# Electronic structure of ACo2As2 (A = Ca, Sr, Ba, Eu) studied using angle-
resolved photoemission spectroscopy and theoretical calculations

R. S. Dhaka  Corresponding author<EMAIL_ADDRESS>The Ames
Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State
University, Ames, Iowa 50011, USA  Department of Physics, Indian Institute of
Technology Delhi, Hauz Khas, New Delhi-110016, India  Y. Lee  The Ames
Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State
University, Ames, Iowa 50011, USA  V. K. Anand  Present address: Department of
Physics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand,
248007, India The Ames Laboratory, U.S. DOE and Department of Physics and
Astronomy, Iowa State University, Ames, Iowa 50011, USA  Abhishek Pandey
Present address: Materials Physics Research Institute, School of Physics,
University of the Witwatersrand, Johannesburg, Gauteng 2050, South Africa The
Ames Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State
University, Ames, Iowa 50011, USA  D. C. Johnston  The Ames Laboratory, U.S.
DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa
50011, USA  B. N. Harmon  The Ames Laboratory, U.S. DOE and Department of
Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA  Adam
Kaminski  The Ames Laboratory, U.S. DOE and Department of Physics and
Astronomy, Iowa State University, Ames, Iowa 50011, USA

###### Abstract

We present a comprehensive study of the low-energy band structure and Fermi
surface (FS) topology of ACo2As2 (A = Ca, Sr, Ba, Eu) using high-resolution
angle-resolved photoemission spectroscopy. The experimental FS topology and
band dispersion data are compared with theoretical full-potential linearized
augmented-plane-wave (FP-LAPW) calculations, which yielded reasonably good
agreement. We demonstrate that the FS maps of $A$Co2As2 are significantly
different from those of the parent compounds of Fe-based high-temperature
superconductors. Further, the FSs of CaCo2As2 do not show significant changes
across its antiferromagnetic transition temperature. The band dispersions
extracted in different momentum $(k_{\it x},k_{\it y})$ directions show a
small electron pocket at the center and a large electron pocket at the corner
of the Brillouin zone (BZ). The absence of the hole FS in these compounds does
not allow nesting between pockets at the Fermi energy (EF), which is in
contrast to AFe2As2-type parent compounds of the iron-based superconductors.
Interestingly, we find that the hole bands are moved 300–400 meV below $E_{\rm
F}$ depending on the $A$ element. Moreover, the existence of nearly flat bands
in the vicinity of $E_{\rm F}$ are consistent with the large density of states
at EF. These results are important to understand the physical properties as
well as the possibility of the emergence of superconductivity in related
materials.

##  I Introduction

Understanding the origin of the unconventional pairing mechanism in high-
temperature superconductors, cuprates Bednorz86 ; Schilling93 ; Chu93  and
iron pnictides Kamihara08 ; Takahashi08 ; XHChen08 ; GFChen08 ; Rotter08 ;
Yuan09 ; Cruz08 ; SefatPRL08 ; WangSc11 , is one of the most challenging
issues in condensed-matter physics. In particular, the superconductivity (SC)
in the iron pnictides has received enormous attention to find its intimate
connection with the magnetic ordering Johnston10 ; CanfieldRev10 . For
example, the parent compound BaFe2As2 shows a phase change from high
temperature tetragonal to low temperature orthorhombic structure at $\approx
135$ K along with an associated antiferromagnetic (AFM) spin density wave
(SDW) transition. It is well known that the common method to induce high-Tc
superconductivity in these materials is to suppress the SDW ground state by
different ways such as partial chemical substitution and/or application of
external pressure Takahashi08 ; XHChen08 ; GFChen08 ; Rotter08 ; Yuan09 ;
Cruz08 ; SefatPRL08 ; Johnston10 ; CanfieldRev10 . One of the most intriguing
aspects is to study how the long-range magnetic order and superconductivity
are related in these materials Cruz08 ; PrattPRL09 . In this context,
investigation of the electronic structure and Fermi surface (FS) topology
using angle-resolved photoemission spectroscopy (ARPES) is vital LiuPRB09 ;
YangPRL09 ; ZhangPRL09 ; KondoPRB10 ; LiuPRL09 ; YiPRB09 ; DhakaPRL11 ;
LiuNP10 . The FS of BaFe2As2 consists of a hole (at the $\Gamma$ point) and an
electron (at the $X$ point) pockets, and their similar volumes suggest that
the material is compensated since the number of electrons and holes are equal.
The nesting between the hole and the electron FSs can give SDW ordering
SinghPRL08 ; Mazin10 ; MazinPRL08  and play a pivotal role in driving the
antiferromagnetic-paramagnetic phase transition Cruz08 ; Mazin10 ; DhakaPRL13
. The FSs of these materials show a remarkable reconstruction at low
temperature due to the presence of an AFM SDW phase LiuPRB09 ; YangPRL09 ;
ZhangPRL09 ; KondoPRB10 ; LiuPRL09 ; YiPRB09 , and the suppression of magnetic
ordering is linked to the onset of the SC dome DhakaPRL11 ; LiuNP10 .
Interestingly, when Fe is replaced by Co in BaFe2As2, a rigid-band-like change
in the band structure occurs and Lifshitz transitions are observed both at the
onset and offset of the SC dome LiuNP10 ; LiuPRB11 ; Thirupathaiah ; Brouet ;
Sekiba ; Ideta . On the other hand, no significant changes in the FS and band
structure were observed for isoelectronic Ru substituted BaFe2As2 across the
SC dome DhakaPRL11 ; LiuPRB15 .

Therefore, one approach is to completely substitute Co/Ru at the Fe site and
investigate how the band structure and FS topology are related to the magnetic
ordering as well as the SC in these materials. In this direction, very
interesting structural and magnetic properties of ACo2As2,(A = Ca, Sr, Ba, Eu)
compounds have been reported VivekPRB14 ; BingPRB19 ; SangeethaPRB18 ;
SapkotaPRL17 ; DingPRB17 ; JayasekaraPRB15 ; Ying12 ; Cheng12 ; Bishop10 ;
Sefat09 ; Pandey13 . For example, powder x-ray diffraction and magnetization
measurements on CaCo2As2 demonstrate the structure to be collapsed-tetragonal
and A-type collinear AFM order is observed below T${}_{\rm N}=$ 52 K,
respectively VivekPRB14 . However, the resistivity and specific heat
measurements show no evidence of the magnetic transition in CaCo2As2
VivekPRB14 . On the other hand, BaCo2As2 exhibits paramagnetic behavior and no
magnetic ordering is reported down to 1.8 K Sefat09 ; AnandPRB14 .
Interestingly, these materials crystallize in the ThCr2Si2-type tetragonal
structure and the $c/a$ ratio of SrCo2As2 is found to be 2.99, which is
intermediate to those of normal-tetragonal BaCo2As2 ($c/a=$ 3.20) exhibiting
ferromagnetic correlations and collapsed-tetragonal-antiferromagnetic CaCo2As2
($c/a=$ 2.58) Pandey13 . Furthermore, the magnetization, NMR, and neutron
diffraction measurements of SrCo2As2 show no evidence for long-range magnetic
ordering above 0.05 K Pandey13 ; Jasper08 ; Jayasekara13 ; BingPRB19 . This is
consistent with the isostructural BaCo2As2 Sefat09 , but is in contrast to the
AFM behavior of CaCo2As2 VivekPRB14 ; Ying12 ; Cheng12 . More interestingly,
SrCo2As2 shows a negative (positive) thermal expansion coefficient along the
$c$ ($a$)-axis in the temperature range from $\approx$7 K to 300 K Pandey13 .
Also, the structural properties of EuCo2As2 indicate a phase transition from
tetragonal at ambient pressure to collapsed-tetragonal at high pressure
Bishop10 . The magnetization measurements at ambient pressure indicate that
the effective paramagnetic moment at high temperatures arises mainly from the
Eu spins with an appearance of AFM ordering $\leq 39$ K Ballinger12 .

Notably, there have been many reports on the structural and magnetic
properties of these ACo2As2 compounds VivekPRB14 ; BingPRB19 ; SangeethaPRB18
; SapkotaPRL17 ; DingPRB17 ; JayasekaraPRB15 ; Ying12 ; Cheng12 ; Bishop10 ;
Sefat09 ; Pandey13 ; however, detailed ARPES studies are very few DhakaPRB13 ;
XuPRX13 ; MansartPRB16  and not reported for EuCo2As2. Therefore, further
investigations of the band structure and FSs of ACo2As2 and comparison with
the AFe2As2 parent compounds are desired to shed light on the pairing
mechanism of Fe-based superconductors.

In this paper, we report a comprehensive ARPES study of ACo2As2 (A = Ca, Sr,
Ba, Eu) and present the FSs as well as low-energy band structures, which are
found to be very different from BaFe2As2 at the Fermi level. The experimental
FSs and band dispersion data are compared with full-potential linearized
augmented-plane-wave (FP-LAPW) calculations, which are found to be in
reasonably good agreement. The corresponding band dispersion data show a small
electron pocket at the center and large electron pocket at the corner of the
Brillouin zone (BZ). This reveals that no obvious FS nesting is present in
these compounds, which is in contrast to the parent compounds of Fe-based
high-Tc superconductors. Moreover, we observe that the hole bands are moved
300–400 meV below the EF compared to the hole bands crossing EF in the AFe2As2
compounds. Here in case of ACo2As2, the rigid-band-like shift in the band
structure results in the appearance of a small electron pocket at the $\Gamma$
point DhakaPRB13 ; XuPRX13 ; MansartPRB16 . Moreover, we find that the bands
in the vicinity of EF are reasonably flat, which are responsible for high
intensity peak in the density of states (DOS) at EF and important to
understand the physical properties of these $A$Co2As2 materials. In addition,
there are no notable changes in the FS topology of CaCo2As2 measured at,
below, and above the AFM transition temperature.

##  II Experimental details

High-quality single crystals of ACo2As2 (A = Ca, Sr, Eu) were grown with Sn-
flux whereas BaCo2As2 out of self flux and the details of bulk physical
property measurements and x-ray analysis can be found in Refs. Pandey13 ;
VivekPRB14 ; AnandPRB14 ; SangeethaPRB18 . We used a Scienta R4000 electron
analyzer to perform high-resolution ARPES measurements at beamline 7.0.1 of
the Advanced Light Source (ALS), Berkeley, California. All samples were
cleaved in situ in an ultrahigh vacuum chamber having $\leq$$4\times 10^{-11}$
mbar pressure, yielding flat mirror-like surfaces in the ab plane. The ARPES
data were collected with $\sim 20$ meV and $\sim 0.3^{\circ}$ energy and
momentum resolutions, respectively. Several samples from different batches
were measured to reproduce the results of the Fermi surfaces and band
structure. We use a gold sample to determine the Fermi energy.

We calculate the Fermi surfaces and band dispersions of $A$Co2As2 with the FP-
LAPW method using the local density approximation Perdew92 . We use $R_{\rm
MT}\times{\it k}_{\rm max}=$ 8 or 9 to find the self-consistent charge
density, where the smallest muffin tin (MT) radius is multiplied by the
maximum $k$ value in the plane wave expansion basis. Here, the MT radii of
2.1, 2.3, 2.5, 2.5, 2.1, and 2.1 a.u. were taken for Ca, Sr, Ba, Eu, Co, and
As, respectively. Note that 828 $k$-points were selected in the irreducible BZ
to perform the calculations untill we reached the total energy convergence
criterion of 0.01 mRy/ primitive cell. Also, we relaxed the As atom z-axis
position to find a minimum total energy, which gave z${}_{\rm As}=$ 0.3622,
0.3515, 0.3441, and 0.3611 for $A=$ Ca, Sr, Ba, and Eu, respectively. To
compute the FSs, we divide the $-2\pi/a\leq(k_{\it x}$, $k_{\it y})\leq
2\pi/a$ ranges of $k_{\it x}$, $k_{\it y}$ planes with different $k_{\it z}$
values into 200$\times$200 meshes.

Figure 1: Fermi surface maps of ACo2As2 (A = Ca, Sr, Ba, Eu) plotted by
integrating the photoelectron intensity within $\pm 10$ meV about EF, for (a)
CaCo2As2 ($T_{\rm S}\approx 20$ K, $h\nu=135$ eV), (b) SrCo2As2 ($T_{\rm
S}\approx 90$ K, $h\nu=140$ eV), (c) BaCo2As2 ($T_{\rm S}\approx 200$ K,
$h\nu=135$ eV), and (d) EuCo2As2 ($T_{\rm S}\approx 200$ K, $h\nu=135$ eV).
The outline of the first Brillouin zone is shown by a black dashed square. The
panels (e–h) are same as (a–d), but calculated. The panels (b, c, f, g) are
reconstructed from our earlier publications DhakaPRB13 ; Pandey13  for
comparison within the $A$Co2As2 family.

##  III Results and discussion

In order to understand how the low-energy band structure changes between
different members of $A$Co2As2 family, in Figs. 1(a–d) we present the
photoemission intensity maps of ACo2As2 (A = Ca, Sr, Ba, Eu) at EF measured at
k${}_{\rm z}\approx 2\pi/c$. To plot the FS maps, we have integrated the
intensity of the photoelectrons within $\pm 10$ meV about $E_{\rm F}$.
Interestingly, we find that the shape of the FSs of ACo2As2 is more
complicated DhakaPRB13 ; XuPRX13  than those of the parent $A$Fe2As2 compounds
of the 122-family DhakaPRL11 . In particular, the FS map of CaCo2As2 [Fig.
1(a)] clearly exhibits small elliptical pockets centered around the corner
($X$ point) of the BZ. Additionally, we also observe four small pockets around
the center ($\Gamma$ point) of the BZ. In the case of SrCo2As2 [Fig. 1(b)],
the FS topology is slightly different in the sense that the elliptical pockets
at the $X$ point become straight and the four small pockets around the
$\Gamma$ point are now less visible. The FS of BaCo2As2 in Fig. 1(c) is
significantly different where the pockets at $X$ point break into small
segments, and the four small pockets around the $\Gamma$ point are become
smaller in size and change in shape. More interestingly, we observe a small
circular pocket at the $\Gamma$ point in the FS map of EuCo2As2. At the corner
($X$ point) of the BZ, long straight segments of intensity pocket for the $A=$
Sr, Ba, and Eu samples are clearly different in shape as compared to CaCo2As2.
In the case of $A=$ Eu, the intensity of the four small electron pockets
(along the $k_{x}$, $k_{y}$ directions) around the center of the BZ almost
disappeared as compared to CaCo2As2, see Figs. 1(a, d).

Interestingly, we observe a significant change in the FS topology of $A$Co2As2
family by changing the element at $A$ site (for example in the present study
$A=$ Ca, Sr, Ba, and Eu) DhakaPRB13 ; XuPRX13 ; Pandey13 , as compared to the
other related parent compounds $A$Fe2As2 DhakaPRL11 ; DhakaPRBrc14 . Moreover,
the appearance of a small intensity pocket at the $\Gamma$(0,0) point at
$E_{\rm F}$ in EuCo2As2 [see Fig. 1(d)] clearly suggests a shift in the Fermi
level, which may be different from the other $A$Co2As2 ($A=$ Ca, Sr, Ba)
compounds.

Therefore, to further understand the electronic structure of these samples, we
performed theoretical calculations for all the samples at the same ${\it k}$z
points and compared the calculated FS maps in Figs. 1(e–h), respectively.

Figure 2: Fermi surface maps of CaCo2As2 measured with 135 eV photon energy
and at different sample temperatures. Figure 3: The photoemission intensity
maps of ACo2As2 (A = Ca, Sr, Ba, Eu) plotted at different binding energies, as
marked on the top of each panel. Panel (a) CaCo2As2 (135 eV, 20 K), panel (b)
for SrCo2As2 (140 eV, 90 K), panel (c) for BaCo2As2 (135 eV, 200 K), and
panels (d, e) for EuCo2As2 [(d) 135 eV and (e) 115 eV, 200 K]. The intensity
of the photoelectrons is integrated within $\pm 10$ meV about the
corresponding binding energy value in each panel.

In case of CaCo2As2, four patches of intensity (along the $k_{x}$, $k_{y}$
directions) around the $\Gamma$ point and large elliptical pockets across the
$X$ points are clearly seen in Fig. 1(e). Overall, the theoretically-
calculated FS topology clearly shows significant changes between the Ca, Sr,
Ba, and Eu members, see Figs. 1(e–h). Also, the FS maps of ACo2As2 (A = Ca,
Sr, Ba, Eu) are very different from the other related parent compounds of the
122 family such as CaFe2As2 and BaFe2As2 DhakaPRBrc14 ; KondoPRB10 . However,
if we see the FS plotted about 400 meV below $E_{\rm F}$ (discussed later)
DhakaPRB13 , it is very similar to that of BaFe2As2, where the FSs are roughly
circular in shape and are roughly similar in size KondoPRB10 . This clearly
indicates a shift of about 400 meV in the Fermi energy by completely replacing
Fe with Co in these systems DhakaPRB13 ; XuPRX13 . It is important to note
here that the overall shape of the measured FSs in Figs. 1(a–d) is in
relatively good agreement with the respective calculations in Figs. 1(e–h).

As discussed above, in case of CaCo2As2 sample, the magnetization measurements
show an AFM transition at 52 K VivekPRB14 . Also, it is important to note here
that the ARPES studies of Ba(Fe1-xRux)2As2 and Ba(Fe1-xCox)2As2 show
significant changes in the band structure with sample temperature DhakaPRL13 ;
Brouet13 . Moreover, it was shown that temperature-dependent FS nesting may
play an important role in driving the AFM-paramagnetic phase transition in
these materials LiuPRL09 ; KondoPRB10 ; DhakaPRL11 ; LiuNP10 . Therefore, to
get more insights for understanding whether there are changes in the band
structure of CaCo2As2 with temperature across the AFM transition temperature
(TN), we measured the FSs with 135 eV photon energy using a synchrotron
radiation source. In Fig. 2, the FSs are shown at different sample
temperatures from 20 to 240 K, which confirm that there are no notable
differences in the FS topology measured below [Fig. 2(a)] and above [Figs.
2(b–d)] ($T_{\rm N}$). Further, as the FS of $A$Fe2As2 below $T_{\rm N}$ shows
a reconstruction LiuNP10 , which is clearly absent in the FS of CaCo2As2
measured at 20 K, see Fig. 2(a). These results indicate that the electron
correlations are moderate in the $A$Co2As2 family, as the overall mass
enhancement of the Co 3$d$ electrons is found to be smaller MaoPRB18  as
compared to the Fe 3$d$ electrons in $A$Fe2As2 based compounds LiuPRL09 ;
KondoPRB10 ; DhakaPRL11 ; LiuNP10 .

Figure 4: Experimental band dispersion data of CaCo2As2 (panel a) and SrCo2As2
(panel c) measured with 135 eV and 140 eV photon energies, and the
corresponding theoretical band dispersions in panels (b) and (d),
respectively. The locations of the cuts #1, #2, #3 and #4 are marked in Fig.
1(a). In panels (c) and (d), cuts#1 and #3 are similar to the reported in our
publication Pandey13 , reconstructed for comparison.

In order to compare the FS topology at different binding energies, we show the
$(k_{\it x},k_{\it y})$ plots from 0 to 700 meV below EF for all the samples
in Fig. 3. For the CaCo2As2, we observe a decrease in the intensity of the
small pockets around the zone center along with a shape change at the corner
of the BZ, see panel (a) in Fig. 3. At 400 meV below EF, a small pocket is
clearly seen at the center of the BZ, which grows in size with further
increase in the binding energy. At the same time, the shape of the pocket at
the corner is very similar to that of the electron pocket observed in
$A$Fe2As2 samples. Similar changes are observed for the SrCo2As2 sample, as
shown in panel (b) except that the center pocket appeared at around 300 meV
below EF, and the size of both the pockets at the center and at the corner of
the BZ is almost similar at 400 meV. For the BaCo2As2 sample, a small
intensity of the central pocket is visible at 200 meV, see panel (c), and
again the size of both pockets is similar at 300-400 meV below EF.
Interestingly, in case of the EuCo2As2, the central pocket is already visible
at EF, see panels (d, e), measured at 135 eV and 115 eV photon energies,
respectively. Further, the size and shape of both pockets at the center and
corner of the BZ look similar for all the samples at around 400 meV below EF
except for EuCo2As2. More carefully, if we compare the size of the pocket at
the BZ center at 700 meV below EF for all the samples, it qualitatively
increases from Ca to Sr to Ba to Eu. These $(k_{\it x},k_{\it y})$ plots of
$A$Co2As2 further motivated us to investigate the low-energy band structure in
detail by plotting the band dispersion and comparing them with those
calculated theoretically along different momentum $(k_{\it x},k_{\it y})$
directions.

Figure 5: Experimental band dispersion data of BaCo2As2 (panel $a$) and
EuCo2As2 (panel $c$) measured with 135 eV photon energy. The plots in panels
$b$ and $d$ are the corresponding theoretical band dispersions. The locations
of the cuts #1, #2, #3 and #4 are marked in Fig. 1(a).

Therefore, to elucidate the character of these FS pockets, we extracted in-
plane dispersions for all the samples and shown the energy-momentum intensity
plots in Figs. 4 and 5 along the four different cuts #1, #2, #3 and #4. These
cuts are from $(k_{\it x},k_{\it y})=$ ($-$2$\pi$, 0 to 2$\pi$, 0), (2$\pi$,
$\pi$ to $-$2$\pi$, $-\pi$), (0, $-$2$\pi$ to 2$\pi$, 0), ($-$2$\pi$, 2$\pi$
to 2$\pi$, $-$2$\pi$), respectively, as marked in Fig. 1(a). The band
dispersions measured with 135 eV photon energy are shown in Fig. 4 for the
$A$Co2As2 ($A=$ Ca, Sr) samples. The photoelectron intensity along the cut #1
at the center of the BZ ($\Gamma$ point) is not very clear for the these
samples; however, we clearly observe two small electron pockets centered at
the Fermi momenta of $k_{\rm F\it x}\approx\pm 0.7\pi/a$. Interestingly, the
top of the hole pocket at the center of the BZ is clearly seen at about 400
meV below $E_{\rm F}$. Moreover, we find a large electron pocket with $k_{\rm
F\it y}=\pm 0.65\pi/a$ in the band dispersion plotted along the cut #2 at the
corner of the first BZ at ${\it X}=(\pi,\pi)$. In the cut #3, the data show a
large electron pocket with $k_{\rm F}=\pm 0.65\pi/a$ and high intensity peak
at the $X$ point. For comparison, we have also plotted the data along the cut
#4, which again shows large electron pockets at the $X$ points. To get more
insights, it is important to compare the experimental results with theoretical
calculations, and therefore, we present the calculated band dispersions in the
lower panels for Fig. 4 along all four different cuts. We find a reasonable
qualitative agreement between the theoretical and measured data.

Moreover, in Fig. 5, we show the low-energy band structure of BaCo2As2 and
EuCo2As2 samples to understand the character of the FS pockets. We note here
that the band dispersions of BaCo2As2 are very similar to those of SrCo2As2
except that the small-intensity electron-like bands are visible at the center
of the BZ for BaCo2As2, which are found to be slightly stronger when measured
with $h\nu=$ 85 eV in Ref. DhakaPRB13 . Also, the slope of the hole bands is
more slanting in $A$Co2As2 ($A=$ Sr, Ba) in comparison to CaCo2As2, see for
example cuts # 1 and #4 in Figs. 4 and 5.

It is intriguing to see the band structure of EuCo2As2, which is found to be
significantly different from the other $A$Co2As2 ($A=$ Ca, Sr, Ba) samples,
see Figs. 4 and 5. We observe that the intensity of two smaller electron
pockets at Fermi momenta $k_{\rm F\it x}=\pm 0.9\pi/a$ reduced significantly
and the top of the hole band at the center of the BZ ($\Gamma$ point) is about
300 meV below $E_{\rm F}$, see along the cut #1. This indicates that in the
case of EuCo2As2, the rigid band shift at the center of the BZ is smaller
($\approx$300 meV) than in the other $A$Co2As2 ($A=$ Ca, Sr, Ba) compounds
(400 meV). Therefore, the Fermi momentum of the electron pocket at the
$\Gamma$ point $k_{\rm F\it x}=\pm 0.15\pi/a$ is also slightly smaller than in
BaCo2As2 DhakaPRB13 . At the corner of the first BZ [$X=(\pi,\pi)$], we
observe a larger electron pocket for $A$Co2As2 with $k_{\rm F}=\pm 0.65\pi/a$
(along both the cuts #2 and #3) as compared to the AFe2As2 compounds
DhakaPRL11 . The data through cut #4 again confirm the presence of large
electron pockets at the $X$ points and a smaller electron pocket at the
$\Gamma$ point. The band structure plots obtained from the FP-LAPW
calculations, shown in the lower panels of Fig. 5, are in reasonable agreement
with the experimentally-observed band dispersions.

Now we discuss the broad comparison of the band structure and FS topology
between ACo2As2 and AFe2As2 compounds. Overall, the electronic DOS($E$) of the
ACo2As2 samples are found to be similar to those of the Fe-based compounds.
However, we observe a band shift of 300–500 meV below EF due to extra $d$
electron in Co as compared to Fe DhakaPRB13 ; Pandey13 ; Sefat09 ; Singh09 ,
which may reflect the high intensity peak at EF. Note that the Co
$d_{x^{2}-y^{2}}$ orbital has a larger bandwidth (between $-5$ eV and 2 eV)
than the Fe $d$ orbitals (from $-2$ eV to 2 eV) SinghPRL08 . Therefore, a
complex multi-band Fermi surface is observed in the ARPES measurements on the
$A$Co2As2 compounds along with the large DOS at EF with no apparent nesting
DhakaPRB13 ; XuPRX13 . In this scenario, the band structure of ACo2As2
MaoPRB18  appears significantly different at EF with respect to that of
BaFe2As2. Also, as noted above, CaCo2As2 shows magnetic ordering at low
temperature; however, APRES measurements across the magnetic transition
indicate no significant changes in the band structure. Similarly, a complex FS
structure of EuRh2As2 and BaNi2As2 has been reported using ARPES, but no
signature of band folding due to magnetic ordering was observed, which
indicates a weak coupling between layers PalczewskiPRB12 ; Zhou11 . Moreover,
a significant decrease in electronic correlation is reported in BaCr2As2
RichardPRB17 ; NayakPNAS17 . Note that in the $A$Co2As2 compounds a
considerable decrease in interlayer distance and zAs results in different
correlation strengths MaoPRB18  when compared with iron pnictides YinNM11 .

Figure 6: (a–c) Fermi surface (FS) maps of $A$Co2As2 ($A=$ Ca, Eu, Sr)
measured with photon energy of 100 eV and at 90 K, where the first BZ
boundaries are shown by black-dashed square. (d–f) Photoemission intensity
maps are plotted at $E_{\rm F}-0.4$ eV. These maps in (a–f) are constructed by
integrating the intensity of the photoelectrons within $\pm 10$ meV. (g–i) The
band dispersions along the (0,$-$2$\pi$ to 2$\pi$,0) direction from (a–c),
respectively, and the corresponding energy dispersive curves (EDCs) are shown
in (j–l).

Finally, we compare the FSs and low-energy band structures, in Fig. 6 of
$A$Co2As2 ($A=$ Ca, Eu, Sr) measured at 90 K with 100 eV photon energy. The
intensity of photoelectrons along ($k_{\it x}$, $k_{\it y}$) is plotted at
$E_{\rm F}$ in Figs. 6(a–c) and at 400 meV below $E_{\rm F}$ in Figs. 6(d–f).
The FS plots at $E_{\rm F}$ show a long segment of intensity across the $X$
points (corners of the BZ). The FS plots at 400 meV below $E_{\rm F}$ show
clear changes in the FS shape at the $X$ point, which changes from a large
segment to an oval–shape pocket and approximately similar size as the pocket
at the center of the BZ ($\Gamma$ point). These results demonstrate the rigid
band-like shift of 300-400 meV (depending on $A$) below $E_{\rm F}$ for
$A$Co2As2 as compared to $A$Fe2As2. Figures 6(g–i) show the band dispersion
data plotted across the corner of the BZ ($X$ point) i.e. from (0, $-$2$\pi$)
to (2$\pi$, 0) and the corresponding energy dispersive curves (EDCs) are shown
in Figs. 6(j–l). Again, for all these compounds we observe a large electron
pocket at the $X$ point and the bottom of this pocket is about 500 meV below
$E_{\rm F}$. More interestingly, we reveal a rather large flat band, driven by
the Co 3$d_{x^{2}-y^{2}}$ orbital, in close vicinity of $E_{\rm F}$ with
strong intensity near the $X$ point in both the experimental and calculated
data of $A$Co2As2 compounds DhakaPRB13 , as shown in Fig. 4 [cuts #2, #3 and
#4 of panel (a)] as well as in Fig. 6. In ARPES measurements on the
Fe1.03Te0.94S0.06 superconductor, Starowicz $etal.$ observed a flat band at
the Fermi level, which gives rise to high density of states at $E_{\rm F}$
Starowicz13 . This was explained in terms of as a Van Hove singularity, which
is believed to play an important role in the emergence of superconductivity in
Fe-based compounds Starowicz13 . The presence of a large density of states
near $E_{\rm F}$ due to a nearly flat band at the corner of the BZ is crucial
to understand the physical properties of the $A$Co2As2 compounds.

##  IV Conclusions

We have presented a comprehensive study of the electronic properties of the
$A$Co2As2 ($A=$ Ca, Sr, Ba, and Eu) compounds using ARPES and theoretical FP-
LAPW calculations. The FSs of these compounds are different from those of the
parent compounds of FeAs-based high-temperature superconductors. The band
dispersion data show a small electron pocket at the center and large electron
pockets at the corner of the Brillouin zone. The experimental data agree
reasonably well with the theoretical calculations. The absence of the FS
nesting in $A$Co2As2 is in contrast to the $A$Fe2As2 compounds. However, the
top of the hole bands is found to be moved 300–400 meV below EF (depending on
$A$) resulting an appearance of a small electron pocket at the center of the
BZ. More interestingly, we observe large flat bands near EF, which result in a
large density of states and could be responsible for the interesting physical
properties of these materials. Furthermore, no significant changes are
observed in the FS topology of CaCo2As2 between 20 and 300 K across the AFM
transition. We discuss similarities and differences in the electronic
properties of $A$Co2As2 with respect to the parent AFe2As2 compounds of 122
family.

##  V Acknowledgments

We thank Aaron Bostwick and Eli Rotenberg for excellent support at the ALS.
This research was supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, Division of Materials Sciences and Engineering. Ames
Laboratory is operated for the U.S. Department of Energy by Iowa State
University under Contract No. DE-AC02-07CH11358. The Advanced Light Source is
supported by the Office of Basic Energy Sciences, U. S. Department of Energy
under Contract No. DE-AC02-05CH11231. RSD also acknowledges the support by
BRNS through a DAE Young Scientist Research Award with Project Sanction No.
34/20/12/2015/BRNS.

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# INODE: Building an End-to-End Data Exploration System
in Practice [Extended Vision]

Sihem Amer-Yahia2, Georgia Koutrika1, Frederic Bastian7, Theofilos Belmpas1,
Martin Braschler9, Ursin Brunner9, Diego Calvanese8, Maximilian Fabricius5,
Orest Gkini1, Catherine Kosten9, Davide Lanti8, Antonis Litke6, Hendrik Lücke-
Tieke3, Francesco Alessandro Massucci6, Tarcisio Mendes de Farias7, Alessandro
Mosca8, Francesco Multari6, Nikolaos Papadakis4, Dimitris Papadopoulos4,
Yogendra Patil2, Aurélien Personnaz2, Guillem Rull6, Ana Sima7, Ellery Smith9,
Dimitrios Skoutas1, Srividya Subramanian 5, Guohui Xiao8, Kurt Stockinger9
(1) Athena Research Center, Greece (2) CNRS, University Grenoble Alpes, France
(3) Fraunhofer IGD, Germany
(4) Infili, Greece (5) Max Planck Institute, Germany (6) SIRIS Academic, Spain
(7) SIB Swiss Institute of Bioinformatics, Switzerland (8) Free University of
Bozen-Bolzano, Italy
(9) ZHAW Zurich University of Applied Sciences, Switzerland

###### Abstract.

A full-fledged data exploration system must combine different access
modalities with a powerful concept of guiding the user in the exploration
process, by being reactive and anticipative both for data discovery and for
data linking. Such systems are a real opportunity for our community to cater
to users with different domain and data science expertise.

We introduce INODE - an end-to-end data exploration system - that leverages,
on the one hand, Machine Learning and, on the other hand, semantics for the
purpose of Data Management (DM). Our vision is to develop a classic unified,
comprehensive platform that provides extensive access to open datasets, and we
demonstrate it in three significant use cases in the fields of Cancer
Biomarker Research, Research and Innovation Policy Making, and Astrophysics.
INODE offers sustainable services in (a) data modeling and linking, (b)
integrated query processing using natural language, (c) guidance, and (d) data
exploration through visualization, thus facilitating the user in discovering
new insights. We demonstrate that our system is uniquely accessible to a wide
range of users from larger scientific communities to the public. Finally, we
briefly illustrate how this work paves the way for new research opportunities
in DM.

##  1\. Introduction

The Data Management (DM) community has been actively catering to Machine
Learning (ML) research by developing systems and algorithms that enable data
preparation and flexible model learning. This has resulted in several major
contributions in developing ML pipelines, and formalizing algebras and
languages to facilitate and debug model learning, as well as designing and
implementing algorithms and systems to speed up ML routines (Boehm et al.,
2016; Sparks et al., 2017). Existing work that leverages ML for DM (Stoica,
2020) is nascent and covers the use of ML for query optimization (Kristo et
al., 2020) or for database indexing (Kraska et al., 2018). This paper makes
the case for democratizing _Intelligent Data Exploration_ by leveraging ML for
DM.

Traditionally, database systems assume the user has a specific query in mind,
and can express it in the language the system understands (e.g., SQL).
However, today, users with different technical backgrounds, roles, and tasks
are accessing and leveraging voluminous and complex data sources. In many
scenarios, they are only partially familiar with the data and its structure,
and their needs are not well-formed. In such settings, _expanding traditional
query answering to data exploration is a natural consequence and requirement
and with it comes the need to redesign systems accordingly_. This need
translates to several challenges at different levels.

(_Interaction_). Regarding interaction with the system, the biggest challenge
is to enable the user to express her needs through a variety of access
modalities, ranging from SQL and SPARQL to natural language (NL) and visual
query interfaces, that can be used and intermingled depending on the user
needs and expertise as well as the data exploration scenario. The second
challenge is that of user guidance, i.e., users should be allowed to provide
feedback to the system, and the system should leverage that feedback to
improve subsequent exploration steps.

Figure 1. Natural language query interface with user assistance. Step 1: User
enters a natural language query. Step 2: System parses query and matches
keywords against the available ontology to enable term disambiguation; the
user iterates the process. Step 3: System visualizes various cancer types that
are similar to lung cancer. The distance metric between the diseases can be
chosen by the user, e.g. by semantic distance.

(_Linking_). Once a user need has been formulated and sent to the system, it
is executed over a (fixed) data set. Users may be aware which additional data
sets could be of interest. However, they do not always know how to correctly
link, integrate, and query more than one data source to generate rich
information. This introduces the challenges of data linking, so that new data
sources can be added to the system, as well as knowledge generation, so that
queries over unstructured data can be supported. Both of these aim at enabling
the continuous expansion of the “pool” of available data sources, thus making
more data available to users.

_(Guidance)_. Traditionally, the system will return to the user a set of
tuples that concludes the search. There is a lot of work on how to improve
performance for query workloads (predict future queries, build indices
adaptively, etc.), but still the system has a rather passive role:
anticipating or at best trying to predict the next query and then optimize its
performance accordingly. Hence, the challenge of system proactiveness arises.
The output is not only the set of results but also recommendations for
subsequent queries or exploration choices. In our vision, the system guides
the user to find interesting, relevant or unexpected data and actively
participates in shaping the query workload.

In a nutshell, a full-fledged data exploration system must _combine different
access modalities with a powerful concept of guiding the user_ in the
exploration process. It must be reactive and anticipative co-shaping with the
user the data exploration process. Finally, while data integration has been
around for a while, the ability to tie together data discovery and linking is
a central question in an intelligent data exploration system.

_(Evaluation)_. An essential part of our proposal is the development of an
evaluation framework to enable the end-to-end assessment of an intelligent
data exploration system. This requires to formalize system and human metrics
that are necessary for data linking and integration, multi-modal data access,
guidance, and visualization.

Related Work. Several systems address components of our vision. A number of
them enable NL-to-SQL (Blunschi et al., 2012), SQL-to-NL (Kokkalis et al.,
2012) or both (John et al., 2017) (see a summary in (Affolter et al., 2019)).
Recommendation strategies can be leveraged to guide users (Liu et al., 2019).
Work on interactive data exploration aims at helping the user discover
interesting data patterns based on an integration of classification algorithms
and data management optimization techniques (Dimitriadou et al., 2016). Each
of the above-mentioned systems tackles specific data management challenges as
so-called insular solutions. However, these insular solutions have not been
integrated to tackle the end-to-end aspect of intelligent data exploration
targeted at a wide range of different end users.

Combining all the challenges above requires an elaborated system whose multi-
aspect behavior and functionality is the result of a synergy between disjoint
technologies, and integrates them into a new ensemble. This gives rise to
multiple approaches that vary in computational complexity, and raises new
challenges that can benefit from recent advances in ML.

In summary, this paper makes the following contributions. We advocate for
using ML to solve DM problems that arise when building intelligent data
exploration systems. We illustrate the need for intelligent data exploration
with relevant use cases (Section 2). We describe the solution we have today,
INODE111http://www.inode-project.eu/, that we are currently building as part
of a European project (Section 3). To fully complete our vision, we provide
open research challenges to be addressed at the intersection of DM and ML
(Section 4).

##  2\. Use Cases

In this section, we describe two use cases from cancer research and
astrophysics and show how INODE can tackle them.

Use Case 1: Cancer Research (Natural Language and Visual Data Exploration).
Fred is a biologist who studies cancer. His goal is to find which specific
biomarkers are indicators for a certain type of lung cancer. He needs natural
language exploration.

INODE offers support for NL queries, query recommendations, and interactive
visualizations triggered by NL queries (see Figure 1). For instance, Fred
starts with a request in NL for the topics related to lung cancer but is not
sure how to continue after inspecting the results. INODE steps up and
recommends different options: to expand the search using experimental drugs
for treating lung cancer, or to focus on a subset of lung cancer types
associated with a certain gene expression. Fred chooses to expand his search
to one of the recommended topics, and receives a new list of lung cancers,
drugs and genes. Additionally, INODE explains in NL how results are related.
That helps him in selecting experimental drugs for certain gene expressions.
After a few such queries, the system visually analyzes the results for Fred to
study. Fred learns about the similarity between different types of cancer
based on distance metrics that he can choose.

Use Case 2: Astrophysics (Exploration with SQL-Pipelines). In the era of big
data, astronomers need to analyze dozens of databases at a time. With the ever
increasing number of publically available astronomical databases from various
astronomical surveys across the globe, it is becoming increasingly challenging
for scientists to penetrate deep into the data structure and their metadata in
order to generate new scientific knowledge. Sri, an astrophysicist, explores
astronomical objects in SDSS, a large sky survey
database222https://www.sdss.org/. Sri would like to examine Green Pea
galaxies, first discovered in a citizen science project called ’Galaxy zoo’,
that recently gained attention in astronomy as one of the potential sources
that drove cosmic reionization.

Figure 2 shows a sequence of three consecutive processes of analyzing
astrophysics data. Sri relies on selected examples at each step and requests
to see comparable ones. In the first query, she asks to find galaxies with
similar colors as Green Pea galaxies, she requests objects with similar
spectral properties, like emission line measurements, star formation rates
etc., as those returned in the first step. The last query finds similar
galaxies in terms of their relative ratios and strength of emission lines. As
a result, Sri discovers that green pea emission line ratios are similar to
high redshift galaxies.

INODE guides any user in making such new discoveries in an intuitive simpler
way, without having to write complicated SQL queries or manual analysis of
thousands of galaxies. For instance, INODE helps a user choose among
similarity dimensions rather than rely on her ability to provide them.
Additionally, INODE shows to the user alternative queries to pay attention to,
thus increasing the chances of making new discoveries.

Figure 2. Exploring astrophysics data.

##  3\. Current INODE Architecture

The main novelty of INODE is bringing together different data management
solutions to enable intelligent data exploration (see Figure 3). Although some
of these solutions and research challenges have been tackled previously, they
have not been combined into such an end-to-end intelligent data exploration
system, which in turn opens up new research challenges.

INODE’s major components are as follows: (1) _Data Modeling and Linking_
enables integration of both structured and unstructured data. (2) _Integrated
Query Processing_ enables efficient query processing across federated
databases leveraging ontologies. (3) _Data Access and Exploration_ enables
guided data exploration in various modalities such as by natural language, by
certain operators or visually.

###  3.1. Data Modeling and Linking

This component links loosely coupled collections of data sources such as
relational databases, graph databases or text documents based on the well-
established _ontology-based data access_ (OBDA) paradigm (Xiao et al., 2018a).
OBDA uses a global ontology (knowledge graph) to _model_ the domain of
interest and provides a conceptual representation of the information in the
data sources. The sources are linked to elements in the global ontology
through declarative _mappings_. It is well-known that designing OBDA mappings
manually is a time-consuming and error-prone task. The Data Modeling and
Linking component of INODE aims at automatizing this task by providing two
mechanisms: data-driven and task-driven mapping generation.

_Data-driven Mapping Generation_. This mechanism deals with linking novel data
sources to the system. The idea is to rely on _mapping patterns_ that describe
well-assessed and sound schema-transformation rules usually applied in the
design process of relational databases. By analyzing (driven by the patterns)
the data sources, it is possible to automatically derive a so-called _putative
ontology_ (Sequeda and Miranker, 2015) describing both the explicit entities
and relationships constituting the schema and the implicit ones inferrable
from the data. From the mapping patterns, one can also automatically derive
mappings that link the data sources to the putative ontology.

_Task-driven Mapping Generation_. This mechanism is applied whenever a task or
a query is formulated that uses specific _target_ ontology elements that are
not yet aligned with the putative ontology. In such scenario, the semantics of
the query are used to automatically generate mappings to align the target
ontology with the putative ontology.

_Knowledge Graph (KG) Generation_. This service transforms unstructured
information hidden in large quantities of text (e.g. repositories of
scientific papers) to an exploitable structured representation through an NLP
pipeline. INODE follows an Open Information Extraction (OIE) approach to
convert each sentence of the corpus into a set of relational triples, where
each triple consists of a subject, an object, and a predicate (relationship)
linking them. We leverage a number of preprocessing techniques, including co-
reference resolution and extractive summarization to improve the quality of
the extracted relational triples. We combine different OIE methods (rule-
based, analytics-based and learning-based) to achieve both high precision and
high recall (Papadopoulos et al., 2020). The relational triples are further
linked with domain-specific ontology concepts before being integrated into the
knowledge graph.

Figure 3. Major components of the INODE architecture.

###  3.2. Integrated Query Processing

This component is responsible for the execution of queries using Ontop (Xiao
et al., 2020), a the state-of-the-art OBDA system. Ontop allows the users to
formulate queries in terms of concepts and properties of their domain of
expertise (represented in knowledge graphs), rather than in terms of table and
attribute names used in the actual data sources. Hence, users do not have to
be aware of the specific storage details of the underlying data sources in
order to satisfy their information needs.

_Query Execution_. This service provides on-the-fly _reformulation_ of SPARQL
queries over the domain ontology to SQL queries over the data sources. An
approach based on reformulation has the advantage that the data available in
the data sources does not need to be duplicated in the query processing
system, but can be kept in the data sources as-is. This means that the Query
Execution service is guaranteed even in the common scenario where the user
does not own the data nor does have the right to copy them. To produce
reformulations that can efficiently be executed over the data, in INODE we use
optimization techniques such as _self-join elimination for denormalized data_
(Xiao et al., 2020) and _optimizations of left-joins_ arising from OPTIONAL
and MINUS operators (Xiao et al., 2018b).

_Source Federation_. The Source Federation service deals with distributing the
processing of queries over the available data sources. INODE provides
different kinds of federation ranging from SQL federation to seamless SPARQL
federation. With respect to SPARQL, we can distinguish between two forms of
federation: _seamless federation_ and SPARQL 1.1 SERVICE federation.

In seamless federation, users send queries against a unified view of the
remote endpoints without the need to be aware of the actual vocabularies used
in the federated endpoints. The challenge is to automatically detect to which
sources which components of the query need to be dispatched, to collect the
retrieved results, and to combine them into a coherent answer. We address this
challenge by relying on the knowledge about the sources encoded in the OBDA
mappings. Given that efficiency is a crucial requirement in this setting, our
approach requires a dedicated cost-model able to minimize the number of
distributed joins over the federation layer, in order to favor more efficient
joins at the level of the sources.

Instead, SERVICE federation might be adopted in those cases where users want
to directly refer to “external” SPARQL endpoints, not yet integrated with the
ontology. In this setting, the user directly references the desired endpoints
at query time using the SPARQL 1.1 SERVICE functionality. Observe that the
user is required to be aware of the vocabulary used in the external endpoint.
Hence, the Source Federation service can simply delegate the execution of the
SPARQL query component referenced in the SERVICE call.

_Data Analytics_. The data analytics service exploits novel and efficient
query reformulation and optimization techniques (Xiao et al., 2020) to compute
complex analytical functions. Such techniques are based on algebraic
transformations of the SPARQL algebra tree, rather than on Datalog
transformations as traditionally done in the OBDA literature. This shift of
paradigm allows for an efficient implementation of analytical functions such
as SPARQL aggregates. It is worth noting that INODE, through Ontop, provides
the first open-source reformulation-based system able to support SPARQL
aggregates.

The Answer Justification service generates in an automatic way compact and
easy to understand explanations for query results. In an OBDA setting, the
explanations for a result must take into account, in addition to the query,
the three components of the input, namely the ontology, the mappings, and the
data sources (Calvanese et al., 2019). The ontology is taken care of by
identifying the ontology axioms used for the rewriting of the input query. As
for the mappings, those considered in the justification are the ones that were
used for the unfolding of the rewritten query to produce the SQL
reformulation. Finally, the data is taken care of by identifying the actual
tables and tuples that contributed to build the considered result, using an
approach based on provenance semirings (Senellart et al., 2018).

###  3.3. Data Access and Exploration

_Exploration by Natural Language_. For translating a natural language question
into SQL or SPARQL, INODE uses pattern-based, graph-based and neural network-
based approaches. For translating from NL to SQL, INODE extends the pattern-
based system SODA (Blunschi et al., 2012) with NLP techniques such as
lemmatization, stemming and POS tagging to allow both key word search queries
as well as full natural language questions. In addition, we use Bio-SODA (Sima
et al., 2019), a graph-based system to enable NL questions over RDF graph
databases. In order to enable federated queries across both relational
databases and RDF graph databases, INODE uses an ontology-based data access
technology leveraging Ontop (Calvanese et al., 2017). The advantage of using
pattern-based or graph-based approaches over neural network-based approaches
is that they do not require training data, which is often very costly to gain.

Since neural network-based approaches typically require large amounts of
training data, we also experimented with various training data generation
approaches. INODE uses an inverse data annotation approach called OTTA (Deriu
et al., 2020). Rather than writing NL questions and then the corresponding SQL
or SPARQL statements, OTTA reverses the process. In particular, OTTA randomly
generates so-called operator trees which are similar to logical query plans
that can easily be understood by non-tech savvy users. Afterwards, given these
operator trees, crowd workers write the corresponding NL questions. In INODE,
we use both crowd workers and domain experts for generating training data.

Finally, INODE integrates the neural network-based approach ValueNet, which
leverages transformer architectures to translate NL to SQL (Brunner and
Stockinger, 2021). The ultimate goal of INODE is to combine all these
techniques into an intelligent hybrid-approach that improves on the errors of
each of the individual systems.

_Exploration by Explanation_. One of the biggest hurdles in today’s
exploration systems is that the system provides no explanations of the results
or system choices. Nor does the system trigger input from the user, for
example, by asking the user to provide more information. In INODE, we enable a
conversational setting, where the system can (a) ask clarifications and (b)
explain results in natural language. This interaction assumes that the system
is capable of analyzing and understanding user requests and generating its
answers or questions in natural language.

Figure 4. Example data exploration pipeline for analyzing galaxies.

One approach used in INODE builds on Template-based Synthesis (Kokkalis et
al., 2012). This approach considers the database schema as a graph and a query
as a subgraph. We use templates that tell us how to compose sentences as we
traverse the graph and we use different traversal strategies that generate
query descriptions as phrases in natural language. Furthermore, to generate NL
descriptions that use the vocabulary of a particular database, INODE enriches
its vocabulary by _leveraging ontologies_ built by the Data Modeling and
Linking components. To further improve INODE’s explanation capabilities, we
are working on an approach to automatically learn templates, which is
especially critical for databases with no descriptive metadata, such as SDSS.
Essentially, we are using _neural-based methods_ to translate from SQL or
SPARQL to natural language.

For example, user questions in natural language inevitably hide ambiguity.
Hence, the system can come up with several possible query interpretations that
may lead to unexpected results or need the user’s help for query
disambiguation.

_Exploration by Example and by Analytics_. By-example is a powerful operator
that encapsulates multiple semantics. It takes a set of examples, such as
galaxies or patients, and explores its different facets, filters them, finds
similar/dissimilar sets, finds overlapping sets, joins them with other sets,
finds a superset, etc. Additionally, by-example operators can be combined with
by-analytics to find sets that are similar/dissimilar wrt some value
distributions. Figures 4 shows an example data exploration pipeline (DEP) for
exploring galaxies with different instances of by-example.

By-example and by-analytics operators can be represented in the Region
Connection Calculus (RCC) (Li and Ying, 2003) and are, in their general form,
computationally challenging. For instance, by-subset is akin to solving a set
cover problem, which has been extensively studied (Cormode et al., 2010).
Similarly, by-join requires to have appropriate indices. In INODE, we adopt
two approaches. One is based on a relational backend in which individual
operators are translated into SQL. The other one is an in-memory Python
implementation that relies on pre-computing and indexing sets. For some
operators such as by-facet, the SQL version is straightforward since it
resolves into generating a GROUP BY-query. For others, such as by-overlap, the
Python version is simpler as it relies on using an index that records pairwise
overlaps between pre-computed sets.

_Exploration by Recommendation_. In a mixed-initiative setting, the system
actively guides the user in what possible actions to perform or data to look
at next. In INODE, we are interested in recommendations in both _cold-start_
(where the user has not given any input) and warm-start settings (where the
user has asked one or more queries but may not know what to do next). In the
former case, the goal is to show a set of example or starter queries that the
users could use to get some initial answers from the dataset (e.g. (Howe et
al., 2011)). In the latter case, the system can leverage the user’s
interactions (queries) to show possible next queries (e.g., (Guilly et al.,
2018)).

A big differentiator is the availability of query logs. In case no query logs
are available, the system should still provide recommendations. In INODE we
are addressing the recommendation problem from different angles, i.e.,
generating recommendations: (a) based on _data analysis_ (Glenis et al., 2020)
(b) by _NL-based processing and query augmentation techniques_ leveraging
knowledge bases (c) by _user log analysis_.

_Exploration by Visualization_. In information retrieval, search queries
result in a list of candidates ranked by their matching score (Manning et al.,
[n.d.]). This also holds true for INODE, as most exploration operators
generate multiple potential answers. However, results are not individual items
such as documents, but data sets (i.e. sets of items) and have to be
communicated to the user differently to support their goals. Not only do users
have to decide, which data set contains the answer they are looking for, but
also to compare the results, to assess redundancies, discrepancies and other
surprising or interesting differences to draw hints on how to continue the
exploration.

The goals of the _by-visualization_ data access and exploration interface are
two-fold: (1) Enable ”explorers” to understand, compare and decide based on
the provided results and (2) enable them to interact with the results by
enabling indirect query manipulation, identifying and highlighting parts that
are of interest for further analysis and guiding them towards interesting
regions (Stahnke et al., [n.d.]; Steiger et al., [n.d.]; Ruotsalo et al.,
[n.d.]; May et al., 2012). Depending on the users information need, the
optimal answer may take different forms. For example, some questions can be
satisfied by a single data cell, while others require aggregated values or
even multiple tables. Hence, making the results explorable with respect to the
users’ needs is very challenging.

Our processes for user requirements elicitation confirms our goals stated
above and is based on the User Centered Design standard (International
Organization for Standardization, 2019). In addition to that, users emphasized
the importance to compare differences as well as similarities of queries and
results. As a base line, we enabled the visualization of multiple tables with
direct manipulation capabilities and currently work on an overview
visualization that spans the result data space.

A simple data exploration process with INODE for exploring EU-projects stored
in the CORDIS333https://cordis.europa.eu/ database is shown in Figure 5.

Figure 5. Data exploration process in INODE. (1) User starts with an NL
question such as Find all projects. (2) INODE translates NL question into SQL
and returns two different results (interpretations). (3) INODE explains the
SQL results in NL. (4) The results can further be explored by pipeline
operators such as by-filter to only show projects from France.

##  4\. Open Research Challenges Beyond INODE

A full-fledged data exploration system should learn about data sources, learn
about users and queries, and leverage this knowledge to facilitate and guide
users. All these challenges constitute new opportunities for ML research to
contribute to DM.

###  4.1. Learning about Data Sources

Traditionally SQL or SPARQL are used to query structured data stored in
relational databases and graph databases, respectively. A manual time-
consuming data integration process is usually required to integrate new data
sources. Additionally, data integration techniques used for structured data
are not directly applicable to unstructured data since they do not have a
schema.

There are several data integration challenges that can be tackled with ML. The
first one is to automate data integration (Golshan et al., 2017), in the
spirit of existing work that improves entity matching using transformer
architectures (Brunner and Stockinger, 2020). The second challenge is to
automatically generate knowledge graphs, in the spirit of neural-network
systems such as Snorkel (Ratner et al., 2017). Another powerful concept to
automate knowledge graph construction is to combine user dialogs with graph
construction (Nguyen et al., 2017). The idea is to augment the knowledge
graphs by learning concepts that are commonly queried but do not exist in the
graph. In summary, there has been a large amount of research on automatic
knowledge base construction. However, the combination of knowledge base
construction with natural language query processing has been largely untapped.

###  4.2. Understanding Users and Queries

Understanding user interests and expertise is a vital component for enabling
intelligent data exploration. For instance, the general public interested in
black holes has different expectations from an experienced astronomer with a
vast knowledge of astrophysics. The challenge is to avoid overwhelming a
novice user while providing interesting and relevant information to an expert
user.

The system should constantly improve its behavior by learning and adapting to
the user from task to task. Our operators are a great opportunity to learn and
adapt to users, as they provide the ability to choose between utility and
novelty, two dimensions that have not been explored together in the past.
Additionally, they enable collecting user feedback at the level of individual
operators and of a DEP. While ML methods for learning user profiles exist in
the context of individual systems for web search or recommendations, they have
not been studied before in the context of determining which operator caters
for which user in the next step. A simple start is to use regression methods
to determine the weight of utility and novelty when exploring data.
Additionally, probabilistic language models (Cao et al., 2017) or matrix
factorization-based approaches (Zhao et al., 2015) can be used to infer users’
topical interests, and latent factor models to mine user groups.

Traditional systems such as SODA, ATHENA, NALIR, or Logos (Blunschi et al.,
2012; Saha et al., 2016; Li and Jagadish, 2014; Kokkalis et al., 2012) use
pattern-based approach for NL to SQL or SQL to NL, or supervised ML (Kim et
al., 2020; Brunner and Stockinger, 2021). A new opportunity here is to train a
neural network for sequence-to-sequence prediction (Sutskever et al., 2014;
Brunner and Stockinger, 2021) for translating from NL-to-SQL and vice versa.
The key research challenge is how to use the feedback provided by users to
disambiguate queries and feed the gained knowledge back into ML models to
improve learning with semantic information for building ML models to tackle
disambiguation and context modeling (Shekarpour et al., 2016).

This should allow to model and solve the two symmetrical translation problems
at once. However, ML methods for query translation typically require large
amounts of training data. Our vision is that a full-fledged exploration system
should be able to leverage both pattern-based and ML-based approaches to
provide the most relevant answers to the user.

###  4.3. Generating Data Exploration Pipelines

Understanding queries and users serves the ability to provide guidance in
generating DEPs. This challenge can be approached in different ways depending
on the user’s expertise and willingness to provide feedback. In a scenario
where a DEP is given (see example in Section 2), the problem could be cast as
finding the right parameters for each query in the DEP. In a scenario where
the user is providing the next query, it could be seen as a query completion
problem. In a scenario where the user does not write exploration queries and
only provides feedback on results, it could be seen as the problem of learning
the user’s DEP. All these cases result in partially-guided or fully-guided
exploration.

Furthermore, since DEPs bring together several data access modalities, which
may be initiated by the user (e.g. a user query) or by the system
(recommendations or explanations), the system needs to learn how to use its
options to help the user in meaningful and unobtrusive ways. While there has
been work on each of these capabilities individually (e.g., recommendations or
query explanations), these efforts only focus on small parts of the problem
lacking a holistic understanding of the behavior and dynamics of a multi-
aspect system. ML approaches and in particular, Reinforcement Learning (RL)
and Active Learning (AL) can be leveraged.

_Partial Guidance with AL_. AL is claimed to be superior to faceted search
when the goal is to help users formulate queries. Systems like AIDE
(Dimitriadou et al., 2016) and REQUEST (Ge et al., 2016) assist users in
constructing accurate exploratory queries, while at the same time minimizing
the number of sample records presented to them for labeling. Both systems rely
on training a decision tree classifier to build a model that classifies
unlabeled records. A bigger challenge is to leverage AL in generating and
refining queries that go beyond SQL predicates.

_Full-Guidance with RL_. RL and Deep RL are becoming (Milo and Somech, 2020)
the methods of choice for creating exploration pipelines and for generating
DEPs based on a simulated agent experience (El et al., 2020; Seleznova et al.,
2020). In (El et al., 2020), a Deep RL architecture is used for generating
notebooks that show diverse aspects of a data set in a coherent narrative. In
(Seleznova et al., 2020), an end-to-end exploration policy is generated to
find a set of users in a collection of groups. Both frameworks accept a wide
class of exploration actions and do not need to gather exploration logs. An
open question is the applicability of this framework to specific data sets and
the transferability of learned policies across data sets.

###  4.4. Evaluating Data Exploration Pipelines

Evaluating data exploration requires a holistic approach that addresses
performance, quality and user experience aspects (Eichmann et al., 2020). The
iterative multi-step nature of DEPs makes evaluation particularly challenging
since it is not simply a matter of summing up multiple local evaluations at
each step. Regarding performance, the challenge lies in the design of logging
mechanisms to export the performance of different steps in DEPs. Such logging
must capture in fine details the time and memory usage each step takes so that
they can be aggregated to assess a full DEP. The aggregation must be carefully
designed to include user actions such as exploring multiple paths and
backtracking. While some users prefer the shortest path to a goal, others may
be more interested in exploring different paths.

Multiple evaluation questions arise: “How good are DEPs? How good are NL to
SQL/SPARQL translations and vice versa? How good are the next-operator or
next-data recommendations and explanations?” The novelty of our approach lies
in the ability to jointly assess performance, quality and user experience for
each use case.

We categorize INODE’s evaluation metrics into system metrics and human factors
(Rahman et al., 2020). To answer above questions, certain key challenges need
to be answered. The first challenge lies in extracting metrics from user
interactions. We are addressing this by designing logging mechanisms to export
various parameters. We use latency and memory usage for evaluating the system
performance of a DEP. We also record the number of clicks, interaction time
and user feedback. While some users prefer the shortest path to a goal, others
may be more interested in exploring different paths.

Another challenge lies in the iterative multi-step nature of DEPs since it is
not simply a matter of summing up multiple local evaluations at each step. An
additional key challenge is human subject bias. To avoid such biases, our
initial studies are designed in multiple stages such as pre-qualification of
users, randomly assigning users to different treatment groups and finally
feedback from users.

User acceptance of our system is strongly related to two key factors: accuracy
\- which reflects the closeness of exploration results to desired results, and
controllability \- which reflects the ability of our system to guide the user
in the exploration (Eichmann et al., 2020). Accuracy is computed using
standard methods such as precision and recall, and controllability is the
inverse of the number of user-interactions. Our first endeavor is to deploy
user studies that explore the relationship between accuracy and
controllability. To do so, we will perform factorial design analysis and
deploy questionnaires for exploration scenarios we are defining with our use
case providers.

The key idea of using ML techniques here is to capture the dependence on users
and data and learn different exploration profiles. A major challenge is to
design pilot studies in a sound manner with direct observations via
questionnaires and indirect ones (such as mouse tracking) to generate labeled
datasets for learning. Using ML techniques, and in particular ensemble
learning and multi-task learning, constitutes an unprecedented opportunity to
adapt the evaluation to users and data.

##  5\. Acknowledgements

This project has received funding from the European Union’s Horizon 2020
research and innovation program under grant agreement No 863410.

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