text:
\section{Introduction}
\label{intro}

Despite the constant improvement in the quality of observations over the last decade, the Standard, $\Lambda$CDM, Cosmological model, still provides a good fit to several cosmological observables \citep{PLANCK2016cp, AlamEtal2016a, ZhaoEtal2017a}. It is therefore clear that the analysis of future galaxy survey data \citep{LaureijsEtal2011, LeviEtal2013, LSST2017} will require accurate predictions, at the percent level or better, since any departure from the standard scenario will likely be relatively small \citep{McDonaldEisenstein2007, EisensteinSeoWhite2007, CarboneMangilliVerde2011, GiusarmaEtal2011, AmendolaEtal2013, WeinbergEtal2013, AudrenEtal2013, JoyceEtal2015, BaldaufEtal2016, DesjacquesJeongSchmidt2016, Koyama2016, AlonsoEtal2017}.

In this context, it has become necessary to properly account for the effects of neutrino masses on cosmological observables. Massive neutrinos represent a small but non negligible fraction of the matter density, characterised by a significant thermal velocity distribution even when non-relativistic, and we should account for the different evolution of their perturbations with respect to the cold dark matter component. Their overall effect consists in a damping of matter perturbations on all scales below their free-streaming scale: a several percent reduction on the {\em total} matter power spectrum, \citep{LesgourguesPastor2006, Lesgourgues2013}. This happens precisely on the range of scales probed by current galaxy redshift surveys (tens to hundreds of Megaparsecs). In fact, cosmological observations are able to provide an upper limit to the (sum of) neutrino masses \citep{PalanqueDelabrouilleEtal2015, PLANCK2016SZClusters, AlamEtal2016a, CuestaNiroVerde2016, VagnozziEtal2017, ArchidiaconoEtal2017} and, in the long run, possibly bridge the gap with the lower limit given by neutrino oscillation experiments \citep{LeviEtal2013, LaureijsEtal2011}. In other terms, neutrino masses are not simply a nuisance in the possible detection of dark energy or new physics effects, but represent an important test for the Standard Model of particles physics and its extensions.

Several studies had appeared, over the last few years, on massive neutrinos effects on the matter power spectrum nonlinear evolution and redshift-space distortions in the context of perturbation theory  \citep{SaitoTakadaTaruya2008, Wong2008, LesgourguesEtal2009, UpadhyeEtal2014, BlasEtal2014, DupuyBernardeau2014, DupuyBernardeau2015, CastorinaEtal2015, FuhrerWong2015, UpadhyeEtal2016, ArchidiaconoHannestad2016, LeviVlah2016, LiuEtal2017A}, on baryonic acoustic oscillations \citep{VillaescusaEtal2014, LiuEtal2017}, on the halo mass function \citep{IchikiTakada2012, CastorinaEtal2014, CostanziEtal2013B, LoVerde2014B, CastorinaEtal2015}, halo bias \citep{BiagettiEtal2014, LoVerdeZaldarriaga2014, LoVerde2016, CastorinaEtal2014, CastorinaEtal2015, ChiangEtal2017} and cosmic voids \citep{MassaraEtal2015}. Novel probes of massive neutrinos have also been recently proposed \citep{ZhuEtal2014, OkoliEtal2016}.

Focusing on the theoretical description of matter perturbations, predictions for the nonlinear matter power spectrum have been first studied in \citep{SaitoTakadaTaruya2008} and \citep{Wong2008}. The model proposed for the {\em total} matter power spectrum approximates neutrino perturbations with their linear prediction (obtained from a Boltzmann code, and therefore acting as a source for cold and baryonic matter), limiting nonlinear corrections only to the {\em cold} dark matter component. The limits of this approximation are carefully studied in both works, estimating systematic errors due to the linear neutrino assumption to be at the sub-percent level. Indeed, comparisons with particle-based N-body simulations show the discrepancies between numerical results and predictions based on Perturbation Theory (PT) in the massive neutrino case to be consistent with the typical accuracy of the standard PT approach in $\Lambda$CDM models \citep{CastorinaEtal2015}.  The validity of the linear neutrino approximation is further explored in \citep{BlasEtal2014, SenatoreZaldarriaga2017} where the authors highlight how the violation of momentum conservation inherent in the scheme might have significant effects in the nonlinear corrections beyond the 1-loop level. They propose an hybrid model combining the full Boltzmann treatment at high redshift and the two-fluid approximation at later times as a starting point for studying the nonlinear evolution. In this approximation, both cold dark matter (including baryons) and neutrinos are described as fluids, the second characterised by a (time-dependent) effective speed of sound, estimated from the neutrino velocity dispersion \citep{ShojiKomatsu2010}. Explicit predictions for the matter bispectrum have been presented, so far, in \citep{FuhrerWong2015} and \citep{LeviVlah2016}. Ref. \citep{FuhrerWong2015} presents a test of the two-fluid and the linear neutrinos approximations, against the exact treatment via the collisionless Boltzmann equation, using the bispectrum as a specific measure of their validity at the level of higher-order corrections. They show how both approximations fail to provide a 1\% accuracy on the total matter bispectrum. In particular, as we will discuss, the linear neutrinos approximation does not correctly reproduce the large scale matter bispectrum for large neutrino masses, while in the limit of a small neutrino density fraction, $f_\nu$, becomes significantly more accurate.  The same limit is also explored in the alternative formulation of \citep{LeviVlah2016}, where a perturbative expansion around $f_\nu=0$ is considered.

In this work we present, for the first time, measurements of the matter and halo bispectrum in N-body simulations that include a massive neutrino component as particles. In the case of the two matter components, neutrinos and cold dark matter/baryons, we provide a first comparison with theoretical predictions assuming neutrinos perturbations at next-to-leading order in PT. In addition,  we attempt an extension of the results of \citep{CastorinaEtal2014} on the ``universality'' of linear halo bias to the nonlinear level, including as well non-local corrections \citep{ChanScoccimarroSheth2012, BaldaufEtal2012}. In fact, the bispectrum, as a direct result of nonlinear evolution, provides a valuable test of nonlinear effects (due to both gravitational instability and bias) in these, by now, standard cosmological models. Moreover, the galaxy bispectrum, is the lowest-order statistic encoding and quantifying the non-Gaussian properties of the galaxy distribution \citep{SefusattiEtal2006}. Several groups have measured three-point statistics in recent data \citep{SlepianEtal2016, GilMarinEtal2017}, showing that the adding this information to the standard power spectrum analysis yield to better constraints on the cosmological parameters.

The paper is organized as follow. In Sec.~\ref{sec:linear_nu} we briefly review basic results on massive neutrinos perturbations. In Sec.~\ref{sec:bispm} we show our measurements of the bispectrum for the various matter components and compare them with theoretical predictions from perturbation theory, while in Sec.~\ref{sec:bisph} we show the halo bispectrum measurements and derive the corresponding halo bias functions.  In Sec.~\ref{sec:conclusions} we conclude summarising  the results obtained.

\section{Cosmological perturbations in the presence of massive neutrinos}
\label{sec:linear_nu}

\subsection{Linear evolution}

In the early Universe neutrinos are kept in equilibrium with baryons and photons via weak interactions, eventually decoupling at a temperature of about $T_{\rm dec} \sim 9\times 10^9\;\rm K$, when their interaction rate becomes comparable to rate of cosmological expansion. After decoupling, neutrinos free-stream with large thermal velocities described by a Fermi-Dirac distribution. As the Universe expands neutrinos slow down, becoming non relativistic at a typical redshift of
\begin{equation}
1+z_{nr} \simeq 1980\,\frac{m_{\nu,i}}{1 \text{ eV}}\,,
\end{equation}
where $m_{\nu,i}$ represents the neutrino mass eigenstate $i$ in electronvolt. As non-relativistic particles, while contributing to the total matter density the fraction
\begin{equation}
f_\nu\equiv\frac{\Omega_\nu}{\Omega_m}=\frac{1}{\Omega_{m,0}h^2}\frac{\sum_i\,m_{\nu,i}}{93.14~{\rm eV}}\,,
\end{equation}
they still travel much longer distances,of the order of tens of Megaparsecs, compared to standard cold dark matter (CDM) particles. We define a free-streaming length $\lambda_{\rm fs} \propto v_{th}/ H(t)$, with $v_{th}$ being the characteristic thermal velocity of neutrino particles. Below this scale we expect a suppression of the neutrino density fluctuations with respect to CDM ones. On scales $\lambda\gg\lambda_{\rm fs}$ we expect neutrinos to behave as CDM. In Fourier-space, the wavenumber corresponding to $\lambda_{\rm fs}$ can be written as
\begin{equation}
k_{\rm fs}\simeq\frac{0.908}{\sqrt{1+z}}\,\sqrt{\Omega_{m,0}}\,\frac{m_{\nu,i}}{1~{\rm eV}}\, h \, {\rm Mpc}^{-1}\,.
\end{equation}

For simplicity we denote with the subscript ``{\em c}'' quantities related to the CDM {\em and} baryonic matter components as no distinction will be made between the two.  We refer to such component generically as ``cold'' matter, as opposed to the neutrinos contribution. Total matter perturbations are therefore given by the weighted sum
\begin{equation}\label{eq:deltam}
\delta_m =(1- f_{\nu})\delta_c +f_{\nu} \delta_{\nu}\, .
\end{equation}
with $ \delta_{\nu}$ denoting neutrinos perturbations.

On scales smaller than $\lambda_{\rm fs}$ neutrinos do not provide support to the Newtonian gravitational potential, and we expect the growth of cold matter perturbations to be different with respect to a standard cosmology. It is possible to show \citep{HuEisensteinTegmark1998} that, in linear theory, for $k\gg k_{\rm fs}$, assuming a constant $\Omega_{m}$ and a constant amplitude for primordial fluctuations, the ratio of the cold matter power spectra in a cosmology with $f_\nu\ne0$ to the massless neutrino case is given by
\begin{equation}\label{eq:suppPcc}
\frac{P_{cc}^{f_\nu \neq 0 }(k)  }{P_{cc}^{f_\nu = 0 } (k) }\, \stackrel{k\gg k_{\rm fs}}{ \simeq}\, 1- 6\, f_{\nu}.
\end{equation}
The total matter power spectrum, from eq.~\ref{eq:deltam}, can be written as
\begin{equation}\label{eq:Pmm}
 P_{mm}(k) = (1-f_{\nu})^2\,P_{cc}(k) + 2f_{\nu}(1-f_{\nu})P_{\nu c}(k)+ f_{\nu}^2 P_{\nu\nu}(k) \,,
\end{equation}
with $P_{\nu c}(k)$ denoting the cold matter-neutrinos cross-power spectrum. Neglecting neutrino perturbations at small scales we obtain the well-known limit \citep{HuEisensteinTegmark1998}
\begin{equation}\label{eq:suppPmm}
\frac{P_{mm}^{f_\nu \neq 0 }(k)  }{P_{mm}^{f_\nu = 0 } (k) }\, \stackrel{k\gg k_{\rm fs}}{ \simeq}\, 1- 8 ~f_{\nu}\,.
\end{equation}

\subsection{Nonlinear evolution}

Numerical simulations \citep{BrandbygeEtal2008, VielHaehneltSpringel2010, BirdVielHaehnelt2012, WagnerVerdeJimenez2012, InmanEtal2015,YuEtal2017} have shown that the suppression expected in linear theory according to eq.~\ref{eq:suppPcc} and \ref{eq:suppPmm} is enhanced at the nonlinear level, as expected from predictions in perturbation theory \citep{SaitoTakadaTaruya2008, Wong2008}, with important consequences for the constraints on neutrino masses \citep{SaitoTakadaTaruya2008, AudrenEtal2013}.

On the other hand, a direct consequence of the nonlinear evolution of matter fluctuations is given by the emergence of non-Gaussianity, quantified, in the first place by a non-vanishing matter bispectrum. Denoting the cold matter fraction as $f_c\equiv 1- f_\nu$, the analogue of eq.~\ref{eq:Pmm} for the total matter bispectrum is given by
\begin{eqnarray}\label{eq:Bmmm}
B_{mmm}(k_1,k_2,k_3) & = & f^3_c\,B_{ccc}(k_1,k_2,k_3)+f_c^2\,f_\nu\,B_{cc\nu}^{(s)}(k_1,k_2,k_3)\nonumber \\
& & + f_c\,f_\nu^2\,B_{\nu\nu c}^{(s)}(k_1,k_2,k_3)+ f_\nu^3\,B_{\nu\nu\nu}(k_1,k_2,k_3)
\end{eqnarray}
where we introduced the symmetrized versions of the cross cold-cold-neutrino bispectrum $B_{cc\nu}^{(s)}$ and neutrino-neutrino-cold bispectrum $B_{\nu\nu c}^{(s)}$ defined, respectively, as
\begin{eqnarray}\label{eq:Bccn}
\delta_D({\bf k}_{123})\, B_{cc\nu}^{(s)}(k_1,k_2,k_3) & \equiv &
\left[\langle \delta_c({\bf k}_1)\delta_c({\bf k}_2)\delta_\nu({\bf k}_3)\rangle\right.\nonumber\\
& & \left.+\langle \delta_c({\bf k}_3)\delta_c({\bf k}_1)\delta_\nu({\bf k}_2)\rangle+\langle \delta_c({\bf k}_2)\delta_c({\bf k}_3)\delta_\nu({\bf k}_1)\rangle\right]
\end{eqnarray}
and
\begin{eqnarray}\label{eq:Bnnc}
\delta_D({\bf k}_{123})\, B_{\nu\nu c}^{(s)}(k_1,k_2,k_3) & \equiv &
\left[\langle \delta_c({\bf k}_1)\delta_\nu({\bf k}_2)\delta_\nu({\bf k}_3)\rangle\right.\nonumber\\
& & \left.+\langle \delta_c({\bf k}_3)\delta_\nu({\bf k}_1)\delta_\nu({\bf k}_2)\rangle+\langle \delta_c({\bf k}_2)\delta_\nu({\bf k}_3)\delta_\nu({\bf k}_1)\rangle\right]\,.
\end{eqnarray}
where we made use of the notation $k_{ij}\equiv{\bf k}_i+{\bf k}_j$ for vectors sums.

Although neutrinos cluster very weakly below the free streaming scale, on larger scales they behave like CDM. This means that assuming {\em linear} neutrino perturbation on {\em any} scale results in a lack of power on the large-scale bispectrum, which is the outcome of the nonlinear evolution of all matter components. As a consequence, numerical simulations treating neutrinos only at the linear level on the grid (or not having neutrino fluctuations at all) will predict the wrong bispectrum as well as any other higher-order correlation function.
On the other hand the two fluids behave similarly only in the very low-$k$ regime, and therefore we expect next -to-leading order, {\em i.e.}~ quadratic, correction to capture most of the neutrino contributions to the bispectrum terms in the above equations.
In analogy with the work in  \citep{SaitoTakadaTaruya2008, CastorinaEtal2015} for the matter power spectrum in cosmologies with massive neutrinos we assume neutrinos to contribute only at tree-level in the PT calculation, whereas we compute CDM density perturbations up to the 1-loop level.
The analysis in \cite{CastorinaEtal2015} showed that this simple approach reproduces the measurements of the power spectrum in simulations to 1\% accuracy. The goal of this section is to test on simulations whether the same assumptions hold true for the bispectrum, within the limits of the precision of our measurements.

At tree-level in PT both the cold matter and the neutrino perturbations in eq.~\ref{eq:Bnnc} contribute to the neutrino-neutrino-cold matter component $B_{\nu\nu c}^{(s)}$, such that
\begin{equation}
B^{(s),tree}_{\nu\nu c}(k_1,k_2,k_3) = B_{\nu\nu c, 112}^{(s)}(k_1,k_2,k_3)  +B_{\nu\nu c, 121}^{(s)}(k_1,k_2,k_3)  + B_{\nu\nu c, 211}^{(s)}(k_1,k_2,k_3) \,,
\end{equation}
where the subscripts ``112'' indicate the order of the perturbations $\delta_\nu$, $\delta_\nu$ and $\delta_c$, respectively. It is easy to see that
\begin{align}
\label{eq:PTBnnc}
& B_{\nu\nu c, 211}^{(s),}(k_1,k_2,k_3) = 2 \,F_2({\bf k}_1,{\bf k}_2) P_{\nu c}^L(k_1) P_{\nu \nu}^L(k_2) + \rm{2~perm}\;\, \\
\label{eq:PTBnnc2}
& B_{\nu\nu c, 112}^{(s),}(k_1,k_2,k_3) =2 \,F_2({\bf k}_1,{\bf k}_2) P_{\nu c}^L(k_1) P_{\nu c}^L(k_2) + \rm{2~perm}\;\,
\end{align}
and $B_{\nu \nu c , 121}^{(s)} =  B_{\nu\nu c, 211}^{(s)}$ (we are assuming the ordering of the subscript to correspond to the perturbations $\delta_c$, $\delta_c$ and $\delta_\nu$ in this order). Setting neutrino perturbations to their linear value on {\em all scales} leads to $B_{\nu \nu c , 121}^{(s)} =  B_{\nu\nu c, 211}^{(s)} = 0$, resulting, in turn, in a $\mathcal{O}(1)$ bias in $B_{\nu\nu c}$ at scales $k<k_{\rm{fs}}$. At the one-loop level, the only contribution is coming from the fourth-order correction to $\delta_c$ so that we only have
\begin{equation}
B_{\nu\nu c, 114}^{(s)}(k_1,k_2,k_3) = 4\,P_{\nu c}^L(k_1)\,P_{\nu c}^L(k_2)\, \int d^3q\,F_4({\bf q},-{\bf q},{\bf k}_1,{\bf k}_2)\,P_{cc}^L+{\rm 2~perm.}\,.
\end{equation}
The full prediction up to one-loop would then be given by
\begin{equation}
B_{\nu\nu c}^{(s)}\simeq B_{\nu\nu c}^{(s),tree}+B_{\nu\nu c, 114}^{(s)}\,.
\end{equation}
For the cold-cold-neutrino component $B_{cc\nu}^{(s)}$  the tree-level expression is the same of eq.~\ref{eq:PTBnnc} with the replacement $\nu\leftrightarrow c$ in all the terms.
At one-loop we have now three types of contributions,
\begin{eqnarray}
B_{cc\nu, 411}^{(s)}  = B_{cc\nu, 141}^{(s)} & = & 4\,\left[P_{\nu c}^L(k_1)\,P_{c c}^L(k_2)+P_{\nu c}^L(k_2)\,P_{c c}^L(k_1)\right]\,\nonumber\\
& & \times \int d^3q\,F_4({\bf q},-{\bf q},{\bf k}_1,{\bf k}_2)\,P_{cc}^L(q)+{\rm 2~perm.}\,,\\
B_{cc\nu, 321}^{(s)}  & = & 6\,P_{\nu c}^L(k_1) \int d^3q\,F_3({\bf k}_1,{\bf k}_2-{\bf q},{\bf q})\,F_2({\bf k}_2-{\bf q},{\bf q})\,P_{cc}^L(|{\bf k}_2-{\bf q}|)\,P_{cc}^L(q)\nonumber\\
& & +{\rm 2~perm.}\,
\end{eqnarray}
with the additional $B_{cc\nu, 231}^{(s)}$ term obtained by exchanging ${\bf k}_1$ with ${\bf k}_2$, and
\begin{equation}
B_{cc\nu, 312}^{(s)}   =  6\,P_{c c}^L(k_1) \int d^3q\,F_3({\bf k}_1,{\bf k}_2-{\bf q},{\bf q})\,F_2({\bf k}_2-{\bf q},{\bf q})\,P_{c\nu}^L(|{\bf k}_2-{\bf q}|)\,P_{cc}^L(q)+{\rm 2~perm.}\,
\end{equation}
with an analogous $B_{cc\nu, 132}^{(s)}$.
Up to one-loop correction we have then
\begin{equation}
B_{cc\nu}^{(s)}\simeq B_{cc \nu}^{(s),tree} + 2 B_{cc\nu, 411}^{(s)}+B_{cc \nu, 321}^{(s)}+B_{cc \nu, 231}^{(s)}+B_{cc \nu, 312}^{(s)}+B_{cc \nu, 132}^{(s)}\,.
\end{equation}
The $B_{ccc}$ is then given by the usual PT expressions in terms of the cold matter linear power spectrum $P_{cc}^L$ \citep{BernardeauEtal2002}.
We notice right away that one-loop corrections to the mixed contributions $B_{\nu\nu c}^{(s)}$ and $B_{cc\nu}^{(s)}$, as we will see in section~\ref{sec:bispm}, are essentially irrelevant. More important, instead, are the implications of the linear neutrinos approximation on the tree-level prediction, since the relevant short-comings will take place at large scales.
We can also anticipate that assuming linear neutrino perturbations will result in an error of order  $f_\nu$ on scales larger than the free-streaming scale, which could exceed the \% level for realistic value of neutrino masses. This is shown in Fig.~(\ref{fig:linear}) for $m_\nu = 0.53$ eV at $z=0$, where we plot, within tree-level PT, the relative contribution of terms up to $\mathcal{O}(f_\nu)$ to the total matter bispectrum of equilateral configurations. The assumption of linear neutrinos on all scales indeed yields an inconsistent result at low $k$, $B_{cc\nu}$ is underestimated by more than a factor of 2, with biases of several \%s on $B_{mmm}$.

\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig_lin.pdf}
\end{center}
\caption{\label{fig:linear} Relative contributions to the equilateral configurations of the total matter bispectrum from the different terms in eq.~(\ref{eq:Bmmm}) up to $\mathcal{O}(f_\nu)$ for $m_\nu = 0.53$ eV at $z=0$. The dashed line shows the assumption neutrinos are linear on all scales. }
\end{figure}

\section{The DEMNUni simulations suite}
\label{sec:nbody}

We make use of  the ``Dark Energy and Massive Neutrino Universe'' (DEMNUni) suite of N-body simulations \cite{CarbonePetkovaDolag2016},
representing one of the best set of simulations of massive neutrino cosmologies both in terms of mass resolution and volume.
A complete description can be found also in \cite{CastorinaEtal2015}, here we briefly summarize the main details.

All the simulations assume a baseline cosmology according to the
{\it Planck}\ results~\cite{PLANCK2013parameters}, namely a flat $\Lambda$CDM\ model
with $ h = 0.67 $ as Hubble parameter, $n_s = 0.96$  as primordial spectral index, and
$A_s = 2.1265 \times 10^{-9}$ for the amplitude of initial scalar perturbations.
This implies that simulations with massive neutrinos have lower value of $\sigma_8$ with respect to the $\Lambda$CDM case.
The total matter energy density and the baryonic energy density are set to $\Omega_m = 0.32$ and $\Omega_b = 0.05$ for all cosmologies,
while the relative energy densities of cold dark matter, $\Omega_c$ (and neutrinos, $\Omega_\nu$)
vary for each model as $\Omega_c =0.27$,  $0.2659$,  $0.2628$ and  $0.2573$, for $m_\nu = 0$, $0.17$, $0.3$ and $0.53$ eV, respectively.

The DEMNUni simulations have been performed using the tree particle
mesh-smoothed particle hydrodynamics (TreePM-SPH) code
\textsc{gadget-3}~\cite{SpringelEtal2005}, specifically modified by~\cite{VielHaehneltSpringel2010} to
account for the presence of massive neutrinos.
They are characterised by a softening length
$\varepsilon=20 \, h^{-1} \, {\rm kpc}$, start at $z_{in}=99$, and have being performed in a cubic box of side $L = 2000 \, h^{-1} \, {\rm Mpc}$,
containing  $N_p = 2048^3$ CDM particles, and an equal number of neutrino particles when $m_\nu \neq 0 $.
These features make the DEMNUni set suitable for the analysis of different cosmological probes,
from galaxy-clustering, to weak-lensing, to CMB secondary anisotropies.

Halos and sub-halo catalogs have been produced for each of the 62 simulation particle snapshots, via the friends-of-friends (FoF) and SUBFIND algorithms
included in \textsc{gadget-3}~\cite{SpringelYoshidaWhite2001,DolagEtal2009}. The linking length was set to be $1/5$ of the mean inter-particle
distance \citep{DavisEtal1985} and the minimum number of particles to identify a parent halo was set to 32,
thus fixing the minimum halo mass to $M_{\rm FoF}\simeq2.5\times 10^{12}$$\,h^{-1}$ $M_\odot$.
In this work we consider three lower threshold for the halo mass, $M > 10^{13}$$\,h^{-1}$ $ M_\odot$ , $M >3\times 10^{13}$$\,h^{-1}$ $ M_\odot$
and $M > 10^{14}$$\,h^{-1}$ $ M_\odot$ and three values for the snapshot redshift,   $z = 0$,  $z = 0.5$, $z = 1$.

\section{The matter bispectrum}
\label{sec:bispm}

We measure the total matter bispectrum $B_{mmm}$ along with all its individual components $B_{ccc}$, $B_{cc\nu}^{(s)}$, $B_{\nu\nu c}^{(s)}$ and $B_{\nu\nu\nu}$ as defined by eq.~(\ref{eq:Bmmm}). For all components we consider all triangular configurations defined by discrete wavenumbers multiples of $\Delta k=3 k_f$ with $k_f\equiv 2\pi/L$ being the fundamental frequency of the box, up to a maximum value of $0.38\, h \, {\rm Mpc}^{-1}$.  The estimator of the bispectrum is given by
\begin{equation}
\hat{B}(k_1,k_2,k_2)\equiv\frac{k_f^3}{V_B(k_1,k_2,k_3)}\int_{k_1}\!\! d^3q_1\int_{k_2} \!\!d^3q_2\int_{k_3} \!\!d^3q_3\,\delta_D({\bf q}_{123})\,\delta_{{\bf q}_1}\,\delta_{{\bf q}_2}\,\delta_{{\bf q}_3}
\end{equation}
where the integrations are taken on shells of size $\Delta k$ centered on $k_i$ and where
\begin{equation}
V_B(k_1,k_2,k_2)\equiv \int_{k_1}\!\! d^3q_1\int_{k_2} \!\!d^3q_2\int_{k_3} \!\!d^3q_3\,\delta_D({\bf q}_{123}) \simeq   8\pi^2\ k_1 k_2 k_3 \Delta k^3
\end{equation}
is a normalisation factor counting the number of fundamental triangles in a given triangle bin. Its implementation is based on the algorithm described in \citep{Scoccimarro2015} and taking advantage of the aliasing reduction technique of \citep{SefusattiEtal2016}. As only one realisation for each cosmology is available, all error bars shown correspond to the Gaussian prediction given, for a generic bispectrum, by \citep{Scoccimarro2000B},
\begin{equation}
\Delta B^2 (k_1, k_2, k_3)  \simeq s_B \frac{k^3_f}{V_B }  P(k_1)P(k_2) P(k_3)\,,
\label{eqerror}
\end{equation}
with $s_B = 6, 2, 1$ for equilateral, isosceles and scalene triangles respectively.

Figure \ref{fig:componentsall} shows the  measurements at $z=0$ of all configurations for all components, {\em rescaled} by the proper factors as a function of the neutrino fraction, according to eq.~(\ref{eq:Bmmm}), in order to  assess directly the relative contribution to the total matter bispectrum. The bottom half of each panel shows the ratio of each component to the total $B_{mmm}$. Triangles are ordered with increasing $k_1$ and assuming $k_1\ge k_2\ge k_3$ so that all configurations shown correspond to large-scales with $k_1\le 0.1\, h \, {\rm Mpc}^{-1}$. Data points from N-body simulations are compared to tree-level predictions in PT. Theoretical predictions are computed for ``effective''  values of the wavenumbers defined, for a given configuration of sides $k_1$, $k_2$ and $k_3$  by
\begin{equation}
\tilde{k}_{1,23}\equiv \frac1{V_B}\int_{k_1}\!\! d^3q_1\,q_1\,\int_{k_2} \!\!d^3q_2\int_{k_3} \!\!d^3q_3\,\delta_D({\bf q}_{123})\,,\end{equation}
and similarly for the other two values. Differences with respect to evaluations at the center of each $k$-bin are marginally relevant only for the largest scales.

\begin{figure}[t!]
\begin{center}
\includegraphics[width=.9\textwidth]{fig_All.pdf}
\end{center}
\caption{\label{fig:componentsall} Measurements of all the components of the total matter bispectrum $B_{mmm}(k_1,k_2,k_3)$ at $z=0$, properly weighted, compared with the tree-level prediction in PT. All triangular configurations re ordered with increasing $k_1$ and assuming $k_1\ge k_2\ge k_3$. In each panel, the bottom-half shows the relative contribution of each component to $B_{mmm}$ (only the relevant ones, contributing above the $0.1\%$ level are shown). Vertical lines correspond to equilateral configurations. }
\end{figure}

The first, rather obvious, observation is that the only relevant, {\em i.e.}~ above 1\% level, contribution to the total matter bispectrum $B_{mmm}$, in addition to the cold matter bispectrum $B_{ccc}$, is given by the cross-bispectrum $B_{cc\nu}^{(s)}$ which is of $\mathcal{O}(f_\nu)$. Therefore a proper theoretical description of the matter bispectrum in massive neutrinos cosmologies should focus on both these two components. Here we show a first comparison with tree-level PT, providing rather accurate predictions to the cold matter component $B_{ccc}$ over the scales shown in the figure. Predictions for the $B_{cc\nu}^{(s)}$ and $B_{\nu\nu c}^{(s)}$ are very well described by the assumption neutrino contribute only at tree-level in PT.

As we consider smaller scales, in the quasi-linear regime, the tree-level approximation becomes more accurate for the cross-bispectra of cold matter and neutrinos because of small-scale suppression of neutrino perturbations. On the other hand, we expect further nonlinear (one-loop) corrections to become important only for the cold matter contribution $B_{ccc}$.  This is the natural extention to higher-order correlation functions of previous results for the total matter power spectrum, where linear theory was sufficiently accurate to describe the neutrinos and cross neutrino-cold matter components $P_{\nu\nu}$ and  $P_{c\nu}$, respectively \citep{SaitoTakadaTaruya2008, BlasEtal2014, CastorinaEtal2015}.

Figure~\ref{fig:BcEq} shows the measurements of the cold matter bispectrum, $B_{ccc}$, at $z = 0.5$ (left panel) and $z=1$ (right panel), for equilateral triangles (left panel). We compare with analytical predictions at  tree (dashed) and 1-loop (continuous) level in PT \citep{BernardeauEtal2002,Sefusatti2009}. Different colors indicate different value of the sum of neutrino masses , $m_\nu =  0,\,0.3,\, 0.53\,\text{eV}$  (black, red and green respectively).

\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.9\textwidth]{fig_Bccc_eq.pdf}
\includegraphics[width=0.9\textwidth]{fig_Qccc_eq.pdf}
\end{center}
\caption{\label{fig:BcEq} Top panels: equilateral configurations of the cold matter bispectrum, $B_{ccc}(k,k,k)$, compared with tree-level (dashed curves) and one-loop (continuous curves) predictions in PT. Bottom panels: same comparison for the {\em reduced} cold matter bispectrum $Q_{ccc}(k,k,k)$. Left panels show the results at $z=0.5$, right panels at $z=1$. In addition to the measurements of $B$ or $Q$, we plot  the residuals with respect to the one-loop predictions (middle panel) and the ratio between the $m_\nu\ne0$ cosmologies to the corresponding massless neutrino case (bottom panel). }
\end{figure}

The analytic curves have been obtained according to the prescription as in \citep{CastorinaEtal2015}; we consider the perturbative kernels in cosmology with massive neutrinos to have the same form as in  $\Lambda$CDM cosmology and we assume all the effects induced by neutrinos encoded in the linear power spectrum. Our assumptions are justified by previous studies \citep{SaitoTakadaTaruya2009, CastorinaEtal2015} which showed this approximation to work better than a $ \%$ on the power spectrum analysis.
Middle panels show the ratio between the data for the three different cosmologies ($\Lambda$CDM  and $m_\nu = 0.53$ eV) with respect to their 1-loop predictions (black and green points);
we also plot the ratio between tree-level and 1-loop prediction with dashed lines. The approximation of neglecting the effects of massive neutrinos on the 1-loop CDM bispectrum other than the different linear theory $P_{cc}(k)$, provides the same level of agreement we find in the $\Lambda$CDM case.
In the bottom panels we present the ratio between the bispectrum measured for $m_\nu \ne  0$ with respect to the  $\Lambda$CDM measurement;  continuous and dashed lines denote instead the same ratio as predicted at the 1-loop and tree-level in PT. The comparison with the power spectrum analysis reveals, as expected, that equilateral configurations are roughly two times more sensitive than the power spectrum to massive neutrinos. We also notice that the suppression of CDM bispectrum with respect to the standard case does not evolve significantly with redshift, in agreement with well known results at the two-point function level. As expected \citep{ScoccimarroEtal1998, SefusattiCrocceDesjacques2010} one-loop predictions in standard PT tend to overestimate the measurements in equilateral configurations at low redshift. We find a good agreement up to $k=0.3\, h \, {\rm Mpc}^{-1}$ at $z=0.5$, but it should be kept in mind that the precision of our measurement is roughly 10\% at these scales.

A better agreement with measurements can clearly be found in the context of the Effective Field Theory of the Large-Scale Structure \citep{CarrascoHertzbergSenatore2012}, see \citep{AnguloEtal2015B} for its application to the matter bispectrum.
We limit ourselves to compare the accuracy of standard PT predictions in massive neutrino cosmology with known results for the $\Lambda$CDM case.

\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.9\textwidth]{fig_Bccc_sq.pdf}
\includegraphics[width=0.9\textwidth]{fig_Qccc_sq.pdf}
\end{center}
\caption{\label{fig:BcSq} Same as figure~\ref{fig:BcEq} but for squeezed configurations $B_{ccc}(k_l,k,k)$ with fixed $k_l=0.009\, h \, {\rm Mpc}^{-1}$ as a function of $k$.}
\end{figure}

More generally, the suppression of the amplitude of the bispectrum in cosmology with massive neutrinos compared to a standard cosmological model is a function of the triangle shape.
For instance it is easy to see that squeezed triangle configurations, $B_{mmm}(q, k , k )$  with $q\ll k$ are less affected by massive neutrinos.
The phyisical interpretation of this is simple: for significantly large scales, $q$, the neutrinos behaves like CDM and therefore the relative suppression with respect to the $\Lambda CDM$ case is reduced compared to other triangular configurations.
At a scale where $q \ll k_{fs}$  then $\delta_{\nu}(q)\simeq \delta_{c}(q)$ and one has $ B_{\nu cc}(q , k , k ) \simeq  B_{c cc}(q , k , k )$ on all scales, even below free-streaming.
While our perturbation theory calculations provide a reasonable fit to the measurements in the N-body, our analysis is in disagreement with the prediction of \citep{LeviVlah2016} who have analytically found that squeezed configurations show the largest neutrinos-induced suppression. Squeezed configurations are shown in Figure~\ref{fig:BcSq} with the same notations as Figure~\ref{fig:BcEq}. The overall accuracy of PT predictions is similar to the equilateral case and we can notice, again, a significant improvement of one-loop predictions over tree-level ones.

\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.9\textwidth]{fig_Bccc_k1_0p24_k2_0p14.pdf}
\includegraphics[width=0.9\textwidth]{fig_Qccc_k1_0p24_k2_0p14.pdf}
\end{center}
\caption{\label{fig:BcSc} Same as figure~\ref{fig:BcEq} but for scalene configurations with fixes sides $k_1=0.14\, h \, {\rm Mpc}^{-1}$ and $k_2=0.23\, h \, {\rm Mpc}^{-1}$ as a function of the angle between ${\bf k}_1$ and ${\bf k}_2$. }
\end{figure}

As another example of the effects massive neutrinos have on the CDM bispectrum, in Fig. \ref{fig:BcSc} we present the bispectrum for scalene triangles as a function of the angle $\theta$ between the two sides for all the cosmologies at $z =0.5$ (left panel) and redshift $z= 1.0$ (right panel).  We select triangle configurations in the mildly nonlinear regime, with $k_1 = 0.14\;h\;Mpc^{-1}, k_2 = 0.23\;h\;Mpc^{-1} $. The labels, colors and plots order correspond to those in figure \ref{fig:BcEq}.  Differently from the previous cases, the bispectrum in massive neutrino cosmologies is suppressed on all scales shown. PT is able to reproduce the measurements in the different cosmologies quite well at $z=1$ and large values of $\theta$ (the ``squeezed limit'') while it shows the usual overestimation, about 10-15\%, for more equilateral triangles and lower redshift.

An additional way to assess the effect of massive neutrinos on the bispectrum and compare it to the effect on the power spectrum, is to compute the reduced bispectrum $Q$ defined as
\begin{equation}
Q(k_1,k_2, k_3) =  \dfrac{B(k_1, k_2, k_3)}{ P (k_1)P (k_2) + P (k_1)P (k_3) + P (k_2)P (k_3)}.
\end{equation}
This quantity, at tree-level in PT, does not depend on the initial amplitude of the linear fluctuations (or $\sigma_8$ in a $\Lambda$CDM cosmology), including the suppression due to neutrinos in linear theory, and it highlights the different level of nonlinearity in the bispectrum w.r.t. the power spectrum.
In all the figures~\ref{fig:BcEq}, \ref{fig:BcSq}  and \ref{fig:BcSc} the bottom part shows the reduced bispectrum for the choosen configurations at $z = 0.5$ and 1. Again, top panels show measurements for $Q$ compared with  tree-level and one-loop predictions; middle panels show the residuals with respect to  one-loop, while in the bottom panels we display the ratios between the reduced bispectrum measured for $m_\nu \ne  0$ with respect to $\Lambda$CDM. The errors are computed by propagating  $\Delta B$ and $\Delta P$ errors neglecting the cross-correlation between $P$ and $B$.

The  small deviations we see in the bottom panels among different cosmologies indicate that any new, nonlinear neutrinos signature specific for the bispectrum is significantly small at scales $k>0.2\, h \, {\rm Mpc}^{-1}$. This implies that the bispectrum alone is not able to probe new physical effects induced by massive neutrinos in the clustering of dark matter; however it still represents a relevant asset as it breaks part of the degeneracy between the cosmological parameters, when combined with the power spectrum.
 One-loop predictions for $Q$  are well within the precision of our measurements. They are also qualitatively consistent with results for the relative effect of neutrino masses shown in the bottom panels, with the exception of the squeezed configurations at small scales where they overpredict significantly a neutrino signature not detectable in the measurements. These are, however, few percent effects, too small to be properly investigated with the limited statistic of a single set of simulations.

\section{The halo bispectrum}
\label{sec:bisph}

\subsection{Bias modeling}

According to the Eulerian bias model, at large scales,  the halo density field $\delta_h$ can be locally described as a function of the underlying smoothed density contrast $\delta$,  \citep{FryGaztanaga1993, BernardeauEtal2002, DesjacquesJeongSchmidt2016}.
In particular if $\delta \ll 1$, we can model  $\delta_h$ as a taylor expansion in $\delta$,
\begin{equation}
\delta_h = \sum_{n} \frac{b_n}{n!}\delta^n,
\label{eulocbias}
\end{equation}
where the $b_n$ correspond to the bias parameters.
In this framework, the halo power spectrum, $P_{hh}$ or the halo-matter cross correlation, at very large scales, are related to the matter power spectrum $P(k)$, through
\begin{equation}
P_{hh}(k) = b_1^2 P(k)\,\quad P_{hm} = b_1 P(k)
\label{eq:halop}
\end{equation}
In a local Eulerian bias model the tree-level halo bispectrum reads
\begin{equation}
B_{hhh} (k_1, k_2, k_3) =   b_1^3 B (k_1, k_2, k_3) + b_2 b_1^2 \Sigma_{123} (k_1, k_2, k_3) ,
\label{halobisp}
\end{equation}
with $B$ being the matter bispectrum, $\Sigma_{123} \equiv P(k_1)P(k_2) + 2~\rm cyc$ and $b_2$  a quadratic bias parameter. The equation above shows that a measurements of the halo bispectrum on large scale could be used not only to constrain cosmological parameters, but also to break the degeneracy between the bias parameters and the amplitude of fluctuations in a power spectrum analysis.

It is well known,  see {{{\em e.g.}}} \citep{Scoccimarro2000B, PollackSmithPorciani2012},  that fitting  $B_{hhh}$ with model in eq.~\ref{halobisp} yields different values of $b_1$ with respect to ones obtained from the halo power spectrum, modeled as in eq.~\ref{eq:halop}. Recent works on bias modelling \citep{BaldaufEtal2012, ChanScoccimarroSheth2012, ShethChanScoccimarro2013}  have shown the intrinsic mistake in considering the bias to be deterministic and local: the nonlinear evolution induced by gravity introduces new, non-local bias contributions proportional to operators built from derivatives of the density field and/or the gravitational potential. In this framework the halo density, at second order in the bias expansion,  takes the form
\begin{equation}
\label{eq:brel}
\delta_h = b_1 \delta + \frac{b_2}{2} \delta^2 + \gamma_2\,\mathcal{G}_2,
\end{equation}
where $\mathcal{G}_2  $ is defined as
\begin{equation}
\mathcal{G}_2 \equiv (\nabla_{ij} \Phi_v)^2 -  (\nabla_{ij}\Phi_v)^2\,,
\end{equation}
with $\Phi_v$ being the velocity potential such that ${\bf v} = \nabla \Phi_v$.
The resulting tree-level halo bispectrum reads
\begin{equation}
B_{hhh} (k_1, k_2, k_3) =   b_1^3 B(k_1, k_2, k_3) + b_2 b_1^2 \Sigma_{123}(k_1, k_2, k_3)   + 2 \gamma_2 b_1^2 K_{123}(k_1, k_2, k_3) \,,
\label{halobispnonloc}
\end{equation}
where $K_{123} \equiv (\mu_{12} -1) P(k_1)P(k_2) + 2\, \rm cyc $, $\mu_{12}$ the cosine of the angle between ${\bf k}_1$ and ${\bf k}_2$.

This model has been widely tested in $\Lambda$CDM cosmologies, and in this section we would like to extend these results to a cosmological model that include massive neutrinos. As first noted in \citep{CastorinaEtal2014}, the linear bias in a cosmology with massive neutrinos is scale independent only if the CDM power spectrum appears on the right hand side of \ref{eq:halop}. This is a consequence of the fact that neutrinos do not cluster on halos or galaxies scales, and therefore fluctuations in the number of halos and galaxies respond to the CDM field only.

Given this result, we will model the halo bispectrum and then fit for the bias parameters in the next section assuming the halo bias relation in \ref{eq:brel} is written in terms of the CDM field only.  Recovering the same linear bias of the power spectrum from the bispectrum would yield a confirmation of the correctness of the argument for linear bias in \citep{CastorinaEtal2014}.

\subsection{Fitting procedure}

\begin{figure}[t]
\begin{center}
\includegraphics[width=.9\textwidth]{fig_chi_k2_bs.pdf}
\end{center}
\caption{ \label{fi2}
Tthe best fits bias parameters in $\Lambda$CDM framework (left panel) and neutrino cosmologies $m_\nu = 0.53 \;eV $,  (right panel), assuming a local  and  non local bias model, at $z= 0.5$.
Green lines indicate the measurements of  $b_1$  $b_2$  for the local model, (top and middle-top panels). Blue color indicates  $b_1$,  the \textit{effective} $b_2$ and the non local corretion $\gamma_2$ (middle-bottom panels) to the bias model. Black lines correspond  $b_1$ as measured from the halo power spectrum $P_{hh}$.
Grey color shows the best fits for $b_2$ and $\gamma_2 $  fixing  $b_1$  from the power spectrum fits.
In the bottom panels we show the $\chi^2$ related to the different fitting formulas.
}
\end{figure}

We measure the halo bispectrum in a $\Lambda$CDM cosmology and in cosmologies with all the three different values of neutrino masses, $m_\nu = 0.17, 0.3, 0.53$ eV. We do not consider a part of the measurements for the high-mass threshold,  $M > 10^{14} M_\odot/h$, and redshift $z = 1.0 $ since they are highly affected by shot-noise contributions, which for the halo bispectrum take the following form
\begin{equation}
\hat{B}_{hhh}(k_1,k_2,k_3) = B_{hhh}(k_1,k_2,k_3) + \frac{1}{\bar{n}}[P_{hh}(k_1) + 2 \,\text{cyc}] + \frac{1}{\bar{n}^2}
\end{equation}

We compare the best fit measurements of $b_1$ and $b_2$ assuming a local model for the bias  the values for  $b_1$, $b_2$ and $\gamma_2$ when assuming the non local model.  At the level of  two-point statistics we fit a linear model to the halo-matter cross-correlation, $P_{hm}(k)$, as a function of the maximum wavenumber $k_{max}$.  For the bispectrum we compute the likelihood $\mathcal{L} $ up to a value $k_{max}$ for the largest side for each triangle configuration. In the case of the non local model we have,
\begin{equation}
\ln \mathcal{L} =\sum_{k }^{ k_{max}} \frac{   B_{hhh} - b_1^3 B_c - b_2 b_1^2 \Sigma_{123}  - 2 \gamma_2 b_1^2 K_{123} - \alpha_1(k_1^2 + k_2^2) (P_1 P_2) + 2\rm\;cyc}{\Delta B^{2}_{hhh} }\,,
 \end{equation}
whith $\Delta B^{2}_{hhh}$ as Eq. (\ref{eqerror}). A similar expression is used to estimate the linear bias from the halo-matter cross power spectrum, for which we also assume Gaussian covariance. Possible, unaccounted scale-dependences in the modeling are marginalized over the amplitude $\alpha$ of a generic $k^2$-like term in both the likelihood for the power spectrum and the bispectrum. This term will take care of higher loop corrections and scale dependent bias on large scales \cite{EFT,Desjacques}. All the fits have been computed using the downhill simplex method, see {{{\em e.g.}}} \citep{PressEtal1992}. We determined the errors on the best-fit values using the Fisher matrix prescription, see for instance \citep{TegmarkTaylorHeavens1997}.
In order to compare the results for $b_2$  from local {\em vs} non local models,  we introduce an effective local quadratic bias, $b_{2, \rm eff} = b_2 - 4/3 \gamma_2$, \citep{ChanScoccimarro2012},  in case of the non local prescription, corresponding to the amplitude of the monopole component of the overall quadratic bias correction.
For simplicity of notation, since we do not make use of the quadratic bias in the case of non local prescription,  we will refer to $b_{2, \rm eff}$ as $b_2$, omitting the second subscript. The CDM bispectrum in the above equation is computed at $1$-loop in perturbation theory, whereas the other terms are evaluated at tree-level, so we expect any failure of the theoretical predictions at low scales to be mainly due to the bias model.

In figure~\ref{fi2} we present  the best fits of the bias parameters from the measurements in two different cosmologies, $\Lambda$CDM (left panels) and with $M_\nu = 0.3$ eV (right panels). Both figures are organised in the same way: the measurements of  $b_1$ and $b_2$  at $z= 0.0$ (left panel) and at $z= 0.5$ (right panel); cyan and orange colours indicate  $b_1$ and $b_2$ for the local model while blue and red colours indicate  $b_1$ and \textit{effective} $b_2$ for the non local prescription. Black lines correspond to the measurement of $b_1$ obtained from the halo-matter power spectrum $P_{hm}$. We noticed that the measurements of $b_1$ in a local bias framework disagree with the estimates from two-point statistics, but that on the other hand when we account for $\gamma_2$, we find a good accordance; this confirms the effect of non-local bias on the halo bispectrum measurements even in a massive neutrino cosmology. It also reinforces our understanding of halo/galaxy bias in these cosmologies in terms of hte CDM field only.

Even though the error budget of our measurements of the Bispectrum in the simulations does not allow us to test the bias model of the Bispectrum at the \% level, it is still interesting to check down to which scale our bias model provides a reasonable fit to the bispectrum in the N-body. On the baryonic acoustic oscillations scales our errors are indeed comparable with those in the real data from \citep{GilMarinEtal2017}.  Figure~\ref{bispectrumhalo} shows the measurements  of the bispectrum for equilateral and squeezed configurations. We selected the halo mass range $A$ at redshifts $z = 0.5$. The dashed lines show the theoretical predictions for the matter bispectrum in case of $\Lambda$CDM (black) and cosmology with $M_\nu = 0.53 \;eV$ (green).
The continuous lines indicate the predictions for the halo bispectrum assuming a non local eulerian model for the bias. The agreement of the model with the data breaks down earlier in the presence of massive neutrinos, as the bias parameters are higher and therefore nonlinearities stronger. Nevertheless we find our bias template is able to fit the measured halo bispsctrum down to $k\simeq 0.15 \, h \, {\rm Mpc}^{-1}$.
It is important also to notice that in comparison with thhe $\Lambda$CDM case the suppression in the halo bispectrum is more ore less constant across the range of scale where PT gives a good fit to the measurements., revealing that difference in the shape of the underlying dark matter power spectrum are very degenerate with the bias parameters.
\begin{figure}[t]
\centering
\includegraphics[width=1. \textwidth]{fig_Bhhh1loop_equi.pdf}
\caption{\label{bispectrumhalo}  The measurements  of the Bispectrum for equilateral and squeezed configurations. Dashed lines show the theoretical predictions for matter bispectrum in  $\Lambda$CDM (black) and in cosmology with $M_\nu = 0.53eV$ (green).
Continuous lines indicate the predictions for the halo bispectrum assuming a non local bias model; black and green points mark the measurements of the halo bispectrum at  $M >10^{13} M_\odot$.}
\end{figure}

\subsection{The universality of the halo bias at quadratic order}

In the context of bias modeling, universality means that the bias coefficients, as a function of mass, cosmology and redshift, can be written in terms of the peak height
$\nu \equiv \delta_{cr}/\sigma(M,z)$, defined as the ratio between the constant critical density $\delta_{cr} = 1.686$ for spherical collapse,  and $\sigma(M,z)$, the r.m.s of the linear density field smoothed at a mass scale $M$ and redshift $z$. Any dependence on the cosmological model, or redshift, is encoded in the function $\sigma(M,z)$.  This is a very strong statement, and in principle of great value for cosmological analyses, as it allows to predict, for instance, the evolution of the bias parameters with redshift. Measurements in the N-body simulations of  $\Lambda$CDM cosmologies show that bias parameters are universal functions of redshift \citep{ShethTormen1999, TinkerEtal2010, HoffmannBelGaztanaga2015, LazeyrasEtal2016, ModiCastorinaSeljak2017}.

In \citep{CastorinaEtal2014} it was shown that the same result applies to linear bias in massive neutrinos cosmologies if the peak height is computed from the variance of the CDM field, $\nu_c = \delta_{cr}/\sigma_c$. An incorrect choice for the variance leads to strong violations of universality with both redshift and cosmology. This is just a consequence of the fact that the proper bias expansion is written in terms of the CDM field.
Given our measurements of the bispectrum and the best fit values of the bias coefficients, we are in the position to test universality beyond linear bias. Such an analysis is presented in Fig.~\ref{fig:bias}. The top panel shows the best fit value for linear bias from the power spectrum as a function of $\nu_c$. Different symbols and colors refer to different halo populations in different cosmologies, redshifts and mass thresholds. The figure agrees with \citep{CastorinaEtal2014} in showing $b_1(\nu_c)$ as a universal prediction, function of $\nu_c$ alone. The middle and bottom panel, in addition, show the universality of quadratic bias coefficients, both local and non local ones.  We find that $b_2$ and $\gamma_2$ are universal functions of cosmology and redshift if the right variable, $\nu_c$, is used. This is non-trivial check of the bias model and confirms our understanding of the clustering of halos in cosmologies with massive neutrinos.
An important consequence of universality is the existence of smooth relations between linear bias and other bias parameters.
Such relations, if calibrated with enough accuracy, can be used to reduce to reduce the number of nuisance parameters in a cosmological analysis. In particular the Eulerian bias model assumes that non local terms are only generated by gravitational evolution, yielding   \citep{ChanScoccimarro2012, BaldaufEtal2012},
\begin{equation}
\label{eq:b1g2E}
\gamma_2 = -\frac{2}{7}(b_1-1)\,,
\end{equation}
which is assumed to be valid in all cosmological analysis of galaxy survey data \citep{SanchezEtal2017b, GilMarinEtal2017, BeutlerEtal2017, SlepianEisenstein2017}. Recently  \citep{ShethChanScoccimarro2013, CastorinaEtal2016, CastorinaParanjapeSheth2017, ModiCastorinaSeljak2017} have shown, in analytical calculations and measurements in N-body simulations of $\Lambda$CDM cosmologies, that, as a results of the fact that halo formation happens in a ellipsoidal fashion, the above equation needs to be modified to include a Lagrangian non local coefficient $\gamma_2^L$,
\begin{equation}
\label{eq:b1g2L}
\gamma_2 = \gamma_2^L-\frac{2}{7}(b_1-1).
\end{equation}

\begin{figure}
\begin{center}
\includegraphics[width= \textwidth]{fig_bias.pdf}
\caption{\label{fig:bias} Upper panels: Best fit value for the bias parameters as a function the peak height for different cosmologies, redshift and halo mass threshold. Lower panels: Relation between second order bias parameter and linear bias for the same cosmological models, redshift and halo masses. }
\end{center}
\end{figure}

As a final application of our results on the halo bispectrum we therefore test the relations between bias parameters in cosmologies with massive neutrinos. In figure~\ref{fig:bias}, we show $b_2$, top panel, and $\gamma_2$, bottom panel, as a function of linear bias. As expected, quadratic density bias is a smooth function of $b_1$ independently of the value of the neutrino masses. This implies that existing fitting formulae for $b_2(b_1)$ as in \citep{HoffmannBelGaztanaga2017, LazeyrasEtal2016} can be used in cosmologies with massive neutrinos. Moving to non local bias, we find that the prediction of Eq. \ref{eq:b1g2E} compare reasonably well with the measurements. For high values of $\nu$ where we expect bigger deviations from Eq. \ref{eq:b1g2E} our best fit values are too noisy to say anything conclusive. We plan to return to this issue in future work, as assumptions on non local bias can affect galaxy clustering analyses that use Lagrangian \citep{ChuangEtal2017, Wang+14, VlahSeljakBaldauf2015} or Eulerian \citep{SanchezEtal2017b, GilMarinEtal2017, BeutlerEtal2017, SlepianEtal2016} perturbation theory.

\section{Conclusions}
\label{sec:conclusions}

In this work we have presented the first analysis of the matter and halo bispectrum from simulations of cosmologies with massive neutrinos described as a additional set of particles. We have measured the CDM and CDM+$\nu$ bispectrum, which we have then compared to perturbation theory predictions. Firstly we have shown, using analytical arguments, that numerical approaches including neutrinos only at linear level or through response functions could potentially predict biased bispectra on large scales.
From measurements in N-body simulations we showed that the CDM bispectrum, $B_{ccc}$ is the dominant three-point statistics, with bispectra involving one or more neutrino fields being highly suppressed. This simplifies a lot the analytical evaluation, since only $B_{ccc}$ needs to be computed beyond the tree level prediction. The perturbative calculations agrees fairly well with the N-body, most importantly at the same level it does in a standard cosmological simulation. We have shown that tree-level perturbation theory is sufficient to describe any bispectra involving one or more neutrino field, as their perturbations are highly suppressed below the free-streaming scale.
We have also estimated non-linear neutrinos signatures in the bispectrum by looking at the reduce bispectrum, finding $<1\%$ effects for the considerably high value of the neutrino masses considered in this paper.

We then devoted our attention to the halo bispectrum in cosmologies with massive neutrinos, the main motivation being the result in \citep{CastorinaEtal2014} that linear halo bias should be written in terms of the CDM field only.
We extend this finding to higher order bias coefficients, showing that the halo bispectrum can be characterized by the same bias expansion is usually performed in a $\Lambda CDM$ universe. This has important consequences for universality of higher order bias parameters, which holds if written in terms of the peak height of the CDM field, $\nu_c = \delta_{cr}/\sigma_c$. This implies, for instance, that quadratic bias, $b_2$, can be written in terms of $b_1$ regardless of the value of neutrino masses.
\bigskip

\acknowledgments
The DEMNUni simulations were carried out at the Tier-0 IBM BG/Q machine, Fermi, of
the Centro Interuniversitario del Nord-Est per il Calcolo Elettronico (CINECA, Bologna,
Italy), via the five million cpu-hrs budget provided by the Italian SuperComputing Resource
Allocation (ISCRA) to the class-A proposal entitled ``The Dark Energy and Massive-Neutrino
Universe''.
RR acknowledge support from the European Research Council
through the Darksurvey grant 614030.
CC acknowledges financial support from the European Research Council through the Darklight Advanced Research Grant
(n. 291521), and the grant MIUR PRIN 2015 ``Cosmology and Fundamental Physics: illuminating the Dark Universe with Euclid''.
EC and ES would like to thank Francisco Villaescusa-Navarro, Matteo Viel and Julien Bel for useful discussions.

redpajama_set_name: RedPajamaArXiv


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For those of us who followed the story when the news first broke, we wondered how in the world any parent except the mom and dad in Home Alone could get in the car and drive away without one of their kids. But as Robert, the father of the little boy, explained to the Salt Lake Tribune, it was a combination of lots of things that led to the little boy's getting accidentally left behind.
More from CafeMom: Mom Makes Daily Halloween Costumes for Her 9-Month-Old Twins -- & She Gives Them Away!
Robert says he has a plural family, though he claims that has nothing to do with what happened with his son. There were lots of kids to keep track of that day, he explains: He and his wife have 14 children, 11 of whom she brought with her to the corn maze -- including the 3-year-old who ended up missing. Her sister also brought two or three of her own kids and they were in multiple cars, so right away you have over a dozen kids to keep track of. Between the siblings and cousins, Robert says there were about four blond-haired boys of about the same size.
When it was time to leave, Robert's wife did take the 3-year-old out of the corn maze and buckled him into his car seat, along with the other younger children. But someone was handing out free donuts, and the older children heard the siren call of sugar. Robert's wife said yes, so the older kids got out of the car and headed into the 15-minute line. She thought the 3-year-old was in the car with her, but it's believed that this is when he managed to get out of the car and head back into the corn maze on his own.
Robert's wife and her sister took the children back to Robert's house, where the kids watched a scary movie. Some of the children fell asleep. The sister left with her children. Robert himself was working late and didn't arrive home until 9:30 p.m., and because the 3-year-old often sleeps in bed with an older sibling, no one noticed he wasn't in the house. They assumed he had fallen asleep somewhere.
The next morning when the parents realized their little boy wasn't home, they panicked, but they were happily and quickly reunited with him at the police station. And while child services has investigated, it appears no charges have been filed.
Obviously a family trip to the corn maze with a huge group of siblings plus cousins, followed by a movie, are deviations from the normal routine. And as we've all heard in the horrific cases where babies are accidentally left in hot cars instead of dropped off at daycare, a change from the normal routine is a common way for a parent to make a major mistake.
For many parents, it's really, really hard not to read about this case and think, BUT WHO LEAVES THEIR 3-YEAR-OLD IN A FREAKING CORN MAZE OVERNIGHT? However, not many of us know what it's like to have 14 kids to keep track of, so who are we to judge?


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text:
Inventors & Discoverers
Jack Kilby Biography
Inventors & Discoverers #65
Died At Age: 81
Also Known As: Jack St. Clair Kilby
Born in: Jefferson City
Famous as: Inventor of integrated circuit
Electrical Engineers Electronics Engineers
Died on: June 20, 2005
place of death: Dallas
Cause of Death: Cancer
U.S. State: Missouri
discoveries/inventions: Integrated Circuit
education: University of Illinois at Urbana–Champaign, University of Wisconsin-Madison, University of Wisconsin–Milwaukee, Great Bend High School
awards: 2000 - Nobel Prize in Physics
1989 - Charles Stark Draper Prize
1986 - IEEE Medal of Honor
1990 - National Medal of Technology and Innovation
1970 - National Medal of Science for Engineering
Jack Kilby can be rightly acknowledged as the face of modern computing, for had it not been for his invention of the integrated circuit and microchip, the computer industry wouldn't have been what it is today. The world today is literally at the palm top, with integrated circuit and microchip meeting much of our daily needs and requirements. Before Kilby invented the integrated circuit, computers were mostly room-sized with a restricted usage. It was his discovery that transformed the machine into the size we use today. The small wonder has revolutionized the way electronic industry works and can be safely regarded as a historical discovery in computer technology. Jack Kilby's association with science and electronics was long. Having an affinity for physics and mathematics since early on, Kilby, after completing his studies, took up job at Texas Instruments. It was while solving the problem of 'tyranny of numbers' that Kilby was first struck with the idea of an integrated circuit. Working along the idea, in 1958, he eventually invented the integrated circuit. For the same, he received numerous prestigious and esteemed awards and honors, including the Nobel Prize. Kilby's other contribution include invention of thermal printer and world's first integrated-circuit based calculator
http://www.computerhistory.org/revolution/calculators/1/63/250
http://www.pcworld.com/article/2048664/the-legend-of-jack-kilby-55-years-of-the-integrated-circuit.html
http://www.dallasnews.com/business/technology/headlines/20140912-texas-instruments-celebrates-innovation.ece
Male Engineers
Scorpio Engineers
Jack Kilby was born on November 8, 1923 in Jefferson City, Missouri. His father owned a small electric company, which ignited in young Kilby the passion for electronics.
During World War II, Kilby served in the military as a technician stationed in India. Since an early age, Kilby, much like his father was hooked to radio so much so that he was often called an amateur radio buff.
Academically proficient, Kilby completed his preliminary education from the Great Bend High School. In 1947, he completed his graduation with a degree in electrical engineering from the University of Illinois. Three years later, he completed his Masters' in the subject from the University of Wisconsin-Extension in Milwaukee.
While studying for his Masters' in Electrical Engineering, Kilby worked at the Centralab in Milwaukee. An electronic manufacturing company, he was involved in making parts of radio, television and hearing aids.
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American Engineers
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American Inventors & Discoverers
In 1958, Kilby commenced his career as an engineer at the Texas Instruments. His long-held interest in working on electronic component miniaturization realized with this appointment.
At the time of his appointment, the 'tyranny of numbers' was a prevalent problem that the electronic industry was facing while designing circuits. Kilby soon dismissed the universal belief that a micro-module would solve the problem. He instead believed that a semiconductor was the only cost-effective way to provide the solution
Working on his ideas, he combined the isolated electronic components so as to make them work in a miniature environment. This led to the evolution of an integrated circuit, the first miniaturized electronic circuit that revolutionized the way technology was used until then. He filed for a US patent on February 1959. Kilby shares the credit of the invention of integrated circuit along with Robert Noyce, an inventor who too developed another type of the integrated circuit.
Following his big breakthrough, Jack Kilby's integrated circuit found a place in military, industrial and commercial application. The microchip technology assisted in building the first of both the military system and the computer-incorporated integrated circuit.
Though the invention of integrated circuit was a revolution for the computing world, people were sceptical of its performance and abilities. As such, to put an end to all cynicism, he went on to develop a calculator which would successfully commercialize the integrated circuit. People were amazed by the creation of the pocket device which though miniature in size was as powerful as the electro-mechanical computer.
Kilby is also credited with devising the thermal printer. The printer served as a useful device in day-to-day application and was primarily used in portable data terminals.
With an aim to work independently, Kilby took a leave of absence from Texas Instruments in 1970. During this time, he explored the use of silicon technology in generating electrical power from sunlight.
For six years, from 1978 to 1984, Kilby held the position of Distinguished Professor of Electrical Engineering at Texas A&M University. Meanwhile in 1983, he retired from Texas Instruments.
Scorpio Men
Kilby's most important contribution in the field of electronic technology has been as the inventor of integrated circuit. It was while solving the problem of 'tyranny of numbers' while at Texas Instruments that Kilby was first struck with the idea of miniaturization of electronic circuits. In September 1958, he finally came up with the design of an integrated circuit. He combined isolated electronic elements to work together in a miniature environment thus leading to his most revolutionary discovery.
Other than discovering the integrated circuit, Kilby is also noted as the inventor of thermal printers and world's first integrated-circuit based calculator. This pocket sized device was first termed Pocketronic.
For his outstanding contribution in the field of engineering and technology, Kilby was bestowed with nation's most prestigious honors of the field such as the National Medal of Science in 1969 and later National Medal of Technology in 1990.
In 1967, he was elected as a member of the National Academy of Engineering and later in 1982 was inducted in the National Inventors Hall of Fame.
The Institute of Electrical and Electronic Engineers recognized the significant contribution made by Kilby in the field of electronic technology and subsequently awarded him with the numerous awards including IEEE Fellow, IEEE David Sarnoff Award, IEEE Cledo Brunetti Award, IEEE Centennial Medal and IEEE Medal of Honor.
In 1998, he received Honorary Professorship from the National Chiao Tung University (NCTU) in Taiwan
Kilby became the proud recipient of the highly esteemed Nobel Prize in Physics in 2000 for his breakthrough invention of the integrated circuit. He shared the honor with Robert Noyce and acknowledged the latter's contribution in the field.
In addition to awards and medals, Kilby was honoured with honorary doctorate degree from several universities including Southern Methodist University, the University of Miami, University of Illinois, University of Wisconsin-Madison, Texas A&M University and Yale and Rochester Institute of Technology.
Personal Life & Legacy
Kilby breathed his last on June 20, 2005 in Dallas, Texas. He was suffering from cancer.
Posthumously, several buildings and institutions have been named after him including The Kilby Center, TI's Research Center for silicon manufacturing, the Jack Kilby Computer Centre at the Merchiston Campus of Edinburgh Napier University and so on.
The calculator which we so often use today bears its emergence to this American electrical engineer who also invented the integrated circuit.
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See the events in life of Jack Kilby in Chronological Order
Jack Kilby Bio As PDF
- Jack Kilby Biography
- https://www.thefamouspeople.com/profiles/jack-kilby-6393.php
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20th Century | Celebrity Names With Letter J | 20th Century Engineers | Male Celebrity Names With Letter J | 20th Century Electrical Engineers | 20th Century Inventors & Discoverers

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In early 1995 the editors of New World Writing put our first literary magazine, then called MROnline, on the Internet. Our idea was to publish a literary magazine that was free, that would be made up of original full-length content, not previously published in print, specifically material not connected to the print edition of Mississippi Review, which the editor was also editing at that time.
In summer 2010 MROnline morphed into Blip Magazine which then became New World Writing, a name selected as homage to the distinguished literary magazine of the 1950s. Our entire back catalog is accessible via the link above. As it happens, a tiny percentage of the material published 1995–2010 came from the print edition of MR, and we thank the authors of these works for permission to reprint those items here. Indeed, we thank all of the authors for permission to reprint their work as part of the New World Writing archive. We hope you enjoy reading these back issues.


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Q: Gravitational attraction as distance approaches zero Imagine a $x$-$y$ plane, which induces an acceleration field  obeyed by the equation $ a= -\frac{C}{z^2} \vec{k}$ where $z$ is the perpendicular distance from the plane to the ball and $C$ is just some constant. Now a ball is thrown from a height of 1 meter from the plane, find trajectory of the ball for an oblique projection.
This is a hypothetical question why my friend made-up. I could solve for an exact solution of differential equation probably but I know I cannot approximate the acceleration as something like $-mg$ because the denominator is starting from $z=0$. If we are on earth, the gravitational law takes the form $ \frac{ GmM}{(R+x)^2}$ and because of the form of the denominator, we can use taylor expansion approximation and solve for acceleration close to the surface.
However we can't do that because we can not taylor expand $ -\frac{1}{x^2}$ around $x=0$, because neither the function nor it's derivatives are defined. Now, how would I find the trajectory considering all of that?
Also, another observation which I made is horizontal component once it's projected would be effected since there is no horizontal force.
On deeper analysis, I realize this is a problem with any point like particle. The reason we don't encounter it with earth, is because the 'bulk' of the earth puts a limit on how close we can get to the earth, so how would we deal with these singularities super dense objects (i.e: point masses?)
Edit:
Is the radial two-body problem solvable?
This stack question goes into detail about solving the differential equation and interpreting solutions to it. I thought this was good, if someone could show how can we interpret the mathematical solution of the differential equation (maybe with solving differential equation)   and apply it in this context then it'd be great. I am not so well versed with solving second order differential equations or interpreting the solution , so I hope someone more knowledgeable can help in this aspect

A: Consider radial infall of two point masses, with the equation of motion
$$\ddot{r}=-\frac{1}{r^2}$$
where we ignore constants like $G$, masses, etc. (Note that the equation in the question you linked to was missing a minus sign. Gravity is attractive.)
The trick to solving this second-order differential equation is to convert it into a first-order one by multiplying both sides by $\dot{r}$:
$$\dot{r}\ddot{r}=-\frac{\dot{r}}{r^2}$$
$$\frac{d}{dt}\left(\frac12\dot{r}^2\right)=\frac{d}{dt}\left(\frac1r\right)$$
$$\frac12\dot{r}^2-\frac1r=\text{const}$$
You can recognize the final equation as simply the conservation of kinetic energy plus gravitational potential energy. The latter is negative because the force is attractive.
You can solve this simpler equation by first separating the variables $r$ and $t$ and then integrating both sides. An especially easy case to start with is when the constant is zero, corresponding to the two masses being released from rest at infinite separation.
Even without solving the equation, you can see that as the separation approaches zero, the infall speed approaches infinity.

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text:
United Student Government
USG Finalizes New Constitution
CAB Hosts First Spring Weekend Carnival
Under the Tent Goes Over the Rainbow for 2019 Event
Ellie Kemper Speaks on Experience in Hollywood
Paul Elie, FCRH '87, Addresses Experience with Clerical Abuse
Meditation Club Brings Relaxation Opportunities to Campus Community
Fordham in the Bronx
Noëlle Santos Opens Lit.Bar: Only Bookstore in the Bronx
Class of 2023 Shows High Academic Calibre
Laura Auricchio, Ph.D., to Serve as Dean of Fordham College Lincoln Center
FAHS Visits "Art After Stonewall: (1969-1989)"
RHA decorated Under The Tent with emerald green lights and "Wizard of Oz" themed decorations.
Paul Elie, FCRH '87, accused Rev. Edward Zogby, S.J., the associate vice president for Lincoln Center for ten years during the 1980's, of sexual misconduct in an article from The New Yorker released on April 8.
Thanks to Noëlle Santos, the Bronx, which has been without a single bookstore since the end of December 2016, now has Lit. Bar.
Laura Auricchio, Ph.D., has been appointed as Dean of Fordham College at Lincoln Center starting August 1, 2019.
Tinder Swipe Off Concert to be Held at New York Expo Center
The #SwipeOff concert will be held April 24th at the New York Expo Center. Doors open at 6pm.
Committee on Sexual Misconduct Hosts Third Annual Week of Action
Week of Action is an event that the national organization Its On Us holds every April for sexual assault awareness month.
USG finalized multiple bylaws in the new constitution and learned that the acai base at Sambazon in Dagger Johns is now a meal swipe.
CAB hosted their first carnival on the Friday of Spring Weekend. The event closed early due to lightning.
Ellie Kemper spoke to Fordham students as CAB's Spring Weekend 2019 speaker.
The Perils of Polarization
With an organized start to fixing the polarization that occurs in our society, I believe it will inspire private conversations of the same depth.
Biden Banking on the Blue Wall
If he wants to have a chance of beating Trump in 2020, Biden must stick close to his pro-worker, blue-collar bonafides.
Notre Dame Effort is Not the Only Worthy Cause
There are numerous causes that could benefit from donations, especially over a billion dollars worth of donations, that are constantly ignored.
For The Benefit and Enjoyment of People
We ought to understand that green spaces such as these are as necessary for well being of the public as access to food or water. They ought to be protected by the government—and made accessible to all Americans.
To safeguard against similar situations in the future, CAB and OSI must maintain a stronger vetting process for potential performers.
It Memes A Lot to Me
By Katie Morris Today, memes are the easily identifiable...
Kim Petras Announces Her New Project: "Clarity"
A pop star with a unique schedule, Kim Petras has released a new single for the eighth consecutive Thursday
Bloodthirsty Rapper with a Poetic Side: Denzel Curry on "ZUU"
He raps with such intrinsic precision, an almost jazz improv sensibility, that every verse and syllable seem like they were born to work with the beat in such harmonious ways.
After 50 Years, "Midnight Cowboy" Stands Alone
Fifty years since its release, "Midnight Cowboy" remains a monument to artistic risk.
Young Nudy and Pi'erre Bourne's Circus of Sedation
Bourne and Nudy have fundamentally different approaches, and it shows.
From Medium to Vogue: A Teary Goodbye
Keeping the Mental Health Dialogue Going
Seeing how many people are affected by mental health issues further proves this need.
Gaitley, Cavanaugh, Goulding Rake in BCANY Honors
By Jimmy Sullivan The awards haven't stopped pouring in for Fordham Women's Basketball's stellar 2018-19 campaign. Head coach Stephanie Gaitley has been named...
Baseball Dropped from NCAA Tournament by West Virginia, Texas A&M
By Jimmy Sullivan Fordham Baseball's first NCAA Tournament appearance in 21 years ended almost as quickly as it started. The Rams dropped their first game by a score...
Baseball Wins Atlantic 10, to Travel to West Virginia in NCAA Tournament
By Jimmy Sullivan Fordham Baseball has done something it hasn't done since 1998: win the Atlantic 10 and go to the NCAA Tournament. With a 4-3, extra-inning win over...
Softball Suffers Two Close Losses at NCAA Tournament
By Jimmy Sullivan Despite an offseason...
Men's Basketball's Honor Transferring to Clemson
Fordham Men's Basketball is losing Nick Honor to Clemson.
Baseball Drops Two of Three in Final Out-of-Conference Series
Despite the loss, the volume of traffic on the basepaths for the Ram offense was an encouraging sign for Fordham baseball head coach Kevin Leighton.
This weekend saw the Fordham Rams Men's and Women's Track & Field teams compete at the Penn Relays, and it became a weekend to remember. In the distance medley, the women's team of Laurel Fisher, Sarinnagh Budris, Aidan Moroz and Katarzyna Krzyzanowski not only won the college division event, but they did it in historic fashion, setting a school record time of 11:34.28.
Women's Tennis Makes a Championship Run to End the Season
Despite Li and Quenville's 6-0 third doubles victory, the team could not come together to win the doubles point or any of the three singles matches.
Fordham Baseball's Jake MacKenzie Swipes His Way Through the Atlantic 10
Fordham Baseball's Jake MacKenzie is one of the country's best base-stealers, and he's also having a breakout season for the Rams.
"The Man Who Killed Don Quixote" Thrives in Dysfunction
Overall, the film does a remarkable job at exploring the novel's themes about trying to live up to flawed ideals through absurd personas.
Sophomore Finds Her Purpose Through WFUV
As her time at Fordham is nearing the halfway mark, she looks forward and contemplates what her Ram legacy will be.
Students Embrace the Mosh at Spring Weekend Concert
The students that had the most fun, however, were those that embraced the mosh pits. Instead of complaining about getting pushed, they pushed back.
iPhones Work Hard But Photographers Work Harder
Does the ease of being able to make hundreds of photographs today with such thoughtless effort cause the meaning and substance of photographs to be lost?
The Final Slice: An Ode to Hometown Pizza
I think we all have a hometown restaurant, cafe, coffee shop, bar or slice shop that holds a special place in our hearts.
Fordham's Graduate Schools Move in U.S. News & World Report Rankings
U.S. News and World Report released its annual graduate school rankings, naming the Gabelli Graduate School of Business as #63 in best Business Schools, and Fordham's Education and Law Schools both at #37.
University Addresses Clerical Abuse Allegations After Jesuit Northeast Province Releases List
The university and its board of trustees addressed the Fordham community after the Jesuit Northeast Province released its list of credible abuse allegations.
University Names Dennis C. Jacobs, Ph.D., As New Provost
The university named Dennis C. Jacobs, Ph.D., of Santa Clara as its new provost. Jacobs will fill the position this July.
Garden of Happiness Supports Community Through Hot Sauce Sales
Local garden focus on community along with commercial partnership.
College Students Face Difficulties in Voting Absentee
Many out-of-state students at Fordham ran into problems while attempting to apply for and mail absentee ballots.
Democrats Narrowly Take House of Representatives
In this midterm election, Democrats took over the House of Representatives while Republicans maintained control of the Senate.
The Fordham Ram condemns the sensationalism of some media outlets' coverage of the death of Sydney Monfries, FCRH '19.
"Join the cultural moment, be one of the millions watching GOT this Sunday – if for no other reason than to strengthen the connections with those around you going forward."


Company Art Hookah is proud to present an improved version of the Aviator hose.
More than a year was spent on the development, production, and testing in the Art Hookah lounge in San Diego, California, and this version promises to provide the best hookah experience possible.
The new model is made of aircraft-grade aluminum 6061-T6, AD-33 (Russia), which has increased strength due to deep hard-anodizing aluminum, has a high resistance to oxidation, and complies with all necessary medical and nutritional requirements and standards. Aircraft-grade aluminum is used in the aviation industry for the manufacture of parts and structures for aircraft, the space industry, and the production of weapons. This material is extremely durable and perfectly fulfills its function at any temperature when using a hookah, even in the most extreme conditions.
The new model comes complete with a black matte hose, made from medical-grade silicone by a platinum-curing method. After washing, the hose leaves absolutely no aftertaste from a hookah session. This makes it a great universal hose that can be used every day.The new model of the hose is thicker and denser, which in turn makes it more durable and prevents multiple folds and creases. The black-colored hose fulfills a practical role and maintains the original appearance of the hose, while the matte finish repels dirt and dust.
The kit also includes a spring, which provides additional support for the hose at the hose port for pure passage of smoke and prevents the hose from bending and quitting.
An important detail in the Aviator mouthpiece is the icetip. The icetip, which is made of plastic, is filled with a specific gel to freeze and be able to store at a cool temperature for an extended period of time. To cool the smoke, simply freeze the icetip then place into the mouthpiece.
All of the improvements to the new Aviator model make for a more durable hookah product and enjoyable hookah experience!


Surprisingly, today marks the 4th anniversary of the move to our smallholding in the North Pennines. This is hard to believe partly because it's just 4 years since we left the suburban semi-detached house but also because it feels longer than 4 years given that so much has happened in that time.
From having 3 chickens in our suburban back garden to a 15 acre smallholding with an assortment of chickens, some rare breed Tamworth pigs (plus piglets) and some pedigree Dexter cows (plus calves). It's been an amazing journey so far even just from a livestock perspective never mind the converted barn for holiday lets.
The ups and downs along the way have been both educational and humbling in equal measure but the overwhelming feeling is that we have been extremely lucky and we should continue trying to make the most of the opportunity.
We have been helped along the way by far too many people to mention but that doesn't mean we don't appreciate all the help and advice provided though. We still have a lot to learn though and without the knowledge and experience of others we definitely wouldn't have made it this far.
Over time it's becoming clear that there will never be a point when we can just sit back and relax. Mostly because there's always a job that needs to be done or another mad idea to plan and pursue. I wouldn't have it any other way!
Time goes pretty quick by pretty quick that's for sure. Beautiful photos!


"PERTAINING TO A BLUE CRAB SANCTUARY"
This chapter established open seasons, for the harvest of crabs, in the area described and defined in § 28.2-709 of the Code of Virginia as a Blue Crab Sanctuary.
This chapter was promulgated pursuant to the authority contained in §§ 28.2-201 and 28.2-709 of the Code of Virginia. This chapter amends and re-adopts, as amended, previous Chapter 4VAC20-1210-10 et seq., which was promulgated April 28, 2009 and made effective on April 30, 2009. The effective date of this chapter is November 30, 2012.


Great 4 bedroom, 2 bath home in Fox Valley... Conveniently located to Interstate 10 & Eglin Air Force Base... Features include open living area with eat-in kitchen opening to the living area with fireplace. There is also a separate dining area. The master bedroom suite features double vanity with gardin tub & seperate shower. The rear of the home features a back deck with fenced back yard, perfect for entertaining.


text:
Johann Simon Hermstedt, född den 29 december 1778 i Langensalza, död den 10 augusti 1846, var en tysk klarinettist.

Hermstedt, som var kapellmästare i Sondershausen, var virtuos på sitt instrument. Spohr skrev enkom för honom flera klarinettsoli.

Källor

Tyska klarinettister
Tyska musiker under 1800-talet
Personer från Bad Langensalza
Födda 1778
Avlidna 1846
Män

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Happy Hump Day! I do love Wednesdays....half way through the week! This week Wednesday is even more welcome as its my last day of work this week....tomorrow I am off to Germany with my family to visit the Christmas markets near the Rhine. I love that part of Germany and cannot wait to get back out there!
But before I go...we have a new challenge for you over at Christmas at Sweet Stampin, and for the last challenge of 2014 we have a winter sports challenge.
I have picked ice skating as my winter sport....and have gone a little overboard with the Christmas jumper inspired backing paper!
My image is coloured with my Promakers and I have made my ice shine and sparkle with my stickles. I have this Do Crafts backing paper for ages and thought it went well with my ice skating theme.
For more winter sports inspiration pop by the Christmas at Sweet Stampin challenge blog and take a peek at all the gorgeous DT cards that have been created this month!
Love penguins and this little guy is so cute! Those are very pretty papers and yes, they do remind me of winter sweaters!
Cute card! The image is adorable and the DP reminds me of a cozy sweater!
Black and White.....and a splash of colour!


text:
The Hon Scott Morrison MP
Senator the Hon Marise Payne
The Hon Ken Wyatt AM MP
The Hon Greg Hunt MP
The Hon Ben Morton MP
Home » The Hon Alan Tudge MP » Sky News AM Agenda Interview with Kieran Gilbert
Sky News AM Agenda Interview with Kieran Gilbert
Topics: Same-sex marriage, Emissions Reduction Target E&OE…
KIERAN GILBERT:
Alan Tudge thanks very much for your time. It was obviously a robust debate last night. A number of your colleagues, 16 frontbenchers, arguing in favor of a free vote. If they cross the floor, they lose their jobs now in terms of if this private members bill on same sex marriage gets to the parliament.
ALAN TUDGE:
The Westminster system has always held that view, that frontbenchers are bound by the party's positions. Backbenchers within the Liberal Party are not, of course, and they can cross the floor as they have done so in the past and there won't be repercussions.
That is in fact different to the Labor Party, where any member of the Labor Party who crosses the floor is expelled from the Party.
Can your frontbench colleagues abstain if they like or do they have to vote in support of the government position?
That's a question I don't know the answer to. Of course they can't vote against it, but I don't know the answer to that question.
I guess on this issue that gets back to the point of why there isn't a free vote on an issue which many argue and many of your own colleagues believe is a conscience vote, more in the context of the party of Menzies, the man who argued that each of your colleagues should be able to vote on their own conscience.
That's true but at the same time my view, and I think the view of most members of the Party Room, was that we wanted to maintain the faith with the Australian people. At the 2013 election, we said to them that we would have a party position maintaining the current definition of marriage.
We reaffirmed that party position for this term of parliament but we also made a very fundamentally important decision. That is, we will likely take to the next election a commitment that we will hold a plebiscite in the next term of parliament should we be reelected.
That will give every single Australian an opportunity should we go down that path.
I'm told there was no such commitment agreed to within the party room yesterday. There was no commitment and there is no policy right now. The Prime Minister's talking about essentially ideas at the moment but hasn't locked in a policy, a commitment.
We had this party room discussion as you know which went for five or six hours. Out of that party room decision, we decided we would investigate that possibility.
So investigate it…
There was some consensus around that as well…
It wouldn't be a referendum though…
It could either be a referendum or it could be a plebiscite. Either way, every single Australian under such a model would have the ability to have their say on this question.
I personally think this is a terrific idea because if we are to change the law to change the definition of marriage we would be changing in essence a 2,000 year old institution. Therefore it would be quite proper, just as Ireland did it, to allow every single Australian to have their say.
But they needed to change their constitution. We don't so a referendum would seem a bit odd in this circumstance. A plebiscite sure, fine, have a vote, that makes sense but a referendum would seem a bit odd here. Why do we need to change the constitution?
Either way, it would give the opportunity for every Australian to have their say and I think that's a good thing and I hope that most Australians would welcome that opportunity for every single one of them to have their say on whether or not we should change the definition of marriage.
Only a few months ago the Prime Minister said it should be a matter for the parliament off the back of the Irish vote. Now he's changed his mind. Is this just trying to placate the conservative wing of your party and base within the electorate?
I think to the Prime Minister's credit, he led this process. He said 'let's have a full discussion in our party room and let the party room decide what our ongoing position will be'. So I give credit to the Prime Minister for doing that and it was an exceptionally good process.
I think it was our party room at our best because every single member of our party room had the opportunity to have their say. And at the end of it, we got to a relatively unified position from what could have been a very divisive issue.
I guess there's still some doubt as to what that position is though, as much as you're categorizing it as that's the direction but to me it seems there's still a fair bit of doubt as to what the government's going to come up with because as I told you earlier, my understanding from your colleagues is that there was no commitment made by the party room to this course of action which you are asserting is the one the Prime Minister's going to pursue.
There was a strong indication that we would be investigating this as a possibility to take to the next election.
Let's move on and look at the climate change issue and the carbon emission reductions. Is this credible on the international stage?
Of course it is. We've committed now to a reduction target of between 26 and 28 per cent below 2005 levels. That lines up in amongst all the other comparable developed countries. It's almost exactly the same as Japan, very similar to the United States, just a little bit below Europe and well above China, Japan and South Korea.
The sources have told me that the New Zealanders wanted to get their target out there before Australia. They did not want to be seen to be coming in after Australia because we're seen a laggards on this. Even the Kiwis are saying that, that they didn't want to come in after us because we are being seen by the OECD and the rest of the international community as being laggards on it.
First of all, let's have a look at our results. We have absolutely delivered upon our Kyoto 1 target, we will absolutely deliver on our Kyoto 2 target. Many countries have not done that. Secondly, our Emissions Reduction Target for 2030 will fall very squarely within the range of those developed countries including New Zealand.
Their target is minus 30 per cent, ours is minus 26-28 so we're splitting hairs in terms of the difference there.
It's something that you believe will stack up credibly given our ranking as the highest emitter per capita in the world?
I do and I'd just point out this other fact actually Kieran on that, yes we do have a high per capita emissions rate at present but our target for 2030 will have the largest reduction of any wealthy country in the world on a per capita basis. It will be a 50 per cent reduction per capita.
Mr Tudge, appreciate your time.
Thanks so much Kieran.
Privacy and legals


Stress is inevitable and sometimes unrelenting. It ranges from mild to toxic, and from helpful to harmful. We've all experienced the full spectrum of stress, from being motivated to immobilized, and we know that much of how it effects us is determined by how we respond to it.
This is REALLY good news, because it means we have agency. We can't stop stress, but we can choose how it will impact us. Just like we can learn to surf a wave or to simply get out of the way, we can learn to manage and reduce stress.
Mindfulness has been studied and taught as a method for stress reduction for over thirty years, and the results are promising. Just as we can count on stress recurring in our lives, we can learn to count on mindfulness as a way to respond to stressful situations and to cope with the feelings and effects of stress.
The first step is to notice that you're stressed. This may sound like an oversimplification, but we all have moments when stress sneaks up on us. Occasionally, stress gets the better of me and I loose my cool. And it's usually my kids who put me over the edge.
Afterwards, I feel terrible. I should know better, I think. Fact is, what I know isn't of consequence in those moments. What makes the difference is how I feel. If I haven't attended to myself and stress has accumulated, like a glass that's been filled to the rim, then all it takes is one small thing–one more drop–to cause an overflow.
Sometimes, I don't realize how full the glass is until I'm in a moment of overflow.
Before deepening my mindfulness practice, these moments were more common. Over the last several years as I've become more mindful, they've become less and less frequent. I'm grateful for the skillful means to manage stress as it's helping me set a better example for my children, though I still have much to learn.
One practice that I return to for stress reduction, is heartbreathing.
Once you have taken the first step and identified that you're feeling stress, the next step is to attend to it. Name it. This is stress. I feel stressed. Then, make a choice to manage it. I'm going to take a few moments to breath and reduce this feeling of stress.
Heartbreathing is a technique developed and taught by the HeartMath Institute.
Find a comfortable place to sit or stand. Silence is preferable, but not necessary.
Close your eyes, or find a gazing point.
Take several normal breaths, noticing where the breath is in your body. Try to breathe all way into your belly, and then to push the breath all the way out on the exhale.
Now, notice the area around the heart. The front, the back, and each side.
Continue normal breathing. Just noticing.
On an in-breath, imagine that you can breath directly through the chest wall and into the heart. Practice a few of these breaths, imagining that you can breathe directly in and out of the heart. This is called heartbreathing.
Next, notice the sensations around the heart. How does the area around your heart feel?
When you're done, notice how you feel. You're likely to feel at least a little bit more relaxed but, if not, that's okay. I once suggested some breathing exercises to a family member new to mindfulness and, after trying them, she reported with frustration that she, "just can't breathe!"I assured her that she could learn to breathe in this new way with practice.
In fact, the only way any of us benefit from mindfulness is through practice, which is also the only way anyone learns to surf a wave, or to cope better with the inevitable stressors of life. The reward for our commitment to practice are moments of calm and ease. I wish you many of both.


text:
Dirk's Five – Road Movies
The title of MULHOLLAND DRIVE is a wonderful paradox. It seems to promise something very specific about a place, yet at the same time it belongs in a strange, disjointed 'non-place' which could be LA or another plane of existence.
CHUNGKING EXPRESS refers to the Chungking Mansions in Tsim Sha Tsui where the film is set but also is an imaginative, cinematic space that exists in the imaginations of the characters.
There are many films that take their name from actual places, PHILADELPHIA, MANHATTAN, and CASABLANCA, to name a few, but this Friday 5 is a celebration of film titles that are at postcode level.
UP OUR STREET
1) 10 RILLINGTON PLACE (1971) I saw this film at a relatively young age on television and it made an indelible mark on my attitudes towards justice, and capital punishment in particular. A simple yet effective film that derives its power from the central performances from John Hurt as 'romancing' simple man, Timothy Evans who ends up being hanged for the murders committed by Richard Attenborough's chilling, calculating Christie who offers his back street abortions to the weak and easily manipulated. Ludovic Kennedy adapted his own book into the screenplay that was filmed at the site where the original murders took place. My impression of Christie is my party-piece, "..or, carbon dioxide as we like to call it." He did the same schtick for MIRACLE ON 34th STREET (1994) his Chris Cringle gives me the shivers.
2) SUNSET BOULEVARD (1950) MULHOLLAND DRIVE offers a homage to Billy Wilder's seminal movie about the movies. Norma Desmond (Gloria Swanson) a former silent movie star who is a fortress of self-belief. She has hidden herself away from the world that does't seem to want her any more and dreams of a come-back; I dream of the remake starring Demi Moore. The films have got smaller.
3) ARLINGTON ROAD (1999) a wonderfully intriguing film that is in danger of being forgotten. A story of a paranoia, where a recently widowed professor played by Jeff Bridges, begins to suspect his neighbours of being terrorists and he becomes obsessed with attempting to foil their plots. Tim Robbins plays against type as a creepy bloke with a strange obsession with the architectural design of a shopping mall he claims to be designing. Although it is lumpen in places, the end is a genuine shocker.
4) NIGHTMARE ON ELM STREET (1984) Child killer Freddy Krueger is one of cinemas's greatest creations with a hat set to a jaunty angle, his stripy pullover and claw-like gloves: he is omnipotent, if you die in your dreams then you die in real-life and he has a great line of cynical quips. He was great. The sequels turned him into a Scooby Doo villain.
ROAD TO RUIN
5) 84 CHARING CROSS ROAD (1987) Epistolary novels try my patience, so film about 'transatlantic business correspondence' will always have to work hard. Anthony Hopkins writes his performance on the back of a fag packet, sticks a stamp on it and sends it by carrier pigeon. It was Ann Bancroft's pet project – the rights were bought for her as a gift from Mel Brooks- pity that they were unable to squeeze at least one joke about nazis.
Mulholland Dr. (thebestpictureproject.wordpress.com)
Sunset Boulevard – Billy Wilder (mrmovietimes.com)
John Christie of Rillington Place (rbkclocalstudies.wordpress.com)
Chungking Express: Electric Youth (larkalong.wordpress.com)
Tags: Billy Wilder, Demi Moore, Gloria Swanson, John Hurt, Mulholland Drive, Norma Desmond, richard attenborough, Sunset Boulevard
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3 responses to "Dirk's Five – Road Movies"
Andy 04/12/2012 at 9:20 am · · Reply →
Nice work. Can't think of many others
Green Street (the film that dared to anger real-life cockney hardman Danny Dyer – "'a can you 'av a f***in' hobbit playing a football hooligan?")
I can't think about '84 Charing Cross Road' without thinking about that Lee & Herring sketch
Lee and Herring blind-spot …
Back to school….
You want a moon on a stick
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