text:
\section{Introduction}

The evolution of galaxies is strongly affected by their capability of retaining their gas and accreting fresh material from the surrounding environment. Galaxies belonging to the so-called  ``blue-sequence'', which are actively forming stars and are dominated by young stellar populations, show an almost constant or a slowly declining star formation rate (SFR) throughout the Hubble time \citep[e.g.,][]{Panter+07}. Since the gas consumption time-scales are always of the order of a few Gyrs \citep{Noeske+07, Bigiel+11}, spiral galaxies need to replenish their gas at rates comparable to their star formation rates \citep{Hopkins+08, Fraternali&Tomassetti12}. These arguments are fully applicable to the Milky Way: with a SFR of 1-3 $\mo$ slowly declining over the last $\sim10$ Gyrs \citep[e.g.,][]{Aumer&Binney09, Chomiuk&Povich11}, the Galaxy would have exhausted its gas reservoir in a few Gyrs without replacement from outside \citep[e.g.,][]{Chiappini+97}.

There are essentially two sources from which disc galaxies can gain new gas: the intergalactic medium (IGM) and other gas-rich galaxies. The IGM is the place where the most of baryons are thought to still reside \citep[e.g.,][]{Bregman07}. Most of this gas should be in a diffuse warm-hot phase \citep[e.g.,][]{Shull+12}. Therefore the IGM represents a huge reservoir of nearly pristine gas but how this material can cool and accrete onto the discs is not well understood.  Current cosmological simulations predict that gas accretion can occur in two modes \citep[e.g.,][]{Ocvirk+08, Keres+09}: the ``hot'' accretion, which dominates the growth of massive galaxies, and the ``cold'' accretion through filamentary streams and clouds, which prevails in lower mass structures and at high redshifts \citep[e.g.,][]{Dekel&Birnboim06}.

The second channel for gas accretion is given by merger events. According to the Extended Press-Schechter theory, the structures in the Universe grow by several inflowing events and have increased their mass content through a small number of major mergers, more common at high redshifts, and through an almost continuous infall of dwarf galaxies \citep{Bond+91,Lacey&Cole93}. Although several theoretical \citep[e.g.,][]{Stewart+09, Kazantzidis+09} and observational studies \citep[e.g.,][]{Patton+00, Lotz+08, Lambas+12} have been carried out in the last years, the predictions and the estimates for the galaxy merger rate and its evolution with redshift remain uncertain and no consensus has been achieved yet \citep[e.g.,][]{Bertone&Conselice09, Hopkins+10}.

In this paper, we use neutral hydrogen (\hi) observations to investigate gas accretion from minor mergers onto star-forming galaxies in the Local Universe. The advantage of using \hi\ observations instead of the optical-UV ones is that both morphological and kinematical information are immediately available. In addition, the gas layers are more easily disturbed by tidal interactions than the stellar disc. Two recent studies, namely \cite{Holwerda+11} and \cite{Sancisi+08}, have taken advantage of \hi\ data and both make use of the WHISP catalogue \citep{vanderHulst+01}.  \cite{Holwerda+11} focused on the galaxy merger fraction and, employing techniques developed for optical-UV observations, found a merger fraction between 7\% and 13\%. Instead, \cite{Sancisi+08} attempted to quantify  the contribution of minor mergers to the total gas accretion. They found that 25\% of local galaxies show signs of minor interactions or have disturbed \hi\ distribution and, assuming lifetimes for these observed features of about 1 Gyr and typical accreted \hi\ mass of order $10^8$-$10^9\, \mo$, they calculated an accretion rate of about 0.1-0.2 $\moyr$. This value is about an order of magnitude lower than typical star formation rates.

In this study, we use a quantitative approach to obtain a reliable estimate for the merger fraction and the gas accretion rate. We make use of a specific-purpose numerical code that is able to quickly analyse a large number of \hi\ data-cubes, find dwarf gas-rich companions around disc galaxies and estimate an upper limit for the gas accretion onto the discs. In section \ref{sec:method}, we describe the main features of our code and the methods adopted. In section \ref{sec:application}, we show the results obtained by applying our analysis on a sub-sample of the WHISP catalogue and we discuss them in section \ref{sec:discussion}.

\section{Method}\label{sec:method}

We wrote a numerical code to automatically identify 3D sources in data-cubes, i.e. image arrays with two spatial dimensions, related to the position on the plane of the sky, and one spectral dimension, which can correspond either to velocity or to frequency. Our code is targeted to work with \hi\ observations as it performs a three dimensional scanning of the data to look for dwarf gas-rich companions around large galaxies. Once the program has found a candidate, it derives its physical properties, such as the \hi\ mass, the projected distance from the main galaxy and an estimate of the accretion rate onto the central disc. In short, the code used in this work is essentially a source finder plus an algorithm for estimating the accretion rate.

The standard flow of our code can be outlined in three steps:

\begin{enumerate}
\item \emph{Identifying the main-galaxy}. The pixels referable to the central galaxy emission are identified and isolated through  an appropriate mask.

\item \emph{Searching for dwarf galaxies}. The data-cube is scanned for three-dimensional sources and dwarf galaxies or \hi\ clouds inside the field of view are identified.

\item \emph{Estimating the gas accretion rate}. For each detected dwarf, a maximum accretion rate onto the disc is calculated by estimating a minimum time of collision between the satellite and the central galaxy.
\end{enumerate}

In the following sections, we describe the most important steps and the main features and limitations of our code.

\subsection{Searching for sources and background statistics}
The searching algorithm is derived from \emph{Duchamp}, a code dedicated to three-dimensional source detection \citep{Whiting12} and developed for the Australian SKA Pathfinder (ASKAP). The basic idea behind this algorithm is to locate and connect groups of bright and contiguous pixels that lie above some flux threshold, without imposing any size or shape requirement to the detection. The search is performed using either a two-dimensional raster-scanning algorithm \citep{Lutz80} or a one-dimensional research along each individual pixel spectrum. Three-dimensional sources (two spatial dimensions and one spectral) are then built up on the basis of adjacency or neighbourhood criteria both in the velocity and in the spatial domain. For a full description of the source finding algorithm, we refer to the \emph{Duchamp} main paper. The one-dimensional technique is less computationally expensive, but it can bring to spurious detections. On the contrary, the Lutz algorithm is generally more reliable at the price of the computational slowness. As discussed later in this section, we used the 1-D method to identify the main galaxy emission and the 2-D technique to detect companions.

The searching algorithm can be schematically summarized as follows:

\begin{enumerate}
\item \emph{Pixel detection}. The data-cube is scanned using one of the  above mentioned techniques and a list of all pixels with a flux greater than a given threshold is produced.

\item \emph{Merging objects}. The detected pixels that are considered close to each other based on spatial and spectral requirements are merged together. Adjacent detections or detections lying within a user-defined range of pixels or channels are expected to belong to the same object. After this step, a list of three-dimensional sources is produced.

\item \emph{Growing objects}. The size of the detections is increased by adding pixels at the edges of the objects that are above some secondary threshold. This step guarantees a smooth transition between the source and the background.

\item \emph{Rejecting objects}. Not all detected objects can be considered reliable. Sources that do not match some agreement criteria, like a minimum number of contiguous pixels and channels, are discarded.
\end{enumerate}

A crucial point of the searching algorithm is the determination of the flux threshold above which a pixel can be considered as a part of a source. In order to do this, the code needs to estimate the central value and width of the noise distribution in the data-cube. The former should be zero or very close to zero for \hi\ data-cubes without systematics (due for instance to problems with the data reduction). The typical data-cube of the WHISP survey is dominated by a large number of noise pixels and a relatively small number of bright pixels that belong to the sources. In such a situation, it is preferable to calculate the noise over the whole data-cube using the median as noise middle and the median absolute deviation from the median (MADFM, hereinafter) as noise spread. These quantities are less sensitive to the presence of very bright pixels than the equivalent normal statistics, the mean $\mu$ and the standard deviation $\sigma$. For a Gaussian distribution, the standard deviation can be written in term of the MADFM as $\sigma=s/0.6745$ \citep[for details, see][and references therein]{Whiting12}. The threshold $\tau$ is then determined with a simple sigma-clipping, i.e., it is set at a number $n$ of standard deviations $\sigma$ above the median $m$:

\begin{equation}
\label{eq:threshold}
 \tau = m + n\sigma
 \end{equation}

Such a value is the minimum flux that a pixel must possess to be selected by the algorithm. We checked that the noise middle and spread calculated using the whole data-cube are the same as those obtained using only the channels with line emission; the differences do not exceed 5\%.

We used the searching algorithms in two different steps: the identification of the main galaxy and the detection of satellites. The former consists in isolating all those regions ascribable to the main galaxy emission. The code performs a search in the data-cube using the one-dimensional technique and selects as the main galaxy the object that covers the largest number of pixels. This approach is not computationally expensive, and it is reliable when the code is analysing an heterogeneous group of galaxies, but it does not allow the code to identify systems in advanced phase of merging, i.e., when a companion is physically connected in space and velocity with the main galaxy. Concerning the satellites, we used the Lutz algorithm, which guarantees a better reliability and minimizes the number of spurious detections. We impose a neighbourhood criterion grounded on the spatial and spectral resolution of the observations: each detected pixel is merged with other detected pixels lying within a spatial beam and within two velocity channels, which is the typical instrumental broadening (FWHM) for \hi\ observations when Hanning smoothing has been applied. Finally, we reject all those detections that are smaller than the beam area of the observations and less extended in velocity than the spectral broadening.
We stress that a three-dimensional source finding algorithm, unlike the two-dimensional methods, can isolate sources with different kinematics even if they are totally or partially overlapped in the plane of the sky. Indeed, if two sources have radial velocities that differ more than the typical velocity resolution ($\sim$10-15 $\kms$), they are always detected as separate sources, no matter whether they overlap or not in the sky.

\subsection{Accretion and star formation rate estimates}

The main purpose of this study is to estimate the maximum gas accretion rate coming from minor mergers. In the following we describe our assumptions.

Firstly, we assume that all dwarf galaxies will collide in the future with the main galaxies and that their gas will be entirely and instantaneously accreted. Secondly, we assume that the collision will occur in the shortest possible time. In order to calculate this time, we make the satellites moving in parabolic trajectories leading to impact the outer regions of the main galaxies. The orbit is defined in the three-dimensional space by fixing the focus of the parabola at the centre of the main galaxy, imposing the passage through the satellite and fixing the position of the orbital peri-centre at a distance equal to the maximum radius of the central galaxy (Fig. \ref{fig:parabola}). For a generic conic orbit, the time-scale of collision can be obtained by using the equation of the true anomaly $\nu$ of celestial mechanics:

\begin{equation}\label{eq:true0}
\int_0^\nu {\frac{d\nu'}{(1-e\cos\nu')^2}} = \sqrt{\frac{\mu}{p^3}}\;(t-T_0)
\end{equation}

\noindent where $e$ is the eccentricity of the orbit, $T_0$ is the time of the peri-centre passage, $p$ is the semi-latus rectum of the conic section and $\mu = G(M_\mathrm{main} + M_\mathrm{sat}) \sim GM_\mathrm{main}$ is the total dynamical mass of the system galaxy plus satellite multiplied by the gravitational constant G. The dynamical mass of the central galaxy $M_\mathrm{main}(R_\mathrm{max})=G^{-1}v_\mathrm{c}(R_\mathrm{max})^2R_\mathrm{max}$ is calculated within the maximum radius $R_\mathrm{max}$ of the source, estimated by the searching algorithm. The circular velocity $v_\mathrm{c}$ is obtained from the velocity widths of the \hi\ global profiles at the 20\% of the peak flux corrected for the inclination taken from the HyperLEDA catalogue.
Solving the integral (\ref{eq:true0}) for parabolic orbits ($e = 1$) one obtains the following formula which describes the variation of the true anomaly $\nu$ as a function of time:

\begin{equation}
\label{eq:true}
\tan\frac{\nu}{2}+\frac{1}{3}\tan^3\frac{\nu}{2} = \sqrt{\frac{\mu}{p^3}}\;(t-T_0)
\end{equation}

\noindent where the semi-latus rectum for parabolic orbit is $p = 2R$, being $R$ the distance between the focus and the vertex of the parabola (Fig. \ref{fig:parabola}).

Using equation (\ref{eq:true}), we can estimate the time of the peri-centre passage $T_0$ by calculating $\nu$ through a de-projection of the projected anomaly $\nu_\mathrm{p}$ of the dwarf galaxy measured in the plane of the sky. The accretion rate of cold gas onto a certain galaxy is then obtained by dividing the \hi\ mass of each dwarf by its time of peri-centre passage:

\begin{equation}
\label{eq:rate}
\dot{M}_\mathrm{HI} = \sum_{i=0}^n M_{\mathrm{HI}\,,\,i}/T_{0\,,\,i}
\end{equation}

\noindent where the sum is taken over all the detected companion galaxies. The \hi\ mass $M_\mathrm{HI}$ is calculated from the flux density using the following relation \citep{Roberts75}:

\begin{equation}
\label{eq:HImass}
M_\mathrm{HI} = 2.356 \times 10^5 \, D^2 \, \int S(v) \, dv
\end{equation}

\noindent where $\int S(v) \, dv$ is the integral across the line of the flux density corrected for the primary beam attenuation and expressed in Jy km s$^{-1}$ and $D$ is the distance in Mpc. The equation (\ref{eq:HImass}) is valid under the assumption that the gas is optically thin, which is generally a good approximation for neutral hydrogen, especially in dwarf galaxies, thus no correction for \hi\ self-absorption was applied. The distances were preferably taken from the Extragalactic Distance Database \cite[EDD,][]{Tully+09}, available for a number of galaxies with $v_\mathrm{sys}$ up to $10000 \, \kms$ and mostly obtained from Cepheids, TRGB, SNIa or Cosmicflows-2 project \citep{Tully+13}. Otherwise, we used the NASA/IPAC Extragalactic Database (NED). For seven galaxies with no available better estimates, we used the Hubble flow $D=v_\mathrm{sys}/H_0$ with $H_0=70$ km s$^{-1}$ Mpc$^{-1}$ and the systemic velocity $ v_\mathrm{sys}$  corrected for Virgo-centric inflow using the values given by the HyperLEDA catalogue.

\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{parabola3.png}
\caption{Schematical view of the parabolic orbit approximation. The blue spiral is the main galaxy, \emph{S}  is the satellite with projected distance \emph{d} and true anomaly \emph{$\nu$}. The distance \emph{p} between the center of the spiral galaxy and the directrix $\Pi$ of the parabola is two times the outer radius of the main galaxy \emph{R}. }
\label{fig:parabola}
\end{figure}

We compare the total gas accretion (\ref{eq:rate}) to the gas depletion due to the star formation process in the discs. The SFR of the central galaxies was calculated from the far-infrared luminosities \citep{Kennicutt98}:

\begin{equation}
\label{eq:kenn}
\mathrm{SFR} = \frac{L_\mathrm{FIR}}{2.2 \times 10^{43}} \quad \mathrm{M_\odot \, yr^{-1} }
\end{equation}

\noindent with the $L_\mathrm{FIR}$ in erg s$^{-1}$ obtained from the far-infrared flux FIR defined after \cite{Helou+85} as:

\begin{equation}
\label{eq:FIR}
\mathrm{FIR} = 1.26\times10^{-11} (2.58f_{60\mu} + f_{100\mu}) \quad \mathrm{erg \, s^{-1} \, cm^{-2}}
\end{equation}

\noindent where $f_{60\mu}$ and $f_{100\mu}$ are the fluxes at 60 and 100 micron expressed in Jansky. In this work we used the IRAS fluxes taken from NED and HyperLEDA. All main galaxies in our sample are detected both at $60\mu$ and $100\mu$. See Tab. \ref{tab:maingalaxies} for their main physical properties.

\subsection{Major and minor mergers}\label{baryonicmass}

We split major and minor mergers depending on the baryonic mass ratio: pair of galaxies with $M_\mathrm{bar, sat}/M_\mathrm{bar, main}\leq0.20$ are classified as minor mergers, otherwise as major. We preferably estimate the baryonic mass as:

\begin{equation}
\label{eq:baryonicmass}
M_\mathrm{bar} = M_\mathrm{*} + 1.4M_\mathrm{HI}
\end{equation}

\noindent where the factor 1.4 take into account the helium gas fraction. We neglected the contribution of molecular gas. The \hi\ mass $M_\mathrm{HI}$ is directly estimated from data-cubes through eq. (\ref{eq:HImass}). A rough estimate of the stellar mass $M_\mathrm{*}$ is obtained by using the total K$_\mathrm{s}$-band magnitude, corrected for extinction, taken from the 2MASS Redshift Survey \cite[2MRS,][]{Huchra+12} and adopting the following formula \citep[e.g.][]{Longhetti&Saracco09}:

\begin{equation}
\label{eq:stellarmass}
\log_{10}(M_\mathrm{*}) = \log_{10}(M/L_\mathrm{K}) -0.4[K+5-5\log_{10}(D_\mathrm{[pc]}) -3.28]
\end{equation}

\noindent where $M/L_\mathrm{K}$ is the stellar mass-to-light ratio (in solar units) in the K-band and 3.28 is the absolute K-band magnitude of the Sun in the Vega system \citep{Binney&Merrifield98}. We assumed a constant value of mass-to-light ratio $M/L_\mathrm{K}=0.6\, \mo/L_{\odot,\mathrm{K}}$, compatible with stellar population models \citep[e.g.][]{Portinari+04} with a Kroupa IMF \citep{Kroupa02}.

When 2MRS magnitudes were not available, namely for most dwarf satellites and a few main galaxies, we directly derived $M_\mathrm{bar}$ from the Baryonic Tully-Fisher Relation (BTFR):

\begin{equation}
\label{eq:BTF}
\log_{10} (M_\mathrm{bar})= a\log_{10} (v_\mathrm{flat})+b
\end{equation}

\noindent with $a=3.82\pm0.22$ and $b = 2.01 \pm 0.41$  \citep{McGaugh12}. The $v_\mathrm{flat}$ was assumed as half of the inclination-corrected velocity widths $w_{20}$ of the \hi\ global profiles at the 20\% of the peak flux. Since inclination angles are not known for most dwarf satellites, we adopted an average inclination of 60 degrees for these galaxies.

\subsection{The data sample}
The Westerbork \hi\ survey of Irregular and Spiral galaxies Project \citep[WHISP,][]{vanderHulst+01} is a survey of the neutral hydrogen content in galaxies selected from the Uppsala General Catalogue \citep[UGC,][]{Nilson73} and observed with the Westerbork Synthesis Radio Telescope (WSRT). WHISP is to date the largest publicly available catalogue of \hi\ nearby galaxies observed with an interferometer and it includes galaxies at $\delta > 20\de$ (B1950) with major axis apparent size $>$ 1.2$'$ (B band) and \hi\ flux densities $F_\mathrm{HI} > 100$ mJy. Objects satisfying these selection criteria have generally systemic velocities less than 6000 $\kms$, i.e., distances lower than 85 Mpc using the Hubble flow with $H_0=70$ km s$^{-1}$ Mpc$^{-1}$. The galaxies were chosen to be reasonably distributed over all Hubble types, even if later-type galaxies are favoured by the observational criteria. The highest spatial resolution for the WHISP data is 12$''$ x 12$''$/sin $(\delta)$, the typical channel separation is of the order of 5 $\kms$. In this work, we used both \hi\ data-cubes spatially smoothed to 30$''$ x 30$''$ and 60$''$ x 60$''$. The original sample comprises 256 data-cubes containing about 370 galaxies.\footnote{ The datacubes, the column density maps and the velocity fields of the WHISP galaxies, at 12$''$, 30$''$ and 60$''$ of resolution, are publicly available for the ``Westerbork on the Web'' project at ASTRON (http://www.astron.nl/wow/).}

\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{dwarf_MF.pdf}
\caption{\hi\ Mass distribution of the detected galaxies in the WHISP sample. Orange shadowed boxes show the spiral galaxies selected as v$_\mathrm{flat}>100 \, \kms$, black boxes show their dwarf satellites. }
\label{fig:MF}
\end{figure}

Since our goal is to study dwarf satellites around large star-forming galaxies, we selected a sub-sample of spiral galaxies by keeping only  those data-cubes containing at least one galaxy with rotation velocity $v_\mathrm{flat}= w_{20}/(2\sin i)>100 \, \kms$. The selection was performed through a cross-correlation between the $w_{20}$ estimated directly from the data-cubes and the $w_{20}$ calculated using the Tully-Fisher relation from \cite{Sakai+00}:

\begin{equation}\label{eq:TF}
M_B = -(7.97\pm0.72)(\log w_{20}-2.5)-(19.80\pm0.11)
\end{equation}

\noindent where $M_B$ is the B-band absolute magnitude (corrected for galactic extinction and k-correction), taken from HyperLEDA. We kept only galaxies for which both methods returned $v_\mathrm{flat}>100 \, \kms$. This cross-correlation is needed to avoid spurious selections related to some unreliable inclination angles in the HyperLEDA catalogue. Our final sample has 148 data-cubes. Spiral galaxies therein have usually neutral hydrogen masses between $10^9 \; \mo$ and few $10^{10} \; \mo$ (Fig. \ref{fig:MF}). The global properties of the main galaxies are listed in Tab. \ref{tab:maingalaxies}.

\section{Results}\label{sec:application}

We ran our code both on data-cubes smoothed to $30''$ and $60''$. The results obtained with these two data sets are thoroughly comparable. We fixed a sigma-clipping threshold for the source finder equal to 4 (see equation \ref{eq:threshold}) and a secondary threshold for growing objects at the edges of 2.5. After extensive experiments, these values appeared the best compromise between reaching low sensitivities and avoiding spurious detections.

\begin{figure*}[!p]
\centering
\includegraphics[width=0.95\textwidth]{maps.png}
\caption{ Three examples of multiple systems in the WHISP sample. From the \emph{top} to the \emph{bottom}, UGC 4666, UGC 7989, UGC 6787 and their dwarf companions. In the \emph{left panels}, the \hi\ column-density maps (0th moment), in the \emph{right panels}, the velocity fields (1st moment) obtained from 30'' smoothed data-cubes.  }
\label{fig:examples}
\end{figure*}

\begin{figure*}[!t]
\centering
\includegraphics[width=0.99\textwidth]{dwarf_prop.pdf}
\caption{ \emph{Left panel}: the gray dots show the \hi\ masses of detected companions as a function of distance, red triangles are the lowest detectable mass in the correspondent data-cubes. \emph{Right panel}: distance from the main galaxies projected onto the plane of the sky of the detected satellites as a function of their \hi\ mass.}
\label{fig:masses}
\end{figure*}

We found that, among 148 data-cubes, 101 ($\sim 68.2\%$) had no detectable companions, whereas 47 ($\sim 31.8 \%$) contained multiple systems. Among these 47 data-cubes, 15 ($\sim 10.1 \%$ of the total, $\sim 31.9 \%$ of multiple systems) contained only galaxies with similar masses ($M_\mathrm{bar, sat}/M_\mathrm{bar, main}>0.20$). Six data-cubes ($\sim 4.1 \%$ of the total, $\sim 12.8 \%$ of multiple systems) show both major and minor companions and 26 data-cubes ($\sim 17.6 \%$ of the total, $\sim 55.3 \%$ of multiple systems) show only dwarf companions. Overall, among 148 analysed data-cubes, 21 ($\sim 14.2 \%$), show companions which could be possible candidates for a future major merging, while 32 data-cubes ($\sim 21.6 \%$) show potential candidates for minor mergers. Some examples of spiral galaxies with minor satellites are shown in Fig. \ref{fig:examples}.

We focused on potential minor mergers and all data-cubes with only major companions were excluded from the further analysis. For the six data-cubes with both type of companions, we assumed as the main galaxy the one with the largest \hi\ mass and we ignored the other spiral galaxies. The total number of dwarf gas-rich satellites detected is 50 (Tab. \ref{tab:galaxies}). Forty-six dwarf galaxies have a clear optical counterpart in the Sloan Digital Sky Survey (SDSS) or in the Digitized Sky Survey (DSS) images. Four detections, marked with an asterisk in  Tab. \ref{tab:galaxies}, are not univocally identifiable and they could be either very faint dwarf galaxies or \hi\ clouds. Most satellites are already catalogued in galaxy archives. Ten galaxies, marked with a dagger in Tab. \ref{tab:galaxies},  seem not to be catalogued. The \hi\ masses of the detected dwarf galaxies vary between about $10^7\,$ M$_\odot$ and few $10^9\,$ M$_\odot$. The \hi\ mass distribution of the main galaxies and their minor satellites is shown in Fig. \ref{fig:MF}. The mass function for spiral galaxies is peaked at $\log \mathrm{M_{HI \, [M_\odot]}}\sim9.5$, consistently with studies on wider \hi\ samples \citep[e.g.,][]{Zwaan+05}. Most dwarf companions have masses of a few $10^8 \; \mathrm{M}_\odot$ and their mass distribution has a cut-off above $5 \times 10^9 \; \mathrm{M}_\odot$. This is partially due to our selection criteria. However, it is interesting to note that this distribution is fairly comparable with that of \hi -rich dwarf galaxies in the Local Group and in Local Group analogues \citep[e.g.,][]{Grcevich&Putman09, Pisano+11}. In Fig. \ref{fig:masses} we show the \hi\ masses of the detected dwarf galaxies as a function of the distance from the Milky Way. The red triangles represent the minimum detectable mass for each data-cube, calculated using equation (\ref{eq:HImass}) on a three-dimensional region with the size of a spatial beam times the velocity resolution (two channels) and a flux of $4\times$R.M.S. noise of the cube. This is the minimum mass that an object must have to be accepted by the source-finding algorithm. Note the bias effect on the detectable mass due to the distance (see discussion in \ref{sec:uncertainties}).

The projected distances of the dwarf satellites from the main galaxies usually range from some dozen to a few hundred kiloparsecs and typical time-scales for collisions, estimated through the parabolic orbit approximation, are between  $\sim100$ Myr and 2 Gyr. The number of dwarfs within 100 \kpc\ from the main galaxies and between 100 and 200 \kpc\ is almost the same. In the \emph{right panel} of Fig. \ref{fig:masses} we show the projected distance as a function of the dwarf \hi\ masses. Within 200 \kpc , dwarf galaxies are quite uniformly distributed over the \hi\ masses. There is a weak tendency for companions to be more massive at larger distances, as we may expect. However, there is an observational bias that can affect this plot. It is a combination of two effects: the linear  field-of-view of the  observations increases with distance, while the minimum detectable mass (Fig. \ref{fig:masses}, \emph{left panel}) and the linear resolution decrease. Thus we may detect preferentially companions with lower masses closer to the main galaxies and vice-versa. Moreover, there is also a selection effect due to the primary beam attenuation, i.e. at large angular distances, only massive systems are detected because of the lower sensitivity of the instrument. These effects make it difficult to compare our findings with studies of dwarfs galaxies in the Local Group.

\begin{table*}[!t]
\small
\caption{\normalsize Detected companions of the WHISP spiral galaxies with $M_\mathrm{bar,sat}/M_\mathrm{bar,main} \le 0.20$: (1) First name in NED archive or DF if not classified, (2) UGC name of the main galaxy, (3) celestial coordinates, (4) adopted distance [same as the main galaxy or taken from EDD catalogue, when specified], (5) systemic velocity,  (6) line width of the global profile at the 20\% level, (6) total \hi\ mass, (8) projected distance from the main galaxy (9) time of collision with the main galaxy in a parabolic orbit, (10) gas accretion rate onto the main galaxy.}
\label{tab:galaxies}
\centering
\begin{tabular}{llcccccccccc}
\hline\hline\noalign{\vspace{5pt}}
Name 	& Main galaxy 	& Coord. (J2000) 	& $D$ & $v_\mathrm{sys}$ & $w_{20}$ & $M_\mathrm{HI}$ & $d_\mathrm{proj}$ & $t_\mathrm{coll}$ & $\dot{M}_\mathrm{HI}$ \\

&	& RA-Dec & Mpc & km/s & km/s & $10^8 \, \mo$ & kpc & $10^8$ yr & $\, \mo$/yr \\
\hspace{5pt} (1) & \hspace{15pt} (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10)\\
\noalign{\smallskip}
\hline\noalign{\vspace{5pt}}
AGC 102802 	&	 UGC 485   	&	J004702.7+301243	&	58.9	&	5296	&	85	&	9.08	&	117	&	15.7	&	0.58	\\
AGC 113996 	&	 UGC 624   	&	J010107.2+304052	&	78.3	&	4762	&	29	&	8.76	&	119	&	11.6	&	0.75	\\
AGC 113884 	&	 UGC 624   	&	J010000.3+302357	&	78.3	&	4717	&	96	&	5.04	&	391	&	17.8	&	0.28	\\
$[$VH2008$]$ J0101+4744 	&	 UGC 625   	&	J010118.4+474432	&	28.3	&	2795	&	62	&	3.02	&	36	&	4.5	&	0.67	\\
DF1$^\dagger$	&	 UGC 1437  	&	J015708.1+354825	&	54.5	&	4592	&	172	&	14.80	&	133	&	9.8	&	1.51	\\
PGC 9994      	&	 UGC 2141  	&	J030653.0+301542	&	24.7	&	812	&	43	&	7.37	&	75	&	5.6	&	1.32	\\
PGC 2328690 	&	 UGC 2459	&	J030225.7+485452	&	32.4	&	2449	&	134	&	16.29	&	131	&	14.3	&	1.14	\\
$[$KLT2208$]$ HI J0302+352$^*$ &	 UGC 2487  	&	J030210.5+351627	&	72.2	&	4933	&	55	&	15.43	&	351	&	18.1	&	0.85	\\
$[$SOS2010$]$ J0301491+3529012 	&	 UGC 2487  	&	J030147.2+352839	&	72.2	&	4876	&	38	&	3.61	&	129	&	8.6	&	0.42	\\
UGC2813 	&	 UGC 2800  	&	J034234.1+711828	&	16.1$^1$	&	1381	&	62	&	0.99	&	33	&	4.2	&	0.24	\\
HFLLZOA G136.96+14.21 	&	 UGC 2916  	&	J040403.5+713707	&	68.0	&	4450	&	158	&	14.36	&	114	&	10.8	&	1.33	\\
2MASX J04550438+3002212 	&	 UGC 3205  	&	J045826.3+295653	&	47.6	&	3239	&	173	&	10.26	&	350	&	17.6	&	0.58	\\
DF2$^\dagger$	&	 UGC 3205  	&	J045504.2+300209	&	47.6	&	3530	&	47	&	5.03	&	184	&	9.7	&	0.52	\\
DF3$^\dagger$	&	 UGC 3205  	&	J045653.8+293602	&	47.6	&	3229	&	110	&	19.34	&	385	&	18.3	&	1.06	\\
DF4$^\dagger$	&	 UGC 3382  	&	J055903.3+621719	&	67.2	&	4407	&	64	&	3.83	&	160	&	12.6	&	0.30	\\
DF5$^\dagger$	&	 UGC 3407  	&	J060841.0+415647	&	39.3	&	3683	&	66	&	3.50	&	96	&	10.1	&	0.35	\\
DF6$^\dagger$	&	 UGC 3407  	&	J060913.3+420104	&	39.3	&	3688	&	114	&	4.51	&	48	&	7.9	&	0.57	\\
DF7$^\dagger$	&	 UGC 3407  	&	J060853.9+420338	&	39.3	&	3693	&	73	&	0.80	&	27	&	3.5	&	0.23	\\
DF8$^{\dagger\,*}$	&	 UGC 3422  	&	J061633.1+705743	&	77.2	&	4009	&	24	&	3.22	&	238	&	9.8	&	0.33	\\
GALEXASC J061256.68+710650.6 	&	 UGC 3422  	&	J061254.8+710659	&	77.2	&	3998	&	104	&	5.52	&	83	&	7.5	&	0.74	\\
NPM1G +60.0018 	&	 UGC 3546  	&	J065150.2+604122	&	17.9	&	1768	&	52	&	1.12	&	58	&	5.8	&	0.19	\\
GALEXASC J070643.91+635521.0	&	 UGC 3642  	&	J070645.1+635515	&	67.3	&	4714	&	106	&	3.56	&	169	&	11.1	&	0.32	\\
UGC 3660 	&	 UGC 3642  	&	J070634.1+635056	&	67.3	&	4261	&	75	&	8.70	&	350	&	17.9	&	0.49	\\
KUG 0829+227B 	&	 UGC 4458  	&	J083247.7+223443	&	68.6	&	4621	&	231	&	12.80	&	105	&	12.4	&	1.03	\\
MCG +10-13-030 	&	 UGC 4666  	&	J085422.1+585908	&	16.0	&	1016	&	90	&	1.26	&	69	&	5.7	&	0.22	\\
SDSS J091001.72+325659.8 	&	 UGC 4806  	&	J091005.0+325607	&	25.5	&	2049	&	125	&	4.23	&	89	&	9.5	&	0.45	\\
KUG 0906+333A 	&	 UGC 4806  	&	J090919.5+330734	&	25.5	&	1897	&	60	&	1.88	&	18	&	5.7	&	0.33	\\
SDSS J093137.13+292533.3 	&	 UGC 5060  	&	J093138.0+292534	&	24.0	&	1608	&	77	&	0.53	&	117	&	9.9	&	0.05	\\
KDG 059 	&	 UGC 5253  	&	J095156.6+720439	&	16.6	&	1121	&	46	&	2.03	&	57	&	6.2	&	0.33	\\
UGC 6797 	&	 UGC 6778  	&	J114940.5+482533	&	17.1	&	962	&	81	&	7.28	&	87	&	8.5	&	0.86	\\
SDSS J115027.42+490105.9	&	 UGC 6778	&	J115027.4+490106	&	17.1	&	1120	&	31	&	1.67	&	138	&	11.2	&	0.12	\\
UGC 6791	&	 UGC 6786	&	J114923.6+264428	&	22.5$^1$	&	1866	&	274	&	5.38	&	111	&	10.0	&	0.54	\\
SDSS J114820.16+562045.7 	&	 UGC 6787  	&	J114820.6+562049	&	22.1	&	1080	&	28	&	0.62	&	105	&	7.6	&	0.08	\\
UGC 6733 	&	 UGC 6787  	&	J114535.7+555313	&	19.1$^2$	&	1158	&	187	&	5.26	&	130	&	10.3	&	0.51	\\
UGC 6816 	&	 UGC 6787  	&	J115047.5+562719	&	17.1$^1$	&	887	&	115	&	5.78	&	146	&	11.0	&	0.52	\\
SDSS J122442.59+544441.3 	&	 UGC 7506  	&	J122440.2+544448	&	36.0	&	2495	&	109	&	2.18	&	154	&	11.6	&	0.19	\\
UGC 8005	&	 UGC 7989  	&	J125149.1+254644	&	14.3$^1$	&	1196	&	198	&	8.84	&	101	&	8.6	&	1.02	\\
UGC 8254 	&	 UGC 8307  	&	J131038.2+363807	&	19.1	&	1088	&	105	&	3.71	&	149	&	16.1	&	0.23	\\
DF9$^{\dagger\,*}$	&	 UGC 8307  	&	J131153.6+362758	&	19.1$^1$	&	954	&	75	&	1.92	&	100	&	14.2	&	0.14	\\
UGC 8271 	&	 UGC 8307  	&	J131131.3+361655	&	18.5$^1$	&	1145	&	150	&	6.99	&	156	&	22.1	&	0.32	\\
DF10$^{\dagger\,*}$ 	&	 UGC 8307  	&	J131134.3+362942	&	19.1	&	1191	&	32	&	0.58	&	109	&	15.5	&	0.04	\\
KUG 1309+362 	&	 UGC 8307  	&	J131146.7+355731	&	19.1	&	1123	&	26	&	0.30	&	245	&	24.9	&	0.01	\\
UGC 8303 	&	 UGC 8307  	&	J131317.6+361303	&	18.5$^1$	&	948	&	92	&	9.77	&	139	&	20.3	&	0.48	\\
UGC 8314 	&	 UGC 8307  	&	J131401.0+361908	&	19.1	&	938	&	71	&	1.06	&	113	&	21.2	&	0.05	\\
MCG +08-27-001 	&	 UGC 9366  	&	J143359.2+492647	&	38.9	&	2122	&	127	&	6.18	&	88	&	6.2	&	1.00	\\
KUG 1512+557	&	 UGC 9797  	&	J151400.2+553222	&	46.6	&	3550	&	154	&	9.66	&	94	&	9.4	&	1.03	\\
SDSS J152617.51+404004.0 	&	 UGC 9858  	&	J152617.9+404008	&	32.2	&	2687	&	51	&	11.80	&	66	&	7.7	&	1.53	\\
MCG +08-34-005 	&	 UGC 11283	&	J183400.4+492233	&	30.0	&	2076	&	63	&	3.75	&	51	&	7.5	&	0.50	\\
GALEXASC J215645.61+275419.5	&	 UGC 11852	&	J215645.7+275418	&	82.4	&	5710	&	46	&	5.30	&	221	&	15.2	&	0.35	\\
ZOAG G095.92-08.72	&	 UGC 11951	&	J221145.4+453649	&	14.2	&	1145	&	78	&	7.52	&	74	&	8.3	&	0.91	\\

\noalign{\vspace{2pt}}\hline
\noalign{\vspace{5pt}}
\multicolumn{3}{l}{$^\dagger$ Not catalogued in the NED, HyperLEDA or SIMBAD archives. } \\
\multicolumn{8}{l}{$^*$ Without a clear optical/UV counterpart in DSS, SDSS or GALEX images. DF8 is not covered by the SDSS survey.} \\
\multicolumn{3}{l}{$^1$ Distance from EDD catalogue.} \\
\end{tabular}
\end{table*}

\begin{figure*}[t]
\centering
\includegraphics[width=0.80\textwidth]{sfr-acr.pdf}
\caption{ Upper limits to the cold gas accretion rates from satellites vs star formation rates in spiral galaxies in the WHISP sample. The inverted dark blue triangles are upper limits to the gas accretion rate for galaxies with detected satellites (including both visible and hidden accretion), the inverted orange triangles are the hidden accretion upper limits for galaxies without companions, estimated as discussed in the text. The star formation rates are lower limits calculated from the far-infrared fluxes. The blue-shadowed region represents a complete feeding of SF through minor mergers.}
\label{fig:sfr-acc}
\end{figure*}

The systemic velocity of dwarf galaxies is calculated as the average midpoint between the velocities at the 20\% and 50\% of the peak flux of their global \hi\ profiles. The $\Delta v_\mathrm{sys} = \,\,\parallel v_\mathrm{sys, main}-v_\mathrm{sys, sat}\parallel\,$ ranges between a few tens to a few hundreds $\kms$. Satellites do not have systemic velocities that differ more than 300 $\kms$ from those of the main galaxies. The velocity widths $w_{20}$ of dwarf galaxies, taken at the 20\% of the peak flux, are usually lower than 200 $\kms$, even if corrected for a mean inclination of 60 degrees, except for three galaxies. Overall, most of the satellites have $w_{20}<100$ $\kms$.

For each data-cube with identified dwarf companions, we calculated the maximum possible accretion rate of cold hydrogen gas $\dot{M}_\mathrm{HI}$ onto the main galaxy, the star formation rate $\dot{M}_\mathrm{SF}$ of the main galaxy and the ratio $\dot{M}_\mathrm{HI}/\dot{M}_\mathrm{SF}$. For all galaxies, with or without identified companions, a potentially hidden accretion from dwarfs below the detectability limit was estimated. The hidden accretion rate was calculated by dividing the above-mentioned minimum detectable mass by the average collision time over the sample, i.e $1.1 \, \Gyr$. Integrating the \hi\ mass function ($\phi_*[\mathrm{Mpc^{-3}\,dex^{-1}}\,h_{70}^3] = 4.8 \pm 0.3 \times 10^3 $, $\log(M_*/M_\odot)+2\log h_{70}=9.96\pm0.02$ and $\alpha = -1.33\pm0.02$, \cite[][]{Martin+10}) below the detection limit and within the volume of each data-cube always gives \hi\ masses lower than minimum detectable mass. Thus, with our choice we are maximizing the mass of the undetected galaxies.

We found a mean upper limit for the accretion in galaxies with identified minor companions of 0.86 $\moyr$, with a mean ratio $\langle \dot{M}_\mathrm{HI}/\dot{M}_\mathrm{SF} \rangle \sim 0.67$. A more meaningful estimate is however the mean upper limit to the accretion over the whole sample, that turns out to be $\dot{M}_\mathrm{HI}=0.28 \, \moyr$ against the average star formation rate of 1.29 $\moyr$, with a mean ratio $\langle \dot{M}_\mathrm{HI}/\dot{M}_\mathrm{SF} \rangle \sim 0.22$. The median of $\dot{M}_\mathrm{HI}/\dot{M}_\mathrm{SF}$ is 0.07. Thus, the ratio of the gas needed for star formation to the maximum gas accretion provided by minor mergers is between 5 and 14. Considering a fraction of gas recycle from stellar feedback of 30\% \citep[e.g.][]{Naab&Ostriker06} leads to a ratio between 3 and 10.

The above results show that the number of dwarf galaxies in the Local Universe is on the average too low to guarantee the continuous gas replenishment needed by star formation. In Fig. \ref{fig:sfr-acc} we show a plot of $\dot{M}_\mathrm{HI}$ versus $\dot{M}_\mathrm{SF}$ for each galaxy individually. If the gas accretion were large enough to sustain the star formation of the main galaxies, the data points would have fully populated the blue-shadowed region in the upper-left corner, whereas the vast majority lie well below the blue straight-line indicating a ratio $\dot{M}_\mathrm{HI}/\dot{M}_\mathrm{SF}=1$.
We conclude that minor mergers can not bring enough gas to the discs and sustain star formation. Once again, our values of gas accretion rates are very strong upper limits, because of our very stringent assumptions, and the real accretion rates could reasonably be one order of magnitude lower than our estimate. Incidentally, we note that our assumptions would imply that all dwarf galaxies disappear in the next 2 Gyr. We stress that our SFRs are likely lower limits as they are calculated using only FIR fluxes. This bias goes in the direction of strengthening our findings.

We repeated the analysis of the WHISP data-cubes using a sigma-clipping threshold for the sources of $3\sigma$ and $5\sigma$. Reducing the detection threshold leads the program to identify many more dwarf companions: more than 100 minor satellites are detected at the lower level, but most of these sources are clearly false detections and the results obtained would be very likely unreliable. Such a large fraction of wrong detections is probably due to the low signal-to-noise of the WHISP data-cubes. Instead, increasing the detection threshold to 5$\sigma$ leads to results very similar to those described above as just two of the dwarf companions found at $4\sigma$ are missed by the rejection criteria, namely the satellites of UGC 7506 and UGC 9858. These companions are actually good detections, as quoted in the literature \citep{Noordermeer+05}, but at a $5\sigma$ level they are discarded by the one beam covering requirement. The mean values of the accretion rate at $5\sigma$ are also in agreement with those found at $4\sigma$.

\section{Discussion}\label{sec:discussion}

The application of our code to the WHISP catalogue led to a firm upper limit for the accretion of cold gas from minor mergers in the Local Universe of $ 0.28 \;\moyr$. The total multiple system fraction for the WHISP sample is $\sim 32\%$, in particular $\sim 22\%$ of galaxies are accompanied by minor companions and $\sim 14\%$ are major systems. Here we discuss the main uncertainties of our results and their relevance.

\subsection{Uncertainties}\label{sec:uncertainties}

Our estimate does not take into account the molecular fraction. The amount of molecular gas in dwarf galaxies is highly unconstrained as they are often undetected in CO emission lines \citep[e.g.,][]{Taylor+98}. They also usually have low metallicities, making the conversion between CO and H$_2$ even more uncertain \citep[e.g.,][]{Boselli+02}. However, any realistic correction for molecular gas should not increase our accretion rate by more than a factor two.

WHISP is a source-targeted survey and it can not be obviously considered as a complete sample. The selection criterion, grounded on the apparent size of the observed galaxies, produces a catalogue that favours progressively larger and more massive galaxies moving to greater distances from the Milky Way. This effect can be appreciated in Fig. \ref{fig:masses} (upper envelop) although it appears to be not too severe.  The growth with the distance of the minimum detectable mass furthermore makes it impossible to detect low mass satellites at large distances. In order to test the importance of these biases, we have considered only those data-cubes with a minimum detectable mass $M_\mathrm{det} \leq 10^8 \mo$. In this way, we can obtain a sub-sample of galaxies where satellites are quite uniformly distributed over the mass and the distance ranges (\emph{left panel} of Fig. \ref{fig:masses}). The maximum accretion rate obtained in this case is  $0.21 \moyr$. Reducing the threshold to data-cubes with $\log M_\mathrm{det} \leq 5\times10^7 \mo$ leads to a maximum accretion rate of $0.18 \moyr$. These values indicate that our accretion rate estimates is not strongly affected by the incompleteness of the sample of the dwarf galaxies.

Another bias effect is related to the linear field of view, which is greater at larger distances. In the farthest systems,  the field of view allows us to observe satellites with projected distances of some hundreds kpc from the main galaxies, whereas we can not go beyond one hundred kpc in the closest systems. The primary beam attenuation of the WSRT is significantly large ( $\sim80\%$ of the flux is missed) beyond $25'$ from the pointing center, corresponding to $\sim70$ kpc at about 10 Mpc.  This indicates that we should be able to detect fairly separated satellites also in the nearest systems. The most distant satellites have larger collision time-scales and their contribution to the global accretion is expected to be smaller. In our sample, considering only satellites within 100 kpc from the main galaxies gives an accretion rate of 0.38 $\moyr$,  0.27 $\moyr$ between 100 and 200 kpc and 0.21 $\moyr$ beyond 200 kpc (the global value being 0.86 $\moyr$) . These results show that the contribution of very distant satellites is progressively less important, thus the limited field of view of the closest systems should not significantly affect our accretion rate estimate.

 In the literature, mergers are usually classified on the basis of their dynamical mass ratio: pair of galaxies with $M_\mathrm{sat}/M_\mathrm{main} \le 0.1-0.2$ are considered minor mergers, otherwise major mergers. Unfortunately, we can not trivially estimate the dynamical masses of satellite galaxies from the \hi\ data. Thus, in this work, we divided satellites depending on the ratio of their baryonic mass to the main galaxy baryonic mass. Satellites with baryonic content lower than 20\% of the main galaxies ($M_\mathrm{bar,sat}/M_\mathrm{bar,main} \le 0.20$) are classified as minor companions. This is an arbitrary but conservative choice, since most detected satellites have mass ratio $\ll 0.05 $. It is however interesting to quantify the accretion rate using different baryonic mass ratios. In our sample, the maximum accretion rate ranges between $0.20 \moyr$ for $M_\mathrm{bar, s}/M_\mathrm{bar,g} \le 0.1$ and $0.56 \moyr$ for $M_\mathrm{bar,sat}/M_\mathrm{bar,main} \le 0.5$. If we consider the whole galaxy pairs as potential mergers and we calculate the accretion rate by accreting the less massive ones onto the most massive ones, we obtain the value of $1.22 \moyr$. Even such an excessive overestimate turns out to be of the same order of the mean SFR. We conclude that mergers in the Local Universe can not sustain the star formation in spiral galaxies.

\begin{comment}
As a final  consistency check, we verified our estimate by analysing the \hi\ data-cubes from the Westerbork Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey \citep{Heald+11}. This survey comprises very deep observations of 24 local spiral galaxies, observed at a sensitivity capable of detecting \hi\ sources of a few $10^5 \mo$. This sample is small, but statistically complete as explained in \cite{Heald+11}. We excluded NGC4631, a strongly interacting spiral galaxy, because of the complexity of its gas distribution. We performed our analysis on the remaining 23 galaxies by using a $3.5\sigma$ flux threshold, we found that 10 of them have at least one detectable companion or \hi\ clouds (J\"{u}tte et al., in preparation) and we estimated a maximum accretion rate onto the main galaxies of 0.19 $\moyr$, a value fully compatible with the one found for the WHISP sample.
\end{comment}

\subsection{Comparison to other estimates}

The accretion of cold gas from minor mergers in the Local Universe has been estimated by \cite{Sancisi+08}, visually inspecting and comparing total maps, velocity fields and position-velocity diagrams for the WHISP galaxies. They found a minor merger fraction of about 25\%. Unlike our approach, they considered only those systems that show clear signs of tidal interactions, such as tails, bridges, disturbed \hi\ morphologies and/or kinematics. Assuming typical \hi\ masses of the  dwarfs of the order $10^{8-9} \; \mathrm{M}_\odot$ and a lifetime for observed features of about 1 Gyr, Sancisi et al. inferred a mean accretion rate of \hi\ gas around $0.1-0.2 \; \moyr$ and they stressed that such a value is likely a lower limit. It is worth noting that most systems we considered as potential minor mergers were not recognized that way by Sancisi et al. and, on the contrary, many interactions they identified were not found by our code. The reason is simple: our code looks for ``separated'' objects and it handles all dwarf companions as candidates for minor mergers, also those showing no signs of ongoing interaction. In other words, we look at the population of dwarfs in the environment of a spiral galaxy that could become a minor merger in the next future. Our code identifies companions until the two galaxies start ``touching'' each other and we estimate the accretion rate using the time-scale for collision as accretion time. Instead, \cite{Sancisi+08} find a later stage of merging, i.e., when galaxies are strongly interacting and the gas is visibly disturbed in the morphology and/or in the kinematics. Consequently, they calculate the accretion rate using as time-scale the dynamical time that it should take for these features to disappear as the gas redistributes uniformly in the disc. In our work the accretion process ends when galaxies touch each other, whereas for \cite{Sancisi+08} that is the starting point. However, since the population of dwarf galaxies has likely remained similar in the last Gyr or so, the two accretion rates should be comparable. Interestingly, our upper limit of $ \dot{M}_\mathrm{HI}< 0.28 \;\mathrm{M}_\odot \; \mathrm{yr}^{-1}$ is not in contradiction with the average accretion rate estimated by \cite{Sancisi+08}.

\subsection{Merger fraction}
Most of recently published studies on the local merging systems have been made using images from optical-UV galaxy surveys \citep[e.g.,][]{Patton+00, Lambas+12, Robotham+12} such as the Second Redshift Survey of Southern Sky (SRSS2), the Sloan Digital Sky Survey (SDSS) and the recent Galaxy And Mass Assembly (GAMA) survey, whereas just a couple of studies have been carried on using \hi\ data \citep{Sancisi+08, Holwerda+11}. These studies have mainly investigated the fraction and the rate  (fraction of mergers per comoving volume and time units) of galaxies showing signs of interactions and their evolution with time.

To date, two main approaches have been used to estimate the galaxy merger fraction and both make use of high resolution imaging. The pair method consists in counting the galaxies spatially separated from each other by less than a few tens of kpc and with spectroscopic radial velocities that do not differ by more than a few hundreds of $\kms$ \citep[e.g.,][]{LeFevre+00, Lin+08}. Using this kind of approach it is possible to estimate a ``progenitor galaxy'' merger fraction.
The second approach identifies mergers by quantifying morphological signatures that can be related to past or ongoing interactions, such as asymmetries and/or tails. This method makes use of several parameters for describing peculiar light distributions, such as the Concentration-Asymmetry-Smoothness parameters \citep[CAS,][]{Conselice03} or the Gini-M$_{20}$ parameters \citep{Lotz+04}. This technique can identify mergers in a relatively late stage, but not all asymmetric galaxies are necessary merger features.
The asymmetry method is similar to the technique used by \cite{Sancisi+08}, whereas our approach on \hi\ data-cubes is conceptually similar to the close pair method.  The main difference is that we do not impose any limit for the projected distance between galaxies, whereas the velocity criterion is implicit in the data-cubes. Moreover, we select objects in 3D space (so potentially also overlapping in the sky) and we estimate the minimum time of collision for each galaxy independently.

The asymmetry and close pairs methods have been widely used with optical galaxy surveys, but, despite the large number of studies, there is little consensus on the galaxy merger rate and its evolution with redshift. Current observations of the fraction of galaxy undergoing a merger differ by an order of magnitude, from $\sim2\%$ \citep[e.g.,][2.3\% and 1.9\%, respectively]{Patton+00, DePropris+07} to 15\% \citep[e.g.,][]{deRavel+09} and its trend with redshift vary from no evolution \citep[e.g.,][]{Jogee+09} to strong evolution \citep[e.g.,][]{Lopez-Sanjuan+09}. These discrepancies mainly arise from the different criteria for galaxy counting, merger selection and bias in the galaxy samples. The value we found ($\sim 32\%$) is a companion fraction rather than a merger fraction as some companions that we considered are fairly far away from the main galaxies (Fig. \ref{fig:masses}, \emph{right panel}). It is therefore difficult to compare our fraction with the above mentioned values. Broadly speaking, our estimate, which is indeed an upper limit, is higher at least of a factor 2-3 because our program treats all multiple systems as mergers and, working with \hi\ data, identifies more easily dwarf gas-rich companions compared to optical observations. However, if we exclude the very far away companions, namely those beyond 100 \kpc\ of projected distance, we obtain a companion fraction of $\sim 14\%\,$, not too different from the values found with optical studies. Finally, we stress that the WHISP sample is insignificant compared to other local references based on large catalogues, such as the SDSS or the Millennium Galaxy Catalogue (MGC), so that our values are less reliable from a statistical point of view.

A recent study carried out by \cite{Holwerda+11} estimated the merger fraction and rate for the whole WHISP sample using both close pair and asymmetry methods on \hi\ total maps. Holwerda et al. found a merger fraction of 7\% based on pairs, and 13\% based on disturbed morphology. We can not compare our merger fraction with the latter value, because our program ignores the galaxy morphology, but the former value is fully comparable and our estimate is significantly higher by about a factor 4. A possible reason of such a discrepancy is that Holwerda et al. based their pair fraction on 24 multiple systems previously identified and classified as interacting by Noordermeer et al. (2005b) and Swaters et al. (2002b), whereas our code detected a much larger number of satellites (see Tab. \ref{tab:galaxies}). If we use this sub-sample, the merger fractions become closely comparable.

\subsection{Other channels for gas accretion}

How star-forming galaxies can sustain their star formation is still an open question. In this study, we demonstrated that gas-rich minor mergers do not play a primary role and other dominant accretion channels must be admitted. A way to fill the discrepancy between the estimated accretion rates and the SFRs could be to assume that the \hi\ mass function were much steeper in the recent past than now, so that the number of dwarf satellites to be accreted were much higher. However, to date no observational evidence in that direction can be achieved with the present generation of radio-telescopes and studies of the Damped Lyman $\alpha$ systems show a remarkable constancy of the \hi\ mass throughout the Hubble time \citep[e.g.,][]{Prochaska&Wolfe09}. Another possibility is that the most accretion is supported by infalling of gas clouds with \hi\ masses of $10^7-10^6 \, \mo$, but recent deep observations of nearby groups of galaxies \citep[e.g.,][]{Pisano+07,  Chynoweth+09}, as well as large blind surveys, such as ALFALFA \citep{Giovanelli+07}, showed no evidence for a significant population of these small \hi\ clouds. Moreover, studies on the Milky Way's High Velocity Clouds (HVCs) estimated a contribution to the total gas accretion of $0.1-0.2 \moyr$ \citep[e.g.,][]{Wakker+07, Putman+12}, a value much smaller than the SFR.
In addition, the gas in the ionized phase could produce a further accretion rate of $\sim 1 \moyr$ \citep[e.g.,][]{Shull+09}, but it is not understood whether this gas can feed the star formation process in the disc. Numerical simulations \citep[e.g.,][]{Fernandez+12} support the idea that the most of the gas infall in Milky Way-like galaxies is continuously provided by a drizzle and filamentary cosmological accretion, which would be almost undetectable or very difficult to identify \citep[e.g.,][]{Lehner+13, Tumlinson+13}. Finally, large amounts of matter could be supplied by the coronal gas cooling potentially triggered by supernova feedback \citep{Marinacci+10}.

\section{Conclusions and future prospects}

In this paper, we estimated the maximum accretion of cold gas from minor mergers in a sample of large spiral galaxies from the WHISP catalogue. We used an algorithm of source finding to detect dwarf \hi -rich satellites around these spiral galaxies and we assumed that they will disappear and merge with the main galaxies in the shortest possible time. We found that $\sim 22\%$ of galaxies have detected dwarf companions ($M_\mathrm{bar,sat}/M_\mathrm{bar,main} \le 0.20$) and we estimated a maximum gas accretion rate onto the main galaxies over the whole sample of  $0.28 \moyr$. Given the assumptions, this value is a strong overestimate and the actual value can easily be an order of magnitude or more lower. From far-infrared luminosities, we calculated a mean star formation rate of $1.29 \moyr$, a value which is nearly five times higher than the maximum gas accretion rate. These results strongly suggest that minor mergers can not bring enough gas to guarantee a long lasting star formation process in the discs of the spiral galaxies. We note that our method can also detect, if present, large floating \hi\ clouds and include them in the accretion budget. We did not find any significant population of these clouds. Thus, most of gas accretion seems to be hidden to the current investigations in \hi\ emission.

WHISP is a fairly large sample of nearby galaxies, but it is very small compared to surveys carried out at other wavelengths. The new generation of radio telescopes, such as the SKA \citep{Carilli&Rawlings04} and its pathfinders, ASKAP \citep{Johnston+08} and MeerKAT \citep{Booth+09} and the restilying of existing interferometers, such as the WSRT with the APERTIF system \citep{Verheijen+08} and the Karl G. Jansky VLA, will largely increase the number of available data samples. In the next future, already scheduled \hi\ surveys, such as WALLABY and DINGO with ASKAP, LADUMA with MeerKAT and WNSHS with WSRT/APERTIF, will increase the number of galaxies observed with radio interferometers by three orders of magnitude, from a few hundreds to about $10^5$. It will be very interesting to apply the kind of analysis performed in this paper to those large galaxy samples.

\begin{acknowledgements}
We thank Renzo Sancisi, Tom Oosterloo, Thijs van der Hulst and Micol Bolzanella for helpful suggestions and fruitful discussions. EdT personally thanks Gabriele Pezzulli for his daily help and useful advices. We used the WHISP data sample and the EDD, NED, HyperLEDA and Simbad catalogues. This research made use of some parts of the Duchamp code, produced at the Australia Telescope National Facility, CSIRO, by Matthew Whiting. We acknowledge financial support from PRIN MIUR 2010–2011, project 'The Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies', prot. 2010LY5N2T.
\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


text:
LinkedIn shows off Project Voyager, its new flagship mobile app
Jordan Novet@jordannovet
LinkedIn Voyager, the new version of LinkedIn's flagship mobile app.
Image Credit: LinkedIn
Check out all the on-demand sessions from the Intelligent Security Summit here.
LinkedIn today gave a first look at a new version of its flagship mobile app. Internally known as Project Voyager, the app for mobile web, iOS, and Android is still in beta and won't be available for another few weeks.
LinkedIn chief executive Jeff Weiner gave a presentation on the new app during the LinkedIn Talent Connect conference in Anaheim, California. It's a big deal because LinkedIn originally initially built its mobile app to replicate some of the functions on desktop, which was where most usage was. Now that's changed, and going forward, LinkedIn on mobile should be considerably more intuitive and useful. That makes sense given that more than 50 percent of LinkedIn's traffic is now coming from mobile devices — which is on track with other social networking companies, like Facebook and Pinterest.
The new version of the LinkedIn core mobile app features Home, Me, Messaging (the user interface rolled out a few weeks ago), My Network, and Search. There's also a new App Launcher that can send users to LinkedIn-owned Lynda.com, among other things.
Above: The Me section in the LinkedIn Voyager beta app.
The Me section contains a whole lot of things, and it's easy to edit. It even includes an area where you can quickly check who's viewed your profile — one of the core features on desktop.
"Ultimately, this could be a dashboard for your professional life," Weiner said.
The search tool is much faster in the revamped app and provides more nuanced results, including jobs, people, and companies.
Above: The search section in the LinkedIn Voyager beta.
The redesigned Home section has more updates with photos, while job updates now appear in the My Network section of the app. The former is easier to scroll down, whereas the latter is more of an interactive feature.
When you use My Network, you can easily see things like mutual connections and causes that you have in common with another user. Here and in other places, LinkedIn is now making better use of its vast pools of data on mobile.
Above: The My Network section in the new LinkedIn core mobile app.
And LinkedIn wants to build on this. Like Facebook, Twitter, Google, Microsoft, and other companies, LinkedIn intends to use artificial intelligence to bolster its product. Specifically, Weiner said, AI could help LinkedIn users figure out if other users will be in the same place at the same time. "If she is, set up a meeting between the two of us," Weiner said.
The new app employs LinkedIn's new Art Deco design library, featuring new typography and other elements.
"What we're releasing is more modern, light, airy, fresh," said LinkedIn user experience design director Hemendra Kumar at a LinkedIn press briefing in San Francisco.
The LinkedIn apps for Windows Phone and Blackberry will not be updated to reflect the new Voyager design, LinkedIn vice president of product Joff Redfern said at the press briefing.

redpajama_set_name: RedPajamaCommonCrawl


text:
Older Adults Homepage
Family Caregiver Support Programs
Disability Rights and Resources
50+ Library Resources
Fairfax 50+ Plan
Fairfax 50+ Podcasts Library
Fairfax Area Student "Shark Tank" Technology Challenge
Golden Gazette
Insurance Counseling - VICAP
Long-Term Care Ombudsman Program
Scams - Silver Shield Anti-Scam Campaign
Videos – Fairfax County Channel 16 Mature Living
Videos – Older Adults Services YouTube Playlist
Volunteer Solutions
May is Older Americans Month and Adult Abuse Prevention Month
November is National Family Caregivers Month
March is Developmental Disabilities Awareness Month
Older Adults Services
Department of Family Services – Older Adults
CONTACT INFORMATION: Monday–Friday 8 a.m.–4:30 p.m.
FairfaxAAA@fairfaxcounty.gov
Trina Mayhan-Webb,
Accessory Living Unit
Eldercare Locator - Out of Area
Fairfax County News
Older Adult Housing
SeniorNavigator
Each year, an estimated 53 million adults in the United States provide care to an older adult, or an adult with a disability, (AARP and National Alliance for Caregiving, 2020). A family caregiver is a person who provides care and assistance to a member of their family of origin or their family of choice, and it includes neighbors and friends. Family caregivers have become the backbone of our caregiving infrastructure. Many of them "struggle to balance their caregiving role with other family responsibilities and employment, and they often forgo rest and self-care" (2022 National Strategy to Support Family Caregivers).
The essential care and assistance family caregivers provide, enable their loved ones to live with dignity and remain in their communities. This has never been more evident than during the COVID-19 pandemic when their responsibilities intensified due to shelter-in-place mandates and the closure of formal services. Many caregivers had to make difficult decisions to keep their loved ones safe and healthy. While the caregiving experience can be overwhelming, caregiving can also be a rewarding and enriching journey.
The month, the Fairfax County Department of Family Services honors family caregivers for their dedication, commitment, and compassionate care to their loved ones. Our Fairfax Area Agency on Aging, specializing in caring for older adults and adults with disabilities, provides caregivers with evidence-based programs, educational webinars, and workshops, as well as resources and services focused on caregivers' needs.
A Salute to Caregivers During National Family Caregivers Month
In honor of family caregivers, the Fairfax County Department of Family Services recognizes their critical role as care partners. The department renews its commitment to providing useful services for caregivers during a time of life that can be complicated and stressful, but very fulfilling. Learn more in this Golden Gazette article.
In honor of National Family Caregivers Month 2022, Supervisor Pat Herrity, chairman of the Older Adults Committee offered a proclamation honoring family caregivers:
Mature Living – Caregiving Around the Clock
This episode explores family caregiving – what it is, and why it's so important. Giuliana Valencia, Social Services Specialist with the Fairfax County Department of Family Services outlines the concept of caregiving, the duties caregivers perform, and the challenges associated with it. Kristin Martin, Case Manager with ElderLink, shares helpful resources that are available for caregivers. In addition, a local caregiver shares her first-hand account of the challenges and triumphs in her own role as a caregiver. Check out the video!
Free Support Groups and Respite
Register for Free Caregiver Webinars
Library of Past Caregiver Webinars
Are you a family caregiver for an older adult? There are a variety of support and respite programs available. Need more information? Please call us at 703-324-7948, TTY 711.
36th Annual Caregiver's Conference: Caregiving with Hope and Inspiration
Wednesday, Nov. 9 – Friday, Nov. 11, 2022 | 10 a.m. - 12:30 p.m.
The Northern Virginia Dementia Care Consortium has been educating caregivers since 1986. This year's conference keynote speaker is Peter V. Rabins, MD MPH, author of "The 36-Hour Day."
This conference is open to family caregivers, volunteers working with older adults, and professionals in aging and related services.
Learn more about the conference and register or call 703-270-0043.
Fairfax Caregiver Alert Notifications Program
If we can't reach you, we can't alert you! Now, family caregivers can receive email or text notifications of Fairfax County caregiver services and programs. These programs include case management, in-home respite, caregiver support and webinars, wellness workshops, and much more.
To sign up: https://www.fairfaxcounty.gov/alerts to create or sign into your Fairfax Alerts account and then select Area Agency on Aging/Caregivers.
Caregiver Consultations
Need an in-depth conversation with a social worker about the caregiving needs of a loved one? Free one-hour consultations are available through ElderLink. Call 703-324-5374, TTY 711, and ask for a caregiver consultation, between 8 a.m. and 4:30 p.m., Monday through Friday.
ElderLink Virtual Support Call for Family Caregivers: National Family Caregivers Month
Tuesday, Nov. 8, 2022 (7-8 p.m.)
Learn more about this event and register.
Caregiver Webinar: Nonpharmacological Approaches for Managing Dementia Behaviors
Wednesday, Nov. 16, 2022 (12-1 p.m.)
Caregiver Panel Conversation: Veteran Family Caregivers: Exploring Unique Challenges and Resources
Friday, Nov. 18, 2022 (2-3 p.m.)


text:
Q: Is it possible to define a scene in a separate class? This may have been asked before but i was not able to find an answer. Im working on a JavaFX app that contains a lot of scenes and a lot of animation. Currently I'm having different Animationtimers and different Scenes all defined inside the start() function, inside the main class that extends Application. However the code gets very messy and long.
Is there a way in which you can define all of these things in a separate Java class, and then simply do something like primaryStage.setScene(MyScene.getScene) - MyScene being the java class that has all your scene code.
Something like this:
public class TestScene {

    private Group root = new Group();
    Scene test = new Scene(root);
    Button button = new Button("test");
    root.getChildren.add(button);

}

And actually having that code be a scene that you can just import and set on primaryStage.
Edit: I have no idea why this was so difficult for my mind, as Bertijn said I obviously just need to use a constructer. For whatever reason I forgot that, and so I obviously couldent perform a root.getChildren.add(button), outside a function of some sort.
If anybody else struggles with this here is the super simple solution:
Class containing our scene:
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.paint.Color;

public class OurScene {
    public Scene getScene() {
        Group root = new Group();
        Scene scene = new Scene(root, Color.GREEN);
        Button button = new Button("Hello world!");
        root.getChildren().add(button);
        return scene;
    }
}

And then to add it to primaryStage:
import javafx.application.Application;
import javafx.stage.Stage;

public class Main extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage primaryStage) throws Exception {
        OurScene ourScene = new OurScene();
        primaryStage.setScene(ourScene.getScene());
        primaryStage.show();
    }
}

A: Try making a class called Scenes. In the constructor, created all your scenes, you can give them an id if you want. In your main class, just create an instance of this class Scenes scenes = new Scenes();. The scenes get created. Then you can access them by creating a getScene(String id) method.
Hope I understand your question correctly, and if this doesn't answer it, feel free to get back to me!

redpajama_set_name: RedPajamaStackExchange


The Zomei Z669C Pro Portable Carbon Filter Tripod is a high-performance mounting solution for photographers who love to get out and explore the great outdoors. The high-density carbon fibre construction makes it resilient yet surprisingly lightweight, while the 360-degree rotation ensures no shot is out of reach. Easily adjusted with rubber feet for stability, this user-friendly, ball-head tripod will become an indispensable accessory for every outdoor shoot.
I bought this tripod for my nephew, as he is just starting in DSLR photography, he wanted something light weight and compact, for when he is out walking with the dog, or going out on a planned day with the DSLR. He was very impressed that the tripod fitted his requirements on weight and size and still did the job it was intended for. I had already read the reviews of this tripod and was happy enough to buy for him based on that, All in all a very good product at a great affordable price, recommended.
This is a great tripod, light to carry, packs up small but extends to a good height. Firm camera mount and easy screw clamp legs. I used to carry a monopod but now there's no need as this versatile tripod doubles up as a monopod as well. Also it has handgrips on two legs and a centre hook to weight it down and comes with a carry case. I use my heavy Brembo and Manfrotto for studio shots and this is my tripod of choice for all location work.
This is one great tripod. The sections lock in firmly, the tripod is rock solid even when fully extended. The camera plate locks in firmly, and the ballhead has a great grip. The panning motion is also very smooth, you can do some amateur video with it. Once folded it's really tiny. All in all, I think you cannot beat it in this price range. Really good tripod!


text:
A STREET ORDERLY SPEAKS OUT
'I'm 42 now and when I was a boy and a young man I was employed in The Times machine office, but I got into a bit of a row, a bit of a street quarrel and frolic, and was called on to pay £3, something about a street lamp; that was out of the question; and as I was taking a walk in the park, not just knowing what I'd best do, I met a recruiting sergeant and enlisted on a sudden . . .' Thus the street-orderly, interviewed by Mayhew for his 'London Labour and the London Poor' published in 1851. This interview is not one of these used by poet John Seed in his 'Pictures from Mayhew' and 'That Barrikins', published by Shearsman - but it does have a certain contemporary relevance.
'I served under General Nott all through the Afghan war' the man tells him. 'Why yes sir, I saw a little of what you may call 'service' . . . I was at the fighting at Kandahar, Bowlingglen, Bowling Pass, Clatigillsy, Ghazni and Kabul. The first real warm work I was in was at Kandahar. I've heard young soldiers say that they've gone into action the first time as merry as they would go to a play. Don't believe them sir . . . You must feel queer and serious the first time you're in action: it's not fear, its nervousness. The crack of the muskets at the first fire you hear in real hard earnest is uncommon startling . . . And then you get excited, just as if you were at a hunt, but after a little service – I can speak for myself at any rate – you go into action as you go to your dinner.
I served thirteen years and four months and was then discharged on account of ill health. If I'd served eight months longer . . . I'd have been entitled to a pension. I believe my illness was caused by the hardships I went through in the campaigns, fighting and killing men that I never saw before, and until I was in India had never heard of, and that I had no ill-will to; certainly not, why should I? They never did me any wrong. But when it comes to war, if you can't kill them they'll kill you.'
When he came back, he tells Mayhew, he got a job at The Times again 'but 'I wasn't master of the work, for there was new machinery, wonderful machinery . . . So I couldn't be kept on.'
So now he's in London sweeping the streets and, like sleep-walkers caught up in some dreadful cycle, a century and a half later we're back there once again.
Posted by John Welch at 09:03 No comments:
'Visiting Exile', my new Shearsman collection, is now out. On 6th November I read from the book at Souheil Sleiman's studio here in Hackney. I've already described (see five or so posts back) Souheil's sculpture 'All Dressed Up And Nowhere To Go' and its role as a powerful presence in the book. Also on the programme were two short films. Ruth Dupre showed her film 'Les', a portrait of a committed smoker. She is an artist specialising in glass who has recently been making films and this is one of a number of film portraits she has done which manage to be very intimate, but non-intrusive. Her 'Childsong', a poignant account of an early 19th century educational experiment where a group of children were brought from Sierra Leone to Dulwich where a school was established for them can be seen on the net. Her website is http://www.ruthdupre.co.uk/. Secondly there was 'Exit' by Palestinian film-maker Mohanad Yaqubi, a film reminiscent of a performance art piece, set in a totally deserted London Underground, where a dancer enacts a sense of entrapment. And then to finish music from Hyberbolic, a group one of whose members is Souheil's son.
Then on 15th November Tom Lowenstein and I joined forces to launch our respective collections at Tom's house in Stoke Newington. Tom's new book is 'Conversations with Murasaki', also available from Shearsman.
BOW-WOW AT THE ARTS CLUB
The Bow-Wow Shop, edited by Michael Glover, must be the only web magazine to manifest itself in flesh and blood form with a launch. Issue 3 was launched with readings a few days ago at the Arts Club. A short Ashbery poem read simultaneously in Polish and Russian translation created a pleasing and oddly soothing effect. Among the other readers was Japan-based Paul Rossiter who read an electrifying poem. 'Komachi', from the current issue. As well as a group of his poems there's a substantial afterword by him, 'Thatched Huts and Instant Noodles', where he describes in some detail the history of his encounters with Japanese poetry, starting, long before he had visited the country, with his reading of Bunting's 'Chomei at Toyama' . 'Komachi' takes off from a contemporary No play he happened on two weeks after arriving in Tokyo in 1981. 'Traditional No', he writes, is performed extremely slowly, but that is as nothing compared to the pace at which this Komachi moved. In the second line of the poem I talk about her moving 'centimetre by centimetre' across the bridge, and this is perhaps an understatement; her pace was almost impossibly slow, and it took her nearly ten minutes to cover the few metres to the centre of the stage. Moreover, the production was also almost completely silent; although there was occasionally some music (Vivaldi, 'La Vie en Rose'), and the figures in the sub-plot (squabbling 1980s' neighbours who live in the apartment next door to Komachi's ancientness) had lines to speak, Komachi herself stayed silent throughout the performance. The speechlessness, the extreme slowness of the movement, and the use of No performance practices, together created an extraordinary intensity. The performance was both phantasmagoric and perfectly controlled, and it made even someone like Peter Brook look a bit sloppy. I'd never seen anything like it.' It sounds like a piece of performance art, and suggests a resemblance that seems to exist between such traditional forms, and Zen, with western modernism. Rossiter's piece concludes with a hilarious account of cross-cultural endeavour and confusion, again in Tokyo, involving Kenneth Koch and the shade of Amy Lowell.
RIMBAUD IN ADEN
Lunch yesterday at Iraqi poet Abdulkarim Kasid's flat near Chancery Lane, to continue working on the English versions of his poems, versions he first made himself working with his daughter Sara. This method of translation has become increasingly common of course, and I've previously worked on the British-based Punjabi poet Amarjit Chandan's poems in a similar way. Some of those versions are among those included in a collection of his poems, 'Sonata For Four Hands', due out very soon from Arc Press. It's a way of working of course that shows up a fundamental asymmetry – they know English, we don't know Arabic, Punjabi . . .
Kasid's first home after he got out of Iraq nearly thirty years ago was in Aden. He lived near to what was Rimbaud's house, and one of the poems we're working on, 'A Volcano', is dedicated to the poet's memory. He has translated Rimbaud from French into Arabic and yesterday he told me he identifies with Rimbaud's wandering lifestyle, having himself like so many others been constantly on the move through force of circumstance, something alluded to in this poem (which was in Shadowtrain a while back):
TERMINAL WISDOM
How could I know
My outbound journey
Could be the way back,
That my dreams were behind me
And I wasn't only the walking shadow
Of a standing-still man?
STUDIES AT DELHI 1876
Sir Alfred Lyall was nothing if not an imperialist, with long service in the most senior ranks of the Indian Civil Service. The sack of Delhi in the aftermath of the 'Mutiny'or 'Great Revolt', depending on your point of view, when Delhi was retaken, sacked and many of its inhabitants killed, was a particularly dreadful episode. Writing some twenty years later Lyall, in his 'Studies at Delhi 1876', evokes a game of badminton being played on the spot where the battle to retake the city had been fought:
Hardly a shot from the gate we stormed,
Under the Moree battlement's shade;
Close to the glacis our game was formed,
There had the fight been, and there we played.
Lightly the demoiselles tittered and leapt,
Merrily capered the players all;
North, was the garden where Nicolson slept,
South was the sweep of a battered wall.
Near me a Musalman, civil and mild,
Watched as the shuttlecocks rose and fell;
And he said, as he counted his beads and smiled,
'God smite their souls to the depths of hell.'
Well at least Lyall could see it . . .
London, Hackney
Born in London in 1942, I have published four full-length collections of poetry. My latest collection, 'Its Halting Measure', appeared from Shearsman in June 2012. Shearsman brought out my 'Collected Poems' in 2008, along with a prose memoir, 'Dreaming Arrival'. As for this blog, well it's poetry, the visual arts, and various odds and ends . . .
Amanda Welch
Beverley Rowe
Blackbox Manifold
Intercapillary Space
Laurie Duggan
Oystercatcher Press
Peter Riley
Robert Sheppard
Shadowtrain
The Bowwow Shop


text:
Restaurants, salons take extra precautions for Phase 2 reopening
Breweries, salons, restaurants and barbershops in North Carolina will open their doors for the first time in eight weeks as part of Governor Cooper's reopening plan.
Author: Ashley Daley
Published: 7:11 PM EDT May 22, 2020
CHARLOTTE, N.C. — North Carolina's Stay at Home Order lifted Friday, as the state now moves into a 'Safer at Home' recommendation, considered to be Phase 2 of the Governor's plan to reopen businesses.
Many of those businesses -- from restaurants to hair salons to breweries -- reopened their doors Friday for the first time in 8 weeks. But what will eating out or getting your hair done look and feel like under the CDC's safety guidelines? WCNC Charlotte spent the day finding out.
"This door is going to be propped open," describes Ken Martino, who owns Italian restaurant, Osteria Lucca, in the Park Road Shopping Center. Martino says when customers arrive, they won't need to touch the door.
He's also installed a clear partition to separate customers from the staff at the host stand, set-up a number of hand sanitizing stations around the restaurant, and says all menus will be disposable, and all staff will be wearing masks.
"We're just excited to serve people again to have people come in and create some positive energy in the space and really provide some good food, some good service," he says.
Martino says customers will also have the option to pay their bill without having to touch it or pass their credit card to servers, using new technology, "Which allows the guest to take a picture of the check and then make the payment on their own phone," he says.
RELATED: What will reopen in North Carolina under Phase 2?
Martino says the restaurant plans to reopen Saturday evening and already has a significant number of reservations.
Changes are also brewing at Suffolk Punch in Charlotte's South End. The restaurant and brewery reopened Friday at 5 p.m. To maintain social distancing, we're told all guests will be asked to sit at their tables, unless visiting the bar. Even in line, green X's are painted on the ground to show where it's safe to wait.
"We're just thrilled to be back and have guests back on-premise and our team back at work," says co-founder, Seth Stidham, who says all staff will also be wearing masks.
In addition to restaurants, hair salons are also allowed to reopen under Phase 2 at 50% capacity.
RELATED: Breweries allowed to reopen during Phase 2 in North Carolina
"It's been hard financially," says hair stylist Mistie Creech, who operates her own hair studio out of Sola Salons in South End. Creech was forced to close for 8 weeks, but as soon as Governor Cooper gave the go-ahead she says she began booking clients.
"I am rearing to go, I am starting at 5 on the dot today," she says.
Creech says she's been in touch with clients alerting them to the new safety protocols in place.
"The client is supposed to text me from the car and then I will let them in once my client that's there has left," she says. "They're to wear a facemask, especially in the common areas and then in the salon too I'm going to ask that of them. Then when they walk in the salon, they will go wash their hands first and then they will sit in a seat that has been sanitized to the 9th degree. They will have a new cape, new towels. There will be no magazines.," she says.
Creech says because of capacity restraints she is already booked solid through June, and plans to work 12- to 13- hour shifts, 6 days a week to make up for lost time.
Each of the business owners we spoke to, all echoing the same plea to the public, to be patient as everyone works to adjust to this new normal.
Turn around could be coming for business at Charlotte Convention


text:
We're Prisoners!
By Coastal Breeze News Staff | on November 27, 2010
By Monte Lazarus
It's the holiday season, so the time has come to tell all. We're all prisoners of computers…every last one of us. When you, or even a little kid, look at that computer screen, you are not really looking at it. Uh-uh. It's looking at you, and sometimes chuckling to itself about how dumb we are. They've quietly and effectively conquered us so-called humans.
Machines control everything, and machines are, in turn, controlled by – yes, computers! IBM, HP, Dell, Gates, Jobs – the whole mob are probably robots designed and built by machine.
How do we vote? By machine. Who counts the votes? Machines. How do we know the vote is correct? The machines tell us. Who controls the machines? The computers. How do we even know the candidates are real? A lot of folks thought Al Gore was robotic, and can the senatorial candidate from Delaware be real?
Take the stock market. Do you believe that shares are bought and sold by people acting in the marketplace? No way. The market is controlled by automatic computerized sales, programmed to buy or sell according to certain changes.
Cell phones. We think they are made so we can talk to each other and also take silly pictures. Wrong. They were designed to keep track of us and know what we are doing. Why else build in a GPS in the new models?
Texting, tweeting, e-mailing. I'm convinced that, at Supreme Computer Headquarters, there's a database and we're all in it. Any of us within five meters (The Computer Empire uses the metric system) of a computer, cellphone or other insidious computer-based system is in that database. They know where we are, and what we're doing at all times. Don't get me started on Facebook. That's probably the most evil of all the devilish computer plots. They learn everything about us in excruciating detail.
Got a Garmin or other GPS in your car? Aha! They not only know where you're going, but they even tell you how to get there! It's so bad that one of the few remaining pleasures for a female passenger – telling the dummy to stop at a gas station for directions – is gone. It's all part of the evil conspiracy to keep us tranquilized by the ubiquitous computer.
Our automobiles are made by – computer – controlled robots. Computer-controlled drills (part of the anti-human conspiracy) are deliberately set to create oil spills. Our aircraft and homes are designed by cad-cam, another computerized system.
How do we wage war? We send up pilotless drones that are controlled by – you got it – computers. They find targets designated by computers and launch rockets fired by computers.
Have you called customer service lately? You did not speak to someone of the human species. You spoke to a computer. You dutifully pressed 1, then 3 or 4, then 7, then something that cut you off. If you are gullible you think you are speaking to someone in Mumbai who pretends to be in the U.S. This is the infamous computer-generated double fandango. I tell you "he's" not even in Mumbai. "He's" a computer voice programmed to sound like an Indian speaking American-style English. So, when you get angry with the "guy" in Mumbai, channel that anger to the computer instead.
What do we teach our innocent, adorable children? How to use computers! Whose idea was that? Of course, the aforementioned IBM, Dell, HP, Gates, Jobs and rest of the robots.
It may be too late, but my call is to all humans to rebel. George Orwell was right, but Big Brother is the computer. Start the rebellion before New Year! I need to sit on Santa's lap and tell him to get rid of the computers!


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As a REALTOR® Sandra often gets asked by her clients if she minds the long, and often unconventional, working hours of a realtor. Her answer is always "Not at all!" The process of buying or selling a home can be stressful with many tasks. Sandra values the opportunity she has to help her clients through the process by protecting and promoting their interests with knowledge, commitment and attention to detail.
Sandra has a Bachelor of Commerce in Marketing, so she brings a business background to each client relationship. Prior to her real estate career, Sandra also spent years in event planning, human resources, and training, which honed her skills in organization, multi-tasking, motivation and communication.
Sandra, along with her husband and two children, has lived in Langley for the past 25 years - the first 11 in Walnut Grove and the last 14 in Fort Langley. When not working, Sandra is likely to be running the trails, attending yoga classes, hiking, camping or simply enjoying time with her family and friends.
With her skills and knowledge of the Fraser Valley real estate market, Sandra's professional goal is to continue to build relationships with family, friends and clients and to work with them as they achieve their real estate dreams.


Hi Karen, I have dealt with suicidal thoughts but certainly not as intense or for as long a period. For you to live with those and still find a way through, and know that you will, is an incredible inner strength. I think, on the whole, it is a good idea to ask for help because not everyone will have the coping skills that you've built up over years (even though at times you may not think you've been coping at all, you have, because you are still with us, and that's something worth ceen)ratilgb. Thanks for sharing your story.
Awww Libby, Im sure he doesnt mean it..You know people sometimes tell hurtful words out of anger or frustration. that's why we need to practice to slow to speak and slow to anngT...rhiges will be fine hun..
, a 'Carbon Market' approach that includes the 'free' trading of such Certificates seems both more reasonable overall and even more attractive for installation owners.The New Jersey approach offering a massive $300 per MWh amount may serve as the best example for micro generation equipment owners and enthusiasts. The latter example may even induce (foreign) investment as all installations in the state are eligible and one would not need a personal residence there in order to only receive &#tee0;r2ba82s" against one's standard utility bill".


text:
title: Raytracing - Rendering Equation Insight
layout: post
image: 2018-06-30-raytracing-rendering-equation/pbr-equation.jpg
---

Where the journey of physically based rendering begins.

# The Rendering Equation
The physical basis for the rendering equation is the **law of conservation of energy**. Assuming that L denotes radiance, we have that at each particular position and direction, the outgoing light (Lo) is the sum of the emitted light (Le) and the reflected light. The reflected light itself is the sum from all directions of the incoming light (Li) multiplied by the surface reflection and cosine of the incident angle.

_[Source](https://blog.demofox.org/2016/09/21/path-tracing-getting-started-with-diffuse-and-emissive/)_

$$L_o( \omega_o)= L_e(\omega_o)+\int_{\Omega}{f(\omega_i, \omega_o)L_i(\omega_i)(\omega_i \cdot n)\mathrm{d}\omega_i}$$

- $L_o$ - light (radiance) directed outward along direction $\omega_o$ (light received by camera)
- $\omega_o$ - the direction of the outgoing light (view direction)
- $L_e$ - light (radiance) emitted
- $\int_{\Omega }\dots \,\mathrm{d}\omega_i$ - integral over $\Omega$
- $\Omega$ - the unit hemisphere centered around $n$ containing all possible values for $\omega_i$
- $f(\omega_i, \omega_o)$ - the [bidirectional reflectance distribution function (BRDF)](https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function), the proportion of light reflected from $\omega_i$ to $\omega_o$
- $\omega_i$ - the [negative](https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function#/media/File:BRDF_Diagram.svg) direction of the incoming light
- $L_i$ - light coming inward from direction $\omega_i$
- $n$ - the surface normal
- $\omega_i\cdot n$ - the weakening factor of outward irradiance due to incident angle $\cos \theta_{i}$ ([Lambert's Cosine Law](https://en.wikipedia.org/wiki/Lambert%27s_cosine_law))

The above equation is one type of simplified versions, and here is the a more extended explanation:

source

source

TBC

redpajama_set_name: RedPajamaGithub


Recent Arrival! Certified. * Non Smoker *, * Heated Seats *, Titan Black w/V-Tex Leatherette Seating Surfaces, Radio: Premium VIII AM/FM Sound System w/8-Speakers, Rear window defroster. 2013 Volkswagen Beetle 2.0 TDI Convertible Black CARFAX One-Owner.


text:
Jeff Greenbaum
Managing Partner at Frankfurt Kurnit Klein & Selz
jgreenbaum@fkks.com
https://fkks.com/attorneys/jeffrey-greenbaum
Advertising lawyer. Specialties: Advertising and marketing law, intellectual property law, branded entertainment,and consumer privacy
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Latinos Unidos Center to welcome Hispanic students
KOKOMO, Ind. – ¡Bienvenido a Indiana University Kokomo!
The campus provides a friendly atmosphere, celebrates the culture, and assists Latino students with the unique challenges they face, with the addition of Latinos Unidos Hispanic Center.
"We want to create a sense of belonging and connection with the Latino community on our campus," said J.R. Pico, senior lecturer in Spanish, who will serve as the center's director.
"We want them to feel welcomed and respected in our university, and to provide resources for them, promote their culture and language, and help them overcome any barriers to earning a degree."
The center initially will be housed in Pico's office, Main Building Room 178 B, until a permanent location is ready.
"Our goal is to create a sense of community," Pico said.
Family is an important part of Hispanic culture, and it's important that the center also welcomes students' parents, who are likely to be involved in their education, and whose well-being impacts their success.
Christine Taff, senior lecturer in Spanish and associate director, said they can connect students and their families to people who can assist with immigration and discrimination or racism issues, and provide materials in Spanish as needed.
That family connection is crucial as students consider their higher education options, and the center will play a role during Visit in Person days as well.
"When students are choosing their college, the families are very involved," said Taff. "We can be a place they can go for information, where there will be someone who speaks Spanish. The parents may not know much about the U.S. university system.
"We can also create a sense of comfort for the parents, because they will see for themselves that their children will be welcomed here."
While the name is Latinos Unidos, students of all backgrounds are encouraged to visit. Pico anticipates the relaunched Spanish club and the Latinx Student Organization will be based out of the center, and Spanish language tutors will be available.
Paola Cubides, a Master of Business Administration (M.B.A.) student, looks forward to improving her English skills while providing tutoring in Spanish at the center.
"It gives the native Spanish speaking student an opportunity to help another student who wants to improve their Spanish skills," she said. "Because I am still learning English, it gives me the chance to grow my knowledge in the language. It will improve confidence on both sides, so it's a win-win."
It will also be a place to learn about Hispanic culture, with plans in the works for guest speakers, movie nights, and other cultural events.
"The whole idea is to bring more of the Latino culture to campus, to share with everybody," Taff said.
For more information contact Pico at jrpico@iuk.edu or 765-455-9320, or Taff at cmtaff@iuk.edu or 765-455-9235.