# The Dance of Logic and Unpredictability: Examining the Predictability of
User Behavior on Visual Analytics Tasks

Alvitta Ottley
Washington University in St. Louis, USA
<EMAIL_ADDRESS>
https://orcid.org/0000-0002-9485-276X

###### Abstract

The quest to develop intelligent visual analytics (va) systems capable of
collaborating and naturally interacting with humans presents a multifaceted
and intriguing challenge. va systems designed for collaboration must adeptly
navigate a complex landscape filled with the subtleties and unpredictabilities
that characterize human behavior. However, it is noteworthy that scenarios
exist where human behavior manifests predictably. These scenarios typically
involve routine actions or present a limited range of choices. This paper
delves into the predictability of user behavior in the context of visual
analytics tasks. It offers an evidence-based discussion on the circumstances
under which predicting user behavior is feasible and those where it proves
challenging. We conclude with a forward-looking discussion of the future work
necessary to cultivate more synergistic and efficient partnerships between
humans and the va system. This exploration is not just about understanding our
current capabilities and limitations in mirroring human behavior but also
about envisioning and paving the way for a future where human-machine
interaction is more intuitive and productive.

##  1 INTRODUCTION

Building intelligent visual analytics systems that can assist and interact
with humans during data analysis is akin to teaching a robot to dance. We
aspire to achieve a dance of data with a fluid exchange of ideas, a graceful
understanding of needs, and a seamless partnership in pursuing hypotheses,
insights, and decisions. However, the human element in this equation is far
from a predictable automaton – humans are complex, driven by emotions,
experiences, and social contexts that often elude the straightforward logic of
machines. This complexity presents the visual analytics community with a
formidable challenge: How do we design systems that intelligently collaborate
with their human counterparts?

As we examine examples beyond visual analytics, a common misconception frames
humans as purely logical entities whose decisions and actions are easily
predictable by well-defined rules. This assumption is evident in technologies
like basic customer service chatbots, which are programmed for simple
inquiries [Sheehan et al., 2020] but falter with complex or emotionally
charged interactions [Prentice and Nguyen, 2020], resulting in unhelpful
customer experiences [Chong et al., 2021, Crolic et al., 2022, Huang and
Dootson, 2022]. Similarly, advertising algorithms that target based on
demographics and past behaviors often fall short [White and Samuel, 2019].
They assume that human preferences are static, overlooking the subtleties of
an individual’s goals and ever-evolving needs [Lambrecht and Tucker, 2013].
Consequently, these approaches can lead to irrelevant, intrusive, or
untrustworthy advertising [Bleier and Eisenbeiss, 2015]. Moreover, the
frequent shortcomings of these systems can largely be attributed to their
inability to cope with the broad spectrum of unpredictable factors inherent in
the given case scenarios. Adopting a one-size-fits-all strategy fails to
consider the unique variances among individuals and the significant role that
emotional factors play in shaping human decisions and preferences under those
circumstances [Bleier and Eisenbeiss, 2015].

(a) The interface used to solve a task related to a kidnapping crime. Users
can (a) view details, (b) filter, (c) list matching results, and (d) sketch an
entity/connection network. Figure 1: The interface and analysis result from
Crouser et al. They analyze the analysis behaviors from a series of exercises
with 22 trained intelligence analysts [Crouser et al., 2020]. Their
preliminary analysis suggests that individual differences in locus of control
can modulate expert behavior in complex analysis tasks.

(b) The analysis revealed correlations between the number of interactions and
participants’ locus of control across the three primary action types.

Yet, in certain situations, human behavior tends to be predictable [Heiner,
1983, Flanagan and Johansson, 2003]. These situations usually involve
routines, repetitive actions, or limited choices. For example, many people
have regular commuting patterns. Most people’s daily routines have only slight
variations [Krumme et al., 2013], making this predictability useful for
traffic forecasting and scheduling public transportation [Song et al., 2010].
People’s interaction with basic technology, like ATMs or elevators, tends to
follow a formulaic script due to the limited actions available. Further,
purchasing patterns for essential goods often show consistency [Kim and Park,
1997, Krumme et al., 2013].

This paper argues that visual analytics systems can capitalize on the
predictable aspects of human behavior. This could mean creating interfaces and
functionalities that cater to routine tasks while providing the flexibility
and depth required for more complex, less foreseeable analytical endeavors.
For instance, if a system recognizes that users frequently perform a specific
sequence of actions, it can automate or simplify these steps. This approach
could enhance efficiency and minimize the user’s cognitive load, allowing them
to focus on more complex data analysis aspects requiring deeper thought and
creativity.

However, the challenge lies in discerning when human actions are routine and
predictable and when they are not. This balance is key to developing visual
analytics systems that are truly collaborative partners in the dance of data
exploration and analysis. This paper discusses some necessary steps for
creating intelligent visual analytics tools:

  * •

A deeper collaboration between humans and ai requires embracing the complexity
of human behavior. We discuss the role of individual differences in visual
analysis in Section 2.

  * •

Section 3 explains how the system’s design can affect action predictability.

  * •

Two case studies in Section 4 demonstrate action prediction based on user
interactions.

  * •

In Section 5 advocates for broadening the conceptual models of human-machine
collaboration in visual analytics. We suggest a framework that integrates ai
capabilities with human expertise.

  * •

Finally, we discuss, among other things, the ethical considerations for human-
AI interactions that must be rigorously addressed.

##  2 The Interplay of Predictability and Individuality in Data Analysis

While it is true that certain scenarios can lead to predictable behavior
patterns, this does not negate the rich tapestry of individual differences
that manifest in various ways during visual analysis tasks. These differences
are influenced by many factors, including personality traits, cognitive
abilities, and situational conditions, each playing a significant role in how
individuals interact with and interpret data [Ottley, 2022, Liu et al., 2020].

Studies show several individual differences have consistently impacted
performance, as evidenced by multiple independent researchers’ replication in
various experimental settings [Ottley, 2022, Liu et al., 2020]. Personality
traits, for example, can greatly influence how a user approaches a visual
analytics task. A notable instance is the influence of locus of control, which
reflects an individual’s perception of control over external events and often
affects the speed and accuracy of visualization tasks [Ottley et al., 2015a,
Ziemkiewicz et al., 2012]. This impact has been observed across studies using
diverse datasets and methodologies and in traditional laboratory experiments
and crowdsourcing research platforms [Crouser et al., 2020, Ottley et al.,
2015b].

For a concrete example, we examine one particular study, described in 1(a),
examining the behavior of 22 Navy Reservists during complex analytical tasks
revealed a correlation between locus of control and expert behavior [Crouser
et al., 2020]. It found that participants with a more internal locus of
control engaged in more actions and covered more data in the same timeframe.
Additionally, other studies underscore the importance of visualization design
in this dynamic, showing that an individual’s locus of control can
significantly influence their search strategy in hierarchical systems.

Similarly, cognitive abilities like spatial reasoning, perceptual speed, and
working memory capacity can impact the speed and accuracy with which different
users understand and analyze complex visual data [Liu et al., 2020].
Situational factors, including time constraints, task complexity, and the
user’s emotional state during analysis, further affect this process [Bancilhon
et al., 2023]. Under time pressure, users may adopt heuristic analysis
methods, whereas more relaxed conditions might encourage deeper exploration
[Bobadilla-Suarez and Love, 2018, Del Campo et al., 2016]. Moreover, a task’s
inherent complexity can elicit varying responses, depending on the user’s
preference for challenge or simplicity [Ziemkiewicz et al., 2012].

After reviewing the research, several key themes emerged regarding the impact
of individual differences on visual analytics tasks:

  1. 1.

Individual differences are more pronounced in complex tasks, with greater
freedom for exploration [Ziemkiewicz et al., 2012, Brown et al., 2014, Ottley
et al., 2015b].

  2. 2.

Conversely, simpler tasks tend to show less variation in user behavior.
Studies often report no substantial effect of individual differences on
simpler tasks [Ziemkiewicz et al., 2012].

  3. 3.

Even with observable differences between individuals, there are often common
behavioral patterns within groups, indicating that for a giving visualization
scenario, certain analysis paths are more frequently traversed, even in
scenarios with the potential for wide exploration diversity [Brown et al.,
2014, Ottley et al., 2015b].

Understanding individual differences can provide insight into inconsistent and
consistent behavior patterns. This knowledge can help create visual analytic
tools that intelligently collaborate and respond based on these differences
and the situations in which they occur. It respects both the complex nature of
human behavior and can improve the functionality of visual analytics systems.

Figure 2: The Tableau interface with a prototype dashboard with an epidemic
data set in the fictitious city of Vastopolis, used as the running example in
section 3. The text displays a map of social media posts with geolocation, a
search and filter sidebar, and a bar chart indicating post frequency over
three weeks.

##  3 How the Design of Visual Analytics Interface Impacts Predictability

In addition to the analyst’s characteristics, the interface design, the nature
of the data, and the task at hand can all greatly influence the predictability
of user behavior in these va scenarios. Well-designed interfaces typically
guide user behavior into predictable patterns by offering clear options and
intuitive paths for data exploration, whether intentionally or not. In
contrast, a disorganized layout may result in erratic and unpredictable
exploration paths, potentially leading users to overlook essential insights
and complicating user behavior prediction.

Consider the dashboard in Figure 2, which features a simple exploratory
interface for analyzing a geospatial dataset. The most dominant feature is a
map, occupying roughly seventy percent of the screen. This design choice
naturally focuses the user’s attention primarily on the map’s data points.
Additionally, given that users typically read from left to right, the
filtering options on the right side will likely be the next focus point,
followed by the bar chart at the bottom. Thus, predicting attention and high-
level areas of interest is feasible.

Interaction affordances, which suggest possible actions through design, also
play a crucial role. For example, the persistent visibility of filtering
options in Figure 2, instead of their placement in hidden menus, increases the
likelihood of their usage. Users will likely engage with the most accessible
actions, such as hover effects, more frequently. Other interactions, like
panning and zooming on the map, brushing on the timeline, or clicking on data
points, are less obvious due to the absence of explicit visual cues and might
be underutilized, especially by new users. The space of possible actions for
this interface is small. One might consider using a probabilistic approach to
predict action for this interface, encoding the assumed likelihood of
observing a specific action as priors and calculating the posterior
probability of observing an action given a set of observations.

Additionally, how data is represented dictates the questions an analyst can
ask and what they will likely notice and consider. In Figure 2, the
interface’s focus on geographical data through maps encourages the exploration
of spatial patterns and regional clusters and differences. Similarly, the
prominently displayed timeline and area chart at the bottom of the interface
are likely to prompt questions about temporal changes. The available filtering
options and zooming capabilities influence the depth and specificity of the
questions an analyst can pose. An interface that supports intricate data
manipulation enables analysts to formulate and test detailed hypotheses, while
a more static interface or those without interaction cues might confine them
to basic, surface-level observations. Predicting objectives and tasks will
require a mapping between them and the observable actions and their
association with the current area of interest[Gathani et al., 2022].

Now, suppose instead, we consider the interactions more broadly in the Tableau
interface or with other advanced statistical analysis tools. This would offer
more opportunities to delve into complex questions about correlations or
predictions. Moreover, the ability to customize the interface or create custom
visualizations significantly broadens the range of potential questions.
Analysts are not confined to predefined views and can adapt their analysis to
meet specific and unique investigative needs. Furthermore, the amount of data
the interface can handle also influences the questions that can be pursued.
Some interfaces, optimized for large datasets or real-time data, facilitate
queries about broad trends or immediate insights, while others are more
suitable for detailed analysis of smaller datasets. Although a more complex
system offers greater flexibility, increased degrees of freedom will decrease
the predictability of user behavior.

Overall, the interface design implicitly provides guidance or scaffolding to
shape the queries, analysis pathways, and questions an analyst considers. This
is especially significant for novice users still learning which questions can
be asked about data or how to use the system. Understanding these design
elements is crucial for developers of visual analytics systems to create
interfaces that facilitate data comprehension and guide users by observing
predictable and insightful data interactions.

##  4 Case Studies from Visualization Research

Prior work in visual analytics has demonstrated actions and scenarios where
behavior prediction was largely successful and the machine learning techniques
used to make these inferences [Xu et al., 2020]. This section highlights two
such papers.

Figure 3: The ForeCache project interface, which visualizes snow levels from
NASA MODIS data [Battle et al., 2016]. The authors used observed navigation
patterns to predict future interactions and pre-fetch data.

###  4.1 Predicting Navigation Paths for PreFetching

Battle et al. explored the feasibility of predicting user navigation behavior
to enhance database caching, a valuable feature for managing large datasets
with potential latency issues during database queries [Battle et al., 2016].
The project was inspired by previous research highlighted that latency can
negatively affect user experience and impede data exploration [Liu and Heer,
2014]. To mitigate this, they introduced dynamic prefetching, which predicts
necessary data to fetch in advance by analyzing users’ recent navigation
patterns.

#### Interface

The research team developed a map-based visualization tool for nasa’s modis
snowfall data across America. Given the high-resolution nature of the complete
dataset, the system aggregated data into lower-resolution tiles for an
overview and increased granularity during user zoom-ins. With its
straightforward design, this map interface was conducive to making accurate
predictions. It allowed only six observable actions: pan up, down, left,
right, and zoom in and out.

#### Task

The tasks assigned to the study participants were simple yet effective.
Participants were required to explore the data to identify areas with
significant snowfall, navigating and searching the interface for regions of
interest.

#### Participants

The study involved domain scientists, suggesting a uniform background and
likely shared expertise. This homogeneity in the participants’ backgrounds
helped minimize individual differences in skills and knowledge, creating an
optimal environment for limiting variability in user interactions.

#### Predictions

The researchers used a Markov chain model that predicted users’ actions. This
model was not pre-programmed but evolved by observing user interactions,
enabling the system to learn and update its predictions based on the user’s
current state. The evaluation of this dynamic prefetching strategy showed
substantial improvements in reducing latency compared to non-prefetching
systems (430% improvement) and significant enhancements in both prediction
accuracy (25% improvement) and latency reduction (88% improvement) compared to
existing prefetching methods.

While the simplicity of this scenario might seem unrepresentative at first
glance, it mirrors common situations in data foraging tasks, which are crucial
for the sensemaking process [Pirolli and Card, 2005]. Even when multitasking,
external actions manifest as sequential rather than concurrent [McFarlane,
1998, McFarlane, 2002, McFarlane and Latorella, 2002]. Moreover, divided
attention is limited by working memory capacity. Thus, the scope of actions
and inquiries at any given time window within a visualization is usually
confined. This indicates that the potential for predictive scenarios, like the
one in Battle et al.’s study, might be more widespread than initially assumed.
Their research provides a solid example of the types of predictions that are
feasible – specifically navigation and data foraging – within an accommodating
situational environment.

Figure 4: The interface used by Monadjemi et al. in evaluating their algorithm
that observes data exploration, infers the relevance of the other points in
the dataset and recommends content to the user [Monadjemi et al., 2022].

###  4.2 Predicting Data Interest for Content Recommendation

Similarly, Monadjemi et al. aimed to assist data exploration and information
foraging. Their approach involved analyzing users’ exploration patterns,
deducing the characteristics of data points likely to interest the user, and
recommending similar points for further exploration. Their primary objective
was to expedite data discovery, thereby boosting the efficiency of analytics
and enhancing the quality of decision-making.

#### Interface

For their evaluation, they adopted a scenario from the VAST 2011 challenge, an
annual competition in the visual analytics community focused on addressing
real-world challenges. This scenario revolves around a fictional city,
Vastopolis, which is grappling with a bio-chemical attack. The authors
developed a visualization interface showcasing a city map embedded with geo-
tagged social media posts from the past three weeks, providing a comprehensive
view of the unfolding situation. Like the ForeCache interface used by Battle
et al., the interface was straightforward for limited available actions. The
user can pan, zoom the map, and save or unsave relevant social media posts.

#### Task

The task assigned to participants was one of reconnaissance and information
foraging. Participants were required to explore the data to gauge the range of
symptoms being reported on social media. The goal was for them to gather data
that downstream analysts could use to understand the extent of the epidemic,
assess containment, and hypothesize potential causes. Given the vastness of
the dataset, each participant had a ten-minute time limit to identify
potentially sick individuals, acknowledging that completing the entire task
was beyond expectation.

#### Participants

The study involved 130 participants recruited through Amazon’s Mechanical Turk
platform. These individuals ranged from 18 to 65 years old, were based in the
United States, and were proficient in English. While they were not trained
analysts, exploring a dataset of social media posts to identify mentions of
illness was deemed manageable without specialized training.

#### Predictions

The team employed an active search methodology, translating social media posts
into numerical values using a standard word2vec model and constructing a
$k$-NN binary classifier using cosine similarity. As users engaged with the
map and bookmarked pertinent posts, the algorithm tagged these data points as
relevant. The model continuously updated its understanding of the data after
each interaction, reassessing the relevance of unlabeled points in light of
recent user actions. It then offered suggestions for additional points the
user might explore.

The analysis of the user study results revealed that the algorithm generated
useful recommendations 79% of the time, on average. Moreover, the data
revealed that participants who utilized the algorithm in their search were
significantly more efficient than those who did not. The assisted participants
discovered a statistically significant greater number of individuals
potentially affected by the illness. They also were more adept at
distinguishing relevant information from irrelevant data in the dataset.

In summary, Monadjemi et al.’s approach demonstrated the predictability of
data interesting in visual analytics, specifically in data foraging tasks
[Monadjemi et al., 2022]. By leveraging machine learning techniques to
interpret user interaction and guide further exploration, their system
accelerated the data discovery process and enhanced the effectiveness and
accuracy of the users’ information foraging activities. This study is a
testament to the potential of integrating intelligent predictive algorithms
into visual analytics systems, paving the way for more intuitive and
productive data analysis experiences.

Figure 5: The agent-based framework for visual analytics proposed by
[Monadjemi et al., 2023]. It adopts terminologies from ai and conceptualizes
visual analytics scenarios as interactions (observations and actions) between
agents and their environment.

##  5 A conceptual framework for human and AI collaboration

The previous section showed successful algorithms that observed human behavior
in real-time, predicted actions, and used these inferences to assist the user
by recommending exploration or pre-fetching data. However, to effectively
develop collaborative systems, it is crucial to establish a comprehensive
framework that recognizes the shared responsibilities and synergistic
partnership between human and AI entities [Crouser et al., 2013]. Traditional
conceptual models in visual analytics have often been limited in scope
[Monadjemi et al., 2023], focusing predominantly on human cognitive processes
[Pirolli and Card, 2005], treating the visual analytic interface as a mere
tool without autonomy [Van Wijk, 2005, Van Wijk, 2006], or maintaining an
imbalanced perspective of the intelligent system, where AI is viewed as having
limited capabilities compared to the human’s ultimate authority [Sperrle et
al., 2022, Ceneda et al., 2017].

However, looking forward to a future where responsibilities are more evenly
distributed between humans and AI, broadening these frameworks is imperative.
Such an expansion should accommodate the potential for each entity to act as a
check and balance against biases that might arise from either side, as
proposed by [Wall et al., 2021] and [Ha et al., 2022]. Additionally, it’s
important to consider scenarios involving multiple human and AI agents
collaborating on a single task, employing a ‘divide and conquer’ approach.
This revised framework must account for the dynamic interactions between
humans and AI, recognizing the unique strengths and limitations of each. In
doing so, we can foster systems where collaboration is about task division and
mutual learning and support, leading to more robust and effective problem-
solving strategies.

###  5.1 An Agent-based Framework

One possible collaborative model is the agent-based framework originally
introduced in [Monadjemi et al., 2023] and summarized in Figure 5. It draws
parallels between human cognitive processes and AI modeling and advocates for
a unified language for the visual analytics and ai communities. This approach,
rooted in the well-established ai literature, simplifies complex problems by
conceptualizing them as interactions between agents and their environments.
Developers and researchers can tailor the specification of this model to their
specific contexts and applications.

Applying the agent-based model to visual analytics presents an opportunity to
enrich our comprehension and improve the dynamics of human-AI interactions
within this domain. In this context, visual analytic agents can be either
human or artificial entities. The model envisions that all agents are capable
of both observation and action, contributing toward a collective analytical
goal.

Human agents here are broadly defined and are data scientists, decision-
makers, domain experts, or novice users. The prior research on understanding
the diverse needs of these groups (e.g., [Wong et al., 2018]) or those that
explore how individual differences might influence analytical workflows [Liu
et al., 2020, Ottley, 2022] can inform the model’s specifications and
considerations. Additionally, developers can consider studies on how humans
perceive data (e.g., [Xiong et al., 2022, Bancilhon et al., 2020]) and the
nature of actions undertaken during analytical sessions (e.g., [Gotz and Zhou,
2009, Brehmer and Munzner, 2013, Gathani et al., 2022]).

Artificial agents can consist of modeling algorithms, guidance systems, and
automated processes interacting within the environment to assist in
collaborative analytical tasks. Prior research in this area has focused on
designing artificial agents capable of identifying patterns in data (e.g. [Kim
et al., 2019, Ha et al., 2022]), learning from user interactions (e.g., [Brown
et al., 2012, Ottley et al., 2019]), and assisting users throughout their
analytical sessions (e.g., [Dabek and Caban, 2016, Monadjemi et al., 2022]).
This body of work also highlights the evolving capabilities and contributions
of both human and artificial agents in visual analytics, underscoring the
potential for synergistic collaboration between these entities in achieving
analytical objectives.

This agent-based approach provides a framework for analyzing complex
interactions in visual analytics. It also creates opportunities for innovative
solutions and advancements in the field. By considering humans and AI systems
as agents within a visual analytics environment, we can analyze and improve
their interactions, decision-making processes, and information processing in a
more effective way.

##  6 Discussion and Future Work

The purpose of this paper is to establish the groundwork for the creation of
intelligent visual analytics systems that can seamlessly interact with humans.
However, given the intricate nature of human behavior and their interaction
with AI, there are both obstacles and prospects that need to be addressed to
progress in this field. This section will outline the primary challenges that
must be overcome to advance this promising area.

###  6.1 Understanding Predictable and Unpredictable Human Behaviors

The advancement of intelligent visual analytic interfaces hinges on their
capability to fluidly navigate between handling routine, predictable tasks and
engaging with tasks that demand a more intricate and nuanced comprehension of
human behavior. The existing body of work, as delineated in section 4,
presents initial examples of predicted actions and tasks. However, this area
is still in its early stages of development. The examples in section 4 suggest
we can use techniques such as Markov models and active learning algorithms to
learn from interactions during data foraging and simple search tasks [Battle
et al., 2016, Monadjemi et al., 2022]. Still, examples of predictive
algorithms validated with real user data are few and limited [Ha et al.,
2022]. There is still much to do.

To advance this area of research, it is crucial to develop more accurate and
reliable predictive algorithms that can be validated with real user data. This
will require a deeper understanding of human behavior and the development of
more sophisticated data analysis techniques. Nonetheless, intelligent visual
analytic interfaces have vast potential benefits and can revolutionize the way
we interact with complex data. Additionally, the community needs to establish
protocols for handling situations where the ai’s confidence in its predictions
is low, as well as expanding the bandwidth of communications between agents.
Future research is essential for understanding individual variances, how to
offer personalized experiences, and how to adjust to users’ evolving needs and
behaviors. Therefore, it is important to continue to invest in this area of
research and development to unlock its full potential. Moving forward in this
field requires not just technological advancements, but also a
multidisciplinary approach involving psychology, cognitive science, and
behavioral studies.

###  6.2 Integrating Multi-agent System

With data analysis’s growing complexity, more sophisticated tools and
techniques are needed to help analysts efficiently and effectively sift
through large amounts of data. One promising area of research is multi-agent
systems for visual analytics. These systems would feature multiple human and
artificial agents, each with specialized skills, working collaboratively to
analyze complex data sets. For example, a human agent could provide the system
with domain-specific knowledge, while an artificial agent could perform data
processing tasks that are beyond human capability. Another agent could be
responsible for data visualization, using its expertise to create interactive
and intuitive visualizations, presenting the right data at the right time.

However, managing the task allocation and coordination among different agents
presents a significant challenge. It is essential to ensure that each agent’s
strengths are utilized effectively and that they work together seamlessly.
This requires developing methods for seamless interaction between diverse
agents.

One of the significant challenges in multi-agent systems is developing
communication protocols that enable agents to share information effectively.
Conflict resolution is also a critical concern, as different agents may have
differing opinions or interpretations of the data. Additionally, it is crucial
to establish a decision hierarchy that ensures that each agent’s contribution
is valued appropriately.

In conclusion, research in multi-agent systems for visual analytics is a
promising area that could lead to more effective and efficient data analysis.
However, to realize its full potential, it is necessary to address the
challenges associated with effectively managing and coordinating multiple
agents with diverse skill sets.

###  6.3 Addressing Ethical Concerns

It is crucial for users to trust ai algorithms, and transparency in how they
function is a key factor in building that trust. This means that algorithms
should be designed in a way that is open and clear about how they make
decisions and that they can be audited for any biases. One way to make ai
decision-making more understandable to humans is through the use of
Explainable ai (xai) techniques.

It is important to make sure that the results produced by ai systems are fair
and unbiased. This is especially crucial when decisions based on these results
can have significant consequences. To achieve fairness, it is necessary to
continuously monitor and evaluate the ai systems, and identify and address any
biases that may arise. Collaborating with experts in ethics, sociology, and
relevant fields can provide valuable insights into the societal implications
of ai decisions, and help create more equitable algorithms.

##  7 CONCLUSIONS

This paper discusses the necessary advancements required to improve
intelligent visual analytics systems. We highlight the importance of
recognizing the full spectrum of human behavior and examine existing user
models that can learn and predict from interaction data. We also suggest
expanding the human-machine teaming model and adopting an agent-based model
framework that recognizes the potential for collaboration between humans and
AI. In addition, we emphasize the need to consider ethical and contextual
dimensions while designing such systems, and we discuss other potential future
directions. By focusing on these areas, we can create systems that assist and
enhance human capabilities in data analysis, embodying a true partnership in
the dance of discovery and decision-making.

## ACKNOWLEDGEMENTS

I thank Stefan Jänicke and Helen C. Purchase for inviting me to deliver the
keynote speech at ivapp 2024, which is the basis of this manuscript. I also
would like to express my gratitude to Sunwoo Ha for her valuable feedback and
to Leilani Battle for allowing the use of her system’s imagery. This material
is based upon work supported by the U.S. National Science Foundation under
grant numbers iis-2142977 and oac-2118201.

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# High Pressure RTSC-Hydrides are Extreme Hard Type-II Superconducors

1,2Miodrag L. Kulić  1Institute for Theoretical Physics, Goethe-University
Frankfurt am Main, Germany
2Institute of Physics, 11080 Belgrade, Serbia

###### Abstract

InHirsch-1  the authors have called into question the existence of the room-
temperature superconductivity (RTSC) in hydrides, as well as the electron-
phonon interaction as the pairing mecanism. Basically, in Hirsch-1  they
assume, that these materials are soft type-II superconductors with point-like
defects as pinning centers. We show here, that $\mathit{RTSC-hydrides}$
$\mathit{are}$ $\mathit{hard}$ $\mathit{type-II\textrm{ }superconductors}$,
with strong pinning centers in form of $\mathit{long}$ $\mathit{columnar}$
$\mathit{defects,}$with length $\mathit{L_{col}}$ much larger than the
superconducting coherence length $\xi(T)$ and penetration depth $\lambda(T)$.
It is shown that the $\mathit{elementary}$ $\mathit{pinning}$
$\mathit{energy}$ for the vortex lying along the long collumnar deffect is
given by $\mathrm{U_{col}\thickapprox U_{point}(L_{col}/\xi)}$. At low
temperatures it gives rise to high critical current density
$\mathrm{j_{c}\backsim 10^{8}A/cm^{2}}$, which is of the order of depairing
current in hydrides. This theory predicts, that the temperature width of the
resistivity broadening (TRB), calculated in the Thinkam theory, depends on
$\mathrm{L_{col}}$, i.e. $\mathrm{\mathrm{\varDelta
T}\sim\left(B\xi_{0}/L_{col}\right)^{1/2}}$. Since
$\mathrm{(\xi_{0}/L_{col})<10^{-4})\textrm{,}}$this width $\mathrm{\Delta
T=\mathit{T_{c}(}1-t)}$ is at least $\mathit{100}$ times smaller in RTSC-
hydrides, than that predicted in Hirsch-1  for standard superconductors.
However, in the C-S-H superconductor with $\mathrm{T_{c}}$$\mathrm{=287}$
$\mathrm{K}$ the experimental TRB is almost field independent, which probably
needs a revision of the Tinkham theory. In an extreme hard type-II
superconductor irreversible phenomena are pronouced and the penetration
(trapping) of the field in and the magnetization hysteresis are treated in the
model of the Bean’s critical state with long columnar pinning centers. For
instance, by assuming that the collective pinning is realized in fields
$\mathit{H\gg H_{c1}}$ one expects a significant shift up of the
irreversibility line $\mathit{B\sim(1-t)^{2}(L_{col}}/\xi).$ Due to the
intrinsic hardness of the RTSC-hydrides they are promissing candidate for
producing high critical currents, especially if they would be realized in
systems which are in metastable state at low pressure.

##  I Introduction

The first room-temperature superconductor is reported in 2015 in sulphur-
hydrides ($H_{3}S$) under high pressure $P\approx 150$ $GPa(\approx 1.5$
$Mbar)$ Drozdov . This opened a new frontier in physics and number of other
RTSC-hydrides were sinthesized. Let us mention some of them with
$\mathrm{T_{c}}$$\geq 200$ $\mathrm{K}$, for instance
$LaH_{10}$$\textrm{with}T_{c}\approx 250$ LaH10 , $\mathrm{LaYH}$x with
$\mathrm{T_{c}}$$\mathrm{=253}$ $\mathrm{K}$ Semenok , C-S-H with
$\mathrm{T_{c}}$$\mathrm{=287}$ $\mathrm{K}$ at $\mathrm{P}$$\approx 267$. In
that sense, the most promissing candidate for the highest $\mathrm{T_{c}}$ is
the metallic hydrogen ($H$) which is the lightest atom in nature. One expects,
that in the metallic crystal state it could give as high as $T_{c}\sim 600$
$K$, as it is theoretically predicted by Maksimov an Savrasov in their seminal
(but rarely cited!) paper in $\mathrm{2011}$ Maks-Savras-H . The pairing in
the hydrogen-based systems is certainly due to the strong electron-phonon
interaction (EPI) via high-frequency $H$-phonons. The pronounced isotope
effect with $\alpha\sim 0.3$ (in the pure EPI theory for light atoms, such as
$\mathit{H}$, even without effects of Coulomb $\mu*$ term, $\alpha$ is smaller
than the bookkeeping value $\mathit{\mathrm{0.5}}$ (!)), is a clear evidence
for the EPI pairing in RTSC-hydides - see Gorkov-Kresin , Kulic-rtsc . More on
the pairing mechanism, especially on the role of the EPI, in RTSC-hydride and
other high-temperature superconductors such as cuprates and Fe-based materials
will be published elsewhere Kulic-rtsc .

Many properties of RTSC-hydrides are unusual, since it turns out, that they
are extreme hard type-II superconductors with $\lambda\gg\xi$, which can not
be explained by the theory of soft superconductors. Namely, in soft
superconductors vortices are mainly pinned by randomly distributed “point”
defects Larkin ,Civale-rev , where the elementary pinning force of a “point”
defect is due the gain in the condensation energy when the vortex core is
sitting on the defect. The mechanism is simple, since in the “point” defect,
with the volume $V_{d}$, the superconductvity is completelly destroyed (with
$\varDelta=0\textrm{)}$ and the condensation energy
$\mathrm{E_{loss}}$$\sim(\mathrm{H_{c}^{2}}/8\pi)$$\mathrm{V_{d}}$is lost. So,
if the part of the vortex (which core of the radius $\xi$ is in the normal
state and the condensation energy is also lost) is sitting on the “point”
defect, then the loss of the condensation energy is minimized. However, in
order to maximize the pinning force the radius of the defect should be
$\sim\xi$ and $\mathrm{V_{d}}\sim\xi^{3}$(very small defects with
$\mathrm{d}$$\ll\xi$ are inapropriate since $\mathrm{V_{d}\sim\xi d^{2}}$ is
small). This means that the gain of the energy is small due the smallness of
the “point” defect, while the Lorenz force acts on the whole vortex line. As
the result the critical current of the single “point” defect is small. On the
other side, in the presence of large densities of the “point” defects (which
are uncorrelated) two facts are against strong pinning. First, vortices can
deform in the zig-zag form, thus gaining pinning energy, but the zig-zag
vortex line increases its elestic energy. Additionally, each vortex interacts
with many (on the average uniformely) distributed defects, thus giving on the
average zero pinning force on it. However, there is still pinning due to the
local fluctuations of defects density but the pinning force is small, since
the maximum pinning force on the volume $\mathrm{V_{c}}$ is
$\mathrm{F_{V_{c}}}$$\backsimeq f_{p}$$\sqrt{N}$. Here, $\mathrm{N=nV_{c}}$ is
the number of the pinning centers in the volume $\mathrm{V_{c}}$and
$\mathrm{f_{{}_{p}}}$is the elementary pinning force. The critical current
density is given by
$\mathrm{\mathrm{j_{c}}B=f_{p}\sqrt{N}/V_{c}}=\mathrm{f}$${}_{p}(n/V_{c})^{1/2}$
Larkin .

Therefore in order to obtain larger critical currant it is desirable to have
$\mathrm{long}$ ($\mathrm{of}$ $\mathrm{length}$ $\mathrm{L}$)
$\mathrm{defects}$ as pinning centers, with the large pinning volume
$\mathrm{V_{d}}$$=\pi\xi^{2}$$\mathrm{L_{col}}$ and the pinning energy
$\mathrm{U_{p}=u_{p}V_{col}}.$ In the case of the vortex (with length
$\mathrm{L_{v}>L_{col}}$sitting on such a defect the critical current density
is

$j_{c}=\frac{c}{\varPhi_{0}}\times\frac{u_{p}\mathrm{V_{col}}}{\xi
L_{v}}=\frac{c}{\varPhi_{0}}\times(\pi u_{p}\xi)\frac{L_{col}}{L_{v}}.$ (1)

It is clear, that in order to optimize the critical current density it is
desirable to have defects with the same length as the vortex line, i.e
$\mathrm{L_{col}\approx L_{v}}$ Kulic-CD  and with the maximal possible
density of the pinning energy $\mathrm{u_{p}.}$

Let us mention, that in the high-temperature superconductors the long pinning
defects were realized in the form of long columnar defects by irradiating
$\mathrm{YBa_{2}Cu_{3}O_{{}_{7}}}$ single crystals with 580 MeV
$\mathrm{{}^{116}Sn^{30+}}$ ions, which produced long tracks with the length
$\mathrm{L_{col}\sim 20\mu m}$ and the diameter 50Å. In that case
$\mathrm{j_{c}}$ reached $\mathrm{1.5}$$\times 10^{7}$$\mathrm{A/cm^{2}}$ at
$\mathrm{T=5K}$ and $\mathrm{10^{6}A/cm^{2}}$at $\mathrm{T=77K}$ Civale ,
which are much higher than in the case of “point” defects. Also, the
irreversible lines $\mathit{B}$${}_{ir}(T)$ lie much higher than in the case
of the “pont” defects.

In the following we argue, that the vortex pinning by such long defects is
intrinsic property of the RTSC-hydrides. First, we introduce the model of
vortex pinning by long columnar defects where both, the core and
electromagnetic pinning, contribute almost equally to $\mathrm{u_{p}.}$ This
is the most optimal situation for pinning. Next, the model is applied to some
ireversible prperties in the RTSC-hydrides, such as temperature resistivity
brodening in magnetic field, critical current in the Bean-model as well as
hysteresis in magnetization.

##  II Pinning of vortices by long columnar defects

In Fig.1 are shown shematically columnar defects - blue coloured cylinders,
which strongly pin vortex lines in RTSC-hydrides, giving rise to large
magnetization hysterezis and critical current density in $\mathit{H}$${}_{3}S$
see Troyan-1 . For simplicity we first analyze isotropis systems Kulic-CD . It
turns out that for the optimal pinning superconductivity is destroyed inside
the defect, i.e. $\Delta=0$ and the radius of the columnar defect should be
small $\mathrm{\xi<R\ll}$$\lambda$ Kulic-CD . In this case both mechanism of
pinning, the core and electromagnetic one, are operative and with almost the
same energy Kulic-CD , $\mathrm{U_{p}=U_{core}+U_{em}}\approx 2U_{cor}$, where
$\mathit{U}_{p}$$\approx
2\pi\xi^{2}L_{col}(H_{c}^{2}/8\pi)=2L_{col}\Phi_{0}^{2}/(8\pi\lambda)^{2}$.
Since the pinning force (per unit vortex length $\mathit{L_{v}}$)
$f_{p}=$$\mathit{U_{p}/\xi L_{v}}$ in the critical state is balanced with the
Lorenz force (per unith length) $\mathit{f_{L}=j_{c}\Phi_{0}/c}$ then the
critical current density is given by Kulic-CD

$j_{c}=\frac{c\Phi_{0}}{32\pi^{2}\lambda^{2}\xi}\left(\frac{L_{col}}{L_{v}}\right).$
(2)

It is obvious that the critical current is maximized when the length of
columnar defect is equal to the vortex length, i.e. $\mathit{L_{col}=L_{v}}$.
In the case of anisotropic superconductors when the axis of the columnar
defect and the vortex are parallel to the crystal axis $\gamma$ and the
current flows along the $\beta$–axis (but
$\alpha\neq$$\beta\neq\gamma\textrm{) it }$holds Kulic-CD

$j_{c}^{\gamma,\beta}=\frac{c\Phi_{0}}{32\pi^{2}\lambda_{\alpha}\lambda_{\beta}\xi_{\alpha}}\left(\frac{L_{col}}{L_{v}}\right).$
(3)

If one assumes that in RTSC-hydrides at $\mathit{T\ll T_{c}}$ one has Drozdov
$\lambda\sim 10^{3}\textrm{\r{A}}$ and $\xi_{0}\sim 20\textrm{\r{A}}$ Drozdov
it follows that $\mathit{10^{7}(A/cm^{2})<j_{c}}$$\leq 10^{8}A/cm^{2}$, which
is of the order of depairing current density.

##  III Temperature broadening of resistivity in magnetic field

The papers by Hirsh and Marsiglio Hirsch-1 , Hirsh-Meissner  are stimulativ in
understanding the physics of superconductivity in the RTSC-hydrides and
therefore deserve tribute, inspite of some controversing claims. Namely, they
were first to pay attention to some very pronounced differences in properties
of RTSC-hydrides and standard superconductors, by including HTSC-cuprates and
Fe-based superconductors. For instance they point, that the temperature
broadening of resistivity ($\mathit{TBR}$) $\Delta T$ in several RTSC-hydrides
is much smaller than in standard superconductors by at least two order of
magnitude. If one interprets this fact in the framework of soft
superconductors it is necessery to invoke unrealistically high critical
current density of the order $\mathrm{10^{11}A/cm^{2}}$Hirsch-1 . Here, we
argue that this effect can be explained by assuming that RTSC-hydrides are
hard type-II superconductors with many intrinsic long pinning defects. Let us
briefly introduce the reader into the subject, which is based on the Tinkham
theory for $\mathit{TBR}$ Tinkham-1 .

Figure 1: Shematic view of the experiment of the flux trapping and penetrating
in the $H_{3}S$ sample Troyan-1 : $\mathit{D=30\mu m;}P=5\mu m$. The non-
superconducting Sn foil ($\mathit{yelow}$) for detection of the penetrated
magnetic field: $\mathit{d=20\mu m;}p=2.6$$\mu m.$ Long columnar defects
($\mathit{blue}$ $\mathit{cylinders}$) strongly pin and trapp vortices making
huge magnetization hysterezis and critical current density
$\mathit{j_{c}\sim\Delta M}$.

Practically in all superconductors there are some defects which pin vortices
allowing a dissipationless current to flow even in the vortex state. However,
when the pinning energy is small there is a possibility that vortices under
temperature fluctuations jump from one center to another thus giving rise to
vortex motion and dissipation of energy. This jumps are activation-like and
proprtional to the escape (from the pinning center) probability
$\mathit{exp(-U_{p}/T)}$ \- this is so called flux creep Anderson . Since for
small defects$\mathit{U_{p}}$$\sim\xi^{3}$ then this energy barrier is small
in superconductors with small $\xi$ what is the origin of prononced
dissipation in HTSC-cuprates due to small $\xi$. In that sense, a long pinning
defect with $\mathit{U_{p}}$$\sim L_{col}\xi^{2}$ make this barier much
higher, thus suppressing the dissipation defects.

Figure 2: Low temperature electric resistance in magnetic field: H=0T, 1T, 3T,
6T and 9T ($\mathit{increasing}$ $\mathit{from}$ $\mathit{right}$
$\mathit{to}$ $\mathit{left}$) at 267 GPa - from Snider . Temperature
broadening of resistivity is extremely small due to strong pinning by columnar
defects.

In magnetic fields much higher than the lower critical field
$\mathit{H_{c1}\ll H<H_{c2}}$one has $\mathit{B\approx H}$ and the vortex
dinstance is given by $\mathit{a\approx l(\Phi_{0}/B)}\ll\lambda$ and the so
called collective pinning of vortices should work (at least it was useful for
HTSC-cuprates) - where the bundlle of vortices are pinned. In that case, one
has $\mathit{U_{p}}$$\sim L_{coll}a^{2}$ (instead of $\mathit{U_{p}}$$\sim
L_{col}\xi^{2}$ for the single vortex pinning). The Thinkam developed the TRB
theory which is based on the Ambegaokar and Halperin theory for the thermaly
activated phase motion in Josephson junctions Ambegaokar . As the result one
obtains the formula for the resistance in superconductors for small currents
Tinkham-1

$R/R_{N}=\left[I_{0}(\gamma_{0}/2)\right]^{-2},\gamma_{0}=U_{p}/T.$ (4)

$\mathit{R}$Nis the resistance of the normal state at $\mathit{T}_{c}$. The
modified Bessel function $\mathit{I_{0}}$gives the asymtotics for
$R/R_{n}\sim\gamma_{0}^{2}$ for $\gamma_{0}<1$ and
$R/R_{n}\sim\gamma_{0}exp(-\gamma_{0})$ for $\gamma_{0}\gg 1$ Tinkham-1 ,
where $\gamma_{0}$ is the dimensionless pinning barrier with respect to
temperature. In the model with long columnar pinning centers and near
$\mathit{T_{c}}$ one has

$\gamma_{0}^{col}=\beta_{K}\frac{L_{col}}{\xi_{0}}\frac{(1-t)^{2}}{b}(2\pi\xi_{0}^{2}\frac{j_{c}(0)\Phi_{0}}{cT_{c}}),$
(5)

where $\mathit{b=B/H_{c2}(0)}$ and $\beta_{K}\approx 1$. In the case of the
“point” defects one has

$\gamma_{0}^{st}\approx\frac{(1-t)^{3/2}}{b}(2\pi\xi_{0}^{2}\frac{j_{c}(0)\Phi_{0}}{cT_{c}}),$
(6)

where $\gamma_{0}^{st}$ is the prediction of the standard Thinkam theory. From
the above equations it is seen that relative barrier in the long columnar case
is larger by factor $\mathit{L_{col}/\xi(T)}$, than the one for the “point”
defects. Let us compare the prediction of the satandard theory Tinkham-1  with
the new one. Let us assume, that we analyze the case when the resistance is
measured at the 10% level, i.e. $\mathit{R/R_{N}=0.1}$ for the field
$\mathit{B\approx 1T}$ and $\mathit{H_{c2}(0)\approx 100T},$i.e.
$\mathit{b=10^{-2}}$. This means that
$\gamma_{0}^{col}=\gamma_{0}^{st}\equiv\gamma_{0}$. Since,
$\mathit{I_{0}(\gamma_{0}/2)=3}$ one has $\gamma_{0}\approx 5$. We assume the
following realistic parameters for the RTSC-hydrides: $\xi_{0}\approx
20\textrm{\r{A}}$, and $\mathit{j_{c}}$$\sim 10^{8}A/cm^{2}$ (in cgs units
$\mathit{j_{c}}$$\sim 3\times 10^{17}esu/cm^{2}$, $\mathit{T_{c}}$$\sim 200K$,
$\Phi_{0}\approx 2\times 10^{-7}G\times cm^{2},$ $\mathit{L_{col}\sim 20\mu
m}$. As the result we obtain for $(\Delta T)/T_{c}$$\approx 2\times
10^{-2}$and the ratio

$\frac{(\Delta T)^{col}}{(\Delta T)^{st}}\sim 5\times 10^{-2}.$ (7)

This result means, that by assuming long columnar pinning defects the
temperature broadening of the resistance is much smaller than in standard
superconductors. This is encoriging result having in mind that the Thinkam
theory might be not quite appropriate for all RTSC-hydrides. This is
demonstrated in Fig.2 where the line broadening das not depend on the magnetic
field. It might be, that the collective pinning theory with
$\mathit{a\sim(\Phi}$/$\mathit{B)^{1/2}}$ is not guaranted in systems with
long and strong pinning defects. This is a matter for further investigation.

##  IV Discussion and conclusions

That the RTSC-hydrides are hard type-II superconductors with strongly pinned
vortices in magnetic field is clearly shown in an inventive experiment by
Troyan et al. Troyan-1 . In the setup shown schematiclly in Fig.1 they have
intended to study the Meissner effect in $\mathit{H}_{3}$$S$ hydride. It was
expected that in the magnetic field $\mathit{H=0,68T}$, which is much larger
than the first critical field $\mathit{H_{c1}}$, that the vortices penetrate
into the sample, what should be detected by the NRS technique in the non-
superconducting Sn foil (yelow in Fig.1). However, even in such a large field
the vorticies do not show up in the Sn foil. This means that they are trapped
in the $\mathit{H}_{3}$$S$ sample, where the magnetization is highly
inhomogeneous and hysteretic. This is strong evidence that the pinning in
$\mathit{H_{3}S}$ is huge. By using the Bean critical state model and the fact
that vortices pentrate into the sample only the distance $\mathit{(D-d)/2}$
and that they are pinned along some long defects with the length
$\mathit{P=50\mu m}$, one obtains that the critical current density is of the
order $\mathit{\mathrm{j_{c}\sim(10^{7}-10^{8})A/cm^{2}}}$. To this point,
recently has appeared very interesting arXiv preprint by Hirsh and Marsiglio
Hirsh-Meissner , were they have realized that their interpretaion of the
Troyan’s paper as the Meissner effect was inadequate. Namely, if it were true
this would mean that the critical current density should be enorm $\sim
10^{11}A/cm^{2},$what is impossible. Since there is a pronounced magnetization
hysteresis they propose the exsistence of strong pinning in the system. They
predict much smaller but realistic critical current density $\sim
10^{7}A/cm^{2}$.

In this paper we assume the existence of long pinning defects in the columnar
form, and the pinning of vorties take place on long defects. As the result of
the strong pinning in RTSC-hydrides, the temperature broadening of the
resistance in magnetic field is drastically smaller than the standard theory
predicts. This reduction is due to the small factor $\xi_{0}/L_{col}$. These
columnar defects cause also large magnetization hysteresis $\Delta M$ \- see
Troyan-1  and accordingly high critical current density $J\sim\Delta M.$ The
irreversible line of the magnetic has the form
$\mathit{H\sim(1-t)^{2}L/\xi_{0}}$, i.e. it is drastically increased compared
to the situation in HTSC-cuprates.

There is an intriguing question - what is the physical origin for these long
defects in RTSC-hydrides? Answering on this question will probably open a new
physicsin hard type-II superconductors.

###### Acknowledgements.

The author would like to thank Professor Dirk Risshke for his support, both
scientific and moral, which has lasted a very long time. I am thankful to Dr
Igor Kulić for discussions and support.

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