PASA 2024

#  pinta: The uGMRT Data Processing Pipeline for the Indian Pulsar Timing
Array

Abhimanyu Susobhanan1<EMAIL_ADDRESS>Yogesh Maan2 Bhal Chandra Joshi3
T. Prabu4 Shantanu Desai5 K. Nobleson6 Sai Chaitanya Susarla7 Raghav
Girgaonkar5 Lankeswar Dey1 Neelam Dhanda Batra8 Yashwant Gupta3 A. Gopakumar1
Manjari Bagchi9,10 Avishek Basu3,11 Suryarao Bethapudi12 Arpita Choudhary9
Kishalay De13 M. A. Krishnakumar14 P. K. Manoharan15 Arun Kumar Naidu16 Dhruv
Pathak9,10 Jaikhomba Singha17 Mayuresh P. Surnis11 1Department of Astronomy
and Astrophysics, Tata Institute of Fundamental Research, Dr. Homi Bhabha
Road, Mumbai 400005, Maharashtra, India  2ASTRON, the Netherlands Institute
for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands  3National
Centre for Radio Astrophysics, Tata Institute of Fundamental Research,
Ganeshkhind, Pune 411007, Maharashtra, India  4Raman Research Institute,
Bengaluru 560080, Karnataka, India  5Department of Physics, Indian Institute
of Technology Hyderabad, Kandi, Telangana 502285, India  6Department of
Physics, BITS Pilani Hyderabad Campus, Hyderabad 500078, Telangana, India
7Indian Institute of Science Education and Research Thiruvananthapuram,
Vithura, Kerala 695551, India  8Department of Physics, Indian Institute of
Technology Delhi, New Delhi-110016, India  9The Institute of Mathematical
Sciences, C. I. T. Campus, Tharamani, Chennai 600113, Tamil Nadu, India
10Homi Bhabha National Institute, Training School Complex, Anushakti Nagar,
Mumbai 400094, Maharashtra, India  11Jodrell Bank Centre for Astrophysics,
University of Manchester, Oxford Road, Manchester, M13 9PL, UK  12Department
of Physics and Astronomy, University of Texas, Rio Grande Valley, Brownsville,
TX 78520, USA  13Cahill Center for Astrophysics, California Institute of
Technology, 1200 E. California Blvd. Pasadena, CA 91125, USA  14Fakultät für
Physik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
15Arecibo Observatory, University of Central Florida, Arecibo, FL 32816, USA
16McGill Space Institute, McGill University, 3550 University Street, Montréal,
QC H3A 2A7, Canada  17Department of Physics, Indian Institute of Technology
Roorkee, Roorkee 247667, Uttarakhand, India

###### Abstract

We introduce pinta, a pipeline for reducing the upgraded Giant Metre-wave
Radio Telescope (uGMRT) raw pulsar timing data, developed for the Indian
Pulsar Timing Array experiment. We provide a detailed description of the
workflow and usage of pinta, as well as its computational performance and RFI
mitigation characteristics. We also discuss a novel and independent
determination of the relative time offsets between the different back-end
modes of uGMRT and the interpretation of the uGMRT observation frequency
settings, and their agreement with results obtained from engineering tests.
Further, we demonstrate the capability of pinta to generate data products
which can produce high-precision TOAs using PSR J1909$-$3744 as an example.
These results are crucial for performing precision pulsar timing with the
uGMRT.

###### doi:

10.1017/pas.2024.xxx

###### keywords:

Astronomy data analysis – pulsars

##  1 Introduction

Ubiquitous galaxy mergers are expected to force their resident supermassive
black holes to merge (Berczik et al., 2006; Pearson et al., 2019). During such
merger and the preceding inspiral phases, the black hole pairs are expected to
emit gravitational waves (GWs) in the nanohertz frequency range (Burke-Spolaor
et al., 2019; Susobhanan et al., 2020). Pulsar Timing Arrays (PTAs: Hobbs &
Dai, 2017) aim to detect such GWs by accurately timing the arrival of pulses
from an ensemble of millisecond pulsars (MSPs) as these are very precise
celestial clocks (Hobbs et al., 2020). The most promising PTA sources include
isolated supermassive black hole binaries (SMBHBs) emitting continuous GWs and
an astrophysical stochastic GW background formed from an ensemble of many
unresolved SMBHBs (Burke-Spolaor et al., 2019). The rapidly maturing PTA
efforts are soon expected to open an additional window to the GW astronomy
landscape inaugurated by the LIGO-Virgo collaboration (Abbott et al., 2019).

At present, there exist three advanced PTA experiments, namely the Parkes
Pulsar Timing Array (PPTA: Hobbs, 2013; Kerr et al., 2020), the European
Pulsar Timing Array (EPTA: Kramer & Champion, 2013; Desvignes et al., 2016),
and the North American Nanohertz Observatory for Gravitational Waves
(NANOGrav: McLaughlin, 2013; Alam et al., 2020a, b). Additionally, PTA efforts
are gaining momentum in India, China and South Africa (Joshi et al., 2018;
Lee, 2016; Bailes et al., 2018), and these collaborations are referred to as
the emerging PTAs. The International Pulsar Timing Array (IPTA) consortium
combines data and resources from various PTA efforts to enable faster
detection of nanohertz GWs (Hobbs et al., 2010; Perera et al., 2019).

The Indian Pulsar Timing Array (InPTA) experiment, operational since 2015
(Joshi et al., 2018), aims to use the unique strengths of the Giant Metrewave
Radio Telescope (GMRT: Swarup et al., 1991)— especially after its recent
upgrade (uGMRT: Gupta et al., 2017)—along with the Ooty Radio Telescope (ORT:
Swarup et al., 1971; Naidu et al., 2015) to complement the other PTA
experiments. The uGMRT, with its ability to observe below 1 GHz, is an ideal
instrument to characterize interstellar medium effects such as dispersion
measure (DM) variations of PTA pulsars, which is necessary to achieve the
nanosecond timing precision required for the first detection of nanohertz GWs
(Joshi et al., 2018).

The first step in using uGMRT and ORT data for InPTA science goals is to
reduce it to an archive format (Hotan et al., 2004) – a pulsar data format
widely used among other PTAs. Then, this data can be further processed using
well-known software to derive various astrophysically relevant quantities
including the pulse time of arrival (TOA) and the DM (van Straten et al.,
2012). This calls for homogeneity in data reduction practices to avoid non-
uniformity in the data products used for PTA analysis, which can introduce
systematic errors. In this paper, we describe a uGMRT pulsar data analysis
pipeline named “Pipeline for the Indian Pulsar Timing Array”
(pinta111Available at https://github.com/abhisrkckl/pinta.), developed for the
InPTA experiment to address these concerns as well as to improve the
efficiency, reliability, and user friendliness of the data reduction process
and to ensure faster turnaround time from observations to PTA analysis. We
have developed pinta with the intention to commission it as a standard
pipeline at the GMRT observatory to be used by the wider pulsar community.
This can help avoid the transfer of large data files by enabling data
reduction at the observatory itself.

For the pipeline to be useful to a wider community, we also discuss how to
interpret the uGMRT observation frequency settings. We also present the
results of our astronomical experiments carried out to validate the definition
of the observing frequency in the engineering specifications of the uGMRT
backend hardware and software. Using the same experiment, we also ascertained
the instrumental delays between various back-end modes used at uGMRT measured
through engineering tests. These delays form a crucial piece of information,
not only for combining data from multiple bands in the InPTA analysis, but
also for other simultaneous multi-frequency observations which use different
back-end modes of uGMRT.

The outline of this paper is as follows. A detailed description of the uGMRT
raw data as well as the workflow and usage of pinta is provided in Section 2.
Details of the uGMRT observation frequency settings and the astronomical
experiments which were used to validate these settings are presented in
Section 3. The performance and RFI mitigation characteristics of pinta are
reported in Section 4. The ability of pinta to generate data products from
which high-precision TOAs can be derived is demonstrated in Section 5 using
J1909$-$3744 as an example. A summary of the pinta pipeline discussed in this
paper is given in Section 6 and our future plans for the development of InPTA-
relevant codes including pinta are summarized in Section 7.

##  2 Description of the pipeline

pinta accepts uGMRT raw pulsar timing data as input, performs RFI mitigation
and folding, and provides the partially folded pulse profile in the Timer
archive format (van Straten & Bailes, 2011) as its output. In what follows, we
give a detailed description of the uGMRT raw data and the workflow of the
pinta pipeline.

The thirty GMRT antennas are divided in groups to form multiple subarrays, and
each subarray is phased to form voltage beams for two polarizations, and the
gains of the two polarizations are equalized during phasing. These voltage
beams are then digitized and Fourier transformed (no polyphase filter is
employed) to form power spectra across a certain number of frequency channels
(Reddy et al., 2017). For the phased array (PA) mode that we use in our InPTA
timing observations, the spectral powers from the two polarizations are added
to form the total intensity $I$ without applying any calibration, and is
integrated maintaining the required spectral and time resolution for the
observation specified in terms of the number of channels $N_{\text{chan}}$ and
the sampling time $T_{\text{smpl}}$. Note that the two polarization voltages
can also be combined to compute the Stokes parameters ($I$, $Q$, $U$, $V$:
Hamaker et al., 1996). While the recording of the full Stokes data is possible
at uGMRT, the implementation of its reduction in the pipeline described here
is currently being developed and tested. In addition, a real-time coherent
dedispersion observing mode is employed to process the voltages to form and
record the coherently dedispersed phased array (CDPA) raw data stream (De &
Gupta, 2016). Lastly, an incoherent array (IA) data stream can be formed by
incoherently adding the spectral powers from different antennas.

The PA and the CDPA total intensity modes are used for InPTA observations
discussed in this paper. The CDPA mode is primarily used at the lower
frequency bands where the effect of interstellar dispersion is prominent. The
raw data stream from either of these modes, namely a data cube of spectral
intensities at $N_{\text{chan}}$ frequency channels for each time sample, are
stored as 16-bit integers in a binary raw data file, and the timestamp (in
Indian Standard Time) at the start of the observation is saved as a separate
ASCII file. An example timestamp file is shown below.

    #Start time and date
    IST Time: 19:59:57.633098240
    Date: 25:08:2018
    #Start ACQ SEQ NO = 17

pinta converts the timestamp given in the timestamp file to MJD using astropy
(Price-Whelan et al., 2018). Note that the raw data files do not store any
metadata required for downstream processing and it must be provided to the
pipeline through a separate file.

Reduction of PTA data involves processing a large number of such high-volume
datasets (obtained from different MSPs at different epochs in separate bands)
through complex processing steps222InPTA currently observes six pulsars at bi-
weekly cadence simultaneously in two bands. Each such observation creates of
the order of 100-150 GB of raw data per band per pulsar.. In order to ensure
that processing can be efficient for such batch processing jobs and to avoid
premature run-time failures, a set of checks are done on all the relevant
files and folders, and the processing is initiated only if all the checks
pass333These checks include the existence and read/write permissions of the
relevant files and folders.. If one of the checks fail, an informative error
message is shown to enable easier troubleshooting.

Figure 1: The workflow of pinta. The pinta pipeline uses uses two separate
packages for the RFI mitigation, namely gptool and RFIClean. A typical data
reduction workflow can optionally engage these RFI mitigation choices. Note
that the profile archives generated by pinta are in the Timer format although
their extension is ‘.fits’. They can be converted to PSRFITS format using
PSRCHIVE (Hotan et al., 2004).

The data processing workflow of pinta is illustrated in Figure 1. pinta uses
two separate packages for Radio Frequency Interference (RFI) mitigation,
namely gptool444Stands for GMRT Pulsar Tool (Chowdhury & Gupta, 2021) and
RFIClean 555Available at https://github.com/ymaan4/rficlean (Maan et al.,
2020). Brief descriptions of these packages are given below.

###  2.1 Details of gptool

gptool is both an RFI mitigation and a data reduction tool for the beamformer
data from GMRT. It mitigates both narrow-band spectral line RFI and broadband
bursty time-domain RFI. For narrow-band RFI, it offers a choice of two options
for flagging RFI-affected frequency channels: (a) it derives a median band-
shape and flags channels for which the median absolute deviation (MAD) exceeds
a defined threshold; or (b) it checks for a drop in mean-to-RMS ratio for each
channel below a specified threshold to identify channels corrupted by RFI. Our
pinta pipeline employs both of these methods available in gptool. For
identifying broadband bursty RFI, gptool once again offers two options for
removal of outlier time samples, based on different ways of estimating central
tendency and variability in the histogram of the frequency-collapsed time
series. In the first method, a standard median and MAD based scheme is
employed to identify RFI-contaminated time samples. However, when strong RFI
is present for a significant duration of the observation time block, the
histogram may deviate from unimodality, affecting the robustness of median and
MAD estimates. In such cases, the major mode and the full width at half
maximum around the major mode provide robust estimates of the central tendency
and variability of the underlying distribution, and a novel scheme for
broadband RFI mitigation has been implemented in gptool based on these
statistics. This novel scheme has been found to give superior results, and
hence is used in our pipeline. For further handling of the channels and time
samples that are flagged as RFI by gptool, it offers two options to the user:
either to replace the existing values by zero or to replace the existing
values by a local median. In our pipeline, we use the replace by the local
median option as it is known to give better results. Both the RFI mitigated
and unmitigated data can then be dedispersed and folded to the ephemeris of
the observed pulsar. When gptool is run in the interactive mode, the time-
series, folded profile and the band-shape are displayed as the tool processes
the raw data. pinta uses the non-interactive mode of gptool, where the RFI
mitigated data, in the same format as the raw input data, is written to an
output file along with estimated statistics in auxiliary files without
performing dedispersion or folding. gptool provides an option for the removal
of a baseline computed by dedispersing the data to zero DM, useful for
broadband RFI mitigation, and an option for flattening the variations of the
band-shape across the observing bandwidth by renormalizing the output of each
frequency channel to the same mean value. The parameters for RFI removal and
the selected modes are specified with a configuration file, named gptool.in.
gptool has also been extensively used for RFI mitigation in the uGMRT for many
other pulsar projects since the beginning of the wide-band observations with
the uGMRT (Pleunis et al., 2020).

###  2.2 Details of RFIClean

RFIClean excises periodic RFI in the Fourier domain, and then mitigates
narrow-band spectral line RFI and broadband bursty time-domain RFI using
robust statistics. The periodic RFI could severely limit the efficacy of
conventional RFI mitigation techniques. There are many terrestrial sources of
periodic interference, the most infamous being the household 50/60 Hz power-
lines. RFIClean identifies and mitigates periodic interference in the time
series of individual frequency channels using Fourier domain analysis. After
the excision of periodic interference, RFIClean uses the more conventional
threshold-based techniques to identify the time samples as well as frequency
channels respectively contaminated by broadband bursts and narrow-band RFI.
The identified time samples and frequency channels are replaced by mean
values, computed robustly in the local regions around the affected samples.
RFIClean has been extensively and successfully tested against any artefacts
which might get incorporated in the data during the periodic RFI excision, and
might be relevant to the PTA analysis. The details of these tests can be found
in Maan et al. (2020). Before inclusion in pinta, RFIClean was also
independently tested as a stand-alone program using InPTA data, and was found
to significantly enhance the quality of the reduced data and the timing
analysis. For some pulsars with their spin frequency or any of its harmonics
unfavourably close to 50 Hz, detection of the pulsar signal at several epochs
was possible only after RFIClean’s mitigation of the periodic and other RFI.
RFIClean has also been used in several other completed and ongoing projects
(e.g., Maan et al., 2019; Oostrum et al., 2020), including in timing
experiments and searches for fast radio bursts Sosa Fiscella et al. (2020);
Pastor-Marazuela et al. (2020).

We note here an important difference between gptool and RFIClean: gptool
performs band shape normalization on the raw data while RFIClean retains the
original band shape. Thus, noticeable difference in shape of the _band-
averaged_ profiles can occur between the two branches of the pipeline,
especially in wide-band observations of pulsars exhibiting significant profile
evolution with frequency and interstellar scintillation. Therefore, we
advocate the use of separate templates for generating TOAs from profiles
obtained through gptool and RFIClean, especially for high precision pulsar
timing applications such as PTAs. In addition, the use of frequency-dependent
two-dimensional templates may also help mitigate this issue (Pennucci, 2019).

gptool accepts uGMRT raw data as input and writes the output in the same
format. The conversion to the filterbank format is carried out by a version of
the filterbank command provided by the sigproc package (Lorimer, 2011),
customized for uGMRT and distributed along with pinta. On the other hand,
RFIClean accepts input either in uGMRT raw data format or in the sigproc-
filterbank format, and outputs a sigproc-filterbank file.

It may be illuminating to compare and contrast the RFI mitigation methods
available in pinta with that available in the CoastGuard data analysis
package666Available at https://github.com/plazar/coast_guard (Lazarus et al.,
2016) developed for the PSRIX backend of the Effelsberg 100-m Radio Telescope.
CoastGuard provides four algorithms to find and mask or replace channels, sub-
integrations and phase bins in the folded profile contaminated with RFI. The
major difference between the RFI mitigation algorithms available in pinta and
CoastGuard is that the former act on raw data whereas the latter acts on
folded profile archives. The mitigation of periodic RFI such as the RFI
generated by power distribution lines implemented in RFIClean is not possible
in the folded profiles. In addition, the time domain bursty RFI removed by
gptool and RFIClean typically occur at GMRT at timescales much shorter than
our sub-integration interval of 10 s. These are our main reasons for opting
for RFI removal in the raw data rather than folded profiles in our analysis.

While both the RFI mitigation packages have been well tested, the possibility
of discovering new artefacts in the future cannot be ruled out. Hence, to
avoid the need of re-analysing all the data in such an unlikely future
situation, we have designed pinta such that it allows the user to process the
data in two separate branches, one for each RFI mitigation package, and
produces two separate outputs. Availability of data reduced by two independent
parts of the pipeline facilitates detailed comparisons and the choice of the
optimal RFI mitigation method.

The RFI-mitigated filterbank files are folded using dspsr (van Straten &
Bailes, 2011) and saved in the Timer format, significantly reducing the data
volume. Finally, a period and DM search is performed on the resulting profile
archive using the pdmp command provided by psrchive, producing a summary
document in the postscript format. This file is used as a visual check to
ensure that the pulsar has been detected and that the analysis has finished
successfully.

###  2.3 Usage

Argument | Description |  |  Mandatory/
---
Optional
Positional Arguments
<input_dir> | The input directory. | Mandatory
<working_dir> | The working directory. | Mandatory
Options
\--help | Output a help message. | Optional
\--test |  | Do not execute data processing commands. All checks are performed on the
---
input files and the commands are printed on the screen. This option is present
for troubleshooting.
Optional
\--no-gptool | Do not run gptool. Produces an output file without RFI mitigation. | Optional
\--no-rficlean | Do not run RFIClean. | Optional
\--nodel |  | The pipeline deletes all intermediate output files by default to conserve disk
---
space. This option preserves the intermediate outputs.
Optional
\--retain-aux |  | Components of the pipeline produce various side products in addition to the
---
primary data products, which are removed by pinta by default. This option
preserves these files by moving them to a folder named aux inside the
working_dir.
Optional
\--log-to-file |  | This option redirects the standard output generated from pinta to a log file
---
in the current_dir.
Optional
\--gptdir <...> |  | Specifies the directory where the gptool configuration files are stored.
---
By default, this is specified in the configuration file (See subsection 2.4).
Optional
\--pardir <...> |  | Specifies the directory where the pulsar ephemeris files are stored.
---
By default, this is specified in the configuration file (See subsection 2.4).
Optional
\--rficconf <...> |  | Specifies the RFIClean configuration file. By default, this is specified in the
---
configuration file (See subsection 2.4).
Optional
Table 1: Command line options available in pinta.

The pinta pipeline can be invoked from the command line with the following
syntax.

      $ pinta [--help] [--test] [--no-gptool]
      [--no-rficlean] [--nodel] [--retain-aux]
      [--log-to-file] [--gptdir <...>]
      [--pardir <...>] [--rficconf <...>]
      <input_dir> <working_dir>

pinta requires specifying two mandatory parameters and a few other optional
parameters as inputs as listed below.

  1. 1.

Input directory (input_dir) — The directory where the raw data files and the
corresponding timestamp files are stored.

  2. 2.

Working directory (working_dir) — The output files, as well as all the
intermediate products, will be written to this directory. This directory must
contain a file named pipeline.in as specified in subsection 2.5, and the user
must have ‘read’ and ‘write’ permissions for this directory. The working
directory can be the same as the input directory.

  3. 3.

gptool configuration directory (gpt_dir) — This directory should contain the
configuration files required to run gptool, named gptool.in.xxx where ‘xxx’
represents the local oscillator frequency of the uGMRT band.

  4. 4.

Pulsar ephemeris directory (par_dir) — This directory should contain the
pulsar ephemeris (.par) files in the tempo2 format, required for folding the
data. Each ephemeris file should be named JNAME.par where “JNAME” is the name
of the pulsar in the J2000 epoch.

  5. 5.

RFIClean configuration file (rficconf) — This file contains the settings and
flags required to run RFIClean for pinta.

In addition, we shall refer to the directory from which pinta is invoked and
the directory where the pinta script is stored as the current directory
(current_dir) and script directory (script_dir) respectively.

Note that both working_dir and the current_dir require write access. The
input_dir and working_dir are mandatory positional arguments to be passed to
pinta, while gpt_dir, par_dir and rficconf are by default read from a
configuration file, detailed in the next subsection. gpt_dir, par_dir and
rficconf can be explicitly specified in the command line through the
\--gptdir, \--pardir and \--rficconf options respectively. The various options
and command line arguments are summarized in Table 1.

Column | Parameter | Description | Data Type | Unit
---|---|---|---|---
1 | JName | The name of the pulsar in J2000 epoch. | String |
2 | RawDataFile |  | Raw data file name. Only the file name is required and
---
not the full path.
String |
3 | TimestampFile |  | Timestamp file name. Only the file name is required and
---
not the full path.
String |
4 | Frequency ($F_{\text{LO}}$) | Local oscillator frequency of the observing band. | Float | MHz
5 | NBins ($N_{\text{bin}}$) | Number of phase bins for the folded profile. | Integer |
6 | NChans ($N_{\text{chan}}$) | Number of frequency channels. | Integer |
7 | BandWidth ($\Delta F$) |  | Bandwidth of the observing band.
---
Float | MHz
8 | TSample ($T_{\text{smpl}}$) | The sampling time used for observation. | Float | s
9 | SideBand |  | The side-band. This should be either LSB (lower side-band)
---
or USB (upper side-band).
String |
10 | NPol ($N_{\text{pol}}$) | Number of polarizations (1:=(I), 4:=(I,Q,U,V)) | Integer |
11 | TSubInt ($T_{\text{subint}}$) |  | The duration of individual sub-integrations within which
---
the data will be folded over the pulsar period.
Float | s
12 | Cohded |  | Whether the data has been coherently dedispersed
---
(De & Gupta, 2016). 1 represents Yes and 0 represents No.
Boolean |
Table 2: Description of various columns in the pipeline.in file.

###  2.4 The Configuration File

The pinta configuration file stores the default settings required to run the
pipeline, such as the gpt_dir, par_dir and rficconf in YAML
format777https://yaml.org/. This file should be named pinta.yaml and stored in
the script_dir.

A sample configuration file is shown below.

    pinta:
      pardir: /path/to/pulsar/ephemeris/dir/
      gptdir: /path/to/gptool/config/dir/
      rficconf: /path/to/rfiClean/config/file/

###  2.5 The pipeline.in File

Since the raw input data files do not contain any metadata required for
downstream processing, such as the number of channels and the bandwidth, it
must be provided separately. pinta accepts this information through a space-
separated ASCII file named pipeline.in stored in the working_dir. Each row in
pipeline.in corresponds to one raw data file and the various columns are
described in Table 2. Rows starting with “#” are treated as comments and
ignored. pinta processes rows in the pipeline.in files serially until all rows
are processed successfully or a validation criterion is not met.

An example pipeline.in file is shown in Figure 2.

    #JName      RawData                         Timestamp                             Freq  Nbin  NChan  BandWidth    TSmpl       SB   NPol  TSubint  Cohded
    J1939+2134  J1939+2134.25032019.B3.cdp.dat  J1939+2134.25032019.B3.cdp.timestamp  500   128   1024   100          0.00008192  LSB  1     10.0     1
    J1939+2134  J1939+2134.25032019.B4.pa.raw   J1939+2134.25032019.B4.pa.hdr         750   128   1024   100          0.00008192  LSB  1     10.0     0
    J1939+2134  J1939+2134.25032019.B5.cdp.dat  J1939+2134.25032019.B5.cdp.timestamp  1460  128   1024   100          0.00008192  LSB  1     10.0     1

Figure 2: An example pipeline.in file

###  2.6 Storage Requirements

The uGMRT raw data file generated by an hour-long observation is typically of
the order of a hundred Gigabytes. A uGMRT raw data file contains, for each
time sample, $N_{\text{pol}}$ polarization intensities/correlations in
$N_{\text{chan}}$ frequency channels represented as 16-bit integers. In
general, the file size of the raw data file for an observation duration
$T_{\text{obs}}$ and sampling time $T_{\text{smpl}}$ is given by

$S_{\text{raw}}=N_{\text{pol}}N_{\text{chan}}\frac{T_{\text{obs}}}{T_{\text{smpl}}}\times
2\text{ Bytes}\,.$ (1)

The intermediate products generated by the pipeline, namely, .gpt and .fil
files, will have roughly the same size as the input file along with a small
header which stores observation metadata. The output archive files are
typically smaller, of the order of hundreds of Megabytes in size, since we
fold the raw data over longer sub-integrations. The size of the output
archive, excluding the header, is approximately given by

$S_{\text{arch}}\sim\frac{T_{\text{smpl}}}{T_{\text{subint}}}N_{\text{bin}}S_{\text{raw}}\,,$
(2)

where $T_{\text{subint}}$ is the duration of a sub-integration and
$N_{\text{bin}}$ is the number of phase bins in the profile. In our analysis,
we typically use $T_{\text{subint}}=10$ s. In general, the maximum amount of
disk space required by pinta is less than four times the total size of the raw
data files, while preserving all intermediate files (i.e., using the \--nodel
option). If the \--nodel option is not used, the maximum amount of disk space
required is approximately the size of the largest raw data file.

##  3 Interpretation of observatory frequency settings

The GMRT Wide-band Back-end (GWB; Reddy et al., 2017) provides three different
observation modes, namely IA, PA or CDPA, as described in Section 2. The
settings used during a pulsar observation depend on the band of observation
and the mode of the observatory back-end. These settings are required for data
reduction using pinta and are communicated to the pipeline through a
pipeline.in file as mentioned in Section 2.5. As the frequency labelling of
the pulsar data cube varies with the back-end mode used, these need to be
determined and encoded in pinta in a manner which simplifies the specification
of observation settings for the user.

The times of arrival (TOAs) of a pulsar pulse recorded simultaneously in two
bands A and B, using back-end modes P and Q respectively, are related by

$t_{AP}-t_{BQ}=\Delta_{PQ}+\mathcal{D}\times\text{DM}\left(F_{1A}^{-2}-F_{1B}^{-2}\right)\,,$
(3)

where $t_{AP}$ and $t_{BQ}$ are the TOAs, $\Delta_{PQ}$ is the relative
instrumental offset between modes $P$ and $Q$, $\mathcal{D}$ is the dispersion
measure constant, DM is the dispersion measure of the pulsar at the epoch of
observation, and $F_{1A}$ and $F_{1B}$ are the frequency labels of the
channels to which the signals in bands A and B are dedispersed. Both the
offsets $\Delta_{PQ}$ and the frequency labels $F_{1X}$ (where $X$ represents
the band of observation) are crucial for performing precision pulsar timing
using uGMRT. These are defined as part of the engineering specifications of
the GWB hardware and software (Reddy et al., 2017; De & Gupta, 2016).
Engineering tests with standard inputs to the hardware were carried out to
verify these definitions and revealed that there is no offset between time
series in IA and PA mode, whereas a 1 buffer (256 Mbytes) offset exists
between IA/PA and CDPA modes. This offset is 0.67108864 s for 200 and 400 MHz
bandwidths and 1.34217728 s for 100 MHz bandwidth, and this was verified up to
5 ns precision in engineering tests. Likewise, the frequency definitions were
worked out from engineering considerations and tested in an engineering sense
with fixed frequency tones. While the precision of astronomical tests is not
likely to be high due to system noise and coarser sampling, nevertheless such
tests with wide-band radio emission are also needed to gain confidence,
particularly for coherently dedispersed data. In this section, we describe the
astronomical tests carried out to validate the frequency labeling $F_{1X}$ to
be encoded in pinta, and to determine the offsets $\Delta_{PQ}$.

###  3.1 Calibration experiment

The required frequency labeling and the instrumental offsets were validated
using observations of the Crab pulsar (PSR J0534+2200) and PSR J0332+5434. The
former is a bright pulsar with 33.7 ms period and a relatively high DM (56.7
pc cm-3 : Lyne et al., 2014). The DM of the Crab pulsar varies from epoch to
epoch and this pulsar exhibits sporadic intense pulses, called giant pulses
(GPs; Lundgren et al., 1995; Hankins et al., 2003), typically once every four
minutes at uGMRT frequencies at uGMRT sensitivity. The GPs provide a time
marker, which is a strong function of frequency due to interstellar
dispersion. Moreover, the arrival times of this marker across different
frequencies vary with epoch due to DM variations. Thus, GPs provide a
sensitive probe to validate the assumed frequency labels for the spectral
data. PSR J0332+5434, with a flux density of $\sim$1500 mJy at 408 MHz, is the
brightest pulsar in the northern hemisphere at metre-centimetre wavelengths
with a period of 714 ms and a DM of 26.76 pc cm-3 (Lorimer et al., 1995;
Hassall et al., 2012). Bright single pulses with pulse-to-pulse intensity
variations interspersed with pulse nulls are seen in this pulsar (see Figure
3(a)).

The GWB can simultaneously be used in its different modes of operation in
different bands using any combination of the four beams provided (Gupta et
al., 2017; Reddy et al., 2017). This capability was exploited to record data
on GPs from the Crab pulsar and single pulses from PSR J0332+5434 in IA, PA,
and CDPA modes of GWB using different frequency bands available with the
uGMRT. For the Crab pulsar, first the GPs were identified in IA, PA and CDPA
mode data at both Band 3 and Band 5. We investigated the cross-correlation in
the recorded time series around the identified GPs from different modes and
frequency-bands to determine the lag in the arrival times of the GPs. This
lag, recorded for example with PA in Band 5 and CDPA in Band 3, depends on the
DM of the pulsar (specified up to a precision of 0.001 pc cm-3) and the
frequency labeling used for the two bands, as given by equation 3. As the DM
time series of this pulsar is known to the required precision from independent
measurements (Lyne et al., 1993; Lyne et al., 2014) made public by the Jodrell
Bank Observatory888http://www.jb.man.ac.uk/pulsar/crab/crab2.txt, the expected
lag in the arrival times of identified GPs was calculated from the DM nearest
to the epoch of observations. Hence, any difference between the expected and
measured lags is due to either (a) incorrect frequency labeling, or (b)
relative time offset between the two modes. As the DM of this pulsar varies
over a timescale of one month, two observations separated by one month will
yield different delays due to frequency labeling, whereas the relative
instrumental delay is expected to be constant. Thus, both the frequency
labeling as well as relative offsets can be simultaneously determined by two
such observations. We check these results for consistency using similar
analysis with PSR J0332+5434.

(a) PSR J0332+5434

(b) PSR J0534+2200

Figure 3: Time series observed using Band 5 (1360 – 1460 MHz : top plot in
each panel) and Band 3 (400 – 500 MHz : middle plot in each panel) was used to
determine the delay between the two bands using pulsars PSRs J0332+5434 and
J0534+2200. The delay is obtained from the lag measured using the cross-
correlation (shown in the bottom plot of each panel) of the two time series.
The delay in each case was compared with that expected (labeled with vertical
red dashed lines in the plot) due to dispersion in ionised interstellar medium
to determine both the frequency definition as well as relative pipeline delays
: (a) Observations of single pulses of the bright pulsar J0332+5434 showing a
delayed single pulse pattern in Band 3 compared to Band 4, (b) Observations of
a Giant pulse of PSR J0534+2200 where the delay between Band 5 (top plot) and
Band 3 (middle plot) was found consistent with that expected due to
dispersion, assuming the correct frequency definitions (Equations 4a & 4b) and
zero relative fixed pipeline delay.

###  3.2 Calibration observations and results

Epoch | DM | Bands and Modes | Sampling Time | Expected | Observed | $\Delta_{PQ}$
---|---|---|---|---|---|---
(MJD) | (pc cm-3) |  | ($\mu$s) | delay (s) | delay (s) | s
58832 | 56.7528 | B5CDPA–B3CDPA | 81.92 | 0.83172 | 0.83165(8) | 0.0
B3CDPA–B5PA | 81.92 | 0.83173 | 0.83173(8) | 1.34218
B5CDPA–B5PA | 81.92 | 0.00001 | 0.00008(8) | 1.34226
B5PA–B3PA | 81.92 | 0.83137 | 0.83141(8) | 0.0
58871 | 56.7401 | B5CDPA–B3CDPA | 20.48 | 0.83259 | 0.83259(2) | 0.0
B3CDPA–B5PA | 81.92 | 2.1748 | 2.1746(2) | 1.342177
B5PA–B3PA | 81.92 | 0.8312 | 0.8312(1) | 0.0
58991 | 56.7781 | B5CDPA–B3CDPA | 5.12 | 0.8374 | 0.8375(1) | 0.0
B5CDPA–B4PA | 40.96 | 0.39062 | 0.39051(8) | 0.0
B3CDPA–B4PA | 40.96 | 0.4468 | 0.4470(2) | 0.0
B4PA–B5PA | 40.96 | 0.4470 | 0.4472(2) | 0.0
B5PA–B5IA | 40.96 | 0.0 | 0.0 | 0.0
Table 3: Results of time delay measurements simultaneously at two different
frequency using PSR J0534+2200 for validating frequency definitions and
relative pipeline delays ($\Delta_{PQ}$) for different modes of pulsar
observations. The epoch of observations is given in the first column along-
with Dispersion measure at that epoch in second column followed by sampling
time used, expected and observed delay in samples for different combination of
modes at the two frequencies in fourth, fifth, sixth, seventh and third column
respectively. The last column presents the relative pipeline delays
($\Delta_{PQ}$). The abbreviations B5CDPA, B3CDPA, B5PA and B3PA indicate data
acquisition using Band 5 in CDPA mode, using Band 3 in CDPA mode, Band 5 in PA
mode, and Band 3 in PA mode respectively.

Calibration observations were carried out on 2019 December 16 (MJD 58832),
2020 January 24 (MJD 58871), and 2020 May 22 (MJD 58991). The estimated lags
for one combination of modes on 2020 January 24 are shown in Figures 3(a) and
3(b). The relative offsets and frequency labeling were then determined by
matching the measured and expected lags, given by equation (3), and the
estimated relative offsets for different modes are tabulated in Table 3. While
the uncertainty on measurements of these relative pipeline delays ranges from
10 to 80 $\mu$s due to coarser sampling and system noise, these measurements
are consistent with the engineering measurements. The relative pipeline delays
measured as a result of tests conducted in the first two epochs were corrected
in the software by the GMRT engineering team in April 2020. This was verified
in the tests conducted on May 22, 2020 as can be seen from Table 3.

The frequency labeling $F_{1X}$ for the different modes are expressed in terms
of the value of the highest frequency channel in the following expressions:

For IA and PA,

$F_{1X}=\begin{cases}F_{\text{LO}}&\text{for LSB}\\\ F_{\text{LO}}+\Delta
F&\text{for USB}\end{cases}\,,$ (4a) and for CDPA,
$F_{1X}=\begin{cases}F_{\text{LO}}-\frac{\Delta F}{N_{\text{chan}}}&\text{for
LSB}\\\ F_{\text{LO}}+\Delta
F\left(1-\frac{1}{N_{\text{chan}}}\right)&\text{for USB}\end{cases}\,.$ (4b)

Here, $F_{\text{LO}}$ refers to the Local Oscillator (LO) frequency (MHz) used
for the observations, $\Delta F$ is the acquisition bandwidth (typically 100
or 200 MHz) and $N_{\text{chan}}$ denotes the number of channels or sub-bands
across the band. The expression is different for each side-band denoted by USB
or LSB. When $F_{\text{LO}}$ is chosen at the lowest edge of the band being
used, this is called upper side-band (USB) where frequencies are ordered from
lowest to highest frequency. The reverse order of frequencies are used in
lower side-band (LSB) with $F_{\text{LO}}$ chosen at the highest edge of the
band. Equations 4a-4b are in agreement with what is expected from the
implementation of the IA, PA, and CDPA pipelines in GWB (Reddy et al., 2017;
De & Gupta, 2016).

These equations are implemented in pinta to make it simpler for the user to
use our data reduction pipeline. The user specifies the LO frequency, the
side-band, the acquisition bandwidth and the number of sub-bands/channels in
the pipeline.in file using the same values as specified for the back-end
observation setup. The relative offsets determined in these experiments are
not coded in pinta, but are included as jumps while performing any timing
analysis of the uGMRT data.

##  4 Performance

To validate the pipeline and investigate its performance, we performed a
series of tests using a variety of uGMRT datasets with varying data volume and
observation frequencies.

To gauge the computational performance of pinta, we sliced the raw data files
from ten different observations (the details of these datasets are given in
Table 4) into file sizes of 1 GiB9991 GiB = $2^{30}$ Bytes., 2 GiB, 4 GiB, 8
GiB, 16 GiB and 32 GiB, processed each slice separately in pinta, and in each
case recorded the execution time of each component of pinta as well as the
total execution time. The result of this exercise is shown in Figure 4 where
the ratio of the execution time to the observation duration (observe-to-reduce
time ratio) is plotted against the observation duration. Each point in Figure
4 represents the median of ten test cases and the error bar represents the
corresponding median absolute deviation. This plot shows the observe-to-reduce
ratio to be approximately between 1.5 and 3, and that it is not strongly
dependent on the data volume. This behavior is desirable and the observe-to-
reduce ratio can indeed be improved to be better than real-time by optimizing
and parallelizing the pipeline, which we plan to do in the future. Such
improvements can in principle allow pinta to be deployed as a real-time
observatory pipeline for pulsar data reduction. We also note that the observe-
to-reduce ratio while using only one of the two branches is close to or better
than real-time.

To ensure the reliability of the pipeline, these tests were repeated by
multiple users on the same datasets mentioned above using different command
line options, and the results were compared with each other as well as with
results obtained by running the various data reduction codes used in pinta
directly to ensure that the results are reproducible.

Figure 4: Ratio of execution time by observation duration (observe-to-reduce
ratio) plotted versus the observation duration. The observe-to-reduce ratio
for each of the two branches of pinta as well as the same for the entire
pipeline is plotted. Each data point represents the median of 10 tests and the
error bars represent the corresponding median absolute deviation.

###  4.1 RFI Mitigation

RFI mitigation is one of the most important processing steps in the pinta
pipeline. In order to illustrate the RFI mitigation in the pipeline, we
present here a study on ten different datasets (see Table 4), each having
varying levels of RFI. Data segments were selected from the uGMRT observation
bands 3, 4 and 5, MJD 58260-58389 with a total length for the segments 11544
seconds. The data quality of each segment prior to and after the pinta RFI
mitigation was studied. The rfifind command of PRESTO (Ransom, 2011) was used
to report the percentage of good intervals in the data. The percentage of good
intervals that is gained after the RFI mitigation is shown (in red) in Figure
5. This study provides a feel for the typical RFI mitigation available in the
pipeline, and we see from Figure 5 that the degree of improvement after
applying RFI mitigation varies greatly from dataset to dataset, which is
expected since the RFI environment itself is highly variable. Dataset 3 is of
specific interest as the percentage of good intervals more than doubles after
applying RFI mitigation, and the pulsar was detected in this dataset only
after applying RFI mitigation.

Figure 5: Effectiveness of RFI Mitigation. Each bar represents one dataset. The details of each dataset is given in Table 4. Dataset | Pulsar | Date | Band |  | Coherent
---
Dedispersion
1 | J1857+0943 | 25/08/2018 | 5 | Yes
2 | J2145$-$0750 | 22/05/2018 | 4 | No
3 | J2145$-$0750 | 25/08/2018 | 3 | Yes
4 | J2145$-$0750 | 10/09/2018 | 3 | Yes
5 | J1939+2134 | 21/05/2018 | 3 | Yes
6 | J1939+2134 | 28/09/2018 | 4 | No
7 | J1713+0747 | 07/06/2018 | 5 | Yes
8 | J2124$-$3358 | 10/09/2018 | 3 | Yes
9 | J1643$-$1224 | 08/07/2018 | 3 | Yes
10 | J1643$-$1224 | 25/08/2018 | 5 | Yes
Table 4: The details of the datasets used for characterizing the performance
and RFI mitigation efficacy of pinta. Bands 3, 4 and 5 represent 400–500 MHz,
650–750 MHz, and 1360-1460 MHz respectively for our observations.

To further illustrate the efficacy of the RFI mitigation available in pinta,
we show in Figure 6 pulse profiles generated using gptool, RFIClean, and
without performing any RFI mitigation for two observations. The profiles
without any RFI mitigation are produced by running pinta with \--no-gptool
--no-rficlean options. The signal to noise ratios (SNRs) quoted in Figure 6
are computed using the
pdmp101010http://psrchive.sourceforge.net/manuals/psrstat/algorithms/snr/
command of PSRCHIVE. In light of the caveat regarding band shape normalization
discussed in Section 2, we have chosen two observations without significant
interstellar scintillation in order to show a fair comparison between gptool
and RFIClean.

Figure 6 shows the gain in profile SNR for both datasets while using RFI
mitigation. Nevertheless, it should be noted that the SNRs for J2124$-$3358
reported by pdmp may be inaccurate due to its large duty cycle. This does not
affect our comparison between the RFI mitigated and non-RFI mitigated datasets
as it is clear from the bottom panel of Figure 6(b) that the RFI mitigated
profiles agree with each other better than with the non-RFI mitigated profile,
indicating a reduction in the noise level.

(a)

(b)

Figure 6: Comparison of frequency collapsed profiles obtained using gptool,
RFIClean, and without any RFI mitigation (noRFIx). The noRFIx profiles are
generated using the \--no-gptool --no-rficlean options. The fluxes are
uncalibrated and are in arbitrary units. The SNRs reported in the plots are
obtained using the pdmp command. Both epochs show significant improvement in
SNR while using RFI mitigation. (a) PSR J2145$-$0750 observed on 16 June 2020
in Band 5 (1260-1460 MHz) with 40.96 $\mu$s sampling time and no coherent
dedispersion. The total integration time is 55 min. (b) PSR J2124-3358
observed on 25 August 2018 in Band 3 (400-500 MHz) with 81.92 $\mu$s sampling
time with coherent dedispersion. The total integration time is 24 min.

##  5 Timing of PSR J1909–3744

In this section, we demonstrate the capability of pinta to generate profiles
from which high-precision TOAs can be derived. We use PSR J1909$-$3744 as an
example for this purpose.

The data presented in this section were obtained as part of the InPTA campaign
from April 2020 to October 2020 with a cadence of $\sim$15 days. The
observations were carried out by splitting the 30 uGMRT antennas into two
phased subarrays, where the innermost 8 antennas were used in Band 3 (300–500
MHz) and 16 of the outer antennas were used in Band 5 (1260–1460MHz). The
pulsar was observed simultaneously in both bands in each epoch, with 200 MHz
bandwidth and 1024 frequency channels in each band. The Band 3 data were
coherently dedispersed to the known DM of the pulsar, and were recorded at
20.48 $\mu$s sampling time, whereas Band 5 data were obtained using the PA
mode with a sampling time of 40.96 $\mu$s. The data were processed using
pinta, and the TOAs were extracted from the resulting Timer archives using
PSRCHIVE after time and frequency collapsing the folded profiles. The
resulting TOAs were fit using TEMPO2 (Hobbs et al., 2006) using the pulsar
ephemeris available in the NANOGrav 12.5 year dataset (Alam et al., 2020a), as
our data span is too short to provide a reliable timing solution. Post-fit
residuals after fitting for pulsar rotational parameters (F0, F1), and DM are
plotted in Figure 7. We do not use any time offsets between the two bands as
such offsets were corrected in GWB software since April 2020 based on results
mentioned in Section 3.1. The corresponding pre-fit and post-fit parameters,
along with the RMS timing residual values are listed in Table 5. A more
thorough timing solution of this data using frequency-resolved TOAs, DM
corrections and rigorous noise analysis will be published elsewhere.

From Table 5, we note that the uGMRT observations processed using pinta are
able to produce an RMS post-fit timing residuals of 1.46 $\mu$s. This
demonstrates that the data products produced using pinta can indeed be used
for high-precision timing applications such as PTAs. We expect to further
reduce the RMS timing residuals after applying DM corrections, which are
discussed elsewhere (Krishnakumar et al., 2021).

Figure 7: The timing residuals for PSR J1909$-$3744 generated using uGMRT observations processed with pinta. Band 3 is 300-500 MHz and Band 5 is 1260-1460 MHz. We used the ephemeris available in the NANOGrav 12.5 year dataset, and after changing the PEPOCH and DMEPOCH to MJD 59050, we fitted for F0, F1 and DM. The fit parameters are listed in Table 5. The timing residuals have an RMS of 1.46 $\mu$s.  Parameter | Post-fit value | Post-fit uncertainty
---|---|---
F0 (Hz) | 339.315691914442 | 1.2e-12
F1 (s-2) | -1.52e-15 | 2.5e-17
DM (pc/cm3) | 10.39090 | 0.00001
RMS Residuals ($\mu$s) | 1.46 |
Table 5: The fit parameters for PSR J1909$-$3744 generated using uGMRT
observations processed with pinta. We used the ephemeris available in NANOGrav
12.5 dataset, and after changing the PEPOCH and DMEPOCH to MJD 59050, and
fitted for F0, F1 and DM. The timing residuals are plotted in Figure 7.

##  6 Summary and Discussion

We have developed a pipeline to reduce uGMRT pulsar timing raw data for the
InPTA experiment, named pinta, which reduces the raw data input to RFI-
mitigated folded profile archives. Since the uGMRT raw data input does not
contain any metadata such as the observation settings, they are provided to
the pipeline via an ASCII input file named pipeline.in, whose contents are
summarized in Table 2. pinta performs RFI mitigation using two different
packages, namely gptool and RFIClean, running them in two different branches
which produce two different output archives. pinta provides various command
line options to control how these two branches are run, and these are
summarized in Table 1.

It is crucial to use the correct interpretation of the observatory frequency
settings while performing the data reduction. We performed validation and
calibration experiments using GPs from the Crab pulsar and single pulses from
the bright pulsar J0332+5434 to ensure that our interpretation of the
observation frequency for IA, PA and CDPA pipelines of uGMRT matches what is
given in equations (4a) and (4b). This experiment also allowed us to measure
the instrumental delays between IA, PA and CDPA pipelines of uGMRT, which are
consistent with the instrumental delays expected from engineering
considerations.

To characterize the computational performance of pinta, we conducted a number
of tests using different datasets. These tests showed that the net observe-to-
reduce time ratio of pinta is approximately 2, while the observe-to-time ratio
of individual branches is less than 1.5. These results lead us to strive to
achieve real-time observe-to-time ratio by employing parallelization
techniques to the pipeline. We also conducted tests to investigate the RFI
mitigation efficacy of pinta on the same datasets, the results of which are
shown in Figure 5. We observe that the RFI mitigation gains seen in different
datasets, having different RFI characteristics, vary significantly as
expected, with some datasets yielding up to $\sim 10\%$ gain after RFI
mitigation. We also demonstrate improvements in the significance of pulse
profiles by using the different RFI mitigation paths in pinta, which further
advocates their importance in the pipeline. These results substantiate the
addition of RFI mitigation tools in pinta. To demonstrate the ability of pinta
to generate data products from which high-precision TOAs can be derived, we
showed the timing of uGMRT observations of PSR J1909$-$3744, and we are able
to produce timing residuals with RMS of the order of 1 $\mu$s.

##  7 Future scope

Our plans for the future development of pinta include the improvement of its
computational efficiency to achieve better than real-time performance. This
may be achieved by (a) running the two branches of the pipeline parallelly
instead of serially, (b) modifying the filterbank program to use GPUs and (c)
utilizing the GPU processing option in dspsr.

Similar pipelines for reducing the data obtained using the legacy GMRT and the
ORT are also under development, ensuring a high level of compatibility with
pinta. In addition, we plan on developing “InPTA Data Management System”, a
database for tracking metadata associated with the observations and data
analysis of the InPTA experiment, which will be tightly integrated with pinta
as well as the legacy GMRT and ORT pipelines.

###### Acknowledgements.

We are grateful to the anonymous referee for a detailed perusal and
constructive feedback on the manuscript. We thank the staff of the GMRT who
made our observations possible. GMRT is run by the National Centre for Radio
Astrophysics of the Tata Institute of Fundamental Research. BCJ, YG and AB
acknowledge the support of the Department of Atomic Energy, Government of
India, under project # 12-R&D-TFR-5.02-0700. AS, AG and LD acknowledge the
support of the Department of Atomic Energy, Government of India, under project
# 12-R&D-TFR-5.02-0200. MPS acknowledges funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No. 694745). AC acknowledges the funding received
from Department of Science and Technology, Government of India, WOS-A scheme,
file no. SR/WOS-A/PM-26/2018.

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