text:
\section{Introduction}

Because of the infrared divergences in a weakly-coupled gauge theory, like QCD at high energy, final states manifest themselves as collections of jets.  To connect the observed final state to final states from fixed-order perturbative calculations, infrared and collinear (IRC) safe jet algorithms \cite{Sterman:1977wj} have been invented to make these jets well-defined.  Traditionally, these jets have been used as a proxy for the short distance degrees of freedom, quarks and gluons, and provide definite objects for matching to fixed-order calculations of cross sections inclusive over the entire final state.  However, with a definite algorithm, individual jets can be studied in their own right, ignoring or integrating over all other radiation in the final state, that is not included in the jet.  This introduces implicit dependence into the jet on the relevant scales of the out-of-jet radiation, the dominant effects of which are referred to as non-global logarithms (NGLs) \cite{Dasgupta:2001sh}.  Non-global effects and logarithms arise generically whenever an observable is only measured on a restricted region of phase space.

For observables measured exclusively on jets, like the jet mass for example, NGLs can introduce large corrections in specific phase space regions, and have proved challenging to understand systematically \cite{Kelley:2011tj,Chien:2012ur,Dasgupta:2012hg,Jouttenus:2013hs}.  There has been significant advances recently in theoretical progress for understanding and calculating NGLs \cite{Dasgupta:2001sh,Dasgupta:2002bw,Dasgupta:2002dc,Banfi:2002hw,Appleby:2002ke,Weigert:2003mm,Rubin:2010fc,Banfi:2010pa,Kelley:2011tj,Hornig:2011iu,Hornig:2011tg,Kelley:2011aa,Kelley:2012kj,Hatta:2013iba,Schwartz:2014wha,Khelifa-Kerfa:2015mma,Caron-Huot:2015bja,Larkoski:2015zka,Hagiwara:2015bia,Becher:2015hka,Neill:2015nya} as well as the development of techniques for eliminating them by removal of appropriate soft radiation in jets \cite{Dasgupta:2013ihk,Dasgupta:2013via,Larkoski:2014wba}.  Despite their importance and relevance, NGLs and non-global correlations in general, have never directly been observed. In particular, their effects on observables such as the jet mass, while potentially large, are difficult to unambiguously disentangle from perturbative and non-perturbative uncertainties when comparing with measurements. In this paper, we introduce a novel procedure which directly measures non-global correlations between in-jet and out-of-jet phase space regions, and which vanishes when such correlations are not present.  We present theoretical calculations of this observable to next-to-leading logarithmic (NLL) accuracy in QCD, and study its properties in Monte Carlo simulation.

While our procedure for measuring non-global correlations can be applied widely, we will restrict our discussion to correlations between hemisphere jets in $e^+e^-$ annihilation to hadrons.  In that case, we first separate events into left and right hemispheres using a cone jet algorithm defined about recoil-free jet axes \cite{Banfi:2004yd,Salambroadening,Larkoski:2014uqa}. This is necessary to eliminate back-reaction of soft particles near the hemisphere boundary on the jet finding.  With identified hemispheres, we then measure IRC safe two-point energy correlation functions $\ecf{2}{\beta}$ \cite{Banfi:2004yd,Jankowiak:2011qa,Gallicchio:2012ez,Larkoski:2013eya}, defined by the angular exponent $\beta$, in each hemisphere.  The energy correlation functions are sensitive to wide-angle, soft radiation and so by measuring the correlation between the measured values in each hemisphere, one defines an observable that is sensitive to non-global correlations.  The problem of measuring non-global correlations is then reduced to defining a measure of the correlation between the left and right hemisphere values of the energy correlation functions.

While there are many measures that can be used to determine the correlation, the one we will use is the mutual information. For the application of non-global correlations, the mutual information measures the number of bits of information that are known about the probability distribution of the right hemisphere energy correlation function, $\ecf{2,R}{\beta}$, given that the distribution of the energy correlation function in the left hemisphere, $\ecf{2,L}{\beta}$, is known (or vice-versa).  The definition of mutual information, $I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)$, is
\begin{align}\label{eq:mutinfdef}
I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right) \\
&
\hspace{-2cm}
= \int d\ecf{2,L}{\beta} \,  d\ecf{2,R}{\beta} \, p\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)\log_2\frac{p\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)}{p\left(\ecf{2,L}{\beta}\right)p\left(\ecf{2,R}{\beta}\right)}\,.
\nonumber
\end{align}
Here $p(a)$ is the probability distribution of an observable $a$ and $p(a,b)$ is the joint probability distribution of two observables $a$ and $b$.  Note that
\begin{equation}
p(a) = \int db\, p(a,b) \,.
\end{equation}
If the left and right hemisphere observables $\ecf{2,L}{\beta}$ and $\ecf{2,R}{\beta}$ are truly uncorrelated, then $$
p\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)=p\left(\ecf{2,L}{\beta}\right)p\left(\ecf{2,R}{\beta}\right)\,,
$$
and the mutual information is zero.\footnote{\Ref{Larkoski:2014pca} discusses other basic properties of the mutual information and its calculation in the context of correlations of multiple observables measured on the same jet.}  Therefore, the mutual information $I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)$ is only non-zero if there are non-trivial correlations between the hemispheres.  Just the absolute value of the mutual information is difficult to interpret because it can range anywhere from 0 to $\infty$.

Mutual information by itself is just one number, and it can potentially be unclear what that number means.  We are able to learn about the origin of the correlation between the left and right hemispheres by measuring the mutual information over a range of angular exponents $\beta$.  As we will discuss in \Sec{sec:mutinfcalc}, the energy correlation functions are defined such that by increasing the angular exponent $\beta$, one becomes increasingly sensitive to soft, wide angle emissions.  These soft wide angle emissions are the most sensitive to non-global correlations between the hemispheres.  Therefore, as the angular exponent $\beta$ increases, $I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)$ should also increase due to the increasing importance of soft emissions sensitive to non-global correlations.  As the $\beta$ dependence of $I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)$ is most important for understanding non-global effects, we will denote $I\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)\equiv I_\beta$.  Monotonically increasing $I_\beta$ with $\beta$ is an unambiguous signal of non-global physics.  There may be baseline correlations due to other effects, but these would not be manifest as a rise in $I_\beta$ with $\beta$.

An important prediction of this framework is that when appropriate methods are used to remove soft wide-angle radiation, so-called jet grooming algorithms, the correlations between the hemispheres should vanish.  It has been shown that the modified mass drop \cite{Dasgupta:2013ihk,Dasgupta:2013via} and the soft drop \cite{Larkoski:2014wba} jet groomers eliminate NGLs, at least through NLL accuracy.  Therefore, in our analytical calculations, when these jet grooming techniques are applied, $I_\beta$ is close to zero and does not increase with $\beta$.  This is also borne out in Monte Carlo simulation of $e^+e^-$ collision events.

We choose to use mutual information to measure correlations as it has been used in some other studies of correlations of QCD jet observables \cite{Carruthers:1989gu,Narsky:2014fya,Larkoski:2014pca}.  However, any procedure that tests the difference between the joint probability distribution of two observables and the product of the individual probability distributions would be sufficient.  Other examples, though not exhaustive, that quantify correlations used in statistical analyses include Hellinger distance, Jensen-Shannon divergence, Kolmogorov-Smirnov test, and R\'enyi divergence.  The Hellinger distance is actually a metric and ranges strictly between 0 and 1. More ambitiously, although we have focused on methods which allow for the reduction of the correlations to a single number, it would also be interesting to directly study the double differential distribution of $p\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)-p\left(\ecf{2,L}{\beta}\right)p\left(\ecf{2,R}{\beta}\right)$. This is, however, considerably more complicated to directly interpret, and we therefore restrict ourselves to the study of the mutual information, which summarizes the correlations in a single number.

It is tempting to draw an analogy between these non-global correlations and quantum entanglement of the two hemispheres, but mutual information is measured on the asymptotic states, long after decoherence.  It is therefore challenging to make a direct connection to the underlying quantum correlations.  More generally, in an experiment that only measures energy deposits it is not possible to construct non-commuting operators at the same point in the detector, so as to test Bell's inequalities \cite{Bell:1964kc}.  It may be possible to do so, however, with idealized detectors in toy models, as was recently proposed in the context of inflation \cite{Maldacena:2015bha}.  We leave a study of possible connections between NGLs and entanglement to future work.

The outline of this paper is as follows.  In \Sec{sec:ngp}, we review the source of dominant non-global correlations and logarithms from fixed-order matrix elements in $e^+e^-$ collisions.  In \Sec{sec:mutinfcalc}, we define the two-point energy correlation functions appropriate for $e^+e^-$ collisions and calculate the mutual information $I_\beta$ to NLL accuracy, capturing non-global logarithms with the dressed gluon expansion of \Ref{Larkoski:2015zka}.  We are also able to include non-perturbative effects by convolving the perturbative distributions with a shape function, and we demonstrate that non-perturbative effects in general increase the correlation between the hemispheres.  In \Sec{sec:mc}, we calculate the mutual information in Monte Carlo simulation and find good agreement between our analytical calculation and the simulations.  We conclude in \Sec{sec:conc} and discuss other scenarios where non-global effects can be directly measured in a similar manner.  Calculational details both of the analytics and algorithms for determining the mutual information on finite data sets are presented in appendices.

\section{Non-Global Physics}\label{sec:ngp}

In this section, we briefly review non-global physics in the context of $e^+e^-\to$ dijets events.  Our goal is to calculate the distribution of observables measured on the left and right hemispheres (appropriately defined) of each event and we choose these observables such that a non-zero value regulates the soft and collinear singularities.  While the two-point energy correlation functions are one example of such observables, other examples include hemisphere masses or hemisphere thrust.  By demanding that both hemisphere masses are non-zero, for example, means that the lowest order contribution to the double differential cross section or joint probability distribution is at ${\cal O}(\alpha_s^2)$.  Sufficient for our analysis here, we can consider purely gluonic radiation from the initial $q\bar q$ dipole.  Then, we must calculate the Feynman diagrams that contribute to this final state.

If we assume that QCD is an abelian gauge theory, then gluons are emitted exclusively off of the $q\bar q$ dipole.  For two positive helicity abelian gluons, the matrix element can be written in spinor helicity notation \cite{Mangano:1990by,Dixon:1996wi} as
\begin{equation}\label{eq:abelme}
\frac{{\cal A}(e_a^-, \bar e_b^+\to q_1^+,g_2^+,g_3^+,\bar q_4^-) }{{\cal A}(e_a^-, \bar e_b^+\to q_1^+,\bar q_4^-)}=\frac{\sab{1}{4}}{\sab{1}{2}\sab{2}{4}}\frac{\sab{1}{4}}{\sab{1}{3}\sab{3}{4}}\,,
\end{equation}
where the quarks are particles $1$ and $4$, the gluons are particles $2$ and $3$, and we have stripped away couplings.  The Born-level matrix element is
\begin{equation}
{\cal A}(e_a^-, \bar e_b^+\to q_1^+,\bar q_4^-) = \frac{\sab{4}{a}^2}{\sab{1}{4}\sab{a}{b}}\,,
\end{equation}
again, stripped of couplings, with the initial electron and positron particles $a$ and $b$.  The spinor products are defined with $|\sab{i}{j}|^2=s_{ij}$.  In \Eq{eq:abelme}, we have dropped the momentum conserving $\delta$-function, also.  Momentum conservation does correlate the two hemispheres, but in the limit that gluons $2$ and $3$ become soft, this correlation vanishes.  Note also that even away from the soft limit the matrix element factorizes into two contributions, one for each gluon.  In the soft limit and demanding that the gluons are in different hemispheres, the gluons are completely uncorrelated.  Therefore, in an abelian gauge theory like QED, there are no NGLs to this order in perturbation theory.

In a non-abelian gauge theory, however, gluons can radiate more gluons.  For the same selection of helicities, the color-ordered matrix element for the emission of two gluons is
\begin{align}
\frac{{\cal A}(e_a^-, \bar e_b^+\to q_1^+,g_2^+,g_3^+,\bar q_4^-) }{{\cal A}(e_a^-, \bar e_b^+\to q_1^+,\bar q_4^-)}= \frac{\sab{1}{4}}{\sab{1}{2}\sab{2}{3}\sab{2}{4}} \,,
\end{align}
where, again, we strip couplings and momentum-conserving $\delta$-functions.  Taking the soft limit of gluons 2 and 3 removes correlations through momentum conservation, but even in this limit, the matrix element does not factorize.  The soft gluons in each hemisphere will know about the other through the matrix element, unlike in an abelian theory.  Therefore, in the soft limit, these correlations will manifest themselves as large logarithms in the cross section of the hemisphere observables.  Resummation of these large logarithms is necessary for convergence of the perturbation theory in the singular region of phase space.  In the next section, we present the details of the method for measuring these correlations directly.

\section{Analytical Calculation of Mutual Information}\label{sec:mutinfcalc}

Isolating non-global correlations between the hemispheres is subtle and robust definitions of the hemispheres and observables measured on them are required.  In this section, we define how we identify hemispheres, measure the energy correlation functions, and present a calculation to NLL accuracy.

\subsection{Observable Definitions}

Because wide angle soft radiation is most sensitive to non-global correlations, we need a procedure for identifying the hemispheres that is insensitive to back-reaction by the soft particles on the boundary.  Effectively, we must define the hemispheres with an algorithm that does not introduce clustering logarithms \cite{Banfi:2005gj,Delenda:2006nf}.  Our procedure for doing this is the following.  We first cluster the event with the exclusive $k_T$ algorithm \cite{Catani:1991hj} to two jets using Winner-Take-All (WTA) recombination \cite{Salambroadening,Larkoski:2014uqa,Larkoski:2014bia}.  WTA recombination ensures that the jet axes lie along the direction of the hardest radiation in the event, and are not displaced by recoil effects from soft, wide angle radiation.  We then identify the axis defined in this way of the highest energy jet in the event and cluster all radiation within an angle of $\pi/2$ of this axis into one hemisphere, and all of the remaining radiation into the other hemisphere.  This effectively defines an exclusive cone jet algorithm.  We then randomly choose one of the hemispheres to be the left hemisphere, and the other to be the right hemisphere.

With these hemisphere definitions, we then measure energy correlation functions on each hemisphere.  The two-point energy correlation functions $\ecf{2}{\beta}$ are defined for $e^+e^-$ collision events as
\begin{equation}
\ecf{2}{\beta} = \frac{1}{E_J^2}\sum_{i< j \in J} E_i E_j\left(
\frac{2p_i\cdot p_j}{E_i E_j}
\right)^{\beta / 2}\,,
\end{equation}
where $E_J$ is the total energy of the jet (or otherwise identified region), the sum runs over all distinct pairs of particles in the jet, and $\beta$ is an angular exponent required to be larger than 0 by IRC safety.  Note that for massless particles,
\begin{equation}
\frac{2p_i\cdot p_j}{E_i E_j} = 2(1-\cos\theta_{ij}) \,,
\end{equation}
and so larger values of $\beta$ give greater weight to wide-angle emissions.  The two-point energy correlation function is non-zero for a jet with two particles.  By separately measuring $\ecf{2}{\beta}$ in each hemisphere and demanding that both are non-zero requires that each hemisphere has at least two particles.  We will denote the energy correlation functions measured on the left (right) hemisphere as $\ecf{2,L}{\beta}$ ($\ecf{2,R}{\beta}$).

We emphasize that no other cuts are performed: the left and right hemisphere energy correlation functions are measured on every $e^+e^-\to$ hadrons collision event.

\subsection{Perturbative Calculation}

With robust jet definitions and observables measured on the jet hemispheres, we now calculate the joint probability distribution or double differential cross section of the measured values of $\ecf{2,L}{\beta}$ and $\ecf{2,R}{\beta}$.  Our calculation will be accurate to NLL order, and here, we will not include fixed-order corrections.  These are expected to be a small effect on our results because the bulk of the distribution is in the region where logarithms of the observables are large, and therefore well-described by a resummed calculation.

The first relevant fixed-order corrections arise at ${\cal O}(\alpha_s^2)$, when each hemisphere has an extra emission.  The ${\cal O}(\alpha_s)$ corrections are not representative of power corrections, because one hemisphere necessarily has zero mass.  That means that at ${\cal O}(\alpha_s)$, the hemispheres are completely uncorrelated (except for total momentum conservation).  Matching fixed-order at ${\cal O}(\alpha_s^2)$ to our resummed expressions will be addressed in future work.

For the resummation of energy correlation functions measured in each hemisphere, there are two components that contribute to NLL accuracy.  First, there are global logarithms, which arise from soft or collinear emissions in each hemisphere that are uncorrelated with emissions in the other hemisphere.  In \App{app:resum}, we present the calculation of the global logarithms of the two-point energy correlation functions measured on a hemisphere to NLL accuracy using soft-collinear effective theory (SCET) \cite{Bauer:2000yr,Bauer:2001ct,Bauer:2001yt,Bauer:2002nz}, though other methods can be used and produce identical results \cite{Banfi:2004yd}.  The global cumulative probability distribution or double cumulative cross section $\Sigma^G$ for the hemisphere energy correlation functions can be expressed as
\begin{equation}
\Sigma^\text{G}\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)\equiv \Sigma\left(\ecf{2,L}{\beta}\right)\Sigma\left(\ecf{2,R}{\beta}\right)\,,
\end{equation}
where $\Sigma\left(\ecf{2,L}{\beta}\right)$ is the global NLL resummed cumulative distribution of the left-hemisphere energy correlation function.  Because the left and right hemispheres are otherwise identical, $\Sigma\left(\ecf{2,L}{\beta}\right)$ is identical to $\Sigma\left(\ecf{2,R}{\beta}\right)$.  If this was the only contribution to the distribution, then the mutual information of the two hemispheres would be zero, as there is no correlation between between the hemispheres.

However, in addition to global logarithms, at NLL accuracy, there are also NGLs that must be included that introduce correlations between the hemispheres.  To this accuracy, NGLs can be included by Monte Carlo simulation \cite{Dasgupta:2001sh} or by solving the Banfi-Marchesini-Smye (BMS) equation \cite{Banfi:2002hw}.  Here, we will use the dressed gluon expansion \cite{Larkoski:2015zka}, including NGLs with the one-dressed gluon approximation.  The one-dressed gluon does not include complete NGLs at NLL accuracy, but was shown to agree with the solution of the BMS equation at the percent level over the range
$$
\frac{\alpha_s C_A}{\pi} \left|\log\frac{\ecf{2,R}{\beta}}{\ecf{2,L}{\beta}}\right| \lesssim 1.5\,.
$$
The one-dressed gluon resummation of non-global logarithms can be expressed as
\begin{align}
S^{(1,\text{NGL})}_{n\bar n}(\mu_L,\mu_R) &= 1-\frac{2 C_F}{\beta_0}\left[
\gamma_E \left| \log\frac{\alpha_s(\mu_R)}{\alpha_s(\mu_L)}\right|\right.\\
&
\hspace{-1cm}
\left.+\frac{\beta_0}{2 C_A}\log \Gamma\left(
1+\frac{2 C_A}{\beta_0}\left| \log\frac{\alpha_s(\mu_R)}{\alpha_s(\mu_L)}\right|
\right)
\right]\ .\nonumber
\end{align}
Here, $\Gamma(x)$ is Euler's Gamma function, $\gamma_E\simeq 0.577$ is the Euler-Mascheroni constant, and $\beta_0$ is the leading coefficient of the $\beta$-function,
\begin{equation}
\beta_0 = \frac{11}{3}C_A -\frac{2}{3}n_f\,,
\end{equation}
where $n_f$ is the number of active quark flavors.  The scales $\mu_L$ and $\mu_R$ are set by the measured values of the left and right hemisphere energy correlation functions.  Up to factors of order 1, the left hemisphere scale is, for example,
\begin{equation}
\mu_L \simeq \ecf{2,L}{\beta} E_L\,,
\end{equation}
where $E_L$ is the energy of the left hemisphere.  This scale can be varied to provide a measure of perturbative uncertainties.

Then, to NLL accuracy with the one-dressed gluon to capture NGLs, the double cumulative cross section of the hemisphere energy correlation functions can be expressed as
\begin{equation}
\Sigma\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right) =\Sigma\left(\ecf{2,L}{\beta}\right)\Sigma\left(\ecf{2,R}{\beta}\right)S^{(1,\text{NGL})}_{n\bar n}(\mu_L,\mu_R)\,.
\end{equation}
The double differential cross section or joint probability distribution is found by the double derivative:
\begin{equation}\label{eq:pertcalc}
p\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right)=\frac{1}{\sigma}\frac{\partial^2}{\partial \ecf{2,L}{\beta}\, \partial \ecf{2,R}{\beta}} \Sigma\left(\ecf{2,L}{\beta},\ecf{2,R}{\beta}\right) \,.
\end{equation}
With this result, we can then calculate the mutual information $I_\beta$ as defined in \Eq{eq:mutinfdef}.\footnote{While other non-global observables have appeared in the literature e.g.~that of \Refs{Bertolini:2013iqa,Bertolini:2015pka}, a key advantage of the use of mutual information between IRC safe observables is that we have a precise definition of the non-global correlations that are probed in terms of an all orders factorization theorem. The above discussion defines precisely what this constitutes for the case of hadronic jets in $e^+e^-$.}

\begin{figure}[t]
\includegraphics[width=7.5cm]{./figures/NLL_mutinf.pdf}
\caption{The mutual information $I_\beta$ as calculated to NLL accuracy with the one-dressed gluon to capture NGLs.  The lighter band reflects conservative theoretical uncertainties.
}
\label{fig:pert_mi}
\end{figure}

In \Fig{fig:pert_mi}, we plot the mutual information $I_\beta$ as calculated from \Eq{eq:pertcalc} as a function of the angular exponent $\beta$ for $e^+e^-$ collisions at 1 TeV center of mass energy.  As expected, the mutual information is non-zero and increases with $\beta$, reflecting the increasing importance of soft, wide angle emissions to the energy correlation functions.  The lighter band is representative of theoretical uncertainties, determined by varying the natural scales appearing in the double differential cross section by factors of 2 and taking the envelope.  While the uncertainties are large, the increase of $I_\beta$ with $\beta$ is robust.

\begin{figure}[t]
\includegraphics[width=7.5cm]{./figures/NLL_mutinf_B.pdf}
\caption{Plot of the dependence of the mutual information on the size of the non-global contributions.  The parameter $B$ controlling the size of the NGLs is varied from $0.5$ to $2$.
}
\label{fig:pert_mi_B}
\end{figure}

It is interesting to study the sensitivity of the mutual information $I_\beta$ to the size of the NGLs.  We can demonstrate this sensitivity by modifying the one-dressed gluon by a coefficient $B$ to be
\begin{align}
\hspace{-0.2cm}S^{(1,\text{NGL})}_{n\bar n}(\mu_L,\mu_R;B) &= 1-B\frac{2 C_F}{\beta_0}\left[
\gamma_E \left| \log\frac{\alpha_s(\mu_R)}{\alpha_s(\mu_L)}\right|\right.\\
&
\hspace{-0.75cm}
\left.+\frac{\beta_0}{2 C_A}\log \Gamma\left(
1+\frac{2 C_A}{\beta_0}\left| \log\frac{\alpha_s(\mu_R)}{\alpha_s(\mu_L)}\right|
\right)
\right]\ .\nonumber
\end{align}
By varying $B$ we can observe the corresponding response of the mutual information.  In \Fig{fig:pert_mi_B}, we plot the mutual information $I_\beta$ for $B = 0.5,\, 1,\, 2$, without including theoretical uncertainties.  $I_\beta$ exhibits roughly linear dependence on $B$, demonstrating that this observable is very sensitive to both the value of $\alpha_s$ and the size of non-global effects.

\subsection{Including Non-Perturbative Effects}

One can additionally include the effects of non-perturbative physics due to hadronization by convolution with a non-perturbative shape function \cite{Korchemsky:1999kt,Korchemsky:2000kp} because the energy correlation functions are additive observables.  Korchemsky and Tafat \cite{Korchemsky:2000kp} introduced a shape function differential in both hemisphere scales $\epsilon_L$ and $\epsilon_R$, $F(\epsilon_L,\epsilon_R)$.  The non-perturbative distribution can then be expressed as
\begin{align}
\sigma(\ecf{2,L}{\beta},\ecf{2,R}{\beta}) &\\
&
\hspace{-1.5cm}
=\int d\epsilon_L\, d\epsilon_R\, F(\epsilon_L,\epsilon_R)\, \sigma_p\left( \ecf{2,L}{\beta} - \frac{\epsilon_L}{E_L},\ecf{2,R}{\beta}-\frac{\epsilon_R}{E_R} \right)\,, \nonumber
\end{align}
where $\sigma_p$ denotes the perturbative distribution.  The shape function is normalized:
\begin{equation}
1=\int d\epsilon_L\, d\epsilon_R\, F(\epsilon_L,\epsilon_R) \,,
\end{equation}
and has support over a region of size set by the non-perturbative scale of QCD, $\Lambda_\text{QCD}$.  The parametrization of the shape function introduced by Korchemsky and Tafat is
\begin{equation}\label{eq:tafat_korchemsky}
F(\epsilon_L,\epsilon_R) = N \left(\frac{\epsilon_L\epsilon_R}{\Lambda^2}\right)^{a-1}e^{-\frac{\epsilon_L^2+\epsilon_R^2+2b\epsilon_L\epsilon_R}{\Lambda^2}}\,.
\end{equation}
$N$ is set by the normalization of the shape function, and $a$, $b$, and $\Lambda$ are parameters of the shape function.  By fitting data for heavy jet mass, they suggested the values $a=2$, $b=-0.4$, and $\Lambda = 0.55$ GeV. It is important to emphasize that this is a parameterization, and other possibilities are possible. Most generally, a complete basis of shape functions should be considered \cite{Ligeti:2008ac}.

The parameter $b$ controls the amount of correlation between the hemispheres introduced by non-perturbative effects.  A value of $b=0$ eliminates non-perturbative correlations, while $b>-1$ is required for the shape function to be normalizable.  In general, we expect the amount of non-perturbative correlation to depend on the angular exponent $\beta$ of the energy correlation functions.  We are able to parametrize this dependence by considering simple limiting cases.  As $\beta\to \infty$, the non-perturbative correlations should become unbounded because the mutual information is controlled by emissions right at the hemisphere boundary.  Therefore, as $\beta \to \infty$, we expect that $b \to -1$.  If $\beta \leq1$, then collinear emissions live at an equal or lower virtuality than soft emissions.  Thus, for $\beta \leq 1$, non-perturbative corrections will be dominated by high energy collinear splittings with relative transverse momentum near the scale $\Lambda_\text{QCD}$.  The non-perturbative correlations should therefore vanish for $\beta \lesssim 1$, because different hard collinear sectors are uncorrelated, up to corrections at higher powers in the observables.  Therefore, as $\beta \to1$, $b\to 0$.  A simple parametrization of $b$ that accounts for these expected limits is
\begin{equation}
b = \frac{1-\beta}{\beta} \,.
\end{equation}
We do not, however, have a proof of this relation. Measurement of $b$ as a function of $\beta$, perhaps using our mutual information observable, would shed light onto the non-perturbative correlations between observables.
For the hemisphere mass, $\beta=2$ and $b=-0.5$, close to the value suggested by Korchemsky and Tafat.  We will therefore use this value of $b$ in our analysis.  Since our perturbative uncertainties are large, we will not study in detail the variation of non-perturbative parameters. Instead, our focus is simply on showing how non-perturbative effects can be incorporated, and understanding their impact on the mutual information.

It is interesting to note that while to leading logarithmic accuracy the mutual information, $I_\beta$, vanishes in perturbation theory, this is no longer true once non-perturbative effects are included with a non-zero value of the shape function parameter $b$. A non-zero $b$ induces correlations between the energy correlation functions as measured on the left and right hemispheres even if they are not present perturbatively. A measurement of the mutual information could therefore also prove useful in constraining non-perturbative correlations in event shape observables, and improving their modeling in Monte Carlo programs.

The non-perturbative scale $\Lambda$ will also have dependence on $\beta$.  From the universality of the leading non-perturbative corrections \cite{Dokshitzer:1995zt,Lee:2006nr}, it has been demonstrated that for observables like the energy correlation functions that are additive and have an angular exponent parameter, the non-perturbative scale $\Lambda$ is
\begin{equation}
\Lambda = \frac{\Omega}{\beta - 1} \,,
\end{equation}
where $\Omega$ is a fixed energy scale set by a non-perturbative matrix element.  Following Korchemsky and Tafat, we set $\Omega = 0.55$ GeV.  Note that this is only sensible for $\beta > 1$, where soft emissions dominate the non-perturbative corrections.

While non-perturbative correlations can be large, they do not necessarily result in a large change of the mutual information.  Non-perturbative corrections are only dominant near the singular regions of phase space.  For large values of the energy correlation functions the effect of the shape function reduces to a shift of the perturbative distribution by an amount proportional to the non-perturbative scale.  However, a shift of the distribution does not affect the mutual information (which can be seen by a simple change of variables in its definition).  So, non-perturbative effects contribute to the mutual information an amount suppressed by the volume of phase space in which they dominate.

\begin{figure}[t]
\includegraphics[width=7.5cm]{./figures/NLL_mutinf_NP.pdf}
\caption{The mutual information $I_\beta$ as calculated to NLL accuracy with the one-dressed gluon to capture NGLs including a non-perturbative shape function (solid).  The lighter band reflects conservative theoretical uncertainties and the purely perturbative result is shown for comparison (dashed).
}
\label{fig:pert_mi_np}
\end{figure}

In \Fig{fig:pert_mi_np}, we plot the mutual information $I_\beta$ including non-perturbative corrections, as a function of $\beta$.  For this plot, we set the parameters in the shape function to be
\begin{align*}
a&= 2\,,\\
b&=\frac{1-\beta}{\beta} \,, \\
\Lambda &= \frac{0.55\ \text{GeV}}{\beta -1} \,.
\end{align*}
Additionally, we include an estimate of perturbative uncertainties by varying scales in the perturbative distribution.  For comparison, we also include the perturbative mutual information.  We can only compute the non-perturbative mutual information for $\beta \gtrsim 1$, for the reasons described above.  Especially as $\beta$ increases, we see that non-perturbative correlations further increase $I_\beta$, as expected.  While we only plot for one value of the non-perturbative parameter $\Lambda$, we found only very weak dependence on this value.

\section{Monte Carlo Study}\label{sec:mc}

\begin{figure*}[t]
\centering
\subfloat[]{\label{fig:nsub_sb1}
\includegraphics[width=7.5cm]{./figures/mutinf_MC_parton.pdf}
} \qquad \qquad
\subfloat[]{\label{fig:nsub_sb2}
\includegraphics[width=7.4cm]{./figures/mutinf_MC_hadron.pdf}
}\\
\caption{ The mutual information $I_\beta$ as calculated in \pythia{} and \vincia{} Monte Carlo at (a) parton-level and (b) hadron-level.
}
\label{fig:mi_MC}
\end{figure*}

In this section, we compare our analytical calculations of non-global correlations to Monte Carlo simulation of $e^+e^-$ collision events.  We generate $e^+e^-$ collision events at 1 TeV center of mass energy with both \pythia{8.210}  \cite{Sjostrand:2007gs,Sjostrand:2014zea} and \vincia{1.2.02} \cite{Giele:2007di,Giele:2011cb,GehrmannDeRidder:2011dm,Ritzmann:2012ca,Hartgring:2013jma,Larkoski:2013yi} Monte Carlos.  For comparison to our analytic calculations, we consider parton level and hadron level events.  We then cluster the event into two jets with the exclusive $e^+e^-$ $k_T$ algorithm \cite{Catani:1991hj} with WTA recombination \cite{Larkoski:2014uqa,Larkoski:2014bia,Bertolini:2013iqa,Salambroadening} as implemented in \fastjet{3.1.3} \cite{Cacciari:2011ma}.  About the axis of the highest energy jet in the event, we cluster particles into one hemisphere if they lie within an angle of $\pi/2$ of this axis, and cluster them into the other hemisphere if they are outside this region.  The hemispheres are then randomly assigned to be left or right and the energy correlation functions are measured on them.

The calculation of the mutual information from these event samples is quite subtle, and a detailed discussion of calculating mutual information from finite statistics is described in \Ref{Larkoski:2014pca}.\footnote{The effects described there have actually been known for a very long time in other applications of mutual information; see, e.g., \Refs{treves1995upward,panzeri1996analytical}.}  While we do not present a detailed discussion of the calculation of mutual information on finite data, we will present the results.  Mutual information can be equivalently defined through the Shannon entropies of the various distributions.  For observables $a$ and $b$, the mutual information can be written as
\begin{equation}
I(a,b) = H(a)+H(b)-H(a,b)\,.
\end{equation}
For binned data, the entropy $H(a)$ is
\begin{equation}
H(a) = -\sum_{i\in \text{bins}}\frac{n_i}{N^{a}_\text{ev}}\log_2\frac{n_i}{N_\text{ev}}\,,
\end{equation}
where $N^a_\text{ev}$ is the total number of events in the $a$ sample and $n^a_i$ is the number of events in bin $i$ for observable $a$.  For a finite data set, the number of events per bin will fluctuate, and the leading effect of these fluctuations on the mutual information can be calculated.  The mutual information is then
\begin{align}\label{eq:mutinf_fluc}
I(a,b) = I_\infty(a,b)- \frac{1}{2\log 2} \left(  \frac{n^a_\text{bins}}{N^{a}_\text{ev}} + \frac{n^b_\text{bins}}{N^{b}_\text{ev}} - \frac{n^{ab}_\text{bins}}{N^{ab}_\text{ev}}  \right) +\dotsc
\end{align}
Here, $I_\infty(a,b)$ is the mutual information with infinite statistics, $n^a_\text{bins}$ is the number of bins in the $a$ sample, and $N^{a}_\text{ev}$ is the number of events in the $a$ sample.  To remove, or at least minimize, effects of finite binning, we want to set the term in parentheses in \Eq{eq:mutinf_fluc} equal to zero with judicious choices of bin and sample sizes.  The choice used in this paper is to set $n^a_\text{bins}=n^b_\text{bins}\equiv n_\text{bins}$ and $n^{ab}_\text{bins} = n_\text{bins}^2$.  With this choice the one dimensional sample sizes are
\begin{equation}
N^{a}_\text{ev}=N^{b}_\text{ev} = \frac{2 N^{ab}_\text{ev}}{n_\text{bins}} \,.
\end{equation}
With this choice, we find that the mutual information that we calculate on Monte Carlo data is largely independent of the number of bins $n_\text{bins}$.  There do exist non-parametric methods for estimating mutual information that often have the advantage that a significantly smaller amount of data can be used.  We discuss one such algorithm in \App{app:nonpara_mi}.

\begin{figure}[t]
\includegraphics[width=7.4cm]{./figures/mutual_info_SoftDrop.pdf}
\caption{  The mutual information for  $e^+e^-\to $ dijets before and after the application of the modified mass drop (mMDT) grooming procedure.
}
\label{fig:mi_softdrop}
\end{figure}

We plot the extracted mutual information $I_\beta$ in both parton level and hadron level Monte Carlo in \Fig{fig:mi_MC}.  Both Monte Carlos exhibit the characteristic increase in $I_\beta$ as $\beta$ increases, indicative of non-global correlations.  The values of $I_\beta$ are nicely consistent with our calculations at both parton level (\Fig{fig:pert_mi}) and hadron level (\Fig{fig:pert_mi_np}), as well as with each other. We do not have a clear explanation for the slight discrepancy between the two generators observed at higher $\beta$ at parton level, as it is well within our perturbative uncertainties.  The Monte Carlo also manifests the expected increase of non-global correlations with the addition of hadronization.

Non-global effects and NGLs in particular, strictly first occur at NLL order, and this observable demonstrates that formally leading logarithmic parton showers do include some amount of NGLs. This is perhaps not too surprising, because even in the Monte Carlos it is possible that an emission in the left hemisphere subsequently emits into the right hemisphere.  What may be surprising is that the strength of these correlations seems to be consistent with that calculated to NLL accuracy.  Because of the slightly different physics incorporated in the Monte Carlo predictions and the analytic calculations, we have chosen not to show them on the same plot. As non-global effects are probed in more detail, it will important to understand, preferably with a proof from the evolution kernels in the parton shower, to what extent parton shower Monte Carlos reproduce, for example, the BMS equation. It would also be interesting to improve the perturbative uncertainties in the analytic calculation of the mutual information by including higher order NGLs, for example using the formalisms proposed in \Refs{Caron-Huot:2015bja,Larkoski:2015zka,Becher:2015hka,Neill:2015nya}, allowing for a more precise comparison between analytic calculations and Monte Carlo programs.

To provide further support for our interpretation of the rise of $I_\beta$ with $\beta$ being due to non-global interactions of soft QCD particles, in \Fig{fig:mi_softdrop} we show a comparison of the mutual information on \pythia{} dijet events measured before and after the application of the modified mass drop (or equivalently, soft drop) grooming procedure \cite{Dasgupta:2013ihk,Dasgupta:2013via,Larkoski:2014wba} with fractional energy cut $z_{\text{cut}}=0.1$. In analytic calculations, this jet groomer has been shown to eliminate NGLs by removing wide angle soft radiation from the jet. This prediction is supported by \Fig{fig:mi_softdrop}, where the groomed $I_\beta$ is small relative to $I_\beta$ measured on the original event, and exhibits minimal dependence on $\beta$. This suggests that soft wide angle radiation is not responsible for the residual correlations. We have restricted the range of the plot to a single unit interval in $\beta$, as for angular exponents $\beta\gtrsim2$, the values of the energy correlation function after grooming become very small and our numerical methods become unstable. Because the characteristic increase of $I_\beta$ with $\beta$ is not present in the groomed events, NGLs have indeed been removed.

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

Despite their importance for precision jet calculations, NGLs have never directly been observed.  In this paper, we introduced a novel procedure that allows us to isolate non-global correlations and their manifestation as NGLs.  The correlation between hemispheres in $e^+e^-$ collisions as quantified by the mutual information is calculable and measurable and we find good agreement between analytics and Monte Carlo simulation.  This correlation is also very sensitive to the value of the coupling $\alpha_s$, which can be brought under better theoretical control with higher-order calculations.  Non-perturbative contributions generically increase the correlation between the hemispheres, but are still subdominant effects to perturbative NGL correlations.  The mutual information $I_\beta$ is sensitive to physics formally beyond the accuracy of Monte Carlo generators, and so could be a powerful observable for tuning.  Additionally, while we focused on correlations in TeV collisions, this procedure could be applied for collisions at the $Z$ pole at LEP.  Perturbative non-global correlations would still exist, but non-perturbative correlations would be significantly larger.

While we have focused our discussion on the mutual in formation in the  context of $e^+e^-$ collisions it, or something similar, can in principle be measured at a hadron collider. A potentially clean measurement which is directly related to our discussion at $e^+e^-$ colliders is the decay of a color singlet initial state into hadrons. One could create such a sample at the LHC by identifying the hadronic decays of electroweak bosons.  With all particles from the decay, one can boost the system to its center of mass, identify the hemispheres, and measure the correlations.  It would also be interesting to use this observable to measure correlations between jet properties in $pp \to$ dijets, or more generally in QCD events. In particular, this procedure can be entirely data driven, and could be used as a powerful probe of correlations for measurements made in distinct regions of the detector. Experimentally, this would be significantly challenging, especially controlling effects from contamination.  Nevertheless, because it probes explicitly higher-order physics, measuring these non-global correlations could provide powerful insight into subleading QCD effects.

\begin{acknowledgments}
We thank Ben Nachman, Duff Neill, Iain Stewart and Jesse Thaler for helpful discussions and comments on the manuscript. This work is supported by the U.S. Department of Energy (DOE) under cooperative research agreements DE-FG02-05ER-41360, and DE-SC0011090.
A.L.~is supported by the U.S. National Science Foundation, under grant PHY--1419008, the LHC Theory Initiative.  I.M.~is also supported by NSERC of Canada.
\end{acknowledgments}


text:
Scarlett Johansson is Joining the Cast of Jojo Rabbit
Nathan Shubert
Scarlett Johansson has signed on to star in the upcoming war drama, Jojo Rabbit.
The film will be set in World War II and it is about a young German boy who discovers that his mother (Johansson), is sheltering a Jewish girl in their home. The film will be directed by Taika Waititi, the director of Thor: Ragnarok. After finishing the successful Marvel film, Waititi was offered other movies to direct, but he made it clear that this would be his next project. Waititi penned the script alongside Carthew Neal and Chelsea Winstanley. Neal is best known for producing The Breaker Upperers, while Winstanley was a producer in What We Do In The Shadows.
While busy filming his What We Do In The Shadows pilot, Waititi met with Johansson previously to talk about her role in the film. Now that the actress has been recruited, Waititi will now be searching for an actor to portray the young German boy.
Jojo Rabbit will mark a change of pace for Johanson as she has primarily been featured in action and comedies in the last couple of years. Last year, Johansson played the hardcore cyber-enhanced soldier, Major, in Ghost in the Shell. She also was featured in the Sony comedy, Rough Night. Her next film will see her reprise her role as the deadly assassin Black Widow, in Marvel's Avengers: Infinity War.
Production of Jojo Rabbit is expected to start this spring.
Liked this article and want to read more like it? Check out Aleksander Gilyadov's Thor: Raganrok Could Be Director Taika Waititi at His Best and Phil Brown's Thor Ragnarok Review – Thor Get Good.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Receivership, in law, the judicial appointment of a person, a receiver, to collect and conserve certain assets and to make distributions in accordance with judicial authorization. A receivership is properly an intermediate or incidental step toward some other principal objective and not generally the object of litigation. The principal objective may be the preservation of the assets pending a decision as to who should receive the property, or it may be the liquidation of the assets and the distribution of the proceeds to the parties entitled to them.
A receivership may be general in character in that it comprises all the assets of the individual, partnership, or corporation, or it may be special, involving only the property subject to litigation.
The powers of the receiver—syndic and Administrator in France and Germany, respectively—in dealing with the assets are based on statutory provisions or judicial decrees. As a practical matter the extent of the receiver's powers often is determined by the nature of the assets. For example, if the asset is unimproved real estate, the receiver's powers may involve simply the payment of taxes. If the asset is an apartment building, the receiver's powers could include management, collecting rents, and signing leases.
If the court feels that, in the best interest of the parties involved, the assets should be liquidated, the court will authorize the receiver to sell the assets at a judicial sale, which is conducted in the form of an auction.
bankruptcy: Roles of the court, the administrator, and the creditors in bankruptcy proceedings
…is undertaken by an official receiver—an office established in 1883—unless a general meeting of creditors or the secretary of state for trade and industry, upon reference by the official receiver, appoints another person qualified to act as an insolvency practitioner to the post of trustee. In cases of summary administration…
Liquidation, discharge of a debt or the determination by agreement or litigation of the amount of a previously unliquidated claim. One important legal meaning is the distribution of the assets of an enterprise among its creditors and proprietors. At the dissolution of a solvent corporation or unincorporated association, the assets…
Bankruptcy, the status of a debtor who has been declared by judicial process to be unable to pay his debts. Although sometimes used indiscriminately to mean insolvency, the terms have distinct legal significance. Insolvency, as used in most legal systems, indicates the inability to meet debts.…
Business law, the body of rules, whether by convention, agreement, or national or international legislation, governing the dealings between persons in commercial matters. Business law falls into two distinctive areas: (1) the regulation of commercial entities by the laws of company, partnership,…
Law, the discipline and profession concerned with the customs, practices, and rules of conduct of a community that are recognized as binding by the community. Enforcement of the body of rules is through a controlling authority. The law is treated in a number of articles. For a description of legal…
More About Receivership
In bankruptcy: Roles of the court, the administrator, and the creditors in bankruptcy proceedings
Fascism, political ideology and mass movement that dominated many parts of central, southern, and eastern…
English language, West Germanic language of the Indo-European language family that is closely related…
Education, discipline that is concerned with methods of teaching and learning in schools or school-like…


October is the perfect time to start growing your winter vegetable garden. If you are trying to save money or grow something unusual, starting vegetables from seed is your best option. Read on to learn tips for growing plants from seed.
It seems to me that if I am going to put the effort into doing this, I might as well grow something that I can't buy at the grocery store. When I think of vegetable gardens, one of my most fond memories is eating yellow pear tomatoes right off the plant of my grandma's garden. This is really my only must-have plant for this season.
One of the most important supplies are healthy seeds. Seeds are most likely to grow, or germinate, the first year. As they age, the germination rate decreases and fewer plants will grow. All seed packages are dated and getting rid of old seed is important. Since I haven't done this before, all of my seed is the very freshest possible.
Many local nurseries and garden centers have seeds available for purchase. For starting vegetables from seed, especially unusual or heirloom varieties, online sources offer countless options. Two favorites for me include johnnyseeds.com and burpee.com, although there are many others.
Yellow Pear Tomato **I can't wait for these!
A variety of containers will work well for starting vegetables from seed, and this is often a good way to reuse old pots from previous purchases. I prefer to use potting soil for starting seeds. The lightweight soil allows small seedlings to grow easily and does not have weeds or pests.
I don't plan to keep in containers for too long, so this cell pack works just fine. It also allows you to start many plants in a small space.
Generally, seeds are planted at a depth twice their size. For very tiny seeds, this may mean they are just scattered on the top of the soil, while large cucumber seeds would be about 1" in depth. Plant seeds in wet soil and keep the container moist until the seedlings begin to grow. These tender plants need adequate moisture while they begin growing roots.
When it is time to plant in the garden, wait until there is a good root system before planting in the ground. Check this by gently removing the plant from the container and looking for healthy, white roots on the outside. Keep plants well watered for the first week or two while they get used to their new home.
Some vegetables can be planted by seed directly in the ground. Beans, corn, cucumbers and radishes are just a few that are best planted this way. Luckily, this reduces the amount of work required and plants will be ready to harvest quickly. While my small tomato seedlings grow I can enjoy the 'Gold Play' bush beans that were planted directly in the soil and are already growing one week later.
Ready to start your own garden? Save money by starting vegetables from seed this year. This is a great way to try new and unusual varieties and harvest your own fresh and nutritious food.


text:
Look Beyond the Arizona Memorial on Your Hawaii Vacation
You may well be planning to visit Pearl Harbor and the USS Arizona Memorial on your Hawaii vacation, but be careful not to limit your experience to the Arizona alone. Pearl Harbor memorializes both the beginning and the end of World War II. The USS Arizona is justifiably the centerpiece of the harbor's historic place on the itineraries of island visitors because of its emotional impact. The USS Missouri, however, has a richer and more varied history.
"Mighty Mo" was launched on January 29, 1944, and went on to participate in critical operations during the final months of World War II, including the Allied invasion of Iwo Jima and Okinawa and the Allied advance on the Japanese home islands.
After the formal signing on its deck of the "Instrument of Surrender" on September 2, 1945 in Tokyo Bay ended the war, the battleship was not retired. She participated in training cruises for naval midshipman and was involved with other peacetime operations.
When North Korean forces suddenly invaded South Korea in 1950, the Missouri provided ongoing gunfire support for U.N. forces ashore and went on to serve two rigorous combat tours between 1950 and 1953. When that service ended, she was decommissioned on February 26, 1955, and entered the Pacific Reserve Fleet at Puget Sound Naval Shipyard, where she would remain for the next 30 years.
Then, in 1984, with tensions rising in the Middle East, Mighty Mo was called back to duty, modernized and re-commissioned, and sent on an historic world cruise, reflecting the one taken by President Teddy Roosevelt's Great White Fleet of 1904. A year later, she participated in an Allied escort of oil tankers through the dangerous waters of the North Arabian Sea.
Then, in early 1991, Battleship Missouri was firing Tomahawk missiles against Iraqi forces as Operation Desert Storm commenced.
Finally, she returned to Pearl Harbor in 1991 to join in the historic commemoration marking the 50th anniversary of attack on the Hawaiian Islands.
Finally, in 1992, the "Mighty Mo" was once again decommissioned — the very last American battleship to be decommissioned. In 1998 she remains a memorial, "standing watch over the hallowed waters of Pearl Harbor," and touring her decks is fascinating.
So, while the USS Arizona remains the first lady of Pearl Harbor, make a day of your Pearl Harbor visit and include Mighty Mo as well. To include a practical and fulfilling tour during your island vacation (Yes, there's even more to see in the immediate area!), pick an agent from our Web site home page (hawaii-aloha.com), or call 1-800-843-8771


text:
WM U.S.: NYSE
Waste Management Inc.
Watchlist CreateWMAlert
WMUS
After Hours Volume: 48.76K
$152.61 0.11 0.07%
Volume: 1.37M 65 Day Avg: 1.7M
81% vs Avg
151.26 Day Range 153.03
138.58 52 Week Range 175.98
WM Overview
Day Range 151.26 - 153.03
Market Cap $62.64B
P/E Ratio 28.35
EPS $5.38
Dividend $0.65
Ex-Dividend Date Dec 1, 2022
Short Interest 4.03M 01/13/23
% of Float Shorted 1.02%
Average Volume 1.7M
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Waste Management, Inc. is a holding company, which engages in the provision of waste management environmental services. It operates through the following segments: Tier 1, Tier 2, and Tier 3. The Tier 1 segment consists of areas in the Southern United States. The Tier 2 segment consists of areas located in the Midwest and Northeast United States. The Tier 3 segment consists of all remaining areas, including the Northwest and Mid-Atlantic regions of the United States and Eastern Canada. The company was founded on September 30, 1987 and is headquartered in Houston, TX.
Ecolab Inc. 0.32% $43.39B
Republic Services Inc. -0.02% $39.14B
Waste Connections Inc. 0.30% $44.94B
GFL Environmental Inc. 1.70% $15.95B
Clean Harbors Inc. -0.26% $6.89B
Stericycle Inc. 0.08% $4.84B
Casella Waste Systems Inc. Cl A -0.56% $4.11B


It's tempting to brush away warning signs that your mom, dad or other senior relative could use help at home.
Most boomers are overworked and overwhelmed by schedules that whittle away personal "me time." So it's only human to hope that elders can make it on their own for a little while longer. Seniors want the same. And they usually can extend independence, often for life, with help at home.
Take this dose of wisdom from national aging experts: It's better to plan and intervene earlier than wait for a crisis call. "Family conversations" about late-life "should take place early and often," while health is fine and there are no problems, says Elinor Ginzler, senior vice president of AARP's Livable Communities in the Office of Social Impact.
Invite senior relatives to discuss how they want to handle possible future difficulties. You might say, "This is all about you staying in control, Mom and Dad. The best way to do that is letting us know how you want stuff to be," Ginzler suggests. It's much easier to modify a home so that a bedroom and accessible full bathroom are on the first floor before a health crisis than during or after one, Ginzler says. That's also the time to learn about in-home services.
Lustbader adds: "When one of those essentials of life is just not possible anymore, you have to face the music. It's a very tough point for people. Accepting a little bit of help is far smarter than accidents." Ginzler suggests that when you're visiting your elder relative, "put on that detective hat." Offer to do some seasonal cleaning and "look at the house with fresh eyes," she says. "You're looking for changes" in the elder and in the home.
Elders often respond to direct personal requests, such as accepting in-home help so their children won't worry about them, she says. Seniors are often reluctant to admit having difficulties because they're afraid of being forced into assisted living or a nursing home. In-home care may prevent that: "Sometimes you can get by with very minimal assistance," Lustbader notes.
If your parent refuses to consider the in-home care they need, sometimes someone else is better able to intervene, such as a trusted doctor, minister, friend, nurse, therapist or lawyer. Other seniors may prefer to plan for disability care for themselves so their children don't have to worry or make decisions. Some parents lament that they can't get children to recognize their need for help.


text:
Justia Patents Robert VanBuskirk Inventions, Patents and Patent Applications
Patents by Inventor Robert VanBuskirk
Robert VanBuskirk has filed for patents to protect the following inventions. This listing includes patent applications that are pending as well as patents that have already been granted by the United States Patent and Trademark Office (USPTO).
Methods and compositions for the preservation of cells, tissues or organs in the vitreous state
Abstract: The invention provides methods for the hypothermic preservation of cells, tissues and organs. In particular, the invention provides methods for the hypothermic preservation or storage of cells, tissues or organs in the vitreous state.
Filed: November 18, 2002
Date of Patent: July 26, 2005
Assignee: Biolife Solutions Incorporated
Inventors: John M. Baust, John G. Baust, Robert VanBuskirk, Aby J. Mathew
Applicant: BioLife Solutions, Inc.
Method and use of protein microarray technology and proteomic analysis to determine efficacy of human and xenographic cell, tissue and organ transplant
Abstract: The present invention is directed to systems and methods for assessing the success of the transplant of a cell, tissue, or organ before and after transplant. Protein array technology is used to obtain a biomarker pattern for the cell, tissue, or organ that is being considered for transplant or that has been transplanted. Samples for the identification of biomarkers and biomarker patterns are obtained from the cell, tissue or organ itself, or from a body fluid of the donor or recipient. Sample biomarker data are compared to reference biomarker data obtained from donors, recipients or cells, tissues or organs that have been transplanted. Correlation of a sample biomarker pattern with the reference biomarker pattern, where transplant outcome for the samples used for the reference biomarkers is known, permits a suggested treatment determination. A computerized system to identify the condition of transplant before or after implantation is also provided.
Filed: February 21, 2003
Inventors: Aby J. Mathew, John M. Baust, Robert VanBuskirk, John G. Baust
System for transferring messages between input and output devices in a communication device
Abstract: A method and system for processing messages is provided. In a preferred embodiment of the present invention, a message scheduler, a job process, and a format resolution module are used. The message scheduler identifies when a new message is to be processed, schedules the new message for processing, invokes the format resolution module to determine a method of converting data in the message to an appropriate format for a destination device or file, and invokes a job process. The format resolution module determines an appropriate method for converting data in the message from a format acceptable to the source devices or files to a format acceptable to the destination devices or files and creates a target message containing a reference to a destination device or file. The job process sends the data between the source devices or files to a destination device or file and performs the appropriate conversion.
Filed: August 11, 1995
Date of Patent: November 23, 1999
Assignee: Microsoft Corporation
Inventors: Sharad Mathur, Arul Menezes, Michael Robert VanBuskirk, Kevin Thomas Gallo


The Reisenthel concept: Products that are extremely functional and versatile – perfect for everyday mobility needs. Made from materials that are remarkably robust and durable, Reisenthel combines first-class design with the high quality into a perfect blend of form and function. It's about ensuring that products solve problems rather than causing them. Reisenthel products make life just that much more pleasant and enjoyable!


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Library Menu
One Book, One College is a year-long, interdisciplinary program engaging the ICC community through the reading and discussion of a shared book.
Fostering interdisciplinary relationships through a shared reading experience.
2019-2020 One Book, One College Selection:
How We Got To Now
In this illustrated history, Steven Johnson explores the history of innovation over centuries, tracing facets of modern life (refrigeration, clocks, and eyeglass lenses, to name a few) from their creation by hobbyists, amateurs, and entrepreneurs to their unintended historical consequences. Filled with surprising stories or accidental genius and brilliant mistakes — from the French publisher who invented the phonograph before Edison but forgot to include playback, to the Hollywood movie star who helped invent the technology behind Wi-Fi and Bluetooth–How We Got To Now investigates the secret history behind the everyday objects of contemporary life.
Johnson examines unexpected connections between seemingly unrelated fields: how the invention of air-conditioning enabled the largest migration of human beings in the history of species — to the cities such as Dubai or Phoenix, which would otherwise be virtually uninhabitable; how pendulum clocks helped trigger the industrial revolution; and how clean water made it possible to manufacture computer chips. — from Penguin Random House.
Steven Berlin Johnson is the bestselling author of eleven books, including Where Good Ideas Come From, Wonderland, and The Ghost Map. He's the host and co-creator of the Emmy-winning PBS/BBC series How We Got To Now, and the host of the podcast American Innovations. He lives in Brooklyn and Marin County, California with his wife and three sons. — from Penguin Random House.
Read more about Steven Johnson at Biography in Context.
View the ICC Library's LibGuide to learn more about How We Got To Now.
Community Leader Presentations
A leader from the Peoria area is invited to campus to speak about the importance of the theme in their work and personal life. (45 minutes)
Faculty Presentations
ICC faculty members use their specialized knowledge and experience to present information about the One Book, One College theme and/or selection. (45 minutes)
Faculty Presentation Request
Have a presentation idea? Tell us about it!
Watch recordings of One Book, One College Community Leader, and Faculty presentations.
Selecting
Selections for One Book, One College are made by a team of librarians and faculty from several departments at ICC.
If you have a suggestion for next year's read, please contact Amy Glass by email or call (309) 694-5748 or complete this online form.
Past Selections
2018-2019 Frankenstein: The 1818 Text
2017-2018 The Book of Joy by the Dalai Lama, Desmond Tutu, and Douglas Carlton Abrams
2016-2017 The Alchemist by Paulo Coelho
2015-2016 March: Book One by John Lewis
2014-2015 Ready Player One by Ernest Cline
Contact Amy Glass by email or call (309) 694-5748 for more information.


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You are here: Accommodation > Self Catering
Self-catering apartments range hugely in size, price and location and can provide the perfect accommodation solution for families or groups who like to cook for themselves and require a little extra living space or individuals and groups who require more in the way of privacy and home-comforts than you can find at a hotel.
The opportunity to cook for yourself can also be a great way to save money! So from city centre apartments offering high-class luxury to seaside cottages bursting with old-fashioned charm you're bound to find your home from home.
If a stay at the coast is more your cup of tea, the cottages at Souter Lighthouse, once occupied by the lighthouse staff and their families, are a guaranteed hit, or visit the Seafront Apartments in Cullercoats for easy access to the four sandy beaches of Whitley Bay and Tynemouth.
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Cottages in Northumberland: Fellstone Cottage
Whickham
Fellstone Cottage is situated within one and a half acres of beautifully landscaped gardens and Meadows, which was once part of the Gibside Estate. The charm and character of this traditional stone built cottage makes it a perfect get away from…
Price £495.00 to £695.00 Per unit per week
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Cottages in Northumberland: Ouseburn Apartment
Ouseburn Apartment is situated in Sandyford, a stone's throw from Newcastle City Centre and the trendy suburb of Jesmond.
This great location means a range of boutique shops, bars and restaurants as well as Newcastle's main shopping area Intu…
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2 Quayside Loft
Quayside Newcastle
Quayside Loft is a stylish, luxury first floor apartment with breath-taking views of The Millennium Bridge and The Sage Gateshead, which offers the perfect base for exploring the vibrant city of Newcastle. The property is located within walking…
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Cottages in Northumberland: Eaststone Cottage
Located within one and a half acres of beautifully kept grounds Eaststone Cottage offers delightful views across the Derwent Valley. Interestingly, the land it is nestled within was once part of the Gibside Estate which was owned by the Royal…
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91 Aparthotel
Situated in the popular leafy suburbs of Jesmond, 91 Aparthotel Jesmond Road is a stylish mix of 16 Serviced Apartments in Newcastle designed & built to the highest standards.
Price £88.80 to £130.80 Per unit per night
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Luxury Scandinavian style lodges on the lakeside of Kielder Water boast panoramic views stretching over the lake and forest. Boasting 27 miles of shoreline fringed by pine forest and heather moorland, the stunning landscape of Kielder Water creates…
More info for Kielder Lodges
Cottages in Northumberland: The Barn
The Barn has just been renovated to a beautiful standard, the building is set within 100 acres of fields and woodland and offers panoramic views across the countryside, a truly idyllic location.
The outdoor space at the cottage is plentiful,…
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Cottages in Northumberland: Coble Cottage
Coble Cottage is a charmingly refurbished terraced property in the Northumberland seaside town of Newbiggin-by-the-Sea - around 17 miles from the City of Newcastle upon Tyne.
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Cottages in Northumberland: Hill Top Cottage
Lamesley
Hill Top Cottage is a lovely detached, stone-built self-catering property for up to 4 guests. It is situated just outside the village of Lamesley which is a short drive from Newcastle upon Tyne and within easy reach of the A1 – the gateway to…
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Cottages in Northumberland: The Piggery
This beautiful, stone-built conversion from a former Piggery offers a fantastic location for a break just outside of Newcastle City Centre.
Relax in the comfort of the peaceful and comfortable lounge, which is a real home from home, whilst…
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They say "When in Rome, do as the Romans do" but we say when in Delhi, do as the Delhi-ites do! Feel some 'shudh', 'desi' Delhi vibes and be as local as it gets at Local, situated in the heart of the New Delhi, Connaught Place! A gigantic beauty ideal for all your moods, be it getting into the party zone or spending some good time with your friends or unwinding with your colleagues, Local is where you can head to for some unadulterated happiness! It is the archetype of class and elegance coupled with a bit of funk and lots of memorabilia! The interiors feature paintings of monuments of Delhi, the color scheme is warm, the lighting is subtle and the vibe, oh-so-perfect! This casual lounge and bar serves a range of North Indian and Continental delicacies that are all a treat to your taste buds. Add to that the selection of heady drinks, concoctions & brews and you know there's no leaving this place unless you absolutely need to! So then people, everything said and done, all there's left for you to do is to put on your favourite outfit, grab your buddies and head to Local to have a fabulous time, Local style!
Offer Description: One coupon entitles you to one complimentary main course item when another main course item is ordered of the same or higher value. Valid on Local Pizzas, Local Pastas, Local Signature Sizzlers, Local B3 Big Bang Burgers, Local Mediterranian Classics, Local Pan Asian Create Your Own Bowl and LOcal Khana Khazana. Valid on all days, including weekends.


what is the total land area of Scandinavia?
Which three European countries make up Scandinavia? What countries make up the Indies? What three countries make up Scandinavia? Is Italy a part of Scandinavia? Is Finland part of Scandinavia-?


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Australia markets open in 3 hours 4 minutes
Black Friday & Cyber Monday Samsung Galaxy S10 Deals 2020: Galaxy S10, S10+ & S10e Sales Ranked by Save Bubble
Save Bubble
Save on Samsung Galaxy S10 deals at the Black Friday & Cyber Monday 2020 sale, including the latest carrier-locked & unlocked model discounts
Black Friday 2020 sales experts at Save Bubble have compared the best Samsung Galaxy S10, S10+ & S10e deals for Black Friday & Cyber Monday 2020, including all the top discounts on Galaxy smartphone deals. Links to the top deals are listed below.
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Contact: Andy Mathews (andy@nicelynetwork.com)
Virgin Orbit carries satellites to space for the first time
Virgin Orbit reaches orbit for the first time
Virgin Orbit has successfully carried satellites into space for the first time.
Virgin Orbit launched its LauncherOne rocket to orbit for the first time today, with a successful demonstration mission that carried a handful of satellites and will attempt to deliver them to low Earth orbit on behalf of NASA. It's a crucial milestone for the small satellite launch company, and the first time the company has shown that its hybrid carrier aircraft/small payload orbital delivery rocket works as intended, which should set the company up to begin commercial operations of its launch system very soon. This is the second attempt at reaching orbit for Virgin Orbit, after a first try in late May ended with the LauncherOne rocket initiating an automatic safety shutdown of its engines shortly after detaching from the 'Cosmic Girl' carrier aircraft, a modified Boeing 747 that transports the rocket to its launch altitude.
Five killed in cottage fire in Norway
Five people, including four children, have died in a fire at a cottage in Norway, with one man surviving and walking barefoot to reach neighbours.
Poisoned Kremlin critic detained in Russia
Leading Kremlin critic Alexei Navalny has been detained by police after landing in Moscow, the first time he has returned home since being poisoned.
Players in the Premier 15s could be tested for Covid-19 when the league returns later this month after it emerged the option is being "considered" by the Rugby Football Union. Last week, the RFU suspended its flagship women's competition for a fortnight in the wake of the deteriorating public health situation. Players had been following adapted law variations designed to reduce face-to-face contact – such as limited scrums and 35-minute halves – before the league was paused. The RFU had sought clarification with Public Health England over whether the adaptations were sufficient. PHE said it was "comfortable" for the elite amateur league to continue, although additional options are now being explored to bring in lateral flow testing for players. Rapid or lateral flow tests provide Covid-19 results in 30 minutes, although concerns have been raised about their accuracy. An RFU spokesperson said: "Testing is something being considered. Public Health England are happy for us to continue under adapted laws and regulated training and continue without testing, but we are looking into testing options to add a measure. We are using this break to explore approved lateral flow testing to complement adapted laws and regulated training and other intensive protocols and are working on how this may be implemented." The Premier 15s is expected to resume on the weekend of Jan 30-31, although that could be pushed back depending on the public health situation. There had been a growing sense of unease that player welfare was being jeopardised with no Covid-19 testing provision in place in the league, which falls under the Government's interpretation of "elite" sport and can therefore technically continue during lockdown.
Bitcoin's Massive Swings Give Pause to CFOs Mulling Reserve Investment: Bloomberg
Bitcoin's 30% price correction was enough to give some CFOs second thoughts.


PORTLAND, OR. Portfolio Financial Servicing Company ("PFSC") announced today that it has entered into a definitive agreement to act as Servicer and Custodian for a new structured settlement credit facility. Terms of the agreement remain confidential.
PFSC has been a leading provider of structured settlement, lottery and annuity servicing since 2002. John Enyart, President of PFSC, commented, "PFSC has provided our structured settlement services to both the lender and borrower for almost a decade and we are gratified that they approached PFSC about playing an important role in this new credit facility. We look forward to providing an outstanding value proposition to our Clients under this new arrangement".
Under the new facility, PFSC will be responsible for substantially all structured settlement servicing, including boarding, funding, document certification and retention, payment posting, collections, customer service, split-payment processing and investor reporting functions.


A local resident, who is unhappy with the current parking situation at Burlington's AMC movie theater, recently brought the issue to the attention of the Planning Board. The problem stems from AMC's lower parking lot being closed off due to National Development's construction of a new restaurant, getting rid of a great deal of parking spaces. With the lack of spaces to park at the theater, moviegoers have taken to parking along Second Avenue; an offense that warrants a ticket.
The resident is requesting that National Developments reopens the lot to accommodate the movie theater's overflow traffic, which is at its height on Thursdays through Sundays.
Planning Director Kristin Kassner attributed the problem to the large amount of construction that is going on the area, but is working to fix the problem.


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Garden Group Management
Affiliate of The Garden Group Makes Inc 5000 List
by siteadmin | Aug 25, 2018 | Company News, Mars Services
The Garden Group announced today that Mars Services, a member of The Garden Group network, was selected for the 2018 Inc. 5000 list of fastest growing companies in America. 2018 marks the second year in a row for Mars Services to make the Inc. 5000 list.
Josh Terry, President of The Garden Group, said:
"We are proud of our team at Mars Services that has worked hard to achieve this prestigious honor for two years in a row."
The Inc. 5000 is a list of the fastest-growing private companies in the nation. Started in 1982, this prestigious list of the nation's most successful private companies has become the hallmark of entrepreneurial success. The list represents a unique look at the most successful companies within the American economy's most dynamic segment— its independent small and midsized businesses. Companies such as Microsoft, Dell, Domino's Pizza, Pandora, Timberland, LinkedIn, Yelp, Zillow, and many other well-known names gained their first national exposure as honorees of the Inc. 5000.
About The Garden Group: The Garden Group is a family-owned diversified holding company based in Dallas, TX that focuses on small business investments.
About Mars Services: Mars Services is a market-leading service provider to customers in the multifamily, residential and commercial markets in the Dallas-Fort Worth Metroplex. Mars Services aims to be its customers' first call for carpet cleaning, countertop resurfacing, HVAC, plumbing, electrical, housekeeping, painting, carpet repair, 24-hour water restoration, tile and grout cleaning, odor control, upholstery cleaning, dryer vent and AC duct cleaning, trauma scene clean-up, tub resurfacing, maintenance, make-ready and pest control services.
About Josh Terry: Josh Terry is the President of The Garden Group, a family-owned diversified holding company based in Dallas, Texas. In 2011, Mr. Terry co-founded Acis Capital Management, LP, a fixed income asset manager, which he helped grow to $3.7 billion in assets under management prior to his departure in 2016. At Acis, Mr. Terry served as Portfolio Manager for all funds under management, including a two-time award-winning hedge fund. Mr. Terry was also previously Partner and Head of Trading and Structured Products at Highland Capital Management, where he served as a member of the Investment Committee and managed fixed income portfolios totaling over $10 billion in assets. He started his career at Stephens Inc. as an analyst in the investment banking division. Mr. Terry has over ten years of experience investing in a wide range of asset classes, including bank loans, high yield bonds, structured products, distressed investments, real estate, equities and derivatives. Mr. Terry currently serves on the Board of Governors of Uplift Education and on the Board of Directors of Friends of the Katy Trail. Mr. Terry received a BBA in Finance and Economics, summa cum laude, from Baylor University. He has earned the right to use the Chartered Financial Analyst designation.
About Inc. Media: Founded in 1979 and acquired in 2005 by Mansueto Ventures, Inc. is the only major brand dedicated exclusively to owners and managers of growing private companies, with the aim to deliver real solutions for today's innovative company builders. Winner of the National Magazine Award for General Excellence in both 2014 and 2012. Total monthly audience reach for the brand has grown significantly from 2,000,000 in 2010 to over 18,000,000 today. For more information, visit www.inc.com.
Mars Services Expands Management Team
Mars Services Announces Launch of Dedicated Service for Residential Investors
The Garden Group's Network Company Mars Services Makes Inc. 5000 List
The Garden Group Announces Launch of New Business for Mars Services
Mars Services
The Garden Group is a family-owned company and does not seek, solicit or accept outside investors.
© 2019THE GARDEN GROUP | ALL RIGHTS RESERVED


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Medicine Lodge is a city in and the county seat of Barber County, Kansas, United States.  As of the 2020 census, the population of the city was 1,781.

History

19th century
The particular medicine lodge, mystery house or sacred tabernacle from which the Medicine Lodge River received its name was in reality an arbor-like shelter of tree trunks and leafy branches which was erected by the Kiowa people for the celebration of their annual sun dance in the summer of 1866. It was in the valley of the Medicine Lodge River, several miles below the present town of Medicine Lodge, which is at the mouth of Elm Creek.  In their own language, the Kiowa people called this stream A-ya-dalda P'a, meaning "Timber-hill River." The Kiowa had considered the site sacred due to the high content of Epsom salts in the river.

In October 1867, the Medicine Lodge Treaty was a set of three treaties signed between the United States of America and the Kiowa, Comanche, Plains Apache, Southern Cheyenne, and Southern Arapaho. The site of the Peace Council camp was about three miles above that of the future town and on the same side of the river. A Peace Treaty Pageant, first presented in 1927 in an outdoor amphitheater on a quarter section of Kansas prairie, commemorates this significant event in Western history.

Settlers led by a man named John Hutchinson founded the town of Medicine Lodge north of the confluence of Elm Creek and the Medicine Lodge River in February 1873. The community grew rapidly with a hotel, stores, and a post office established within a year.

In 1874, in response to Native raids in the region, residents and the state militia constructed a stockade. A group of Osage killed three settlers within a few miles of the compound, but no direct attack on the fortifications occurred. Medicine Lodge was incorporated as a city in 1879.

Temperance activist Carrie Nation launched her crusade against the sale of alcohol while living in Medicine Lodge in 1900. Her home and a reproduction of the 1873 stockade are open to the public.

Geography
Medicine Lodge is located at  (37.284352, -98.580977) in south-central Kansas in the Red Hills region of the Great Plains. The city sits immediately north of the confluence of the Medicine Lodge River and Elm Creek. The city is on the northeast side of the river. Elm Creek flows south around the eastern and southern sides of the city. A tributary of Elm Creek, which flows south through Medicine Lodge, has been dammed immediately north of the city to form a reservoir, Barber County State Lake.

The city is located at the junction of U.S. Routes 160 and 281.

According to the United States Census Bureau, the city has a total area of , all of it land.

Climate
Medicine Lodge has a humid subtropical climate (Köppen Cfa) with hot, humid summers and cold, dry winters. The average temperature in Medicine Lodge is 57.3 °F (14 °C), and the average yearly precipitation is 26.2 inches (660 mm). On average, January is the coolest month, July is the warmest month, and June is the wettest month. The hottest temperature recorded in Medicine Lodge was 118 °F (48 °C) in 1936; the coldest temperature recorded was -22 °F (-30 °C) in 1905.

Demographics

2010 census
As of the census of 2010, there were 2,009 people, 876 households, and 530 families residing in the city. The population density was . There were 1,031 housing units at an average density of . The racial makeup of the city was 96.3% White, 0.7% African American, 0.3% Native American, 0.4% Asian, 1.4% from other races, and 0.9% from two or more races. Hispanic or Latino of any race were 2.4% of the population.

There were 876 households, of which 29.5% had children under the age of 18 living with them, 46.3% were married couples living together, 8.4% had a female householder with no husband present, 5.7% had a male householder with no wife present, and 39.5% were non-families. 35.6% of all households were made up of individuals, and 14.9% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.93.

The median age in the city was 40 years. 25.6% of residents were under the age of 18; 7% were between the ages of 18 and 24; 22.4% were from 25 to 44; 27.3% were from 45 to 64; and 17.9% were 65 years of age or older. The gender makeup of the city was 50.7% male and 49.3% female.

2000 census
As of the census of 2000, there were 2,193 people, 922 households, and 609 families residing in the city. The population density was . There were 1,085 housing units at an average density of . The racial makeup of the city was 98.08% White, 0.36% African American, 0.09% Native American, 0.09% Asian, 0.36% from other races, and 1.00% from two or more races. Hispanic or Latino of any race were 1.69% of the population.

There were 922 households, out of which 30.9% had children under the age of 18 living with them, 53.8% were married couples living together, 9.1% had a female householder with no husband present, and 33.9% were non-families. 30.7% of all households were made up of individuals, and 16.7% had someone living alone who was 65 years of age or older. The average household size was 2.34 and the average family size was 2.90.

In the city, the population was spread out, with 25.1% under the age of 18, 7.2% from 18 to 24, 24.7% from 25 to 44, 22.2% from 45 to 64, and 20.9% who were 65 years of age or older. The median age was 41 years. For every 100 females, there were 93.6 males. For every 100 females age 18 and over, there were 88.6 males.

The median income for a household in the city was $35,262, and the median income for a family was $41,053. Males had a median income of $30,319 versus $18,750 for females. The per capita income for the city was $16,231. About 7.4% of families and 9.4% of the population were below the poverty line, including 8.7% of those under age 18 and 4.6% of those age 65 or over.

Economy
 National Gypsum

Government
Medicine Lodge has a mayor-council form of government. The city council consists of five members, who are elected on a rotating schedule. The day-to-day operations of city government are managed by a City Administrator who operates under the supervision of the elected officials. The current City Administrator is Brian Daily who started in November 2022.

Education
Barber County North USD 254 provides public primary and secondary education with two schools in Medicine Lodge: Medicine Lodge Grade School (Grades Pre-K-6) and Medicine Lodge Junior-Senior High School (7-12).

Transportation
U.S. Route 281, which runs north-south, and U.S. Route 160, which runs east-west, intersect in the southwest corner of the city.

Medicine Lodge Airport, which hosts general aviation, is located approximately  southeast of the city.

Medicine Lodge is the western terminus of the Medicine Lodge line of the V&S Railway. The rail line runs northwest-southeast through the southwestern part of the city.

Media

Print
Newspapers
The Gyp Hill Premiere, weekly

Radio
The following radio stations are licensed to Medicine Lodge:

FM

Culture
Triennially, Medicine Lodge holds a pageant to commemorate the 1867 Medicine Lodge Treaty, signed near the city's present-day location. The city first held the pageant in 1927 and has held it every three years since 1961.

Area attractions
 Carrie Nation House
 Stockade House.
 Peace Treaty Statue, located on North Main Street.
 Wisner Fountain, originally used to water horses on North Main Street.
 Kansas Historical Marker - Medicine Lodge Peace Treaties, located 1 mile east of Medicine Lodge.

Notable people
 Carleton Beals (1893–1979), journalist, author, historian, political activist
 B. H. Born (1932–2013), All American basketball player
 Dorothy DeLay (1917–2002), violin instructor at Juilliard, Sarah Lawrence College, University of Cincinnati.
 Edward Hunkeler (1894–1970), Roman Catholic Archbishop
 Chester Long (1860–1934), U.S. Representative and U.S. Senator from Kansas
 Carrie Nation (1846–1911), radical member of the temperance movement which opposed alcohol before the advent of prohibition of alcohol
 Jerry Simpson (1842–1905), U.S. Representative from Kansas
 Jasper Tincher (1878–1951), U.S. Representative from Kansas

References

Further reading

 Yost, Nellie Snyder. Medicine Lodge: The Story of a Kansas Frontier Town. Sage Books: Chicago, 1970.

External links

 City of Medicine Lodge
 Medicine Lodge - Directory of Public Officials
 USD 254, local school district
 Lincoln Library
  Medicine Lodge Peace Treaty Pageant
 Medicine Lodge, Kansas Barber County, Kansas: History and Genealogy
 Digital Medicine Lodge History
 Medicine Lodge city map, KDOT

Cities in Kansas
County seats in Kansas
Cities in Barber County, Kansas
1873 establishments in Kansas
Populated places established in 1873

redpajama_set_name: RedPajamaWikipedia


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Јован Лакатош (Апатин, 15. јул 1944) је српски орнитолог и фотограф природе.

Биографија
Истраживањем фауне птица бави се од 1968. године. Већ 1969. године постаје сарадник Југословенске академије знаности и умјетности у Загребу. У заводу за орнитологију ЈАЗУ сарађује до краја 1989. године. Те године постаје сарадник Комисије за проучавање и заштиту птица Друштва еколога Војводине.

Са познатим режисером Петром Лаловићем, снима серију документарних и играних филмова о природи.

Књигу Птице Апатина објављује 1979, а на сличним пројектима је радио као коаутор или фотограф и са другим ауторима. Из области орнитологије је објавио 64 наслова у стручним и популарним часописима.

Сарађује са телевизијским кућама у земљи и иностранству. Награђен је на "Олимпусовом" конкурсу на којем је за награду конкурисало 38.000 радова из читавог света.

Путовања и експедиције
Почев од 1987. године интензивно путује по свету, и као орнитолог и фотограф учествује на међународном пројекту о белорепанима света. Као орнитолог и фотограф провео је многе дане на експедицијама по Блиском и Далеком истоку, Централном Сибиру, архипелагу Шантари, на Камчатки, у пределима Хималаја, Националним парковима Кеније, Танзаније, Занзибара, Националном парку "Еверглејдс" на Флориди, и у многим пределима широм Европе.

С планинарима Србије освајао је многе врхове, међу којима су Килиманџаро (6895 м), Имја Тсе (Хималаји, 6160 м), Кала Патар (Хималаји, 5565 м), Чукунг Ри (Хималаји, 5065 м) и многи други у Европи. Последњих година приређује путовања широм наше земље, у Румунији, Мађарској и Немачкој.

Филмографија (избор)
Са Петром Лаловићем
 Последња оаза
 Свет који нестаје
 Брига за потомство
 Животиње и љубав

Референце

Спољашње везе

 Фото галерија, Јанош Лакатош, Градска библиотека "Карло Бијелицки", Сомбор
 "Апатинац обишао пола света", Слободан Мирић, Вечерње новости, Београд 18. фебруар 2012.
 "Од Таре до Казахстана: Јован Лакатош из Апатина светски признат сниматељ флоре и фауне" Ј. Бањац, Вести, 05. 04. 2011.

Рођени 1944.
Српски фотографи
Орнитолози
Апатинци