Go on a Fall walk through the school neighborhood, collecting colored leaves, acorns, etc. in lunch bags or in student-created "Baskets of Beauty".
Before the walk, sit in a quiet spot and have the children close their eyes. Speak in hushed tones. Ask them to listen carefully to the sounds they hear. Ask them to smell the scents of autumn. Weather permitting, have them lie on their backs and look at the fall sky.
While on the walk, look for colorful leaves, seeds, nuts, flowers, squirrels, and migrating birds. Take along some magnifying glasses for a closer look.
Collect a few leaves of various colors, nuts and seeds. Later, discuss how the leaves, nuts and seeds are the same and different, how they smell, could they be eaten, and how they feel.
Make a regular graph or a use masking tape to create a floor graph to show the colors of their favorites.
We also used tiny candy leaves (the ones you usually sprinkle on frosting) to make individual leaf graphs.
Copy this Fall Concentration game on two colors of paper. Use as a center or as a take-home activity to review the signs of fall.
Copy this fall leaves blackline of 9 leaves on three different colors of paper to use for sorting activities. Sort the leaves by color, shape and size. Give students a copy of each color to cut up and use at home for sorting practice.
We learned that there are other colors "hidden" in the leaves, but the green color covers them up. In the fall, the other colors in the leaves can be seen when they change colors.
Use a popsicle stick to rub some of the green color (chlorophyll) from a green leaf on to a coffee filter strip.
You can see some of the green color here.
Take out the strip and dry. There is a small band of yellow color that separated from the green.
We made a book about some leaf activities. Cut the pages in half. The first page consists of a cover.
On the next page, the children either draw or trace a leaf and describe it.
Cubes are used to measure the leaf on page 3.
On page 4, the children drop their leaves and record how high they can count before their leaf reaches the floor.
On page 5, the children measure the area of their leaf by covering it with pennies.
On the last page, the children discover that their leaves float. Then they place one penny at a time on their leaf to discover how many pennies it will take to sink their leaf.
Click on the link if you would like a copy of the Leaf Book.
Trace a child's arm and hand to make a fall tree. Glue colored tissue pieces on for the leaves.
Make a fall wreath by gluing leaves and acorns to a paper plate with the center cut out.
This is a TLC type scarecrow where the children cut and glue on shapes and then embellish it with crayon drawings.
This scarecrow pouch was made by cutting a foam plate in half and lacing the edges together with rope. The children drew on a face, glued on a bow, and stuffed it with straw.
These are examples of rotating center activities to celebrate the season. Parent volunteers and teachers are in charge of these centers and classes rotate to a new center every 20 minutes (or any designated time limit). This can be done with all of the kindergarten classes or in one classroom on a smaller level. Click here for additional center ideas that are Halloween related.
Have the children decorate sugar cookies. Add a drop of red and yellow food coloring to white frosting in a dixie cup. The children stir it and frost the cookie. They may also add decorations–sprinkles, M&M's, etc.
Do spider web paintings, rolling marbles in white paint and then over black paper. Attach spider rings when dry.
List fall words and then write a story and illustrate a picture.
Find the letter in the hay. Fill a large tub with hay and add large letters for them to find and match to a fall item, such as "I" by the Indian Corn, etc.
Make book marks with fall stamps.
Glue sunflower seeds onto a sunflower worksheet that has numbers in the center of each flower. (such as 5).
Loved your Leaf Book! Thanks so much!
How can we get a copy of the leaf report worksheet? I LOVE this idea!!!!
Great ideas for a 'leaf' themed week! Thanks!
What a nice ideas, I just love the leaf report.
Is it possible to find the report somewhere as a worksheet, and not just as a photo?
Leave a Reply to Charmaine Click here to cancel reply.


Stags lose 4-2 at Port Vale. Reports from CHAD, ananova & footymad.net.
The Scandinavian Statto strikes again with a preview of tomorrow''s clash at Vale Park.
Stags complete the loan signing of Manchester City defender Ryhs Day.
Stags Reserves beat Lincoln City Reserves 6-3 on Wednesday - Doom Merchant tells it how it was!!
Team Mansfield will be holding a Special General Meeting followed by a Fans Forum on 3rd December, from 7pm. SSA members & TM Trust members are invited to attend, though non-SSA members can join on the night.
... Hassell expected to be included in squad for Port Vale.
Stags Reserves beat Lincoln Reserves 6-3 this afternoon. Bobby Hassell started the game but Allen Tankard limped off.
A Stagsnet poll has revealed three quarters of Stags fans believe the decision to release Michael Sisson is the wrong one.
Post match interview with Paul Holland - See Match Centre for a Stagsnet Report.
More Stats from Sweden as the Stags take on Bristol City this weekend.
Stags Physio Barry Statham has spoken to mansfieldtown.net about the current injury situation at Field Mill.
Long term injured Stags midfielder Michael Sisson has been told his contract will not be renewed due to financial reasons.
A report on Mansfield 103.2 says that loan deals for Colin Little & Andy White have been extended.
Following the suggestion by SSA last season, The Stags will again be selling half season tickets - valid from Boxing Day.
reports from BBC.co.uk, nationwide.co.uk, CHAD - see Match Centre for the Stagsnet report.
While many Stags supporters will be up with the lark to get down to Bath for tomorrow''s noon kick-off, spare a thought for two fans who will be rising even earlier.
Team Bath manager Ged Roddy, who watched Mansfield''s recent 4-2 win over Colchester, is under no illusions as to the task facing his team tomorrow.
WATKISS - SHOW THEM WHAT YOU CAN DO!!
Mansfield Town boss Stuart Watkiss sees tomorrow''s Sky clash with Team Bath as a great opportunity for his young team to show the country what they can do.
Stags fans intending on travelling to see the FA Cup first round clash at Team Bath this Saturday have until 4.30pm Friday to buy their tickets from Field Mill.
Stags youth team lost their Football League Youth Alliance Cup game against Walsall last night by 3-2.
Mansfield 103.2 report that Tony Vaughan has returned to Nottingham Forest after sustaining a knee injury at Notts County on Saturday.
Liam Lawrence has been voted Player of the Month for October by Stagsnet visitors.
A late Iyseden Christie goal gave the Stags a deserved point after dominating most of the match at Notts county this afternoon. Reports from ananova, Teamtalk, footymad, CHAD, plus Match Stats.
Yes its time for our man in Sweden to take an analytical look at the Stags v County tie.
Stags given 800 seats/Tickets will be on sale from Monday 11 November for Season Tickets Holders and SSA Members ONLY.
BBC Radio Nottingham report that the Stags are set to sign Matt Gadsby whilst Stuart Reddington has joined Burton.
while Stags have only 12 professionals available.
Radio 5 Live will also be covering the game.
SSA will be taking a supporters bus to the FA Cup clash with Team Bath.
News on Sellars, Vaughan, Lawrence, Christie, Moore, Jervis, Scott, Reddington.


Help - How to send to marketing suspended people within a particular list?
How do I suppress marketing suspended people that are within a certain group of people? Whenever I use the filter in a smart list marketing 'suspended is true' the list then contains everyone lead that is marketing suspended instead of those within a particular list. I know there is a simple fix but it's escaping me right now.
Re: Help - How to send to marketing suspended people within a particular list?
You will have to combine the "Marketing suspended" filter with a "member of smart list" and include in the latter a reference to the group of people you want to avoid.


The Rockwall County Historical Foundation was organized January 16, 1978, with the intent to preserve the heritage of Rockwall County. Ongoing projects of the Foundation include maintaining a permanent museum showcasing artifacts of Rockwall County history, taping and preserving oral histories from long-time local residents, designating historic sites and structures within the County, sponsoring events that educate the public about Rockwall County history, preserving and safekeeping photos and other documents relative to Rockwall County, and distribution and publication of educational materials.
The Rockwall County Historical Foundation Museum is housed in the Manson-LaMoreaux-Hartman House located at 901 E. Washington Street in Harry Myers Park. The museum is open to the public Wednesdays and Saturdays from 10 a.m. - 2 p.m., and by appointment. Admission is free.


This parachute testing for NASA's InSight mission to Mars was conducted inside the world's largest wind tunnel, at NASA Ames Research Center, Moffett Field, California, in February 2015.
Lockheed Martin Space Systems, Denver, is building the InSight spacecraft. The InSight Project is managed by NASA's Jet Propulsion Laboratory, Pasadena, California, for the NASA Science Mission Directorate, Washington. InSight is part of NASA's Discovery Program, which is managed by NASA's Marshall Space Flight Center in Huntsville, Alabama.


text:
Carriera
Con la  ha disputato i Campionati europei del 1989.

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


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Paris Convention for the Protection of Industrial Property
Living in a global economy means that certain laws must stretch across nations, including intellectual property laws. An inventor who wants his or her invention protected in foreign countries has the option of filing for a patent in each country in which protection is sought or can file an international patent application. The Paris Convention for the Protection of Industrial Property, for example, governs almost all international reciprocal patent filing rights. Parties to the Paris Convention also have an option to join the Patent Cooperation Treaty (PCT), which allows inventors to file an international patent application effectively providing inventors with simultaneous patent protection in participating countries.
This article provides information about what the Paris Convention provides to contracting countries as well as an overview of the Patent Cooperation Treaty.
What Does the Paris Convention Provide?
The Paris Convention was signed in Paris, France, on March 20, 1883 and is administered by the World Intellectual Property Organization (WIPO). There are over 170 countries who are contracting parties to the Paris Convention. The Paris Convention doesn't only apply to patents; it also includes protection for trademarks, trade names, and services marks. Basically, the Paris Convention establishes a right of priority, which means that an applicant can use his or her first filing date as an effective filing date in other contracting countries. One of the requirements to this right of priority is that the subsequent filings must occur within a year from the first filing. The countries that are contracting parties to the Paris Convention also have the opportunity to join the Patent Cooperation Treaty (PCT), which allows contracting parties to file international patent applications.
What Is the Patent Cooperation Treaty?
The PCT provides a standard application format and centralizes the filing procedures for patents, which makes filing for patent protection in multiple countries easier. Nationals and residents of countries that are a party to the PCT are eligible to file for this type of application. An applicant has the option to file an international application with the International Bureau of WIPO in Geneva or in the national patent office of the applicant's residency or nationality. For example, a resident or citizen of the United States can file the application with the U.S. Patent and Trademark Office (USPTO).
The PCT not only provides advantages to inventors seeking international patent protection, but also benefits patent offices and the general public. For example, patent offices can reduce or even eliminate the work involved in searching and examining a patent application because of the international search report and written opinion. The published international search report also puts third parties in a better position to decide whether or not an invention can be patented. The PCT procedures also provide more time to decide whether or not to seek patent protection in foreign countries and to take the steps that are necessary to seek foreign patent protection.
Even though filing for a patent doesn't require attorney representation, a patent application must include detailed and specific information, so having experience filing such applications is helpful for ensuring that the application is complete and correct. Providing incomplete or incorrect information can lead to limited coverage of your patent or rejection of your application. If you have questions about the Paris Convention, or would like some help to determine if your invention or discovery qualifies for patent protection, you may want to contact a local patents attorney for guidance.
For more information and resources related to this topic, you can visit FindLaw's section on Patents.
Contact a qualified business attorney to help you identify how to best protect your business' intellectual property.
Patent Forms
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IP Forms and Contracts

redpajama_set_name: RedPajamaCommonCrawl


My father, Adrian Steinberg, lost his battle with colon cancer on July 28, 2017 at the age of 76. At the time of his diagnosis at age 70, he was healthy, energetic, and full of life. He ran a small family business and often worked 18 hours a day. He and his loving wife, Maria, enjoyed trips to the beach, Florida, and visiting family. He loved spending time with me, my sister Jennifer, his 4 grandchildren, and many close friends.
Cancer robbed my father of his health, energy, and time with us. However, it did not steal his incredibly loving spirit and his will to live and care for his family.
Please consider donating to Colon Cancer Alliance, in Adrian's memory, to advance prevention, diagnosis, and treatment of this devastating disease.
Our deepest sympathy, Amber and family.
We are keeping Adrian in our thoughts and prayers.
Love and Comfort from our family to yours.
My heart felt condolences. It's a horrible horrible disease.
He will always be remembered by all who knew him.


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text:
Antonio Conte guided Inter Milan to victory against his former club…
Home Rugby Premiership: Leicester and Bristol bosses want carefully planned Premiership return
Premiership: Leicester and Bristol bosses want carefully planned Premiership return
Leicester Tigers head coach Geordan Murphy has said Premiership players will need two months to properly prepare for a full return to action.
Premiership Rugby hopes to restart the season in July, with clubs waiting for the go-ahead from the rugby union authorities before resuming training amid the coronavirus pandemic.
Murphy said the union's physicality means players must "ramp up" training.
"There has to be a slow, graded re
"There has to be a slow, graded return," he told BBC Radio Leicester.
"That would be a minimum of eight weeks, which is what we're planning. It will be decided though by the Rugby Football Union and Rugby Players Association, so I don't know where we will end up."
Murphy takes over as director of rugby when Steve Borthwick officially becomes head coach on 1 July. Tigers were 11th in the Premiership, the same position they finished in 2018-19 when the season was suspended on 16 March.
But the uncertainty surrounding when the sport will return, how and when this season will be completed and the effect it will have on player contracts is adding further confusion.
"The reality is that we'll be back as soon as we can in front of crowds, and we expect that our early games will be played behind closed doors," Murphy added. "It will be unusual to play matches without crowds, but the players will just want to be back on the field and getting rugby back under their belts.
"Our contracts are starting on 1 July, and that's what we are working towards, fulfilling those contracts. If someone is out of contract, they will join a new club, and we are expecting new players to arrive to start their jobs.
"Having said that, there are a lot of unknowns in that, we need to speak to the RFU and RPA. We are still working towards a start date, and when we know, we will make those assessments."
Previous articleOlivier Giroud Chelsea and France striker to stay at Stamford Bridge next season
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text:
\section{Introduction}

Higher dimensional theories offer new avenues to address longstanding fine tuning problems. Regarding the gauge hierarchy problem, there are now other possible solutions in addition to 4D supersymmetry, such as the Randall-Sundrum \cite{Randall:1999ee,Randall:1999vf} and the Large Extra Dimensions scenario \cite{Arkani-Hamed:1998rs} (which requires, in its minimal formulation, at least two extra dimensions). Still the cosmological constant problem remains an unsolved issue in theoretical physics.

 A combination of the concepts of supersymmetry and (large) extra dimensions has been proposed \cite{Aghababaie:2003wz}  as a way to attack the cosmological constant problem, postulating two extra dimensions and  codimension two 3-branes. Whether this approach can be successful, it is still unclear (for criticisms and replies see e.g. \cite{Garriga:2004tq}-\cite{Burgess:2004dh}), however, an interesting property of this scenario would be  the prediction of the Kaluza-Klein (KK) scale at $10^{-3}$eV. One immediate consequence would be the onset of deviations from standard gravity at that scale, which corresponds to the submillimeter. Thus, a  natural question is whether the matching with experimental and observational tests of gravity can impose (additional) tuning of the brane tensions, once a 4D flat background solution is chosen.

The aim of the present paper is to answer this question by considering a realization of 6D supergravity called the Salam-Sezgin model\footnote{For an analysis of deviations from Newton's law in different types of 6D supergravity see \cite{Callin:2005wi}.} \cite{Salam:1984cj} (and its anomaly free \cite{seifanomaly} extensions \cite{Nishino:1984gk}). String theory derivations of this 6D supergravity have been provided \cite{Cvetic:2003xr} and its vacuum structure has been investigated in great detail. Gibbons, G\"uven and Pope (GGP) proved \cite{Gibbons:2003di} that the only smooth solution of the Salam-Sezgin model is the 4D flat unwarped space with internal spherical geometry and a non vanishing gauge field \cite{RandjbarDaemi:1982hi}. As soon as 3-branes are introduced, conical singularities are generated and the most general solution with 4D Poincar\'e symmetry and axial symmetry in the internal space has been derived \cite{Gibbons:2003di,Aghababaie:2003ar} (we consider this class of solutions here and refer to it as the GGP solution). There are no solutions of the Salam-Sezgin model having a curved 4D space with maximal symmetry and without singularities stronger than conical \cite{Burgess:2004dh,Tolley:2005nu}. These properties render the GGP solution an interesting
set of configurations, whose 4D spectrum has been indeed studied in a series of works \cite{Parameswaran:2006db,Burgess:2006ds,Parameswaran:2009bt}.

Here we focus on the minimal coupling between gravity and branes required by general covariance and compute the brane interactions mediated by massive KK gravitons. We derive their general form at the leading order in perturbation theory and their corrections to Newton's law on the brane. We show that these quantities can be independent of the brane tensions and we comment on the physical implications of this property. The origin of such independence is identified with the presence of codimension two branes on a compact space.

\section{The class of Models}

We consider a class of models in $D$ dimensions possessing 3-brane solutions with 4D Poincar\'e invariance. The complete (covariant) action is $S= S_B+S_b$, where $S_B$ is the bulk action (see below for specific forms) and $S_b$ is the brane one:
\begin{equation} S_b=\int d^4 x \sqrt{-g}(-T+ I(x)), \label{Sb}\end{equation}
where $g$ is the determinant of the brane metric, defined in terms of the higher dimensional metric $G_{MN}$ by \cite{Sundrum:1998sj}:
\begin{equation} g_{\alpha \beta}\equiv G_{MN}(Y(x))\partial_{\alpha}Y^M(x) \partial_{\beta}Y^N(x). \label{branemetric}\end{equation}
Here $M,N,...=0,...,D-1$ and $\alpha, \beta,...$ are the brane world volume indices: $x\equiv\{x^\alpha\}$. The functions $Y^M(x)$ give the position of the generic point $x$ on the brane in the higher dimensional coordinate system. The function $I(x)$ instead can be a generic functional of $g_{\alpha \beta}$ and additional brane fields $\chi_b$, but below we will consider it as a gravitational source localized on the brane. The constant $T$ is the brane tension that may include the vacuum energy produced by the brane fields. It is trivial to generalize this to an arbitrary number of branes: all we have to do is to add an index to the various quantities appearing in (\ref{Sb}), but from now on (unless otherwise stated) we suppress it.

We are interested in the 6D case and in a class of models which can describe 6D Einstein-Yang-Mills systems (with a cosmological constant $\Lambda$), which we refer to as EYM$\Lambda$, and 6D N=1 gauged supergravities \cite{Nishino:1984gk,seifanomaly}. Also we will focus on the bosonic bulk dynamics, as, in our setup, only bosons couple to the brane sources. The bulk fields (which depend on all the space-time coordinates $X^M$) include, in addition to the higher dimensional metric, the gauge field $\mathcal{A}_M$ of a compact Lie group $\mathcal{G}$. In order to complete the bosonic part of 6D supergravity, one should also add a
dilaton $\phi$ and a 2-form field $B_{MN}$, which emerges from the
graviton multiplet and an antisymmetric tensor multiplet
\cite{Nishino:1984gk}. Moreover,
concerning 6D supergravity, we shall assume that $\mathcal{G}$ is
a product of simple groups that include a $U(1)_R$ gauged R-symmetry.
In general one can also add some hypermultiplets
\cite{Nishino:1984gk}, which turn out to be important to cancel gauge
and gravitational anomalies \cite{seifanomaly}. In the
bosonic sector this leads to additional scalar fields $\Phi^{\alpha}$; however, from
now on we consistently set $\Phi^{\alpha}=0$.

The bulk action is
\begin{eqnarray} S_B=\int d^6X
\sqrt{-G}\left\{\frac{1}{\kappa^2}\left[R-\frac{1}{4}\left(\partial
      \phi\right)^2\right]
-\frac{1}{4}e^{\phi/2}F^2 \right. \nonumber \\ \left.
-\frac{\kappa^2}{48}e^{\phi}H_{MNP} H^{MNP} -\mathcal{V}(\phi)\right\},
\label{SB} \end{eqnarray}
where $\kappa$ is the six-dimensional Planck scale, $F_{MN}$ is the usual gauge field strength and
\begin{equation} H_{MNP} \equiv \partial_M B_{NP} +
F_{MN}{\cal A}_P - \frac{g}{3}{\cal A}_M\left({\cal A}_N
\times {\cal A}_P \right) + \,\rm{2 \,\, cyclic \,\, perms} \,, \label{HKR}\end{equation}
where $g$ is the gauge
coupling that  in fact represents a collection of
independent gauge couplings, which may include that of a $U(1)_R$
subgroup, $g_1$.
In the
supersymmetric model the dilaton potential is fixed to be $\mathcal{V}(\phi)=8\,g_1^2
\,e^{-\phi/2}/\kappa^4$.  With obvious truncations we can recover the EYM$\Lambda$ model: $\phi=0$, $ H_{MNP}=0$ and $\mathcal{V}(0)=\Lambda$.

The GGP solutions \cite{Gibbons:2003di} are
\begin{eqnarray} ds^2&=&e^{A(u)}\left(\eta_{\mu \nu}dx^{\mu}dx^{\nu}+du^2\right)
+ e^{B(u)} \, \frac{r_0^2}{4} \, d\varphi^2 \, ,\nonumber \\
 e^A&=&e^{\phi/2}=\sqrt{\frac{f_1}{f_0}}, \quad e^B=4\,\alpha^2
e^A\frac{\cot^2(u/r_0)}{f_1^2},\nonumber\\
\mathcal{A}&=&-\frac{4\alpha}{q\kappa f_1}\, Q\,
d\varphi,\label{GGPsolution}\end{eqnarray}
where $r_0^2\equiv \kappa^2/(2g_1^2)$, $u$ is a compact coordinate ($0\leq u \leq \overline{u}\equiv \pi r_0/2$), $\varphi$ is an angular coordinate ($\varphi \sim \varphi +2\pi$), $\alpha$ and $q$ are real numbers and $Q$ is a generator
of a $U(1)$ subgroup of a simple factor of $\mathcal{G}$, satisfying
Tr$\left(Q^2\right)=1$. Also,
\begin{equation} f_0\equiv 1+\cot^2\left(\frac{u}{r_0}\right), \quad f_1 \equiv
1+\frac{r_0^2}{r_1^2}\cot^2\left(\frac{u}{r_0}\right), \label{GGPsolution2}\end{equation}
with  $r_1^2\equiv 8/q^2$. These solutions are supported by two branes at $u=0$ and $u=\overline{u}$, with $Y^{\mu}=\overline{Y}^{\mu}=x^{\mu}$. As $u \rightarrow 0$ or $u \rightarrow
\overline{u}$, the metric tends to that of a cone, with respective
deficit angles
\begin{equation} \delta = 2\pi \left(1-|\alpha| \, \frac{r_1^2}{r_0^2}\right)
\quad \mbox{and}\quad
\overline{\delta}=2\pi\left(1-|\alpha| \right) \, . \label{deltadeltabar}\end{equation}
 The two brane tensions $T$ and $\overline{T}$ are related to the deficit angles \cite{chenlutyponton}:
$ T=2\delta/\kappa^2
$ and $\overline{T}=2\overline{\delta}/\kappa^2$.
Also, the internal space corresponding to the GGP has the $S^2$ topology (its Euler number
equals 2). Observe that the warp factor in (\ref{GGPsolution}) satisfies
\begin{eqnarray} && e^A\stackrel{u\rightarrow 0}{\rightarrow}constant \neq 0,\quad
e^A\stackrel{u \rightarrow \overline{u}}{\rightarrow}
constant \neq 0, \label{Aproperty1}\\&& \partial_u e^A\stackrel{u\rightarrow 0}{\rightarrow} 0 \quad
\partial_u e^A\stackrel{u \rightarrow \overline{u}}{\rightarrow} 0. \label{Aproperty2}\end{eqnarray}
The relation between the 6D Planck scale $\kappa$ and our observed
4D Planck scale $\kappa_4$ is $ V_2/\kappa^2=1/\kappa_4^2$, where the volume $V_2$ is given by
$ V_2=\pi r_0\int du \,e^{(3A+B)/2}$.
For the GGP solutions we have $ V_2=4\pi \alpha \left(r_0/2\right)^2$.

We now discuss the independent parameters of our model (in the absence of sources). Before the compactification the action $S_B+S_b$, given  by (\ref{SB}) and (\ref{Sb}) with $I=0$, has the following independent parameters
\begin{equation} \kappa, g', g_1, T, \overline{T}, \label{parametersBC} \end{equation}
where $g'$ represent the collection of independent gauge couplings different from $g_1$. Solving {\it locally} the equations of motion (EOMs) with the GGP configuration does not constraint (\ref{parametersBC}). However, the fact that the internal space has a spherical topology imposes a {\it topological} constraint on the tensions. This is the usual Dirac quantization condition, which for a field interacting with  the background gauge field $\mathcal{A}$ through a unit charge gives
\begin{equation} \left(1-\frac{\kappa^2}{4\pi}T\right)\left(1-\frac{\kappa^2}{4\pi} \overline{T}\right)\left(\frac{\overline{g}}{g_1}\right)^2=N^2,\label{topological}\end{equation}
where $N$ is an integer (the monopole number) and $\overline{g}$ is the gauge constant associated with $\mathcal{A}$. So after the compactification we have the same number of independent parameters, which can be taken as
\begin{equation} \kappa_4, r_0, g',T, \overline{T}, \label{parametersAC}\end{equation}
but with the topological constraint (\ref{topological}). In Section \ref{gravity-spin-2} we shall see that the gravitational interactions mentioned in the introduction are independent of $T$ and $\overline{T}$ (and obviously of $g'$ because 4D gravitons are not charged under any 6D gauge group).

The GGP solutions solve the 6D supergravity equations in the absence of external sources (other than pure tensions), that is for $I(x)=0$. However, below we will consider perturbations that include couplings between bulk fields and gravitational sources on the brane.

\section{Perturbations and Leading Interaction}

In order to study the massive graviton interactions between sources we have to expand the theory in powers of small fluctuations around the background solutions. In particular, regarding the bulk metric, we substitute
\begin{equation} G_{MN} \rightarrow G_{MN} + h_{MN}\label{metricpert}\end{equation}
 in the action, so that we can interpret $G_{MN}$  as the background metric and $h_{MN}$ as the small fluctuation. We also perform similar replacements for the other bulk fields  (which we do not display for the sake of brevity) and for the brane fields:
\begin{equation} Y^M\rightarrow Y^M + \xi^M, \, \chi_b\rightarrow \chi_b + \tilde{\chi}_b. \label{branepert}\end{equation}
The mixing (in the linearized theory) between $\tilde{\chi}_b$ and the other perturbations depends on $I(x)$. For the sake of simplicity, we restrict our attention to the cases in which this mixing is absent at the linear level; for example this is true  if we take $I(x)$ to be the standard model Lagrangian with the usual 4D Poincar\'e invariant vacuum.

The complete bilinear action for the bulk fields and $\xi^M$ has been derived in \cite{Parameswaran:2009bt}. As a consequence of the local symmetries in the initial theory, such bilinear action has the local symmetries
\begin{eqnarray} \delta h_{MN} &=& -\eta_{N;M} - \eta_{M;N},  ...  \label{h-gauge} \\
      \delta \xi^M &=&
\eta^M(Y)-\zeta^{\alpha}\partial_{\alpha}Y^{M}, \end{eqnarray}
where the dots represent the transformation rules of the other bulk fields and $\eta_M=\eta_M(X)$ and $\zeta^\alpha=\zeta^\alpha(x)$ are the gauge parameters associated with the higher dimensional and 4D general coordinate invariance respectively. We use the latter invariance to fix the so called static gauge: $Y^{\mu}= x^{\mu}$ and $\xi^{\mu}=0$. In this gauge we still have the fields $\xi^{m}(x)$, ($ m=4,5$) representing the fluctuations of the brane position along the extra dimensions.

Here we want to include the leading interactions between bulk fields and sources on the branes, which emerge from the action $\int d^4 x \sqrt{-g} I(x)$. To this end we have to perturb the brane metric (\ref{branemetric}) at the linear order in $h_{MN}$ and $\xi^m$:
\begin{eqnarray} g_{\mu \nu}& \equiv & G_{MN}(Y(x))\partial_{\alpha}Y^M(x) \partial_{\beta}Y^N(x) \rightarrow G_{\mu \nu}(x,Y_2)+h_{\mu \nu}(x,Y_2)
\nonumber \\ &&+\left(\partial_mG_{\mu \nu}(x,Y_2) \right) \xi^m +2 G_{m\nu}(x,Y_2)\partial_{\mu} \xi^m + ..., \nonumber \\ &=&e^A \eta_{\mu \nu} +h_{\mu \nu}(x,Y_2)+ ...\label{metricexpansion}\end{eqnarray}
where the dots represent non linear terms and $Y_2\equiv \{Y^m\}$. In the last step in (\ref{metricexpansion}) we used explicitly the fact that\footnote{We also used the fact that the background brane positions $Y_2$ do not depend on $x$, as it is the case for the GGP solutions.} the brane metric at the background level is $e^A \eta_{\mu \nu}$ and $G_{m \mu}=0$ and $\partial_mG_{\mu \nu}(x,Y_2)=0$. The latter property comes from the axisymmetry of the background and from (\ref{Aproperty2}).
Therefore, the brane sources produce the following leading interaction term
\begin{equation} \frac{1}{2}\int d^4x \sqrt{-g}\, t^{\mu \nu}(x) h_{\mu \nu}(x, Y_2). \label{brane-bulk}\end{equation}
We call $t^{\mu \nu}$ the brane energy momentum tensor. Notice that we do not include the tension $T$ in the definition of $t^{\mu \nu}$. Notice also that the bulk fields in (\ref{brane-bulk}) are evaluated at the background brane position rather than at the perturbed one $Y^{m}+ \xi^{m}$ and so only bulk fields which have a non vanishing value at background brane positions can contribute to those interactions.

In order to extract the physical properties of these models one has to fix the bulk local symmetries in addition to the brane ones. Before doing so we have to know the bulk local transformation which leaves (\ref{brane-bulk}) invariant. Such transformation is exactly (\ref{h-gauge}), at least for the GGP solutions (for which (\ref{Aproperty2}) holds) and for covariantly conserved $t^{\mu \nu}$ (that we assume):
$ \nabla_{\mu}t^{\mu \nu} =0$, where $\nabla_{\mu}$ is the covariant derivative computed with the (background) brane metric. Since (\ref{h-gauge}) leaves invariant both the bilinear action and the interaction in (\ref{brane-bulk}), it is that transformation that has to be used in order to fix the bulk gauge symmetries.

\section{Massive Spin-2 Contributions \\ to 4D Effective Gravity}\label{gravity-spin-2}

{\it Leading spin-2 brane interactions}. We want to derive an effective action which describes the exchange of massive gravitons between brane sources. This leads to deviations from Newton's law at short distances. We split (\ref{brane-bulk}) as follows
\begin{equation} \frac{1}{2}\int d^4x \sqrt{-g}\,\left[ t^{\mu \nu}(x) \tilde{h}_{\mu \nu}(x, Y_2) + \frac{1}{4}t^{\mu}_{\,\,\mu}(x) h^{\nu}_{\,\,\nu}(x, Y_2)\right],\label{decomposition}\end{equation}
where $h^{\mu}_{\,\,\mu}\equiv e^{-A} \eta^{\mu \nu}h_{\mu \nu}$ and $\tilde{h}_{\mu \nu}\equiv h_{\mu \nu} - e^A \eta_{\mu \nu} h^{\tau}_{\,\, \tau}/4 $ are respectively the trace and the traceless part of $h_{\mu \nu}$ (the indices are raised and lowered by the background metric). We use the bulk local symmetries in (\ref{h-gauge}) to set
\begin{equation} \partial_{\mu}\tilde{h}^{\mu \nu}=0. \label{gaugeSpin-2}\end{equation}

The advantage of this gauge is that it produces no mixing between $\tilde{h}_{\mu \nu}$ and the other fields, as it can be proved by using the general bilinear Lagrangian in \cite{Parameswaran:2009bt}. An explicit computation gives the following bilinear action for $\tilde{h}_{\mu \nu}$
\begin{equation} -\frac{1}{4\kappa^2} \int  d^6X \sqrt{-G}\partial_M \tilde{h}_{\mu}^{\,\, \nu} \partial^M \tilde{h}_{\nu}^{\,\, \mu} \label{bilineaSpin-2}.\end{equation}
The field $\tilde{h}_{\mu \nu}$ leads, after dimensional reduction, to the massless graviton and the tower of massive gravitons. Indeed, if we go to the momentum space $\tilde{h}^{\mu \nu}(x)\rightarrow \tilde{h}^{\mu \nu}(p) e^{ipx}$, we can easily see that  a generic mode $\tilde{h}^{\mu \nu}(p)$ has five degrees of freedom (as a consequence of (\ref{gaugeSpin-2}) and the traceless condition) and that these five degrees of freedom can be reduced on-shell\footnote{Here ``on shell'' means that the EOMs in the absence of $t^{\mu \nu}$ have been used.} to two in the massless case by using a residual 4D gauge invariance compatible with (\ref{gaugeSpin-2}). Also, as we discuss below, the 4D mass spectrum emerging from $\tilde{h}_{\mu \nu}(x)$ is exactly that of the spin-2 particles derived in \cite{Parameswaran:2009bt}. The effective action describing the leading spin-2 brane-bulk interactions reads
\begin{equation} S_{eff}= -\frac{1}{4\kappa^2} \int d^6X \sqrt{-G}\partial_M \tilde{h}_{\mu}^{\,\, \nu} \partial^M \tilde{h}_{\nu}^{\,\, \mu}+\frac{1}{2}\int d^4x \sqrt{-g}\, t^{\mu \nu}(x) \tilde{h}_{\mu \nu}(x, Y_2). \label{effective action}\end{equation}
We should notice that, according to the decomposition (\ref{decomposition}), $h^{\mu}_{\,\,\mu}(x, Y_2)$ also couples to the brane sources (unless the trace of $t^{\mu \nu}$ vanishes). This represents a coupling between bulk scalars and brane sources. The treatment of such interactions requires a way to remove singularities due to codimension two branes, which appear in the scalar sector \cite{Parameswaran:2009bt}.  Here we therefore  consider the graviton-brane couplings only, which will be sufficient to obtain our results.

In order to compute corrections to ordinary 4D gravity we perform a KK expansion for the bulk fields:
\begin{equation} \tilde{h}_{\mu}^{\,\, \nu}(X)= \sum_{{\bf n},{\bf m}} \tilde{h}_{\mu\,{\bf n,
    m}}^{\,\, \nu}(x)F_{{\bf n,  m}}(u,\varphi),\label{spin-2expansion}\end{equation}
where ${\bf m}$ and ${\bf n}$ are KK
numbers. Since the internal space has the sphere topology we can take $F_{{\bf n,  m}}(u,\varphi)=f_{{\bf n,  m}}(u) e^{i {\bf m }\varphi}$. Also we observe that the bilinear action in (\ref{bilineaSpin-2}) is formally identical to the helicity-2 action in the light-cone gauge analyzed in Ref. \cite{Parameswaran:2009bt}, as expected from 4D Lorentz invariance. So the 4D mass spectrum coming from $\tilde{h}_{\mu \nu}$ is exactly that of the spin-2 particles derived there and we can use the same KK expansion as in Ref. \cite{Parameswaran:2009bt} (for more details see \cite{Parameswaran:2006db}). We summarize here the resulting $f_{{\bf n,  m}}$ and the mass spectrum.
Suppressing ${\bf n}$ and ${\bf m}$, the explicit
expression for $f\equiv (2N/r_0) e^{-(3A+B)/4} \psi$ is given by
\begin{equation} \psi =  z^{\epsilon}(1-z)^{\beta}F(a,b,c,z), \label{psi1}
\end{equation}
where $N$ is a normalization factor, $z\equiv\cos^2\left(u/r_0\right)$, $F$ is Gauss' hypergeometric
function and
\begin{eqnarray} \epsilon &\equiv& \frac{1}{4}\left(1+2|{\bf
    m}|\overline{\omega}\right), \,\,
\beta\equiv \frac{1}{4}\left(1+2{\bf m}\omega\right),
\,\, c\equiv 1+|{\bf m}|\overline{\omega}, \nonumber \\
a&\equiv&\frac{1}{2}+\frac{{\bf m}}{2}\omega+\frac{|{\bf
    m}|}{2}\overline{\omega}
+\frac{1}{2}\sqrt{r_0^2M^2+1+{\bf m}^2\left(\omega-\overline{\omega}\right)^2},
\nonumber\\
b &\equiv&\frac{1}{2}+\frac{{\bf m}}{2}\omega+\frac{|{\bf
    m}|}{2}\overline{\omega}
-\frac{1}{2}\sqrt{r_0^2M^2+1+{\bf m}^2\left(\omega-\overline{\omega}\right)^2},
\label{gbetaabcV}\end{eqnarray}
with
\begin{equation} \omega\equiv(1-\delta/2\pi)^{-1}, \qquad
\overline{\omega}\equiv(1-\overline{\delta}/2\pi)^{-1}\end{equation}
and
\begin{equation} M^2= \frac{4}{r_0^2} \left[{\bf n}({\bf n}+1) + \left(\frac{1}{2}
    + {\bf n}\right)|{\bf m}| \left(\omega +\overline{\omega}\right)
  +{\bf m}^2 \omega \overline{\omega}\right] \geq 0,
\label{spin-2-masses}\end{equation}
where ${\bf n}=0,1,2,3,...\,$. Notice that the functions $\psi$ and the masses $M$ depend on the brane tensions in the non-axisymmetric case (${\bf m}\neq 0$) only.

By inserting (\ref{spin-2expansion})  into $S_{eff}$
we obtain
\begin{eqnarray} S_{eff} = \int d^4x \sum_{{\bf n,m}}\left\{\frac{1}{4\kappa^2}\left[\tilde{h}_{\mu\,{\bf n,
    m}}^{\,\, \nu}(x)\right]^*(\partial^2 - M_{{\bf n, m}}^2)\tilde{h}_{\nu\,{\bf n,
    m}}^{\,\, \mu}(x) \right.\nonumber \\ \left.+ \frac{1}{\sqrt2 \kappa}\lambda_{{\bf n,m}} \eta_{\nu \tau}t^{\mu \tau}(x) \tilde{h}_{\mu\,{\bf n,
    m}}^{\,\, \nu}(x)\right\}, \label{SeffKK}\end{eqnarray}
where $\partial^2\equiv \eta^{\mu \nu}\partial_{\mu}\partial_{\nu}$ and we chose the following normalization
\begin{equation} 2\pi \int du  \sqrt{-G} e^{-A}f_{{\bf n,m}}^* f_{{\bf n,m}}=1. \label{normalization}\end{equation}
From the first term in (\ref{SeffKK}) we can see that $M_{{\bf n,m}}$ are the masses of the spin-2 particles, whereas the second term of (\ref{SeffKK}) represents the interaction between the gravitons and the brane sources, whose strength is measured by
\begin{equation} \lambda_{{\bf n,m}}=\frac{1}{\sqrt{2}} \kappa e^{3 A_b} F_{{\bf n,m \, }b} , \label{lambdanm}\end{equation}
where the label $b$ indicates that the corresponding function is computed at the brane position.

The values of $f_{{\bf n,m \, }b}$ determine which KK modes interact with the brane sources: the effective coupling is indeed $\lambda_{{\bf n,m}}$ and $e^{3A_b}$ is a finite constant (see (\ref{Aproperty1})). An explicit calculation, which makes use of the expression for $f_{{\bf n,m \, }b}$ given above, shows that  $f_{{\bf n,m \, }b}=0$ unless ${\bf m}=0$. This result can be understood remembering  that the  internal space has the $S^2$ topology. A field should be a single valued function at any space-time point, including the north and south poles. In order for this to be true, functions $f$ which depend non trivially on $\varphi$, that is ${\bf m}\neq0$, should go to zero on the poles (see Figure \ref{fig:wavefns}).

\begin{figure}
\centering
\begin{tabular}{cc}
\includegraphics[scale=0.50]{n0m1.eps} &
\includegraphics[scale=0.50]{n1m0.eps}  \\ \\ \includegraphics[scale=0.50]{n3m2.eps} & \includegraphics[scale=0.50]{n2m0.eps}
\end{tabular}
\caption{\footnotesize Wave functions $f$ (multiplied by $r_0/(2N)$) for different values of $\{ {\bf n,m} \}$. For definiteness we set $\omega=8$ and $\overline{\omega}=2$, which corresponds to deficit angles $\delta=7\pi /4$ and $\overline{\delta} = \pi$. On the right we give two axially symmetric modes, whereas, on the left, two modes that break the axial symmetry. As one can see only the axially symmetric modes are non vanishing on the branes, which are located at $u/r_0=0$ and $u/r_0= \pi /2$. The number of intersections with the $u/r_0$-axis equals ${\bf n}$, in agreement with quantum mechanics.}
\label{fig:wavefns}
\end{figure}

Also, a closed form for the couplings $\lambda_{{\bf n,m}}$ can be derived. Let us first consider the brane at $u=\overline{u}$, that is $z=0$. Eq. (\ref{lambdanm}) tells us that we only need the warp factor $e^{A_b}$ evaluated on the brane (which at $u=\overline{u}$ is simply $1$) and the value $f_{{\bf n,m}\,b}$ of the wave functions on the brane:
\begin{equation} f_{{\bf n,m}\, b}\stackrel{z\rightarrow 0}{\rightarrow}\frac{2}{r_0} \delta_{{\bf m},0} N_{{\bf n, m}=0}e^{-B_b/4} z^{\varepsilon},  \end{equation}
where we used $F(a,b,c,z)\stackrel{z\rightarrow 0}{\rightarrow}1$ and the fact that only axially symmetric modes have non trivial values on the branes and we  showed explicitly the $\{ {\bf n,m} \}$-dependence of the normalization constants. The factor $e^{-B_b/4} z^{\varepsilon}$ is finite and a simple calculation leads to
\begin{equation} \lambda_{{\bf n,m}}=\delta_{{\bf m},0} \sqrt{\pi} \kappa_4 N_{{\bf n,m}=0}. \label{step}\end{equation}
We can also compute explicitly the normalization constants for axially symmetric modes. Condition (\ref{normalization}) can be rewritten as
\begin{eqnarray} && N_{{\bf n,m}=0}= \frac{1}{\sqrt{2\pi I_{{\bf n}}}},\nonumber \\  && I_{{\bf n}}\equiv \frac{2}{r_0}\int_0^{\overline{u}} du \cos\left(u/r_0\right) \sin\left(u/r_0\right)F^2({\bf n}+1,-{\bf n},1,\cos^2\left(u/r_0\right))
\end{eqnarray}
and, by using the known formulae $F({\bf n}+1,-{\bf n},1,z)=P_{\bf n}(1-2z)$, where the $P_{\bf n}$ are the Legendre polynomials, and $\int_{-1}^1dyP^2_{\bf n}(y)=2/(2{\bf n}+1)$, we obtain
\begin{equation} N_{{\bf n,m}=0}=\sqrt{\frac{2{\bf n}+1}{2\pi}}.\end{equation}
Inserting this result into (\ref{step}) leads to a closed form for the couplings $\lambda_{{\bf n,m}}$. A similar procedure can be used to determine the couplings for the brane at $u=0$, the only difference is that there we have a non trivial value of the warp factor $e^{A_b}=\sqrt{\omega/\overline{\omega}}$. We give the explicit expressions\footnote{In deriving Eq. (\ref{lambda2}) we used $F({\bf n}+1,-{\bf n},1,1)=(-1)^{\bf n}$.}:
\begin{eqnarray} \lambda_{{\bf n,m}}&=& \sqrt{\frac{2{\bf n} + 1}{2}} \delta_{{\bf m},0} \,\kappa_4, \quad \mbox{at}
\,\, u=\overline{u} \label{lambda1}\\
\lambda_{{\bf n,m}}&=& (-1)^{{\bf n}}\sqrt{\frac{2{\bf n} + 1}{2}}  \delta_{{\bf m},0}\left(\frac{\omega}{\overline{\omega}}\right)^{3/2}\kappa_4, \quad  \mbox{at}
\,\, u=0\label{lambda2}\end{eqnarray}
We observe that the effective 4D gravitational coupling at the $u=0$ brane is rescaled with respect to that at $u=\overline{u}$ by a factor which depends on $\omega/\overline{\omega}$. This is the usual redshift/blueshift due to the warp factor that in our case is trivial at $u=\overline{u}$ and non-trivial at $u=0$.

\vspace{0.3cm}{\it Independence of the brane tensions.}
We now observe an interesting phenomenon in this class of compactifications. Let us first consider the $u=\overline{u}$ brane. The leading spin-2 interactions between brane sources turn out to be independent of the brane vacuum energies $T$ and $\overline{T}$ (among the parameters in (\ref{parametersAC})), because the sole contribution to such interactions comes from the axisymmetric modes, which have both\footnote{The couplings $\lambda_{{\bf n,m}} $ and the masses $M_{{\bf n,m}}$ are indeed the only physical parameters appearing in the effective action (\ref{SeffKK}) (to see it rescale $\tilde{h}_{\mu}^{\,\, \nu}\rightarrow \sqrt{2}\kappa \tilde{h}_{\mu}^{\,\, \nu}$).} $\lambda_{{\bf n,m}}$ and $M_{{\bf n,m}}$ independent of $\omega$ and $\overline{\omega}$. Such property also implies that these gravitational interactions have exactly the same form as in the round sphere case, which coincides with the GGP solutions only in the limit $\omega\rightarrow 1$ and $\overline{\omega}\rightarrow 1$.

 A physical consequence of this is that the brane vacuum energy decouple from such interactions, and the latter turn out to be the same as in the probe brane limit. All the quantities that can be derived from the interactions we have studied (including modifications to Newton's law, which we discuss below) will turn out to be independent of the brane vacuum energy, and therefore no tuning of the tensions can be produced by requiring these quantities to match experiments and observations.

Finally we observe that the same result remains valid for the $u=0$ brane up to the redshift/blueshift of the 4D gravitational coupling, which disappears in the unwarped limit.

\vspace{0.3cm}

{\it Deviations from Newton's law.}
We are now interested in the potential generated by a slowly moving particle with mass $M$ on a brane, in the limit of weak stationary fields, that is the Newton's law (and its corrections due to KK fields). To compute this we should look at the fluctuation $H_{\mu \nu}(x,Y_2)$ of the Minkowski metric $\eta_{\mu \nu}$ on the brane. From (\ref{metricpert}) and the metric in (\ref{GGPsolution}) we see that $H_{\mu \nu}\equiv e^{-A} h_{\mu \nu}$. Since $h_{\mu \nu}$ is a bulk field, so is $H_{\mu \nu}$ and it  can be expanded as a sum over the KK fields. However, here we are only interested in the stationary field $H_{00}(\vec{x},Y_2)$ because it is related to the gravitational potential $V$ through the well-known relation
\begin{equation} V(\vec{x})=-\frac{1}{2}H_{00}(\vec{x},Y_2),\label{standard}\end{equation}
The KK expansion of the bulk field $H_{00}(x,u,\varphi)$ is
\begin{equation} H_{00}(x,u,\varphi)= -\sum_{{\bf n,m}}h_{0\,{\bf n,
    m}}^{\,\, 0}(x)f_{{\bf n,  m}}(u) e^{i{\bf m}\varphi} \label{00decomposition}\end{equation}
The fact that we have a slowly moving particle on a brane means that we can approximate the brane energy momentum tensor with $t^{\mu \nu}(\vec{x})=\delta^{\mu}_0 \delta^{\nu}_0 m \,\delta^{(3)}(\vec{x})$, where $m$ is the mass of the particle. A source generates graviton fields according to the equation
\begin{equation} (\partial^2-M^2_{{\bf n,  m}})\tilde{h}_{\nu \,{\bf n, m}}^{\,\, \mu} = -\sqrt2 \kappa \lambda_{{\bf n,  m}} \eta_{\nu \tau} \tilde{t}^{\mu \tau}, \end{equation}
which can be derived from the action in (\ref{SeffKK}) by means of the minimal action principle. Also $\tilde{t}^{\mu \nu}\equiv t^{\mu \nu}-\eta^{\mu \nu}\eta_{\lambda \sigma} t^{\lambda \sigma}/4$. In particular the $00$-component of the graviton equation with the source $t^{\mu \nu}(\vec{x})=\delta^{\mu}_0 \delta^{\nu}_0 m\, \delta^{(3)}(\vec{x})$  generates stationary KK fields satisfying
\begin{equation}  (\vec{\nabla}^2-M^2_{{\bf n,  m}})\tilde{h}_{0 \,{\bf n, m}}^{\,\, 0} (\vec{x})= \frac{3}{4} \sqrt2 \kappa \lambda_{{\bf n,  m}}m\, \delta^{(3)}(\vec{x}), \end{equation}
where $\vec{\nabla}^2$ is the (3D) spacial Laplacian on flat space.  Therefore, by using a standard technique,
\begin{equation} \tilde{h}_{0 \,{\bf n, m}}^{\,\, 0} (\vec{x})= -\frac{3\sqrt2}{16 \pi} \kappa \lambda_{{\bf n,m}} m \frac{e^{-M_{{\bf n,m}}r}}{r}, \end{equation}
where $r\equiv |\vec{x}|$.
If we now use Eqs. (\ref{standard}) and (\ref{00decomposition}), and we remember that only axially symmetric wave functions are non vanishing on the branes, we deduce the following deviation $\Delta V$ of the Newton's potential due to massive gravitons
\begin{equation} \Delta V(r) = -\frac{1}{8\pi} \frac{m}{r}\sum_{{\bf n=1}}^{\infty} \frac{3}{2}e^{-3A_b}\lambda^2_{{\bf n, m}=0}e^{-M_{{\bf n,m}=0}r}. \end{equation}
The latter expression is valid  both for the brane at $u=\overline{u}$ and for that at $u=0$ and, by using Eqs. (\ref{lambda1}) and (\ref{lambda2}) we respectively obtain ($G\equiv \kappa_4^2/(16\pi)$)
\begin{eqnarray} \Delta V(r) &=& -\frac{Gm}{r}\sum_{{\bf n}=1}^{\infty} \left(3{\bf n} + \frac{3}{2}\right) e^{-2\sqrt{{\bf n}({\bf n}+1)}\,r/r_0}, \quad \mbox{at}
\,\, u=\overline{u}, \\
\Delta V(r) &=& -\frac{Gm}{r}\left(\frac{\omega}{\overline{\omega}}\right)^{3/2}\sum_{{\bf n}=1}^{\infty} \left(3{\bf n} + \frac{3}{2}\right) e^{-2\sqrt{{\bf n}({\bf n}+1)}\, r/r_0},  \quad  \mbox{at}
\,\, u=0.\end{eqnarray}
We see that these corrections to Newton's law confirm the fact that the $T$- and $\overline{T}$-dependence falls out in the final result (up to the redshift/blueshift\footnote{Indeed $\omega/\overline{\omega}=(1-\kappa^2\overline{T}/(4\pi))/(1-\kappa^2T/(4\pi))$.}
 $\left(\omega/\overline{\omega}\right)^{3/2}$ due to the warping) and so no tuning of the brane vacuum energy can be introduced by matching this type of models with the short distance precision tests of gravity, if our 4D phenomena take place on the unwarped brane. Clearly this property remains true if we consider an extended mass distribution rather than a particle.

\section{Final Remarks}

We have computed the leading effective interactions of massive gravitons with 3-brane sources in a 6D brane world scenario which includes the Salam-Sezgin model (and its anomaly free extensions) with its most general solution compatible with 4D Poincar\'e invariance and internal axial symmetry. The internal manifold has a spherical topology and this leads to a discrete KK spectrum with a finite mass gap.

 Up to the usual redshift/blueshift due to the warping (which is trivial on one brane), these interactions turn out to be independent of the brane tensions. In particular this implies that no tuning of the brane tensions are required to match observations and experiments with the above-mentioned interactions. A key feature that has led to this result is the codimension two nature of our branes, and the fact that they live on a compact space (the compactness is required to have a discrete spectrum).  Indeed, the same phenomenon does not arise in the classic codimension one scenarios such as Randall-Sundrum models, where e.g. short distance precision tests of gravity lead to bounds on the brane tensions. These results support the idea that in such models the gravitational interactions are decoupled from the brane vacuum energy.

Further remarks are now in order.

 If $t_{\,\,\,\mu}^{\mu}\neq 0$, brane interactions mediated by 4D scalars coming from the bulk generically emerge. The proper treatment of this contribution requires a way to remove the singularities due to the codimension two branes, which emerge in the scalar sector \cite{Parameswaran:2009bt}. Different ways of dealing with these singularities can lead to different physical predictions; therefore,  we focused here on the sector (graviton interactions) that is independent of the regularization procedure. There are nevertheless physical situations where one can take $t_{\,\,\,\mu}^{\mu}= 0$, such as the light bending due to  massive sources.

Also, this type of supergravity models predicts classically massless scalar particles, which could modify the large distance behaviour of gravity. A way to lift these marginal directions, and deal at the same time with the singularities sourced by codimension two branes, has been proposed in \cite{Burgess:2007vi}. However, some difficulties emerge in reconciling this approach with the smallness of the cosmological constant \cite{Arroja:2007ss}. We leave this point as an open issue.

\vspace{0.5cm}

{\bf Acknowledgments.} The author gratefully acknowledges valuable discussions with S. Randjbar-Daemi. This work has been
supported by  CICYT-FEDER-FPA2008-01430.

\vspace{0.5cm}

redpajama_set_name: RedPajamaArXiv


text:
Here's Something to Think About the Next Time You Grab a Plastic Straw
It's time to limit Americans' profligate suckage.
Kriston Capps
Monrudee\Getty
This story was originally published by CityLab and appears here as part of the Climate Desk collaboration.
Summer is here and so are frozen daiquiris, iced lattes, lemonades, hibiscus mint teas, root-beer floats, frozen margs, Arnold Palmers, chocolate milk, nitro cold brews, bloody marys, Capri Suns, milkshakes, adult milkshakes, caipirinhas, rosé in a can, tiki drinks, and ice-cold water out of a mason jar. Kick off your shoes, throw on some shades, and carefully peel back the individual wrapper to sunny vibes. The world's most utterly disposable product is the coin of the realm: Unwrap, sip, noisy-gurgling-sound, repeat—every day, twice a day, three times in a single happy hour. It's straw season, mofos.
But, like everything else that's easy, cheap, and pleasurable, using a straw is fundamentally wrong. Straws consume a lot of energy to produce and distribute for vanishingly little purpose. Billions wind up in the trash without ever being opened. They're too light to be reliably recycled; tons of them find their way into the ocean. Straws that don't end up spiraling in awful trash gyres or clogging sea turtles' sinuses wash up on the beach, where they'll outlive us all.
Straws that don't end up spiraling in awful trash gyres or clogging sea turtles' sinuses wash up on the beach, where they'll outlive us all.
June 5 was the UN's World Environment Day, whose theme this year is "beat plastic pollution," so it's a good time to point this out. Stirrers and straws were the fifth-most common type of debris picked up along the California coastline, according to a cleanup count conducted by Upstream, an organization devoted to getting rid of single-use and disposable plastic packaging. No one pays the hidden costs tucked in each individually wrapped straw.
It's enough to make you pause as you open a straw and plop it into your iced coffee. It does not, however, appear to be enough to make you stop using straws. Hence the straw backlash: Communities nationwide are now attempting to use stronger means to limit Americans' profligate suckage.
This would be a different story if we actually needed straws, but, beyond disabled communities and the elderly, most humans can drink without a straw just fine. True, it's harder to sip while simultaneously doing other stuff, like zip-scooting the boardwalk, or parasailing the bay, or hopping sand dunes in a bitchin' jeep, without one. But in general, straws are a solution in search of a problem.
Probably nobody knows just how many straws Americans consume, but one very popular guesstimate is 500 million. That's half a billion pairs of puckered lips sucking on plastic every single day, a number greater than the U.S. population. But it turns out that this figure was invented by a precocious 9-year-old: As Reason reports, Milo Cress, the founder of a campaign called Be Straw Free, conducted a phone survey of single-use straw manufacturers in 2011, when he was of single-digit age. That hasn't stopped environmentalist virtue-signaling types (and major media outlets) from citing the 500 million number at every opportunity.
If my own straw consumption is any sign, though, that figure is a preposterous undercount. There are more stars in the sky than grains of sand on the earth but whoa, I use so many straws. Sure, I could do my part by carrying around a trendy stainless steel eco-straw (and accompanying tiny brush), along with my clay bowl and wooden spork everywhere I go—like a good itinerant barefoot hedge-monk—but so far, well, I have not done that. It doesn't take a sailboat trip trawling for trash in local waterways to see that there's a major problem, though. With more than a little shame, I acknowledge my role in this crisis, as well as my deep-seated unwillingness to redirect my daily routines to help solve it.
There are two paths for getting over straws: disruptive tech or paternalistic regulation. So far, neither has forced Big Straw to bend.
Luckily, some jurisdictions are willing to legislate the moral behavior that I am unwilling to freely adopt. There are two paths for getting over straws: disruptive tech or paternalistic regulation. So far, neither has forced Big Straw to bend.
Regulatory efforts to ban or curb the ubiquitous single-use straw are gathering steam in all the places you'd expect, and a few you might not. A California state bill that prevents restaurants from offering straws to diners unless they specifically ask for them passed the Assembly last week and will move forward to a Senate vote. Punny campaigns against straws include "Straw Wars" in London and "Straws Suck" in Vancouver. Less smirky pushes include a single-use straw ban proposed for New York Cityor a sweeping edict against all plastic dinnerware in France.
A well-received 2017 documentary on straws may be greasing the regulatory wheels. In Florida, the cities of Surfside, Fort Myers Beach, and St. Petersburg have banned single-use straws, and Miami Beach might expand its limited ban this year. The downside to local regulation, of course, is state preemption, as drinking-straw laws are the kind of easily-mockable nanny-state regulations that tend to draw conservative and libertarian ire. (There may be a class dynamic in the straw standoff, too, with Nalgene-toting elites squaring off against Big Gulp-carrying red staters in yet another front of the culture wars.) A Florida state senator has floated an amendment to preempt local municipalities from banning plastic straws or utensils, in an effort to safeguard Floridians' freedom to suck. The state has already banned any city from banning single-use plastic containers.
Unfortunately, it must be said that current straw alternatives leave much to be desired. Biodegradable straws made of paper or hay pose a specific problem for disabled people who rely on straws, since paper straws don't handle hot liquids or soups very well. They're also more expensive to produce than plastic straws. On the tech front, one startup proposal for a collapsible reusable straw has raised $1.8 million in pledges from 38,000 backers. FinalStraw works like a spring-loaded tube that fits into a carrying case a little larger than a car key fob. While this fix is a bit bigger than pocket sized, it has the advantage of being extremely visible during lunch, a boon to any ostentatious environmentalist.
It might be best if straws would just go away—not out-of-sight-out-of-mind, but off the table entirely. But that may be a tall order: Straws are as old as civilization. The first-known straw was discovered in a Sumerian tomb dated 3,000 B.C., a gold and lapis lazuli number that would make a fashionable and sustainable choice for today's carbon-footprint-minded consumer. Although the first (paper) straw patent was issued in 1888, the straw only truly found its stride in the 1930s, when Joseph B. Friedman invented the bendy straw for improving milkshake circulation.
While the flexible straw has enjoyed nearly 80 years of dominance, one restaurant management company declared last week that it will stop supplying plastic straws at its more than 1,000 campus and museum cafe locations. It may be too much to hope that corporate ethics will come to the rescue: McDonald's is experimenting with compostable straws in the U.K., but shareholders recently voted against conducting a study on single-use plastic straws for other markets. Not a ban—a study.
Until the tide turns against plastic straws, plastic straws will continue to turn up in the tide. The best answer for single-use plastics may be all the answers: taxing or banning these disposables, eliminating car trips in which an iced latte makes oh-so-much sense, and generally trying to use your lips and tongue when circumstances permit. Even design and aesthetics have roles to play, in building straws into reusable water bottles or making standard glasses and ceramic mugs trendy again.
In any case, the straw's position is slipping. Disrupting all the circumstances in which a straw is a given, not merely an option, is at least a possibility that's out there now. Next year, straws might be just a little bit less inescapable than they are today, a little more taboo. If there's one thing that's utterly necessary every summer, after all, it's the ocean.
The Global Crisis of Plastic Pollution
Emily Atkin
There May Soon Be More Plastic in the Oceans Than Fish
Gregory Barber


text:
Q: Prevent Excel's clipboard from "taking over"? I'm an encountering a weird problem with Excel, and it's especially annoying because it wasn't happening yesterday, and hasn't happened ever before. Here's an explanation of what I'm doing:

*

*I copy a cell from a spreadsheet

*I paste the contents into a browser

*A bit later,  I copy something from the browser and attempt to paste it into the spreadsheet

But what happens is that when I attempt to paste the text into the spreadsheet, I just end up pasting the data from the cell that I copied in step 1. It seems that the Office clipboard "takes over" or something. If I clear the selection (using ESC) it just thinks I have nothing copied at all.
Even weirder, if I open the Office clipboard, I can see the URL that I copied from the browser on there, and if I click on it and choose "paste", it pastes the data from the cell I had copied instead. It's like it gives that cell (which is still highlighted with the "ant trail") total priority over everything else.
I'm not sure why this started happening or what I can do to fix it. Any help would be appreciated!
Here's a brief gif I made that shows what I'm talking about.
https://i.gyazo.com/c5f87e5dc231e38f0ef30879a68dd0fb.mp4
I copy the cell with "cats" and paste it into notepad, then copy "asdf" from notepad but when I paste into excel again, it just pastes "cats".
Edit #2: I just remembered that my computer updated and restarted itself overnight, so I'd bet it has something to do with that. Doesn't look like there was a MS Office update though.

A: The "asdf" was never Copied to the Clipboard, Windows or otherwise. It was simply highlighted. Presumably Copied via a keyboard command as the mouse was not used for it. But it never made it to the Clipboard.
If I saw the GIF and in it the mouse right-clicked and chose "Copy" I'd see things differently. But that is not the case.
As to the "not Copied to the Clipboard" I have encountered times when I used Ctrl-C and then tried to paste to Excel, and to other programs, only to get the last thing I Copied before trying that copying. In those cases, I have never, in 30 years of using Windows, been able to get the keyboard copying to succeed. ONLY using the mouse breaks the impasse. After which, no problem, but without, no copying at all.
I believe that to be a mouse and Windows issue as it does not have to involve Excel. So I believe the same thing happened to the poster:  he used the keyboard copying, but it did not occur, hence the "marching ants" never ceasing and accordingly getting the last thing Copied from Excel, not from Notepad.
As I believe it occurs in Windows and is a partial success of the process, but not the worthwhile portion at that, I see no problem with the partial success adding an entry to the Office Clipboard but failing before actually placing the desired material onto the Windows Clipboard, and therefore to the Office Clipboard:  The process fails in between so you do not see the marching ants go away either, along with not replacing the contents with the new Copy.
Will be looking at that the next time I encounter this with Excel instead of another program.

redpajama_set_name: RedPajamaStackExchange


text:
Common Good Beer Company - Brew Pub Review
tags: Beer Brew Pubs
Common Good Beer Company
475 Ellesmere Road
http://commongoodbeer.com/
My Map of Toronto's Brew Pubs
... we're constantly brewing up a rotating cast of Common Good originals.
But beer's a social thing. It's about community. So we also contract brew a
lot of your local favourites, all of which are available in our Craft Brew
store.
The above is from their website, and is important to understanding who and what they are. They're located in a massive industrial space in a strip mall on the northern border between Toronto and Scarborough. The space is occupied 90% by stainless steel brewing tanks, but on the street side of the building by the huge floor-to-ceiling glass, they've installed four or five rough-hewn picnic tables for those who want to test the currently available brews. But that doesn't seem to be their primary business: that would be the contract brewing. Second is the in-house bottle shop. Third and last is people drinking beer on the premises: my friend and I were the only people in there when we arrived at 1800 on Saturday. A couple came in for a short time later, and then the sole employee turned off the "Open" sign a bit before 1900 and started scrubbing the floor in among the vats. The only thing that isn't beer that's for sale is some bags of chips and some t-shirts - no other drinks or food.
I got a flight of four from the six beers on tap: "Hazy" New England IPA, an Imperial IPA, a Doppelbock, and a stout. A couple of these were contract beers (the IPAs?) and a couple were Common Good's own (the Doppelbock and the stout?). I was interested to notice that not only did they not provide IBU ratings, they didn't even provide alcohol content ratings. This turned out to be surprisingly important with this flight, as three out of four of them were probably at or above 10% alcohol and I felt the effects. The Hazy IPA was very good, the Imperial IPA was good with a more complex flavour. The Doppelbock is a style I'm not very familiar with: Wikipedia says a bock "... taste is rich and toasty, sometimes with a bit of caramel ... hop presence is low to undetectable, providing just enough bitterness so that the sweetness is not cloying and the aftertaste is muted." This beer certainly conformed to that description, but a doppelbock has a higher alcohol content and is sweeter. Not bad, but the flavour was too rich for me. The stout was also good.
While their primary role seems to be contract brewer to small local beer companies, they do have drinking on the premises. Check their hours before you go, as they're VERY short (more like a store than a bar). I'd really like to see what's available in their bottle shop listed on their website - as a bottle shop, that would make a lot of sense. But instead you have to take your chances every time you show up - or call in first. Good beers, but not a place that's really meant for drinking.
Prev: 'Saulter Street Brewery' - Brew Pub Review Next: 'The Librarians,' Season 3 - TV Review
http://www.gilesorr.com/blog/common-good-beer.html


After our day in Oudamxay it was off to Luang Namtha. Our bus left at 8:30 and was supposed to be a 3 hour ride. We were once again the only non-locals on the bus which I like much better. We were really cruising along, making good time, until we hit this line of cars not moving. It was on one of those windy mountain roads so you couldn't really see very far, but no one was coming the other way either so there was something wrong ahead. Everyone just was sitting there, some got out and roamed around a bit, but I was so so glad we didn't have other tourists on the bus to complain about the delay.
There was this super friendly guy sitting behind us who was super excited to try out his english skills with us. We sat there for about an hour before we started moving again and then it was a quick ride into town. We didn't have far to go and we passed the problem - a landslide that had to be cleared as it was blocking the road.
When we got to the bus station it is a bit outside of town so we jumped in a tuk tuk with everyone else. There was an older lady who wanted to get dropped off by the one temple so we got there and the tuk tuk pulled over like here you go. She was just like no this isn't right! And everyone else was arguing with her, that this is where she wanted. She wandered off for a bit then came back with some other people and was still like no this isn't right! I don't really know what she wanted, but whatever it was the tuk tuk driver was not giving in. Eventually everyone else was just like leave her! or something. We eventually started going and got dropped off in town.
Now Luang Namtha is not that big. The main road with shops and the market and everything is only a couple blocks long. You can walk farther in either direction, but there isn't much to see. Then lots of side roads with houses and then rice fields bordering the town. There were a ton of puppies though! Every side road had at least 3 puppies wandering around!!
Our hotel was right across the street and seemed to be where everyone who was visiting was staying. There were not that many visitors in town. They had a restaurant so we had lunch there once we got settled - tofu burgers and fries! Pretty tasty and something different after tons of noodles and rice.
It was raining off and on while we were eating, but there was a break in the rain after we finished so we went to explore the town and see what we might want to do the next day.
I'm glad they had this in english as well so I knew what it was! In our exploring we found a jungle trek that sounded like fun so we signed up for that. Then back to the room to laze around and play cards since it was so stormy out.
There was a vegetarian restaurant in town so I wanted to eat there, but it was closed! So we just had dinner at the bakery cafe next to our hotel. More fried noodles! So much food we saved half for breakfast the next morning. When we walked in there was a couple sitting at the table next to the one we sat at and they were just like excuse me, where are you from? Apparently they play a game where they try and guess where everyone is from. I said originally the US, but we live in Germany and the girl was just like yes! I said Germany! But the guy was all, no you said Israel first! I asked what he guess and he thought Switzerland. It was fun.
The next day didn't start out the best. We had a room at the very end of the hall by some houses with roosters and chickens. I didn't think anything of it when I went to bed, but at 3am the rooster started crowing...the windows didn't block out anything. It sounded like it was in the room next to me. Not a problem, I thought, I can block it out. I turned on the fan to high to try and block it out - didn't work. I put in ear plugs as that should block it out. Nope. I couldn't hear anything else, couldn't hear the fan, and the rooster was slightly muffled, but still way too loud. It was driving me crazy!! Me and rooster were not bff. Needless to say I was a bit tired, and luckily we were able to switch rooms for the next night.
Then our jungle trek was supposed to go to a village and learn about their customs and how they make some things, try some things out, then walk through the jungle to the waterfalls. Well that is not what happened. We showed up and things were a bit chaotic, and the guy was just like this will be fun! We are going to be cutting the trail as we go! This is the first time on forever that we have gone on this path! Yeah...I just thought I don't want to do that. But I knew Raymond would enjoy it and they gave him something to cut the path with. Only it wasn't very sharp so he couldn't really do much, but he was excited when we started out.
So we had a guide, someone who lives in the area, but we also got a guide from the village where we started to show us where to go. It actually was good that they were cutting the path as then I could stop and take photos and not fall behind.
Rubber trees. I don't know that I have ever seen them before, definitely not with it dripping out like that. They were at the start of the hike and really neat. Sure I have heard of rubber trees, but didn't realize it came out kind of like maple syrup. Crazy.
Then we stopped for lunch around 11:30 and our guide was like alright. We will eat and then the local guide will head back - I hope we don't get lost! hahaha....So lunch was sticky rice, veggies, tomato jeow, and long beans with a tiny banana for dessert.
After lunch we continued on and didn't end up where we were supposed to.
We had to back track a few times and just wandering all over down different trails until I was just like I don't really care where we go, I just want to get down off the hillside.
And then finally we saw some rubber trees! Then I knew we were almost down.
There was a small cabin and someone tending the rubber trees and we stopped for a short break there. Our guide was talking to him about where he should have gone to end up at the waterfalls.
Once we got out of the rice fields we came across this brick factory which was interesting to look around.
And the ducks and chickens sitting in the ash. They were so silly.
And down the rocky road until we got our tuk tuk. We could have walked 6km more to go down to the waterfalls, but they didn't look amazing and we were both tired so we planned to go see them the next day instead.
We sat and played some cards until dinnertime. The vegetarian place was open so we had some wood fire pizza and potatoes which were both delicious! An adventurous day even if it was not the adventure we were expecting.


text:
In-person classes with covid regulations present challenges for students with disabilities
By Tristan Lorei, contributor
Weeks before students return to Harrisonburg schools and universities for the first time since March, educators have begun implementing safety measures for classes to resume, which includes measures to help students with disabilities navigate the educational landscape amid the pandemic.
JMU, for instance, announced in June its plan to return to in-person classes by inserting three cleaning blocks during the day — twice in the morning and once at night. Face-to-face classes will proceed, especially for first-year students who will be on campus for the first time. Also detailed in the June 8 email announcement was plans to work with the Office of Disability Services to address specific accommodations for students and faculty.
That office, known on campus as ODS, serves students on an individual basis to ensure reasonable accommodations, whether they are aimed at mitigating learning disabilities or physical challenges. These accommodations vary per student but might include, for instance, allowing extra time for taking tests, or if the student has a hearing impairment, ODS would direct the student's professors to provide closed captioning on videos for the class.
Instead of holding individual face-to-face meetings with students as ODS staff members usually do, they now will meet with students over Zoom or Webex to discuss accommodations for the fall.
Raja Abdul-Badee is a student at JMU who is registered with ODS. Abdul-Badee has retinitis pigmentosa, which is a rare disorder that causes the loss of sight over time. ODS provides her with extra time for tests, the ability to use her computer or phone during class and other accommodations to help with her classes.
Abdul-Badee said she isn't concerned that the new fall schedule will affect her accommodations with ODS — but rather her other illness.
"My concerns are health concerns when it comes to my respiratory illness because I do have asthma," Abdul-Badee said. "So, if I do get it, I will have to go to the hospital."
Abdul-Badee said she plans to take as many classes online as she can for the fall semester to avoid making contact with people and to protect herself from getting COVID-19.
Valerie Schoolcraft, the director of disability services, wrote in an email to The Citizen that ODS has begun discussing plans for the new semester and how the safety measures will affect its students.
"Like all programs on campus, we are adjusting the delivery of our services to be able to meet physical distancing guidelines," Schoolcraft wrote. "As in other spaces, we are employing signage and staggering staffing."
For instance, students with hearing impairments often rely on lip-reading so having a teacher wear a mask would hinder their ability to learn in class. One example of a fix for this would be wearing face shields. These are clear plastic shields that are commonly used by healthcare workers and allow the whole face to be seen.
"If for some reason a mask will not work, then we will look at alternative protection options such as face shields," Schoolcraft said. "We will be flexible to meet the needs of the people involved, accomplish the task, and ensure accessibility."
When the COVID-19 pandemic began in March, classes and programs moved online, including programs for students with disabilities.
ODS has programs in place that provide easier access to classwork and materials via technology, such as its Accessible Media and Technology program. The AcMe program provides students with access to resources such as "accessible course materials" and technology to help them. This includes captioning videos — especially when it comes to online classes as well as increasing independent access to reading materials.
ODS has seen the demand for the AcMe program increase over the past few years and works to provide more options for independent access to certain materials.
"We also partnered with our colleagues in the Libraries to increase independent access to reading materials," Schoolcraft wrote. "We were in the process of adding SensusAccess to the list of university resources at the same time the COVID news was unfolding. This service will make it much easier for students and faculty to have accessible materials regardless of the delivery methods for courses."
Harrisonburg High School, like the other city schools, will have students in the building on Mondays, Tuesdays, Thursdays and Fridays with many students alternating days, according to the new plan. (File photo by Tristan Lorei)
City schools's preparation
For Harrisonburg City Public Schools, the possibility of returning to in-person classes presents similar challenges.
Stone Spring Elementary, Waterman Elementary, Thomas Harrison Middle, Skyline Middle and Harrisonburg High School all have programs in place to accommodate needs of students with disabilities as they return to in-person classes.
In a statement to The Citizen after a phone interview, Michael Richards, the superintendent of Harrisonburg City Public Schools, said district leaders have been working on addressing challenges and how they especially affect students who rely on one-on-one and in-person teaching. Under the plan, families of students with special needs will have the option of sending their children to school for up to four days each week. Other students will be limited to two days of in-person classes, according to that plan which the school board approved July 7.
"While all students are better served in personalized, in-person settings, this is especially true for many of our students eligible for special education services," Richards wrote. "The HCPS Return to School Task Force has a Subcommittee that is planning for the most effective use of our buildings in providing instruction and related services for some of our most vulnerable students."
Richards said school districts have "received essentially no guidance from the U.S. Department of Education, which governs special education" but instead has relied on state guidelines as the district drew up its plan.
EMU's campus quad is quiet after the pandemic moved classes online. (File photo by Tristan Lorei)
EMU's preparation
EMU has begun discussions as well to plan for in-person classes this fall. Steve Yoder, the coordinator of academic access at EMU, says that with new social distancing and mask-wearing policies in place, accommodations for students with disabilities will continue on an individual basis.
"Accommodations are always offered on an individual student basis," he said. "I fully anticipate that new needs will emerge this fall as we continue in our hybrid online format that haven't emerged before."
college studentscovid-19EMUHarrisonburg City Public SchoolsJMUOffice of Disability Servicesstudents with disabilities
Tristan Lorei, contributor
Tristan is a photojournalist set to graduate from James Madison University in the fall of 2020. He loves photography's ability to capture fleeting moments in time, preserve them and use them to tell a story. He plans to continue his career in photojournalism after he graduates and continue to meet and tell the stories of people across the country that he wouldn't hear otherwise.