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The first session of TMR Dispatches, held on Friday, June 26, 2020 focused on the media in North India
Murtaza Ali Khan 4:34:00 PM Media , North India , The Media Rumble , TMR Dispatches Edit
TMR Dispatches is a new fortnightly series in the lead-up to the September main event, with an overarching theme of "NEWS" – North, East, West and South. This will include leading news professionals across geographies, and will feature conversations and discussions on some of the most pressing issues and challenges facing India's news media sector.
The first session of TMR Dispatches, held on Friday, June 26, 2020 focused on the media in North India, titled "Myth or Reality? Hindi and proximity to Delhi give North India an advantage is the news space".
Newslaundry's Executive Editor, Manisha Pande, was joined by Arfa Khanum Sherwani, Senior Editor at The Wire, Dr Himanshu Dwivedi, Chief Editor of Hari Bhoomi, Shahid Siddiqui, Managing Director and Chief Editor of Nai Duniya, and Sukirat, a writer and columnist from Punjab, on this discussion.
Acknowledging North India's undisputed penetration into the news media, Arfa said that Hindi channels assume that Hindi-speakers are only interested in news from the Hindi belt and, therefore, think only they should be represented. "Even the channels who call themselves Indian channels are primarily from Uttar Pradesh and Bihar, while the national channels are only limited to Delhi-NCR, which is funny and tragic," she said.
Pointing to the media discourse being dominated by the Hindi-speaking belt, Sukirat said that people "naturally gravitate towards Delhi" since the media is "extremely politics-oriented". While Himanshu agreed that Hindi enjoys undivided importance, he also thought this domination in newsrooms is not "imposed"; instead, it's only natural in a country that is largely Hindi-speaking.
The discussion also covered the upper-caste dominance in newsrooms. Shahid brought up the media's obsession of not only being Delhi-centered, but also having a largely urban-elitist narrative. An Urdu writer himself, Siddiqui said he's disappointed with Hindi "destroying" the Urdu language. He also addressed the monopolisation of media houses, like the Times of India or Hindustan Times, who not only "address the viewers, but also manufacture news for their sponsors, politicians, and those from whom they will benefit".
The hour-long discussion also touched upon news media building and running propaganda, the advocacy of the "real" and the "representation", the objectivity of truth, and the communalisation of the media.
TMR Dispatches Schedule
5:00 PM IST
East India – We don't need no mainstream: Our stories, our storytellers
Friday, 24 July, 2020
West India – Mumbai's Lutyens: Is entertainment journalism all about access?
South India – Reclaiming centre space in news: A robust market and innovation hub
Readers, please feel free to share your opinion by leaving your comments. As always your valuable thoughts are highly appreciated!
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All transactions are safe and secure with a reliable history in online purchasing behind each of our associates. Buy the Simpsons Springfield Isotopes t-shirts to own Simpsons clothing and merchandise.
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The never ending pile of paper was driving me crazy! You move the pile to wipe the counter, which ends up creating a new pile when the old one catches more paper clutter. Papers are thin so they don't necessarily stand out until they become a pile. By then, it's a problem!
This led to a search for the best paper organizer to clear the counter clutter. I've ended up with three go-to tools to tame the paper beast over the years. These tools have helped me reclaim the corner of the counter…win!
I'm going to share what three paper organizer tools I use and then I'll share how I use them (and a picture). Hope this helps give you some ideas if you're also looking for a paper organizer to clear the counter clutter!
I decided on this organizer tool to store important paperwork because there's no lid to deal with, it's ideal for envelope sizes, it fits in a cabinet, and the folders are easily labeled. I have two. One just like the image above and another mesh metal one that I got from Target.
In the mesh metal one, I file all important tax documents. In the black one, I file important papers that I need throughout the year, but not necessarily for taxes. Things like current insurance policies and medical receipts.
The basket is the real trick to preventing the counter clutter. If I have something that needs to be filed, but I'm pushed for time or in the middle of something else, it goes in the basket to file on the weekend. The basket essentially becomes the catch all spot, but it becomes the designated catch all spot instead of random piles on the counter.
These are things that I want to have handy throughout the year for quick reference.
School paperwork, which could be an article by itself, is always a work in progress. My goal is to keep one notebook for PK-2 and another for 3-5 school years with a few papers and photos of special projects too big to go in the notebook. I struggle with this and I realize it's me hanging on, not my child!
Our dining room has two pieces of furniture. The table and a matching buffet table. The buffet table is where our paperwork system is set up. Here's a picture of the tools we use (1) hanging file folders (2) basket and (3) three ring binders in the buffet table.
What about "to do" papers or bills, or anything that you can't file because it requires some type of action?
We don't have a lot of those because we automate every bill possible. I highly recommend using automation whenever possible. It prevents late fees and you can still monitor everything by checking your online statements.
For school papers, I go through my son's backpack every afternoon and sign papers or send money for different things that come up. The only paper that ends up staying in our home are any papers to keep (in the three ring binder) or the weekly newsletter that contains dates and other information (on the fridge with a magnet).
What about important papers to keep for several years?
Our most recent tax returns and mortgage paperwork is in a desk drawer. We're hanging on to those until it's safe to shred them according to paper retention guidelines.
After more discussion, I got some good ideas from them and wanted to share because we all have different organizing methods and spaces in our homes. So, in no particular order, are three honorable mentions for different tools for paper organizers to clear the counter clutter.
Also, one of my friends uses a cascading wall organizer to collect her important tax documents and I love it! I'm going to get this for work because I have some file folders that I constantly use for reference and when I travel. It expands if you want to hang it and then folds up too to save space!
These eliminate the need for hanging files and they are easily portable. A great alternative to an open hanging file folder box.
Please share your favorite paper organizer tool, or anything you want to try! Hope this gave you some ideas to keep papers organized and reclaim your counter space!
***Helpful article by Clark Howard on opting out of junk mail.


Half of Germans would like immigrants to adapt to mainstream society. One third would prefer a merging of cultures – and among younger people, this is even the majority view. These are the findings of a special analysis of our Religion Monitor, in which we investigated attitudes among the German population about successful coexistence in cultural diversity.
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European cities of the twentieth century must embrace cultural and ethnic diversity. A visit to the Belgium city of Mechelen shows just how this works – thanks to its exceptional mayor and a series of initiatives that have paved the way forward.
Cultural diversity offers valuable opportunities – such as helping companies increase their innovative power. As the study we conducted for the 2018 Reinhard Mohn Prize shows: Businesses that hire people of diverse cultural backgrounds are better positioned to develop ideas for new products, services and processes. Companies, however, are not yet living cultural diversity to the same degree.
This year's Reinhard Mohn Prize on the topic of "Living Diversity - Shaping Society" goes to former German President Joachim Gauck. The Bertelsmann Stiftung recognizes Gauck as a bridge builder in a culturally diverse society. Gauck will receive the €200,000 award on June 7th in Gütersloh.
As part of this year's Reinhard Mohn Prize and in the tradition of Reinhard Mohn's vision of learning from the world, we're searching the globe for urban settings where living together in cultural diversity is a proven success. The United Kingdom has considerable experience with multiculturalism and a long tradition of embracing diversity. We went to visit one of the UK's most diverse cities – Leicester in the English Midlands. With its Community Cohesion Strategy targeting a "community of communities," the city has taken a pro-active approach to fostering good relations between the various cultural and religious communities that call Leicester home.
Germany has long been the country of immigration that it doesn't yet officially want to be. An unbiased reality-check of one's own personal environment as well as countless social-science studies provide ample proof of this.


The internet has proved itself useful and has given us the Comic Sans trick. Read on to learn how the font we love to hate can help you cure writer's block.
For the past two weeks, I've been immersing myself in some reflection. This book, TEACHING WRITERS TO REFLECT, has been an excellent tool as I pass along reflective practices to my students.
I remember when I started blogging with my first graders, I dove right in without a thought! Despite my lack of preparedness I never looked back. Blogging inspired and connected my students in ways I never imagined. I know you'll find the same joy in blogging!
Three ways YOU can be a kinder, more generous, better person to work with.
A place to make meaning of ourselves and the world around us, writing is a powerful tool for self-discovery. However, when idea-collection tools and drafts are stored in folders, we miss a valuable opportunity to make the diverse lives and experiences of our communities visible. Instead, we can rely on classroom as a tool for making children, their identities, and experiences seen.
I want to see others first and I want to see everyone for who they are and how they want to be seen.


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\section{\label{introduction}Introduction}
Collective motion is an ubiquitous emergent phenomena observed in a wide array of different living systems and on an even wider range of scales. Examples range from fish schools and flocks of birds to bacteria colonies and cellular migrations \cite{ramaswamy2010mechanics}. Its importance cannot be underestimated: cellular migration, for instance,  is a key driver of embryonic development, wound healing, and some types of cancer invasion \cite{Trepat2020}. Animal group movement may reduce risk of predation and underlies many foraging and migratory processes \cite{Krause2002}.

Collective motion -- or {\it flocking} -- involves a large number of active units, capable of self-propelled motion, that mutually synchronize their direction of motion. By doing so, they break their (continuous) rotational symmetry selecting a well defined mean direction for the entire group. This symmetry breaking process may be {\it spontaneous}, so that the emerging direction of motion is chosen by chance among the many available ones, as it has been observed in starling flocks \cite{cavagna2010scale}. But symmetry breaking may also be directed by  external cues or by some {\it a priori} knowledge of the group target (e.g.: a known foraging site). Cell motility, for instance, is known to be sensitive to a wide range of external gradients of chemical (chemotaxis), mechanical (durotaxis) and electrical (electrotaxis) origin \cite{directedcellmigration}.

A natural question when observing flocking phenomena, such as cellular migration or the coordinated movement of animal groups, thus regards the nature of collective motion. Is it a spontaneous phenomena, exclusively driven by the interactions between individual active units, or the observed group movement is being directed by some external factor?\\
While this distinction can be simply made {\it in vitro}, where experimental factors are easily controlled, {\it in vivo} observations are typically conducted in rather complex environments, making the task much more arduous \cite{VitrotoVivo}. Chemotactic guidance, for instance, is known to be involved in many instances of embryonic development \cite{embryogenesis}, but {\it in vivo} chemical or mechanical gradients have not systematically been observed for all cellular migration phenomena, leading authors to speculate about other types of spatial guidance clues which may be at play in certain instances \cite{voituriez2015}.

It may thus be desirable to formulate simple criteria capable of discriminating in the first place between spontaneous and directed collective motion, simply by observing the static and dynamical features of the active units involved, without the need to detect and establish correlations (or the lack of) with gradients or other environmental cues. Intuitively, the simplest signature of such a difference should lie in the persistence of the mean direction of motion, which is expected to be lower for spontaneous flocking. However -- as we will show in the following -- this simple criteria may fail for short observation times and/or small environmental anisotropies. An alternative approach we propose involves the observation of large wavelength {\it static} fluctuations in the active particles density, which are encoded by the density structure factor $S(q)$. Indeed, spontaneous collective motion implies a diverging structure factor at small wavenumbers $q$ \cite{toner1995long, toner1998flocks}, as experimentally confirmed in {\it in vitro} experiments of cellular migration \cite{giavazzi2017giant}. Here, we argue that such a divergence is suppressed in directed collective motion and that this fact can be used to successfully detect directed motion even on short or instantaneous observation timescales.\\

In this paper we discuss collective motion in the presence of  static and homogeneous small external fields of amplitude $h$ (i.e. in a {\it linear response} regime), showing that directed motion can be inferred from the fluctuations of the mean group direction (our so-called {\it dynamical approach}) only for observation times $t > \tau_c \sim h^{-1}$. On the contrary, the study of the system density fluctuations in large enough systems, may reveal directed motion also for much shorter observation times. In particular, we show that the free system structure factor's divergence is suppressed for wavenumbers $q<q_c \sim h^{1/z}$, where $z$ is the dynamical scaling exponent of the celebrated Toner \& Tu theory of Flocking \cite{toner1995long, toner1998flocks}. This defines a complementary {\it static} approach.

\section{\label{dynamical method}Dynamical approach}

We begin discussing the most intuitive approach: in the absence of a driving field or any other anisotropy, collective motion is achieved by spontaneous breaking of the continuous rotational symmetry. The mean direction of any finite flock, however, is not constant, but freely diffuses since small transverse perturbations are not dumped and free to propagate (these are the so-called {\it Nambu-Goldstone} modes).\\

On the other hand, when collective motion is driven by an external field breaking rotational isotropy, fluctuations of the mean direction are confined and do not lead to free diffusion. Thus, one may discriminate between spontaneous and driven collective motion of any finite flock by simply observing the mean direction dynamics for a sufficiently long timescale. In the following, we precisely quantify this idea by developing a closed stochastic equation for the mean flocking direction.

\subsection{Mean field dynamics of the flock's orientation}

For simplicity, we work in two spatial dimensions and consider the prototypical collective motion model introduced by Vicsek and coworkers \cite{vicsek1995novel} in the presence of an homogeneous external field of amplitude $h$ and orientation $\theta_h$, ${\mathbf h}= h (\sin\theta_h,\cos\theta_h)$ \cite{kyriakopoulos2016leading}. It describes the discrete-time stochastic dynamics of $N$ active particles with position ${\mathbf r}_i^t$ and unit direction $\textbf{s}_i^t=(\cos\theta_i^t,\sin\theta_i^t)$,

\begin{equation}\label{ev_r}
{\mathbf r}_i^{t+1} = {\mathbf r}_i^t + v_{\rm 0} {\mathbf s}_i^t
\end{equation}
\begin{equation}\label{micro_evo}
    \theta_i^{t+1}= \mbox{Arg}\bigg[\bigg(\sum_{j \sim i} \textbf{s}_j^t +\textbf{h}\bigg) \bigg] + \eta_i^{t},
\end{equation}
where $v_{\rm 0}$ is the particles speed and $\mbox{Arg}({\mathbf v})$ gives the angle defining the orientation of ${\mathbf v}$. Moreover, the sum is intended over the $m_j^t$ neighbours of particle $i$ (including $i$ itself) \footnote{The neighbouring criteria may be either metric, such that $\lvert {\mathbf r}_i^t - {\mathbf r}_j^t \rvert < R_0$, or topological \cite{ginelli2010relevance}} at time $t$, $\eta_i^t$ is a microscopic zero-average white noise such that $\langle \eta_i^t \eta_j^{t'}\rangle = \Gamma \delta_{ij}\delta_{tt'}$.

We consider the Vicsek model (VM) \eqref{ev_r}-\eqref{micro_evo} in the homogeneous and highly ordered regime, deep in the so-called Toner and Tu (TT) phase \cite{ginelli2016physics}.
In the presence of an external field, the direction of motion $\theta_i^t$ of particle $i$ can be expressed in terms of deviations  $\delta \theta_i^t$ from the field direction,  $\theta_i^t = \theta_h +\delta \theta_i^t$. If we assume $\delta \theta_i^t \ll 1$, which is reasonable in the ordered phase, we can expand \eqref{micro_evo} in a {\it spin-wave} approximation \cite{nishimori2010elements}.\\
To the first order in $\delta\theta$ we get
\begin{equation}\label{micro_evo_2}
        \theta_i^{t+1}  \approx \text{Arg} \bigg[ \hat{e}_{\parallel} \bigg(\sum_{j \sim i}1 + h \bigg)  +\hat{e}_{\perp}\sum_{j \sim i} \delta\theta_{j}^{t}  \bigg] +\eta_{i}^{t}.
\end{equation}
where $\hat{e}_{\parallel}=(\cos\theta_h,\sin\theta_h)$ is the unit vector identifying the direction of the field ${\mathbf h}$ and $\hat{e}_{\perp}=(-\sin\theta_h,\cos\theta_h)$ its perpendicular unit vector.\\
We note that in Eq. \eqref{micro_evo_2} the component along the perpendicular direction is small with respect to the longitudinal one. We can thus expand the Arg function as Arg($\textbf{v}+\delta \textbf{w} ) \approx $Arg$(\textbf{v}) + \frac{\textbf{v} \vee \delta \textbf{w}}{\lvert v \rvert^2}$ where $\delta {\mathbf w} \ll {\mathbf v}$ and $\vee$ denotes the \textit{skew product}\footnote{For vectors ${\mathbf a}, {\mathbf b}$ lying in a plane perpendicular to a unit vector $\hat{\mathbf e}_3$ one has $\textbf{a}\vee \textbf{b}=\hat{\mathbf e}_3 \cdot(\textbf{a}\times\textbf{b})$.}\\
By the above first order expansion Eq. \eqref{micro_evo_2} becomes
\begin{equation}\label{arg_expansion}
    \theta_i^{t+1} \approx \theta_h + \frac{\sum_{j\sim i}\delta \theta_i^t}{m_i^t+h}+\eta_i^t
\end{equation}
where $m_i^t$ is the number of neighbours of particle $i$ (including particle $i$ itself) at time $t$.
Further expanding the denominator for $h \ll m_i^t$ (we assume a sufficiently high local density, as in many systems of interest such as confluent tissues \cite{Giavazzi2018})
 \begin{equation}\label{theta_h_tilde}
     \delta\theta_i^{t+1} \approx \frac{1}{m_i^t}\sum_{j \sim i } \Big( 1-\Tilde{h}_i^t \Big)\delta\theta_j^t+\eta_i^t
 \end{equation}
where we have defined $\Tilde{h}_i^t \equiv h/m_i^t$.\\
The flocking mean direction $\psi(t)$ can be similarly expanded around the field direction
\begin{equation}   \label{psi_t}
    \psi(t) \equiv Arg(\Omega(t)) \approx \theta_h +\frac{1}{N}\sum_{i=1}^N\delta\theta_i^t
\end{equation}
where $\Omega(t) \equiv \frac{1}{N} \sum_{i=1}^{N} \textbf{s}_i$ is the flock's global order parameter. Eq. \eqref{psi_t} implies
\begin{equation}\label{deltapsi_t}
    \delta\psi(t)\equiv\psi(t) - \theta_h \approx \frac{1}{N}\sum_{i=1}^N\delta\theta_i^t
\end{equation}

Feeding Eq. \eqref{theta_h_tilde} in \eqref{deltapsi_t} we thus obtain
\begin{equation}  \label{psi_tp1_t}
        \delta \psi(t+1) \approx \frac{1}{N} \sum_{i=1}^{N} \frac{1}{m_i^t}(1-\Tilde{h}_i^t)\sum_{j \sim i}\delta\theta_j^t +\xi(t),
\end{equation}
where we have defined $\xi(t) \equiv\frac{1}{N}\sum_{i=1}^N \eta_i^t$ and for the central limit theorem we have that
\begin{equation}
   \langle \xi(t) \rangle =0 \;,\;\;\;\;\langle \xi(t) \xi(t') \rangle = \frac{\Gamma}{N}\delta_{tt'}
\end{equation}
In order to obtain a closed equation for $\delta \psi^t$, we finally resort to a mean field approximation, $m_i^t \approx \bar{m} \equiv \langle m_i^t\rangle_{i,t}$ where the latter average is conducted over all particles $i$ and time $t$. Noting that in \eqref{psi_tp1_t} every fluctuation $\delta\theta_j$ appears roughly $\bar{m}$ times we get
\begin{equation}\label{OU_samp}
    \delta \psi(t+1) \approx  \delta\psi(t) (1-h')+ \xi(t)\,,
\end{equation}
where we have defined the reduced field amplitude $h'\equiv h/\bar{m}$.\\
Eq. \eqref{OU_samp} defines an auto-regressive process of order one, which is the time-discrete sampling of an {\it Ornstein-Uhlenbeck} process \cite{livi2017nonequilibrium}
\begin{equation}  \label{OU}
    d x(\tau) = - \gamma \, x(\tau) d\tau + \sqrt{2 D} \, d W_\tau
\end{equation}
where $d W_\tau$ is a Wiener process, $h' = \gamma \Delta t$, $\Gamma/N = 2 D \Delta t$ and $\tau=t\,\Delta t$ with $\Delta t \ll 1$.
The two processes share the same statistics,
\begin{equation}  \label{FLutt_OU}
 \langle \delta \psi(t)^2 \rangle = \langle x(\tau)^2 \rangle =

 \frac{\Gamma}{2 N} \frac{1}{h'} \left(1-e^{-2 h' t}\right) \,,
\end{equation}
showing that the mean flocking direction behaves as a one dimensional Brownian particle in an harmonic potential with stiffness proportional to the external field amplitude $h$. For large times, $t \gg 1/(2 h')$, the process is stationary with
\begin{equation}  \label{FLutt_OUS}
 \langle \delta \psi(t)^2 \rangle =
 \frac{\Gamma}{2 N} \frac{1}{h'}  \,,
\end{equation}
while for $t \ll 1/(2 h')$ we recover diffusive behavior
\begin{equation}  \label{FLutt_OUD}
 \langle \delta \psi(t)^2 \rangle =
 \frac{\Gamma}{ N} \,t  \,.
\end{equation}
For $h\to 0$ therefore, our mean field approximation yields a free diffusive behavior. One may indeed repeat the above argument in the zero external field case with a spin wave expansion around the mean flocking direction, $\theta_i^t = \psi(t) + \delta \theta_i^t$. By the same mean field approximation, one finally obtains the discrete time diffusive dynamics
\begin{equation}
    \psi(t+1) = \psi(t) +  \xi(t) \,.
\end{equation}

Arguably, our mean field approximation is rather crude; in particular, by assuming a constant number of interacting neighbours, $m_i^t \approx \bar{m}$, it ignores the non-reciprocal part of Vicsek model (VM) interactions \cite{vitelli2021, chepizhko2021revisiting}. However, it should be noted that the comparison between flocking dynamics with reciprocal and non-reciprocal interactions carried on in Ref. \cite{chepizhko2021revisiting} mainly reveals significant differences at the onset of order and in confined geometries. Our theory, on the other hand, describes the behavior of the flock's mean direction (a global quantity) in the strongly ordered regime, where we expect our approximation to be harmless. In the next section, we will verify its correctness by direct numerical simulations.
\begin{figure}[tb!]
 \includegraphics[width=0.48\textwidth]{figures/Diff_spont_vs_driv_256.eps}
	\caption{Spontaneous (full black line) vs. directed ($h=0.01$, full red line) mean direction squared fluctuations as a function of time. The dashed blue line is the best fit of the spontaneous symmetry breaking data (see text). We have chosen noise amplitude $\eta_{\rm 0}=0.18$ and system size $L=256$, so that $N=\rho_{\rm 0} L^2 \approx 10^5$. In the inset: zoom of the first $500$ time-steps.}
	\label{diff_spont_vs_driv}
\end{figure}
\subsection{Numerical simulations}\label{numsim}
We simulate the microscopic Vicsek dynamics \eqref{ev_r} and \eqref{micro_evo} in a two-dimensional system of linear size $L$ with periodic boundary conditions and metric interactions. We take the white noise term $\eta_i^t$ to be uniformly distributed in the interval $[-\eta_{\rm 0} \pi, \eta_{\rm 0} \pi]$, so that its variance is
\begin{equation}\label{eq_noise}
    \langle \eta_i^t \eta_j^{t'} \rangle = \Gamma \delta_{ij}\delta_{tt'} = \frac{\eta_{\rm 0}^2 \pi^2}{3}\delta_{ij}\delta_{tt'}
\end{equation}
In the following we fix the global particle density $\rho_{\rm 0}=N/L^2=2.0$ and particle speed $v_{\rm 0}=0.5$. Noise amplitude $\eta_{\rm 0}$ is chosen so that our the zero field system lies in the homogeneous ordered phase \cite{solon2015phase} -- the so-called Toner \& Tu (TT) phase -- comfortably far away from the ordered band regime appearing as the transition to disorder is approached \cite{gregoire2004onset, chate2008collective}.

Particles positions are initialized from a uniform distribution, while initial velocity are aligned in the external field direction (or in a given direction for $h=0$). A proper transient $T_0 \approx 10^4$ is then discarded from the dynamics to ensure convergence to the stationary ordered state. Squared fluctuations
\begin{equation} \label{mean_fluct}
\langle \delta \psi(t)^2\rangle =\langle [\psi(t) - \psi(0)]^2 \rangle
\end{equation}
in the flock's mean direction \eqref{psi_t} are then typically evaluated averaging $10^2$ independent runs for $t\leq T=10^4$.

As shown in Fig.~\ref{diff_spont_vs_driv}, the difference between spontaneous ($h=0$, black line) and a directed collective motion ($h=0.01$, red line) is readily evident for long enough observation times. However, if one is restricted to a shorter time interval (e.g.: $10^3$ timesteps as in the inset Fig.~\ref{diff_spont_vs_driv}), discrimination between the two cases becomes problematic (especially if one is not comparing a directed with a spontaneous case but has only access to one set of data).

A linear fit of the spontaneous case
\begin{equation}
    \langle \delta \psi^2 \rangle \approx 2D_{\rm 0}\,t
\end{equation}
returns a diffusion constant $D_{\rm 0} \approx 5.0(1) \cdot 10^{-7}$, to be compared with our mean-field prediction \eqref{FLutt_OUD}
\begin{equation}\label{mf1}
D_{\rm 0}=\frac{\Gamma}{2 N} = \frac{\eta_{\rm 0}^2 \pi^2}{6 N}
\end{equation}
\begin{figure}[tbp!]
\includegraphics[width=0.46\textwidth]{figures/Diff_scaling.eps}
\caption{Scaling of the diffusion constant in the zero field case. (a) Diffusion vs. noise amplitude for system size $L=256$. The dashed red line marks quadratic growth, $D_{\rm 0}\sim \eta_{\rm 0}^2$. (b) Diffusion vs. total particle number for noise amplitude $\eta_{\rm 0}=0.18$ and constant density. The dashed red line marks $1/N$ decay.
Error bars are given by two standard errors and plot are in a double logarithmic scale.}
\label{Fig2}
\end{figure}
where we have made use of Eq. \eqref{eq_noise} and, in $d=2$, $N=\rho_{\rm 0}L^2$. With our choice of parameters, Eq. \eqref{mf1} gives $D_{\rm 0} \approx 4.1\cdot 10^{-7}$. Despite being around $20\%$ off quantitatively, Fig. \ref{Fig2} shows that the qualitative scaling with noise amplitude and particles number predicted by mean field theory is nicely verified. \\

\begin{figure}[b!]
 \includegraphics[width=0.24\textwidth]{figures/diffusione_all.eps}
    \includegraphics[width=0.23\textwidth]{figures/scan_h_collassati.eps}
    \caption{(a) Mean squared fluctuations of the flocking average direction as a function of time $t$ for different external field values. From bottom to top $h=0.2, 0.1, 0.05, 0.02, 0.01, 0.005, 0.002, 0.001, 0$. Data has been obtained with noise amplitude $\eta_{\rm 0}=0.18$ and system size $L=256$.
    (b) Same data with both axes rescaled by $h$ (the $h=0$ case has been removed). The dashed red line marks the rescaled crossover time $h \tau_c$. Both graphs are in a doubly logarithmic scale.}
    \label{all_collassi}
\end{figure}

We now turn to the directed case scaling, testing different values of the field intensity $h$. Our result are shown in Fig.~\ref{all_collassi}. According to Eqs. \eqref{FLutt_OUS}, \eqref{FLutt_OUD}, rescaling by $h$ both time and the mean squared fluctuations nicely collapses the curves obtained with different $h \in [0.001,0.2]$.  This confirms that the minimum observation time needed to discriminate spontaneous from directed motion scales as the inverse of the field amplitude, with a crossover time
\begin{equation}\label{tauc}
\tau_c(h) \sim h^{-1}\,.
\end{equation}
Note that the number of active particles $N$ controls the magnitude of mean direction fluctuations but not the scaling of the crossover time.
\begin{figure}[tbp!]
\includegraphics[width=0.48\textwidth]{figures/num_teo.eps}
   	\caption{(a) Asymptotic value of $\langle\delta\psi^2\rangle$ as a function of $h$. Red diamonds report numerical estimates, while blue dots are the mean field estimate of Eq. \eqref{FLutt_OUS2} (see text). The dashed black line marks the $\sim 1/h$ scaling. Here $\eta_{\rm 0}=0.18$ and $L=256$ and the plot is in double logarithmic scale. In the inset: linear plot of the mean number of interacting active particles as a function of $h$. Error bars are given by two standard errors.}
   	\label{num_theo}
\end{figure}

Finally, we verify quantitatively the asymptotic expression for the flock's direction mean squared fluctuations \eqref{FLutt_OUS} that, by our mean field approximation reads
\begin{equation}  \label{FLutt_OUS2}
 \langle \delta \psi(\infty)^2 \rangle =
 \frac{\Gamma}{2 N} \frac{\bar{m}}{h} = \frac{\eta_{\rm 0}^2 \pi^2}{6 N} \frac{\bar{m}}{h}\,.
\end{equation}
We estimate $\bar{m}$ from direct numerical simulations and use it to compute the mean field prediction for $\langle \delta \psi(\infty)^2 \rangle$ from Eq. \eqref{FLutt_OUS2}. They are reported in Fig.~\ref{num_theo} as blue dots. The numerically measured values (red diamonds) turn out to be larger by a factor 2, possibly due to the inability of the mean field fluctuations to properly account for the anomalously large \cite{ginelli2016physics} local fluctuations in the number of interacting neighbours. Note also that numerical estimates of $\bar{m}$ (inset of Fig.~\ref{num_theo}) exhibit a weak dependence on $h$. \\

In any case, we conclude that despite the quantitative mismatch, mean field theory faithfully captures the Ornstein-Uhlenbeck scaling with $h$ (the external field playing the role of a stiffness) of the mean squared fluctuations in the flocking direction. More generally, our analysis shows that one is able to discriminate between collective and directed motion by the analysis of the mean-squared fluctuations of the average flock's direction, but only provided the observation time is larger of a crossover threshold, scaling with the inverse of the external field amplitude. As we anticipated, this might not be possible in several scenarios where the observation time is limited and/or the magnitude of spatial anisotropy is too small.

\section{\label{static method} Static approach}
We now propose a second approach, based on the observation of spatial correlations. In particular, here we focus on the static density structure factor, which is easily accessible in experimental set ups. In the absence of any external field or other anisotropies, TT theory \cite{toner1995long, toner1998flocks} predicts a long-ranged behavior for the slow fields spatial correlations, as observed in starling flocks \cite{cavagna2010scale}. Equivalently, the static structure factors, which may be obtained by Fourier transforming spatial correlation functions, exhibits a diverging behavior at small wave numbers $q$. This happens since  fluctuations transversal to the mean directions are {\it soft modes}, i.e. they are not damped and free to propagate over arbitrary distances. They are known as {\it Nambu-Goldstone} modes \cite{nishimori2010elements}.

In the presence of an external field, on the other hand, transversal fluctuations are damped (they acquire a "mass" in the pseudo-particles language) and spatial correlations are cut-off exponentially at a finite characteristic length scale $L_c$. Correspondingly, the structure factor's divergence for $q \to 0$ is suppressed for $q < q_c \sim 1/L_c$. The cut-off length $L_c$ depends on the external field amplitude $h$ and diverges for $h \to 0$. This is well known at equilibrium since the pioneering studies of \cite{pata73, patashinskii1979fluctuation}, but as we show here it is relatively straightforward to derive the exact scaling of the cut-off length and of the static structure factor with $h$.\\

Here we focus on the static density structure factor
\begin{equation}\label{eq:sf}
    S({\mathbf q})= \frac{1}{N}\left\langle \sum_{n, m} e^{i {\mathbf q}\cdot({\mathbf r}_n - {\mathbf r}_m)}\right\rangle
\end{equation}
where ${\mathbf r}_n$ with $n=1,\ldots,N$ are the position of the $N$ active particles, $i$ the imaginary unit and in principle the average $\langle \cdot \rangle$ should be taken over different experimental realizations or uncorrelated snapshots of the same experiment.
In particular, its average over all wavevector orientations
\begin{equation} \label{eq:sf_iso}
    S(q)\equiv \langle S({\mathbf q})\rangle _{|{\mathbf q}|=q}
\end{equation}
can be measured relatively easily in experimental data \cite{giavazzi2017giant}.

Introducing the number density $\rho({\mathbf r},t)=\sum_n \delta ({\mathbf r}-{\mathbf r}_n^t)$ and the density fluctuations $\delta \rho({\mathbf r},t)=\rho({\mathbf r},t)-\rho_0$, the density structure factor becomes
\begin{equation}\label{eq:sf2}
S({\mathbf q},h) = \frac{1}{N} \langle \lvert \delta \hat{\rho}(\textbf{q},t) \rvert^2 \rangle\,.
\end{equation}
For a zero external field, Toner $\&$ Tu  theory \cite{ginelli2016physics} predicts that the isotropically-averaged density structure factor of spontaneous collective motion diverges algebraically for small wave numbers $q$ as
\begin{equation}    \label{div_S}
    S(q) \sim q^{-\zeta}
\end{equation}
where $\zeta>0$ is a universal exponent (see below). In the following, we show that, in the presence of a small and static external field of modulo  $h$, this divergence is suppressed and
\begin{equation} \label{div_S_h}
    S(q,h) \sim \frac{1}{ q^\zeta+ C \,h}
\end{equation}
with $C$ being a phenomenological constant.

\subsection{\label{theory static method}Linearized density structure factor}
We briefly recall the Toner and Tu hydrodynamic equations \cite{toner1998flocks} in the presence of a constant and homogeneous driving field ${\mathbf h}$ \cite{kyriakopoulos2016leading}. They rule the slow, long-wavelength dynamics of the conserved density $\rho({\mathbf r}, t)$ and velocity ${\mathbf v}({\mathbf r}, t)$ fields and consist in the continuity equation
\begin{equation}
\partial_t\rho +\nabla\cdot(\rho{\mathbf v})=0
\label{rho1}
\end{equation}
and the velocity field dynamics
\begin{equation} \label{second_v}
    \begin{split}
        \partial_t \textbf{v} &+\lambda_1(\textbf{v} \cdot \nabla)\textbf{v} +\lambda_2 (\nabla \cdot \textbf{v})\textbf{v} + \lambda_3\nabla \lvert \textbf{v} \rvert^2 \\ =& (\alpha - \beta \lvert \textbf{v} \rvert^2 ) {\mathbf v} -\nabla P_1 -\textbf{v}(\textbf{v} \cdot \nabla P_2) + D_1 \nabla(\nabla \cdot \textbf{v})\\& +D_3 \nabla^2 \textbf{v} +D_2(\textbf{v} \cdot \nabla)^2 \textbf{v} + \textbf{f} +\textbf{h}\,.
    \end{split}
\end{equation}
Here all the phenomenological convective ($\lambda_i$, with $i=1,2,3$) and viscous ($D_i>0$) coefficients, as well as the two symmetry breaking ones, $\alpha$ and $\beta$ can, in principle, depend on $\rho$ and
$|{\mathbf v}|$ and the pressures $P_{1,2}$ may be expressed as a series in the density \cite{toner2012reanalysis}. The additive noise term ${\mathbf f}$ has zero mean, variance $\Delta$ and is delta correlated in space and time. The coarse-grained constant field ${\mathbf h}=h \hat{e}_{\parallel}$ is, by analyticity and rotational invariance of the free system, linearly proportional to the applied microscopic field, as long as those fields are sufficiently small.

In the absence of fluctuations Eqs. \eqref{rho1}-\eqref{second_v} admit a homogeneous steady state solution
$\rho({\mathbf r}, t)=\rho_0$,
${\mathbf v}({\mathbf r}, t)=v_{\rm 0}(h) \hat{e}_{\parallel}$\,,
where $v_0(h)$ is determined by the condition
\begin{equation}
    \alpha v_0 - \beta v_0^3 +h = 0 \,.
\end{equation}
In the zero external field case (and for $\alpha>0$), $v_0 = \sqrt{\alpha/\beta}$, with the direction $\hat{e}_{\parallel}$ randomly selected by the spontaneous symmetry breaking mechanism. Assuming analyticity of the symmetry breaking coefficients, we have for small $h$
\begin{equation}
v_0(h)-v_0(0) \propto h
\end{equation}

To deal with fluctuating hydrodynamics, we follow \cite{toner1998flocks}-\cite{toner2012reanalysis}-\cite{kyriakopoulos2016leading} and proceed to linearize Eqs. \eqref{rho1}-\eqref{second_v} around the homogeneous solution,
\begin{equation} \label{fluct}
    \begin{split}
        & \rho(\textbf{r},t)=\rho_0 +\delta \rho(h,\textbf{r}, t)\\
        & \textbf{v}(\textbf{r},t)=[{v}_{\rm 0}(h)+ \delta v_{\parallel}(h,\textbf{r},t)] \hat{e}_{\parallel}+ \textbf{v}_{\perp}(h,\textbf{r},t)
    \end{split}
\end{equation}

where $\textbf{v}_{\perp}$ measures velocity fluctuations transversal to $\hat{e}_{\parallel}$. In the Toner and Tu phase, the longitudinal velocity fluctuations $\delta v_\parallel$ are a fast mode enslaved to the slow fields of the unperturbed theory, $\textbf{v}_{\perp}$ and the density fluctuations $\delta \rho$. Thus, they can be eliminated from Eqs. \eqref{rho1}-\eqref{second_v} to yield the linearized hydrodynamics
\begin{equation}\label{rho_lin}
\begin{split}
        \partial_t \delta\rho &+\rho_0 \nabla_{\perp}\cdot \textbf{v}_{\perp} +v_2 \partial_{\parallel}\delta\rho -\rho_0 \mu_2\partial_t \partial_{\parallel}\delta\rho \\
        & =D_{\rho_{\parallel}} \partial_{\parallel}^2 \delta\rho + D_{\rho_{\perp}} \nabla_{\perp}^2 \delta\rho +D_{\rho v}\partial_{\parallel} (\nabla_{\perp} \cdot \textbf{v}_{\perp})  \\
\end{split}
\end{equation}
and
\begin{equation}  \label{v_perp_lin}
    \begin{split}
        \partial_t \textbf{v}_{\perp} &+ \gamma \partial_{\parallel} \textbf{v}_{\perp}\\ & = -\frac{c_0^2}{\rho_0}\nabla_{\perp} \delta\rho +D_B \nabla_{\perp}(\nabla_{\perp}\cdot \textbf{v}_{\perp}) +D_3 \nabla_{\perp}^2 \textbf{v}_{\perp} \\ & +D_{\parallel}\partial_{\parallel}^2\textbf{v}_{\perp}
        +g_t \partial_t \nabla_{\perp}\delta\rho + g_{\parallel} \partial_{\parallel} \nabla_{\perp}\delta\rho +\textbf{f}_{\perp}-h_v \textbf{v}_{\perp}
    \end{split}\,,
\end{equation}
where we have introduced the reduced field
\begin{equation}\label{reduced-f}
    h_v \equiv \frac{h}{v_{\rm 0}(0)}
\end{equation}
and all the various constants introduced above can be expressed as a function of the phenomenological constants appearing in Eqs. \eqref{rho1}-\eqref{second_v}. Their precise expressions are not important in what follows, but they can be found -- together with all the details of the linearization -- in Ref. \cite{kyriakopoulos2016leading}.

The linearized density structure factor can straightforwardly computed from \eqref{rho_lin} and \eqref{v_perp_lin} in Fourier space, where
\begin{equation}\label{fourier_campi}
    \begin{split}
        &\hat{\mathbf v}_\perp(\textbf{q},\omega)\sim \int d\textbf{r}dt \,e^{-i(\textbf{q}\cdot \textbf{x}-\omega t)}\textbf{v}_\perp(\textbf{r},t)\,,\\
        & \delta\hat{\rho}(\textbf{q},\omega) \sim \int d\textbf{r}dt\, e^{-i(\textbf{q}\cdot \textbf{x}-\omega t)}\delta \rho(\textbf{r}, t)\,.
    \end{split}
\end{equation}

This calculation closely resembles the one for the zero field case \cite{toner2012reanalysis}, and for compactness we report its details in the appendix. To leading order in wave vector ${\mathbf q}$ the linearized structure factor is
\begin{equation} \label{autocorr_eqt}
\begin{split}
        S({\mathbf q},h)\equiv \langle \lvert \delta \hat{\rho}(\textbf{q},t) \rvert^2 \rangle=&\frac{1}{2} \bigg( \frac{\Delta\, \rho_0^2 \,\sin(\theta_q)^2}{[c_+(\theta_q)-c_-(\theta_q)]^2} \bigg) \\
        &\times \bigg( \frac{1}{\epsilon_+(h,{\mathbf q})}+ \frac{1}{\epsilon_-(h,{\mathbf q})} \bigg)\,,
        \end{split}
\end{equation}
where  $q=|{\mathbf q}|$ and $\theta_q$ is the angle between $\textbf{q}$ and $\hat{e}_\parallel$. We have also introduced the sound speeds $c_\pm(\theta_q)$ and the field dependent dampings
\begin{equation}\label{epsilon_pm}
\epsilon_\pm (h, {\mathbf q}) = \epsilon_\pm (0, {\mathbf q})+ a_\pm(\theta_q) h \equiv b_\pm(\theta_q) q^2 + a_\pm(\theta_q) h\,,
\end{equation}
where
\begin{equation}\label{eq:apm}
a_\pm(\theta_q)=\frac{(c_{\pm}(\theta_q)-v_2\cos(\theta_q)^2)}{v_{\rm 0}(0)[2c_{\pm}(\theta_q)-(v_2+\gamma)\cos(\theta_q)]}\,.
\end{equation}
They are respectively the real ($c_\pm$) and imaginary part ($\epsilon_\pm$) of the linearized system eigenfrequencies (see appendix).
The precise form of $c_\pm(\theta_q)$ and $b_\pm(\theta_q)$ is not relevant for what follows and its reported in the appendix for compactness. Here it suffice to note that they are only a function of the angle $\theta_q$.\\
We conclude that a small static and homogeneous external field only affects the damping terms, which acquire a correction linear in the field amplitude but independent of the wavevector magnitude $q$. This suppresses the small wavelength divergence of the free theory, since
\begin{equation} \label{autocorr_q0}
       \lim_{q \to 0} S({\mathbf q},h) \sim h^{-1}
\end{equation}

\subsection{Nonlinear corrections}
The structure factor \eqref{autocorr_eqt} is only valid in linear approximation. Nonlinear terms, ignored in the linearized approach, are known to be relevant in $d<d_c=4$ \cite{toner1998flocks,toner2005hydrodynamics} and can be accounted for by a dynamical renormalization group (DRG) analysis \cite{forster1977large, DRG2}. The original DRG analysis of field-free flocks has been carried on in \cite{toner1998flocks}-\cite{toner2012reanalysis}, while the driven case has been first analyzed in \cite{kyriakopoulos2016leading} in order to compute linear response. Here we follow the same approach to compute the scaling behavior of the density structure factor.\\

The DRG procedure is carried on in the transversal directions and consist in two steps. In the first one, the nonlinear equations of motion are averaged over the short-wavelength fluctuations: i.e., we average over the slow fields Fourier modes \eqref{fourier_campi} with wavevector lying in the (hyper-cylindrical) shell of Fourier space $b^{-1} \Lambda \!
\le q_{_\perp}  \le \Lambda$. Here
$\Lambda$ is an ``ultra-violet cutoff" (essentially dictated by the inverse of the microscopic interaction range), and $b>1$ is an arbitrary rescaling factor. Here and in the following we use the subscripts $\perp$ and $\parallel$ to denote, respectively, the directions perpendicular and parallel to the broken symmetry one, i.e. $q_\perp=|{\mathbf q}_\perp|=q \sin(\theta_q)$ and $q_\parallel=q \cos(\theta_q)$.\\

In the second step, in order to restore the ultraviolet cut-off to $\Lambda$, one rescales transversal distances $r_\perp=|{\mathbf r}_\perp |$ and wave numbers as
\begin{equation}
r_\perp = b r_\perp'\;\;\;\;,\;\;\; q_\perp = b^{-1}q_\perp'\,.
\end{equation}
Also time, parallel distances and the fields rescale according to \footnote{One may show that transversal velocity and density fluctuations have the same scaling \cite{toner1998flocks}}
\begin{equation}
r_\parallel = b^{\xi} r_\parallel'\;,\;\;\; q_\parallel = b^{-\xi} q_\parallel'\;,\;\;\;
t= b^{z}t'\;,\;\;\;\delta \rho = b^{\chi} \delta \rho'\,.
\end{equation}
This procedure leads to a new "renormalized" set of equations of motion with the same form w.r.t. to the original ones but with 'renormalized' parameter values. If we denote collectively the initial full parameter set of the nonlinear equations of motion as $\{\mu_i^{(1)}\}$, we can represent their evolution by the above DRG flow as $\{\mu_i^{(1)}\}\to \{\mu_i^{(b)}\}$. The scaling exponents  $\xi$, $z$, and $\chi$, known respectively as the "anisotropy", "dynamical" and "roughness" exponents, are in principle arbitrary. For a suitable choice of their value, however, a "renormalization group fixed point"
$\{\mu_i^*\}$, that is, a situation in which the renormalized parameters do not change under this renormalization group process, is obtained in the $b \to \infty$ limit. Analyzing the DRG flow near this fixed point one can thus deduce the system scaling properties.\\

The averaging step has to be performed perturbatively in the equations' of motion nonlinearities, and generally produces nonlinear corrections (the so-called {\it graphical} corrections) in the DRG flow equations. This makes arduous an exact treatment of the nonlinear DRG fixed point, and indeed no exact values for the zero external field Toner \& Tu theory scaling exponents at the nonlinear fixed point are known below the upper critical dimension \cite{toner2012reanalysis}. Recent high precision simulations of the microscopic Vicsek model, however, provide fairly good estimates in $d=2,3$ \cite{mahault2019quantitative}.

Including an external field in the DRG analysis is, as usual, fairly simple, and we actually may discuss it without the need to specify the exact form of the nonlinear equations of motion (they may be checked in \cite{kyriakopoulos2016leading}). It suffice to know that they have to be rotationally invariant with the only exception of the rescaled field $h_v$, the only term explicitly breaking the rotational symmetry. As a consequence, it may not gain any graphical correction in the short wavelength averaging step. Moreover, trivial dimensional analysis of Eq. \eqref{v_perp_lin} shows that $h_v$ scales as the inverse of time, yielding the linear recursion
\begin{equation}
    h_v \to h_v'=b^{z} h_v
\end{equation}
We are now able to write down the recursive equation for the density structure factor in the presence of an external field,
\begin{equation}\label{scaling1}
S({\mathbf q}_\perp, q_\parallel, \{\mu_i^{(1)}\}, h_v) = b^{\zeta} S(b {\mathbf q}_\perp, b^{\xi} q_\parallel, \{\mu_i^{(b)}\}, b^{z} h_v)\,,
\end{equation}
where we have introduced $\zeta\equiv(d-1) + \xi + 2 \chi$ and the scaling of the structure factor has been determined considering that it is given by the Fourier transform of the equal time, real space density correlation function. Thus, it involves two powers of the density fluctuations and one volume element.

The scaling of the structure factor with the field can be now deduced by fixing a reference value $h_v^*$ for the reduced field \eqref{reduced-f} and choosing the rescaling factor $b$ such that $b^{z} h_v=h_v^*$, which
implies
\begin{equation}
    b=\left(\frac{h_v}{h_v^*}\right)^{-1/z}\,.
\end{equation}
In practice, one adapts the DRG magnifying glass to the value of the external field \cite{nishimori2010elements}. Furthermore, if $h\ll 1$ and thus also $h_v$, this choice implies $b\gg 1$, so that all other parameters $\{\mu_i\}$ will flow to their fixed point value, $\{\mu_i^{(b)}\} \to \{\mu_i^*\} $. Therefore, from Eq. \eqref{scaling1} we have
\begin{equation}\label{scaling2}
S({\mathbf q}_\perp, q_\parallel, \{\mu_i^{(1)}\}, h) = h^{-\zeta/z} g(h^{-1/z} {\mathbf q}_\perp, h^{-\xi/z} q_\parallel)\,,
\end{equation}
where we have introduced the universal scaling function
\begin{equation}\label{scaling-g}
g({\mathbf x},y)=b^{\zeta/z} S(h_{\rm 0}^{1/z} {\mathbf x}, h_{\rm 0}^{\xi/z} y , \{\mu_i^*\}, h_v^*) \,,
\end{equation}
and $h_{\rm 0}=h_v^* v_{\rm 0}(0)$.

While for an anisotropy exponent $0<\xi<1$ correlations behave differently in the longitudinal and transversal directions, it may be convenient to consider the isotropically-averaged density structure factor
\begin{equation}
    S(q,h) = \langle S({\mathbf q},h)\rangle_{|{\mathbf q}|=q}
\end{equation}
which is more easily accessible in experimental measures \cite{giavazzi2017giant}. Note also that the most accurate numerical estimates of correlation functions suggest little or no anisotropy in $d = 2,3$ dimensions \cite{mahault2019quantitative}. In any case, Toner and Tu theory predicts that the short wavelength structure factor is dominated by contributions in the $q \sim q_\perp \sim q_\parallel$ direction \cite{ginelli2016physics} so that
\begin{equation}\label{s_free}
    S(q,0) \sim q^{-\zeta}\,.
\end{equation}
Along the $q_\perp \sim q_\parallel$ line and for small $h$ one has $h^{-1/z} q \sim h^{-1/z} q_\perp \gg h^{-\xi/z} q_\parallel$, so that the structure factor is dominated by transverse wavevectors ${\mathbf q}_\perp$ and we can replace $g$ with the universal scaling function $w(x)=g(x,0)$ (if $\xi=1$ one otherwise chooses $w(x)=g(x,x)$). This finally yields the scaling for the isotropic structure factor
\begin{equation}\label{scaling3}
S(q, h) = h^{-\zeta/z} w(h^{-1/z} q)\,.
\end{equation}

The behavior of the universal scaling function $w$ can be inferred by the request that, for $h\to0$, the structure factor's scaling coincides with the one of Eq. \eqref{s_free}, so that
\begin{equation}
w(x) \sim \left\{ \begin{array}{cc}
   x^{-\zeta}&\;\;\;\mbox{for}  \;\;x\gg1    \\
 \mbox{const.} & \;\;\;\mbox{for}\;\; x \ll 1
\end{array}\right.\,,
\end{equation}
and the isotropically averaged structure factor takes the form
\begin{equation} \label{scaling5}
    S(q,h)\sim  \frac{h^{-\zeta/z}}{h^{-\zeta/z} q^\zeta +C} = \frac{1}{q^z+C\, h^{\zeta/z}}\,.
\end{equation}
where $C$ is a phenomenological parameter.
Numerical estimates of the scaling exponents \cite{mahault2019quantitative} give
\begin{equation}\label{hypers}
z=\zeta = \left\{ \begin{array}{cc}
   1.33(2) &\;\;\;\mbox{in}  \;\;d=2    \\
 1.77(3) & \;\;\;\mbox{in}\;\; d=3
\end{array}\right.\,,
\end{equation}
which strongly supports the hyperscaling relation
\begin{equation}\label{hyper}
z=d-1+\xi+2\chi=\zeta
\end{equation}
conjectured in \cite{toner1995long, toner1998flocks, toner2012reanalysis}. If this is the case, Eq. \eqref{scaling5} simplifies to finally yield Eq. \eqref{div_S_h}.

\begin{figure}
	\centering
	\includegraphics[width=0.45\textwidth]{SF_comparison.eps}
	\caption{Isotropically averaged density structure factor $S(q,h)$ for the spontaneous (black dots) and directed ($h=0.01$, red squares) case for systems of size $L=1024$.  Data has been obtained averaging the structure factor of ten different configurations sampled every 50 timesteps (see text). The dashed blue line marks the power law divergence $\sim q^{-\zeta}$, with $z=1.33$. Other parameters are $\rho = 2.0$, $v_0=0.5$, $\eta=0.18$. Inset: same parameters as in the main panel, but with system size $L=256$. All axes are in a double logarithmic scale.}
	\label{2048_final_sq}
\end{figure}

\subsection{\label{simulations static method}Numerical scaling }

We tested our static method on two dimensional synthetic data generated from the Vicsek model \eqref{ev_r}-\eqref{micro_evo} with metric interactions.
We consider systems in the stationary TT phase (in the following: $\rho=2.0$, $\eta=0.18$, $v_{\rm 0}=0.5$ with periodic boundary conditions) with or without an external field. We compute the structure factor from Eq. \eqref{eq:sf2}, starting from real space density field, coarse-grained in boxes of size one. The resulting structure factor $S({\mathbf q})$ is further averaged over all the ${\mathbf q}$ orientations to obtain its isotropic average, $S(q)$ (see Eq. \eqref{eq:sf_iso})\footnote{The isotropic average is finally binned over channels of width $2 \pi/L$.}. Invoking the ergodicity of the stochastic process, the average over different realizations may be replaced by time-averages.

We first consider an external field of magnitude $h=0.01$. In Section \ref{numsim}, we have seen that its presence may be inferred from the dynamic of the flock's mean direction only when observation times are larger than $\tau_c \approx 500$ (see Fig. \ref{diff_spont_vs_driv}). In order to test the static approach in a regime where the dynamic one fails, we have restricted the time averages of the structure factor over a time-window of $T=500$ timesteps. Due to temporal correlations between subsequent spatial configurations, this may yield a low statistics, especially for the lowest $q$ modes, so we have cut-off frequencies $q\leq \pi/L$.

In Fig.~\ref{2048_final_sq} we consider a relatively large ($L=1024$) system and compare results for the directed ($h=0.01$) collective dynamics with the ones for spontaneous collective motion ($h=0$). The latter case shows a behavior compatible with the free scaling $S(q) \sim q^{-\zeta}$ with $\zeta=1.33$ \cite{mahault2019quantitative}, while in the former case, the suppression of the low $q$ divergence is rather evident for $q<q_c$, where $q_c$ is a crossover wavenumber.  This shows the viability of our static approach for large enough systems.
In smaller systems ($L=256$, inset of Fig.~\ref{2048_final_sq}), on the other hand, directed collective motion cannot be detected by the observation of the low $q$ behavior since the divergence suppression becomes effective at wavenumbers not accessible due to the limited system size.

\begin{figure}[tp!]
    \includegraphics[width=0.49\textwidth]{figures/sq_h.eps}
    \caption{(a) Isotropically averaged structure factor $S(q,h)$ for different external field amplitudes $h$. From top to bottom $h=0, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2$. The dashed The dashed orange line marks the power law divergence $\sim q^{-\zeta}$, with $z=1.33$.
    (b) same as (a), but with the data rescaled by $h^{-1/z}$ (horizontal axis) and $h$ (vertical axis) in order to collapse the structure factor curves. The $h=0$ data has been omitted.
    The vertical dashed red line marks the location of the (rescaled) crossover wavenumber (see text).
    All axes are in a double logarithmic scale, and model parameters
	are $\rho = 2.0$, $v_0=0.5$, $\eta=0.18$ and $L=512$.}
	\label{final_sq}
\end{figure}

To better probe the structure factor scaling, we now run longer time-averages for systems of size $L=512$ and different external field amplitudes $h\in [0, 0.2]$. They are shown in Fig.~\ref{final_sq}a. According to the scaling law \eqref{scaling3} and the hyperscaling relation \eqref{hypers}, the field rescaled structure factor $h S(q)$ should be only a function of $h^{-1/z} q$, and this is verified nicely in Fig.~\ref{final_sq}b where we have once again used used the 2d numerical estimate $z=1.33$. This also implies the crossover wavenumber scaling
\begin{equation}\label{crossover_size1}
    q_c(h) \sim h^{1/z}\,.
\end{equation}
Equation \eqref{crossover_size1} immediately implies that observations need to be carried on in large enough systems, with a threshold linear system size
\begin{equation}\label{crossover_size2}
    L_c(h) \sim h^{-1/z}\,.
\end{equation}
Note that the crossover temporal and spatial scales are indeed related through the dynamical exponent,
\begin{equation}\label{crossover_size3}
    \tau_c \sim L_c^z \,.
\end{equation}

\section{Conclusions}

We have discussed the behavior and scaling properties of the mean flocking direction and static density correlations in the presence of a small homogeneous external field. For large enough times, fluctuations in the mean direction depart from the diffusive behavior exhibited by finite flocks in the zero field case, following the statistics of an Ornstein-Uhlenbeck process. For the first time, we have also discussed explicitly the scaling of the diffusive process exhibited by the mean direction of motion of finite flocks in the spontaneous, zero-field case.

In large enough systems, a complementary signature of directed motion can be found in the small $q$ behavior of the static density structure factor, which saturates in the presence of an external field rather than showing the divergent behavior typical of spontaneous symmetry breaking.

These facts can be used to detect directed collective motion, that is flocking behavior guided by external cues such as concentration gradients or other global anisotropies. Observations of the mean flock's direction (the {\it dynamical} method) may be useful for long enough observation times, while computing the density structure factor (the {\it static} method) is informative in sufficiently large systems.
Note also that in order to apply our analysis it is not necessary that all active particles are able to detect the environmental cues. In Ref \cite{giomi}, it has been shown that the effect of an external static field only affecting a finite fraction of the flocking particles is equivalent to that of a rescaled (by the fraction of affected particles) homogeneous field. The equivalence holds provided the affected particles are randomly distributed in the flock. On the contrary, we do not expect our considerations to be directly applicable to localized or time-varying perturbations \cite{cavagna2013boundary}.

It is finally fair to stress that while our method can detect the presence of external fields/environmental cues, it cannot exclude their presence: negative results may simply mean that the external field is so small that the accessible spatial or temporal observational scales are too small to detect it.

In the future, we plan to test our method on data obtained from {\it in vitro} cellular migrations\cite{malinverno2017endocytic}  taking place on a grooved substrate, but we also expect our considerations to be useful to biologist to detect clear signatures of the directed nature collective motion in {\it in vivo} cellular migration phenomena.

\begin{acknowledgments}
We acknowledge support from PRIN 2020PFCXPE\_004. FG thanks Clement Zankoc for earlier numerical tests.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


This is a digital stamp and I enjoyed making this piece. I used prisma pencils and accessories.
Looks great! Love how you colored her with the P-pencils.
Oh WOW this is so very beautiful, great job! I so love this! It's very sweet!


text:
Maiyro
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Meet Nickson, the furniture-as-a-service startup that Barack Obama's ex-financial adviser just ba... - 4 minutes read
Ever toured an apartment and fell in love with the model unit?
You're not alone. Harvard Business School grad Cameron Johnson is a former institutional real estate investor and Greystar exec turned startup founder who realized that very often, "renters would try to rent the model apartment."
This got him thinking. People would love to rent a model apartment in a building, and no one likes to move. This spelled opportunity in Johnson's mind.
So in 2017, he came up with the idea of Nickson, a Dallas-based startup that fully furnishes apartments on demand.
Image Credits: CEO and founder Cameron Johnson / Nickson
"I thought 'What if you gave people the ability to simply rent the model, or the ability to add everything in their space needs with a few clicks, similar to how a cable modem comes to your house,'" CEO Johnson said. "I wondered, 'Why can't we do that for everything else?'"
But Nickson doesn't just provide furniture such as beds and sofas, it delivers all the essentials too — from extension cords to pots and pans to silverware to curtain rods. By partnering with a variety of retailers, the startup claims that it allows users "to make their new spaces move-in ready in as little as 3 hours."
Users take a style quiz and share apartment layout details. Nickson's designers create an initial layout based on the dimensions of an apartment, desired functions (such as work from home) and the volume of furnishings based on a person's lifestyle. Once the layout is complete, Nickson creates a custom design, including all furnishings and home goods.
Upon signing up, users pay a one-time installation fee for the furniture-as-a-service offering, and then a monthly subscription charge for the duration of a lease — starting at $199 a month for a studio to $500 a month for a three-bedroom apartment. The startup also offers concierge services such as a household supply starter kit and maid service, as an add-on to its flat monthly subscription.
Nickson is currently only live in the Dallas market, but plans to expand into other cities over the next 12 months, including expanding its beta tests in Austin and Houston. And it's just raised a $12 million Series A to help it advance on that goal.
A fund managed by Pendulum Opportunities LLC, a wholly owned subsidiary of Pendulum Holdings LLC, led the Series A round, which also included participation from Motley Fool Ventures, Revolution's Rise of the Rest and Backstage Capital.
The COVID-19 pandemic has disrupted the global supply chain, leading to delivery delays for consumers. Nickson has purchased items over time that it stores as local inventory, making it even more attractive to renters who don't want to deal with delays and hunting down furniture and essentials, Johnson said. The convenience Nickson offers led to its user base growing 700% in 2020 compared to the year prior, he added.
Robbie Robinson, co-founder and CEO of Pendulum, said his firm was drawn to invest in Nickson due to a combination of Johnson's "vision, secular shifts toward renting and subscription consumption and the company's disruptive business model." (Robinson is President Barack Obama's former financial adviser, and recently founded Pendulum to invest $250 million in founding startups of color).
Kabir Ahmed, vice president at Pendulum, added that he believes Nickson's model is superior to the concept of renting one-off furniture pieces in that it offers an "end-to-end, turnkey solution."
"This seamless experience is highly differentiated and offers a compelling value proposition for the consumer," he said.
Of course, Nickson is not the only company attempting to turn the stodgy furniture rental industry on its head. Other startups offering similar services as Nickson include Oliver Space, Fernish and The Landing.
But Nickson claims that it stands out from the competition in that it "takes care of everything" beyond furniture (including artwork and toilet brushes) and that it can curate space and bring it all in before a renter even shows up.
"No other competitor in this space offers this level of service, detail or turnaround," Johnson says. "You can literally arrive at your new home with a suitcase and toothbrush, and it's ready to 'live in.'"
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Sulpicians in the United States
The Sulpicians came to the United States at the very rise of the American Hierarchy. When the French Revolution was threatening to involve them in the impending ruin of the Church the superior-general, Father Emery, looking for a place of refuge abroad, was meditating an establishment at Gallipolis, a French settlement on the Ohio ; but the papal nuncio at Paris, Cardinal Dugnani, made the happier suggestion of Baltimore, which had just been erected into the first American see. An interview in London between Bishop Carroll, who had come to England (1790) for episcopal consecration, and Father Nagot resulted in the bishop gladly accepting the offer of Father Emery to found a theological seminary at Baltimore. On 10 July, 1791, four Sulpicians landed at Baltimore : Francis Charles Nagot, Superior, Anthony Gamier, Michael Levadoux, and John Tessier. They purchased the One Mile Tavern on the edge of the city, dedicated the house to the Blessed Virgin, and in October opened classes with five students whom they had brought from France. This was the beginning of St. Mary's, the first American seminary, which still stands on the same spot. The number of Sulpicians was augmented the following year by the arrival of Flaget, David, Chicoisneau, Ambrose Maréchal, Richard, and Ciquard, and in 1795 by the accession of Dubourg, nearly all of whom were destined to become important figures in the history of the American Church. These ten or eleven new workers were a large accession to the small body of American priests, then only about thirty-five, who were endeavouring to serve a diocese extending from the Atlantic to the Mississippi Valley. The Church was in its infancy; there was no organized community of priests (since the suppression of the Jesuits ), no teaching sisterhood, no Catholic schools. An academy for boys was about to open at Georgetown. Non- Catholic education in Maryland was almost as backward as the Catholic. In these conditions Bishop Carroll's greatest need and most difficult task, as he had long recognized, was to recruit a sufficiently numerous and fit clergy, if possible native, which he could hope for only from a seminary. Naturally, he welcomed the coming of the Sulpicians as "a great and auspicious event" for his diocese.
But the time was not ripe for a seminary as there were no students prepared to enter it. Georgetown Academy, founded chiefly to develop priestly vocations, instead of being an aid to the seminary drew on St. Mary's few students to recruit its teaching staff. The natural remedy of opening a preparatory seminary at Baltimore was forbidden (see below). The almost hopeless condition may be judged from the fact that during each of the first three years there were only five students and in the next year, 1794, only two, nearly all of whom were from Europe ; from 1795 to 1797 there were none at all. So with little or no opportunity of cultivating their own field, the Sulpicians offered themselves to the bishop for any work at hand. Flaget, David, Ambrose Maréchal, and Dubourg taught at the Georgetown Academy; Dubourg, an enterprising and energetic man, being made president (1796-99), greatly increased its numbers and prestige. Ciquard worked among the Indians of Maine ; Levadoux, Dilhet, and Richard among the French and the Indians of Illinois and Michigan. Richard, still well remembered at Detroit, which some years ago placed his statue on the city hall, deserves special mention. He restored religion, established Catholic schools, founded a young ladies' academy and a preparatory seminary for young clerics set up the first printing press in the West, published the first newspaper in Michigan and the first Catholic paper in the United States ; was a founder, vice-president, and professor of the University of Michigan and the only Catholic priest ever elected to Congress. Gallitzin, a pioneer priest in Western Pennsylvania, converted six thousand non-Catholics. The Sulpicians at Baltimore ministered in the churches of the city and the missions of the country. They were considered as clergy of the cathedral and are credited with having introduced into the United States some of the dignity and splendour of old-world Catholic worship.
St. Mary's Seminary
After a trial of ten or eleven years the seminary at Baltimore had no prospects of success; an academy which Dubourg had opened for foreign boys was not allowed to receive Americans (see below); the Sulpicians there had no means of support. Meanwhile, the Revolution in France had passed, religion was restored by Napoleon, and the seminaries were being reopened. In these circumstances of 1802 only one course seemed possible to the superior-general in Paris : to recall his subjects to France gradually. Bishop Carroll , who had the highest esteem for the Sulpicians and regarded them as the hope of his diocese, was very deeply afflicted by this resolution, and in many letters begged Father Emery not to carry it out. "If it be necessary for me", he wrote, "to bear the terrible trial of seeing the greater number of them depart, I implore you to leave here at least a germ which may produce fruit in the season decreed by the Lord." Nevertheless, Gamier (who afterwards became superior-general), Ambrose Maréchal, and Levadoux departed for France in 1803, though with the greatest reluctance; Nagot was detained from going by ill-health. The seminary seemed doomed. It was saved by Pius VII, whom Father Emery, moved by the bishop's appeals, consulted at Paris in 1804. "My son," said the pope, "let it stand, let that seminary stand. It will bear fruit in its own time." Father Emery accepted these words as the voice of God, and the Sulpicians remained. But progress was slow; St. Mary's College, Baltimore, and Mt. St. Mary's, Emmitsburg, both founded by the Sulpicians (see below), furnished few students to the seminary. Still, Bishop Carroll had the consolation of seeing thirty priests ordained from there before his death in 1815.
Under the second superior, Father Tessier (1810-29), the seminary became solidly established, although the number of ordinations averaged only two or three a year. His chief support up to 1817 was Father Ambrose Maréchal, whose abilities raised him in that year to the Archbishopric of Baltimore. In 1822 St. Mary's Seminary was endowed by Pius VII with all the privileges of a Catholic university. The third superior, Father Louis Regis Deluol (1829-49), a man of exceptional ability and character, exerted a strong influence not only on the seminary and college over which he presided, but on the general affairs of the Church in America. St. Charles' College was founded during his administration. St. Mary's College was suppressed under his successor, Father Francis L'Homme (1849-60). The Irish immigration, the spread of Catholicism, and the foundation of St. Charles' College, contributed to render the seminary as fruitful in vocation in the one decade of Father L'Homme's administration as it had been in the preceding sixty years. Two directors at St. Mary's, Fathers Alphonse Flammant (1856-64) and Francis Paulinus Dissez (1857-1907), deserve mention here as saintly men who deeply influenced Cardinal Gibbons, the first Archbishop Keane of Dubuque, and other leaders of the American Church. A half-century of teaching at St. Mary's made Father Dissez one of the best known and most venerated priests of America.
St. Mary's prospered and grew under the fourth superior, Father Joseph Paul Dubreul (1860-78), and still more under his successor, Father Alphonse Magnien (1878-1902), who saw an enrolment of over three hundred students. Father Dubreul built the central portion of the present seminary in 1878: the building was completed by Father Magnien. All that remains from the old days is the sisters house, in which Mother Seton began her work as a Sister of Charity, and the seminary chapel, built in 1806, which long served as a parish church and was regarded in those days as a gem of architecture. Both Dubreul and Magnien were marked types of the true ecclesiastic, and moulded the character of hundreds of priests now living. Probably no priest in our day was better known or better loved by priests than the good and genial "Abbé" Magnien. He was the close friend and trusted adviser of Cardinal Gibbons, who said of him some time after his death: "I had been so much accustomed to consult the venerable Abbé on important questions, and to lean upon him in every emergency, that . . . I feel as if I had lost my right arm. He was indeed dimidium animœ meœ ." The present superior, Father Edward Randall Dyer, D.D., was appointed in Aug., 1902, after Father Magnien's health had failed. St. Mary's Seminary has given over thirty bishops and eighteen hundred priests to the Church of America, of whom more than fourteen hundred are still living. The largest of our American seminaries, and national in its scope, it draws its students from every quarter of the country. It has always taken a leading part in the seminary conferences of the Catholic Educational Association. It was the scene of the Third Plenary Council and of many notable ecclesiastical gatherings. Its archives and library are rich in materials of early American Church History.
St. Mary's College , Baltimore
The impossibility of getting students for the seminary led the fathers to teach Latin to a few boys in 1793-94, in the hope of recruiting vocations; but this was discontinued through fear of injuring the Georgetown Academy. Father Dubourg resigned the presidency of Georgetown in 1799 in order to found a college at Havana. Unsuccessful in the attempt, he returned to Baltimore in Aug., 1799, with three young Spaniards ; these, with a few French boys, he lodged and instructed at the seminary. In the following year a building was erected for them alongside the seminary, and the institution was named St. Mary's College. In deference to the wishes of the bishop, no American boys were admitted, but many students came from Cuba, San Domingo, Jamaica, and Porto Rico, besides French boys from the United States. In 1803 the doors were opened to American students, without distinction of creed ; and in 1805 the college was raised to the rank of a university by an act of the legislature. The students numbered then, or in the following year, 106, which was considered a remarkable success; for the history of all higher education in Maryland up to that time had been, almost without exception, a record of failures. It drew students from the whole country, but chiefly from Maryland and the neighbouring states, north and south. Many were non-Catholics. Some continued to come from the West Indies and from Central America. The college had vicissitudes chiefly financial, but it maintained a high standard and enjoyed a high reputation, for it was conducted by able men who brought the culture of France to a country where education was still in a very crude condition. Its student roll rose at times to two hundred or over. Among its eleven presidents are numbered Archbishops Dubourg and Eccleston, and Bishops David, Bruté, and Chance; and the names of many bishops and notable priests and citizens are found on the list of its professors and students.
Despite its half-century of useful and distinguished work, it did not adequately fulfil the main purpose of its foundation; a college, frequented by sons of rich parents, and containing many non-Catholics, was found unfavourable to the fostering, and even to the preservation, of priestly vocations. Accordingly it was resolved in 1848, on the occasion of the official visit of Father Faillon from Paris, to suppress St. Mary's College and start an ecclesiastical college. In the autumn of that year, St. Charles' College was opened (see below); and in 1852 St. Mary's College by order of the superior-general, Father de Courson, was closed at the height of its prosperity. By an understanding with the Jesuits, Loyola College supplied its place.
Mount St. Mary's , Emmitsburg
The necessity of a strictly clerical school had forced itself upon the mind of Father Nagot in the first years of St. Mary's College . In 1806 this saintly old man of over seventy gathered about a dozen boys around him at Pigeon Hill, Adams Co., Pennsylvania, in a Catholic region that had long been ministered to by the Jesuits. After two years of instruction, they were transferred to the care of the Rev. John Dubois, pastor of Emmitsburg, Maryland, who himself was already instructing a few boys. In 1808 Father Dubois, who had become a Sulpician, acquired land and built Mount St. Mary's College, in the name of the Society of St. Sulpice. He did heroic work, single-handed, as teacher and as pastor. In 1812 he was joined by Father Bruté. Together they were the main factors in creating a flourishing college where the spirit of Catholic piety reigned and was very fruitful in vocations. Mount St. Mary's, founded to supply vocations to St. Mary's Seminary, became a rival by force of circumstances, for it could obtain teachers only by retaining the graduates of the college who taught the younger boys at the same time they pursued their clerical studies. It also became a rival of St. Mary's College when it began to admit boys who did not aspire to the priesthood, and even non-Catholics. For these, and also for financial reasons, the Society of St.Sulpice in 1826 made an amicable separation from Mount St. Mary's, which has continued the noble spirit of Bruté and Dubois and done invaluable services to the Church of America.
St. Charles' College , Ellicott City
Persisting in the effort to establish a purely clerical college, according to the spirit of their vocation and the mind of the Church, the Sulpicians, in 1831, laid the cornerstone of St. Charles' College, near Ellicott City, Maryland. The ground, together with a small sum of money, had been donated by Charles Carroll of Carrollton, who survived to witness the cornerstone laying. Lack of funds long delayed the completion of the college. It was opened in 1848 with four students by the Rev. Oliver Jenkins, who became its first president. In ten or twelve years the students numbered over a hundred. Here, at last, was a strictly clerical college, firmly established, giving a solid classical education and maintaining the purest traditions of clerical discipline and spirit. St. Charles' became well known throughout the country, no section of which has not been well represented among its student body. The enrolment for years has been about two hundred. It has trained over fourteen hundred priests for the American Church and pointed the way to the clerical colleges now becoming numerous and most helpful. Father Jenkins remained president till 1869, though he had been temporarily replaced by the Revs. G. Raymond (1849-51) and S. Ferté, D.D. (1851-52). His successors have been Father Ferté (1869-76), Revs. P. P. Denis (1876-86), F. M. L. Dumont (1886-94), Charles B. Rex (1894-97), Charles B. Schrantz (1897-1906), and F. X. McKenny. To the older generations of students the best remembered of the professors is Father J. B. Menu, who for forty years (1849-88) "hammered Latin and Greek into the most stubborn heads". The best known to the outside world is Father John B. Tabb, a true poet, whose exquisite lyrics have won him a secure place in English literature . The spacious building, with its beautiful chapel, its libraries, and valuable documents, was destroyed by fire on 16 March, 1911. Classes were resumed in a few weeks in temporary quarters at Cloud Gap, near Baltimore. On that spot the fathers have now begun (1912) the construction of a new and greater St. Charles.
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St. John's Seminary , Brighton
Opened in 1884 and entrusted by the Most Rev. John J. Williams, Archbishop of Boston, to the care of the Sulpicians, whose pupil he had been at Montreal and Paris. Its presidents have been the Very Revs. John Hogan (1884-89, 1894-1901), Charles B. Rex (1889-94), Daniel E. Maher (1901-06), and Francis P. Havey (1906-11). In June, 1911, at the request of the Most Rev. William H. O'Connell, Archbishop of Boston, the Sulpicians withdrew from the seminary.
St. Joseph's Seminary , Yonkers
Archbishop Hughes, who had been their pupil at Mount St. Mary's, had desired the Sulpicians, in 1862, to assume charge of the seminary about to be opened at Troy, New York. This wish was carried out only in 1896, under Archbishop Corrigan, when St. Joseph's Seminary was transferred to Dunwoodie, Yonkers, New York. The first rector was the Very Rev. E. R. Dyer, 1896-1902. Called to the presidency of St. Mary's Seminary, Baltimore, he was succeeded by the Very Rev. James F. Driscoll. In January, 1906. Father Driscoll and four of his associates withdrew from the Society of St-Sulpice, and were accepted by Archbishop Farley into his diocese, continuing their work in the seminary, which thus passed from the charge of the Sulpicians.
St. Patrick's Seminary , Menlo Park
The Sulpicians, whose houses had hitherto been located in the Atlantic states, accepted a call to the Far West in 1898. Most of the students for the San Francisco archdiocese had for many years been sent to St. Mary's Seminary, Baltimore. A long-cherished desire of Archbishop Riordan was realized when St. Patrick's Seminary was opened 20 Sept., 1898, under the care of the Sulpicians. The institution was to comprise a preparatory seminary or college and a seminary proper, of philosophy and theology. It began with only three classes of the college department, the succeeding classes in the college and seminary being added according as the students were prepared. Very Rev. A. J. B. Vulbert was the first president of the college department, and had under him, at the beginning, seven professors, four of whom were Sulpicians, and twenty-eight students. He was succeeded in 1911 by Rev. John J. Doran, S.S. The theological department was opened in 1904, when Very Rev. Henry A. Ayrinhac, S.S., D.D., became president of the seminary. The magnificent structure was greatly damaged in the earthquake of 1906, but was soon restored, thanks to the characteristic energy of Archbishop Riordan. There are at present over one hundred students in this flourishing and hopeful young seminary.
Catholic University
Leo XIII, in granting a constitution to the Catholic University of America , laid upon the Sulpicians the duty of caring for the discipline and spiritual direction of the ecclesiastical students and of assisting them in the choice and pursuit of their studies. Divinity College was opened in October, 1889, under Very Rev. John B. Hogan, who remained president till 1894. His successors have been Very Revs. F. M. L. Dumont (1894-1911), and John F. Fenlon.
St. Austin's College
The aspirants to the Society of St-Sulpice pursue their studies in the seminary, undistinguished from the other students; until recently, the American aspirants generally were sent to Rome or Paris for post-graduate studies after ordination and to the Solitude at Issy, near Paris, for their novitiate. In Oct., 1901, the American scholasticate of the Sulpicians, known as St. Austin's College, was opened near the Catholic University, Washington. The students, who are received only after having completed their seminary studies, follow courses at the university in philosophy, theology, science, or letters, to prepare themselves for work in college or seminary. It has been presided over by Very Revs. James F. Driscoll (1901-02), Daniel P. Duffy (1902-04), John F. Fenlon (1904-11), and Francis P. Havey. In 1911 the first American novitiate of the Sulpicians, known as the Solitude, was begun in this house under Father Havey as director.
The government of the Sulpician houses in the United States was, until recent years, dependent directly upon the superior-general in Paris. In 1903 the President of St. Mary's Seminary, Father Dyer, was appointed vicar-general of the Superior of St-Sulpice, an office resembling that of provincial in a religious order. He governs ordinary Sulpician affairs in the United States with the advice and assistance of his council. In the early days of the American hierarchy several Sulpicians were among its members: Ambrose Maréchal (1817-28), and Eccleston (1834-51), Archbishops of Baltimore ; Flaget, first Bishop of Bardstown (1810-50), with David (1819-41), and Chabrat (1834-47), as coadjutors; Dubourg, Bishop of New Orleans (1815-26), died Archbishop of Besançon in 1833; Dubois of New York (1826-42); Bruté, first Bishop of Vincennes (1834-39), who, with Flaget and David, is well remembered for great sanctity of life; Chance, first Bishop of Natchez (1841-52); Vérot, Bishop of Savannah (1859-70); afterwards first Bishop of St. Augustine (1870-76), of which he had been vicar Apostolic in 1858; and O'Farrell, Bishop of Trenton (1881-94). More than twenty American archbishops, past and present, and more than sixty bishops have received their clerical formation, at least in part, in Sulpician houses at home or abroad. All the rectors of the Catholic University have been their pupils. Father David, sent by Father Emery with Bishop Flaget to establish a seminary, founded St. Thomas's Seminary at Bardstown, and taught its students almost singlehanded for many years. The diocese had only three priests when he arrived in 1810; he trained up forty-seven, mostly natives, of whom the most illustrious is Martin J. Spalding. To this little-known seminary is attributed the greatest part in the preservation and spread of Catholicism in Kentucky.
Six seminaries in all, Baltimore, Bardstown, Brighton, Emmitsburg, Dunwoodie, and Menlo Park were founded or directed by Sulpicians, and their traditions and spirit have been carried into many new institutions by their alumni. Largely through their efforts, the Propagation of the Faith was established in this country and for a long time developed. The Sisters of Charity at Emmitsburg were established by their direction and co-operation, and united, through Father Deluol, to the foundation of St. Vincent de Paul at Paris. Father Joubert founded the coloured sisterhood of the Oblates at Baltimore, and Father David the Sisters of Nazareth, in Kentucky. Bishop Dubourg introduced the Vincentians into the United States, also the Religious of the Sacred Heart. He was the founder of St. Louis Latin Academy which developed, under the Jesuits, into the St. Louis University. On Flaget's invitation the Good Shepherd Sisters came to this country. In the early days the Sulpicians ministered to the coloured Catholics of Baltimore, and since the foundation of St. Joseph's Seminary for work among the negroes, its students have made their seminary studies at St. Mary's. The secretarial work of the Negro and Indian Commission has always been carried on in connexion with St. Mary's Seminary. The fathers of the seminary have acted as secretaries or theologians in the synods and in the provincial and plenary council of Baltimore. The literary productions of the Sulpicians have, almost without exception, grown directly out of their work as educators; they have written books on Latin grammar, history ancient and modern, English literature , liturgy, rubrics, dogmatic and moral theology, Holy Scripture , devotion, etc. They have translated many standard French works into English, and English into French. Their best-known writers are Father Hogan, whose "Clerical Studies" is the classic of its subject, and Father Adolphe Tanquerey, whose text-bocks on dogmatic and moral theology are used in numerous seminaries throughout the world.
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3" 1 - 0 : It's wonderful play from Sadio Mane as he plays a one-two on the edge of the Leicester area at the end of a 30-pass move before curling a sumptuous shot into the far corner beyond Schmeichel.
Liverpool in front before Leicester even had the chance to touch the ball.
45" 1 - 1 : And there is a twist in the tail for Liverpool! The free-kick is whipped into the area, it cannons around before a second cross is sent back in. A handful of Leicester players are offside but Harry Maguire isn't as he ghosts in at the back post to calmly finish into the bottom left-hand corner to stun Anfield.
Shaqiri 4, Salah 5, Firmino 6, Mane 6. Subs: Fabinho 6, Lallana 6, Sturridge 6.
Leicester City FC : Schmeichel 6, Ricardo 7, Evans 7, Maguire 8, Chilwell 7, Albrighton 7, Mendy 6, Ndidi 6, Maddison 6, Gray 6, Vardy 5. Subs: Choudhury 6, Okazaki 6, Okazaki 6.
Liverpool have won their last three league games against Leicester - they last won four in a row against them between February 1987 and September 1996.
Leicester have lost six of their last seven away Premier League games against Liverpool (D1), with their last win at Anfield coming in May 2000 (2-0).
Liverpool haven't lost any of their last 19 home midweek games in the Premier League (Tuesday, Wednesday, Thursday), winning 13 and drawing six since a 0-1 loss vs Fulham in May 2012.
Liverpool are looking to win eight consecutive Premier League home games for the first time since March 2010. The Reds conceded as many goals in their last home league game against Crystal Palace as they had in their previous 15 at Anfield combined (3).
Leicester have lost each of their last 11 Premier League games against sides starting the day top of the table, conceding at least twice every time (27 in total) and netting just five in return. Their last such win came on January 31, 1998 at Manchester United.


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C# interview questions: - What is exception bubbling in C#?
Many times when you catch exception, do not want them to be handled during that time. Rather you would like to propagate the same to the caller and let the caller handle the same. For such kind of scenarios we use exception bubbling.
For instance if you have raised exception in a business class, you would probably like to bubble it to the UI so that it can be displayed in a message box for the end user.
Below is a sample code where "Method1" raises the error to the calling code and the calling handles the same by displaying the same using "Console.Write" function. In order to bubble the error up we need to say "throw" or "throw ex". The code is also circled below.
C# interview questions video: - What is the difference between Constant and Read only?


"Residue analyses on a grinding tool recovered at Grotta Paglicci sublayer 23A [32,614 ± 429 calibrated (cal) B.P.], Southern Italy, have demonstrated that early modern humans collected and processed various plants....the exploitation of plant resources was very important for hunter–gatherer populations, to the point that the Early Gravettian inhabitants of Paglicci were able to process food plants and already possessed a wealth of knowledge that was to become widespread after the dawn of agriculture."
"Researchers from the University of Florence in Italy have found residue of oats on a Paleolithic grinding tool found in southern Italy, at a site known as Grotta Paglicci. The finding not only expands current knowledge about what real Paleos ate, but also how they ate it—our ancestors processed foods more than originally thought.
"The pestle-grinder tool was found in 1989 and identified as being about 32,000 years old. In the course of the researchers' study, it was sampled twice, in 2010 and 2012, to identify any residues. In one of the samples, researchers identified as many as 250 starch grains per square centimeter.
So much for the hypothesis that humans did not consume whole grains or starch-based diets prior to 10 thousand years ago.
Since humans were heat-processing and grinding grains of grasses and "heavy plant eaters" 32,000 years ago in southern Italy, and there is evidence for use of grass seed consumption extending back 100,000 years, as well as evidence that African hominins obtained 55% of their diet from grasses and sedges by 1.4 million years ago [and even 3-3.5 million years ago], it seems that humans have eaten a grain-/grass-based diet for millions of years in order to obtain the starch required to fuel their brains.
Human dependence on whole grains for millions of years has resulted in a dietary requirement for phytates present in whole grains and legumes, as supported by the evidence I presented in the following video.
The importance of whole grains to human health and happiness did not escape the Chinese. The Chinese character for "peace" is composed of the characters for mouth, cereal grains, and calm. Chinese sages recognized that consumption of cereal grains brings peace to the body, the mind, and human society.
Macrobiotic teacher Ed Esko talks a bit about the psychophysiological effects of eating whole grains compared to those of eating dead animal carcasses in this video I made.
Humans are symbiotic with whole grains. We can reclaim our health, happiness, and heritage by returning to a diet based on whole cereal grains.
Ötzi the Iceman, who lived around 3,300 BC seemed to eat a lot of grain.
Analysis of Ötzi's intestinal contents showed two meals (the last one consumed about eight hours before his death), one of chamois meat, the other of red deer and herb bread. Both were eaten with grain as well as roots and fruits. The grain from both meals was a highly processed einkorn wheat bran, quite possibly eaten in the form of bread. In the proximity of the body, and thus possibly originating from the Iceman's provisions, chaff and grains of einkorn and barley, and seeds of flax and poppy were discovered, as well as kernels of sloes (small plumlike fruits of the blackthorn tree) and various seeds of berries growing in the wild.