# Pseudorandom selective excitation in NMR

Jamie D. Walls<EMAIL_ADDRESS>Department of Chemistry, University of Miami,
Coral Gables, FL 33124  Alexandra Coomes

###### Abstract

In this work, average Hamiltonian theory is used to study selective excitation
in a spin-1/2 system evolving under a series of small flip-angle
$\theta-$pulses $(\theta\ll 1)$ that are applied either periodically [which
corresponds to the DANTE pulse sequence] or aperiodically. First, an average
Hamiltonian description of the DANTE pulse sequence is developed; such a
description is determined to be valid either at or very far from the DANTE
resonance frequencies, which are simply integer multiples of the inverse of
the interpulse delay. For aperiodic excitation schemes where the interpulse
delays are chosen pseudorandomly, a single resonance can be selectively
excited if the $\theta$-pulses’ phases are modulated in concert with the time
delays. Such a selective pulse is termed a pseudorandom-DANTE or p-DANTE
sequence, and the conditions in which an average Hamiltonian description of
p-DANTE is found to be similar to that found for the DANTE sequence. It is
also shown that averaging over different p-DANTE sequences that are selective
for the same resonance can help reduce excitations at frequencies away from
the resonance frequency, thereby improving the apparent selectivity of the
p-DANTE sequences. Finally, experimental demonstrations of p-DANTE sequences
and comparisons with theory are presented.

##  I Introduction

Of the multitude of radiofrequency (RF) schemes used for exciting and
controlling spin dynamics in NMR, most can be placed into one of two
categories: aperiodic RF pulse sequences or periodic RF pulse sequences. For
many aperiodic sequences, the RF phases, amplitudes and pulse delays are often
chosen randomly or in a pseudorandom manner. Such sequences have been used to
generate white noise or broadband excitation in NMR noise spectroscopyErnst
(1970); Kaiser (1970, 1974); Bartholdi  _et al._ (1976), while sequences that
generate colored noise have been used in early spin decoupling schemes, such
as in noise decouplingErnst (1966). Theoretical models of a spin system’s
response to pseudorandom pulse sequences typically use a Volterra or
perturbation series in the randomly applied RF pulsesB.Blumich (1987). Since
many pseudorandom sequences are designed by considering only the first term in
the Volterra series, pseudorandom sequences are typically low power and result
in small, linear spin excitations.

Unlike aperiodic sequences, periodic RF pulse sequences are commonly used in a
variety of NMR experiments and are often found to be superior to their
pseudorandom counterparts; for example, two periodic sequences, MLEVLevitt and
Freeman (1981) and WALTZ-16Shaka  _et al._ (1983), provide better
heteronuclear decoupling over noise decoupling under most conditions. Many
periodic RF pulse sequences are designed using average Hamiltonian theory
(AHT)Haeberlen and Waugh (1968), where the necessary RF pulse sequence that
generates a desired average Hamiltonian $\overline{H}_{avg}$ over a time
$\tau_{c}$ must be determined ($\tau_{c}$ is the length of the pulse
sequence). Repeated application of the pulse sequence introduces frequencies
into the dynamics that are integer multiples of $\frac{1}{\tau_{c}}$, which
may result in higher-order contributions to $\overline{H}_{avg}$ that degrade
the sequence’s performance. It has been previously noted that random or
asynchronous pulse imperfections placed into pulse sequences can often improve
their performanceBosman  _et al._ (2004). Recently, Uhrig dynamical decoupling
(UDD) sequencesUhrig (2009) which utilize unequally spaced $\pi-$pulses, were
shown to be superior in preserving spin coherence to the standard Carr-
Purcell-Meiboom-Gill (CPMG) sequenceCarr and Purcell (1954), which uses
equally spaced $\pi-$pulses.

Selective pulsesFreeman (1991) are one class of pulses that do not fall neatly
into either category. The design of most commonly used selective pulses, such
as the gaussian and the sinc pulse shapes, is guided by the fact that a spin
system’s response to an applied pulse as a function of frequency/offset is
proportional to the Fourier transformation of the applied pulseTomlinson and
Hill (1973). Using linear response to design selective pulses has been used to
develop colored noise sequences for selective excitation in imaging
applicationsOrdige (1987). While sequences designed from the linear response
are valid for small flip-angles, these pulses fail as the degree of excitation
increases. As such, most methods for designing selective pulses of arbitrary
flip-angles use the linear response pulse shapes as starting points in
numerical searchesVeshtort and Griffin (2005). However, pulse shapes generated
by these numerical techniques often do not lend themselves to an easy physical
interpretation behind their selectivity.

One of the earliest and most easily understood periodic selective pulses that
is rigorously valid for all flip-angles is the DANTE sequenceBodenhausen  _et
al._ (1976), which is shown in Fig. 1(A). The DANTE sequence consists of a
series of $N$ small-tip, broadband $\theta$-pulses that selectively rotate
those spins resonating at integer multiples of the interpulse delay by
$\Theta=N\theta$ about an axis in the transverse plane. The DANTE sequence’s
periodicity is responsible for this frequency response, which can be
calculated analyticallyCanet  _et al._ (1995). To excite a single frequency,
however, the periodicity of the DANTE sequence must be violated. Breaking
DANTE’s symmetry for removing excitation at other frequencies has been
previously accomplished by modulating the phasesKacynski  _et al._ (1992),
amplitudes, and delays of the $\theta-$pulsesRoumestand and Canet (2000).
However, these excitation sculpting modifications of the DANTE sequence are
still based on the assumptions of linear response.

In the following paper, we use AHT to provide insight into the selective
excitation of a spin-1/2 system by a series of periodically and aperiodically
small-flip $\theta$-pulses. First, the conditions where an AHT description of
the DANTE pulse sequence is valid is determined. Next, an AHT description for
a series of aperiodically spaced and phase-modulated $\theta-$pulses is
developed. Such sequences are referred to as pseudorandom-DANTE or p-DANTE
selective pulses [Fig. 1(B)]. Finally, experiments performed in acetone and in
an acetone/DMSO/water solution are used to demonstrate and validate the
selectivity of the p-DANTE sequences.

##  II General Theory

Both the DANTE [Fig. 1(A)] and the p-DANTE [Fig. 1(B)] pulse sequences involve
the application of a series of $N$ small flip-angle $\theta-$pulses that
selectively rotate spins about an axis lying in the transverse plane by an
angle $\Theta=N\theta$. For the DANTE sequence, spins resonating at
$\nu_{Z}=\frac{n}{\tau}$ are selectively rotated by $\Theta$ (where $n$ is an
integer), whereas for the p-DANTE sequence, only those spins resonating at
$\nu_{Z}=\nu_{0}$ are rotated by $\Theta$.

Figure 1: Pulse sequence for (A) DANTEBodenhausen  _et al._ (1976) and (B)
pseudorandom-DANTE or p-DANTE selective excitation. (A) The DANTE sequence
consists of a series of $N$ small-flip, $\theta$-pulses, equally spaced
between periods of free evolution of time $\tau$. The periodicity of the
sequence results in a rotation of $\Theta=N\theta$ about an axis perpendicular
in the transverse plane for those spins resonating (in the rotating frame) at
a frequency $\nu_{Z}=\frac{n}{\tau}$ where $n$ is an integer. (B) The p-DANTE
sequence consists of a series of $N$ unequally spaced small-flip,
$\theta$-pulses where $\tau_{k}$ is the time delay between the $k^{th}$ and
$(k+1)^{th}$, and $\phi_{k}=2\pi\sum_{k=1}^{k-1}\nu_{0}\tau_{k}$ is the phase
of the $k^{th}$ pulse with $\phi_{1}=0$. In the p-DANTE sequence, only those
spins resonating (in the rotating frame) at a frequency given by $\nu_{0}$ are
rotated by an angle $\Theta=N\theta$.

To understand the selectivity of both the DANTE and p-DANTE sequences within
the framework of AHT, it is useful to revisit the dynamics of a spin-1/2
system under a non-resonant RF irradiation. The Hamiltonian during the
application of an RF pulse is given by:
$\frac{\widehat{H}}{\hbar}=\omega_{z}\widehat{I}_{Z}+\omega_{RF}\left(\widehat{I}_{X}\cos(\phi)+\widehat{I}_{Y}\sin(\phi)\right)$,
where $\phi$ and $\omega_{RF}$ are the phase and amplitude of the RF pulse,
and $\omega_{Z}=2\pi\nu_{Z}$ is the resonance offset that the spin experiences
in the rotating frame. The propagator for an RF pulse applied for a time
$T_{p}$ can be written as:

$\displaystyle\widehat{P}^{\text{exact}}_{\phi}(T_{p})$ $\displaystyle=$
$\displaystyle\exp\left(-i\frac{\widehat{H}}{\hbar}T_{p}\right)=\exp\left(-i\left[\omega_{Z}\widehat{I}_{Z}+\omega_{RF}\left(\widehat{I}_{X}\cos(\phi)+\widehat{I}_{Y}\sin(\phi)\right)\right]T_{p}\right)$
$\displaystyle=$
$\displaystyle\cos\left(T_{p}\frac{\sqrt{\omega_{Z}^{2}+\omega_{RF}^{2}}}{2}\right)\widehat{1}-i\frac{2\sin\left(T_{p}\frac{\sqrt{\omega_{Z}^{2}+\omega_{RF}^{2}}}{2}\right)}{\sqrt{\omega_{Z}^{2}+\omega_{RF}^{2}}}\left(\omega_{Z}\widehat{I}_{Z}+\omega_{RF}\left(\cos(\phi)\widehat{I}_{X}+\sin(\phi)\widehat{I}_{Y}\right)\right)$

Alternatively, the propagator in Eq. (LABEL:eq:pulexact) can be transformed
into an interaction frame defined by $\omega_{Z}\widehat{I}_{Z}$ and is given
by:

$\displaystyle\widehat{P}^{\text{exact}}_{\phi}(T_{p})$ $\displaystyle=$
$\displaystyle\exp\left(-i\omega_{Z}T_{p}\widehat{I}_{Z}\right)\widehat{T}\exp\left(-i\int^{T_{p}}_{0}\text{d}t^{\prime}\frac{\omega_{RF}}{2}\left[\widehat{I}_{+}e^{i\left(\omega_{Z}t^{\prime}-\phi\right)}+\widehat{I}_{-}e^{-i\left(\omega_{Z}t^{\prime}-\phi\right)}\right]\right]$
(2) $\displaystyle=$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}T_{p})\widehat{T}\exp\left(-i\int^{T_{p}}_{0}\text{d}t^{\prime}\frac{\widehat{H}_{INT}(t^{\prime})}{\hbar}\right)$

where $\widehat{T}$ is the Dyson time-ordering operator,
$\widehat{U}_{\text{free}}(\omega_{Z}T_{p})=\exp\left(-i\omega_{Z}T_{p}\widehat{I}_{Z}\right)$,
and $\widehat{H}_{INT}(t^{\prime})$, the Hamiltonian in the interaction frame,
represents a purely phase-modulated RF pulse. The time-dependent propagator in
Eq. (2) can be approximated by:

$\displaystyle\widehat{T}\exp\left(-\frac{i}{\hbar}\int^{T_{p}}_{0}\text{d}t^{\prime}\widehat{H}_{INT}(t^{\prime})\right)=\exp\left(-\frac{iT_{p}}{\hbar}\overline{H}_{p,\phi}\right)$
(3)

In Eq. (3), $\overline{H}_{p,\phi}$ is the average HamiltonianHaeberlen and
Waugh (1968) and is given by
$\overline{H}_{p,\phi}=\sum_{n=1}^{\infty}\overline{H}_{p,\phi}^{(n)}$ where
the first two terms in the series are:

$\displaystyle\frac{\overline{H}_{p,\phi}^{(1)}}{\hbar}$ $\displaystyle=$
$\displaystyle\frac{1}{T_{p}}\int^{T_{p}}_{0}\text{d}t^{\prime}\widehat{H}_{INT,\phi}(t^{\prime})$
$\displaystyle=$
$\displaystyle\frac{\omega_{RF}}{2}\text{sinc}\left(\frac{\omega_{Z}T_{p}}{2}\right)\left(\widehat{I}_{+}e^{i\left(\frac{\omega_{Z}T_{p}}{2}-\phi\right)}+I_{-}e^{-i\left(\frac{\omega_{Z}T_{p}}{2}-\phi\right)}\right)$
$\displaystyle\frac{\overline{H}_{p,\phi}^{(2)}}{\hbar}$ $\displaystyle=$
$\displaystyle\frac{1}{2iT_{p}}\int^{T_{p}}_{0}\text{d}t^{\prime}\int^{t^{\prime}}_{0}\text{d}t^{\prime\prime}\left[\widehat{H}_{INT,\phi}(t^{\prime}),\widehat{H}_{INT,\phi}(t^{\prime\prime})\right]$
(4) $\displaystyle=$
$\displaystyle\frac{\omega_{RF}^{2}}{4it_{p}}\widehat{I}_{Z}\int^{T_{p}}_{0}\text{d}t^{\prime}\int^{t^{\prime}}_{0}\text{d}t^{\prime\prime}\left(e^{i\omega_{Z}(t^{\prime}-t^{\prime\prime})}-e^{-i\omega_{Z}(t^{\prime}-t^{\prime\prime})}\right)$
$\displaystyle=$
$\displaystyle\frac{\omega_{RF}^{2}}{2\omega_{Z}}\left(1-\text{sinc}(\omega_{Z}T_{p})\right)\widehat{I}_{Z}$

$\widehat{P}^{\text{exact}}_{\phi}(T_{p})$ in Eq. (2) can be approximated as:

$\displaystyle\widehat{P}_{\phi}^{\text{exact}}(T_{p})$ $\displaystyle\approx$
$\displaystyle\widehat{P}_{\phi}(T_{p})\approx\exp\left(-iT_{p}\omega_{Z}\widehat{I}_{Z}\right)\exp\left(-\frac{iT_{p}}{\hbar}\left(\overline{H}_{p,\phi}^{(1)}+\overline{H}_{p,\phi}^{(2)}\right)\right)$
(5)

For $\omega_{RF}T_{p}\leq\frac{2\pi}{9}$,
$||\widehat{P}_{\phi}^{\text{exact}}(T_{p})-\widehat{P}_{\phi}(T_{p})||\leq
10^{-3}$ for all $\omega_{Z}$, where $||A||=\sqrt{\text{Tr}[A^{\dagger}A]}$
represents the Frobenius matrix norm (if $A$ represents the difference of two
unitary matrices, then the maximum value of $||A||$ is $2\sqrt{n}$ where $n$
is the matrix dimension). Since the DANTE and p-DANTE sequences both consist
of a series of small flip-angle $\theta-$pulses with $\theta<\frac{2\pi}{9}$,
the approximation
$\widehat{P}^{\text{exact}}_{\phi}(T_{p})\approx\widehat{P}_{\phi}(T_{p})$ in
Eq. (5) will be used in the rest of this paper.
For future comparison of the propagator in Eq. (2) with the propagator for a
spin-1/2 evolving under either the DANTE or the p-DANTE sequences in Fig. 1,
it is useful to consider an alternative description of
$\widehat{P}_{\phi}^{\text{exact}}$ in the interaction frame by dividing
$\widehat{T}\exp\left(-\frac{i}{\hbar}\int^{T_{p}}_{0}\widehat{H}_{\text{INT}}(t^{\prime})\text{d}t^{\prime}\right)$
in Eq. (2) into $N\gg 1$ smaller propagators, which is illustrated in Figure
2(A). In this case, $P_{\phi}^{\text{exact}}(T_{p})$ can be rewritten as:

$\displaystyle\widehat{P}_{\phi}^{\text{exact}}(T_{p})$ $\displaystyle=$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}T_{p})\widehat{T}\exp\left(-i\int^{T_{p}}_{0}\text{d}t^{\prime}\frac{\widehat{H}_{INT}(t^{\prime})}{\hbar}\right)$
(6) $\displaystyle\approx$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}T_{p})\widehat{T}\prod_{j=1}^{N}\exp\left(-i\int^{j\frac{T_{p}}{N}}_{(j-1)\frac{T_{p}}{N}}\text{d}t^{\prime}\frac{\widehat{H}_{INT}(t^{\prime})}{\hbar}\right)$
$\displaystyle\approx$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}T_{p})\widehat{T}\prod_{j=1}^{N}\exp\left(-i\frac{T_{p}}{N}\omega_{RF}\text{sinc}\left(\frac{\omega_{Z}T_{p}}{2N}\right)\left(\widehat{I}_{X}\cos\left(\phi_{j}^{*}\right)-I_{Y}\sin\left(\phi_{j}^{*}\right)\right)\right)$

where $\phi_{j}^{*}=\frac{\omega_{Z}(j-1)T_{p}}{N}+\frac{T_{p}}{2N}-\phi$.
With respect to Eq. (6) and Fig. 2(A), the total propagator for an RF pulse of
strength $\omega_{RF}$ applied off-resonance by $\omega_{Z}$ for a time
$T_{p}$ is equivalent to the application of $N$ continuous, small-flip
$\theta=\frac{T_{p}}{N}\text{sinc}\left(\frac{\omega_{Z}T_{p}}{2N}\right)$,
phase-modulated RF pulses where the phase of the $j^{th}$ pulse is
$-\phi_{j}^{*}$, followed by a rotation about the $\widehat{z}-$axis by
$\omega_{Z}T_{p}$.

###  II.1 DANTE Pulse Sequence

The DANTE sequenceBodenhausen  _et al._ (1976) consists of a series of $N$,
equally spaced small-tip, $\theta$-pulses of constant phase and duration
$t_{p}$ where $\omega_{RF}t_{p}=\theta\ll 1$ [Figure 1(A)]. The full
propagator for the DANTE pulse sequence can be written as:

$\displaystyle\widehat{U}_{\text{exact}}(T_{\text{tot}})$ $\displaystyle=$
$\displaystyle\widehat{P}_{0}(t_{p})\left(\widehat{U}_{\text{free}}(\omega_{Z}\tau)\widehat{P}_{0}(t_{p})\right)^{N-1}=\left(\widehat{P}_{0}(t_{p})\widehat{U}_{\text{free}}(\omega_{Z}\tau)\right)^{N-1}\widehat{P}_{0}(t_{p})$
(7) $\displaystyle=$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}\left((N-1)\tau_{t}+t_{p}\right))\widehat{T}\prod_{k=0}^{N-1}\widehat{P}_{-k\omega_{Z}\tau_{t}}(t_{p})$

where $\tau$ is the time delay between pulses, $\tau_{t}=\tau+t_{p}$ and

$\displaystyle\widehat{P}_{-k\omega_{Z}\tau_{t}}(t_{p})$ $\displaystyle=$
$\displaystyle\widehat{U}^{\dagger}_{\text{free}}(\omega_{Z}k\tau_{t})\widehat{P}_{0}(t_{p})\widehat{U}_{\text{free}}(\omega_{Z}k\tau_{t})\equiv\exp\left(-i\widehat{H}_{k}t_{p}\right)$
(8) $\displaystyle\widehat{H}_{k}$ $\displaystyle=$
$\displaystyle\overline{H}_{p,-k\omega_{Z}\tau_{t}}$ $\displaystyle\approx$
$\displaystyle\frac{\omega_{RF}}{2}\text{sinc}\left(\frac{\omega_{Z}t_{p}}{2}\right)\left(\widehat{I}_{+}e^{i\omega_{Z}\frac{2k\tau_{t}+t_{p}}{2}}+\widehat{I}_{-}e^{-i\omega_{Z}\frac{2k\tau_{t}+t_{p}}{2}}\right)+\frac{\omega_{RF}^{2}}{2\omega_{Z}}\left(1-\text{sinc}(\omega_{Z}t_{p})\right)\widehat{I}_{Z}$

As has been previously notedShinnar and Leigh (1987); Shinnar  _et al._ (1989,
1989), the propagator for the DANTE sequence in Eq. (7) is the same as the
propagator for a continuous series of $N$, phase modulated small-flip pulses,
where the phase modulation depends upon the spin’s chemical shift,
$\omega_{Z}$, followed by a rotation about the $\widehat{z}-$ axis by
$\omega_{Z}T_{\text{tot}}$. This is illustrated in Figure 2(B). If
$\text{mod}\left[\omega_{Z}\tau_{t},2\pi\right]\approx 0$, then all $N$ pulses
are effectively applied along the same direction since
$\phi_{k}\approx\phi_{j}$ for all $k$ and $j$. The small rotations are
therefore additive and lead to an overall rotation of $\Theta\approx N\theta$
about an axis in the transverse plane is generated. When
$\text{mod}\left[\omega_{Z}\tau_{t},2\pi\right]\neq 0$, the pulses are
effectively applied about different directions ($\phi_{k}\neq\phi_{j}$ for
$k\neq j$ in general) thereby reducing the overall spin rotation. Comparing
Fig. 2(B) and Eqs. (7) and (LABEL:eq:Hk) with Fig. 2(A) and Eq. (6), the
propagator for the DANTE sequence is similar to that of an off resonant, RF
pulse of duration $Nt_{p}=T_{p}$ followed by a rotation about the
$\widehat{z}$-axis. That is,

$\displaystyle\widehat{U}_{\text{exact}}(T_{\text{tot}})$
$\displaystyle\approx$
$\displaystyle\widehat{U}_{\text{free}}(\omega_{Z}T_{\text{tot}}-\omega_{Z}^{\prime}Nt_{p})\exp\left[-iT_{p}\left(\omega_{Z}^{\prime}\widehat{I}_{Z}+\omega_{RF}^{\prime}\left(\widehat{I}_{X}\cos(\phi^{\prime})+\widehat{I}_{Y}\sin(\phi^{\prime})\right)\right)\right]$

where
$\omega_{Z}^{\prime}=\frac{2\pi}{t_{p}}\text{mod}\left[\omega_{Z}\tau_{t},2\pi\right]$,
$\omega_{RF}^{\prime}=\frac{\text{sinc}\left(\frac{\omega_{Z}t_{p}}{2}\right)}{\text{sinc}\left(\frac{\omega_{Z}^{\prime}t_{p}}{2}\right)}\omega_{RF}$,
and $\phi^{\prime}=\frac{t_{p}}{2}(\omega_{Z}^{\prime}-\omega_{Z})$. As
mentioned above, when $\text{mod}\left[\omega_{Z}\tau_{t},2\pi\right]=0$, then
$\omega_{Z}^{\prime}=0$, and the effective pulse is applied on resonance and
rotates the spin by $\Theta$. When
$\text{mod}\left[\omega_{Z}\tau_{t},2\pi\right]\neq 0$, then
$\omega_{Z}^{\prime}$ can be quite large since $\frac{2\pi}{t_{p}}\gg 1$ for
short pulses ($t_{p}\ll 1$). In this case, the pulse appears to be applied
very far off resonance when $\omega_{Z}^{\prime}\gg\omega_{RF}^{\prime}$.

Figure 2: The connection between the DANTE pulse sequence and the application
of an off-resonant RF pulse. (A) An RF pulse applied off resonance by
$\omega_{Z}$ and with strength $\omega_{RF}$ for a time $T_{p}$ is equivalent
to applying $N\gg 1$ phase-modulated, small flip-angle
$\theta=\omega_{RF}\frac{T_{p}}{N}\text{sinc}\left(\frac{\omega_{Z}T_{p}}{2N}\right)$
pulses followed by a rotation about the $\widehat{z}$-axis by an angle
$\omega_{Z}T_{p}$. The phase of the $j^{th}$ pulse is given by
$-\phi_{j}^{*}=(j-1)\omega_{Z}\frac{T_{p}}{N}+\omega_{Z}\frac{T_{p}}{2N}-\phi$
(in Fig. 2(A), $\phi=0$). In (B), a DANTE pulse sequence is equivalent to a
series of $N$ phase-modulated small-flip pulses followed by a rotation about
the $\widehat{z}-$axis by an angle $N\omega_{Z}\tau$ [Eq. (7)]. The phase of
the $k^{th}$ pulse is
$\phi_{k}=\omega_{Z}\left((k-1)(\tau_{t})+\frac{t_{p}}{2}\right)$ where
$\tau_{t}=\tau+t_{p}$, $t_{p}$ is the length of the small-flip pulses, and
$T_{\text{tot}}=(N-1)\tau_{t}+t_{p}$.

In order to make the above arguments more quantitative, AHT can be used to
rewrite $\widehat{U}(T_{\text{tot}})$ in Eq. (7) as
$\widehat{U}(T_{\text{tot}})\approx\widehat{U}_{\text{AHT}}(T_{\text{tot}})$
where
$\widehat{U}_{\text{AHT}}(T_{\text{tot}})=\widehat{U}_{\text{free}}(\omega_{Z}T_{\text{tot}})\exp\left(-iNt_{p}\overline{H}_{avg}\right)$,
where the first two terms in the average Hamiltonian,
$\overline{H}_{avg}=\sum_{n=1}^{\infty}\overline{H}_{avg}^{(n)}$, are given by
[setting $a=\omega_{RF}\text{sinc}\left(\frac{\omega_{Z}t_{p}}{2}\right)$ and
$b=\frac{\omega_{RF}^{2}}{2\omega_{Z}}\left(1-\text{sinc}\left(\omega_{Z}t_{p}\right)\right)$]:

$\displaystyle\overline{H}_{avg}^{(1)}$ $\displaystyle=$
$\displaystyle\frac{1}{Nt_{p}}\sum_{k=1}^{N-1}t_{p}\widehat{H}_{k}$
$\displaystyle=$ $\displaystyle
a\frac{\text{sinc}\left(\frac{N\omega_{Z}\tau_{t}}{2}\right)}{\text{sinc}\left(\frac{\omega_{Z}\tau_{t}}{2}\right)}\widehat{I}_{T}(\omega_{Z},\tau_{t},t_{p},N)+b\widehat{I}_{Z}$
$\displaystyle\overline{H}_{avg}^{(2)}$ $\displaystyle=$
$\displaystyle\frac{1}{2iNt_{p}}\sum_{k>j}\left[\widehat{H}_{k}t_{p},\widehat{H}_{j}t_{p}\right]=-\frac{a^{2}t_{p}}{2\omega_{Z}\tau_{t}}\frac{\text{sinc}\left(N\omega_{Z}\tau_{t}\right)-\text{sinc}(\omega_{Z}\tau_{t})}{\left(\text{sinc}\left(\frac{\omega_{Z}\tau_{t}}{2}\right)\right)^{2}}\widehat{I}_{Z}$
$\displaystyle+$
$\displaystyle\frac{abt_{p}(N^{2}-1)}{4N\omega_{Z}\tau_{t}}\frac{\text{sinc}\left(\frac{(N+1)\omega_{Z}\tau_{t}}{2}\right)-\text{sinc}\left(\frac{(N-1)\omega_{Z}\tau_{t}}{2}\right)}{\text{sinc}^{2}\left(\frac{\omega_{Z}\tau_{t}}{2}\right)}\widehat{I}_{T}(\omega_{Z},\tau_{t},t_{p},N)$

where
$\widehat{I}_{T}(\omega_{Z},\tau_{t},t_{p},N)=\widehat{I}_{X}\cos\left(\frac{\omega_{Z}T_{\text{tot}}}{2}\right)-\widehat{I}_{Y}\sin\left(\frac{\omega_{Z}T_{\text{tot}}}{2}\right)$.
Although the form of $\overline{H}_{avg}$ in Eq. (LABEL:eq:Havg) is somewhat
complicated, the physical picture behind $\overline{H}_{avg}$ in Eq.
(LABEL:eq:Havg) can be seen in Fig. 2(B). When $\omega_{Z}\tau_{t}=2\pi n$ for
integer $n$, $\phi_{j}=\phi_{k}$ and therefore
$\left[\widehat{H}_{k},\widehat{H}_{j}\right]=0$ for all $k\neq j$, so
$\overline{H}_{avg}=\overline{H}_{avg}^{(1)}$ exactly. In this case, the
propagator represents a rotation about an axis in the transverse plane of
phase $(-1)^{n}\omega_{Z}t_{p}/2$ by a total angle of
$\Theta=N\omega_{RF}t_{p}\text{sinc}\left(\omega_{Z}t_{p}/2\right)\approx
N\omega_{RF}t_{p}=N\theta$ for $\omega_{Z}t_{p}\ll 1$. For
$\omega_{Z}\tau_{t}\neq 2\pi n$ for integer $n$, the various $\widehat{H}_{k}$
are pointing in different directions, so that the average transverse field in
$\overline{H}_{avg}^{(1)}$ is lessened. Furthermore, since the effective
rotation directions no longer commute with one another, i.e.,
$[\widehat{H}_{k},\widehat{H}_{j}]\neq 0$ for $k\neq j$, there is a
contribution to $\overline{H}_{avg}$ at second-order,
$\overline{H}_{avg}^{(2)}$, of an effective field along the $\widehat{z}$
direction. When $|\overline{H}_{avg}^{(2)}|\gg|\overline{H}_{avg}^{(1)}|$, the
effective field lies mostly about the $\widehat{z}-$axis and the spins are
minimally excited (this argument is similar to the concept of second-
averagingDybowski and Vaughan (1975)).

In order to see under what conditions AHT can be used in calculating the DANTE
pulse sequence, Figure 3 shows
$||\widehat{U}_{\text{exact}}(T_{\text{tot}})-\widehat{U}_{\text{AHT}}(T_{\text{tot}})||$
using
$\overline{H}_{\text{avg}}\approx\overline{H}_{\text{avg}}^{(1)}+\overline{H}_{\text{avg}}^{(2)}$,
as a function of $N$ and $\omega_{Z}/\omega_{RF}$. Two calculations are shown
in Fig. 3, one for a total pulse rotation for an on-resonant RF pulse of
$\Theta=\pi/2$ [Fig. 3(A)] and one for $\Theta=2\pi$ [Fig. 3(B)]. For both
calculations, $\frac{\tau}{t_{p}}=1000$. As mentioned above,
$\widehat{U}_{\text{AHT}}(T_{\text{tot}})\approx\widehat{U}_{\text{exact}}(T_{\text{tot}})$
when $2\pi
n=\omega_{Z}\tau_{t}=\frac{\omega_{Z}}{\omega_{RF}}\omega_{RF}t_{p}\left(\frac{\tau}{t_{p}}+1\right)=\frac{\omega_{Z}}{\omega_{RF}}\frac{\Theta}{N}\left(\frac{\tau}{t_{p}}+1\right)$,
where $n$ is an integer. Therefore, at a resonance condition for $n\neq 0$,
there exists a linear relationship between $N$ and
$\frac{\omega_{Z}}{\omega_{RF}}$ that is given by

$\displaystyle N$ $\displaystyle=$
$\displaystyle\text{INT}\left[\frac{\omega_{Z}}{\omega_{RF}}\frac{\Theta}{2\pi
n}\left(\frac{\tau}{t_{p}}+1\right)\right]$ (12)

where $\text{INT}[x]$ gives the nearest integer near $x$. From Fig. 3, for
$\theta\leq\frac{\pi}{60}$ [$N\geq 30$ in Fig. 3(A) and $N\geq 120$ in Fig.
3(B)], $\widehat{U}_{\text{AHT}}(T_{\text{tot}})$ is a good approximation to
$\widehat{U}_{\text{exact}}(T_{\text{tot}})$ for all
$\frac{\omega_{Z}}{\omega_{RF}}$ except near the resonance conditions in Eq.
(12). The deviations of $\widehat{U}_{\text{AHT}}(T_{\text{Tot}})$ from
$\widehat{U}_{\text{exact}}(T_{\text{tot}})$ occur when $\omega_{Z}$ is
slightly away from the resonance condition, $\omega_{Z}=\frac{2\pi
n}{\tau_{t}}$ for integer $n$. From numerical calculations, the range of
frequencies in which $\widehat{U}_{\text{AHT}}(T_{\text{Tot}})$ is a good
approximation to $\widehat{U}_{\text{exact}}(T_{\text{tot}})$ is found to be
approximately given by $\delta\omega_{Z}\gg\frac{6\theta\pi}{5\tau_{t}\Theta}$
or $\delta\omega_{Z}\ll\frac{6\theta\pi}{5\tau_{t}\Theta}$, where
$\delta\omega_{Z}=\text{min}\left[|\omega_{Z}-\frac{2\pi n}{\tau_{t}}|\right]$
is the smallest frequency difference between $\omega_{Z}$ and the nearest
integer multiple of the DANTE resonance frequency, $\frac{2\pi}{\tau_{t}}$.
Although the range of $\omega_{Z}$ where
$\widehat{U}_{\text{AHT}}(T_{\text{tot}})$ is a good approximation increases
with decreasing $\theta$ (increasing $N$), the maximum of
$||\widehat{U}_{\text{AHT}}(T_{tot})-\widehat{U}_{\text{exact}}(T_{tot})||$
mainly depends upon the overall rotation angle, $\Theta$. For
$\Theta<\frac{5\pi}{9}$,
$\text{max}\left[||\widehat{U}_{\text{AHT}}(T_{tot})-\widehat{U}_{\text{exact}}(T_{tot})||\right]\leq
0.1$ for all $N$ and $\omega_{Z}$. Physically, this can be understood as
follows: for $\delta\omega_{Z}t_{p}\gg\frac{6\theta\pi}{5\tau_{t}\Theta}$, the
effective phases of the pulses [see Fig. 2(B)] are modulated faster than the
effective tip of the pulse, $\omega_{RF}t_{p}=\theta$, so that
$\omega_{Z}\gg\omega_{RF}$. In this case, AHT works well, just as in using the
typical rotating wave approximation. For
$\omega_{Z}\ll\frac{6\pi\theta}{5\tau_{t}\Theta}$, the phases of the pulses in
Fig. 2(B) are relatively unchanged during the course of the sequence; in this
case, the various Hamiltonians, $\widehat{H}_{k}$ in Eq. (LABEL:eq:Hk) commute
with one another, so $\overline{H}_{avg}\approx\overline{H}_{avg}^{(1)}$ and
$\widehat{U}_{\text{exact}}(T_{tot})\approx\widehat{U}_{\text{AHT}}(T_{tot})$.

Figure 3: The Frobenius norm of
$||\widehat{U}_{\text{exact}}(T_{\text{tot}})-\widehat{U}_{\text{AHT}}(T_{\text{tot}})||$
as a function of the number of small tip $\theta$-pulses, $N$, with
$\theta=\frac{\Theta}{N}$, and $\frac{\omega_{Z}}{\omega_{RF}}$. In Fig. 3,
two calculations are shown for total maximum flip angle of (A)
$\Theta=\frac{\pi}{2}$ and (B) $\Theta=2\pi$.
$\widehat{U}_{\text{exact}}(T_{\text{tot}})$ [Eq. (7)] is the exact propagator
for the DANTE sequence, and $\widehat{U}_{\text{AHT}}(T_{\text{tot}})$ is the
propagator calculated using the average Hamiltonian,
$\overline{H}_{avg}\approx\overline{H}_{avg}^{(1)}+\overline{H}_{avg}^{(2)}$
in Eq. (LABEL:eq:Havg). In both calculations, $\frac{\tau}{t_{p}}=1000$. The
greatest deviations between $\widehat{U}_{\text{exact}}(T_{\text{tot}})$ and
$\widehat{U}_{\text{AHT}}(T_{\text{tot}})$ occur about the resonance
conditions in Eq. (12), and the maxima in
$||\widehat{U}_{\text{exact}}(T_{\text{tot}})-\widehat{U}_{\text{AHT}}(T_{\text{tot}})||$
are approximately described by two parallel lines given by
$N=\text{INT}\left[\frac{\omega_{Z}}{\omega_{RF}}\frac{\Theta}{2\pi
n}\left(\frac{\tau}{t_{p}}+1\right)\pm\frac{3}{5n}\right]$ for integer $n\neq
0$. The agreement between $\widehat{U}_{\text{AHT}}(T_{\text{tot}})$ and
$\widehat{U}_{\text{exact}}(T_{\text{tot}})$ improves with decreasing
$\Theta$.

###  II.2 pseudorandom DANTE (p-DANTE)

In the DANTE sequence, a natural frequency of $\frac{1}{\tau_{t}}$ is
introduced into the dynamics due to the periodicity of the pulse sequence;
this leads to efficient excitation at frequencies
$\nu^{\text{DANTE}}_{n}=\frac{n}{\tau_{t}}$ for integer $n$. However, suppose
that one was interested in using a DANTE-like sequence to efficiently excite
only one particular frequency, say at $\nu^{\text{DANTE}}_{0}=0$ Hz. One way
to accomplish this using a DANTE sequence would be to make $\tau_{t}$ small
enough such that all $\nu^{\text{DANTE}}_{n\neq 0}$ lie outside the relevant
spectral width. If the spectral width for the system of interest is large,
however, this would necessitate using small $\tau_{t}$, where the smallest
time possible $\tau_{t}$ is $\tau_{t}\approx t_{p}$ (i.e., when $\tau=0$). The
selectivity or width of the excitation spectrum about $\nu^{\text{DANTE}}_{n}$
is approximately given by $\frac{1}{N\tau_{t}}$. For $\tau_{t}\approx t_{p}$,
this means the selectivity is roughly proportional to
$\frac{1}{Nt_{p}}=\frac{2\pi\nu_{RF}}{\Theta}$. In this limit, the effect of
the DANTE sequence is similar to evolution under continuous RF irradiation,
which leads to a very broad excitation profile unless $\nu_{RF}$ is weak or
$\Theta\gg 2\pi$. Under these conditions, the DANTE sequence would be
equivalent to applying a long, low-amplitude RF pulse.

An alternative way to excite only a single resonance using a DANTE-like
sequence would be to violate the periodicity of the DANTE sequence. This could
be accomplished in a variety of ways, such as using aperiodic delays,
modulating the pulse amplitudes and delays, etc. One example of such an
aperiodic DANTE sequence is illustrated in Figure 1(B) where $N$ small-flip
$\theta$-pulses are applied with a delay of $\tau_{k}$ between the separation
between the $k^{th}$ and $(k+1)^{th}$ pulse, where in general,
$\tau_{k}\neq\tau_{j}$. For such pulse sequences to selectively and
efficiently excite spins at a single resonance frequency $\nu_{0}$, the phases
of the pulses, $\phi_{k}$, must be modulated. In this case, the phase of the
$(k+1)^{th}$ pulse is given by
$\phi_{k+1}=-2\pi\nu_{0}\left(kt_{p}+\sum_{j=1}^{k}\tau_{j}\right)=-2\pi\nu_{0}T_{k}$
with $T_{k}=kt_{p}+\sum_{j=1}^{k}\tau_{j}$, and $\phi_{1}=0$ and $T_{0}=0$.
Such a set of aperiodic DANTE sequences are referred to as pseudorandom-DANTE
or p-DANTE sequences.

As in the DANTE case, the propagator for the p-DANTE sequence can be written
as
$\widehat{U}(T_{\text{tot}})=\widehat{U}_{\text{free}}(\omega_{Z}(T_{\text{tot}}))\exp\left(-\frac{i}{\hbar}Nt_{p}\overline{H}_{avg}\right)$,
where $T_{\text{tot}}=T_{N-1}+t_{p}$, and $\overline{H}_{avg}$ is the average
Hamiltonian for the p-DANTE sequence, with the first two terms given by:

$\displaystyle\overline{H}^{(1)}_{\text{avg}}$ $\displaystyle=$
$\displaystyle\frac{a}{N}\sum_{k=1}^{N}\left(\widehat{I}_{+}e^{i\left(\Delta\omega
T_{k}+\frac{\omega_{Z}t_{p}}{2}\right)}+I_{-}e^{-i\left(\Delta\omega
T_{k}+\frac{\omega_{Z}t_{p}}{2}\right)}\right)+b\widehat{I}_{Z}$ (13)
$\displaystyle\overline{H}^{(2)}_{\text{avg}}$ $\displaystyle=$
$\displaystyle\frac{abt_{p}}{2N}\left[\sum_{j<k}\sin\left(\frac{\Delta\omega(T_{j}-T_{k})}{2}\right)\left(\widehat{I}_{+}e^{i\frac{\Delta\omega(T_{j}+T_{k})+\omega_{Z}t_{p}}{2}}+\widehat{I}_{-}e^{-i\frac{\Delta\omega(T_{j}+T_{k})+\omega_{Z}t_{p}}{2}}\right)\right]$
(14) $\displaystyle+$
$\displaystyle\frac{a^{2}t_{p}}{2N}\widehat{I}_{Z}\sum_{j<k}\sin\left(\Delta\omega(T_{k}-T_{j})\right)$

where $\Delta\omega=2\pi\left(\nu_{Z}-\nu_{0}\right)$, and $a$ and $b$ were
previously defined before Eq. (LABEL:eq:Havg). Unlike in the DANTE case, the
average delay between pulses fluctuates within the p-DANTE sequence, i.e.,
$\frac{T_{k}}{k}\neq\frac{T_{j}}{j}$ for $k\neq j$. For $\nu_{Z}\neq\nu_{0}$,
a p-DANTE sequence is effectively equivalent to applying an RF field with a
fluctuating offset [Fig. 2(A)], the result of which is a seemingly random
excitation profile for those spins with $\Delta\omega_{Z}\neq 0$. Spins with
$\Delta\omega_{Z}=0$ are rotated by $N\theta=\Theta$. This is illustrated in
Figures 4(A) and 4(B), which show the excitation and
$\widehat{z}-$magnetization profiles under a p-DANTE sequence respectively. In
Figs. 4(A) and 4(B), the various $N-1$ $\tau_{k}$’s were chosen randomly but
were scaled to ensure that $\sum_{k=1}^{N-1}\tau_{k}=46.4$ ms, and one hundred
different sets of randomly generated p-DANTE sequences were generated.
Consider the excitation and $\widehat{z}-$magnetization profile for a single
p-DANTE sequence [red curve ($N_{avg}=1$)] shown in Figs. 4(A) and 4(B). A
maximum rotation by $\Theta=\frac{\pi}{2}$ occurs at $\delta\nu=0$, where
$-\langle\widehat{I}_{Y}\rangle=1$ and $\langle\widehat{I}_{Z}\rangle=0$. Away
from $\delta\nu=0$, the excitation and $\widehat{z}-$magnetization profiles
are quite noisy, but $|\langle\widehat{I}_{Y}\rangle|<1$ and
$\langle\widehat{I}_{Z}\rangle>0$. Note that the $\widehat{z}-$magnetization
profile is less noisy, since rotations away from the $\widehat{z}$ direction
go as $\cos(\theta)\approx 1-\frac{\theta^{2}}{2}$ whereas excitations go as
$\sin(\theta)\approx\theta$ for $\theta\ll 1$.

If the excitation and $\widehat{z}-$magnetization profiles are averaged over
different p-DANTE sequences that possess the same total pulse length and are
all selective for $\nu_{0}$, then the fluctuations in both the excitation
[Fig. 4(B)] and $\widehat{z}-$magnetization [Fig. 4(B)] profiles for
$\delta\nu\neq 0$ decrease relative to the excitation at $\delta\nu=0$ roughly
as $\frac{1}{\sqrt{N_{avg}}}$. However, even when $N_{avg}\gg 1$, there still
exists a ”baseline” excitation at $\delta\nu\neq 0$ which is nonzero
(averaging simply decreases the fluctuations about the baseline excitation).
The average ”baseline” excitation is approximately given by
$\overline{|\langle\widehat{I}_{Y}\rangle|}\approx\frac{\Theta}{N+2}$ and
$\langle\overline{\widehat{I}_{Z}\rangle}=1-\frac{(N+1)\theta^{2}}{2}$. Thus
decreasing $\theta$ and $N$ will decrease the ”baseline” excitation as
$\theta\propto\frac{1}{N}$. Similar schemes averaging over random sequences
have been previously used for stochastic dipolar recouplingR.Tycko (2007);
Tycko (2008).

Figure 4: Theoretically calculated "averaged" excitation [(B) and (D)] and
$\widehat{z}-$magnetization profiles [(A) and (C)] for a series of p-DANTE
sequences [Fig. 1(B)]. In all p-DANTE sequences, $N=30$,
$\theta=\frac{\pi}{60}$, and $\phi_{k}=0$ for all $k$ so that only spins
resonating at $\delta\nu=0$ Hz are rotated about the $\widehat{x}$-axis by
$\Theta=\frac{\pi}{2}$. In (A) and (B), one hundred different p-DANTE
sequences with randomly chosen delays were generated such that the average
pulse delay, $\frac{1}{29}\sum_{k=1}^{29}\tau_{k}=1.6$ ms, was the same for
all p-DANTE sequences. The excitation and $\widehat{z}$-magnetization profiles
were averaged over $N_{avg}$ p-DANTE sequences with $N_{avg}=1$ (red curve),
$N_{avg}=25$ (blue curve), and $N_{avg}=100$ (green curve(. In (C) and (D),
one hundred different p-DANTE sequences were chosen such that the $k^{th}$
delay for the $p^{th}$ experiment was
$\tau^{p}_{k}=\tau_{p}\left[1+\frac{\delta\tau}{\tau}\cos\left(\frac{2\pi
k}{f_{p}}\right)\right]$ where $\frac{\delta\tau}{\tau}=\frac{1}{\sqrt{2}}$
and $f_{p}$ was inversely proportional to the square root of the $p^{th}$
prime number (e.g., $f_{1}=1/\sqrt{2}$, $f_{2}=1/\sqrt{3}$,
$f_{100}=1/\sqrt{541}$). $\tau_{p}$ was chosen to ensure that the averaged
delay was $\frac{1}{29}\sum_{k=1}^{29}\tau^{p}_{k}=1.6$ ms for all $p$. The
averaged excitation and $\widehat{z}$-magnetization profiles for $N_{avg}=1$
(red curve with $f_{1}=1/\sqrt{2}$), $N_{avg}=25$ (blue curve, averaging from
$f_{1}=1/\sqrt{2}$ to $f_{25}=1/\sqrt{97}$), and $N_{avg}=100$ (green curve,
averaging from $f_{1}=1/\sqrt{2}$ to $f_{100}=1/sqrt{541}$) are shown. As
$N_{avg}$ increases, the "fluctuations" in both $\langle I_{Z}\rangle$ and
$-\langle I_{Y}\rangle$ decrease, and the results are similar for p-DANTE
sequences using randomly chosen delays [(A) and (B)] and those using
periodically modulated delays [(C) and (D)].

Besides randomly chosen delays, averaging over different sets of delays that
are periodically modulated can also lead to selective excitation. Consider a
series of delays where the $k^{th}$ delay is given by
$\tau_{k}=\tau+\delta\tau\cos\left(\frac{2\pi k}{f}\right)$, where $f$ is a
real number, and $\tau\geq\delta\tau$ so that $\tau_{k}\geq 0$. For such a
sequence to selectively excite spins resonating at $\nu_{0}$, the phase of the
$k^{th}$ pulse must be given by $\phi_{k}=-2\pi\nu_{0}T_{k-1}$ with $T_{0}=0$
and :

$\displaystyle T_{k}$ $\displaystyle=$
$\displaystyle\sum_{j=1}^{k}\tau_{k}=k\tau-\frac{\delta\tau}{2}\left(1-\csc\left(\frac{\pi}{f}\right)\sin\left(\frac{2k+1}{f}\pi\right)\right)$
(15)

where the total time of the sequence is given by
$T_{\text{tot}}=Nt_{p}+T_{N-1}=Nt_{p}+(N-1)\tau-\frac{\delta\tau}{2}+\frac{\delta\tau}{2}\csc\left(\frac{\pi}{f}\right)\sin\left(\frac{\pi(2N-1)}{f}\right)$.
Using the values of $T_{k}$ in Eq. (15), $\overline{H}_{avg}^{(1)}$ in Eq.
(13) can be evaluated and is given by:

$\displaystyle\overline{H}^{(1)}_{avg}$ $\displaystyle=$
$\displaystyle\frac{a}{2N}\sum_{k=1}^{N}\left(\widehat{I}_{+}e^{i\left(\Delta\omega
T_{k}+\frac{\omega_{Z}t_{p}}{2}\right)}+I_{-}e^{-i\left(\Delta\omega
T_{k}+\frac{\omega_{Z}t_{p}}{2}\right)}\right)+b\widehat{I}_{Z}$ (16)
$\displaystyle=$
$\displaystyle\frac{a}{2}\sum_{n=-\infty}^{\infty}J_{n}\left(\frac{\Delta\omega\delta\tau}{2}\csc\left(\frac{\pi}{f}\right)\right)\frac{\text{sinc}\left(\frac{N(\Delta\omega\tau+\frac{2n\pi}{f})}{2}\right)}{\text{sinc}\left(\frac{\Delta\omega\tau+\frac{2n\pi}{f}}{2}\right)}\left(I_{+}e^{i\chi_{n}}+I_{-}e^{-i\chi_{n}}\right)+b\widehat{I}_{Z}$

where $\Delta\omega=\omega_{Z}-\omega_{0}$, $J_{n}$ is a bessel function of
order $n$, and
$\chi_{n}=\Delta\omega\frac{(N-1)\tau-\delta\tau}{2}+\frac{Nn\pi}{f}+\frac{\omega_{Z}t_{p}}{2}$.
From Eq. (16), $\overline{H}^{(1)}_{\text{avg}}$ is maximal at the conditions
$2\pi\Delta\nu\tau+\frac{2n\pi}{f}=2m\pi$ or at
$\Delta\nu=\frac{m}{\tau}-\frac{n}{f\tau}$ where $m$ and $n$ are integers.
These define the resonance conditions for this type of p-DANTE sequence.
However, $\overline{H}_{avg}^{(1)}$ is scaled by
$J_{n}\left(\left(m-\frac{n}{f}\right)\frac{\pi\delta\tau}{\tau}\csc\left(\frac{\pi}{f}\right)\right)$,
which is greatest when $m=n=0$. For $m\neq 0$ and $n\neq 0$, this scaling is
less than one, which results in a smaller total rotation.

Figure 4(C) and (D) show the numerically averaged $\widehat{z}$-magnetization
and excitation profiles respectively, averaged for up to one hundred different
p-DANTE sequences using periodically modulated delays. In the simulations,
$N=30$ and $\frac{\delta\tau}{\tau}=\frac{1}{\sqrt{2}}$. For the $p^{th}$
p-DANTE sequence, $f_{p}$ was set to be equal to the inverse of the square
root of the $p^{th}$ prime number, i.e., $f_{1}=1/\sqrt{2}$,
$f_{2}=1/\sqrt{3}$, $f_{100}=1/\sqrt{541}$. In order to better compare these
results to the results for the p-DANTE sequences using random delays [Figs.
4(A) and 4(B)], $\tau_{p}$ for the $p^{th}$ experiment was chosen so that
$\frac{1}{29}\sum_{j=1}^{29}\tau_{j}^{p}=1.6$ ms. First consider the
$N_{avg}=1$ case (red curve) in which $f=\frac{1}{\sqrt{2}}$ and
$\frac{1}{\tau}=625.13$ Hz. Unlike the case of using random delays [red curves
in Fig. 4(A) and 4(B)] where the resulting excitations appear randomly
distributed throughout the spectral range, the excitation profile using
periodically modulated delays occur at discrete $\delta\nu$ given by the
resonance condition $\delta\nu=625.13\left(m-\sqrt{2}n\right)$ Hz [Eq. (16)].
Note that while the resonance at $\delta\nu=0$ ($m=0$ and $n=0$) is maximally
excited ($\langle\widehat{I}_{Z}\rangle=0$ and
$-\langle\widehat{I}_{Y}\rangle=1)$, the degree of excitation at other
resonance conditions is less. In particular, the resonances at $\delta\nu=\pm
625.13$ Hz ($m=\pm 1$, $n=0$) are not observed in the calculated profile,
since at these conditions, $\overline{H}_{avg}^{(1)}$ is scaled by
$J_{0}(-2.3046)=0.053$, whereas the resonances at $\delta\nu=\pm 366.2$ Hz
($n=\mp 1$ and $m=\pm 2$) are clearly observed $(|J_{1}(1.35)|=0.5325$). As
was the case for p-DANTE sequences using randomly chosen delays, averaging
over different sets of periodically modulated p-DANTE sequences reduces the
excitation for all resonances except at $\delta\nu=0$, which is a common
resonance for all p-DANTE sequences. From Fig. 4, the
$\widehat{z}$-magnetization and excitation profiles using periodically
modulated delays [Figs. 4(C) and 4(D)] become similar to those using the
randomly chosen delays [Figs. 4(A) and 4(D)] as $N_{avg}$ increases.

Finally, it should be noted that the conditions under which the average
Hamiltonian in Eq. (16) provides a valid description ofthe p-DANTE sequence
are approximately the same as those found for the DANTE sequence [Fig. 3].
Figure 5 shows the difference in the excitation and
$\widehat{z}$-magnetization profiles calculated using either the exact
propagator or the propagator calculated using the average Hamiltonian up to
second-order [Eq. 14 and Eq. (16)] for the p-DANTE sequences used in Figs.
4(C) and 4(D). AHT works well for all $\delta\nu$ away from resonance
conditions which is evident from Fig. 5 for the $N_{avg}=1$ curve. The
magnitude of the error in this approximation is the same as that found for a
DANTE sequence with $\Theta=\pi/2$. The agreement of the AHT calculations with
the exact calculations appears to improve upon averaging over different
p-DANTE sequences, except for the $\delta\nu=0$ resonance. This is due to the
fact that only the $\delta\nu=0$ resonance is the same for all p-DANTE
sequence used in Fig. 5.

Figure 5: Difference in the calculated (A) $\widehat{z}$-magnetization and (B)
excitation profiles for the p-DANTE sequences used in Fig. 4(C) and 4(D)
between the profiles calculated using the propagator from AHT,
$\widehat{U}_{\text{AHT}}(T_{\text{tot}})=e^{-iT_{\text{Tot}}\omega_{Z}\widehat{I}_{Z}}e^{-iNt_{p}\left(\overline{H}^{(1)}_{\text{avg}}+\overline{H}^{(2)}_{\text{avg}}\right)}$
[Eq. (16) and Eq. (14)] and the profiles calculated using exact propagator,
$\widehat{U}_{\text{exact}}(T_{\text{tot}})$. The agreement is relatively good
over a wide frequency range except near the $\delta\nu=0$ Hz resonance
condition, $\delta\nu\approx\pm\frac{3\theta}{5\Theta\tau_{t}}=\pm 13$ Hz. For
all $|\delta\nu|>>\frac{3\theta}{5\Theta\tau_{t}}$ and
$|\delta\nu|\ll\frac{3\theta}{5\Theta\tau_{t}}$, the agreement between AHT and
the exact calculation improves with averaging over different p-DANTE
sequences.

##  III Experimental

All experiments were performed on a 300 MHz Avance Bruker spectrometer (static
magnetic field of 7 T and an operating frequency for ${}^{1}H$ of 300.13 MHz),
using a 5-mm Bruker BBO probe. A 2M solution of acetone in acetone$-d_{6}$ was
used to experimentally determine the excitation and
$\widehat{z}$-magnetization profiles as a function of frequency offset from
the acetone resonance for both the DANTE and two pseudorandom pulse sequences.
The carrier frequency was incremented between $-580$ Hz below to $580$ Hz
above the acetone resonance in intervals of 10 Hz in order to experimentally
determine the excitation and $\widehat{z}$-magnetization profiles (a total of
1161 measurements), and the integral of the acetone peak was measured. In
order to measure the $\widehat{z}$-magnetization, a $\frac{\pi}{2}$ pulse
(Rabi frequency of 21.4 kHz) was applied after the DANTE and p-DANTE
sequences, which was phase cycled in concert with the receiver phase so that
only the $\widehat{z}-$magnetization prior to the last $\frac{\pi}{2}$ pulse
was measured. A delay of 40 seconds was used between scans in all experiments
in order to ensure that the system had relaxed back to equilibrium which was
necessary to avoid any distortions in the observed profiles.

In order to demonstrate the improved selectivity in the excitation and
$\widehat{z}-$magnetization profiles by signal averaging over different
p-DANTE sequences (as shown in Fig. 4), experiments using different p-DANTE
sequences were performed on a solution of acetone, dimethyl sulfoxide
(DMSO),and water diluted in $D_{2}O$, such that
$\frac{[\text{Acetone}]}{[\text{DMSO}]}=0.822$ and
$\frac{[\text{H}_{2}\text{O}]}{[\text{DMSO}]}=1.4355$. All chemicals were
obtained from Sigma-Aldrich.

##  IV Results and Discussion

The experimentally determined excitation and $\widehat{z}-$magnetization
profiles under the DANTE and two different p-DANTE sequences obtained using a
2M acetone solution in acetone-$d_{6}$ are shown in Figure 6, where the blue
and red curves correspond to the theoretical and experimentally observed
profiles respectively. In these experiments, $N=30$, $\theta=\frac{\pi}{60}$,
and $t_{p}=720$ ns were used with a maximum rotation of
$\Theta=N\theta=\frac{\pi}{2}$. For the DANTE sequence, $\tau=2$ ms. Over the
spectral range shown in Fig. 6(A) and 6(D), excitations at frequencies
$\delta\nu=\frac{\pm 1}{\tau}=\pm 500$ Hz and at $\delta\nu=0$ Hz were
observed. For the p-DANTE sequences, the $k^{th}$ delay was given by either
[Figs. 6(C) and 6(F)]
$\tau_{k}=2.063\left[1-\cos\left(\frac{k\pi}{29+1}\right)\right]$ms=$4.126\sin^{2}\left(\frac{k\pi}{2(29+1)}\right)$
(which is a similar set of delays used in the UDD sequencesUhrig (2009)) or
[Figs. 6(B) and 6(E)]
$\tau_{k}=2.096\left[1+\frac{1}{3}\cos\left(\frac{2k\pi}{23}\right)\right]$ms.
In both cases, the average delay between pulses was equal to
$\frac{1}{29}\sum_{k=1}^{29}\tau_{k}=2$ ms in order to allow for better
comparison with the DANTE sequence used in Figs. 6(A) and 6(D). Both p-DANTE
sequences generated a maximum excitation at $\delta\nu=0$ Hz, and smaller
excitations for $\delta\nu\neq 0$ Hz were also observed, as expected. Note
that for the UDD-like p-DANTE sequence [Fig. 6(C) and 6(F)], the excitation
and $\widehat{z}$-magnetization profiles look similar to that of a p-DANTE
sequence using randomly chosen delays [the red curve in Figs. 4(A) and 4(B)],
whereas excitations using the other p-DANTE sequence [Figs. 6(B) and 6(E)]
appear to be concentrated within a smaller frequency range.

Figure 6: The experimental (red) and theoretical (blue) excitation [(A)-(C)]
and $\widehat{z}$-magnetization [(D)-(F)] profiles under application of the
DANTE [(A),(D)] and p-DANTE sequences [(B),(E),(C),(F)] as a function of the
applied RF’s offset away from the acetone resonance, $\delta\nu$. In all
experiments, $N=30$ and $\theta=\frac{\pi}{60}$. The profiles were generated
using a 2M acetone solution in acetone-d6 by changing the RF carrier frequency
from $-580$ Hz to $580$ Hz in 10 Hz increments, and the resulting acetone
resonance was integrated. For the DANTE sequence, $\tau=2$ ms; with these
parameters, the acetone resonance was maximally excited at
$\delta\nu\approx\pm\frac{1}{\tau}=\pm 500$ Hz and at $\delta\nu=0$ Hz over
the spectral range $[-580$ Hz, $580$ Hz]. For the p-DANTE sequences, the
$k^{th}$ delay was either given by
$\tau_{k}=2.096\left[1+\frac{1}{3}\cos\left(\frac{2k\pi}{23}\right)\right]$ms
[Figs. 6(B) and 6(E)] or by the UDDUhrig (2009)-like delay
$\tau_{k}=2.063\left[1-\cos\left(\frac{k\pi}{29+1}\right)\right]$ms=$4.126\sin^{2}\left(\frac{k\pi}{2(29+1)}\right)$
[Figs. 6(C) and 6(F)]. In both cases, the average delay between pulses was
$\frac{1}{29}\sum_{k=1}^{29}\tau_{k}=2$ ms in order to enable comparison with
the results from the DANTE sequence in Figs. 6(A) and 6(D). For both p-DANTE
sequences, there is minimal excitation at $\delta\nu=\pm 500$ Hz, although the
UDD-like sequence [Figs. 6(C) and 6(F)] appears to generate smaller
excitations over a wider frequency range than the other p-DANTE sequence
[Figs. 6(B) and 6(E)]. In all cases, there is good agreement between theory
(blue) and experiment (red).

In order to examine the effects of averaging over different p-DANTE sequences,
experiments were performed on a DMSO-acetone-water solution in $D_{2}O$. The
spectrum of the solution after a simple $\frac{\pi}{2}$-acquire sequence is
shown in Fig. 7(A), where the RF was applied on resonance with respect to the
water resonance [$\delta\nu_{\text{acetone,water}}=-768$ Hz and
$\delta\nu_{\text{DMSO,water}}=-620.2$ Hz]. The experimental excitation and
$\widehat{z}-$magnetization weighted spectra after the application of a DANTE
sequence with $N=30$, $\theta=\frac{\pi}{60}$ ($t_{p}=630$ ns), and
$\tau\approx\frac{1}{|\delta\nu_{\text{DMSO,water}}|}=1.6$ ms are shown in
Figure 7(B) and Figure 7(C) respectively. With this choice of $\tau$, the
DANTE sequence efficiently excites both the water
$\left(\delta\nu=\frac{0}{\tau}\right)$ and DMSO
$\left(\delta\nu=-\frac{1}{\tau}\right)$ resonances [Fig. 7(B)] and leaves the
acetone magnetization mostly about the $\widehat{z}-$axis [Fig. 7(C)].

The averaged excitation [Fig. 8(B)] and $\widehat{z}-$magnetization weighted
spectra [Fig. 8(A)] for the DMSO/acetone/water solution was obtained using up
to one hundred different p-DANTE sequences, and the results are shown for
$N_{avg}=1$ (red curve), $N_{avg}=25$ (blue curve), and $N_{avg}=100$ (green
curve) in Figure 8. The p-DANTE sequences used in Fig. 8 were the same used in
the theoretical calculations shown in Figs. 4(C) and 4(D), where the $k^{th}$
delay used in $p^{th}$ experiment was given by:

$\displaystyle\tau^{p}_{k}=\frac{46.77\text{ms}}{29-\frac{1}{2\sqrt{2}}\left(1-\csc\left(\frac{\pi}{f_{p}}\right)\sin\left(\frac{59\pi}{f_{p}}\right)\right)}\left(1+\frac{1}{\sqrt{2}}\cos\left(\frac{2\pi
k}{f_{p}}\right)\right)$ (17)

which ensured that the average delay,
$\frac{1}{29}\sum_{k=1}^{29}\tau_{k}^{p}\approx\frac{1}{|\delta\nu_{\text{DMSO,water}}|}=1.6$
ms, was the same as the delay used in the DANTE sequence shown in Figs. 7(B)
and 7(C). As in Figs. 4(C) and 4(D), the water ($\delta\nu=0$ Hz) was
maximally excited whereas the averaged excitation at the acetone and DMSO
resonances decreased upon averaging over different p-DANTE sequences.
Similarly, the $\widehat{z}$-magnetization weighted spectra indicated that the
acetone and DMSO magnetization remained mostly about the $\widehat{z}$-axis
after application of the p-DANTE sequence, whereas there was little
$\widehat{z}$-magnetization at the water resonance.

Figure 7: (A) The spectrum after a $\frac{\pi}{2}$-acquire experiment for a
DMSO, acetone, and water solution. The spectrum is centered on the water
resonance $(\delta\nu=0)$. (B) The spectrum after application of a DANTE pulse
sequence with $N=30$, $\theta=\frac{\pi}{60}$, $\Theta=N\theta=\frac{\pi}{2}$,
and $\tau=\frac{1}{|\delta\nu_{\text{DMSO,water}}|}\approx 1.6$ ms. In this
case, both the water and DMSO resonances are excited whereas very little
excitation occurs at the acetone resonance
($\delta\nu_{\text{acetone,water}}=-768$ Hz). (C) The
$\widehat{z}-$magnetization weighted spectrum after application of the DANTE
pulse sequence. As expected from (B), there is substantial
$\widehat{z}$-magnetization for the acetone resonance and little
$\widehat{z}$-magnetization for both the water and DMSO resonances after
application of the DANTE sequence. Figure 8: Experimental stacked plots of the
(A) $\widehat{z}$-magnetization weighted spectra and the (B) excitation
spectra after averaging over $N_{avg}=1$ (red), $N_{avg}=25$ (blue), and
$N_{avg}=100$ (green) p-DANTE sequences [same sequences used in Figs. 4(C) and
4(D)] applied to the acetone, DMSO, and water solution used in Fig. 7. From
Figs. 4(C) and 4(D), only the water resonance at $\delta\nu=0$ Hz should be
efficiently excited. From Fig. 6(B) the water resonance $(\delta\nu=0)$ is
efficiently excited, and the amount of excitation at the acetone and DMSO
resonances decreases with averaging over more p-DANTE sequences. In 8(A), the
$\widehat{z}-$ magnetization weighted spectra are shown, illustrating that
both the acetone and DMSO magnetization lie mostly along the
$\widehat{z}$-direction after application of the p-DANTE sequences.

##  V Conclusions

In this work, average Hamiltonian theory (AHT) was used to calculate the
effective propagators for the both the DANTE [Fig. 1(A)] and pseudorandom-
DANTE or p-DANTE [Fig. 1(B)] sequences. It was found that an AHT description
the DANTE sequence is valid when $\theta=\frac{\pi}{60}$ and for total pulse
flip-angles of $\Theta=N\theta\leq\frac{5\pi}{9}$ over all frequencies [Fig.
3]. The validity of the AHT description was also found to depend upon the
spin’s resonance frequency, $\nu$, and an AHT description of DANTE works well
for frequencies in the range $\delta\nu\gg\frac{2\theta}{5\tau_{t}\Theta}$ and
$\delta\nu\ll\frac{2\theta}{5\tau_{t}\Theta}$ where
$\delta\nu=\text{min}\left[\left|\nu-\frac{n}{\tau_{t}}\right|\right]$ is the
smallest frequency difference between $\nu$ and the nearest resonance of the
DANTE sequence, $\frac{n}{\tau_{t}}$ where $n$ is an integer. Understanding
the limitations of an AHT description for DANTE enabled us to develop an AHT
description of the p-DANTE sequences [Fig. 1(B)] where the delays and phases
of the pulses are modulated in concert throughout the sequence. This
modulation of delays and phases breaks the periodicity of the DANTE sequence
and enables the p-DANTE sequence to excite spins at a single frequency,
$\nu_{0}$. The ability to use an AHT description for the DANTE and p-DANTE
sequences might also provide additional insights into other selective pulse
sequences, since any shaped pulses can be cast into a DANTE-like
descriptionShinnar and Leigh (1987); Shinnar  _et al._ (1989, 1989). While the
excitation and $\widehat{z}-$magnetization profiles for a single p-DANTE
sequence are not particularly clean, i.e., small excitations exist at many
frequencies, averaging over different p-DANTE sequences helps to ”clean-up"
the excitation profiles so that only a baseline excitation exists everywhere
except at $\nu_{0}$, which is excited. Experimental demonstrations [Fig. 6 and
Fig. 8] of the p-DANTE sequences were found to be in good agreement with
theoretical predictions.

For future work, determining the existence of an optimal set of p-DANTE
sequences that generate the "cleanest" excitation profiles using the smallest
number of p-DANTE sequences will be investigated. Since the frequency
selection in p-DANTE sequences is determined by correlating the pulse phases
with the delays, the p-DANTE sequences could also be incorporated into
ultrafast NMRFrydman  _et al._ (2002, 2003) techniques to selectively excite
certain resonances in different parts of the sample volume. Furthermore,
extending the AHT results obtained in this paper to coupled spin systems is
currently underway, whereby a DANTE-like or p-DANTE-like sequences can be used
to selectively excite a particular multiple-quantum spin transition. The
conditions under which such an AHT description can be applied in these systems
are approximately the same as those found in this paper, since any subspace of
two transitions can be describedFeynman  _et al._ (1957) as an effective
spin-1/2. Coupling these techniques with ultra-fast NMR should enable the
quick determination of all spin transitions in a given molecular system.

Acknowledgments We would like to thank Alex Burum for a careful reading of
this manuscript. This work was supported by a Camille and Henry Dreyfus New
Faculty award, a Provost Research award and startup funds from the University
of Miami.

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11institutetext:  TH Köln - University of Applied Sciences, Germany
11email<EMAIL_ADDRESS>
22institutetext: GESIS - Leibniz Institute for the Social Sciences, Germany
22email<EMAIL_ADDRESS>
33institutetext: ZB MED - Information Centre for Life Sciences, Germany
33email<EMAIL_ADDRESS>
# Overview of LiLAS 2020 – Living Labs for Academic Search

Philipp Schaer 11 0000-0002-8817-4632 Johann Schaible 22 0000-0002-5441-7640
Leyla Jael Garcia Castro 33 0000-0003-3986-0510

###### Abstract

Academic Search is a timeless challenge that the field of Information
Retrieval has been dealing with for many years. Even today, the search for
academic material is a broad field of research that recently started working
on problems like the COVID-19 pandemic. However, test collections and
specialized data sets like CORD-19 only allow for system-oriented experiments,
while the evaluation of algorithms in real-world environments is only
available to researchers from industry. In LiLAS, we open up two academic
search platforms to allow participating research to evaluate their systems in
a Docker-based research environment. This overview paper describes the
motivation, infrastructure, and two systems LIVIVO and GESIS Search that are
part of this CLEF lab.

###### Keywords:

Evaluation, living labs, academic search, reproducibility

##  1 Introduction

The field of Information Retrieval (IR) originated in the domain of
scientific/academic information and documentation. Back in the 1960s, the
original Cranfield studies dealt with the indexation and the retrieval of
scientific documents. Cleverdon et al. established their whole evaluation
methodology around the use-case of scientific and academic retrieval
requirements. Today, the search for relevant scientific documents is still an
open endeavor, and although retrieval systems show substantial performance
gains, it is not a solved problem yet. The current COVID-19 pandemic, for
example, showed once again that even old problems like the search for
scientific documents are not solved. Therefore, current efforts like the
CORD-19 collection111https://www.semanticscholar.org/cord19 and the TREC COVID
retrieval campaign222https://ir.nist.gov/covidSubmit/index.html gather much
attraction and are in the spotlight of the IR community, even though at their
core, they deal with the same – timeless – problem set as Cleverdon more than
50 years ago.

Besides these timeless retrieval issues, the need for innovation in academic
search is shown by the stagnating system performance in controlled evaluation
campaigns, as demonstrated in TREC and CLEF meta-evaluation studies [15, 1].
User studies in real systems of scientific information and digital libraries
show similar conditions. Although massive data collections of scientific
documents are available in platforms like arXiv, PubMed, or other digital
libraries, central user needs and requirements remain unsatisfied. The central
mission is to find both relevant and high-quality documents - if possible,
directly on the first result page. Besides this ad-hoc retrieval problem,
other tasks such as the recommendation of relevant cross-modality content
including research data sets or specialized tasks like expert finding are not
even considered here. On top of that, relevance in academic search is multi-
layered [5] and a topic that drives research communities like the
Bibliometrics-enhanced Information Retrieval (BIR) workshops [10].

The Living Labs for Academic Search (LiLAS) workshop fosters the discussion,
research, and evaluation of academic search systems, and it employs the
concept of living labs to the domain of academic search [13]. The goal is to
expand the knowledge on improving the search for academic resources like
literature, research data, and the interlinking between these resources. To
support this goal, LiLAS introduces an online evaluation infrastructure that
directly connects to real-world academic search systems [12]. LiLAS cooperates
with two academic search systems providers from Life Sciences and Social
Sciences. Both system providers support LiLAS by allowing participants of the
lab to employ experimental search components into their production online
system. We will have access to the click logs of these systems and use them to
employ A/B tests or more complex interleaving experiments. Our living lab
platform STELLA makes this possible by bringing platform operators and
researchers together and providing a methodological and technical framework
for online experiments [3].

##  2 Related Work from CLEF and TREC

CLEF and TREC hosted the Living Labs for Information Retrieval (LL4IR) and
Open Search (TREC-OS) initiatives that are the predecessors to LiLAS. Both
initiatives shared a common evaluation infrastructure that was released as an
API333https://bitbucket.org/living-labs/ll-api. This API allows academic
researchers to access the search systems of other platforms. Participants of
LL4IR and TREC-OS had access to the search systems’ head queries and document
sets. They had to precompute ranked result lists for a given set of candidate
documents for the given head queries. Therefore it was a typical ad-hoc search
task. Another task was run during the CLEF NewsReel campaign, where
participants had to recommend news articles. This was possible by employing an
offline test collection or in real-time via the Open Recommendation Platform
(ORP) used by PLISTA.

All these labs can be considered living labs and represent a user-centric
study methodology for researchers to evaluate retrieval systems’ performance
within real-world applications. Thus, they aim to offer a more realistic
experiment and evaluation environment as offline test collections and
therefore, should be further investigated to raise IR-evaluation to a more
holistic level.

Within TREC and CLEF, only very few tracks or labs focused on the evaluation
of academic search systems. Some used scientific documents or use-cases to
generate test collections but did not necessarily focus on the unique
requirements of the academic domain. Within CLEF, the Domain-specific track
[8] compiled a collection of bibliographic records and research project
descriptions from the Social Sciences to test the needs of scientific
retrieval tasks. This test collection was created to contrast the then usual
“general-purpose news documents” and to employ “different search criteria than
those used for reference retrieval in databases of scientific literature
items, and also offer no possibility for comparable test runs with domain-
specific terminology”. More recently, the TREC Precision Medicine / Clinical
Decision Support Track released a large test collection in 2016 based on open
access full-text documents from PubMedCentral. TREC-COVID is the latest
retrieval campaign aiming at academic search with a particular focus on the
rapidly growing corpus of scientific work on the current COVID-19 pandemic.

The LiLAS workshop is a blend of the most successful parts of these previous
evaluation campaigns. The Domain-specific track had a strong focus on
scientific search, thesauri, and multilingual search. NewsREEL had an active
technological component, and LL4IR/TREC-OS turned from product search to
academic search but was not able to implement the scientific focus into the
last iteration. There is much potential that is still not used in the question
of how to evaluate academic search platforms online.

##  3 STELLA – Evaluation Infrastructure for LiLAS

Nowadays, testing approaches are commonly used to try out and evaluate how
users interact when presented with some new or modified features on a website.
Whenever the new or modified features differ from what has been done before,
when multiple features change at once, or when the user interaction is to be
gathered in a systematic way, A/B testing comes into place. An A/B testing, a
controlled online experiment, allows to expose a percentage of real users and
life-test those new or modified features [2, 9] offering to website designers
and developers a living lab where to assess reactions and usage of new
features better, allowing them for more accurate tuning based on data
collected from production systems.

Figure 1: STELLA workflow, an online living lab supporting testing from ideas
to evaluation: Participants package their systems with the help of Docker
containers that are deployed in the backend of academic information retrieval
and recommendation systems. Users interact directly with the system, with a
percentage diverted to the experimental features. Researchers and developers
retrieve results and deliver feedback to tune and improve changes.

For LiLAS, we use STELLA as our living lab evaluation infrastructure. STELLA
is aiming to make it easier to evaluate academic retrieval information and
recommendation systems [3]. Figure 1 shows an overview of how the steps flow
from a researcher’s or developer’s idea to the evaluation feedback so the
changes can be tuned and improved. It all starts with an idea, for instance
adding synonyms to the keywords used by an end-user when searching for
information. Developers will work on a modified version of the production
system, including this change they want to analyze. Whenever an end-user goes
to the system, everything will look as usual. Once the search keywords are
introduced, STELLA will show end-user some results from the experimental
system and some results from the regular production system. End-users will
continue their regular interaction with the system. Based on the retrieved
documents and the following interaction, STELLA will create an evaluation
profile together with some statistics. Researchers and developers will then
analyze STELLA’s feedback and will react accordingly to get the usage level
they are aiming at.

STELLA’s infrastructure relies on the container virtualization environment
Docker [11], making it easier for STELLA to run multiple experimental systems,
i.e., a multi-container environment, and compare them to each other and the
production system as well. The core component in STELLA is a central
Application Public Interface (API) connecting data and content providers with
experimental systems, aka participant systems or participants, encapsulated as
Docker containers. Further information can be found at the project
website444https://stella-project.org/, including some technical details via a
series of blogs published regularly.

Currently, STELLA supports two main tasks: ad-hoc retrieval and
recommendation. In the following subsections, we will introduce two systems
used during the STELLA development phase to understand better, learn, and test
these two tasks. Although a fully functional version is already available,
there is still room for improvement, particularly regarding the events
logging, statistics analysis, and overall evaluation. LiLAS will promote an
early discussion with future adopters and participants that will benefit not
only STELLA but living labs in general.

###  3.1 LIVIVO

Figure 2: LIVIVO, the ZB MED retrieval platform. Users can search by keywords,
title, author or year and obtain a result set sorted by relevance together
with additional features such is filters, publication details, access links,
other publications like the one on display and library stock.

LIVIVO555https://livivo.de is a retrieval platform provided by ZB MED –
Information Centre for Life Sciences. It serves the Life Sciences domain with
a focus on medicine, health, nutrition, environment, and agriculture. LIVIVO
includes unique features tailored to the German public and the national inter-
library loan system, making it easier for researchers, practitioners,
students, and the general public to access material licensed and hosted at
different German libraries. LIVIVO brings together publication from 30
different sources, e.g., Medline, AGRICOLA, and AGRIS, including more than 58
million publications in different languages including English, German,
Spanish, French and Portuguese. It uses automatic and semantic links to well-
known vocabularies, for instance the Medical Sub-heading (MeSH) [14] for
medical sciences, UMTHES [6] for environmental sciences, and AGROVOC [4] for
agricultural sciences. The resultset ranked by relevance and can be narrowed
down using filters such as the ZB MED subject fields. We include a sample
query and corresponding results in 2. From March 2020, there is a dedicated
portal serving Covid-19 related information.

Regarding the integration to STELLA, a test instance of LIVIVO has been set up
with a twofold purpose: introducing those elements needed in LIVIVO to
integrate it to the STELLA framework, e.g., calling the STELLA API whenever a
search is triggered in the production system, and evaluating the STELLA
framework itself, i.e., how the containerization. Communication via the API
and central STELLA server work with real production systems. We are also
working on a LIVIVO dataset suitable for participant systems, mainly targeting
MEDLINE articles written in English, about 25 million abstracts with their
corresponding metadata including title, authors, affiliations, MeSH term among
others.

###  3.2 GESIS Search

Figure 3: GESIS Search, social science information portal. It provides
different types of information from the social sciences, like literature,
research data, questions and variables, as well as instruments and tools.

The internal GESIS academic search GESIS Search666https://search.gesis.org/
aims to aid their users in finding appropriate scholarly information on the
broad topic of social sciences [7]. To this end, it provides different types
of information from the social sciences, comprising literature (95k
publications), research data (84k), questions and variables (12.7k), as well
as instruments and tools (370). The publications are mostly in English and
German and are annotated with further textual metadata like title, abstract,
topic, persons, and others. With the Social Science Open Access Repository
(SSOAR)777https://www.gesis.org/en/ssoar/home, GESIS Search also provides
access to nearly 60k open access publications. Metadata on research data
comprises (among others) a title, topics, datatype, abstract, collection
method, primary investigators, and contributors in English and/or German.

Regarding STELLA, the amount of different types of data allows not only for
typical recommendations, such as from publications to publications but also
for _cross-domain recommendations_ , i.e., recommendations from different
types such as from publications to research data. While this is still work in
progress, the GESIS Search data and possible relevance indicators, such as
click-paths, can be obtained. The data can be used to train a recommender and
report lessons learned, and file issue requests on how to improve the training
data.

##  4 Conclusion and Outlook

We presented the artifacts we would like to use for the actual evaluation
tasks at CLEF 2021. These artifacts are: (1) the STELLA living lab evaluation
infrastructure, and (2) the two academic search systems LIVIVO and GESIS
Search. These systems are from the two disjunct scientific domains life
sciences and social sciences and include different metadata on research
articles, data sets, and many other entities.

With this at hand, we will derive the CLEF 2020 workshop participants’
evaluation tasks for CLEF 2021. Promising task candidates are:

  * •

Ad-hoc retrieval for life Science documents

  * •

Dataset recommendation

These tasks allows us to use the different data types available in the
platforms.

## Acknowledgements

This work was partially funded by the German Research Foundation (DFG) under
the project no. 407518790.

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