[1]N. K. Nisar 11footnotetext: On behalf of the Belle Collaboration

# Study of $B$ and $B_{s}$ Decays at Belle

###### Abstract

We report results on the search for $B_{s}\to\eta^{\prime}\eta$ decay, and the
searches for $B^{0}\to\textrm{invisible}$ and
$B^{0}\to\textrm{invisible}+\gamma$ decays. The former result is based on a
data sample of $121.4~{}\textrm{fb}^{-1}$ recorded at the $\Upsilon(5S)$
resonance while the later results are obtained from a $711~{}\textrm{fb}^{-1}$
of data sample collected at $\Upsilon(4S)$ resonance with the Belle detector
at the KEKB $e^{+}e^{-}$ collider. We observe no significant signal for the
decays and set upper limit on their branching fractions at 90% confidence
level of $\mathcal{B}(B_{s}\to\eta^{\prime}\eta)<7.1\times 10^{-5}$,
$\mathcal{B}(B^{0}\to\textrm{invisible})<7.8\times 10^{-5}$ and
$\mathcal{B}(B^{0}\to\textrm{invisible}+\gamma)<1.6\times 10^{-5}$.

##  1 Introduction

In the Standard Model (SM), $B_{s}^{0}\rightarrow\eta^{\prime}\eta$ decay
proceeds via tree-level $b\to u$ and penguin $b\to s$ transitions. Penguin
transitions are sensitive to Beyond-the-Standard-Model (BSM) physics scenarios
and could affect its branching fraction and CP asymmetry [1]. Once the
branching fractions for two-body decays
$B_{s,d}\to\eta\eta,\eta\eta^{\prime},\eta^{\prime}\eta^{\prime}$ are
measured, and the theoretical uncertainties are reduced, it would be possible
to extract CP violating parameters from the data using the formalism based on
SU(3)/U(3) symmetry [2]. The formalism requires at least four of these six
branching fractions and the result on $B_{s}^{0}\rightarrow\eta^{\prime}\eta$
is a potential input. The predicted branching fractions of the decays
$B^{0}\to\textrm{invisible}$ and $B^{0}\to\textrm{invisible}+\gamma$, where
“invisible” defined as particles that leave no signal in the Belle detector,
could be as high as $10^{-6}-10^{-7}$ in the New Physics (NP) models [3, 4].
Decays with similar signature such as $B^{0}\to(\gamma)\nu\bar{\nu}$ and
$B^{0}\to\nu\bar{\nu}\nu\bar{\nu}$ are highly suppressed in the SM [5, 6, 7].
A very low background from the SM indicates that a signal of
$B^{0}\to\textrm{invisible}+(\gamma)$ in the current B-factory data would
indicate NP.

##  2 Belle detector

The Belle detector [8] was a large-solid-angle magnetic spectrometer that
operated at the KEKB asymmetric-energy $e^{+}e^{-}$ collider [9]. The detector
components include a tracking system comprising a silicon vertex detector
(SVD) and a central drift chamber (CDC), a particle identification (PID)
system that consists of a barrel-like arrangement of time-of-flight
scintillation counters (TOF) and an array of aerogel threshold Cherenkov
counters (ACC), and a CsI(Tl) crystal-based electromagnetic calorimeter (ECL).
All these components are located inside a superconducting solenoid coil that
provides a 1.5 T magnetic field. Outside the coil, the $K_{L}^{0}$ and muon
detector (KLM) is instrumented to detect $K_{L}^{0}$ mesons and to identify
muons.

##  3 Search for the Decay $B_{s}^{0}\rightarrow\eta^{\prime}\eta$

In this paper we report the preliminary result of the first search for the
decay $B_{s}^{0}\rightarrow\eta^{\prime}\eta$ using the full Belle data sample
of $121.4~{}\textrm{fb}^{-1}$ collected at the $\Upsilon(5S)$ resonance. The
$\Upsilon(5S)$ decays into $B_{s}^{*0}\bar{B}_{s}^{*0}$,
$B_{s}^{*0}\bar{B}_{s}^{0}$ or $B_{s}^{0}\bar{B}_{s}^{*0}$, and
$B_{s}^{0}\bar{B}_{s}^{0}$ pairs followed by the decays of the excited vector
states to $B_{s}^{0}$, by emitting a photon. Our data sample contains
$(6.53\pm 0.66)\times 10^{6}$ $B_{s}^{(*)0}\bar{B}_{s}^{(*)0}$ pairs [10]. A
set of Monte Carlo (MC) simulated events are used for the selection
optimization and estimation of reconstruction efficiency.

We reconstruct $\eta$ candidates using pairs of photons of energy that exceeds
50 (100) MeV in the barrel (end-cap) region of the ECL and requiring the
invariant mass to be in the range $515\leq M(\gamma\gamma)\leq 580$ ${\rm
MeV/c}^{2}$. Candidates for the decay $\eta^{\prime}\to\pi^{+}\pi^{-}\eta$ are
reconstructed using pairs of oppositely-charged pions and $\eta$. We require
the reconstructed $\eta^{\prime}$ invariant mass to be in the range $920\leq
M(\pi^{+}\pi^{-}\eta)\leq 980$ ${\rm MeV/c}^{2}$. To identify
$B_{s}^{0}\rightarrow\eta^{\prime}\eta$ candidates we use beam-energy
constrained $B_{s}^{0}$ mass, $M_{\rm bc}=\sqrt{E_{\rm
beam}^{2}-p_{B_{s}}^{2}}$, the energy difference, $\Delta E=E_{B_{s}}-E_{\rm
beam}$, and the reconstructed invariant mass of the $\eta^{\prime}$, where
$E_{\rm beam}$, $p_{B_{s}}$ and $E_{B_{s}}$ are the beam energy, the momentum
magnitude and the reconstructed energy of $B_{s}^{0}$ candidate, respectively.

The primary source of background are $e^{+}e^{-}\to q\bar{q}$ ($q=u,d,c,s$)
continuum events. Because of large initial momenta of the light quarks,
continuum events exhibit a “jet-like” event shape, while
$B_{s}^{(*)0}\bar{B}_{s}^{(*)0}$ events are distributed isotropically. We use
modified Fox-Wolfram moments [11], which describe the topology of the event,
to discriminate between signal and continuum background.

To extract the signal yield, we perform an unbinned extended maximum
likelihood fit to the three-dimensional (3D) distribution of $M_{\rm bc}$,
$\Delta E$, and $M(\pi^{+}\pi^{-}\eta)$. MC sample is used to determine signal
and background probability density functions (PDF). We use
$B^{0}\to\eta^{\prime}K_{S}^{0}$ data recorded at the $\Upsilon(4S)$ resonance
to adjust the PDF shape parameters used to describe the signal.

To test and validate our fitting model, ensemble tests are performed by
generating MC pseudoexperiments using PDFs obtained from the simulation and
the $B^{0}\rightarrow\eta^{\prime}K_{S}^{0}$ data. We use the results of
pseudoexperiments to construct classical confidence intervals using Neyman
construction [12]. These confidence intervals are then used to prepare a
classical confidence belt [13] and used to make a statistical interpretation
of the results obtained from fit to data.

We obtain $2.7\pm 2.5$ signal and $57.3\pm 7.8$ background events from the 3D
fit to data. We show the signal-region projections of the fit in Fig. 3. We
observe no signal and estimate the 90% confidence-level (CL) upper limit on
the branching fraction of the decay $B_{s}^{0}\rightarrow\eta^{\prime}\eta$
using the frequentist approach [12] and the following formula:

Signal-region projections of 3D fit to $B_{s}^{0}\rightarrow\eta^{\prime}\eta$
data. Points with error bars represent data, blue solid curves show the
resulting fit-projection, while the red dash-dotted and blue dash-dotted
curves show the signal and background components.

$\mathcal{B}(B_{s}^{0}\rightarrow\eta^{\prime}\eta)<\frac{N_{\textrm{UL}}^{90\%}}{2\cdot
N_{B_{s}^{(*)0}\bar{B}_{s}^{(*)0}}\cdot\varepsilon\cdot\mathcal{B}_{\textrm{dp}}},$
(1)

where $N_{B_{s}^{(*)0}\bar{B}_{s}^{(*)0}}$ is the number of
$B_{s}^{(*)0}\bar{B}_{s}^{(*)0}$ pairs in the full Belle data sample,
$\varepsilon$ is the overall reconstruction efficiency for the signal
$B_{s}^{0}$ decay, and $\mathcal{B}_{\textrm{dp}}$ is the product of the
secondary branching fractions for all daughter particles in our final state.
Further, $N_{\textrm{UL}}^{90\%}$ is the expected signal yield at 90% CL
obtained from the confidence belt, which is approximately 6 events. Using Eq.
(1) we obtain a 90% CL upper limit on the branching fraction of
$\mathcal{B}(B_{s}^{0}\rightarrow\eta^{\prime}\eta)<7.1\times 10^{-5}$. The
total systematic uncertainty on the upper limit is estimated to be 17%.

##  4 Search for $B^{0}$ decays to invisible final states $(+\gamma)$

These searches are based on a data sample containing $772\times 10^{6}$
$B\bar{B}$ pairs accumulated at the $\Upsilon(4S)$ resonance, corresponding to
an integrated luminosity of $711~{}\textrm{fb}^{-1}$. Ten million MC simulated
events for $B^{0}\to\nu\bar{\nu}$ and $B^{0}\to\nu\bar{\nu}\gamma$ decays are
generated and used to determine signal efficiency and optimize signal event
selection.

Since the signal side particle, except photon, cannot be detected, the other
$B$ meson in the event ($B_{\textrm{tag}}$) is reconstructed. Then the signal
is searched in the remaining part of the event. $B_{\textrm{tag}}$ mesons are
reconstructed from 494 hadronic decay modes by assigning signal probability to
reconstructed particles using a neural network (NN) package [14]. After
reconstruction of $B_{\textrm{tag}}$, no extra particles but photons are
expected in the event. Thus events with extra tracks, $\pi^{0}$s, or
$K_{L}^{0}$s are rejected.

The sum of all remaining energies of ECL clusters that are not associated with
$B_{\textrm{tag}}$ daughters and signal photons in case of
$B^{0}\to\textrm{invisible}+\gamma$, denoted by $E_{\textrm{ECL}}$, is a
strong variable to identify signal events. Since the distribution for signal
events peaks at zero, the $E_{\textrm{ECL}}$ signal box is defined as
$E_{\textrm{ECL}}<0.3$ GeV and the sideband is defined as
$0.3\textrm{GeV}<E_{\textrm{ECL}}<1.2\textrm{GeV}$. Continuum events are the
dominant source of background (Non-$B$) followed by $B\bar{B}$ decay with a
$b\to c$ transition (Generic $B$). Two NNs are implemented to suppress these
backgrounds.

A two dimensional (2D) extended unbinned maximum likelihood fit is applied
with fitting variables $E_{\textrm{ECL}}$ and $\cos\theta_{T}$ to extract
signal yield for the decay $B^{0}\to\textrm{invisible}$. Here $\cos\theta_{T}$
is the cosine of the angle between the two thrust axes in the $e^{+}e^{-}$
c.m. frame. The two thrust axes are defined as the directions that maximizes
the longitudinal momenta of $B_{\textrm{tag}}$ daughters and particles in the
remaining part of the event. All PDFs are obtained from signal MC and off-
resonance data. The projections of the 2D fit results are shown in Fig. 4 and
the corresponding fitting yiels for each component are listed in Table. 1. No
significant signal is observed and a 90% CL upper limit on the branching
fraction is estimated to be $\mathcal{B}(B^{0}\to\textrm{invisible})<7.8\times
10^{-5}$ [15]. Systematic uncertainty is estimated to be $7.9\%$ using control
samples $B^{0,\pm}\to B^{*,\pm}l\nu$.

Projections of the fit result on $\cos\theta_{T}$ (left) and
$E_{\textrm{ECL}}$ (right) for $B^{0}\to\textrm{invisible}$. Points with error
bars are data, black solid line is the fit result, red dotted line is the
signal component, green short-dashed line is the generic $B$ background
component and blue dash-dotted line is the non-$B$ background component.

Component | Yields
---|---
Signal | $18.8^{+15.3}_{-14.5}$
Generic $B$ | $68.1^{+12.2}_{-11.7}$
Non-$B$ | $-3.9^{+19.5}_{-17.5}$
Table 1: Fitting yield ($B^{0}\to\textrm{invisible}$).

$B^{0}\to{\textrm{invisible}}+\gamma$ decays are searched by counting events
in $E_{\textrm{ECL}}$ signal box in the bins of squared missing mass defined
as:

$M_{\textrm{miss}}^{2}=(\vec{P}_{\textrm{beam}}-\vec{P}_{B_{\textrm{tag}}}-\vec{P}_{\gamma})^{2}/c^{2},$
(2)

where $\vec{P}_{\textrm{beam}}$, $\vec{P}_{B_{\textrm{tag}}}$ and
$\vec{P}_{\gamma}$ are four-momenta of $e^{+}e^{-}$ system, the
$B_{\textrm{tag}}$ and the signal photon. The number of background events in
the $E_{\textrm{ECL}}$ signal box is estimated from the data sideband by
multiplying the fraction of events in signal box to the sideband, estimated in
the MC. The counting results in $E_{\textrm{ECL}}$ signal box and in bins of
$M_{\textrm{miss}}^{2}$ are summarized in Table. 2. The observed number of
events is consistant with no signal. We set a 90% CL upperlimit on the
branching fraction $\mathcal{B}(B^{0}\to\textrm{invisible}+\gamma)<1.6\times
10^{-5}$ [15] with an associated systematic uncertainty of $8.4\%$.

| $N^{\textrm{data}}_{\textrm{bkg,box}}$ | $N^{\textrm{data}}_{\textrm{box}}$
---|---|---
$B^{0}\to{\textrm{invisible}}+\gamma$ | $16.1\pm 6.3$ | 11
$M_{\textrm{miss}}^{2}<5~{}{\rm GeV}^{2}/c^{4}$ | $3.2\pm 2.1$ | 2
$5~{}{\rm GeV}^{2}/c^{4}<M_{\textrm{miss}}^{2}<10~{}{\rm GeV}^{2}/c^{4}$ | $1.0\pm 0.8$ | 2
$10~{}{\rm GeV}^{2}/c^{4}<M_{\textrm{miss}}^{2}<15~{}{\rm GeV}^{2}/c^{4}$ | $4.4\pm 2.6$ | 3
$15~{}{\rm GeV}^{2}/c^{4}<M_{\textrm{miss}}^{2}<20~{}{\rm GeV}^{2}/c^{4}$ | $7.1\pm 2.9$ | 4
$20~{}{\rm GeV}^{2}/c^{4}<M_{\textrm{miss}}^{2}$ | $6.6\pm 2.9$ | 7
Table 2: Estimated number of background events in the signal box
($N^{\textrm{data}}_{\textrm{bkg,box}}$) and the number of events in the
signal box ($N^{\textrm{data}}_{\textrm{box}}$ ) for
$B^{0}\to{\textrm{invisible}}+\gamma$ and $M_{\textrm{miss}}^{2}$ bins.

##  5 Conclusions

In summary, we have used the full data sample recorded by the Belle experiment
at $\Upsilon(5S)$ and $\Upsilon(4S)$ resonances to search for the decays
$B_{s}^{0}\rightarrow\eta^{\prime}\eta$ and
$B^{0}\to\textrm{invisible}+(\gamma)$ and no evidence is found. We set world’s
first upper limits on the branching fraction of
$B_{s}^{0}\rightarrow\eta^{\prime}\eta$ and improved the existing upper limit
on $B^{0}\to\textrm{invisible}+\gamma$.

## References

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# The irresistible call of $\tau=i$

Ferruccio Feruglio  Istituto Nazionale di Fisica Nucleare, Sezione di Padova,
I–35131 Padova, Italy

###### Abstract

We analyze a large set of modular invariant models of lepton masses and mixing
angles, pointing out that many of them prefer to live close to the self-dual
point $\tau=i$. We show that in the vicinity of this point a universal
behavior naturally emerges, independently from details of the theory such as
the finite modular group acting on the lepton multiplets, the weights of the
matter multiplets and even the form of the kinetic terms, which are not
required to be neither minimal nor flavour blind. The neutrino mass spectrum
is normally ordered and universal relations describe the scaling of the
physical observables in terms of the parameter $|\tau-i|$.

Introduction

Of all unsolved problems in particle physics, the flavor puzzle is perhaps the
most intriguing one. Despite the rich and precise available data, a baseline
theoretical interpretation of them is still missing. Most attempts to
characterize the fermion spectrum are based on the idea of flavor symmetry, an
alleged invariance of the theory under transformations among members of
different generations.

Exact flavor symmetries are not realized in nature and a symmetry breaking
mechanism is required, representing the source of most complications and loss
of predictability in realistic constructions. One of the simplest order
parameter of flavor symmetry breaking is provided by the modulus $\tau$, a
single complex field living in the upper part of the complex plane. The
modulus is a key degree of freedom in string theory where it describes the
geometry of two extra dimensions arising from the partial compactification of
the ten dimensional spacetime. An intrinsic redundancy in this description is
removed by a set of discrete modular transformations Hamidi:1986vh ;
Dixon:1986qv ; Lauer:1989ax ; Lauer:1990tm , playing the role of gauge
symmetries. Such a setup offers a simple and well-motivated framework to the
idea of flavor symmetry Baur:2019kwi . A finite copy of the modular group acts
in generation space. At the same time the modulus transforms non trivially
under the modular group and plays the role of symmetry breaking order
parameter. Moreover, this setup is suitable to be explored in a bottom-up
approach Feruglio:2017spp .

Despite its simplicity and appeal, the approach is undermined by two major
factors. On the one hand, there is a large freedom in choosing the
transformation properties of the matter fields. Unlike the more familiar
linear transformations, the modular ones are specified by two additional
integers, the weight and the level. Varying these extra parameters, hundreds
of explicit realizations have been proposed in the last years. On the other
hand, modular invariance proved too weak in constraining the kinetic terms of
the matter multiplets Chen:2019ewa . Such a drawback is usually bypassed by
assuming flavor-universal kinetic terms, but this assumption cannot be
justified in a bottom-up approach, which allows for more general and flavor-
dependent kinetic terms, thus reducing the predictability.

The variety of different realizations allowed in a pure bottom-up approach
have not permitted so far the identification of a unique scenario. What can be
learned from the large number of models already proposed? Is there any common
feature emerging from the different constructions?

In this letter we analyze the existing modular invariant flavor models
describing the lepton sector. Most of them successfully reproduce the data in
terms of a limited number of free parameters, which include the modulus $\tau$
itself, varied to maximize the agreement between data and theory. We start by
observing that, in a large number of cases, the preferred value of the modulus
falls close to the self-dual point $\tau=i$, where the modular transformation
$\tau\to-1/\tau$ is unbroken. This preference is even more pronounced for the
subclass of CP invariant models. We investigate the behavior of these models
in a neighborhood of $\tau=i$, also allowing for the most general kinetic
terms. We find that, quite surprisingly, all these models exhibit a universal
behavior, which does not depend on the details of the theory, such as its
level, the modular weights of matter fieds and the precise form of the kinetic
terms.

This class of models predicts normal ordering of neutrino masses. Small
quantities such as $\Delta m^{2}_{sol}/\Delta m^{2}_{atm}$,
$\sin^{2}\theta_{13}$ and $(\sin^{2}\theta_{12}-1/2)$ have well-defined
scaling laws in terms of the parameter $|u|=|(\tau-i)/(\tau+i)|$. All
seemingly different and independent modular invariant lepton models, built by
varying all possible finite modular symmetries, all weights of the matter
fields, and adopting the most general kinetic terms, fall in the same
universality class when $\tau$ approaches the self-dual point.

Modular invariant models of lepton masses

We focus on (${\cal N}=1$ rigid) supersymmetric modular invariant theories
whose field content includes, among the chiral supermultiplets, the modulus
$\tau$, whose scalar component has a positive definite imaginary part, and a
set of matter fields $\varphi$. The relevant part of the action reads:

${\mathscr{S}}=\int d^{4}xd^{2}\theta d^{2}\bar{\theta}~{}K+\int
d^{4}xd^{2}\theta~{}w+\int d^{4}xd^{2}\bar{\theta}~{}\bar{w}~{},$ (1)

where $K$ is the Kähler potential, describing kinetic terms and $w$ is the
superpotential, describing Yukawa interactions. Supersymmetry breaking effects
have been shown to be negligible in a large portion of the parameter space
Criado:2018thu , especially for normally ordered neutrinos, and will be
ignored here. Modular invariance requires ${\mathscr{S}}$ to remain unchanged
under the transformations:

$\displaystyle\begin{array}[]{l}\tau\xrightarrow{\gamma}\displaystyle\frac{a\tau+b}{c\tau+d}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\gamma=\left(\begin{array}[]{cc}a&b\\\
c&d\end{array}\right)\\\\[10.0pt]
\varphi\xrightarrow{\gamma}(c\tau+d)^{-k_{\varphi}}\rho^{N}_{\varphi}(\gamma)\varphi~{}~{}~{}.\end{array}$
(6)

The matrix $\gamma$ belongs to the modular group $SL(2,\mathbb{Z})$ ($a$, $b$,
$c$ and $d$ are integer and $ad-bc=1$), generated by the elements

$S=\left(\begin{array}[]{cc}0&1\\\
-1&0\end{array}\right)~{},~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}T=\left(\begin{array}[]{cc}1&1\\\
0&1\end{array}\right)~{}.$ (7)

The transformation law of $\varphi$ is characterized by a unitary
representation $\rho^{N}_{\varphi}$ of the finite modular group
$SL(2,\mathbb{Z}_{N})$ and by the integer weight $k_{\varphi}$ (irreducible
components of $\varphi$ admitting independent weights). The choice of $N$, the
level of the representation common to all matter fields, specifies the finite
flavour group effectively acting on $\varphi$. For the first few levels
$N=2,3,4,5$ the group $SL(2,\mathbb{Z}_{N})$ is isomorphic to the double
covering of small permutation groups $S_{3},A_{4},S_{4},A_{5}$, respectively.
The modular group allows to restrict the scalar component of the modulus
within the fundamental domain ${\cal F}=\\{{\tt Im}\tau>0,|{\tt Re}\tau|\leq
1/2,|\tau|\geq 1\\}$. In a generic point of ${\cal F}$ the modular group is
fully broken. At the fixed points,
$\tau=(i,\omega\equiv-1/2+i\sqrt{3}/2,i\infty)$ a finite subgroup of
$SL(2,\mathbb{Z})$ is preserved. Invariance under CP requires ${\mathscr{S}}$
to remain unmodified under the transformations (we use a bar(asterisk) to
denote conjugation of fields(numbers)) Baur:2019kwi ; Novichkov:2019sqv :

$\displaystyle\tau\xrightarrow{CP}-\bar{\tau}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\varphi\xrightarrow{CP}\bar{\varphi}~{}~{}~{}.$
(8)

If the theory is CP invariant, CP violation can only arise from a spontaneous
breaking. This occurs everywhere in ${\cal F}$, except along the imaginary
$\tau$ axis and along the border of ${\cal F}$, see fig. 1.

Figure 1: Fundamental domain ${\cal F}$ (light blue region) and fixed points
(see text). Dots are the best fit values of $\tau$ in models of ref.
Criado:2018thu ; Ding:2019zxk  ($\Gamma_{3}$ \- light red), Yao:2020qyy ;
Okada:2020brs  ($\Gamma_{3}\&CP$ \- red), Novichkov:2018ovf  ($\Gamma_{4}$ \-
light magenta), Novichkov:2019sqv  ($\Gamma_{4}\&CP$ \- magenta), Liu:2020akv
($\Gamma_{4}^{\prime}$ \- light blue), Liu:2020akv  ($\Gamma_{4}^{\prime}\&CP$
\- blue), Wang:2021mkw  ($\Gamma_{5}^{\prime}\&CP$ \- black), Li:2021buv
($\Gamma_{6}^{\prime}$ \- light green), Li:2021buv  ($\Gamma_{6}^{\prime}\&CP$
\- green), Ding:2020msi  ($\Gamma_{7}$ \- brown). We use the notation
$\Gamma_{N}^{\prime}=SL(2,\mathbb{Z}_{N})$ and
$\Gamma_{N}=SL(2,\mathbb{Z}_{N})/\\{\pm\mathbb{1}\\}$. In the left panel all
models are displayed. The right panel includes only CP invariant models, for
which the full pair of points $\tau$ and $-\bar{\tau}$ is shown. The dashed
line represents the contour $|\tau-i|=0.25$.

Such a setup has been exploited to describe lepton masses, mixing angles and
phases in a large number of models. The matter multiplets $\varphi$ include
two Higgs doublets $H_{u,d}$, electroweak doublets $L$, singlets $E^{c}$ and,
when neutrino masses arise from the seesaw mechanism, heavy Majorana singlets
$N$. To minimize the number of free parameters, $L$ is usually assigned to an
irreducible triplet of $SL(2,\mathbb{Z}_{N})$. We have investigated more than
100 such models that reproduce accurately the data and predict nine physical
quantities (neutrino masses, mixing angles and phases) in terms of the value
of $\tau$ and 2 or 3 additional Lagrangian parameters. They adopt flavour
universal kinetic terms, but rely on different choices of level and weights.
In all cases, $\tau$ is treated as a free parameter, scanned to maximize the
agreement between data and theory. There is no prejudice about the value of
$\tau$, nor about possible dynamical mechanisms that can determine $\tau$ or
favour some region of ${\cal F}$. In fig. 1 (left panel) we plot 103 best fit
points.

Models are not equally spread in ${\cal F}$. There is a preference for regions
along the boundary of ${\cal F}$, and in particular around the fixed point
$\tau=i$. If we focus on models where CP is spontaneously broken (right panel
of fig. 1) such a preference is more pronounced. CP invariant models evaluated
at symmetric points $\tau$ and $-\bar{\tau}$ only differ in the sign of the CP
violating phases, and have been considered equally successful in fig. 1 (right
panel) that includes $27$ pairs of points. Two thirds of these points fall
close to the self-dual point: $|\tau-i|<0.25$. We regard this feature as an
indication of an intrinsic property of the theory, deserving an explanation.

Figure 2: Mixing angles, mass parameters and phases of 14 pairs of CP and
modular invariant models featuring normal ordering and $|\tau-i|<0.25$ (see
text). For mixing angles and $\Delta m^{2}_{sol}/\Delta m^{2}_{atm}$, the
intervals covered by the model predictions are shown (upper panel). For
neutrino masses, $m_{\beta\beta}$ and CP violating phases, the full
distributions of predictions are displayed (lower panels). The color code is
identical to the one of fig. 1. A star shows the average over the 14 models.
CP violating phases refer to models where ${\tt Re}\tau>0$.

In fig. 2 we show the predictions of a homogeneous set of $14$ pairs of CP
invariant models. We have discarded nine pairs by requiring $|\tau-i|<0.25$,
two pairs not relying on the seesaw mechanism, one pair - the only one -
predicting inverted ordering and a last pair, for which full data were not
available. The average of some combinations of observables over $13$ models of
our sample is listed in eq. (14) 111We have removed the model of ref.
Wang:2021mkw , denoted by black points in the fig. 2, for which $\rho_{L}$ is
reducible.. The quoted error has no statistical meaning: it only illustrates
the spread of the actual predictions for each combination. All the
dimensionless values are of the same order of magnitude and close to the
average deviation of $\tau$ from the imaginary unit. We will see that this
behavior is a universal feature of modular invariant models living close to
$\tau=i$.

$\displaystyle\begin{array}[]{lcl}|\tau-i|=0.20\pm
0.04&&|u|=|\frac{\tau-i}{\tau+i}|=0.095\pm 0.015\\\\[10.0pt]
\sum_{i}m_{i}=73.9\pm 4.6~{}{\rm meV}&&m_{\beta\beta}=5.5\pm 4.2~{}{\rm
meV}\\\\[10.0pt] \frac{m_{2}+m_{1}}{2}=11.5\pm 2.2~{}{\rm
meV}&&\frac{m_{2}+m_{1}}{2m_{3}}=0.23\pm 0.04\\\\[10.0pt]
2\frac{m_{2}-m_{1}}{m_{2}+m_{1}}=0.34\pm 0.25&&\left(\frac{\Delta
m^{2}_{sol}}{\Delta m^{2}_{atm}}\right)^{1/3}=0.310\pm 0.001\\\\[10.0pt]
\sin\theta_{13}=0.148\pm
0.001&&\left|\displaystyle\frac{1}{\sqrt{2}}-\sin\theta_{12}\right|=0.14\pm
0.01~{}.\end{array}$ (14)

Universal behavior near $\tau=i$

At $\tau=i$ both CP and the $\mathbb{Z}_{4}$ subgroup of $SL(2,\mathbb{Z})$
generated by the element $S$, are preserved. The element $S$ acts non linearly
in the field space and it is convenient to move to a basis where CP and
$\mathbb{Z}_{4}$ are linearly realized. We define Feruglio:2021dte ;
Novichkov:2021evw :

$u=\displaystyle\frac{\tau-i}{\tau+i}~{},~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\Phi=(1-u)^{k_{\varphi}}\varphi~{}.$
(15)

The new fields transform as:

$\displaystyle\begin{array}[]{lcccl}u\xrightarrow{S}-u&&&&\Phi\xrightarrow{S}\Omega_{\varphi}(S)~{}\Phi\\\\[10.0pt]
u\xrightarrow{CP}\bar{u}&&&&\Phi\xrightarrow{CP}\bar{\Phi}~{},\end{array}$
(18)

where the unitary matrices $\Omega_{\varphi}(S)$ are

$\displaystyle\Omega_{\varphi}(S)=i^{k_{\varphi}}\rho_{\varphi}(S)~{}.$ (19)

The most general (${\cal N}=1$, rigid) supersymmetric theory depending on $u$
and $\Phi$ and invariant under the linear transformations (18), extends the
setup of eqs. (1) and (6). Indeed ${\mathscr{S}}$ is also invariant under the
transformations generated by the element $T$ which, evaluated in terms of $u$,
reads:

$\displaystyle
u\xrightarrow{T}\displaystyle\frac{1-(1-2i)u}{(1+2i)-u}=\frac{1-2i}{5}+\frac{4}{25}(3+4i)u+...~{}~{}~{}.$
(20)

The new, more general, theory has non-canonical and flavour-dependent kinetic
terms. After moving to the basis where such terms are canonical, it is not
difficult to prove that charged lepton and neutrino mass matrices,
$m_{e}^{2}(u,\bar{u})\equiv m_{e}(u,\bar{u})^{\dagger}m_{e}(u,\bar{u})$ and
$m_{\nu}(u,\bar{u})$, should satisfy the relations:

$\displaystyle
m_{\nu}(\bar{u},u)=m_{\nu}(u,\bar{u})^{*}~{},~{}~{}m_{e}^{2}(\bar{u},u)=[m_{e}^{2}(u,\bar{u})]^{*}~{},$
(21)

and

$\displaystyle\begin{array}[]{l}\Omega(S)^{T}m_{\nu}(-u,-\bar{u})~{}\Omega(S)=m_{\nu}(u,\bar{u})\\\\[5.0pt]
\Omega(S)^{\dagger}m_{\nu}(-u,-\bar{u})^{-1}~{}\Omega(S)^{*}=m_{\nu}(u,\bar{u})^{-1}\\\\[5.0pt]
\Omega(S)^{\dagger}~{}m_{e}^{2}(-u,-\bar{u})\Omega(S)=m_{e}^{2}(u,\bar{u})~{},\end{array}$
(25)

where we have defined:

$\displaystyle\Omega(S)\equiv\Omega_{H_{u}}(S)\Omega_{L}(S)=i^{k_{H_{u}}+k_{L}}\rho_{H_{u}}(S)\rho_{L}(S)~{}.$
(26)

A key observation of the present note is that, under the only assumption that
$\rho_{L}$ is irreducible, which is adopted in the vast majority of existing
models, the combination $\Omega(S)$ is completely fixed up to an overall phase
factor. Once diagonalized, $\Omega(S)$ reads:

$\displaystyle\Omega(S)=i^{k_{S}}{\tt diag}(1,-1,-1)~{},$ (27)

where $k_{S}$ is an integer depending on $k_{H_{u}}$, $k_{L}$ and
$\rho_{H_{u}}$, as well as on the specific 3-dimensional representation
$\rho_{L}$ of $SL(2,\mathbb{Z}_{N})$. This result can be proved by directly
inspecting all 3-dimensional irreducible representations of
$SL(2,\mathbb{Z}_{N})$ that, for $N$ a power of 2 or a prime, exist only for
$N=3,4,5,7,8,16$ nobs . There are 33 inequivalent such representations, easily
rebuildable from Appendix A of ref. Eholzer:1994th . For these levels we can
also construct the 1-dimensional representations of $SL(2,\mathbb{Z}_{N})$. A
straightforward computation leads to eq. (27), valid for all $N$. It is also
possible to prove eq. (27) without relying on explicit representations
222G.-J. Ding, private communication..

Working in the vicinity of $u=0$ and exploiting eq. (27), we can explicitly
write the expansion of $m_{e}^{2}(u,\bar{u})$ and $m_{\nu}(u,\bar{u})$ in
powers of $u$ and $\bar{u}$. We cannot make us of the invariance under $T$,
since the transformation of eq. (20) spoils the power expansion. Here we
discuss the case of $k_{S}$ odd and $m_{\nu}(0,0)$ singular, relevant if the
neutrino masses arise from the seesaw mechanism. After moving to the basis
where $m_{e}^{2}(u,\bar{u})$ is diagonal, we obtain:

$\displaystyle
m_{\nu}^{-1}=m_{0\nu}^{-1}\left(\begin{array}[]{lll}x_{11}~{}x&x^{0}_{12}&x^{0}_{13}\\\
\cdot&x_{22}~{}x&x_{23}~{}x\\\ \cdot&\cdot&x_{33}~{}x\\\
\end{array}\right)+{\cal O}(x^{2})~{},$ (31)

where $m_{0\nu}$ is a mass parameter and we used the definitions

$\displaystyle\begin{array}[]{l}u=x~{}e^{\displaystyle
i\theta}~{}~{}~{}~{}~{}~{}~{}~{}~{}(x>0,2\pi>\theta\geq 0)\\\\[8.0pt]
x_{ij}~{}x\equiv(x^{10}_{ij}e^{\displaystyle
i\theta}+x^{01}_{ij}e^{\displaystyle-i\theta})~{}x~{},\end{array}$ (34)

$x^{0}_{12}$, $x^{0}_{13}$, $x^{10}_{ij}$ and $x^{01}_{ij}$ being real
coefficients. From eq. (31) we derive the first few terms in the $x$-expansion
of neutrino masses, mixing angles and phases:

$\displaystyle\begin{array}[]{l}m_{1,2}=\displaystyle\frac{m_{0\nu}}{h}\left(1\mp\displaystyle\frac{s}{2h}x\right)~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}m_{3}=\displaystyle\frac{m_{0\nu}}{|q|x}\\\\[10.0pt]
\sin^{2}\theta_{12}=\frac{1}{2}\left(1+\displaystyle\frac{l\bar{k}+\bar{l}k}{hs}x\right)~{}~{}~{}~{}~{}\sin^{2}\theta_{13}=2\displaystyle\frac{|n|^{2}}{h^{2}}x^{2}\\\\[10.0pt]
\sin^{2}\theta_{23}=\displaystyle\frac{(x^{0}_{13})^{2}}{h^{2}}(1+{\cal
O}(x))\\\\[10.0pt]
\delta_{CP}=\pi-\arg\left[\displaystyle\frac{(c_{\nu}-is_{\nu})^{2}x^{0}_{12}x^{0}_{13}}{n}\right]+{\cal
O}(x^{2})\\\\[10.0pt] \alpha_{21}=\pi+{\cal O}(x)\\\\[10.0pt]
\alpha_{31}=\arg(q)-\arg\left[(c_{\nu}-is_{\nu})^{2}\right]+{\cal
O}(x)~{}.\end{array}$ (41)

We have defined:

$\displaystyle\begin{array}[]{l}h=\sqrt{(x^{0}_{12})^{2}+(x^{0}_{13})^{2}}~{}~{}~{}~{}~{}~{}~{}~{}~{}s=\sqrt{(k+\bar{k})^{2}-(l-\bar{l})^{2}}\\\\[7.0pt]
k=+\displaystyle\frac{x_{11}}{2}+\displaystyle\frac{1}{2h^{2}}\left((x^{0}_{12})^{2}x_{22}+(x^{0}_{13})^{2}x_{33}+2x^{0}_{12}x^{0}_{13}x_{23}\right)\\\\[7.0pt]
l=-\displaystyle\frac{x_{11}}{2}+\displaystyle\frac{1}{2h^{2}}\left((x^{0}_{12})^{2}x_{22}+(x^{0}_{13})^{2}x_{33}+2x^{0}_{12}x^{0}_{13}x_{23}\right)\\\\[7.0pt]
n=\displaystyle\frac{1}{2h^{2}}\left[\left(x^{0}_{12})^{2}-(x^{0}_{13})^{2}\right)x_{23}+x^{0}_{12}x^{0}_{13}\left(-x_{22}+x_{33}\right)\right]\\\\[7.0pt]
q=\displaystyle\frac{1}{2h^{2}}\left((x^{0}_{13})^{2}x_{22}+(x^{0}_{12})^{2}x_{33}-2x^{0}_{12}x^{0}_{13}x_{23}\right)\\\\[7.0pt]
\displaystyle\frac{2c_{\nu}s_{\nu}}{c_{\nu}^{2}-s_{\nu}^{2}}=i\displaystyle\frac{l-\bar{l}}{k+\bar{k}}+{\cal
O}(x^{2})~{}~{}~{}~{}~{}~{}~{}~{}~{}i(l-\bar{l})={\mathcal{O}}(1)~{}.\end{array}$
(48)

Other combinations of interest are:

$\displaystyle\begin{array}[]{l}\displaystyle\frac{m_{1}+m_{2}}{2m_{3}}=\frac{|q|}{h}x~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}2\displaystyle\frac{m_{2}-m_{1}}{m_{2}+m_{1}}=\frac{s}{h}x\\\\[10.0pt]
\left(\displaystyle\frac{\Delta m^{2}_{sol}}{\Delta
m^{2}_{atm}}\right)^{1/3}=\displaystyle\frac{(2|q|^{2}s)^{1/3}}{h}x\\\\[10.0pt]
m_{\beta\beta}=\displaystyle\frac{m_{0\nu}}{h}\displaystyle\frac{\left|x_{23}^{2}-x_{22}x_{33}\right|}{2h|q|}x~{}~{}~{}.\end{array}$
(52)

Making use of eqs. (41), (48) and (52), we see that the averages of eqs. (14)
can be reproduced by $x\approx 0.1$, $m_{0\nu}/h=11.5$ meV and

$\displaystyle\begin{array}[]{l}\displaystyle\frac{|q|}{h}\approx
2.3~{}~{}~{}~{}~{}~{}~{}~{}\displaystyle\frac{s}{h}\approx
3.4~{}~{}~{}~{}~{}~{}~{}~{}\displaystyle\frac{\sqrt{2}|n|}{h}\approx
1.5\\\\[10.0pt] \displaystyle\frac{|l\bar{k}+\bar{l}k|}{2\sqrt{2}hs}\approx
1.4~{}~{}~{}~{}~{}~{}~{}~{}~{}\displaystyle\frac{\left|x_{23}^{2}-x_{22}x_{33}\right|}{2h|q|}\approx
4.8\end{array}$ (55)

We conclude that all the dimensionless quantities in eq. (14) scale linearly
with $x$, with proportionality coefficients of order one. The only relatively
large coefficient is that of the combination controlling $m_{\beta\beta}$,
whose value in eq. (14) has the largest relative fluctuation.

This result holds for the most general Kähler potential compatible with
modular invariance. If a flavour universal Kähler potential is adopted, the
anti-holomorphic variable $\bar{u}$ only affects the overall scale of the mass
matrices, can be absorbed in the parameter $m^{0}_{\nu}$ of eq. (31) and drops
from all dimensionless quantities. If so, all the complex parameters $x_{ij}$
have a common phase, up to a sign. The result of eqs. (41), (48) and (52) is
valid for any level $N$ and for all possible assignment of weights
$k_{\varphi}$, provided the combination $k_{S}$ of eq. (27) is odd and
$m_{\nu}(0,0)$ is singular. Indeed $k_{S}$ is odd in all but one of the $14$
pairs of CP invariant models selected above. If $k_{S}$ is even, another set
of universal scaling laws analogous to those in eqs. (41) and (52) applies.
Their agreement with the data is less satisfactory, since they predict $\Delta
m^{2}_{sol}/\Delta m^{2}_{atm}$ of order one and both $\sin\theta_{12}$ and
$\sin\theta_{13}$ of order $x$. A singular $m_{\nu}(0,0)$ can only arise
through the seesaw mechanism. If neutrino masses are described by the Weinberg
operator and $m_{\nu}(0,0)$ is regular, we can easily derive other scaling
relations predicting both $\Delta m^{2}_{sol}/\Delta m^{2}_{atm}$ and
$\sin\theta_{13}$ of order $x$, in tension with the data. Finally, our
analysis can be easily extended to the other fixed points. Under the
assumption that $\rho_{L}$ is irreducible, an expansion around $\tau=\omega$
leads to universal but phenomenologically disfavored predictions, while a
similar analysis around $\tau=i\infty$ leads to results depending on the level
$N$. The interest in those fixed points is related to the generation of
natural mass hierarchies in the charged lepton sector Novichkov:2021evw , an
aspect that we have not touched in the present discussion.

Conclusions

Modular invariance may represent one important piece for the solution of the
flavour puzzle. Many concrete bottom-up realizations suggest that a single
modulus can dominate the description of the neutrino sector. Nevertheless
model building suffers from the large freedom related to the choice of the
level and the weights, as well as to possible non-universal kinetic terms. We
have shown that, even freely varying all these ingredients, a universal
behavior emerges in the vicinity of the self-dual point $\tau=i$, under the
sole assumption that the lepton doublets are assigned to a irreducible
representation of the finite modular group. Few cases survive, one of which
perfectly matches the experimental data. If the neutrino mass matrix is
singular at the fixed point and the discrete parameter $k_{S}$ is odd, a
normal ordering is predicted. The sum of neutrino masses lies around 74 meV.
Universal relations characterize the scaling of several observable quantities
in terms of $|\tau-i|$. The independence of these results from the effective
flavour group $SL(2,\mathbb{Z}_{N})$ acting on the matter fields and from the
specific form of the kinetic terms is a remarkable feature of the theory.
Although universal predictions are highly desirable and constitute an
outstanding theoretical property, there are no reasons a priori for the data
to privilege a small region of the modulus around $\tau=i$. It is really
impressive that, over all the allowed parameter space, this is precisely the
region preferred by most of the constructions we have examined.

Acknowledgements The author thanks Gui-Jun Ding, João Penedo and Arsenii Titov
for very helpful comments and for invaluable assistance during the final
revisions of this note. This work was supported by the INFN.

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» «

# What’s Your Value of Travel Time?
Collecting Traveler-Centered Mobility Data via Crowdsourcing

Cristian Consonni,1 Silvia Basile,1 Matteo Manca,1 Ludovico Boratto,1 André
Freitas,2
Tatiana Kovacikova,3 Ghadir Pourhashem,3 Yannick Cornet3

###### Abstract

Mobility and transport, by their nature, involve crowds and require the
coordination of multiple stakeholders - such as policy-makers, planners,
transport operators, and the travelers themselves. However, traditional
approaches have been focused on time savings, proposing to users solutions
that include the shortest or fastest paths. We argue that this approach
towards travel time value is not centered on a traveler’s perspective. To
date, very few works have mined data from crowds of travelers to test the
efficacy and efficiency of novel mobility paradigms. In this paper, we build
upon a different paradigm of _“worthwhile time”_ in which travelers can use
their travel time for other activities; we present a new dataset, which
contains data about travelers and their journeys, collected from a dedicated
mobile application. Each trip contains multi-faceted information: from the
transport mode, through its evaluation, to the positive and negative
experience factors. To showcase this new dataset’s potential, we also present
a use case, which compares corresponding trip legs with different transport
modes, studying experience factors that negatively impact users using cycling
and public transport as alternatives to cars. We conclude by discussing other
application domains and research opportunities enabled by the dataset.

## Introduction

The extraction of actionable knowledge from user mobility has been a central
perspective mainly for mobility stakeholders - such as policy-makers,
planners, and transport operators - who, in turn, used this knowledge to adapt
the services to the end users. This process, known as behavioral-data mining,
aims at extracting patterns from the travelers’ behavior, in order to better
characterize them (Manca, Boratto, and Carta 2018; Boratto et al. 2018). Under
this paradigm, end-users have mostly been passive actors.

In the last 20 years, the integration between information and communication
technologies (ICT) and transport have radically changed mobility: from the
mere availability of information about transport such as bus lines or time
tables, we now have new forms of offerings in terms of on-demand services and
even whole new business models for transport, where new services offer the
opportunity to share rides or even private cars. New Web platforms, such as
journey planners (Sourlas and Nathanail 2019), have transformed users into
active actors in providing their mobility preferences. Users can sort trips
based on different types of preferences (e.g., length, duration, emissions)
and decide to complete a trip by combining services of different operators.
Hence, novel mobility paradigms emerged, in which users’ value of travel time
(VTT) is defined as the combination of different factors (e.g., a trip by bike
could be longer than taking other means of transport, but might valuable from
multiple perspectives, such as emissions, costs, and fitness for the user)
(Devarasetty, Burris, and Douglass Shaw 2012).

However, other aspects of transportation, such as the reliance upon private
cars have not changed. We argue that one of the main opportunities offered by
the integration between ICT and transport lies in the possibility of gather
data from a vast audience of travelers about both their travel preferences and
wishes and their actual day-to-day transport usage. In this sense,
crowdsourcing, intended as the process of collecting data contributed by vast
amounts of people, mainly via the Internet, can become a valuable means
towards the accomplishment of this goal.

While novel paradigms related to value of travel time have been introduced
(Karadimce, Lugano, and Cornet 2018; Kováčiková, Lugano, and Pourhashem 2018;
Lugano et al. 2019), existing studies capture user behavior in mobility from a
single perspective. When moving from academic research to industrial
applications, a one-to-one relationship between value of travel time and
shortest path exists, so that existing services - such as Google Maps and Waze
- mainly rank trips by shortest path. We believe that this might be due - at
least from the research side - to the lack of knowledge on what is actually
valuable for the users in their mobility choices. While several existing
datasets capture mobility by considering a single perspective (e.g., one
transport mode, or only trip coordinates), no dataset capturing both explicit
preferences in terms of value for the users when making their mobility choices
and implicit information coming from the trip (e.g., coordinates) exist. This,
in turn, has been reflected in industrial applications, which do not capture
explicit feedback on additional factors. Hence, value of travel time remains a
concept trapped inside the mobility community, which cannot be fully exploited
by the Web community, to create actionable knowledge for Web platforms. We
believe that crowdsourcing can be a powerful tool to directly collect feedback
on the travelers’ value of travel time and their mobility choices.

To overcome these issues, in this paper we present the _MoTiV_ dataset, a
collection of traveler-centered information about trips and the value of
travel time behind traveler’s choices.

To show how the extraction of knowledge on users’ value of travel time can
concretely impact transport stakeholders, we also present a use case that
characterizes what are the negative factors associated to a trip, when this is
performed by means of public transport or by cycling, w.r.t. the same trip
performed by car.

This dataset was collected in the context of the Horizon 2020 _MoTiV_
(Mobility and Time Value) project, whose goal was to provide novel definitions
of value of travel time (VTT) (Malichová et al. 2020).

## Related Work

In this section, we present datasets related to the one presented in this
paper, and conclude by highlighting the difference between our dataset and the
existing ones.

### User Behavior Mining

Data coming from online platforms was previously used to mine user behavior,
to consider aspects such as their willingness to pay for services (Zografos,
Androutsopoulos, and Apospori 2012) and challenges in behavior change
(Schrammel et al. 2015). Manca et al. (Manca et al. 2017) presented a survey
on mobility patterns considering social media data. González, R., and Barabási
(González, R., and Barabási 2008), instead, consider mobile phone data, while
Calabrese et al. (Calabrese et al. 2013) extract mobility patterns from urban
sensing data. Goulias (Goulias 2018) surveyed the existing travel behavior
models. Data analysis can produce insights that serve as input for other
purposes, such as the improvement of transport services by considering user
needs (Sierpiński and Staniek 2017), the promotion of changes of the user
habits (Schrammel et al. 2015), and the improvement of journey planners and
transport portals (Esztergár-Kiss 2016; Vargas, Weffers, and da Rocha 2011).
Other studies go beyond data analysis, e.g., to extract topic models from geo-
location data (Hasan and Ukkusuri 2014), to forecast the evolution of
preferences over time thanks to a Markov model (Zarwi, Vij, and Walker 2017),
or to provide a personalized journey planning (Jakob et al. 2014). As
previously mentioned, the knowledge coming from the user analytics can also be
used as a form of actionable knowledge, e.g., to improve transport service
according to the user needs (Sierpiński and Staniek 2017), to promote changes
in the user habits (Schrammel et al. 2015) such as the adoption of greener and
healthier solutions (Gabrielli et al. 2014), or improve the usability and
services provided by journey planners and transport portals (Esztergár-Kiss
2016; Vargas, Weffers, and da Rocha 2011).

### Crowdsourced Datasets

#### Social and trip data

Microsoft GeoLife is a social network that also allows users to share their
experience, both through GPS data and with pictures. The publicly available
GPS trajectory dataset was collected by 182 users, for over two
years111https://www.microsoft.com/en-us/research/project/geolife-building-
social-networks-using-human-location-history/#!downloads. No explicit info
about the means of transport is available, and no evaluation of the trips is
offered.

#### Check-in data

Check-in data, coming from platforms such as Twitter, Foursquare, or Gowalla,
is usually used to consider user preferences related to their mobility.
Indeed, knowing where the users go and with which frequency, allows to
characterize users’ mobility and their preferences (especially if check-ins
can be paired with reviews). Examples of datasets belonging to this class can
be found here 222https://sites.google.com/site/yangdingqi/home/foursquare-
dataset. While this class of datasets is widely employed in various
personalization algorithms, the concept of a trip is entirely missing, thus
losing all the information about the means of transport, or the relevant
factors for the users.

#### Trip-only data

Another class of datasets collect trip information. A selection of 250
datasets available for research purposes can be found
here333https://data.world/datasets/trips. Trip datasets usually do not
associate the trips to a user, thus not allowing a characterization of the
individual user mobility. In addition, they are usually associated to a single
transport of mode (e.g., taxis).

### Contextualizing our Contributions

As this analysis has presented, mobility datasets usually capture a single
perspective and usually the full user-mobility picture as lost. The aim of our
data collection is to capture multiple perspectives behind user mobility. This
is done by:

  * •

having trips with different transport modes (something not available in
classic trip datasets);

  * •

collecting trip coordinates (this is usually not available in check-in
datasets);

  * •

collecting reviews and evaluations of each trips;

  * •

working at a lower granularity, by not only considering the trip as a whole,
but also the activities that compose it; This allows to consider the different
experience factors in user mobility, at different stages of the trip.

## Background and Crowdsourcing Process

Worthwhile time. Worthwhile time is a central concept for our data collection.
While the traditional view is to consider travel time as something to
minimize, we consider travel time as an opportunity, i. e. time that that can
be characterized by other activities. We have collected data through a
dedicated mobile app, called _Woorti_ 444The name of the app is a play on the
words “worth it” referring to worthwhile travel time., to ground the
definition of worthwhile time into multiple dimensions.

A key challenge of collecting a European-wide dataset was engaging users
across multiple countries for an extended time. In fact, from a traveler’s
point-of-view, the data collection translated to using the smartphone app
actively for at least 14 days. We framed the process as a challenge between
user: data-collection campaigns (DCCs) would group users together and reward
the most active ones in each campaign. To facilitate the process, we have
partnered with thematic organizations across Europe - such as cycling
associations - and we have appointed DCC managers as liaison with the
community, whose tasks were recruiting participants, promoting and monitoring
the data collection process. The application supported both Android and iOS
devices and was available in 11 languages. Data collection targeted 10
European countries: Belgium, Croatia, Finland, France, Italy, Norway,
Portugal, Slovakia, Spain, and Switzerland. Overall, the data considered in
this paper cover a period of 8 months, from May 1st, 2019 to December, 13rd
2019.

The use of the app consists of three main phases:

  1. 1.

_Onboarding_ : upon installing the application and registering a new account,
the user is introduced to the functionalities of the app. During this process,
the user enters their travel preferences as well as some basic demographic
information.

  2. 2.

_Trip recording_ : the user can start a new trip and the app automatically
collects data in background.

  3. 3.

_Trip validation_ : when a trip is finished, the user can review the data,
validate it and insert other data regarding the trip (trip purpose, mood,
etc). When validating a trip, the user must choose one leg of the trip as the
reviewed leg.

Within the application, a user can access their data and visualize and edit
their profile information and trips. Furthermore, the application features a
dashboard that presents to the user statistics related to their validated
trips.

The value of travel time is analyzed from a traveler’s perspective, assuming
that time and cost savings are not always the main criteria influencing route
and mode choice. Depending on the traveler’s transport attitude and context,
other criteria such as environmental impact, comfort, or even weather
conditions may influence the perceived value of a trip. In particular, we
adopt the perspective that travel time can be worthwhile, i. e. it can be
allocated for activities that the user finds useful, enjoyable, or productive.
For this reason, when validating a trip, the user is asked about which
activities they have performed during the trip, which factors in their have
influenced the trip positively or negatively, and which was the trip purpose.

By collecting this data, we are able to shifts perspective from considering
travel time as spent - or, worse, wasted - to time that can be characterized
by other activities. Furthermore, this characterization is not limited by
defining time as productive or unproductive time, because it is not
necessarily related to its evaluation in terms of cost. Worthwhile time is
independent of what can be monetized.

The _MoTiV_ dataset and the analyses presented here contain only validated
trips. During data collections, local campaign managers stressed to users that
validating a trip meant sharing it with the project, i. e. validated trips
were uploaded to a central server. This process preserves users’ privacy since
they were always in control of what data they are willing to share with the
project. Furthermore, the data collection process was overseen and approved by
an independently appointed ethics advisor and the ethics committee at the
University of Z̆ilina, _MoTiV_ ’s coordinator.

## Dataset Description

Dataset. The dataset can be downloaded at:
https://zenodo.org/record/4027465.
The code used for pre-processing the raw data and performing the case study is
available at:
https://github.com/MoTiV-project/data-analysis

The dataset is comprised of $13$ tables saved as comma-separated value (.csv)
files:

  1. 1.

user_details.csv

  2. 2.

user_generic_worthwhileness_values.csv

  3. 3.

user_specific_worthwhileness_values.csv

  4. 4.

mots.csv

  5. 5.

trips.csv

  6. 6.

legs.csv

  7. 7.

legs_coordinates.csv

  8. 8.

activities.csv

  9. 9.

experience_factors.csv

  10. 10.

purposes.csv

  11. 11.

weather_legs.csv

  12. 12.

weather_raw.csv

  13. 13.

worthwhileness_elements_from_trips.csv

#### User Details

The table user_details.csv $(1)$ contains the data collected during the
onboarding phase. Only the fields user_id, registration_timestamp, gender, and
age are required.

  * •

user_id: the user identifier, a string of 29 characters.

  * •

registration_timestamp: the trip start date, formatted as %Y-%m-%d
%H:%M:%S.%f.

  * •

gender: the gender of the user. Three values are possible: Other, Male,
Female.

  * •

age: the user’s age in a range. Possible values are: 16-19, 20-24, 25-29,
30-39, 40-49, 50-64, 65-74, 75+.

  * •

language: the language used within the app expressed as a 3-letter ISO 639-2/B
code.

  * •

city: the user’s city of residence.

  * •

country: the user’s country of residence expressed in ISO 3166-1 alpha-3 code.

  * •

education_level: the user’s education, possible values are: Basic (up to 10th
grade), High School (12th grade), and University.

  * •

marital_status: the user’s marital status, possible values are: Single,
Registered relationship, Married, Divorced, Widowed.

  * •

number_of_people: the number of people in the household, it can be a number
from $1$ to $4$ or $5+$.

  * •

labour_status: the users’ labour status. Possible values are: Student,
Employed full-time, Employed part-time, Pensioner, Unemployed.

  * •

years_of_residence: the number of years of residence in the household.
Possible values are: Less than 1, 1 to 5, More than 5.

#### User’s Generic and Specific Worthwhileness Elements

Users’ preferences and experiences are characterized along the three
dimensions of fitness, enjoyment, and productivity, defined as follows (in
parenthesis, we report a description of each dimension, visualized by users
during data collection):

  * •

fitness measures how much the user values the fact that when traveling they
can exercise («When you walk, cycle, or even run on your travels, you are
getting exercise and keeping in shape»);

  * •

enjoyment is related to how the travel can be used for fun or relaxing
activities («Relaxing or having fun: taking time to listen to music, rest or
meditate; engaging in social media; observing the surroundings»);

  * •

productivity captures how much the user values the possibility of using travel
time to complete some tasks, either personal or work-related. («Using travel
time to get things done, not only for work or study, but also personal things
like managing home or family stuff»). It is further diving in two aspects:
_Paid work_ and _Personal tasks_.

User preferences and experiences are encoded in two main sets of values,
called worthwhileness555Although this diction of the word is less widespread
than the more common variant “ _worthiness_ ,” it is used throughout the
project, so we keep it for consistency with the project itself. values:

  * •

_generic worthwhileness values:_ they are a triplet of values $(F,E,P)$ for
_fitness_ , _enjoyment_ , and _productivity_ , respectively. They measure how
much the user values these dimension in general when traveling;

  * •

_specific worthwhileness values:_ they are triplets of values $(F,E,P)$ that
the user is asked to assign for each specific mode of transport chosen in the
onboarding phase. The transport modes that the user selects during the
onboarding phase are called _preferred transport modes_. Specific
worthwhileness values are the measure of how much the user values _fitness_ ,
_enjoyment_ , and _productivity_ when using that particular transport mode.

During the onboarding phase, the user is asked to provide both the generic and
specific worthwhileness values on a scale from 1 to 100. When evaluating
trips, the user is asked to provide an evaluation for each dimension of
_fitness_ , _enjoyment_ , and _productivity_ using a scale from low to high
(low, medium, high). This difference in data collection depended on the design
of the app, whose description is out of scope for this paper. For consistency
with the evaluation values, we scale the onboarding values to the same three
classes: low, for values in $[0-33]$; medium, $[34-66]$; and high, $[67-100]$.

Generic worthwhileness values are stored in the table
user_generic_worthwhileness_values.csv $(2)$, its columns are:

  * •

userid, the user identifier;

  * •

fit, the value for fitness $[0-100]$;

  * •

prod, the value for productivity $[0-100]$;

  * •

enjoy, the value for enjoyment $[0-100]$;

Specific worthwhileness elements are related to specific mode of transports,
chosen by the user during the _Onboarding_ phase. These are referred as the
traveler’s favorite modes of transport. Specific worthwhileness values are
stored in the table user_specific_worthwhileness_values.csv $(3)$. Its columns
are:

  * •

userid, the user identifier;

  * •

motid, the mode of transport identifier;

  * •

fit, the value for fitness $[0-100]$;

  * •

prod, the value for productivity $[0-100]$;

  * •

enjoy, the value for enjoyment $[0-100]$;

The mapping between mode of transport ids and text is contained in mots.csv
$(4)$.

Field |  Description and admissible values
---|---
tripid |  Trip identifier, a string in the format #{n1}:{n2} where n1 and n2 are two numbers.
userid |  User identifier.
start_date |  Trip start date, formatted as ’%Y-%m-%d %H:%M:%S.%f’.
end_date |  Trip end date, formatted as ’%Y-%m-%d %H:%M:%S.%f’.
average_speed |  Average speed during trip in km/h.
max_speed |  Max speed during trip.
distance |  Leg distance in meters.
duration |  Leg duration in seconds.
mood_rating |  Evaluation of trip mood on a scale from 1 to 5.
did_you_have_to_arrive |  Answer to the question _“Did you have to arrive on time”_ , a boolean value.
how_often |  Answer to the question _“How often do you make this trip?”_ , possible values are integers from 0 to 3. -1 means that the question was not answered.
use_trip_more_for |  Answer to the question _“How often do you make this trip?”_ , possible values are integers from 0 to 3. -1 means that the question was not answered.
manual_start |  Answer to the question _“Has the trip recording been started manually?”_ , a boolean value.
manual_end |  Answer to the question _“Has the trip recording been ended manually?”_ , a boolean value.
validation_date |  Trip validation date, formatted as ’%Y-%m-%d %H:%M:%S.%f’.
os |  Operating system of the phone, can be iOS or Android, a string.
os_version |  Operating system version, a string.
model |  Model of the phone, a string.

Table 1: Trip information stored in trips.csv.

Field |  Description and admissible values
---|---
legid |  Leg identifier, a string in the format #{n1}:{n2} where n1 and n2 are two numbers.
class |  Leg type, either Leg or WaitingEvent.
userid |  User identifier.
tripid |  Trip identifier.
motid |  Mode of transport identifier, an integer number.
start_date |  Leg start date, formatted as %Y-%m-%d %H:%M:%S.%f.
end_date |  Leg end date, formatted as %Y-%m-%d %H:%M:%S.%f.
true_distance |  Leg distance in meters.
leg_distance |  Leg distance in meters.
leg_duration |  Leg duration in seconds.
worthwhileness_rating |  Worthwhileness rating, $-1$ if not set.
transport_category |  Transport category.
campaign |  Data collection campaign.
weekday |  Day of the week when the leg was performed.
weekday_class |  Classification of the day, either Working_day or Weekend.

Table 2: Leg information stored in legs.csv.

Field |  Description and admissible values
---|---
leg_id |  The identifier of the leg in the format #n1:n2, with n1 and n2 being two integer numbers.
start_lat |  a real number with 3 decimals. The latitude of the starting point of the leg.
start_lon |  a real number with 3 decimals. The longitude of the starting point of the leg.
end_lat |  a real number with 3 decimals. The latitude of the ending point of the leg.
end_lon |  a real number with 3 decimals. The longitude of the ending point of the leg.
start_name |  The inferred name of the city where the starting point of the leg is located. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data.
start_country |  The ISO 3166 Alpha-3 code of the inferred country where the starting point of the leg is located. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data1b.
start_class |  Possible values are: urban, sub-urban, or rural. The classification of the starting point of the leg. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data1c.
end_name |  The inferred name of the city where the ending point of the leg is located. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data.
end_country |  The ISO 3166 Alpha-3 code of the inferred country where the ending point of the leg is located. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data1b.
end_class |  Possible values are: urban, sub-urban, or rural. The classification of the ending point of the leg. This field is obtained in the preprocessing by integrating the leg coordinates with OECD data1c.

Table 3: Legs coordinates stored in legs_coordinates.csv

#### Trips Info

Trip data are contained in the table trips.csv $(5)$, whose fields are
reported in Table 1. A trip is a collection of _legs_ and _waiting events_ :
the former are parts of a journey where the app has detected some
movement55footnotetext: The app offers mode detection algorithms to infer the
type of mode of transport used; however during the trip validation ad
evaluation the user was able to override the modes suggested., while waiting
events are intervals of time where the app did not detect any significant
displacement. We processed trip data to merge legs that were erroneously split
by the app, furthermore we performed outlier detection to eliminate the trips
that were in top and bottom percentiles in terms of length and duration.

#### Legs Info

Leg data are contained in the table legs.csv $(6)$, whose fields are reported
in Table 2.

#### Legs Coordinates

Leg coordinates are contained in the table legs_coordinates.csv $(7)$, whose
fields are reported in Table 3. Coordinates are anonymized depending on the
fact that the point is located in a urban, suburban or rural area. To classify
the points we used the “functional urban areas by country” classification
provided by the Organisation for Economic Co-operation and Development
(OECD).666Functional urban areas by country,
https://www.oecd.org/regional/regional-statistics/functional-urban-areas.htm

Points were anonymised using the following criterion, applied both to latitude
and longitude:

  * •

for urban areas, points are rounded to the third decimal place;

  * •

for sub-urban areas, the third decimal place is rounded to the nearest $0.5$;

  * •

for rural areas, the second decimal place is rounded to the nearest $0.5$;

#### Activities

Data about activities performed during trips are contained in table
activities.csv $(8)$. A user can select multiple activities during a trip, but
we do not record their duration. Columns in activities.csv are:

  * •

legid, leg identifier

  * •

activity, activity name, possible values are Accompanying, Browsing, Cycling,
Driving, Eating, Listening,
PersonalCare, ReadingDevice, ReadingPaper, Relaxing, Talking, Thinking,
Walking, Watching, and Other

#### Experience Factors

Table experience_factors.csv $(9)$ contains information about experience
factors affecting trips, its columns are:

  * •

legid, leg identifier;

  * •

factor, experience factor name. There are 48 possible values, for context we
list here a sample: Air_Quality, Cleanliness, Crowdedness_Seating,
Internet_Connectivity, Privacy, Reliability_Of_Travel_Time, Todays_Weather,
Toilets, Vehicle_Quality, Vehicle_Ride_Smoothness;

  * •

type, factor categorization;

  * •

minus, a boolean value, the factor was rated as negative;

  * •

plus, a boolean value, the factor was rated as positive.

#### Trip purposes

The table purposes.csv $(10)$ contains information about trips purposes, its
columns are:

  * •

tripid, the trip identifier;

  * •

purpose, the trip purpose, possible values are
Business_Trip, Everyday_Shopping, Home,
Leisure_Hobby, Personal_Tasks_Errands,
Pick_Up_Drop_Off, Work, and Other.

#### Weather data

Weather data has been collected through the API provided by
OpenWeatherMap.777https://openweathermap.org/, OpenWeatherMap is an online
service owned by OpenWeather Ltd. The API was queried regularly for a set of
$66$ cities of interest in the scope of the project. Weather information was
collected for the times of 09:00, 12:00 and 18:00 for each day from July 8th,
2019 to December 18th, 2019. The dataset contains two tables related to
weather data: weather_raw.csv $(11)$ and weather_legs.csv $(12)$.

The table weather_raw.csv contains the data parsed has obtained from the
OpenWeather API, the documentation of each field is available on the
OpenWeatherMap website.888OpenWeatherMap historical weather API guide,
https://openweathermap.org/history. The table weather_legs.csv contains the
association between trips legs and the corresponding weather for the time and
place, the available fields are presented in Table 4.

Field |  Description and admissible values
---|---
weatherid |  Weather identifier, a string of 24 characters.
legid |  Leg identifier.
request_date |  Weather request timestamp, formatted as ’%Y-%m-%d %H:%M:%S.%f’.
centroid_x |  Longitude of the centroid of the leg.
centroid_y |  Latitude of the centroid of the leg.
country |  Country the leg is located in.
weather_scenario |  Classification of weather scenarios.
apparent_temperature |  Apparent temperature, computed using Steadman’s equation.
net_radiation |  Net radiation received by the terrain in the location of the centroid.
temperature_category |  Categorization based on apparent temperature.
temperature_description |  Description of the temperature based on apparent temperature.
cloud_category |  Categorization based on cloud cover.
cloud_main |  Description based on cloud cover.
precipitation_category |  Categorization based on precipitation level.
precipitation_main |  Description based on precipitation level.
wind_beaufort_number |  Categorization using Beaufort’s number, based on wind speed.
wind_category |  Categorization based on wind speed.
wind_description |  Description based on wind speed.

Table 4: Weather info stored in weather_legs.csv.

For the computation of weather scenarios, different sources of data were
combined. Specifically, we computed the apparent temperature, which is
equivalent of the temperature perceived by humans, based on effects of air
temperature, relative humidity and wind speed. The formula for apparent
temperature introduced by Robert Steadman in 1984 (Steadman 1984) was used,
which takes into consideration four environmental factors: wind, temperature,
humidity and radiation from the sun.

#### Worthwhileness elements from trips

Table worthwhileness_elements_from_trips.csv $(13)$ contains the evaluation of
each trip along the worthwhileness elements dimensions on scale from 0 (low)
to 2 (high). The fields of the table are:

  * •

tripid, the trip identifier;

  * •

legid. the leg identifier;

  * •

worthwhileness_element, name of the wortwhileness element. Possible values are
Enjoyment, Fitness, Paid_work, Personal_tasks and Unknown;

  * •

value, the value of the wortwhileness element, possible values are: 0, 1, 2
and -1;

Records where the wortwhileness element and the value is -1 are the same.

### A User’s Story

In the following section, we present a brief user story of a user using the
dedicated app to describe the data collected in context. We will call our user
Luigi.

One day, Luigi sees an advertisement of a new app just released: _Woorti_.
_Woorti_ keeps track of personal trips along with all the aspects that
influenced the travel, it seems interesting! So he decides to download it. He
registers to the app and inserts some demographic information (user_details).
After that, he is asked how much he values three aspects of life while he
travels: enjoyment, how much fun he has; productivity, if he is able to work
or do personal tasks; and fitness, if he is able to exercise and stay healthy;
both in general terms (user_generic_worthwhileness_values) and with respect to
his favorite transport modes (user_specific_worthwhileness_values).

Luigi wants to try the app while going to work (purposes). He starts from his
apartment, walks until the bus stop where he waits for 5 minutes the bus. He
gets on the bus for 20 minutes and in the meantime he reads a book and use the
smartphone to check something on internet (activities). He easily finds a seat
and enjoys his time on the bus since it is not crowded and he likes to watch
the landscape outside (experience_factors). The bus stop is just few minutes
from his office and since it’s a beautiful and sunny day (weather) he decides
to walk until there. Before starting his working day, he stops at the bar to
take a coffee and spends some minutes filling the questionnaire on the app
after his trip. He validates the trip checking that the start and end points
were correct (legs_coordinates): he did in total four legs during his trip
(walking, waiting event, bus, walking) (legs). He decides to review his leg on
the bus and he completes all the questions, giving also a rate for the whole
trip and for the leg he reviewed (trips), included a score for the enjoyment,
productivity and fitness (worthwhileness_elements_from_trips).

## Case Study

Experience Factors Impacting Negatively Use of Public Transport, Cycling and
Walking versus Private Cars. We leverage the experience factor evaluations to
compare trips done by cars versus trips conducted with other modes of
transport: public transport, cycling and other emerging micromobility, and
walking. With this use case we want to answer the question: “What are the
negative experience factors of cyclists and users of public transport for the
same trip legs performed by car?”.

We find users that have traveled a given route multiple times using both cars
and alternative modes of transport and look at which are the factors that have
impacted negatively the travel experience when using bikes or public
transport. In this way, we want to get some insights on which are the
experience factors that are hindering the use of modes of transports
alternative to cars. This analysis is performed along the following steps:

  1. 1.

we select trip legs performed by car and those users that have performed at
least one such trips;

  2. 2.

we restrict this set to the users that have chosen at least one preferred
transport mode within the transport categories: _cycling and emerging
micromobility_ , _public transport (short distance)_ , and _public transport
(long distance)_. For the sake of the study we call these the alternative
transport category

  3. 3.

we identify users that have performed similar trips using different transport
modes; specifically, we select users that performed the same journey using a
car - in the _private motorized_ category - or using a bike or public
transport.

  4. 4.

For the same user, we look at negative experience factors for trip legs
performed using modes of transports in the alternative categories.

For the definition of similar trips we match trips using their starting and
ending points: When using different modes of transport can lead to taking
different paths, but for our analysis we are interested in the fact that a
user needs to travel from a given pair of locations. To identify points that
are close in space we adopt the following procedure, illustrated in Figure 1:
each point is transformed to a curved square, where each side is an arc of
length $0.004$ degrees. If the squares representing two points intersect, we
consider them a matching pair. To simplify the computational complexity of the
matching process we only compare trip legs in the same country. To estimate
the distance between these two point we use an approximate conversion between
the precision of decimal degrees in the EPSG:7030/WGS
84,999http://epsg.io/7030-ellipsoid, taken as the E/W at 45 degrees N/S.
$0.001$ degrees correspond $78.71\,\mathrm{m}$ so at most two points are
matching if they are within a maximum distance of $445\,\mathrm{m}$:

$D=\sqrt{2}\cdot 0.004\,\mathrm{deg}\cdot 78.71\,\mathrm{km/deg}\approx
445\,\mathrm{m}$

Figure 1: Procedure to identify close points in space: each point is
transformed to a curved square, where each side is an arc - with sides of
length $0.004$ degrees. If the squares of two points intersect, we consider
them a matching pair.

Step |  Step description | Trips | Legs | Users
---|---|---|---|---
1 |  All trips, legs, users | $64,098$ | $158,897$ | $3,269$
2 |  Users that have performed at least one trip leg by car | $21,764$ | $62,227$ | $2,083$
3 |  Users that have selected at least one preferred alternative transport mode | $51,973$ | $132,259$ | $1,771$
4 |  Users that have performed at least one trip leg by car and by alternative transport modes | $20,032$ | $27,921$ | $1,376$

Table 5: User statistics considered by our case study.

Cycling and micromobility | Public transport (short distance) | Public transport (long distance)
---|---|---
Factor |  # |  Factor |  # |  Factor |  #
Cars other vehicles |  $1,751$ |  Privacy |  $500$ |  Internet connectivity |  $53$
Air Quality |  $1,277$ |  Crowdedness seating |  $499$ |  Privacy |  $49$
Road path availability and safety |  $1,219$ |  Other people |  $463$ |  Seating quality personal space |  $44$
Noise level |  $1,097$ |  Seating quality personal space |  $445$ |  Reliability of travel time |  $43$
Road path quality |  $969$ |  Noise level |  $437$ |  Noise level |  $36$
Traffic signals crossings |  $854$ |  Internet connectivity |  $418$ |  Other people |  $35$
Crowding congestion |  $837$ |  Charging opportunity |  $406$ |  Vehicle ride smoothness |  $34$
Today’s weather |  $591$ |  Air quality |  $349$ |  Today’s weather |  $34$
Simplicity difficulty of the route |  $417$ |  Scenery |  $309$ |  Crowdedness seating |  $33$
Facilities shower lockers |  $371$ |  Reliability of travel time |  $290$ |  Food drink available |  $31$

Table 6: Overall top-ten negative experience factors for all trip legs in the
categories cycling and emerging micromobility, public transport (short
distance), and public transport (short distance).

Cycling and micromobility | Public transport (short distance) | Public transport (long distance)
---|---|---
Factor |  # |  Factor |  # |  Factor |  #
Road path availability and safety |  $315$ |  Privacy |  $133$ |  Today’s weather |  $2$
Road path quality |  $307$ |  Other people |  $111$ |  Reliability of travel time |  $2$
Cars other vehicles |  $267$ |  Air quality |  $103$ |  Vehicle ride smoothness |  $1$
Air quality |  $173$ |  Noise level |  $100$ |  Ability to do what I wanted |  $1$
Noise level |  $132$ |  Crowdedness seating |  $99$ |  Privacy |  $1$
Road path directness |  $131$ |  Seating quality personal space |  $99$ |  Other people |  $1$
Today’s weather |  $123$ |  Today’s weather |  $84$ |  Cleanliness |  $1$
Traffic signals crossings |  $122$ |  Internet connectivity |  $77$ |  |
Crowding congestion |  $111$ |  Charging opportunity |  $76$ |  |
Lighting visibility |  $88$ |  Scenery |  $67$ |  |

Table 7: Top negative experience factors for the trip legs selected by our
case study.

Table 5 presents some statistics related to each step of the process as
presented above. For brevity, we will refer to trip legs performed with a mode
of transport in the category _private motorized_ as legs performed “by car”
and trips in the categories _cycling and emerging micromobility_ , _public
transport (short distance)_ , _public transport (long distance)_ as legs
performed “by alternative modes of transport.”

Tables 6 and 7 present the results of our case study: Table 6 contains the
overall top-ten negative experience factors for all trip legs in the
categories _cycling and emerging micromobility_ , _public transport (short
distance)_ , and _public transport (short distance)_. Table 7 presents the top
negative experience factors only for the trip legs select by our case study
for the same transport categories.

When cycling we find two main areas of concern: safety (availability of
bicycle paths, safety from other cars, visibility and traffic signals) and
quality (noise level, air quality). Road path directness has a somewhat a more
important role when cycling is used as an alternative to traveling by car
w.r.t. the general negative experience factors. Weather is ranked among the
top-10 negative experience factors in both bases. For short-distance public
transport the main obstacles are lack of privacy and crowdedness in many forms
(including noise level and air quality), while reliability of travel time do
not appear in the top-10.

## Research Opportunities

Our dataset can support numerous research initiatives, with applications that
can provide benefits both to the end users and to transport stakeholders, such
as transport operators.

#### Cost-benefit Analyses

The approach showed in this study challenges conventional cost-benefit
narratives and paradigms on the value of travel time, which is the current
bedrock of how policy decision in the realm of transport are made. We envision
that the “worthwhile time” approach can be further developed to become a
viable alternative that takes more into account the travelers’ perspective,
especially when addressing significant infrastructure investments.

#### User profiling and clustering

Crossing user mobility with their experience factors can be directly used to
profile and cluster the users (Basile et al. 2020). The identification of
users with similar behavior and a similar value of travel time might directly
impact the shaping of journey planners, with solutions that target that
cluster being presented first (e.g., if a user belongs to a cluster associated
with low emissions, a sorting by emissions might be the default options).

#### Recommender systems

Current systems associate mobility to Point-of-Interest recommendation (Liu et
al. 2017). While in this domain collaborative filtering can be enriched with
geographical information, our dataset can offer much richer notions of peer
users. With the new prospective provided by our analysis, a peer user is not
only someone who visited PoI similarly to another, but can be someone who
gives values to the same experience factors. In addition, our dataset can
enable novel forms of recommendation, based on the previous observations, such
as the suggestion of activities to perform given a type of trip (e.g., reading
in trains).

#### Ad targeting

Most platforms nowadays survive thanks to advertisements, which are usually
personalized based on the experience of the users in a platform (Saia et al.
2016). It is clear that in the context of value of travel time, ad targeting
should go beyond this, to consider the factors that positively or negatively
impact user mobility, and tailor ads around them. These ads would be much more
effective, thus benefiting the platform, and by presenting the users with
“complementary” services, based on their preferences.

## Conclusions and Future Work

Extracting actionable knowledge from user behavior in traveling can help
knowing them more and providing them with better services (e.g., personalized
rankings). For this reason, it is important not only to monitor the users, but
to understand them and the choices they make, according to the value of their
travel time. Plus, trips are complex entities, made up of several legs, which
might disclose information about user behavior at a finer granularity.

To accomplish the goal of knowing users, their travel preferences and their
value of travel time, we presented a mobility dataset collected via an app and
we performed an analysis of factors impacting negatively the usage of cycling
and public transport. Our dataset collects information about user mobility,
capturing both raw information about trips and their legs (e.g., coordinates,
time, and weather), plus information about the worthwhileness of a trip leg.

To assess the impact that our dataset can have in the real-world, we presented
also a use-case to analyze what are experience factors that can negatively
impacting the use of public transport, by comparing cycling and walking versus
private cars. As our use case has shown, our dataset can provide valuable
information to transport operators and service providers, so that their
services can be tailored on the needs of their users. Our deliverable also
presents opportunities in other domains, such as personalized recommendation
or customer clustering. In addition, we plan to use the dataset to take action
in concrete real-world scenarios, such as the design of cost-benefit analyses,
to see how to improve infrastructures and services, thanks to the needs and
preferences of the users.

## Acknowledgements

This work received the support of the _MoTiV_ project, funded from the
European Union’s Horizon 2020 research and innovation programme under grant
agreement No 770145 (https://motivproject.eu/). The authors would like to
acknowledge the contribution to the project provided by the local data
collection managers for their invaluable support in the coordination of the
activities in each country.

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