Blog / What Is My SpamAssassin Score and What Does it Mean?
SpamAssassin is an open-source, content-matching spam filter from the Apache Software Foundation. Many different mail servers enable SpamAssassin to help filter spam messages for its users.
SpamAssassin uses several different filtering techniques to catch spam, including DNS blocklists, text analysis, Bayesian filtering, and collaborative filtering databases. It uses a scoring system and plug-ins to analyze your email header and the email body copy. The filter then produces a header that outlines your SpamAssassin score and how your email performed against its various checks.
Email on Acid's Spam Testing feature includes a SpamAssassin analysis, which will produce your SpamAssassin score with a pass/fail, as well as some feedback on how your email performed. Try it free today.
Now, we'll take a look at each header section and what it means.
The X-Spam-Checker-Version tells us the version of SpamAssassin that evaluated your email. The most current stable release is 3.4.2, with the latest release on September 16, 2018.
Messages with a score of less than one will show no stars in the header.
What Is Your Spam Status?
The X-Spam-Status header starts by telling you flat out if the message is spam or not, then it gives you the exact spam score (in this case, -0.4), as well as the default score threshold for the recipient ("required=5.0"). If an email score lands higher than the threshold, the recipient will mark it as spam.
The default SpamAssassin setting for the threshold is 5.0, but some SpamAssassin installations can use a more or less aggressive threshold. We use a threshold of 5.0 in our Spam Testing service.
In the example above, the email's spam score was -0.4, and the threshold was set at the default score of 5.0, which means the email is not spam.
Now, let's get into the different tests SpamAssassin will run.
As you can see, the name of each test is in all caps, followed by a short description of what that test looks for. Some of the checks include looking for the email's Domain Keys Identified Mail (DKIM), analyzing URLs that are on blacklists, body copy and more.
SpamAssassin can perform hundreds of different tests, so how can you know what you should avoid? Check out ten crucial tips below.
Be honest. Make sure your "from" name is accurate, the "to" name is the recipient, and you are sending the email using your domain name. Don't be sneaky.
Avoid all caps.Using all caps in your subject is like shouting through email. Spam filters don't like it (your recipients probably don't like it, either). Don't use all caps or use them sparingly.
Use conversational language.Avoid using too many spaces, extra capitalizations, or using odd characters or numbers in words ("3mail" or "Em@il").
Don't use sketchy phrases. Phrases that you see commonly in spam messages get higher spam scores with filters like SpamAssassin. Even if you're talking about getting some extra inches of reach with your product, the GrabExtender, you're going to get flagged. Find another way to say things like this and you should be fine.
Use a verifiable domain. Make sure someone can identify your domain with a verifiable IP address. Someone who checks the domain for the "from" and "reply-to" address should be able to see that the addresses are valid.
Don't include disclaimers about spam. Avoid saying "this email isn't spam" or spell out that your email is in compliance with certain laws. If your email message isn't spam, you shouldn't need to say this.
Include text. Spammers often use image-only emails to get by spam filters. If you have lots of images, make sure to include a plain text version of your email.
Avoid over-using the word "free". This word is dangerous to use in email subject lines because of its popularity with spammers. You can try using a synonym like "complimentary" or something similar.
Be careful about other domains in your email. If you link to another site or allow someone to advertise in your email, check that their domain is not on a blacklist.
Test your email! Running a test with a spam checker before sending your email can help save you from the spam traps. Email on Acid's Spam Testing tool checks your message against 23 of the most common spam filters, including SpamAssassin.
If you'd like to learn more about what triggers SpamAssassin's ire, check out their extensive list.
This post was updated on January 16, 2019. It was originally published in December 2012.
Make sure your email looks flawless before you send it out to your subscribers. Remember: A broken email is an unengaged email. With Email on Acid, you can preview your email in more than 70 email clients and devices before you hit "send." Sign up for our free trial and start testing today.


Only in Saints Row 3 would a man consider the name 'Killbane' not ostentatious enough and instead dub himself 'The Walking Apocalypse'. Of course when this man is a Mexican wrestler by day and a violent gang leader by night it all begins to make sense. The trailer above outlines your missions against Killbane's gang, topping it off with your character facing him in the ring to fight him for his luchador honour. There's also a lot of explosions along the way, because Saints Row is like that.
We also get a brief look at Angel de la Muerte, a rival Luchador who sides with your gang and is voiced by Hulk Hogan. You'll get to join him in the ring on the 15th of November in North America and the 18th in Europe.


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text:
THEODORE W. LENZEN- ARCHITECT, San Joe, California, 1892
From the Commemorative Edition January 1, 1892, San Jose Daily Mercury
MEN WE ALL KNOW
THEODORE W. LENZEN- ARCHITECT, SAn Jose, California- 1892
Biographical Sketches of Well-Known San Joseans
THE STORY OF THEIR SUCCESS.
Theodore W. Lenzen
Of the well-known firm or architects of Jacob Lenzen & Son, was born in San Jose November 17, 1864. His father, the senior member of the firm, came from Chicago, establishing an office which has become one of the best known in the county.
Theodore W. was educated in the High School at the University of the Pacific, and commenced the study of his profession in San Francisco, completing the course in Europe. Mr. Lenzen did not confine his investigations in the old country to any one place, but visited various great cities making studies and sketches of some of the most noted edifices, many of them the work of masters of by-gone centuries. This work has been invaluable to him, many of his recent conceptions showing the
results of his study abroad.
The Santa Clara valley is noted for its many beautiful residences and public buildings, of which the firm of Jacob Lenzen & Son has planned and superintended the construction of no small number. The beautiful Hotel Vendome, the Y.M.C.A. building opened in November, the Hall of Records, one of the finest public edifices in the State, St. Josephs College, Postoffice
building, the Rucker, Straus, Doerr, Archer, Letitia, San Carlos, Sweigert and I.O.O.F. building, the vast insane asylum at Agnews, are among the many notable specimens of architecture which have established the reputation of
this firm.
T.W. Lenzen was married in February, 1889 to Miss Kate A. Berlingen of Contra Costa, and has one son, Victor Lenzen. Mr. Lenzen is extremely popular with a large circle of friends and a life-long residence in San Jose has made him familiar with the requirements for homes, business or public buildings in this section of the county.
transcribed by jchavnar
The Scheller House-at San Jose State University, designed by Lenzen- now preserved
RETURN TO BIOGRAPHIES OF SANTA CLARA COUNTY PIONEERS

redpajama_set_name: RedPajamaCommonCrawl


text:
Zanko Iwanow Lawrenow (; * 24. November 1896 in Plowdiw; † 19. Oktober 1978 in Sofia) war ein bulgarischer Maler.

Leben
Das Malen erlernte Lawrenow als Autodidakt. In seinen Werken setzte er die Malereitradition der Bulgarischen Wiedergeburt fort. Seine Motive zeigen häufig historische Bauten und Städte Bulgariens, wie in seinem Klosterzyklus, oder befassen sich mit sozialen bzw. historischen Themen. Darüber hinaus setzte er sich mit der sozialistischen Gesellschaft Bulgariens auseinander. Auch Gebirgsansichten wurden von ihm geschaffen.

Lawrenow war außerdem als Kunstwissenschaftler und Kunstkritiker tätig.

Er wurde als Held der Sozialistischen Arbeit, mit dem Orden Georgi Dimitrow und dem Dimitroffpreis ausgezeichnet. In Plowdiw wurde eine Straße nach ihm benannt. Entsprechendes gilt seit 2008 für den Lavrenov Point, eine Landspitze von Robert Island in der Antarktis.

Werke
Klöster der Halbinsel Athos, 1937, 1940, 1942, 1956
Plowdiw, 1938, 1946
Rilakloster, 1942, 1950
Der rote Reiter, 1944
Weliko Tarnowo, 1946
Wesselin Staikov, Monographie, 1956
Verklärung-Christi-Kloster, 1957

Literatur
 Lawrenow, Zanko Iwanow. In: Taschenlexikon Bulgarien, Bibliographisches Institut Leipzig 1983, Seite 108.

Weblinks

Maler (Bulgarien)
Held der Sozialistischen Arbeit (Bulgarien)
Bulgare
Geboren 1896
Gestorben 1978
Mann

redpajama_set_name: RedPajamaWikipedia


text:
Home » VenVest Opens Sales Brokerage
VenVest Opens Sales Brokerage
John R. Hall
ST. LOUIS, MO — VenVest, majority interest owner of some well-known hvacr businesses, has just added another business — and another business model — to its stable of growing contractor-member groups.
Jim Abrams and John Young, familiar names in the hvacr industry as co-founders of Contractor's Success Group and Service Experts, Inc., have added another page to their résumés with the founding of Wealth Now!, a sales brokerage and its "$2 million business model."
VenVest is the parent company of AirTime 500, Plumbers' Success International, and Clean Indoor Air. Among these groups are contractors who are looking to sell their businesses. That was a good motivation for the founding of Wealth Now.
Wealth Now
"We have a relationship with 750 contractors," said Abrams. "There is a segment of them who want to sell their businesses now instead of later."
Abrams believes that by readying the businesses for sale and "packaging" them together with other similar businesses in different locations, Wealth Now can offer an attractive package to consolidators looking to acquire and grow into new or existing markets.
Lon Cassel, managing consultant for Wealth Now, said, "It became clear that some contractors were joining PSI and AirTime with the overriding goal of selling their businesses as soon as possible at prices reflecting the true value they had built up — not just the asset value that many contracting businesses sell for.
"We knew that we could find buyers for some of the businesses right away, and that's why we created Wealth Now."
Cassel added that the brokerage services are available to VenVest companies as long as the sellers have achieved double-digit profitability and are engaged primarily in residential service. "Some buyers are looking for companies that they can incorporate into existing operations; others are looking for a company that can serve as the platform for future acquisitions," he said.
$2 Million Business Model
Abrams said the $2 million model, available to AirTime 500 contractors, has at least two distinct benefits to hvacr business and their owners.
"We need to make our businesses more attractive to young people," he said. "The creation of manageable $2 million businesses creates career opportunities.
"A bright young person would be attracted to a business where they could move into a general manager's position without having to take the owner's last name. In this model, a general manager can earn $100,000 a year."
The second benefit is making a business more manageable. Abrams cited the example of a contractor who is doing $8 million/year and has too much square footage to support the operation.
"The guy could split the business into four $2 million units," he added. "And, if the owner has three sons, there wouldn't be a problem of who to give the business to. They could all run their own $2 million business."
Splitting up a business into smaller units would be a matter of dividing up the markets served by the original company. If one of the businesses then grew beyond $2 million, they'd be able to start up another new unit.
"Now the exceptional guys with the bigger businesses will have an easier way to manage," Abrams said. "Besides, the guy with the $2 million business is the exception."
For more information on VenVest, call 800-524-1954; for Wealth Now, call 866-932-5846, ext. 313.
Recent Articles by John Hall
Most Popular Mobile Device? Too Obvious
Mobile Office Changes How HVAC Business Is Done
Having No Inventory — And Loving It
Mid-Year 2011 Business Report Card: HVAC's Passing Grades
Phone Apps, Field Techs: A Good Combination?
John Hall is the Business Editor. E-mail him at johnhall@achrnews.com.


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text:
\section{Introduction}

There is overwhelming observational evidence that the largest fractions of the matter-energy content of our universe are not properly understood in terms of their physical properties and are thus commonly termed dark. The observational evidence is entirely based on phenomena on large scales measured via gravitational effects. However, the strongest attempts to address such phenomena as dark matter (DM) are focused on particle physics models. This has to do, on the one hand, with the fact that our understanding of gravity, which roots in the theory of Einstein's General Relativity (GR), has withstood so many experimental tests across a vast range of length scales. On the other hand, while it is straightforward to modify gravity at short scales, it turns out to be conceptually very challenging  to modify GR at large scales without running into inconsistencies, such as ghost degrees of freedom, or contradictions with experiments on shorter scales. However, it would be desirable to test if gravity can indeed be modified at large scales, and what this would imply for such observables as the mass density of DM. This investigation is crucial, since our attempts to test the above mentioned particle physics models are guided strongly by assumptions about the local DM density, which on the other hand is calculated under the assumption of pure Einstein GR.

A sufficiently wide framework of consistent extensions of GR, has in fact recently been discovered, based on multi-metric gravity~\cite{Hinterbichler:2012cn}. For the sake of concreteness, we will focus on the bimetric case in this work, where two tensor fields are present. The theory is constructed such that one tensor mode remains massless while the other obtains a non-vanishing mass, comprising in total seven degrees of freedom. A priori, such a theory contains too many degrees of freedom and, related to that, massive gravity is often plagued by the Boulware-Deser ghost~\cite{Boulware:1973my}. This was a long standing issue, beginning with the proposal of a linear spin-2 theory in the first half of the 20\textsuperscript{th} century by Fierz and Pauli~\cite{Fierz:1939ix, Fierz:1939zz}. Only recently it has been proven~\cite{deRham:2010ik,deRham:2010kj,deRham:2011rn,Hassan:2011hr,Hassan:2011vm,Hassan:2011tf,Comelli:2012vz,Deffayet:2012nr,Deffayet:2012zc} that the construction of massive gravity using a second reference metric removes these pathological degrees of freedom and is free of the Boulware-Deser ghost. This framework, due to de Rham, Gabadadze and Tolley (dRGT), was later extended to a bimetric theory in Refs.~\cite{Hassan:2011zd,Hassan:2011ea}, where both tensors are dynamical. An important feature of theories of massive gravity is that, at small distances, GR is restored by non-linear effects resolving the long-standing van Dam-Veltman-Zakharov discontinuity found when the graviton mass goes to zero.~\cite{vanDam:1970vg,Zakharov:1970cc} This phenomenon was conjectured by Vainshtein already in the 1970s~\cite{Vainshtein:1972sx} and has been demonstrated explicitly for bimetric and dRGT massive gravity~\cite{Babichev:2009us,Babichev:2009ee,Babichev:2009jt,Babichev:2010jd,Babichev:2013pfa,Gruzinov:2011mm,Volkov:2012wp,Platscher:2016adw}.

Let us first give a brief overview of existing studies considering similar effective, non-relativistic potentials as ours. Following a pioneering work~\cite{Sanders:1984aa}, most follow-up studies of modified gravity models that induce mixed Yukawa-Newton potentials, tried to argue that DM is obsolete. This was done either by means of a proof of principle studying individual examples~\cite{Drummond:2001rj,Stabile:2013jon}, or larger data sets~\cite{Moffat:2013sja,Rahvar:2014yta}, some even including galaxy clusetrs as we do~\cite{Capozziello:2008ny, Mota:2011iw}. While these studies argued against the existence of DM, others were less biased allowing a for a DM component~\cite{Piazza:2003ri,Stabile:2011zp}. And yet others quantified the observational bias on galaxy haloes that would be induced by assuming instead of the Yukawa force, Newtonian gravity~\cite{Cardone:2011ze}. A more recent idea, including for the first time the phenomenological impact of the Vainshtein screening, was made in Ref.~\cite{Enander:2015kda}. There, the authors have derived constraints by demanding that the galactic scale is contained entirely in the Vainshtein regime, such that the GR predictions apply. Also, an attempt was made recently in studying the long-range effects of dRGT massive gravity on galaxy dynamics~\cite{Panpanich:2018cxo}; however, only in a specific regime, and once again neglecting the Vainshtein screening. Similarly, in Ref.~\cite{deAlmeida:2018kwq} the authors explored generic Yukawa-type modifications of the gravitational potential on galaxy rotation curves, also disregarding the Vainshtein effect. See also \cite{2018arXiv180701725H} for a recent review.

Our work, in contrast, focusses on bimetric gravity while simultaneously trying to be as unprejudiced as possible. To be more specific, we put the model to test at galactic and extra-galactic scales, attempting to account for the Vainshtein screening mechanism. We quantify how large a deviation from GR one actually finds, how much of it is tolerable and maybe even favourable in the sense of improving the fits to the data. In addition, we study not one scale of physical systems, namely galaxies, but also take into account galaxy clusters, and attempt to implement the Vainshtein mechanism into our phenomenological survey. This work is only meant as a pilot study of some individual measurements, and is by no means a full-fledged survey of galactic and extra-galactic effects. However, we believe that the results are encouraging for further, more detailed studies.

The remainder of this manuscript is structured as follows. In Sec.~\ref{sec:framework} we introduce the framework and derive the induced non-relativistic gravitational potential and the lensing potential in bigravity. In Sec.~\ref{sec:clusters} we use these results to obtain constraints on the massive spin-2 field from cluster X-ray and weak lensing observations. In Sec.~\ref{sec:rotCurves} we study galaxy rotation curves and the impact on the expected DM abundance. In Sec.~\ref{sec:scaling} a general scaling argument for systems with a Vainshtein mechanism is discussed. Finally, we summarise and discuss our results in Sec.~\ref{sec:discussion}.

\section{The Bimetric Framework}
\label{sec:framework}
We study a variant of the dRGT theory of massive gravity, which gives a simple explanation for late-time acceleration in terms of the graviton mass~\cite{Volkov:2011an,vonStrauss:2011mq,Comelli:2011zm,Akrami:2012vf,Konnig:2013gxa,Comelli:2014bqa,DeFelice:2014nja,Nersisyan:2015oha,Akrami:2015qga}. However, it has been found that phenomenologically viable, cosmological solutions are unstable and therefore some modifications are required~\cite{deRham:2010tw,DAmico:2011eto,Gumrukcuoglu:2011ew,Gumrukcuoglu:2011zh,Vakili:2012tm,DeFelice:2012mx,Fasiello:2012rw,DeFelice:2013awa}. Arguably, the simplest modification is to render the background metric dynamical itself and thereby obtain what is called bimetric gravity, or simply bigravity~\cite{Hassan:2011zd}. In fact, one could argue that bigravity is the more fundamental framework, as it arises naturally from extra-dimensional models, e.g.~via dimensional deconstruction~\cite{ArkaniHamed:2001nc,deRham:2013awa}. Following such a procedure, one is led to matter coupling diagonally to the two tensors, i.e.~visible and hidden matter sectors each have their own metric tensor. While more exotic settings display some interesting cosmological effects~\cite{Gumrukcuoglu:2014xba,Comelli:2015pua,Heisenberg:2016dkj,Gao:2016dwl,Bouhmadi-Lopez:2016fgd}, we will disregard such a hidden matter sector, and focus on the visible matter coupling only to one tensor --~including however a DM component~-- as other couplings typically lead to inconsistencies~\cite{deRham:2014naa,Hassan:2014gta,Schmidt-May:2014xla,deRham:2014fha,Yamashita:2014fga}.

The action for the two tensor fields $g$ and $f$ is given by
\begin{equation}\label{eq:action}
  \begin{gathered}
    S_\mathrm{bi} =   \int \mathrm{d}^4x \left\lbrace\frac{M_g^2}{2} \sqrt{-\det g}\, R_g + \frac{M_f^2}{2}  \sqrt{-\det f}\, R_f +
     m^2 M_\text{eff}^2 \sqrt{-\det g}\, \sum_{n=0}^4 \beta_n e_n(\mathbb{X}) \right. + \\
   	 \hspace{10.7cm}\left. + \sqrt{-\det g}\, \mathcal{L}_\textrm{matter} \right\rbrace.
  \end{gathered}
\end{equation}
Here, $M_g$ is the Planck scale for the physical $g$ metric, $M_f$ the Planck scale for the $f$ metric, $M_\text{eff}^2 \equiv \left( \frac{1}{M_g^2}+  \frac{1}{M_f^2}\right)^{-1}$,  and $\mathbb{X}$ is defined via the relation $\mathbb{X}^\mu_\alpha \mathbb{X}^\alpha_\nu = g^{\mu\alpha}f_{\alpha\nu}$. It is a rank-2 tensor field and is the building block of the interaction between the two metric fields. Finally, $e_n(\mathbb{X})$ denotes the $n$\textsuperscript{th} so-called elementary symmetric polynomial of the eigenvalues of $\mathbb{X}$, written most compactly as
\begin{equation}
  \begin{gathered}
  	e_0 = \mathbb{1},\quad e_1 = \tr{\mathbb{X}},\quad e_2 = \frac{1}{2} \left[ \tr{\mathbb{X}}^2 - \tr{\mathbb{X}^2}\right],\\
    e_3 = \frac{1}{6} \left[ \tr{\mathbb{X}}^3 - 3\, \tr{\mathbb{X}}\tr{\mathbb{X}^2}+2\, \tr{\mathbb{X}^3}\right],\quad
    e_4 = \mathrm{det}(\mathbb{X}).
  \end{gathered}
\end{equation}
The variation of this action yields two sets of Einstein equations,
\begin{subequations}\label{eq:Einstein}
  \begin{align}
   &  G(g)_{\mu\nu} + m^2 \sin^2(\theta)\sum_{n=0}^3 \beta_n V^{(n)}(g)_{\mu\nu} = 8 \pi G_N T_{\mu\nu} \\%+ \Lambda g_{\mu\nu},\\
 &    G(f)_{\mu\nu} + m^2  \cos^2(\theta)  \sum_{n=1}^4 \sqrt{\frac{|\det g|}{|\det f|}} \beta_n V^{(n)}(f)_{\mu\nu} = 0,
  \end{align}
\end{subequations}
where $  \sin^2(\theta) \equiv \frac{M_\text{eff}^2}{M_g^2} $, $  \cos^2(\theta) \equiv \frac{M_\text{eff}^2}{M_f^2} $ , and $8 \pi G_N = M_g^{-2}$ is the relation between Newton's constant and the (reduced) Planck mass for $g$. Moreover, the interaction or mass terms $V^{(n)}(g)$ follow from the variation of the polynomials $e_n$:
\begin{subequations}
  \begin{align}
  	{V^{(0)}(g)^\mu}_\nu =& {\delta^\mu}_\nu\\
    {V^{(1)}(g)^\mu}_\nu =& \tr{\mathbb{X}}{\delta^\mu}_\nu - {\mathbb{X}^\mu}_\nu ,\\
    {V^{(2)}(g)^\mu}_\nu =& {\left(\mathbb{X}^2\right)^\mu}_\nu - \tr{\mathbb{X}} {\mathbb{X}^\mu}_\nu + \frac{{\delta^\mu}_\nu}{2}\left[\tr{\mathbb{X}}^2 - \tr{\mathbb{X}^2}\right],\\
    {V^{(3)}(g)^\mu}_\nu =& -{\left(\mathbb{X}^3\right)^\mu}_\nu + \tr{\mathbb{X}} {\left(\mathbb{X}^2\right)^\mu}_\nu
			  - \frac{1}{2} \left[\tr{\mathbb{X}}^2 - \tr{\mathbb{X}^2}\right]{\mathbb{X}^\mu}_\nu +\nonumber \\
			  & + \frac{{\delta^\mu}_\nu}{6} \left[ \tr{\mathbb{X}}^3 - 3\, \tr{\mathbb{X}}\tr{\mathbb{X}^2}+2\, \tr{\mathbb{X}^3}\right].
  \end{align}
\end{subequations}
The corresponding expressions $V^{(1,2,3)}(f)$ are obtained from the $V^{(2,3,4)}(g)$ by dropping the parts proportional to ${\delta^\mu}_\nu$ and multiplying by $(-1)$, while for $n=4$, one obtains ${V^{(4)}(f) ^\mu}_\nu= {\delta^\mu}_\nu$.

Finally, energy-momentum conservation can be enforced by demanding the vanishing of the $g$-covariant derivative of the $g$-interaction term,
\begin{equation} \label{eq:Bianchi}
  \nabla(g)_\mu {T^\mu}_\nu\stackrel{!}{=} 0 \ \Rightarrow \ \nabla(g)_\mu {V^{(n)}(g)^\mu}_\nu = 0.
\end{equation}
Equivalently, we find for the $f$-metric $\nabla(f)_\mu \left(\sqrt{\frac{|\det g|}{|\det f|}} {V^{(n)}(f)^\mu}_\nu\right) = 0$. These additional equations are known as Bianchi constraints, which are in general \emph{not} independent.
We now show the phenomenological consequences of the bigravity extension for the non-relativistic gravitational potential and gravitational lensing effects.

\subsection{Gravitational Potential in Bigravity}
The effective Newtonian potential felt by a non-relativistic observer in a static and spherically symmetric potential of a point source of mass $M$ has been calculated in~\citep{Babichev:2015xha, Platscher:2016adw} and reads
\begin{equation}
\label{Eq:FullPotential}
\phi(r) =
\begin{cases}
 - \frac{M G_N}{r}   & r \ll r_V,

 \\
- \frac{M G_N}{r} \left[  \alpha(\theta) + \beta(\theta) e^{- m_gR}\right]  & r \gg r_V,
\end{cases}
\end{equation}
with $\alpha(\theta) := \cos^2(\theta)\left(1+\frac{2}{3}\sin^2(\theta)\right)$, $\beta(\theta) :=  \frac{2}{3} \sin^2(\theta) \left(1 + 2 \sin^2(\theta)\right)$, and $m_g^2  = m^2 (\beta_1 + 2 \beta_2 + \beta_3)$. In the above expression, $r_V$ is the scale below which non-linearities become important and conspire to reproduce the GR result, as conjectured by Vainshtein in 1972~\cite{Vainshtein:1972sx}. Below, we will assume that, as we lower $r$ below $r_V$, the two regimes are smoothly interpolated. As a working hypothesis, we propose an effective mixing angle to account for this phenomenon, which is defined as follows:
\begin{equation}\label{eq:Vainshtein}
	\theta_\text{eff} \equiv \frac{\theta}{2} \left[1 + \tanh \left(\frac{r - r_V}{\Delta r}\right) \right],
\end{equation}
where $\Delta r $ is treated as a free parameter in our analysis. This parameter encodes the effect of the extended matter distribution on the Vainshtein mechanism, which are difficult to calculate from first principles. Thereby, we find that for $r \gg r_V$, $\theta_\text{eff} = \theta$ and for $r \ll r_V$, we have that $\theta_\text{eff} = 0$, i.e.~GR is recovered. Finally, we use the following expression for the Vainshtein radius, motivated by the study of spherically symmetric solutions, cf.~Refs.~\cite{Babichev:2009us,Babichev:2009ee,Babichev:2009jt,Babichev:2010jd,Babichev:2015xha,Platscher:2016adw}:
\begin{equation}\label{eq:rVdef}
	r_V = \sqrt[3]{\frac{r_S}{m_g^2}}\,,
\end{equation}
with the Schwarzschild radius $r_S = 2G_N M$. For scales $r \ll r_V$ one finds that non-linearities become important and conspire to restore GR.\footnote{An interesting observation is that this exact screening could be broken and thereby be testable~\cite{Salzano:2017qac}.} The regime $r \gg r_V$ turns out to be well approximated by a linearised treatment.  We will discuss the finite matter extension effects in Sec.~\ref{sec:rotCurves}.

\subsection{Bending of light in Bigravity \label{sec:lensing}}

As discussed above the metric and thus the lensing potential in bigravity are exactly the same as in GR inside the Vainshtein sphere. However, outside we find the deviation by considering the metric around a spherical body in a linear approximation~\cite{Babichev:2015xha}, which can be written as
\begin{equation}
\begin{gathered}
ds^2 = -dt^2 e^\nu + e^\lambda d r^2 + r^2 \mathrm{d}\Omega^2\,, \quad  \text{with}\\
 \nu(r) = -\frac{r_S}{r} \left( \alpha(\theta) + \beta(\theta) e^{-m_g r}  \right)
\quad\text{and}\quad  \lambda(r) = \frac{r_S}{r} \left( \alpha(\theta) + \frac{\beta(\theta) (1+ m_g r)}{2} e^{-m_g r}  \right) \,.
\end{gathered}
\end{equation}
The null-geodesic equation for an impact parameter $b$ is readily derived from this and reads
\begin{equation}\label{eq:light_geodesic0}
	\left(\frac{1}{r^2} \frac{\mathrm{d}r}{\mathrm{d}\phi}\right)^2 = \frac{ e^{-(\lambda+\nu)}}{b^2} -  \frac{e^{-\lambda}}{r^2} \,.
\end{equation}
To solve this equation, we introduce the variable $u \equiv \frac{R}{r}$, where $R$ is the radius of closest approach, obtained by setting  $\left.\frac{\mathrm{d}r}{\mathrm{d}\phi}\right|_{r=R} = 0$, and which is related to $b$ via
\begin{equation}
	\frac{1}{b^2} = \frac{e^{\nu}}{R^2}\, .
\end{equation}
Finally, expanding the exponentials in $\frac{r_S}{R}$, we arrive at the geodesic equation,
\begin{equation}\label{eq:light_geodesic}
	\left(\frac{\mathrm{d}u}{\mathrm{d} \phi}\right)^2 = \big[1 - \lambda (r=R/u) \big] (1 - u^2) + \nu(R) - \nu(r=R/u)\,.
\end{equation}
Furthermore, the final expression for the light deflection angle is given by
\begin{equation} \label{eq:deltaPhi_1}
	\Delta \phi = 2\, \int \mathrm{d} \phi = 2 \, \int_0^1 \mathrm{d} u\, \frac{\mathrm{d} \phi}{\mathrm{d} u}\,,
\end{equation}
which can be solved in principle via Eq.~\eqref{eq:light_geodesic}. In GR one makes use of the fact that $e^\nu \, e^\lambda =1$, which is no longer true in bigravity; in fact, $e^\nu \, e^\lambda \sim e^{-m_g r}$, i.e.~it is the piece that carries the information about the massive spin-2 mode. In order to arrive at a final result, we plug Eq.~\eqref{eq:light_geodesic0} into~\eqref{eq:deltaPhi_1} before expanding in powers of $\frac{r_S}{R}$.

\begin{figure}
	\centering
	\includegraphics[width=\textwidth]{lensing_test}
	\caption{\label{fig:lensing_test}The ratio of the deflection angle of light in bigravity and GR with the two different approximate solutions. All expressions agree when $m_g R \gg1$, however only the careful approximation~\eqref{eq:deltaPhi_2} gives a good estimate of $\Delta \phi$ when $m_gR < 1$.}
\end{figure}

Unfortunately, we cannot give a closed form expression for $\Delta \phi$ obtained from the integration of Eq.~\eqref{eq:deltaPhi_1} due to the $u$-dependent  exponentials in the integrand. However, one can find a satisfactory approximation by observing that the exponentials of the form $e^{-m_g\, R /u}$ are only relevant in the case where $m_gR <1$. In this case, they are close to unity when the integration variable $u\to 1$, and approach zero as $u < m_gR$. We capture this behaviour by replacing these exponentials as $e^{-m_g\, R /u} \mapsto e^{-m_g\, R}$, and shifting the lower integration boundary from $u=0$ to $u=m_gR$. The resulting expression reads
\begin{equation} \label{eq:deltaPhi_2}
	\Delta \phi \simeq 2 \frac{r_S}{R} \left[ \alpha(\theta) + \frac{1}{4} \beta(\theta) e^{-m_gR} \left( \left(3 + m_gR\right) \sqrt{\frac{1+ m_gR}{1- m_gR}} + m_gR\, \arccos \left(m_gR\right)\right)   \right]\,.
\end{equation}
Note that this expression develops an imaginary part when $m_g R >1$; however, one can safely disregard the part proportional to $\beta(\theta)$ in this regime, e.g.~numerically via a Heaviside step-function. Another approximation one can make is $m_g R \gg 1$, keeping only the exponential in Eq.~\eqref{eq:deltaPhi_2}, which yields
\begin{equation}\label{eq:deltaPhi_3}
	\Delta \phi \simeq 2 \frac{r_S}{R} \left[ \alpha(\theta) + \frac{3}{4} \beta(\theta) e^{-m_gR} \right]\,.
\end{equation}
We compare the different results for $\Delta \phi$ in Fig.~\ref{fig:lensing_test} and conclude that Eq.~\eqref{eq:deltaPhi_2} gives a fair approximation to the numerical solution, while Eq.~\eqref{eq:deltaPhi_3} does not reproduce the numerical result for $m_gR <1$	--~as was to be expected.

\section{Constraints from Galaxy Clusters}
\label{sec:clusters}

Our goal is to break the degeneracy of the effect of bigravity and the potential effect of a DM component. To this end we study physical systems of different size and mass. We will begin by investigating the effect of bigravity in the largest gravitationally bound systems in the Universe, namely galaxy clusters. As we will illustrate now for bigravity, the ratio of kinematic mass and lensing mass estimates differs from unity, which is never the case in GR. Thus we are able to set limits on the bigravity model, without any assumptions on the mass-to-light ratio of the object.

\subsection{Gravitational Lensing}

Depending on the graviton mixing angle $\theta$, the deflection angle of light changes according to
\begin{equation}
  \Delta\phi \to \Delta\phi\,f_\mathrm{GL}(\theta)
\label{eq:1}
\end{equation}
where $  f_\mathrm{GL}(\theta)$ is found by performing the integral in Eq.~\eqref{eq:deltaPhi_1} and is well approximated by
\begin{equation}
 \alpha(\theta) + \frac{1}{4} \beta(\theta) e^{-m_gR} \left( \left(3 + m_gR\right) \sqrt{\frac{1+ m_gR}{1- m_gR}} + m_gR\, \arccos \left(m_gR\right)\right) \,,\quad
  0\le\theta\le\frac{\pi}{2}\,,
\label{eq:2}
\end{equation}
as we have seen in the previous section. Since this function does not depend on the radius, derivatives of the deflection angle (such as lensing shear and convergence) will change by the same factor $f_\mathrm{GL}$. Mass estimates from gravitational lensing (taken outside the Vainshtein radius) will hence change as
\begin{equation}
  M_\mathrm{lens} \to \frac{M_\mathrm{lens}}{f_\mathrm{GL}}\;.
\label{eq:2a}
\end{equation}
Thus, observing the strength of the lensing effect, we can reconstruct the lensing mass responsible for the light bending $M_\text{lens}$, which depends on the bigravity parameters $m_g$ and $\theta$. We will now turn to a method to reconstruct the gravitational potential in a cluster, by X-ray observations to have an independent observable of the induced metric.

\subsection{X-ray Emission of Galaxy Clusters}

As discussed above the gravitational potential is replaced by
\begin{equation}
  \phi \to \phi\,f_\phi(\theta, r)
\label{eq:3}
\end{equation}
with
\begin{eqnarray}
  f_\phi(\theta, r) &:=& \cos^2\theta\left(1+\frac{2}{3}\sin^2\theta\right)+
  \frac{2}{3} \sin^2 \theta \left(1+2\sin^2 \theta\right)\,e^{-m_g r}
  \nonumber\\ &\,=&
    \alpha(\theta)+\beta(\theta)\,e^{-\lambda r}\;.
\label{eq:4}
\end{eqnarray}
In hydrostatic equilibrium,
\begin{equation}
  \frac{\vec\nabla P}{\rho} = -\vec\nabla\phi\;.
\label{eq:5}
\end{equation}
According to (\ref{eq:3}),
\begin{equation}
  -\vec\nabla\phi \to -\vec\nabla\phi\,f_\phi-\phi\,\vec\nabla f_\phi\;.
\label{eq:6}
\end{equation}
In spherical symmetry and ordinary gravity,
\begin{equation}
  \phi = -\frac{GM(r)}{r}\;;\quad
  -\vec\nabla\phi = -\frac{GM(r)}{r^2}\;,
\label{eq:7}
\end{equation}
and thus from (\ref{eq:6})
\begin{equation}
  \frac{GM(r)}{r^2} \to
  \frac{GM(r)}{r^2}\,\left(f_\phi-r\mathrm{d}_rf_\phi\right) =
 \frac{GM(r)}{r^2}\,\left(\alpha+\beta(1+\lambda r)e^{-\lambda r}\right)\;.
\label{eq:8}
\end{equation}
For an ideal gas,
\begin{equation}
  \vec\nabla P = P\left(\vec\nabla\ln\rho+\vec\nabla\ln T\right)\;,
\label{eq:9}
\end{equation}
so that hydrostatic equilibrium (\ref{eq:5}) requires
\begin{equation}
  -\frac{k_\mathrm{B}T}{\bar m\,r}
  \left(\frac{\mathrm{d}\ln\rho}{\mathrm{d}\ln r}+\frac{\mathrm{d}\ln T}{\mathrm{d}\ln r}\right) =
  \frac{GM(r)}{r^2}\,\left(\alpha+\beta(1+\lambda r)e^{-\lambda r}\right)\;.
\label{eq:10}
\end{equation}
Since the left-hand side of this equation is measured and thus remains unchanged, Eq.~\eqref{eq:10} implies that the mass inferred from X-ray data will change according to
\begin{equation}
  M_\mathrm{kin}(r) \to
\frac{M_\mathrm{kin}(r)}{\alpha+\beta(1+\lambda r)e^{-\lambda r}}\;.
\label{eq:11}
\end{equation}
Therefore, we can determine the effective underlying parameter $M_\text{kin}$ which sources the gravitational potential. The ratio of cluster masses inferred from X-rays and gravitational lensing is therefore expected to change according to
\begin{equation}
  \left\langle\frac{M_\mathrm{kin}(r)}{M_\mathrm{lens}(r)}\right\rangle \to
  \left\langle\frac{M_\mathrm{kin}(r)}{M_\mathrm{lens}(r)}\right\rangle\,
    \frac{f_\mathrm{GL}}{\alpha+\beta(1+\lambda r)e^{-\lambda r}} \equiv R_M \left\langle\frac{M_\mathrm{kin}(r)}{M_\mathrm{lens}(r)}\right\rangle\;.
\label{eq:12}
\end{equation}
This ratio $R_M$ contains non-trivial  information about both principal functions  of the induced metric  $\lambda$ and $\nu$. It will be useful to search for deviations from the GR result, which is unavoidably $R_M=1$.

Notice that in order to arrive at Eq.~\eqref{eq:12}, we have to assume that light propagates outside the Vainshtein sphere, which turns out to be a sensible approximation for the physical systems under consideration. Otherwise a more involved analysis of the gravitational potential inside cluster is needed which is beyond the scope of this work, cf.~Appendix~\ref{app:potentials}.

\subsection{Identifying Clusters against the CMB}

The CMB temperature fluctuations normalise the small-scale density fluctuations via the shape of the power spectrum. Thus, the expected number of galaxy clusters can be predicted from it. Via the thermal  Sunyaev -- Zel'dovich (SZ) effect, clusters can directly be seen against the CMB. The inverse Compton scattering off high energy electrons in clusters causes distortions of the CMB spectrum. However, the observed number of clusters is substantially lower than that expected. Since the thermal SZ effect needs hot gas, one solution could be that clusters of a given mass are cooler than expected. Tentatively reconciling this conclusion with hydrostatic equilibrium, there must be non-thermal pressure support, or a deviation from the relation $ M_{\rm kin}/M_{\rm lens} =1$. This is quantified by the hydrostatic bias factor introduced above, which needs to be smaller than unity, $R_M = 0.66 \ldots 0.99 $ (depending on the prior chosen), cf.~Ref.~\cite{Ade:2015fva}.

\subsection{Bigravity effect on observations of lensing in clusters}

\begin{figure}[t]
	\centering
	\includegraphics[width=.75\textwidth]{contours.pdf}
	\caption{\label{fig:Contours}Contour plot of the ratio $\left\langle\frac{M_\mathrm{kin}}{M_\mathrm{lens}}\right\rangle$ relative to the GR value for a cluster size of $5\,\mathrm{Mpc}$ in percent. The blue star indicates the best fit point, favoured by data from the cluster J1206.2-0847 studied below.}
\end{figure}

Combining the results of the previous subsections, we can explore the effects of the modified potentials by producing Fig.~\ref{fig:Contours}, where the ratio $R_M$ is shown for a cluster of radius $R_c = 5\,\mathrm{Mpc}$. We quote the aforementioned value for the bias parameter $R_M = 0.66 \ldots 0.99 $, suggested by CMB observations.

We see that in a region where the mass of the massive spin-2 mode lies roughly between $10^{-31}\,\mathrm{eV}$ and  $10^{-28}\,\mathrm{eV}$, a reduction of the ratio $R_M$ is indeed feasible for large ($\theta \gtrsim \pi/4$) mixing angles. Moreover, in the limit of pure massive gravity ($\theta = \pi/2$), there is a mass window $10^{-28}\,\mathrm{eV} \lesssim m_g \lesssim 10^{-27} \,\mathrm{eV}$, where the ratio nearly vanishes. Therefore, it remains an intriguing question whether the tension with the GR prediction of $R_M$ is indeed due to deviations from hydrostatic equilibrium or a hint for new physics in the gravitational sector.

Finally, we remark that for masses well below $10^{-31}\,\mathrm{eV}$, the Vainshtein mechanism sets in, i.e.~$\theta_\text{eff}=0$, while for masses $m_g > 10^{-27}\,\mathrm{eV}$, we find that the Compton wavelength of the graviton, $\lambda_c = m_g^{-1} \ll R_c$ and the exponential $e^{m_g R_c} \to 0$. Consequently, the ratio $R_M = 1$ in both regimes.

\subsection{The MACS J1206.2-0847 Cluster}\label{sec:MACSlensing}

We now use data of the MAssive Cluster Survey (MACS) galaxy cluster J1206.2-0847, located at a redshift $z = 0.44$~\cite{Ebeling:2000nh,Ebeling:2009sn,Postman:2011hg,Annunziatella:2014vsa},  to explicitly demonstrate the effect of the deviation of the kinetic and lensing masses. In Ref.~\cite{Biviano:2013eia} two different techniques were used to obtain information about the kinematic mass $M_\text{kin}$, i.e.~the mass inducing the gravitational potential. Combining both, a reconstruction of the mass was possible within the viral radius as well as beyond it. The crucial part for our analysis is the comparison between the reconstructed $M_\text{kin}$ and the lensing mass $M_\text{lens}$ obtained for the same cluster in \cite{Annunziatella:2014vsa}. As discussed above,  outside the Vainshtein radius the ratio $R_M$ of these masses will deviate from one.

\begin{figure}[t]
	\centering
	\subfloat[exclusion region and best-fit point]{
		\includegraphics[width=.47\textwidth]{MACS_chisquared.pdf}\label{fig:ClusterExample} }
	\subfloat[$R_M$ as function of the radius]	{
		\includegraphics[width=.47\textwidth]{MACS_fit.pdf}\label{fig:MACSfit} }
	\caption{\emph{Left:} $\chi^2$ parameter study in bigravity for the ratio $R_M$ of the MACS J1206.2-0847 cluster assuming the hypothesis of graviton mixing with a massive spin-2 state. The $\chi^2$ value is converted into an exclusion region at the 95\% C.L.~and a best-fitting point (blue star). \emph{Right:}
	Ratio of kinetic to lensing mass $R_M$ of the  MACS J1206.2-0847 cluster as a function of radial distance, given the best fit parameters $m_g  = 2  \cdot 10^{-31}\,\mathrm{eV},\ \theta =1.2,\ \Delta r = 0.23\, r_V,\ \Delta {\chi^2} \equiv (\chi^2 - \chi^2_0)/\chi^2_0 = -0.35$.}
\end{figure}

In order to draw quantitative conclusions, we compare the observations of $R_M$ and the model prediction of bigravity as a function of the two parameters graviton mass, $m_g$, and the graviton mixing angle, $\theta$.  We perform a $\chi^2$ analysis and show the results in Fig.~\ref{fig:ClusterExample}. We find that a large region of the mass window of interest is already ruled out at the $95\%$ confidence level (C.L.) when the mixing angle is large enough. This is consistent with previous studies of lensing constraints in pure massive gravity \cite{Choudhury:2002pu}. An intriguing observation is that for $m_g \gtrsim 10^{-31}\,\mathrm{eV}$  and large mixing angles the $\chi^2$ of the fit is reduced significantly relative to the null hypothesis $R_M =1$. For this particular choice of parameters, which yield the best fit as indicated by a blue star in Figs.~\ref{fig:Contours} and~\ref{fig:ClusterExample}, we present the fit to the data in Fig.~\ref{fig:MACSfit}.

\subsection{The Bullet Cluster}

The main idea behind this analysis is the difference in the gravitational effect of compact structures and extended gravity sources in theories with a Vainshtein mechanism at work.
Let us first define the radius $r_M$ within which the major matter fraction is concentrated. Furthermore,  under a certain graviton mass hypothesis we find the would-be Vainshtein radius given the enclosed mass $r_V(M_\text{in}, m_g)$. We distinguish two cases,   1) $r_M < r_V(M_\text{in}, m_g)$ and 2) $r_V(M_\text{in}, m_g) < r_M $. In case 1) the Vainshtein radius is equivalent to the one found in the Schwarzschild spacetime, while in case 2) the matter backreaction effect stops the longitudinal mode from propagation within $r_M$, as discussed in Ref.~\cite{Babichev:2013usa}.  Thus we find that the effective region where GR is restored is within the $r_V^\text{induced} = \max ( r_V(M_\text{in}, m_g) , r_M)$.

The two galactic core components of the bullet cluster~\cite{Tucker:1998tp}, correspond to the case 1). On the other hand, the plasma component, which is located at the center of the cluster collision and is displaced due to ram pressure, is not sufficiently compact and corresponds to case 2). As mentioned above, the matter coupling in the plasma clouds leads to the non-propagation of the longitudinal polarisation of the graviton. Thus, within the plasma cloud, GR is restored in the same way, as in the Vainshtein sphere around the more compact stars. For the our analysis we assume that within the region approximately homogeneously filled with gas, the gravitational law of massless gravity holds.

\begin{figure}[t]
	\centering
	\subfloat[GR limit $\theta  = 0 $]	{
		\includegraphics[width=.45\textwidth]{BulletClusterPi0.pdf}}
	\subfloat[$(m_g, \theta)=(10^{-30}\,\mathrm{eV}, \pi/4)$]{
		\includegraphics[width=.45\textwidth]{BulletClusterPiover4.pdf}}\\
			\subfloat[$(m_g, \theta)=(10^{-30}\,\mathrm{eV}, \pi/3)$]{
		\includegraphics[width=.45\textwidth]{BulletClusterPiover3.pdf}}
	\subfloat[$(m_g, \theta)=(10^{-30}\,\mathrm{eV}, \pi/2)$]{
		\includegraphics[width=.45\textwidth]{BulletClusterPiover2.pdf}}
	\caption{ \label{fig:bullet} The parameter $\kappa$, which is the lens convergence and is a good approximation to the surface mass density of the mass distribution in the Bullet Cluster.  The four panels show $\kappa$ reconstructed under different hypotheses of the lensing potential (a) GR and (b,c,d) bigravity. }
\end{figure}

In Fig.~\ref{fig:bullet} we show how the mass of the Bullet cluster, reconstructed from weak lensing~\cite{Markevitch:2003at,Clowe:2003tk} changes when the effective mixing angle in bigravity is varied. In particular assuming only the stellar and plasma masses as sources of gravity, the surface mass density is computed in pure GR (Fig.~\ref{fig:bullet} a)), which is well approximated by the lens convergence $\kappa$. Then in  (Fig.~\ref{fig:bullet} b),c),d)) the massive mode mixing in bigravity is included and the lens convergence is modified according to the prescription described in section \ref{sec:lensing}. The enhanced lens convergence outside the Vainshtein sphere of the compact stellar source leads to a stronger apparent lensing potential. This would lead to a larger perceived mass surface density around the stars than in GR, but does not affect the lensing of the plasma cloud.
In the regime with significant graviton mixing, it becomes obvious that indeed the displacement of the largest mass fraction, with respect to the plasma, is due to the fact that galaxies are collisionless. However, the modification of the lensing potential in bigravity lets their lensing mass appear higher at large scales than expected in GR. The qualitative picture seems to match the observations presented in Ref.~\cite{Clowe:2006eq}.

The above observation can be formulated in the following way. The Vainshtein radius of a baryon dominated system scales as $ r_V = (2 G_N \lambda_g^2 M_b)^{1/3}$, where $M_b$ is the baryonic mass. It can thus be written in terms of the baryonic density as $ r_V = (8 \pi/ 3 \, G_N \lambda_g^2 \rho_b)^{1/3} r_b$. The relevant ratio is $R_V = r_V/r_b$. This ratio has to be larger than one  $(R_V > 1$) in order for the Vainshtein radius to be outside the region where non-linear matter back-reaction restores GR. Thus, given a fixed graviton mass, there is a minimal baryonic matter density needed in order to induce observable deviations from GR. For example for a graviton mass of $10^{-30}$ eV, systems with lower densities than $2.5 \cdot 10^5\, M_\odot/\text{kpc}^3$ would be completely GR dominated. Therefore, we find that in bigravity the existence of systems which lack the DM phenomenon could occur naturally and is an interesting tool to constrain the graviton parameter space. We will discuss the impact of a recently observed, baryon-dominated galaxy on the graviton parameter space in the next section.

\section{Galaxy Rotation Curves} \label{sec:rotCurves}
The previous section showed that, due to the Vainshtein mechanism, gravitational interactions are modified in the framework of bigravity on extra-galactic scales. Given that the Vainshtein radius itself is a function of the Schwarzschild radius, and hence of the mass of the system under consideration, one is led to ask if galactic dynamics are influenced, too. In the following we try to answer this question by means of galactic rotation curves; however, we emphasise that conclusive statements could only be drawn from a survey of many galaxies, while in this work we study only a few examples. We proceed as follows: first, we find a model for a galaxy that gives a good fit to the data with GR interactions and a DM halo, which we take to have a profile as proposed by Navarro, Frenk and White (NFW)~\cite{Navarro:1996gj}. We then turn on bigravity, i.e.~choose a non-zero mixing angle and graviton mass and repeat the analysis. We then quantify how much particle DM is needed with respect to GR. Interestingly, we find that the best-fitting point is one with reduced DM content, a non-zero mixing angle, and a graviton mass within one order of magnitude of the best-fitting point from the previous section.

Let us now go through the details. We demonstrate our analysis using  the ESO138-G014 galaxy, which was observed at a distance of 18.57~Mpc~\cite{OBrien:2010dps,Aaronson1982} and has a well measured velocity profile, see also Ref.~\cite{Hashim:2014mka}. Moreover, we perform a fit to a set of low surface brightness galaxies from Ref.~\cite{KuziodeNaray:2007qi} to derive bounds on the bigravity parameter space.

\begin{figure}[t]
	\centering
	\subfloat[rotation curve parameter scan with 95$\%$ exclusion limits from the $\chi^2$ distribution. Best-fit point (red star) and the least DM point (yellow star).]{
	\includegraphics[width=.45\textwidth]{DM_chisquare}\label{fig:MassratioChisquared}}
	\subfloat[	mass ratio of DM to baryonic matter consistent with the rotation curves, within the central galactic region.]{
	\includegraphics[width=.47\textwidth]{DM_contour}\label{fig:Massratio}}
	\caption{\label{fig:rotCurveScan}Parameter scan over the bigravity parameters $(m_g,\theta, \Delta r)$. The best fit point is marked in red, while the parameter point with the least DM content is marked in orange.}
\end{figure}

In order to fit the rotation curves, we assume that the relation $v(r) = \sqrt{r \frac{\mathrm{d}\phi}{\mathrm{d} r}}$ holds, and modify the potential $\phi$, following the above reasoning, as
\begin{equation} \label{eq:potentialDefinition}
	\phi (\vec{r}) = - G_N \int \mathrm{d}^3 \vec{r}\,'\ \rho(\vec{r}\,') \left[ \frac{\alpha(\theta)}{ |\vec{r} - \vec{r}\,'|} + \frac{\beta(\theta) e^{- m_g |\vec{r} - \vec{r}\,'|}}{ |\vec{r} - \vec{r}\,'|} \right],
\end{equation}
where the mixing angle is replaced by an effective mixing angle, as defined in Eq.~\eqref{eq:Vainshtein}, to account for the Vainshtein mechanism. Since the potential is a solution to a linear, inhomogeneous Poisson equation, the squared angular velocities related to the different mass components simply add up linearly as is the case in GR. We assume that the galaxy is composed of gas, a disk of ordinary (baryonic) matter and a DM halo. The gas component is inferred from the HI emission and is modelled by assuming a proportionality of mass and luminosity and an exponentially decreasing profile,
\begin{equation} \label{eq:surfaceMassGas}
	\Sigma(r) = \Sigma_0 e^{-r/r_0} \quad \Rightarrow \quad M_\text{HI}(r) = L\, \Sigma_0 \times \int_0^r \mathrm{d}r'\, \Sigma(r') = L\, \Sigma_0 \left(r_0- (r + r_0) e^{-r/r_0}  \right),
\end{equation}
where the mass-to-light ratio $L$ is a free parameter. Following Ref.~\cite{Hashim:2014mka}, we model the baryonic disk such that, given a $1/r$ potential, the effective mass distribution would be
\begin{equation}
	M_D(r) = 0.5 M_D^0 (3.2 x)^3 (I_0 K_0 - I_1 K_1),
\end{equation}
where $x \equiv r/R_\text{opt}$ and $R_\text{opt} \equiv 3.2 r_0$, and evaluating the modified Bessel functions $I_{0,1}$ and $K_{0,1}$ at $1.6x$. In this expression, only  $M_D^0$ is a free parameter, while $r_0$ is fixed by the HI observation.

The final component is the DM halo, which we assume to have an NFW profile,
\begin{equation}
	M_\text{DM}(r) = M_\text{DM}^0 \left[ \log\left( 1 + \frac{r}{r_h}\right) - \frac{r}{r+r_h}\right],
\end{equation}
with the free parameters $M_\text{DM}^0$ and $r_h$.
\begin{figure}[t]
	\centering
	\subfloat[GR, $\theta = 0$]{
		\includegraphics[width=.45\textwidth]{rotCurve_GR}\label{fig:rotCurveFitGR}}
	\subfloat[$(m_g, \theta, \Delta r / r_V)=(1.4\cdot 10^{-30}\,\mathrm{eV},  0.7, 0.5)$]	{
		\includegraphics[width=.45\textwidth]{rotCurve_bestfit}\label{fig:rotCurveFitBiGra}}
	\caption{\label{fig:rotCurveFit}ESO138-G014 rotation curve. Shown is the data with error bars, the final fit, and the three components making up the galaxy in our analysis. Panel (a) shows the fit in pure GR ($\chi_0^2=26$), while panel (b) shows the best-fitting point found in our analysis for which $\Delta \chi^2 \equiv (\chi^2-\chi_0^2)/\chi_0^2 = -0.16$.}
\end{figure}
Let us stress once again that it is not sufficient to assume $v^2(r) = r \frac{\mathrm{d}\phi}{\mathrm{d} r} = G_N M(r) / r$, because the Yukawa factor inside the integral in Eq.~\eqref{eq:potentialDefinition} no longer allows the contributions for $|\vec{r}\,'| > |\vec{r}|$ to cancel, as would be the case for the Newtonian relation. Due to computational limitations, we integrate the potentials analytically and implement these expressions in our numerical analysis. The rather lengthy expressions are shown in Appendix~\ref{app:potentials}.

The HI fit is straightforward and details are not shown here. In agreement with Ref.~\cite{Hashim:2014mka}, we find that $M_\text{HI} (20\,\mathrm{kpc}) = 6.4 \cdot 10^{9} M_\odot$. A fit to the rotation curve in GR is displayed in Fig.~\ref{fig:rotCurveFitGR} and illustrates the typical fall-off in velocity for the baryonic matter which is counteracted by the DM to fit the data. In GR, one needs approximately 57\% of the total mass inside the central galactic region to be DM, in order to fit the rotation curve.\footnote{We chose a \emph{fiducial} volume of radius $r=20\,\mathrm{kpc}$ to quantify how much DM is needed to fit the rotation curve. However, it should be emphasised that this does not correspond to the total mass of the DM halo, since the latter may extend far beyond the visible components. Alternatively, one may proceed as was done e.g.~in Ref.~\cite{deAlmeida:2018kwq}, where the mass parameter of the NFW density profile was used instead.}

We now repeat this fit with the modification indicated in Eq.~\eqref{eq:potentialDefinition}. For each value $(m_g, \theta)$, we obtain a fit to the data, similar to that shown in Fig.~\ref{fig:rotCurveFitGR}. The collection of these fits carried out over the bigravity parameter space is then summarised in Fig.~\ref{fig:rotCurveScan}, where we show the regions excluded by a $\chi^2$ analysis, the point representing the best fit (red star) and the point with lowest DM component (orange star) in panel~(a), while panel~(b) displays the ratio of DM mass and total mass within a `fiducial' volume of radius $20\,\mathrm{kpc}$.

Several important features of Fig.~\ref{fig:rotCurveScan} should be highlighted at this point. First, we observe that for large mixing angles and masses $\gtrsim 10^{-29}\,\mathrm{eV}$, more DM than in GR is needed. This is to be expected, as for large mixing we are close to massive GR, while the large mass induces an early exponential fall-off of the Yukawa force. Thus, the missing gravitational force has to be counteracted by even more DM than needed in GR.

The point in the $m_g$-$\theta$ plane with the lowest $\chi^2$, is marked with a red star in Fig.~\ref{fig:MassratioChisquared}.\footnote{While the region we display as exclusion region is based on a sound statistical foundation, we emphasise that the best-fit points shown in this work have a generally low statistical significance. We merely indicate these to highlight that the fits can be improved, in principle.} Notice that this point is within one order of magnitude of the best-fitting point shown for the lensing in Fig.~\ref{fig:ClusterExample}. While this point improves the value of $\chi^2$ compared to the GR result, it results in a DM component of only slightly lower mass, $M_\text{DM} / M_\text{GR} \simeq 95\%$, also cf.~Fig.~\ref{fig:rotCurveFitBiGra} where the corresponding fit to the rotation curves is shown. Indeed, we observe that most of the data points are inside the Vainshtein sphere, while the transition to the modified regime is used to fit a feature for the most out-lying data points.

Next, one may observe that there is a region of intermediate mixing and masses $10^{-29} \,\mathrm{eV} \leq m_g \leq 10^{-27}\,\mathrm{eV}$, where the fit \emph{reduces} the amount of DM needed to a point where very little non-baryonic matter is required to obtain a good fit to the data. Again, we show an example in Fig.~\ref{fig:rotCurveminDM}, which corresponds to the point in parameter space which requires about a factor 15 less DM mass compared to GR, corresponding to $M_\text{DM} / M_\text{GR} \simeq 7\%$, and is thereby the point in parameter space with the smallest DM component. Finally, we point out to the reader that the Vainshtein mechanism sets in as we lower $m_g$ further, and no deviations from GR are expected.

\begin{figure}[t]
	\centering
	\subfloat[$(m_g, \theta, \Delta r/ r_V)=(2 \cdot10^{-27}\,\mathrm{eV},  1.2, 0.04)$]	{
		\includegraphics[width=.45\textwidth]{rotCurve_minDM}\label{fig:rotCurveminDM}}
	\subfloat[$(m_g, \theta, \Delta r/ r_V)=(2 \cdot 10^{-29}\,\mathrm{eV}, 1.0, 0.4)$]{
		\includegraphics[width=.45\textwidth]{rotCurve_pureBiGra}\label{fig:rotCurvepureBigra}}
	\caption{\label{fig:rotCurveFit2}Rotation curves fitted with low (left) and zero (right) DM mass fraction. We find $\Delta \chi^2$ of $-0.03$ and $+0.2$, respectively.}
\end{figure}

A final exercise is trying to fit the data without any DM. This is shown in Fig.~\ref{fig:rotCurvepureBigra}, where we find the best-fitting point at a mass $m_g= 2 \cdot 10^{-29}\,\mathrm{eV}$, slightly below the best-fitting point found above. However, we note that the fit is slightly worse ($\Delta \chi^2 = 0.2$) when no DM halo is included, which disfavours this scenario.

The main conclusion of this section is that in most of the graviton parameter space where an effect on the rotation curve is expected, the degeneracy with the unknown DM component does not allow to place any limits. Only in a small range of graviton masses the $\chi^2$ function gets worse and disfavors this scenario. This graviton mass range, however, is already excluded by the cluster observations considered in the previous section. One caveat to this conclusion is the limit of pure massive gravity ($\theta=\pi/2$). For masses $m_g \gtrsim 10^{-26}\,\mathrm{eV}$ the Yukawa-suppression becomes too strong to yield any acceptable fit and this regime is therefore ruled out, cf.~Fig.~\ref{fig:combined} below. Any parameter point close to $\theta = \pi/2$ could then in principle be rendered viable at the expense of a very large DM component, counteracting the smallness of the long-range force. This behaviour has been confirmed with two more sets of galactic rotation curves containing low surface brightness galaxies \cite{KuziodeNaray:2007qi} and \cite{McGaugh:2001yc}, which we do not show explicitly at this point, but include in our combined exclusion plot which can be found in our discussion, Sec.~\ref{sec:discussion}.

\subsection{A galaxy without Dark Matter}
Recently, astronomers have observed the galaxy NGC1052-DF2, which appears to contain no, or very little DM~\cite{vanDokkum:2018vup}. This interesting observation has been used to constrain the viability of modified gravitational theories such as modified Newtonian dynamics (MOND),~\cite{Milgrom:1983ca} which try to replace DM by modifying gravity on appropriate scales~\cite{Sanders:2002pf}. The absence of DM in an object of galactic size is therefore a challenging --~if not impossible~-- task for such theories. The point of view taken in this paper is quite different to the approach of MOND etc. Knowing that bigravity modifies the gravitational potential on a certain scale, we ask how much DM do we need to explain the observed data, instead of trying to replace it entirely. In this spirit, we can use the observation of the galaxy NGC1052-DF2, assuming the absence of DM in it, to put constraints of the viable parameter combinations in bigravity.

Excluding the region $m_g > 10^{-25} \,\mathrm{eV}$ from our analysis, where one could add more and more DM to counteract the very strong Yukawa suppression, it is assumed that the galaxy contains no DM. Given the rotation curve data, we then find a fit to the data points and demand that the total mass remains below $3.2 \cdot 10^8 M_\odot$~\cite{vanDokkum:2018vup}. This excludes a small parameter region above $\theta > \frac{5\pi}{16}$ and $10^{-30} \,\mathrm{eV} \leq m_g \leq 10^{-27} \,\mathrm{eV}$. This region is included in our summary plot, Fig.~\ref{fig:combined}.

\section{Scaling behaviour}\label{sec:scaling}

\begin{figure}[t]
	\centering
	\includegraphics[width=.6\textwidth]{DMScaling.pdf}
	\caption{\label{fig:Scaling} The general scaling of the virial volume of gravitationally bound systems vs.~the estimated stellar mass component in the central region of the objects. The tentative scales of the objects are taken from \cite{Buckley:2017ijx}. The deviations from the GR behaviour set in at scales above the blue and magenta lines for theories with Vainshtein scaling and MOND, respectively.}
\end{figure}

In the previous sections we observed a curious effect. It turns out, that the induced metric in bigravity has quantitatively an effect of enhancing the gravitational effect of the matter source. This leads to emergent but spurious additional matter if the GR metric only is used. In particular, there are parameter choices at which the effect becomes relevant simultaneously at galactic and cluster scales.  We will now present a generic scaling argument based on the Vainshtein mechanism, wich supports this observation.

The gravitational anomaly, which is commonly explained entirely by the presence of a mainly gravitationally interacting, non-baryonic, non-relativistic matter component is observed in various physical systems. Thus, DM seems to have an effect on the gravitational interaction on vastly different scales.  Alternative explanations to the DM phenomenon involve theories with a new scale at which the gravitational law is modified. But how should this scale depend on the mass of the object to affect all astrophysical systems in which the DM effect is observed? To answer this question, we note that, if the critical length scale has a power law mass dependence $r_c \propto M^n$, then the critical volume around which gravity is modified scales as $V_c \propto M^{3n}$.

We compare in Fig.~\ref{fig:Scaling} the scaling behaviour of MOND and the scaling of the critical length scale found in massive extensions of gravity with data. It is widely known that while MOND can be adjusted to explain some of the DM effects on galaxy scales,~\cite{Sanders:2002pf,Gentile:2010xt,McGaugh:2016leg,Lelli:2017vgz,Li:2018tdo} it seems to fail in galaxy clusters~\cite{Sanders:2002ue,Angus:2006qy,Angus:2006ev}.\footnote{In fact, it was recently found in Ref.~\cite{Frandsen:2018ftj,Rodrigues:2018duc} that it is not possible to explain all galactic dynamics in MOND, and hence certain classes of MOND are disfavoured.}  The failure of MOND in clusters can be easily seen from Fig. (\ref{fig:Scaling}) as the scaling behaviour of the critical length scale in MOND is $r_c \propto M^{1/2}$, since the potential is modified at critical accelerations $a_0 = F/m \propto M r_c^{-2}$, and thus $V_c \propto M^{3/2}$. We observe that the virial volume of clusters lies below the dashed magenta MOND line in Fig. (\ref{fig:Scaling}), but only systems larger than the critical value indicated by this line can exhibit MOND-like modifications of gravity. Qualitatively, this is in agreement with the considerations of Ref.~\cite{Capozziello:2017rvz} that go beyond the non-relativistic MOND framework.

On the contrary the Vainshtein mechanism in massive gravity extensions has a critical length which scales as $r_V \propto ( M \lambda_g^2)^{1/3}$, with $\lambda_g$ being the wavelength of the graviton. Thus, the volume around which gravity is modified scales as the central mass source of the system $V_c \propto r_V^3 \propto M$. This is also trivially the case in DM halo models. Hence, we observe that massive gravity could alter our predictions of the amount of DM in compact gravitationally bound systems. A further unavoidable consequence of this modification of gravity is that the scale of the enhanced gravitational potential is linked to the baryonic matter scale. Observational evidence of this has been recently discussed in \cite{0004-637X-836-2-152}.

In general the Vainshtein mechanism in non-linear theories of massive gravity can be described by studying the equation of motion for the helicity-0 mode in the decoupling limit. As discussed in Ref.~\cite{Babichev:2013usa} we have the following equations of motion for the canonically normalised helicity-0 and helicity-2 modes:
\begin{equation}
\mathcal{E}_{\mu \nu}^{\alpha \beta} \hat{h}_{\alpha \beta} = \frac{T_{\mu \nu}}{M_{Pl}}\,, \quad
 3 \Box \phi +\mathcal{E}_{\phi}= \frac{T}{M_{Pl}}\,,
\end{equation}
 where $\mathcal{E}_{\mu \nu}^{\alpha \beta}$ follows from the linearisation of the Einstein tensor. When the term $\mathcal{E}_\phi$ is sub-dominant, it can be estimated that $\phi \sim T \equiv {T^\mu}_\mu$ and $\hat{h}_{\mu\nu} \sim T_{\mu\nu}$. Since the physical metric is a linear combination, $h_{\mu\nu} \sim \hat{h}_{\mu\nu} -\eta_{\mu_\nu}\phi$, this corresponds to the regime of massive gravity. Contrarily, when $\mathcal{E}_\phi$ dominates the evolution of $\phi$, the latter becomes non-dynamical and sub-dominant, $\phi \ll \hat{h}_{\mu\nu}$. Therefore the physical metric comprises only two degrees of freedom, $h_{\mu\nu} \sim \hat{h}_{\mu\nu}$, i.e.~GR is restored. This simple argument has been studied and confirmed in more detail in Refs.~\cite{Babichev:2009us,Babichev:2009ee,Babichev:2009jt,Babichev:2010jd}, and was also confirmed via numerical studies for massive and bimetric gravity~\cite{Gruzinov:2011mm,Volkov:2012wp}.

Quite generally, the non-linear interactions lead to
\begin{equation}
\mathcal{E}_\phi \propto \partial^{n-k+3} \phi^k/m_g^{n-1} M_{Pl}  = \partial^{n-k+3} \phi^k/\Lambda^n\,,
\end{equation}
where $\Lambda_n^n = M_{Pl}\, m_g^{n-1}$ is the strong coupling scale and leads to a Vainshtein radius $r_V = (M_{Pl}\, r_S)^{\frac{k-1}{n}} \Lambda^{-1}$. Our observation shows that only those theories will be relevant for DM observations on multiple scales in which $(k-1)/n = 1/3$. This implies that $\mathcal{E}_\phi \propto (\partial^{2} \phi)^k/ m_g^{3k-4} M_{Pl} $ and $r_V^3 =2 M^* M_{Pl}^{\frac{k}{1-k}} \lambda_g^{\frac{3k-4}{k-1}}$, with $M^*$ being the central mass. Thus, the restriction on the space of viable theories is that non-linear interactions of the helicity-0 modes have to only contain interactions with two powers of derivatives per one power of the field. Bigravity is an example of such a theory with $k=2$, but certainly not the only one.

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

Massive gravity, i.e.~gravity mediated exclusively by a massive spin-2 field, is subject to very strong constraints, most notably from weak lensing surveys, $m_g < 6 \cdot 10^{-32}\,\mathrm{eV}$~\cite{deRham:2016nuf,Desai:2017dwg,Rana:2018vxn}. Although this bound is somewhat model-dependent, it tightly restricts the available parameter space of the massive spin-2 mode. In this work, we have considered a framework where the second tensor field, which is a necessary ingredient for the graviton to become massive, becomes dynamical itself. Thereby, two tensor modes are present in the particle spectrum and mediate different forces, one long-range Coulomb-type force and one Yukawa-type force. A peculiar feature of massive spin-2 fields is the Vainshtein mechanism, an intrinsically non-linear effect, which is hard to implement in simple calculations. We have taken a pragmatic point of view, assuming that GR is continuously restored within a spherical volume of radius $r_V$, and studied the effects of the superimposed spin-2 mediated forces.

\begin{figure}[t]
\centering
\includegraphics[width=.8\textwidth]{exclusion_combined_DMcontours}
\caption{\label{fig:combined}Combined 90\% exclusion regions derived in this and previous publications. The largest region is excluded due to the lensing constraints discussed in Sec.~\ref{sec:MACSlensing} (blue region). For completeness, we have also included the best-fitting points in corresponding color coding. The grey, hatched region is excluded from solar system tests~\cite{deRham:2014zqa}, while the magenta and green regions are excluded from gravitational wave observations~\cite{Max:2017flc}. Finally, we exclude the region where the graviton Compton wavelength exceeds the observable universe, $m_g < H_0$. The dashed contours indicate the predicted local DM density in percent of the GR expectation.}
\end{figure}

First, we have derived the deflection angle of light in bigravity, which is considerably more complex than in GR, and found a sufficiently accurate analytical approximation. To the best of our knowledge this is a new result and has not been derived in the literature so far. We have then used this result to study the differences expected in mass estimates of galaxy clusters inferred from weak lensing and hydrostatic considerations. We have found that the results may differ drastically from the GR prediction, where the masses are predicted to be equal, and which has allowed us to derive new constraints on the bigravity parameter space. We have also used this finding to explain a tentative anomaly in cluster mass ratios that has been observed and quantified with a `hydrostatic bias parameter' by the Planck collaboration~\cite{Ade:2015fva}, and that, depending on the analysis method, seems to indicate a deviation from the GR prediction. Furthermore, we have studied the MACS J1206.2-0847 cluster to illustrate how the data can be fitted by means of the modified mass ratio and derived constraints on the bigravity parameters $(m_g,\theta)$ wherever possible.

In a next step, we have used data from spiral galaxies to fit the corresponding rotation curves. We find that this, too, provides strong constraints, allows one to lower the required DM fraction in the galactic center to maximally 7\% of the amount needed in GR, or improve the fit to the rotation curve data; albeit, not simultaneously.

Fig.~\ref{fig:combined} shows a compilation of all constraints and best-fitting points found in our analysis. We have also included the bound from solar system tests (grey hatched region), and gravitational wave observations (green and magenta regions), see e.g.~\cite{deRham:2016nuf,Max:2017flc}. Finally, we disregard the region, where the graviton Compton wave length exceeds the observable Universe, $m_g < H_0$.

While this manuscript is certainly only a first step towards fully understanding the long-distance behaviour of bigravity, the results are quite encouraging to extend these surveys beyond our simple treatment, and, e.g., fully take into account non-linear effects and/or to study, in addition, the CMB, structure formation to name only a few more observables of interest. Given the scaling behaviour of the Vainshtein mechanism discussed in Sec.~\ref{sec:scaling}, studying the modified astrophysical and cosmological predictions is an important and powerful tool, since any best-fitting point for some observable, say for the tentative cluster anomaly, will have consequences for a variety of length scales and must therefore pass a series of constraints on these scales to be a viable explanation. Similarly, this scaling allows one to probe all of the available parameter space through whichever observation is most sensitive. Ultimately, it is crucial to further constrain this scenario, because of the fact that the local dark matter density and the gravity modification by theories with Vainshtein scaling have a considerable degeneracy. Otherwise, our searches for particle dark matter might be based on incorrect premises about the local density.

\acknowledgments
J.S. would like to thank Annika Peter and Mads Frandsen for helpful discussions. J.S. is grateful to the support by the CP$^3$-Origins centre. The CP$^3$-Origins centre is partially funded by the Danish National Research Foundation, grant number DNRF90. M.P.~receives funding from the International Max Planck Research School for Precision Tests of Fundamental Symmetries (IMPRS-PTFS) and is enrolled at the University of Heidelberg. S.M.~acknowledges support by the DFG grant BA 1369 / 20-2 .

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A round-up of all improvements and changes to the Buzz platform in version v3.0.73, available on September 27, 2018.
Added fixed headers to grids in the For Me, People, and Past Courses screens.
Added fixed header and footer to the Activity Grader grid.
Fixed some styling issues in the Question Editor where divider lines were overlapping editable fields.
Fixed an issue in the Activity Editor where you could not link to an assessment as Companion material.
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Updates in version 2018.09.25.3354. Learn more.
GetSubmissionState: Assessments with a customtype node in the item data are allowed to be started even if no questions have been defined.
Help our teacher doesn't have a password to the unit 1 exams and we are prevented from moving forward with curriculum until my child completes the unit tests. This is holding her back from keeping on pace with her education. HELP! We can't find a number for customer support or technical support. Please contact @ tffnyprkns@gmail.com ASAP.
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text:
Q: Netbeans release mode C++ is twice as slow as Visual Studio 2012? I have some code which runs on Visual Studio (MSVC compiler) with an average speed per message of 127 CPU cycles. I ported it over to Linux (Mint 16), Netbeans 7.4 and GCC 4.8. The code is C++ standard compliant.
The only changes I had to make was to replace __rdtsc() with an inline GCC version. To run the code I changed Netbeans to Release mode, went in to the properties and changed the setting so that this was a "Performance Release". I then click on the green arrow and the program is taking on average 229 CPU cycles per message- nearly double the MSVC time.
Am I running Netbeans release mode correctly? I know on Visual Studio you have to press ctrl + f5 for a proper performance release. I werent sure if there was an equivalent mistake to make using Netbeans? I was expecting the code to be faster on Linux!
The code doesn't use any containers except for raw arrays.
Timing:
Windows I used:
unsigned long long start = __rdtsc();
//Code
unsigned long long finish = __rdtsc();

Linux, same as above except I used:
#if defined(__i386__)

static __inline__ unsigned long long rdtsc(void)
{
    unsigned long long int x;
    __asm__ volatile (".byte 0x0f, 0x31" : "=A" (x));
    return x;
}

#elif defined(__x86_64__)

static __inline__ unsigned long long rdtsc(void)
{
    unsigned hi, lo;
    __asm__ __volatile__ ("rdtsc" : "=a"(lo), "=d"(hi));
    return ( (unsigned long long)lo)|( ((unsigned long long)hi)<<32 );
}

#endif

Which I got from this SO answer: https://stackoverflow.com/a/9887899/997112

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text:
Home Original Series On This Day CM Punk and the Pipebomb – 06/27/11 | On This Day
CM Punk and the Pipebomb – 06/27/11 | On This Day
Marc Madison (Editor in Chief)
On June 27th, 2011 CM Punk came out and laid down the Pipebomb promo. It was a promo unlike any in recent memory. After suffering a loss, a wounded John Cena began to slowly make his way to his feet. While battered and bruised, Cena laid there until CM Punk came out. Dressed in his ring gear and a very fitting Stone Cold Steve Austin T-Shit, Punk crossed his legs sat on the stage at the top of the rampway. What followed was CM Punk and the infamous Pipebomb promo. It is as follows below.
CM Punk & The Pipebomb
John Cena, while you lay there, hopefully as uncomfortable as you possibly can be, I want you to listen to me. I want you to digest this because before I leave in 3 weeks with your WWE Championship and I have a lot of things I want to get off my chest.
I don't hate you, John, I don't even dislike you, I do like you and I like you a hell of a lot more than I like most people in the back, I hate this idea that you're the best. Because you're not. I'm the best. I'm the best in the world. There's one thing you're better at than I am and that's kissing Vince McMahon's ass.
You're as good as kissing Vince's ass as Hulk Hogan was. I don't know if you're as good as Dwayne though. He's a pretty good ass kisser. Always was and still is.
Whoops! I'm breaking the fourth wall!
[Punk waves to the camera]
Photo / Bleacher Report
What was happening here? Within the first couple of minutes, fans began to stop and take notice. He wasn't just calling himself the best but doing so by taking direct jabs to Cena, McMahon, Hogan, and The Rock all at once.
I am the best wrestler in the world.
I've been the best ever since day one when I walked into this company. And I've been vilified and hated since that day, because Paul Heyman saw something in me that nobody else wanted to admit. That's right, I'm a Paul Heyman guy. You know who else was a Paul Heyman guy? Brock Lesnar. And he split just like I'm splitting. But the biggest difference between me and Brock is I'm going to leave with the WWE Championship.
I've grabbed so many of Vincent K. McMahon's brass rings that it's finally dawned on me that they're just that, they're completely imaginary. The only thing that's real is me and the fact that day in and day out, for almost six years, I have proved to everybody in the world that I am the best on this microphone, in that ring, even in commentary! Nobody can touch me!
As we weave in a few more minutes into this promo, we have him inciting terms such as 'brass rings', 'the fourth wall', and that he's a Paul Heyman guy. He even goes as far as to mention Lesnar's departure years earlier and distance from the promotion. He is going beyond just stating details that many had heard about, believed but now it wasn't a whisper it was being shouted for all to hear!
And yet no matter how many times I prove it, I'm not on your lovely little collector cups. I'm not on the cover of the program. I'm barely promoted. I don't get to be in movies. I'm certainly not on any crappy show on the USA Network, I'm not on the poster of WrestleMania, I'm not on the signature that's produced at the start of the show and I'm not on Conan O'Brian. I'm not on Jimmy Fallon. But the fact of the matter is, I should be.
And trust me, this isn't sour grapes. But the fact that Dwayne is in the main event at WrestleMania next year and I'm not makes me sick!
Oh hey, let me get something straight. Those of you who are cheering me right now, you are just as big a part of me leaving as anything else. Because you're the ones who are sipping on those collector cups right now. You're the ones that buy those programs that my face isn't on the cover of. And then at five in the morning at the airport, you try to shove it in my face so you can get an autograph and try to sell it on eBay because you're too lazy to go get a real job.
I'm leaving with the WWE Championship on July 17th. And hell, who knows, maybe I'll go defend it in New Japan Pro Wrestling. Maybe…I'll go back to Ring of Honor.
[Punk looks at the camera and waves]
Photo / Medium
Hey, Colt Cabana, how you doing?
Just when we feel Punk couldn't say anything else he mentioned other promotions and his best friend at the time and former WWE superstar Colt Cabana. He addresses marketing and fans that can be in talent's face and not respecting their distance and privacy.
The reason I'm leaving is you people. Because after I'm gone, you're still going to pour money into this company. I'm just a spoke on the wheel. The wheel is going to keep turning and I understand that. Vince McMahon is going to make money despite himself. He's a millionaire who should be a billionaire. You know why he's not a billionaire? Because he surrounds himself with glad-handed, nonsensical, douchebag (censored) yes men, like John Laurinaitis, who's going to tell him everything he wants to hear, and I'd like to think that maybe this company will be better after Vince McMahon is dead. But the fact is, it's going to be taken over by his idiotic daughter and his doofus son-in-law and the rest of his stupid family.
Let me tell you a personal story about Vince McMahon, alright? We do this whole [anti] bully campaign…
[Microphone cuts off]
I've been silenced!
Photo / CBR.com
CM Punk & this Pipebomb promo still lives in infamy today. As a promo peeled back the layers of what many believed online for some time. Whether it was true or not, the statements, emotions, and names mentioned certainly put forth a number of scathing comments that we are still talking about it today.
https://Prowrestlingpost.com
As a wrestling enthusiast for over 30 years, my fondness for professional wrestling explores the irrational in a rational way. I will explore the details inside and outside the ring and hopefully have a laugh with you in the process. I've had the fortune to interview wrestlers from Lucha Underground, TNA, Ring of Honor, GFW, and former WWE talent as well. Feel free to follow me on Twitter @TheMarcMadison


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Home//Radio//Only A Game
Cardinal Michael Wacha Is A Rookie Star02:17
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Michael Wacha is one of many talented rookie pitchers on the St. Louis Cardinals. (Matt Slocum/AP)
This postseason, Michael Wacha of the St. Louis Cardinals is 4-0, his latest win coming in Game 2 of the World Series on Thursday night at Fenway Park.
You want understatement on that subject? Here's Cardinals Manager Mike Matheny.
[sidebar title="Historic Rivalry" width="330" align="right"] ESPN's Tim Kurkjian looks back at past Red Sox-Cardinals meetings. [/sidebar]"The kid continues to impress," Matheny said. "He and [catcher] Yadi [Molina] work well together and make good adjustments along the way. He stuck with his strengths and really went out and was aggressive, and that's exactly what we needed him to do."
Wacha's strengths are his fastball and his changeup. On Thursday night, the Cardinals rode Wacha and the relief pitching of two other rookies, Carlos Martinez and Trevor Rosenthal, to a 4-2 win. Afterward, Wacha, whose postseason ERA is 1.00, was asked if his success had changed everything.
"Yeah, I went to go eat at a little restaurant, and they had a milkshake named after me, which was pretty weird, so I had to try it out," he recalled. "It was pretty good."
The milkshake, called The Wacha Wacha, is vanilla, with chocolate chips and Cracker Jack.
On Friday morning SI.com's Tom Verducci provided the overstatement Mike Metheny avoided. He said Wacha might be the greatest young pitcher in postseason history.
If the Series goes to a sixth game, the Red Sox will likely see Michael Wacha again. Could he win for the fifth time in the postseason? Among those who might not be surprised if it happened is Sox Manager John Farrell.
"When you get guys in the first full year of pro baseball to be able to maintain this kind of stuff in October, it's remarkable, with what he's doing," said Farrell. "Obviously a very talented guy."
Talented, poised, still only 22, and the winner of the game the Cardinals needed to avoid going back to St. Louis down 2-0. No wonder they've named a milkshake after him.
This segment aired on October 26, 2013.
Bill Littlefield Twitter Host, Only A Game
Bill Littlefield was the host of Only A Game from 1993 until 2018.


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The ADTS 405 is the latest in a series of reliable, high accuracy, air data test systems.
The rugged, compact design has evolved as a result of GE Druck's continuous research and development, customer feedback and experience gained from manufacturing thousands of automatic pressure controllers. This has enabled performance, maintainability, and operational simplicity to be optimised.
The ADTS 405 is a twin-channel Ps and Pt pressure control system used for the precision calibration/verification of aircraft pitot statics, compliant with RVSM (Reduced Vertical Separation Minima) requirements.


Old School Runescape Bond Giveaway!
This holiday season I've decided to give back a little, so we're going to be giving away one Old School Runescape BOND (current value – 3.3m) every day over the holidays for ten days!
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text:
Forty years ago, Don and Marilyn Praisner moved to a newly developed subdivision on the furthest edges of Silver Spring called Calverton. While the community they settled in has changed dramatically since then, they remained as stewards and leaders. Many newer residents such as myself, whose family moved here in 1999, cannot fully appreciate former Councilmember Marilyn Praisner's impact on our community as we were not here to witness much of her work.
While Marilyn and I did not agree on a lot of issues, I recognize that a piece I wrote last month, entitled "is marilyn praisner the new ronald reagan?", was insensitive. In it, I suggest that County Executive Ike Leggett's attempts to commemorate her life and career were excessive. However, I appreciate what she has done, and I want to see her legacy carried on in some form.
We all mourn the passing of Marilyn, though none of us can comprehend the loss her widower carries in his heart. Tomorrow morning - just in time for the special election - the "District 4 Head-to-Head Tour" draws to a close as we interview County Council candidate Don Praisner.
labels: calverton, housekeeping and random, politics
You need make no apology. This naming of public buildings and places for politicians whose job it is is to serve their employers, the public, is vastly overdone---dedicating New Hampshire Ave to former State Senator Ida Ruben, dedicating I-270 to former U.S. Senator Charles Mathias, naming a Silver Spring bus terminal for former Senator Paul Sarbanes, naming a Silver Spring Court House for former legislator Leonard Ruben, trying to name the Rockville Library for former County Executive Doug Duncan. Plastering the names of Governors Ehrlich and O'Malley over every new building project. Giving U.S. Senators advance information of the awarding of public grants so the Senators can announce them as if these grants came from the largesse of the Senators rather than the public.
The fact is those who truly deserve the monuments don't need them. This whole legacy of naming rights is vastly done. Don't apologize just because some politicians have asked you to for their perceived political purposes.
Did Don Praisner refuse an interview until you gave him an apology? Vote for Nancy Navarro!
retgroclk said...
Then there is the story of a couple walking through the town center and one comments on the names of all the buildings honoring someone.
He turns to his friend and says - would you like to have a bulding named after you.
The friend thinks for a moment and says -"No."
I would rather have them look at all these buildings and wonder-- "Why are there no buildings named after me?
Kevin Gillogly said...
Why the delay with posting the Praisner interview?
Can you explain why all the others have been up for awhile. You also mentioned that you would post your interview with Don this weekend.
So now you are going to post it on Tuesday morning? Some good that will do.
It sure sounds like Praisner refused the interview until you retracted your comments. Isn't that how the Bush administration controls the media?
If it's true, you shouldn't have done the interview at all.
Marilyn Praisner voted for the largest tax increase in Montgomery County history, a 20% increase in the county piggyback tax. Then she voted three times from FY03-FY05 to exceed the charter property tax limit. That is one legacy we don't need when the county executive has proposed the largest property tax increase in 20 years. Anybody who says any of the above is "fiscally prudent," needs to apologize. Stop the spin.
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