | 58973 | 58969 | 0.30794566(9) | 0.38(1.20)
7 | 58970 | 58984 | 58977 | 0.30794430(3) | -2.99(1.32)
8 | 58987 | 59007 | 58996 | 0.30794063(3) | -3.67(18)
9 | 58998 | 59041 | 59017 | 0.307934203(8) | -3.50(3)
Table 2: The timing parameters of the two Glitches in SGR J1935+2154.

Parameters | G1 |  G2∗
---|---|---
Epoch (MJD) | 57214 | 58088
$\nu$(${\rm Hz}$) | 0.3081264533(3) | 0.30803203(2)
$\dot{\nu}$(${\rm pHzs^{-1}}$) | -1.35922(4) | -1.415(19)
Glitch epoch (MJD) | 57822(22) | 58964.5(2.5)**
$\Delta\nu({\rm{\mu}Hz})$ | 9.5(2) | 19.8(1.4)
$\Delta\nu_{p}({\rm{\mu}Hz})$ | – | 23.2(1.4)
$\Delta\dot{\nu}({\rm pHzs^{-1}})$ | -0.0558(0.0123) | 6.3(1.1)
$\Delta\dot{\nu}_{\rm p}({\rm pHzs^{-1}})$ | – | -2.031(19)
$\Delta\nu_{\rm d1}({\rm{\mu}Hz})$ | – | -5.88(9)
$\tau_{\rm d1}({\rm d})$ | – | 8(1)
$\Delta\nu_{\rm d2}({\rm{\mu}Hz})$ | – | 2.50(16)
$\tau_{\rm d2}({\rm d})$ | – | 131(6)
$\Delta\nu/\nu(10^{-6})$ | 30.8(9) | 64(4)
$\Delta\dot{\nu}/\dot{\nu}$ | 0.041(9) | -4.4(7)
$Q$ | – | 0.13(1)
Time range | 56822–58130 | 58046–59120
Residuals (ms) | 90.9 | 105.6

*: In the analyses we assume that the timing behaviors between MJD 58110 and 58965 follow the trend in MJD 58054-58110.

**: The uncertainty of the occurrence time of G2 is 2.5 day. But as discussed
in the text, it happened definitely before MJD 58967.2, which is 0.4 day
before FRB 200428 at MJD 58967.60857593.

## Acknowledgments

This work is supported by the National Key R&D Program of China
(2021YFA0718500) from the Minister of Science and Technology of China (MOST).
The authors thank supports from the National Natural Science Foundation of
China under Grants U1938109, U1838201, U1838202, 12173103, 12003028, U2038101,
U1938103 and 11733009. This work is also supported by International
Partnership Program of Chinese Academy of Sciences (Grant
No.113111KYSB20190020), SKA Fast Radio Burst and High-Energy Transients
Project (2022SKA0130101), and the China Manned Spaced Project (CMS-
CSST-2021-B11).

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## Appendix

Table 1: The observation catalogue of SGR J1935+2154. The time resolutions of Chandra observations 15874, 15875, 17314, and 18884 are 0.44 s, 2.85 ms, 2.85 ms, and 2.85 ms, and those of XMM-Newton and NICER are 68.7 ms and 1 $\mu{\rm s}$, respectively. Telescope | ObsID | MJD | Exposure
---|---|---|---
|  |  | ks
Chandra | 15874 | 56853 | 10
Chandra | 15875 | 56866 | 75
Chandra | 17314 | 56900 | 29
Chandra | 18884 | 57576 | 20
XMM-Newton | 0722412501 | 56926 | 22
XMM-Newton | 0722412601 | 56928 | 23
XMM-Newton | 0722412701 | 56934 | 22
XMM-Newton | 0722412801 | 56945 | 23
XMM-Newton | 0722412901 | 56954 | 10
XMM-Newton | 0722413001 | 56957 | 17
XMM-Newton | 0748390801 | 56976 | 22
XMM-Newton | 0764820101 | 57106 | 46
XMM-Newton | 0764820201 | 57302 | 68
XMM-Newton | 0871190201 | 58982 | 51
NuSTAR | 80602313002 | 58971 | 37
NuSTAR | 80602313004 | 58979 | 38
NICER | 1020560101 | 58053 | 3.0
NICER | 1020560102 | 58054 | 13.9
NICER | 1020560103 | 58055 | 8.1
NICER | 1020560104 | 58056 | 5.8
NICER | 1020560105 | 58057 | 0.4
NICER | 1020560106 | 58058 | 2.3
NICER | 1020560107 | 58079 | 1.9
NICER | 1020560108 | 58080 | 6.4
NICER | 1020560109 | 58081 | 2.7
NICER | 1020560110 | 58082 | 5.3
NICER | 1020560111 | 58084 | 2.9
NICER | 1020560112 | 58087 | 1.7
NICER | 1020560113 | 58088 | 0.8
NICER | 1020560115 | 58115 | 0.9
NICER | 1020560116 | 58116 | 0.7
NICER | 2020560101 | 58763 | 0.3
NICER | 2020560102 | 58764 | 2.2
NICER | 2020560103 | 58765 | 2.3
NICER | 2020560104 | 58794 | 1.7
NICER | 3020560101 | 58967 | 3.1
NICER | 3020560102 | 58968 | 0.9
NICER | 3655010101 | 58968 | 0.8
NICER | 3655010102 | 58969 | 3.9
NICER | 3020560103 | 58969 | 0.7
NICER | 3020560104 | 58980 | 0.9
NICER | 3655010201 | 58987 | 4.7
NICER | 3020560105 | 58988 | 0.9
NICER | 3020560106 | 58989 | 0.6
NICER | 3020560107 | 58991 | 5.2
NICER | 3020560108 | 58992 | 3.2
NICER | 3020560109 | 58994 | 0.8
NICER | 3020560110 | 58997 | 1.7
NICER | 3020560111 | 58998 | 1.0
NICER | 3020560112 | 58999 | 1.3
NICER | 3020560113 | 59000 | 1.1
NICER | 3020560114 | 59001 | 2.7
NICER | 3020560115 | 59002 | 1.0
NICER | 3020560116 | 59003 | 0.7
NICER | 3020560117 | 59004 | 1.4
NICER | 3020560118 | 59005 | 1.2
NICER | 3020560119 | 59006 | 1.0
NICER | 3655010301 | 59017 | 1.2
NICER | 3655010302 | 59018 | 6.6
NICER | 3655010303 | 59018 | 4.1
NICER | 3020560120 | 59020 | 0.9
NICER | 3020560121 | 59021 | 0.8
NICER | 3020560122 | 59022 | 1.7
NICER | 3020560123 | 59023 | 3.2
NICER | 3020560124 | 59024 | 1.8
NICER | 3020560125 | 59025 | 1.7
NICER | 3020560126 | 59027 | 0.8
NICER | 3020560127 | 59028 | 1.7
NICER | 3020560128 | 59029 | 1.7
NICER | 3020560129 | 59030 | 2.2
NICER | 3020560130 | 59031 | 0.6
NICER | 3020560131 | 59032 | 1.2
NICER | 3020560132 | 59033 | 1.1
NICER | 3020560133 | 59034 | 0.8
NICER | 3020560134 | 59038 | 0.5
NICER | 3020560135 | 59040 | 0.4
NICER | 3020560136 | 59041 | 1.3
NICER | 3020560137 | 59042 | 0.7
NICER | 3020560138 | 59045 | 3.1
NICER | 3020560139 | 59046 | 1.4
NICER | 3020560140 | 59047 | 0.9
NICER | 3020560141 | 59049 | 0.8
NICER | 3020560142 | 59056 | 0.2
NICER | 3020560143 | 59061 | 1.3
NICER | 3020560144 | 59062 | 1.4
NICER | 3020560145 | 59063 | 0.5
NICER | 3020560146 | 59064 | 2.0
NICER | 3020560147 | 59065 | 0.8
NICER | 3020560148 | 59067 | 2.2
NICER | 3020560149 | 59089 | 0.3
NICER | 3020560150 | 59102 | 0.1
NICER | 3020560151 | 59103 | 2.1
NICER | 3020560152 | 59111 | 1.2
NICER | 3020560153 | 59117 | 1.5