text:
New technologies are changing humanitarian action, but don't assume they're inclusive
Written by John Bryant
Hero image description: Drones in humanitarian action, Malawi, 2018.© European Union/Anouk Delafortrie. CC BY-NC-ND 2.0.
The promise of new technology to meet the needs of people in humanitarian crises has been in the news recently, but not always for the right reasons.
What stories such as non-functioning 'food computers' and dubious assertions of being an early adopter of drone technology in disaster response have in common is that their advocates successfully tapped into the sector's enthusiasm towards, and often uncritical adoption of, new technologies that often promise a lot, but deliver little.
Humanitarian organisations have long sought to apply the latest technologies to better meet the challenges of disaster and conflict response, and this eagerness has only increased in recent years. Various technologies promise more accurate targeting and a reduction in fraud and corruption to ensure that aid is going where it's needed most.
The seductive appeal of tech-based solutions
Perhaps more cynically, tech-based solutions are also attractive because they make competing organisations look 'innovative' and 'high-impact' in the eyes of donors and the public. Some are presented as a 'quick fix' to the challenges of humanitarian response – fixes that don't require grappling with the long-term, complex political, social and economic drivers of crises.
The result has been a proliferation of technology-based tools and approaches in humanitarian contexts. The vast majority come from a genuine desire for positive change in the way assistance is delivered. However, their users often make ambitious promises and assumptions about who benefits, particularly when it comes to including the people most vulnerable in a humanitarian crisis.
Inclusivity in the digital age
Inclusion is an important goal for the humanitarian sector, but it has proved difficult to achieve in practice.
While careful adaptation of existing tools has been used to increase coverage and inclusion – such as participatory mapping of communities by residents of informal settlements, training drone pilots in affected countries or messaging applications disseminating information to displaced people – these benefits are still too often assumed as a natural consequence of adopting technology-based approaches.
In reality, differences in access to and use of technology, often along gender, income or racial lines, constitute a 'digital divide' that means the benefits of these approaches are not evenly distributed, and leave many excluded.
Inclusion is also limited by in-built biases in many applied technologies – for instance facial recognition software, whose 'coded gaze' has not been taught to recognise diverse datasets of faces, or automated mapping technologies without the contextual understanding to recognise houses in disaster-affected areas.
These examples reinforce the idea that technologies, like the humanitarian organisations using them, are not 'neutral', but a product of the perspectives, priorities and biases of their developers.
Technology can entrench power inequalities
Uncritically adopting technologies in crises may reinforce the ingrained power dynamics of the sector or violate humanitarian principles, either through a shift to digital registration unintentionally excluding those most in need, or humanitarian independence being compromised through partnerships with the private sector, including the surveillance and security industry.
Instead, these new tools will require active correction and contextual knowledge to be adapted to particular humanitarian crises, in order to include and protect the people humanitarian assistance is intended to serve. In some cases, tools such as biometric registration or mapping of improvised settlements may not be appropriate, with poor data protection practices presenting unacceptable risks to populations made vulnerable by persecution, conflict or displacement.
Learning from past experience is crucial
The missing part of the story of technology, inclusion and humanitarian crisis is learning the lessons of previous initiatives and assessing the impact of technologies that have been implemented at scale. Tools such as spatial mapping increased in prominence following the volunteer mapping movement in the Haiti earthquake response a decade ago, and five years have passed since UNCHR began the roll-out of its biometric identification system.
The widespread adoption of such technologies since then has already significantly changed humanitarian responses, including how needs are identified and assistance is distributed.
While these tools have also created new considerations for humanitarian protection, many in the sector still misunderstand the magnitude of the risks involved, and the implications such technologies present for the power dynamics of the sector remain under-analysed.
At the Humanitarian Policy Group we've considered these issues in a new working paper. It marks the beginning of a research programme on inclusion that will explore the impact of these technologies, how they have changed the design and delivery of humanitarian responses – and whether their promise to reach the most vulnerable in crises is borne out in practice.
Senior Research Officer
Humanitarian system


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Bangkok, former Prime Minister Yingluck Shinawatra to be tried for negligence
The Supreme Court orders the trial for her role in the controversial rice subsidy scheme. If convicted, she faces up to 10 years in prison. The politician denies the charges. For critics it is just the latest in a series of establishment attacks on Shinawatra.
Bangkok (AsiaNews / Agencies) - Thailand's Supreme Court has indicted former Prime Minister Yingluck Shinawatra for "negligence", for her role in the controversial subsidy scheme for rice production.
According to prosecutors the program, aimed at buying votes, cost billions of dollars taken from state coffers; the former prime minister has always strongly rejected any wrongdoing. The first woman to head a government in the Asian country, Yingluck - sister of former prime minister and billionaire Thaksin, in exile to escape a two-year sentence for corruption - could face up to 10 years in prison if convicted.
According to some analysts, the judges' go-ahead for the indictment is just the latest in a long series of attacks by the judiciary and the government on the Shinawatra empire, which for more than a decade dominated Thai politics, thanks to the large consensus among a substantial part of the population. However, the elite of the capital accuse the family of corruption and have long waged a battle - in the political and judicial - to eliminate the clan from the public life in the country.
The former prime minister was deposed from office in May following a military coup. The Army's show of force put an end to months of street protests by movements close to the establishment and urban elite: those calling for the resignation of an executive deemed "incompetent and populist."
On January 23, the Parliament voted for the impeachment of the former head of the government and a ban for five years from active politics. This was followed by the opening of a criminal case against Yingluck, for "negligence" and "corruption".
Now the country - at the crossroads in its history, with an issue of succession to the throne - is under the control of the military, with the head of the Armed Forces appointed Prime Minister with the task of reforming the state. However, the Army appear to be ignoring the content of the reform with the risk of a creeping authoritarianism. In fact it was the current prime minister who masterminded and led the bloody repression of 2010, but no member of the armed forces has ever been brought to trial.
Yingluck
Shinawatra
Thailand's Constitutional Court keeps Prayut in power
Bangkok, more legal woes for ex- Prime Minister Yingluck Shinawatra
Thai army imposes martial law, censors media as stock market crashes
Thaksin Shinawatra's shadow hangs over premier-elect Yingluck
Thai PM resigns out of respect for the king

redpajama_set_name: RedPajamaCommonCrawl


This massive walk-out rambler with 10 acres and in-ground heated pool, pool house, horse barn, & work shop. Only 30 mins from downtown Mpls &10 mins from Elk River Train Station. Great Rambler, beautiful private home w/ spacious finished lower level including roughed in 4th bedroom in LL. The property can accommodate up to 9 horses. indoor box stalls, tool crib, hay storage. Fence around horse paddock.


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Lachau  es una población y comuna francesa, en la región de Auvernia-Ródano-Alpes, departamento de Drôme, en el distrito de Nyons y cantón de Séderon.

Demografía

Referencias

Enlaces externos

 INSEE

Localidades de Drôme

redpajama_set_name: RedPajamaWikipedia


Just how heavy is your child's school bag?
I often ask parents how heavy their children's school bag is and the reply almost every time is 'far too heavy'. A great new research paper has just come out titled "The weight of pupils' schoolbags in early school age and its influence on body posture". I will summarise points below and there is also a link to the paper (full text is available) at the bottom of this post.
The study looked at 168 children aged 7-9 over a period of 1 year and looked at school bag weight, length of straps and certain body posture measurements.
If you have any concerns about the effects of your child's backpack on their spinal health, bring them in to see one of the chiropractors here at Mona Vale Chiropractic Centre.


Idaho's October 10th reporting deadline showed who is truly behind our opposition–United Against Prop 1. The opposition is being funded by the Coeur d'Alene Tribe. Yes, you read that right. The people who are trying to tell you that HHR is bad for Idaho are funded by big casino money.


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12 Wright Ct
-- Beds, -- Baths, 2,437 sqft
RE/MAX Best Realty
Your info has been successfully sent to Bruce Parker.
12 Wright Ct is a single family residence located in East Brunswick, NJ 08816. Built in 1985, this property features 7,501 sq ft lot, and 2,437 sq ft of living space. The estimated market value for 12 Wright Ct is $457,000.
For the surrounding community of East Brunswick, NJ 08816, the average sale price for similar homes to 12 Wright Ct is $457,703. The nearby schools are excellent and include East Brunswick High School, Churchill Jr High School and Hammarskjold Middle School. For this area, there are 1 criminal and sex offenders residing within 1 mile. The natural disaster risk for this area includes very low earthquake risk, low tornado risk, and minimal flood risk.
The price that the current owner purchased the property for.
Property Details: 12 Wright Ct
Lot Size: 7,501 sqft
Parcel Number: 0400087 0800042
Subdivision: COLONIAL OAKS VILLAGE SEC 01-A
Tract: 6500
Zoning: VG1
Cooling Type: NP
7/24/2007 Sold $495,000 $203 Public Records
2018 $13,053 (+10.96%) $25,000 $94,000 $119,000
2015 $12,259 (+10.3%) $25,000 $94,000 $119,000
2014 $11,537 (+9.69%) $25,000 $94,000 $119,000
2012 $10,949 $25,000 $94,000 $119,000
10 Wright Ct, East Brunswick, NJ 08816
17 Vreeland Ct, East Brunswick, NJ 08816
8 Wright Ct, East Brunswick, NJ 08816
3 loans found for this home view hide sample
Comparable Sales$457,703 AVG SALES Price
The average sales price of homes similar to 12 Wright Ct is $457,703 ($188/sq.ft.)
Address Sold Price Sold Date Price/sq ft Sq.Ft. Beds, Baths Distance
71 Tall Oaks Dr $525,000 06/28/2019 $214 2,454 sq.ft. -- Bed, -- Bath 1.2 mi away
291 Rues Ln $399,000 06/25/2019 $170 2,344 sq.ft. -- Bed, -- Bath 0.6 mi away
7 Barton Ct $325,000 06/19/2019 $136 2,389 sq.ft. -- Bed, -- Bath 1.5 mi away
70 Overhill Rd $498,500 06/18/2019 $221 2,252 sq.ft. -- Bed, -- Bath 1.5 mi away
11 Deer Run Ct $480,000 06/12/2019 $205 2,344 sq.ft. -- Bed, -- Bath 2 mi away
10 Raven Ct $442,000 06/11/2019 $170 2,599 sq.ft. -- Bed, -- Bath 0.9 mi away
20 Southerland Dr $505,000 06/06/2019 $208 2,430 sq.ft. -- Bed, -- Bath 1.4 mi away
8 Fieldcrest Dr $480,000 06/06/2019 $185 2,600 sq.ft. -- Bed, -- Bath 0.6 mi away
40 Tall Oaks Dr $465,000 05/30/2019 $181 2,569 sq.ft. -- Bed, -- Bath 1 mi away
10 Thrush Dr $450,000 05/28/2019 $187 2,410 sq.ft. -- Bed, -- Bath 0.9 mi away
12 Packard Rd
11 Noel Ln
75 Deerfield Rd
14 Willis Ct
157 Dutch Rd
Situated at 12 Wright Ct, East Brunswick, NJ 08816, this is a Single Family Residence with and approximately 2,437 square feet of living space and a 7,501 square foot lot. The property was built in 1985 and is in the neighborhood of Middlesex County, New Jersey.
During the month of 06/2019, a total of 14 properties had foreclosure filings in the 08816 zip code surrounding 12 Wright Ct, with one in every 1,207 housing units receiving a foreclosure filing. In Middlesex County, where 12 Wright Ct, East Brunswick, NJ 08816 is located, there were 183 properties with foreclosure filings documented during the month of 06/2019, a foreclosure rate of one in every 1,638 housing units. In New Jersey, one in every 1,191 housing units had a foreclosure filing in 06/2019, while one in every 2,814 housing units had a foreclosure filing nationwide.


Room additions are a specialty at KBC Remodel Services. We are a design and build general contractor which means we have the capability to take your home addition from concept to completion!
Room additions are a great way to increase your living space and add value to your Longmont area home. Building onto an existing structure requires knowledge of all the elements of a new structure from top to bottom. We have done so many home additions we have become adept at blending new and existing materials to provide continuity with your homes existing exterior. We arrange all needed paperwork– permits and inspections–and supervise all phases of the project, including the essential services of plumbing, electrical, and HVAC. Down to the last detail, smooth and painless for homeowners.
KBC Remodeling Services will always provide the best possible home addition workmanship along with using top quality materials. We genuinely care about customer's needs and we aim for complete customer satisfaction on every job.
If you're a homeowner in Longmont or the surrounding area looking to upgrade with a beautiful home addition, don't hesitate to call us and learn more about how we can help make that happen.


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\section{Introduction}

The classification of compact, connected symplectic toric manifolds by their moment images was completed by Delzant in 1988 \cite{D}. Since then, a number of extensions of Delzant's Theorem have been proved. Notably, a classification of compact, symplectic toric {\em orbifolds} was given by Lerman and Tolman in \cite{LT} and, more recently, Karshon and Lerman classified {\em noncompact} symplectic toric manifolds (\cite{KL}). Generally speaking, classification results of this kind rely on existence and uniqueness results: for each classifying gadget one must show there exists a corresponding class of manifolds and that, up to some topological restriction, this class contains only one isomorphism type.  This paper deals with a different type of extension of Delzant's results. Instead of changing the general assumptions about the manifold, we instead focus on properties of the differential form. Namely, we consider {\em folded symplectic forms}.

A folded symplectic form is, colloquially, a closed two-form that is symplectic away from a hypersurface, $Z$, in a $2n$-dimensional manifold, $M$, whose degeneracies are reasonably well-controlled on $Z$. Here is the precise definition.

\begin{definition}
Let $\omega$ be a two-form on $M^{2n}$ such that the top exterior power, $\omega^n$, is transverse to the zero section of the orientation bundle $\bigwedge^{n}(T^*M)$. The zero locus, $Z:=(\omega^n)^{-1}(0)$, is then a codimension one submanifold of $M$. Let $i:Z \hookrightarrow M$ be the inclusion. If $i^*\omega^{n-1}$ is nonvanishing on $Z$, the two-form $\omega$ is a {\bf folded symplectic form}. A {\bf folded symplectic manifold} is a pair $(M,\omega)$ where $\omega$ is a folded symplectic form on the manifold $M$. The hypersurface $Z$ is called the {\bf fold}. The complement, $M/Z$ of the fold is the {\bf symplectic locus}. A {\bf folded symplectomorphism} between folded symplectic manifolds $(M,\omega)$ and $(M',\omega')$ is a diffeomorphism $f:M \to M'$ such that
\begin{displaymath}
f^*\omega' = \omega.
\end{displaymath}
\end{definition}

The theory of folded symplectic forms has some similarity with that of symplectic forms, but there are some important and striking differences.

\begin{example}\label{foldedsympex}
\begin{enumerate}
\item The two-form
\begin{displaymath}
\omega_{\textrm{fstd}}=x_1dx_1\wedge{dy_1}+\sum_{j=2}^{n}dx_j \wedge dy_j
\end{displaymath}
is the standard folded symplectic form on real Euclidean space
\begin{displaymath}
\mathbb{R}^{2n} = \{(x_1,\ldots,x_n,y_1,\ldots,y_n) \hspace{1pt} | \hspace{1pt} x_j,y_j \in \mathbb{R}\}.
\end{displaymath}
The fold is the hypersurface $\{x_1=0\}$. By pulling $\omega_{\textrm{fstd}}$ back by a choice of isomorphism,  any even dimensional vector space admits a folded symplectic form. In particular, the standard folded symplectic form on $\mathbb{C}^n$ is
\begin{displaymath}
\frac{i}{2}\Re(z_1)dz_1\wedge d\bar{z}_1 + \frac{i}{2}\sum_{j=2}^{n} dz_j \wedge d\bar{z}_j.
\end{displaymath}

\item Let $\Sigma$ be a closed, orientable surface and $\Omega$ a nonvanishing two-form on $\Sigma$. Let $f:\Sigma \to \mathbb{R}$ be a smooth function transverse to $0 \in \mathbb{R}$. Then, $f\Omega$ is a folded symplectic form on $\Sigma$.  For example, the two-form $\omega=hdh\wedge{d\theta}$ is a folded symplectic form on the sphere $S^2$ with fold $\{h=0\}$.

The antipodal map
\begin{eqnarray*}
f:S^2 &\to& S^2 \\
(h,\theta) & \mapsto & (-h,\theta+\pi)
\end{eqnarray*}
satisfies $f^*\omega = \omega$ and so $\omega$ descends to give the quotient  $S^2/f$ the structure of a folded symplectic manifold. This quotient is diffeomorphic to the real projective plane $\R\mathbb{P}^2$ and so, in contrast to symplectic manifolds, folded symplectic manifolds need not be orientable.

\item Cannas da Silva, Guillemin, and Woodward show (in \cite{dSGW}), that every even-dimensional sphere, $S^{2n}$, has a folded symplectic form obtained by pulling back the standard symplectic form on $\mathbb{R}^{2n}$ by the map on $S^{2n}$ that folds about a great circle. Note that a sphere admits a symplectic form if and only if it is two-dimensional.

\item In \cite{CdS2}, Cannas da Silva proves that every orientable four-manifold admits a folded symplectic structure. This result indicates that folded structures are natural, ubiquitous, and worthy of further study.

\item If $(M,\omega)$ is a folded symplectic manifold  and $(N,\eta)$ is a symplectic manifold, then $M \times N$ is a folded symplectic manifold with fold-form $\omega \oplus \eta$. Note, however, that the product of two arbitrary folded symplectic manifolds may not be a folded symplectic manifold: the form $h_1dh_1\wedge d\theta_1 + h_2dh_2\wedge d\theta_2$ is {\em not} a folded symplectic form on $S^2 \times S^2$ since the second wedge power is not transverse to the zero section of $\bigwedge^{2n}(T^*(S^2 \times S^2))$.
\end{enumerate}
\end{example}

By Darboux's Theorem, we know that every symplectic manifold looks locally like $\mathbb{R}^{2n}$ with its standard symplectic form. Similarly, there is a local normal form theorem for folded symplectic manifolds. Following \cite{dSGW}, we assume that $M$ is an {\em oriented} folded symplectic manifold and define a vector bundle $\ker(\omega) \to Z$ by setting
$$
\ker(\omega)_{z} = \{X \in T_{z}M \hspace{2pt} | \hspace{2pt} \iota_{X}\omega_{z} = 0 \}
$$
for each $z \in Z$. This is a rank two bundle and is oriented over $Z$ via the orientations induced on $i^*TM/\ker(\omega)$ by $\omega$ and that of $TM$. Using the inclusion $i:Z \to M$, we regard $TZ$ as the subbundle of $TM$ of vectors tangent along $Z$. Then, the intersection $\ker(\omega) \cap TZ \to Z$ is an oriented line bundle of tangent vectors along $Z$. We also note that
$$
T_{z}Z+\ker(\omega)_{z} = T_{z}M
$$
since the kernel of $\omega_{z}$ is two-dimensional and $\omega^{n-1}$ is nonvanishing on $Z$. The following it our version of the statement of Theorem 1 in \cite{dSGW}.

\begin{theorem}\label{thmoneindSGW}
Let $(M,\omega)$ be a compact, oriented, folded symplectic manifold with fold $Z$. Choose a positively oriented section $V$ of $\ker(\omega)\cap TZ$. Then, for any $\alpha \in \Omega^{1}(Z)$ with $\alpha(V) \equiv{1}$, there exists a neighborhood $U$ of $Z$ and a diffeomorphism $\psi:Z\times{\mathbb{R}} \to U$ such that $\psi^*\omega = p^*i^*\omega+d(t^2p^*\alpha)$ where $p:Z\times{\mathbb{R}} \to Z$ is projection on the first factor and $i:Z \to Z\times{\mathbb{R}}$ is the inclusion.
\end{theorem}

For the remainder of this paper, our focus will be on Hamiltonian actions of tori on folded symplectic manifolds.

\begin{definition}
An action of a Lie group $G$ on a folded symplectic manifold $(M,\omega)$ is a {\bf folded Hamiltonian action} if there is a {\bf moment map}. That is, for every $\xi$ in the Lie algebra $\mathfrak{g}$ of $G$ there exists a smooth function $\Phi: M \to \mathfrak{g}^*$ that is equivariant with respect to the coadjoint action of $G$ on $\mathfrak{g}^*$ and is such that $\iota(\xi_{_M})\omega = -d\Phi^{\xi}$. (Here, $\xi_{M}$ is the vector field on $M$ induced by $\xi$, {\em i.e.}, $\xi_M = \left.\frac{d}{dt}\right|_{t=0} \exp{(t\xi)}$.) A folded symplectic manifold admitting a folded Hamiltonian action of a Lie group $G$ will be called a {\bf folded Hamiltonian $G$-manifold} and we denote such via a triple $(M,\omega,\Phi)$. An {\bf isomorphism} of folded Hamiltonian $G$-manifolds $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ is an equivariant folded symplectomorphism $\psi:M \to M'$ such that $\psi^*\Phi' = \Phi$.   For a torus $\mathcal{T}$, a {\bf folded symplectic toric manifold} is a compact, connected, folded Hamiltonian $\mathcal{T}$-manifold $(M,\omega,\Phi)$ such that the torus action is effective and $2\dim{\mathcal{T}}=\dim{M}$.
\end{definition}

\begin{remark}
The assumption that a folded symplectic toric manifold be connected is included for convenience. However, unless otherwise specified, we will assume that a folded symplectic toric manifold is compact.
\end{remark}

\begin{comment}
\begin{remark}
Note that if a Lie group $G$ acts on a folded symplectic manifold $(M,\omega)$ preserving the folded symplectic form, the action also preserves the fold $Z$.
\end{remark}
\end{comment}

Since the torus is Abelian, the coadjoint action of $\mathcal{T}$ on the dual Lie algebra $\mathfrak{t}^*$ is trivial. Hence, the moment map $\Phi:M \to \mathfrak{t}^*$ of a folded symplectic toric manifold is invariant and thus descends to a map
\begin{displaymath}
\underline{\Phi}:M/\mathcal{T} \to \mathfrak{t}^*
\end{displaymath}
called the {\bf orbital moment map}. The orbital moment map has the same image in $\mathfrak{t}^*$ as the moment map; that is, $\Phi = \underline{\Phi} \circ \pi$ where $\pi:M \to M/\mathcal{T}$ is the orbit projection.

A general classification of folded symplectic toric manifolds is not yet complete. A certain subclass, however, has been classified. In \cite{CdSGP}, Cannas da Silva, Guillemin, and Pires classify the so-called {\em origami manifolds}, which are orientable folded symplectic toric manifolds having extra conditions regarding the restriction of the fold form to the folding hypersurface. In what follows, we present a first step in the classification of folded symplectic toric manifolds, a uniqueness result in the case of compact, orientable, four-dimensional manifolds. Our main theorem follows.

\begin{theorem}\label{maintheorem}
Let $(M, \omega, \Phi)$ and $(M', \omega', \Phi')$ be orientable folded symplectic toric four-manifolds. Suppose that $H^2(M/\mathcal{T}; \mathbb{Z})=0$. Then, $M$ and $M'$ are isomorphic if there exists a diffeomorphism $h:M/\mathcal{T} \to M'/\mathcal{T}$ of manifolds with corners such that $h^*\underline{\Phi}' = \underline{\Phi}$.
\end{theorem}

We will prove this theorem in two steps. The first establishes a condition under which folded symplectic toric manifolds are locally isomorphic. We then turn to questions of global isomorphisms. In the last section, we provide a proof of Theorem \ref{maintheorem} by passing our local results to the global setting.

\section{The Local Picture}\label{localsection} In this section, we establish the existence of local equivalence of folded symplectic toric four-manifolds given a diffeomorphism of orbit spaces that preserves the orbital moment maps.  The first step is understanding the differential structure of the orbit space. We then use that structure to help in determining when two folded symplectic toric four-manifolds are locally isomorphic, as defined below.

\begin{definition}
Let $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ be folded symplectic toric manifolds. Denote by $\pi:M \to M/\mathcal{T}$ and $\pi':M' \to M'/\mathcal{T}$ the orbit maps. We say that $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ are {\bf locally isomorphic} if there exists a diffeomorphism $h:M/\mathcal{T} \to M'/\mathcal{T}$ such that for each $x \in M/\mathcal{T}$, there exists a neighborhood $U$ of $x$ and an isomorphism
$$
\psi_{x}:\pi^{-1}(U) \to (\pi')^{-1}(h(U))
$$
of (open) folded symplectic toric manifolds such that $(h \circ \pi)(p) = (\pi' \circ \psi_{x})(p)$ for every $p \in \pi^{-1}(U)$.
\end{definition}

\begin{remark}\label{orbitpreservingismomentpreserving}
When two folded symplectic toric manifolds $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ are locally isomorphic, it can be convenient to identify their orbit spaces via a choice of diffeomorphism that lifts locally to isomorphisms. When this is done, we can write $\phi' = \underline{\Phi} \circ \pi'$ where $\pi':M' \to M/\mathcal{T}$ is the orbit projection and $\underline{\Phi}:M/\mathcal{T} \to \mathfrak{t}^*$ is the orbital moment map.
\end{remark}

\subsection{The structure of the orbit space}  We certainly cannot expect the orbit space of a folded symplectic toric four manifold to be a manifold itself, but there is a differential structure on the orbit space that we may exploit. In particular, we will show that the orbit space is a {\bf manifold with corners}. Briefly, a manifold with corners is a second countable Hausdorff space with a maximal atlas of charts modeled on sectors $[0,\infty)^k \times \mathbb{R}^{n-k}$ with $0 \leq k \leq n$. The reader is referred to Appendix A of \cite{KL} for more details.  To establish such a differential structure on the orbit space, we proceed as follows. At points not in the fold, we may appeal to well-known results from symplectic geometry. At points in the fold, however, it is necessary to know the types of stabilizer subgroups that can appear. We begin by observing that, in the fold, orbits may be stabilized by a circle subgroup of the torus.

\begin{example}\label{circlestabilizers}
Consider the product $S^2 \times S^2$, equipped with local coordinates $(h_1,\theta_1,h_2,\theta_2)$, $-1 \leq h_j \leq 1$.  This is a folded symplectic manifold with folded symplectic form $\omega = h_1dh_1 \wedge d\theta_1 + dh_2\wedge d\theta_2$. The fold is the copy of $S^1 \times S^2$ defined by $\{h_1=0\}$.  The folded symplectic form is invariant under the action of the two-torus given by
$$
(\lambda_1,\lambda_2)\cdot(h_1,\theta_1,h_2,\theta_2) = (h_1,\theta_1+\lambda_1,h_2,\theta_2+\lambda_2).
$$
In fact, this is a folded Hamiltonian action with moment map
$$
\Phi(h_1,\theta_1,h_2,\theta_2) = \left(\frac{1}{2}h_1^2,h_2\right).
$$
The circle $S^1$ stabilizes every point in $\Phi^{-1}(0,1)$.
\end{example}

The other stabilizers that can appear in the fold are limited. In particular, the following result states that, at least in dimension four, no nontrivial discrete subgroup of the torus can stabilize points in the fold. This in turn implies that for a four-dimensional folded toric symplectic manifold, the set of free orbits is dense (Theorem 4.27 in \cite{Ka}).

\begin{lemma}\label{nofixedpoints}\label{principalorbitsarefree}
Suppose a torus, $\mathcal{T}^n$, acts effectively on a connected, orientable manifold, $M^{2n}$, preserving a hypersurface $Z$. Then, there are no fixed points of the action in $Z$. Furthermore, if $M$ is four-dimensional, the only discrete subgroup of $\mathcal{T}^n$ stabilizing points in the fold is the trivial subgroup.
\end{lemma}

\begin{proof}
By the Slice Theorem, there is a neighborhood $U$ of an orbit in $M$ that is equivariantly diffeomorphic to $\mathcal{T} \times_{G_p} \mathcal{V}_{p}$ where $p$ is any point in the orbit, $\mathcal{V}_p$ is the differential slice at $p$, and $G_p$ is the stabilizer of the point $p$. Since the torus acts effectively on $M$, it acts effectively on $U$, hence on $\mathcal{T}\times_{G_p}\mathcal{V}_p$. Since the torus is Abelian, the isotropy action of $G_p$ on $\mathcal{V}_p$ is effective. If $p$ is a fixed point, then $G_p=\mathcal{T}$. So, if $p\in Z$, by utilizing a choice of invariant metric, we get a faithful representation
$$
\mathcal{T}^n \hookrightarrow O(2n-1) \times O(1)
$$
since $Z$ is an invariant hypersurface. The torus is connected, and so the image lies in $SO(2n-1)$. Since the maximal torus in $SO(2n-1)$ has dimension $n-1$, we have arrived at a contradiction. Hence $p$ cannot be a fixed point in $Z$.

Now suppose that $\dim{M}=4$ and let $H$ be a  nontrivial discrete subgroup of $\mathcal{T}$ stabilizing a point $p \in Z$. Again by the Slice Theorem, there is a neighborhood of an orbit through $p$ is equivariantly diffeomorphic to $U=\mathcal{T} \times_{H} (\mathbb{R} \times \mathbb{R})$. Since $M$ is orientable, so are $U$ and $Z$. We then have a faithful representation $H \hookrightarrow SO(1) \times SO(1)$ and conclude that $H$ is trivial. \end{proof}

We are now in a position to prove the following.

\begin{prop}\label{orbitspaceisamanifoldwithcorners}
Let $(M,\omega,\Phi)$ be an orientable, folded symplectic toric four-manifold. Then, the orbit space $M/\mathcal{T}$ is a smooth surface with corners, wherein the fold $Z$ descends to a one-dimensional submanifold with boundary.
\end{prop}

\begin{proof}
On the components of the symplectic locus $M\setminus{Z}$ the result follows by the local normal form theorem for symplectic toric manifolds (Proposition 1.1 in \cite{KL}). On the fold $Z$, Lemma \ref{nofixedpoints} and Example \ref{circlestabilizers} assert that the only possible stabilizers are $S^1$ and the trivial subgroup. A neighborhood of a point in the orbit space with trivial stabilizer is homeomorphic to an open two-disk. If the orbit corresponding to a point in $Z/T$ has a circle stabilizer, then it has a neighborhood homeomorphic to $\mathbb{R}^2/S^1\times \mathbb{R} = [0,\infty) \times \mathbb{R}$.
\end{proof}

\subsection{Local equivalence of folded symplectic toric manifolds}
Local models for neighborhoods of orbits through points in a folded symplectic toric manifold $(M,\omega,\Phi)$ depend necessarily on whether the point lies in the symplectic locus $M\setminus{Z}$ or in the fold $Z$. Knowing the image of the moment map is not enough to specify the local structure of an arbitrary folded symplectic toric manifold; we must also incorporate information about the orbital moment map. Critical to this is the fact that orbits are isotropic. Recall that a submanifold $L$ of a manifold $N$ equipped with a two-form $\Omega$ is {\bf isotropic} if $\Omega|_{L}$ vanishes.

\begin{prop}\label{orbitsareisotropic}
Orbits in a folded Hamiltonian $\mathcal{T}$-manifold $(M,\omega,\Phi)$ are isotropic.
\end{prop}
\begin{proof}
Since $\mathcal{T}$ is Abelian, the moment map $\Phi:M \to \mathfrak{t}^*$ is invariant and hence constant on orbits. Therefore, for any $\xi,\zeta \in \mathfrak{t}$ and $p \in M$,
\begin{eqnarray*}
0 &=& \iota(\xi_{_M}(p))d\Phi_{p}^{\zeta} \\
&=& \omega_{p}(\xi_{_M}(p),\zeta_{_M}(p)).
\end{eqnarray*}\end{proof}

\begin{lemma}\label{Vtangenttoorbits}
Let $(M,\omega,\Phi)$ be an orientable, folded symplectic toric four-manifold. If $V$ is a section of $\ker(\omega) \cap TZ$, then $V$ is tangent to orbits in $Z$.
\end{lemma}
\begin{proof}
We first consider a neighborhood of a free orbit $\mathcal{T} \times \mathbb{R}$ in $Z$ with coordinates $(\theta_1,\theta_2,s,0)$. By Proposition \ref{orbitsareisotropic}, orbits are isotropic so the restriction of the folded symplectic form to this orbit is
\begin{eqnarray*}
i^*\omega &=& f_1d\theta_1\wedge{ds}+f_2d\theta_2\wedge{ds} \\
&=& (f_1d\theta_1+f_2d\theta_2)\wedge{ds}
\end{eqnarray*}
where $f_1$ and $f_2$ are invariant functions. It follows that if $V$ is in the kernel of $i^*\omega$, then  $V$ is tangent to the orbit.

Now we consider singular orbits. By Proposition \ref{orbitspaceisamanifoldwithcorners}, the orbit space $Z/\mathcal{T}$ is a compact one-manifold whose boundary components are images of singular orbits under the orbit map. Since the boundary of a compact one-manifold consists of isolated points and the orbit map is continuous,  singular orbits are isolated in $Z$. Pick a singular orbit $\mathcal{O}$ in $Z$ and suppose $V$ is a section of $\ker(\omega) \cap TZ$ that is not tangent to $\mathcal{O}$. Since the orbit is isolated, there exists a neighborhood $U$ of $\mathcal{O}$ whose intersection with the set of singular orbits contains only $\mathcal{O}$. Let $\phi_{t}$ denote the flow of $V$. Then, since $V$ was assumed not to be tangent to $\mathcal{O}$ and free orbits are dense by Lemma \ref{principalorbitsarefree},  if $x \in \mathcal{O}$ there exists $\epsilon >0$ such that  $\phi_{\epsilon}(x) \not\in \mathcal{O}$ and $\phi_{\epsilon}(x)$ lies in a free orbit $\mathcal{F}$. Since $V$ is tangent to free orbits and $\mathcal{T}^2$ is compact, $\phi_{t}(x) \in \mathcal{F}$ for all $t \in \mathbb{R}$. This contradicts the fact that $\phi_{-\epsilon} \in \mathcal{O}$. Hence, $V$ is tangent to the singular orbit $\mathcal{O}$.   \end{proof}

In order to get local isomorphisms of folded symplectic toric manifolds, we need a diffeomorphism of orbit spaces that lifts locally to isomorphisms. We now show that any diffeomorphism of orbit spaces that preserves the orbital moment maps also preserves orbital folds.

\begin{lemma}\label{orbitdiffeospreserveZ}
Let $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ be orientable, folded symplectic toric four-manifolds. Suppose $h:M/\mathcal{T} \to M'/\mathcal{T}$ is a diffeomorphism such that $h^*\underline{\Phi}' = \underline{\Phi}$. Then, $h(Z/\mathcal{T}) = Z'/\mathcal{T}$.
\end{lemma}
\begin{proof}
Choose $p \in \pi^{-1}(x)$ and consider
\begin{eqnarray*}
F:\mathfrak{t} &\to& T^*_pM \\
\xi &\mapsto& \iota(\xi_{_M})\omega_{p}.
\end{eqnarray*}
This map is the transpose of
$$
d\phi_{p}:T_pM \to\mathfrak{t}^*
$$
since $\langle d\Phi(Y),\xi \rangle = \omega(\xi_{_M},Y)$ for any vector field $Y$ on $M$. It follows that the image of $d\Phi_p$ is isomorphic to the annihilator in $\mathfrak{t}^* $ of the kernel of $F$. The kernel of $F$ consists of vectors in the stabilizer algebra $\mathfrak{t}_{p}$ as well as any $\xi \in \mathfrak{g}$ with $\xi_{_M}(p) \in \ker(\omega)_p$. By Lemma \ref{Vtangenttoorbits}, any nonzero vector spanning $\ker(\omega)_p \cap T_pZ$ lies in the image of the map $\mathfrak{g} \to T_pM$ given by $\xi \mapsto \xi_{_M}(p)$.  Hence, $p$ is a fold point if and only if $\dim(\textrm{im}(d\Phi_p)) = \dim(\mathfrak{t}^{\circ}_p)-1$ where $\mathfrak{t}^{\circ}_{p}$ is the annihilator of $\mathfrak{t}_p$.

Let $x \in M/T$. Denote by $\textrm{stab}(x)$ the stabilizer of any point $p \in \pi^{-1}(x)$ where $\pi:M \to M/\mathcal{T}$ is the orbit projection. Since $h:M/\mathcal{T} \to M'/\mathcal{T}$ is a diffeomorphism, the proof of Proposition \ref{orbitspaceisamanifoldwithcorners} implies that $\textrm{stab}(x) = \textrm{stab}(h(x))$. This in turn implies that $\mathfrak{t}^{\circ}_{p} = \mathfrak{t}^{\circ}_{p'}$ for any $p' \in (\pi')^{-1}(h(x))$. The result then follows since $\textrm{im}(d\Phi) = \textrm{im}(d\underline{\Phi})$.  \end{proof}

The next result states that moment preserving diffeomorphisms also preserve restriction of the folded symplectic form to the fold.

\begin{lemma}\label{lemmarestriction}
Let $(M,\omega,\Phi)$ and $(M',\omega',\Phi')$ be orientable, folded symplectic toric four-manifolds. Suppose $g:M \to M'$ is an equivariant diffeomorphism such that $g^*\Phi' = \Phi$. Then, $i^*\omega = i^*(g^*\omega')$ where $i:Z \hookrightarrow M$ is the inclusion of the fold.
\end{lemma}
\begin{proof}
It suffices to show that $i^*\omega = i^*(g^*\omega')$ on a dense set and hence, by Lemma \ref{principalorbitsarefree},  it is enough to show the condition holds on free orbits. Let $U'$ be a neighborhood in $M'$ of a free orbit in $Z'$. By the Slice Theorem, $U$ is equivariantly diffeomorphic to $\mathcal{T}^2 \times \mathbb{R} \times \mathbb{R}$. Choose coordinates $(\theta'_{1}, \theta'_{2}, s',t')$ on $U$ where fold points have $t'=0$. Let $U = g^*(U')$ be given coordinates $(\theta_1,\theta_2,s,t) = (g^*\theta'_{1}, g^*\theta'_{2}, g^*s',g^*t')$. With respect to theses coordinates, using the fact that the orbits are isotropic, the folded symplectic forms on $U$ and $U'$ are
$$
\omega = f_1ds \wedge{d\theta_1} + f_2ds \wedge{d\theta_2} + \alpha \wedge dt $$
and
$$\omega' = f'_1ds' \wedge{d\theta'_1} + f'_2ds' \wedge{d\theta'_2} + \alpha' \wedge dt'
$$
where the coefficient functions are invariant and $\alpha,\alpha'$ are invariant one-forms on $\mathcal{T}^2 \times \mathbb{R} \times \mathbb{R}$. It follows that
$$
d\Phi = (f_1ds + k_1dt, f_2ds+k_2dt)
$$
and
$$d\Phi' = (f'_1ds' + k'_1dt', f'_2ds'+k'_2dt').
$$
Now, since $g^*\Phi' = \Phi$, and $d(g^*\Phi') = g^*(d\Phi'$), we see that $f_1 = g^*f'_1$ and $f_2 = g^*f'_2$. Thus, restricting to the fold $Z$, we have $i^*\omega = i^*(g^*\omega)$.  \end{proof}

\begin{remark}\label{locallemmarestriction}
If $U$ is an invariant open set in $M$ and $g:U \to U'$ is an equivariant diffeomorphism preserving moment maps, then the conclusion of Lemma \ref{lemmarestriction} still holds. If $i:U \cap Z \to U$ is the (restriction of) the inclusion of the fold, then $i^*\omega = i^*(g^*\omega')$.
\end{remark}

We now state and prove an equivariant version of Theorem 1 in \cite{dSGW}, which provides a local normal form for a folded symplectic form on an orientable manifold.

\begin{lemma}\label{equivariantlocalnormalform}
Let $G$ be a compact Lie group acting on a folded symplectic manifold $M$ preserving folded symplectic forms $\omega_0$ and $\omega_1$. Let $i:Z \hookrightarrow M$ be the inclusion of the fold. Then, if $i^*\omega_0=i^*\omega_1$, there exists an invariant neighborhood $U$ of $Z$ and an equivariant diffeomorphism $\psi:U \to U$ such that $\psi^*\omega_1 = \omega_0$.
\end{lemma}
\begin{proof}
For each $z \in Z$, choose a basis $\{V_{z},W_{z}\}$ of $\ker(\omega)_z$ with $W_{z} \in T_{z}M$ and $V_{z} \in T_{z}Z$. We can equivariantly identify an invariant neighborhood of $Z$ with $Z \times \mathbb{R}$ in such a way that the vector field $W$ corresponds to $\frac{d}{dt}$. By the proof of Theorem 1 in \cite{dSGW}, we may write $\omega_0 = p^*i^*\omega_0+t\mu_0$ where $p:Z \times \mathbb{R} \to Z$ is the projection and $\mu_0(W_z,V_z)_z >0$ for all $z \in Z$. Let $\eta = p^*i^*\omega_0 + d(t^2p^*\alpha)$ where $\alpha$ is an invariant one-form such that $\alpha(V)>0$. Then, $\eta$ is an invariant folded symplectic form on $Z \times \mathbb{R}$ with fold $Z$.

For all $s \in [0,1]$, the form $\omega_{s}:=(1-s)\omega_0+s\eta$ is an invariant folded symplectic form with fold $Z$. Since $i^*\omega_0=i^*\eta$ and $\omega_0-\eta$ is closed, we may find an invariant one-form $\beta$ on $Z \times \mathbb{R}$ such that $\beta_z=0$ for all $z \in Z$ and $d\beta = \omega_0-\eta$. For each $s \in [0,1]$ there is an invariant vector field $X_s$ such that $\iota(X_s)\omega_s = \beta$. The flow $\{\phi_s\}$ of $X_s$ consists of equivariant diffeomorphisms and $\phi_{1}^*\eta = \omega_0$. Since $\beta_{z}=0$ for all $z \in Z$, the flow of $X_s$ fixes $Z$ for all $s \in [0,1]$.

We next note that
$$
\begin{array}{rcl}
\mathcal{L}_{X_{s}}\omega_{s} &=& \iota(X_s)d\omega_{s}+d\iota(X_s)\omega_s \\
&=& d\beta
\end{array}
$$
so that

$$
\begin{array}{rcl}
\frac{d}{ds}(\phi_{s}^*\omega_{s}) &=& \phi^*_{s}\left(\frac{d}{ds}\omega_{s}+\mathcal{L}_{X_{s}}\omega_{s}\right) \\
&=& \phi^*_{s}(\eta-\omega+d\beta) \\
&=& \phi^*_{s}(\eta-\omega+\omega-\eta) \\
&=& 0.
\end{array}
$$
We conclude that $\phi^*_{s}\omega_{s}$ is independent of $s$. Noting that $\omega=\phi^*_{0}\omega_{0}=\phi^*_{1}\omega_1=\phi^*_{1}\eta$, we define $\psi_0 := \phi_1$. This yields an equivariant diffeomorphism satisfying $\psi_0^*\omega_0 = \eta$.

Since $i^*\omega_0 = i^*\omega_1$, this construction works for $\omega_1$ as well so that there is an equivariant diffeomorphism $\psi_1$ satisfying $\psi_1^*\omega_1 = \eta$. The equivariant diffeomorphism $\psi:=\psi_{1} \circ \psi_0^{-1}$ then satisfies $\psi^*\omega_1 = \omega_0$. \end{proof}

\begin{remark}\label{localequivariantlocalnormalform}
From the proof of Lemma \ref{equivariantlocalnormalform}, we can see that if $X$ is a closed, invariant subset of the fold $Z$ (in particular, an orbit), and there is an invariant neighborhood of $X$ such that the restrictions of folded symplectic forms $\omega_0$ and $\omega_1$ to $X$ are equal, then we can find an equivariant diffeomorphism $\psi$ of a neighborhood $U$ of $X$ in $M$ such that $\psi^*\omega_1=\omega_0$.
\end{remark}

\begin{theorem}\label{localstructure}
Let $(M, \omega, \Phi)$ and $(M', \omega', \Phi')$ be orientable, compact, folded symplectic toric four-manifolds. If there exists a diffeomorphism $h:M/\mathcal{T} \to M'/\mathcal{T}$ of manifolds with corners such that $h^*\underline{\Phi}' = \underline{\Phi}$, then $M$ and $M'$ are locally isomorphic.
\end{theorem}

\begin{proof}
The result follows from Lemma B.4 in \cite{KL} on the symplectic loci $M\setminus{Z}$ and $M'\setminus{Z'}$. We therefore need only focus on points in the fold. Choose $x \in Z/\mathcal{T}$. By the Slice Theorem and Lemma \ref{orbitdiffeospreserveZ}, the diffeomorphism $h \colon M/\mathcal{T} \to M'/\mathcal{T}$ lifts to an equivariant diffeomorphism $g \colon N \to N'$ of neighborhoods of the orbits $\pi^{-1}(x)\subset Z$ and $(\pi')^{-1}(h(x)) \subset Z'$ respectively. Since $h$ preserves orbital moment maps, $g$ preserves the restrictions of $\Phi$ and $\Phi'$ to $N$ and $N'$. By Lemma \ref{lemmarestriction} and Remark \ref{locallemmarestriction}, $i^*\omega = i^*(g^*\omega)$ on $N$ where $i\colon N \cap Z \to N$ is the inclusion. Lemma \ref{equivariantlocalnormalform} and Remark \ref{localequivariantlocalnormalform} now imply that there exists a neighborhood $U$ in $N$ containing $\pi^{-1}(x)$ and an equivariant diffeomorphism $\psi\colon U \to U$ with $\psi^*(g^*\omega') = \omega$. It follows that $\phi=g \circ \psi$ is an equivariant diffeomorphism on a neighborhood of the orbit $\pi^{-1}(x)$ such that $\phi^*\omega' = \omega$. \end{proof}

\section{The Global Picture}

As we saw in the previous section, a diffeomorphism of orbit spaces preserving orbital moment maps is enough to guarantee that two folded symplectic toric four manifolds are locally isomorphic. We will now show that under a suitable topological restriction on the orbit spaces, the existence of a moment-preserving diffeomorphism of folded symplectic toric four manifolds gives rise to an isomorphism between them. In all that follows, when given a diffeomorphism $g:M \to M'$ of folded symplectic toric four-manifolds, we denote by $\omega_{s}$ the convex combination of $\omega$ and $g^*\omega'$. That is, for $s \in [0,1]$, $\omega_s = (1-s)\omega+sg^*\omega'$.

\begin{lemma}\label{kerneltalk}
Let $(M,\omega,\Phi)$ and $(M'\omega',\Phi')$ be orientable, folded symplectic four-manifolds, $Z \subset M$ the folding hyperurface, and $g:M \to M'$ an equivariant diffeomorphism such that $g^*\Phi' = \Phi$. Then
\begin{itemize}
\item[(i)] $\ker(\omega) \cap TZ = \ker(\omega_{s}) \cap TZ$, and
\item[(ii)] for each $z \in Z$, if $W_{z} \in \ker(\omega)_{z} \cap T_{z}M$ and $W^s_{z} \in \ker(\omega_s)_{z} \cap T_{z}M$, $W^s_z$ and $W_z$ differ by a vector tangent to the orbit through $z$.
\end{itemize}
\end{lemma}
\begin{proof}
By Lemma \ref{lemmarestriction}, if $i:Z \hookrightarrow M$ is the inclusion, then $i^*\omega = i^*g^*\omega$ everywhere on $Z$. Hence, $i^*\omega_{s} = i^*\omega$. This establishes (i).

As in the proof of Lemma \ref{Vtangenttoorbits}, it suffices to show (ii) assuming the orbit through $z$ is free. On a neighborhood $U$ of such an orbit, the projection $\pi:U \to U/\mathcal{T}$ is a map of manifolds and
\begin{eqnarray*}
d\pi(\ker(g^*\omega)) &=& d\pi(d(g^{-1})(\ker{\omega})) \\
&=& d\pi(\ker(\omega)),
\end{eqnarray*}
which proves (ii) on free orbits. \end{proof}

Before continuing, it will be beneficial to recall some facts about the {\bf basic cohomology} of a manifold $M$ admitting an action of a compact Lie group $G$. A {\bf basic form} on $M$ is an element $\beta \in \Omega^*(M)$ such that $\beta$ is invariant and satisfies $\iota(\xi_{_M})\beta=0$ for all $\xi \in \mathfrak{g}$. The collection of basic forms is a subcomplex $\Omega^*_{\textrm{bas}}(M) \subset \Omega^*(M)$ whose cohomology is isomorphic to the singular cohomology $H^*(M/G;\mathbb{R})$ of the orbit space. Thus, the basic cohomology of a manifold is a topological invariant so that if $M$ and $N$ are homotopy equivalent, then $H^*_{\textrm{bas}}(M) = H^*_{\textrm{bas}}(N)$. Furthermore, the Poincar\'{e} Lemma holds for basic cohomology. If $p:M \times \mathbb{R} \to M$ is projection on the first factor, then the induced map $p^*:\Omega^*(M) \to \Omega^*(M \times \mathbb{R})$ induces an isomorphism on basic cohomology.

\begin{lemma} \label{basichomotopyproperty}
Suppose a compact Lie group, $G$, acts on a manifold, $M$. Let $i:Z  \hookrightarrow U$ be the inclusion of a submanifold into an invariant tubular neighborhood in $M$. If $\eta$ is a basic $(k+1)$-form on $U$ with $i^*\eta=0$, then there exists a basic $k$-form $\sigma$ with
\begin{enumerate}
\item $\sigma_{z}=0$ for all $z \in Z$, and
\item $d\sigma=\eta$ on $U$.
\end{enumerate}
\end{lemma}
\begin{proof}
Define
$$
\sigma =K\eta :=  \int_{0}^{1} \rho^*_{s}(\iota(\chi_{s})\nu) \ ds
$$
where
\begin{eqnarray*}
\rho_s:U \times [0,1] &\to& U \\
(z,v,s) &\mapsto& (z,sv)
\end{eqnarray*}
 is equivariant and
$$
\chi_{s}(\rho_{s}) = \left.\frac{d}{dr}\right|_{r=s} \rho_{r}
$$
is invariant.
Note that the form $\sigma$ is invariant. When $s=0$ ({\em i.e.}, at points of $Z$), $\sigma=0$. Finally, since $\eta$ is basic, for any $\xi \in \mathfrak{g}$ we have
\begin{eqnarray*}
\iota(\xi_{M})\sigma &=& \iota(\xi_{M})K\eta \\
&=& \iota(\xi_{M})\int_{0}^{1} \rho^*_{s}(\iota(\chi_{s})\eta) \ ds \\
&=& \int_{0}^{1} \iota(\xi_{M})\rho^*_{s}(\iota(\chi_{s})\eta) \ ds \\
&=& \int_{0}^{1} \rho^*_{s}(\iota(d(\rho_{s}^{-1}))(\xi_{M})\iota(\chi_{s})\eta) \ ds \\
&=& 0.
\end{eqnarray*}
We now prove that $d\sigma = \eta$. Let $p:U \to Z$ be the projection of $U$ onto $Z$ and note that since $\eta$ is closed and $i^*\eta=0$,
\begin{eqnarray*}
d\sigma &=& dK\eta+Kd\eta \\
&=& d\int_{0}^{1} \rho^*_{s}(\iota(\chi_{s})\eta) \ ds+\int_{0}^{1} \rho^*_{s}(\iota(\chi_{s})d\eta) \ ds \\
&=& \int_{0}^{1} \rho_{s}^*\mathcal{L}_{\chi_{s}}\eta \ ds\\
&=& \int_{0}^{1} \frac{d}{ds} \rho_{s}^*\eta \ ds\\
&=& \rho^*_{1}\eta-\rho^*_0\nu \\
&=& \eta-(i \circ p)^*(\eta)\\
&=& \eta.
\end{eqnarray*}\end{proof}

We are now ready to state a technical lemma that, along with a variant of Moser's Trick, we will use to prove the existence of an equivariant folded symplectomorphism given an equivariant diffeomorphism preserving moment maps.

\begin{lemma}\label{basicform}
Let $(M,\omega, \Phi)$ and $(M', \omega', \Phi')$ be orientable, folded symplectic toric four-manifolds. Suppose that $g:M \to M'$ is an equivariant diffeomorphism such that $g^*\Phi' = \Phi$. Then, if $H^2(M/\mathcal{T}; \mathbb{Z})=0$, there exists a basic one-form $\beta$ on $M$ such that
\begin{enumerate}
\item $d\beta = g^*\omega'-\omega$, and
\item for all $z \in Z$, $\beta_z(W_z)=0$ whenever $W_z \in \ker(\omega_s)_z$.
\end{enumerate}
\end{lemma}

\begin{proof}\label{techlemma}
The first fact to note is that $\eta = g^*\omega'-\omega$ is a basic form on $M$: it is closed, and it is invariant since $\omega,\omega'$ are invariant and $g$ is equivariant. Also, for any $\xi \in \mathfrak{t}$,
\begin{eqnarray*}
\iota(\xi_{_M})\eta &=& \iota(\xi_{_M})g^*\omega'-\iota(\xi_{_M})\omega \\
&=& -d\Phi^{\xi}+d\Phi^{\xi} \\
&=& 0
\end{eqnarray*}
since $g$ is moment-preserving. By assumption, $H^2(M/\mathcal{T};\mathbb{Z})=0$ and so $H^2(M/\mathcal{T};\mathbb{R})=0$. It follows that the basic cohomology $H^2_{\textrm{bas}}(M)=0$ as well. We conclude that there exists a basic one-form $\alpha$ on $M$ such that $d\alpha=\eta$.

By Lemma \ref{lemmarestriction}, the restriction $i^*g^*\omega'-i^*\omega=0$. In light of Lemma \ref{basichomotopyproperty}, there exists a basic one-form $\sigma$ on an invariant tubular neighborhood $U_1$ of $Z$ in $M$ such that $\sigma_{z}=0$ for all $z \in Z$ and $d\sigma = \eta|_{U_1}$. Note that $U_1$ is orientable and is equivariantly diffeomorphic to $Z \times \mathbb{R}$.

Let $U_2=M\setminus{Z}$ and be $\{\rho_{U_1},\rho_{U_2}\}$ an invariant partition of unity subordinate to the open cover $\{U_1,U_2\}$. Define on $M$ the one-form
$$
\tau:=\rho_{U_1}\sigma+\rho_{U_2}\alpha.
$$
Note that $\tau$ is basic and $\tau_{z}=0$ for all $z \in Z$, but
$$
d\tau = \eta+d\rho_{U_1}\wedge{\sigma}+d\rho_{U_2}\wedge{\alpha}.
$$

The form $\sigma-\alpha$ is a closed, basic one-form on the tubular neighborhood $U_1$. By the Poincar\'{e} Lemma for basic cohomology, the map $p^*:H^1_{\textrm{bas}}(Z)\to H^1_{\textrm{bas}}(U_1)$ induced by the projection $p:U \to Z$ is an isomorphism and so $\sigma - \alpha = p^*\nu+df$ where $\nu \in H^1_{\textrm{bas}}(Z)$ and $f \in C^{\infty}(U_1)$. Rewriting, we have $\alpha = \sigma-p^*\nu-df$.

Define
$$
\beta:= \tau -\rho_{U_1}(p^*\nu)+fd\rho_{U_1}.
$$
Then, $\beta$ is a basic one-form on $M$ and
\begin{eqnarray*}
d\beta &=& d\tau-d\rho_{U_1}\wedge{p^*\nu}-d\rho_{U_1}\wedge{df} \\
&=& \eta + d\rho_{U_1}\wedge{\sigma}+d\rho_{U_2}\wedge{\alpha}+d\rho_{U_1}\wedge{p^*\nu}-d\rho_{U_1}\wedge{df} \\
&=& \eta +d\rho_{U_1}\wedge{\sigma}-d\rho_{U_1}\wedge{\alpha}+d\rho_{U_1}\wedge{p^*\nu}-d\rho_{U_1}\wedge{df} \\
&=& \eta.
\end{eqnarray*}
Since $\beta$ is basic, $\iota(V)\beta=0$ for all $V \in \ker(i^*\omega)=\ker(i^*\omega_{s})$ by Lemma \ref{Vtangenttoorbits}. Lemma \ref{kerneltalk} implies that the vector field $W^{s} \in \ker(\omega_s)$ tangent to $M$ differs from the radial vector field $W=\frac{\partial}{\partial{t}} \in \ker(\omega)$ by a vector field tangent to orbits,  Hence,
\begin{eqnarray*}
\iota(W^{s}_{z})\beta_z &=& \iota\left(\frac{\partial}{\partial{t}}\right) \beta_{z} \\
&=& \iota\left(\frac{\partial}{\partial{t}}\right)(\tau_z+\rho_{U_1}(z)(p^*\nu)_z-f(z)(d\rho_{U_1})_z) \\
&=& \iota\left(\frac{\partial}{\partial{t}}\right)\rho_{U_1}(z)(p^*\nu)_z\\
&=& 0
\end{eqnarray*}
(recall that $p^*\nu$ is the pullback of a form on $Z$). Thus, $\ker(\beta) = \ker(\omega_s)$ at all points $z \in Z$. \end{proof}

We end this section with a theorem stating that, under a topological assumption on the orbit space, the existence of a moment-preserving equivariant diffeomorphism forces the existence of an isomorphism in the orientable, four-dimensional case.

\begin{theorem}\label{global}
Let $(M,\omega, \Phi)$ and $(M', \omega', \Phi')$ be compact, orientable, folded symplectic toric four-manifolds. Suppose that $H^2(M/\mathcal{T}; \mathbb{Z})=0$. If there exists an equivariant diffeomorphism $g:M \to M'$ such that $g^*\Phi' = \Phi$, then $M$ and $M'$ are isomorphic.
\end{theorem}

\begin{proof}
By Lemma \ref{basicform}, there exists a basic form $\beta$ such that $d\beta = g^*\omega'-\omega$. Since $\beta_{z}(W_z)=0$ for all $W_z \in \ker(\omega_{s})_z$, there exists $X_s$ such that $\iota(X_s)\omega_s = -\beta$. For all $\xi \in \mathfrak{t}$ we have
\begin{eqnarray*}
-\iota(X_s)d\Phi^{\xi} &=& \iota(X_s)\iota(\xi_{M})\omega_s \\
&=& \iota(\xi_{M})\beta \\
&=& 0
\end{eqnarray*}
since $\beta$ is basic. Hence, the flow $\{\phi_s\}$ preserves the moment map $\Phi$.

The pullbacks $\phi_s^*\omega_s$ are independent of $s$ since
\begin{eqnarray*}
\frac{d}{ds}(\phi_s^*\omega_s) &=& \phi_s^*\left(\frac{d}{ds}\omega_s+\mathfrak{L}_{X_s}\omega_s\right) \\
&=& \phi_s^*\left(g^*\omega'-\omega-d\beta\right) \\ &=& 0.
\end{eqnarray*}
Consequently, $\omega = \phi_0^*\omega_0=\phi_1^*\omega_1=\phi_1^*g^*\omega'$. Define $\psi:M \to M'$ by $\psi:=g \circ \phi_1$. By construction, $\psi$ is an isomorphism. \end{proof}

\section{From Local to Global}

We conclude by combining the results of the previous sections to prove Theorem \ref{maintheorem}, which we restate for convenience.

\begin{theorem*}
Let $(M, \omega, \Phi)$ and $(M', \omega', \Phi')$ be orientable folded symplectic toric four-manifolds. Suppose that $H^2(M/\mathcal{T}; \mathbb{Z})=0$. Then, $M$ and $M'$ are isomorphic if there exists a diffeomorphism $h:M/\mathcal{T} \to M'/\mathcal{T}$ of manifolds with corners such that $h^*\underline{\Phi}' = \underline{\Phi}$.
\end{theorem*}

\begin{proof}
Since $h:M/\mathcal{T} \to M/\mathcal{T}$ is a diffeomorphism preserving orbital moment maps, Theorem \ref{localstructure} implies that $M$ and $M'$ are locally isomorphic. So, $h$ lifts locally to a collection of isomorphisms $\{g_{i}\}$ on an open cover $\mathcal{V}=\{V_i\}$ of $M$. The maps
\begin{eqnarray*}
V_i \cap V_j &\to& V_i \cap V_j \\
p &\mapsto& (g_{i}^{-1}\circ{g_j})(p)
\end{eqnarray*}
are equivariant diffeomorphisms that fix orbits. By a theorem of Haefliger and Salem (Theorem 3.1, \cite{hs}), there exists a collection $\{a_{ij}\}$ of smooth maps $a_{ij}:V_i \cap V_j \to \mathcal{T}$ such that $(g_{i}^{-1}\circ{g_j})(p) = a_{ij}(p)\cdot{p}$.

Note that since the $a_{ij}$ preserve orbits, we may think of them as smooth, $\mathcal{T}$-valued functions on $M/\mathcal{T}$ and the collection $\{a_{ij}\}$ forms a class $[a] \in \check{H}^1(M/\mathcal{T},\mathcal{T})$, the \v{C}ech cohmology of the orbit space with respect to the sheaf of smooth functions with values in $\mathcal{T}$.
Let $\ell$ and $\mathfrak{t}$ be the sheaves of smooth functions on $M/\mathcal{T}$ with values in the lattice $\ker\{\exp:\mathfrak{t} \to \mathcal{T}\}$ and the Lie algebra of $\mathcal{T}$, respectively. The short exact sequence
$$0 \to \ell \to \mathfrak{t} \to \mathcal{T} \to 0$$
induces the long exact sequence in cohomology
$$
\cdots \to H^{k-1}(M/\mathcal{T},\mathfrak{t})\to H^{k-1}(M/\mathcal{T},\mathcal{T}) \to H^{k}(M/\mathcal{T},\ell) \to H^{k}(M/\mathcal{T},\mathfrak{t}) \to \cdots .
$$
Since $M/T$ is paracompact, it admits partitions of unity so the sheaf $\mathfrak{t}$ is fine and hence acyclic. Thus, $H^{k}(M/T,\mathfrak{t})=0$ for all $k>0$. As a consequence, $H^1(M/T,\mathcal{T})$ is isomorphic to $H^2(M/T,\ell)$. By assumption, $H^2(M/T,\mathbb{Z})=0$ implying $H^2(M/T,\ell)=0$ as well. The class $[a]$ is thus trivial in $H^1(M/T,\mathcal{T})$ and the diffeomorphisms $g_i$ glue to give a global diffeomorphism $g:M \to M'$. Since $g$ is a lift of $h$ and $h$ preserves orbital moment maps, we have $g^*\Phi' = \Phi$. By Theorem \ref{global}, this implies that there exists an isomorphism $\psi:M \to M'$.
\end{proof}

\bibliographystyle{amsalpha}

redpajama_set_name: RedPajamaArXiv


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text:
GMAC Commercial Mortgage Takes 24,000 SF at 48 Wall St.
NEW YORK CITY-Occupancy of the 73-year-old building, now undergoing renovation, is slated for next February. More than a third of the property is now leased. Renovations underway include installation of a fiber-optic backbone, a tenant-controlled HVAC system, ADA-compliant bathrooms and thermopane windows.
By John Howe | October 25, 2000 at 01:01 AM
NEW YORK CITY-GMAC Commercial Mortgage Corp. has leased 24,000 sf at 48 Wall St., bringing its occupancy to more than 33%. The 34-story, 324,000-sf office tower recently signed Rockefeller Center Business Centers, which provides executive office space, for 41,000 sf, and Nextset, an Internet software firm, for 17,500 sf. In addition, Stockhouse Media, an information source for on-line investors, has taken space on the ground floor, grand mezzanine and upper mezzanine. Occupancy is scheduled for February 2001. Cushman & Wakefield represented the owner and GMAC in the transaction.
Erected in 1927, the building was formerly occupied by the Bank of New York. Swig Burris Equities LLC acquired it two years ago in association with MacDonald & Cie. They are only the third owners of the property since the Dutch conveyed the land to the bank in 1796.
48 Wall St. is now undergoing major renovations that include installation of a fiber-optic backbone for broadband Internet access, a tenant-controlled HVAC system, new electrical service incorporating a minimum of 6 watts per sf of electric power above that required by the HVAC system and an Otis Elevonic elevator system. Other enhancements include a new cooling tower and thermopane windows, ADA-compliant bathrooms, and private terraces on the upper floors.
Bank Economists See Brighter Days Ahead
While economic growth should accelerate, the labor market will recover more slowly.
Middle Market Digest: This Week in the South and Mountain Regions
Lisa Brown | August 10, 2018
Here's a look at the trends, announcements and deals you may have missed in Texas, New Mexico, Colorado, Oklahoma and Arkansas.


text:
Journals & Conferences
Volume 1 Issue 1 March 2002
Alexia: Antigone Kefala's overdue fairytale
fulgor_v1i1_tsianikas.pdf (239.44 KB)
Tsianikas, Michael
Department of Languages, Flinders University
The aim of this paper is to examine the way in which Antigone Kefala constructs her story to become an author. She narrates her experience in her book Alexia (Antigone Kefala"s persona) in a fairytale manner. In the book we learn that Alexia spent some of the most important years of her young life in New Zealand, as a migrant. The most important part of this experience is based on her difficulty to come to terms with, and learn, a new language (English). What begins by being a traumatic experience for Alexia, later evolves into a creative force that guides her decision to become an author. In that way the English language becomes the most powerful, the most creative and the most productive tool in her life. In order to challenge Alexia's process of becoming an author, her experience is compared to that of two famous French authors, Aragon and Sartre, who also decided to become authors in their childhood years. There was an obvious parallel between the French authors' experiences through their first language, which corresponded in an astonishing way to Alexia's. Therefore, no matter whether one wishes to express oneself in one's mother tongue or a foreign language, the process of becoming an author is always to consider a language as an unknown field of strange sounds, musicality and scattered grains of meanings.
Languages, Language Studies, Aragon, Satre, Narrative, Refugee, Vasia, Greek, English, French, Nickas, fairy tale
Tsianikas, Michael 2002. Alexia: Antigone Kefala's overdue fairytale.'FULGOR', vol.1, iss.1, March.
http://hdl.handle.net/2328/84
Flinders Open Access Research


text:
@echo off
REM net user
echo %TIME%
echo ===%TIME%
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redpajama_set_name: RedPajamaGithub


Imagine a dining experience that transports you to the café culture of Rome or Milan, where your senses are enticed and manipulated by; the smell of fresh lemons & basil & the reflections of vine leaves & cherub frescos, while you sample cuisine that makes you covet the genius of your taste buds.
It is boastful to say that The Chubby Cherub is the best Italian Ristorante in the city but this is substantiated time & time again by the responses of our patrons. We have a purpose and vision to provide familiar food with love & genius. We are confident that your experience at The Chubby Cherub will be delightful.
The Chubby Cherub Ristorante was established in 2010. The founders are from a large, close family. They grew up eating wonderful food prepared by their parents who were both great cooks. They learned to love and appreciate food at an early age, and then spent most of their lives working in the service industry, fuelling their passion for the restaurant business while allowing them to hone their innate ability to create fabulous meals.
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Value investors like Warren Buffett have only two goals: 1) find excellent businesses and 2) determine what they are worth. But in order to determine what a company is worth, you will have to predict how fast the business will be able to grow its earnings in the future. How to come up with a realistic growth rate for your intrinsic value calculations is what this post is all about.
This is the second edition of the ongoing Money Reports I'm writing each month to discuss the developments regarding the blog and my investments, as well as lessons I've learned during the month. At the end of the reports I share my plans for the upcoming month, both to get you excited and to keep myself on course.
When I asked my readers if there was a topic they wanted me to write a blog post about, Carlos urged me to explain how to know if the stock market is under- or overvalued. I'm guessing more people are interested in knowing the answer to this, so here it is.
It is obviously very easy to shout from the sidelines that our current education system is, to put it at its mildest, seriously flawed. Therefore I will describe in detail why I absolutely believe this to be the case.
Welcome! This is the first in a series of reports I'm writing at the end of every month about the progress I'm making with my investments and businesses. I talk about things that impacted my portfolio, newsworthy events regarding my businesses, and the lessons I learned during that month. Every report ends with an announcement of my plans for the upcoming weeks. I will be as open as possible with you.


text:
Over the last week or so I've been deep diving in our backup hard drives. The goal is to look for certain photos for my friend Eliana but as I've been sifting through photos I'm finding all sorts that we never edited—especially photos Chris took. Along the way I'm shuffling over files that I want to edit but I know I'll be going back through the drives to pick out favorites and revisit some items.
One of those sets were these handful of photos you see above of an atala butterfly and several larvae. We had seen them at Mounts Botanic Garden in West Palm Beach in March of 2008. I remembered visiting the garden and have thought about the place from time to time over the years but apparently we never edited photos and put them on Flickr—Flickr is basically my photo repository on the cloud at this point in time and I'm tied to it forever. Don't ever go away, Flickr!
This feels like maybe the only time we came across an adult atala but I feel like we've come across other larvae on its larval host plant, the cycad coontie, but I'm not certain. So, the story with this butterfly is that in the late 1800s it was considered to be incredibly abundant in southeast Florida and a handful of Caribbean islands. The host plant, coontie, had been used by the various tribes in Florida for sustenance but considering coontie is a slow growing plant and already confined to certain habitats and locales, it wouldn't take much for habitat loss and over harvesting to affect the populations of coontie. Well, while a balance had been struck between humans and coontie, that was thrown to the wind when Florida really opened up to settlers as the they also in time began to also harvest the coontie, without all the respect and balance for nature that the tribes had been using when harvesting the plant.
Subsequently the atala population plummeted and by the mid 1900s the butterfly was thought to be extirpated from Florida. Ah, isn't this usually the story? Abundance and then something tips and boom! a species is now extinct. (See: passenger pigeons)
In the late 70s a population of atala butterflies was found on Key Biscayne, though in my readings it isn't clear if this is a repopulation from butterflies in the Bahamas or hold outs from the original population that managed to survive. Either way, biologists began rearing butterflies on cultivated coonties and started reintroducing them across their native range. Then, as coontie began to show up in the nursery trade, the plant became more abundant in landscaping throughout south Florida, thus creating a different habitat for the atala larvae. Now a once potentially extinct species is considered to be somewhat abundant once again. It is still considered rare and vulnerable by various agencies due to general habitat loss and other factors that affect insects such as pesticides, but what a remarkable turnaround in 40 years!
I'm including some links below for further reading if you are interested!
+The Coontie and the Atala Hairstreak by Roger Hammer in the FNPS The Palmetto magazine. I saw several references that mention Roger as the person who rediscovered this population but he doesn't state that himself in this article. I wouldn't be surprised that Roger found it, he's a renowned naturalist in south Florida. It's a great article worth reading.
+Atala History via the Atala Chapter of North American Butterfly Association
+Eumaeus atala via UF IFAS
+A Nearly Extinct Butterfly Makes a Comeback in South Florida via Entomology Today
+BAMONA Sightings—including two stray historical sightings in the lower and mid-south.
+iNaturalist sightings—far more are included here so you can see how widespread it is being seen now.
One thought on "Atala, Eumaeus atala | Wildlife Wednesday"
Great story. It reminds me of the brown pelican, of course. Also: bison and whooping cranes, and perhaps others I don't remember or know about. It is possible to turn things around, given enough committed people and ways to preserve and expand habitat.


text:
Home Local News Secret Service admits it has some Biden Delaware visitor records
Secret Service admits it has some Biden Delaware visitor records
WASHINGTON — What a difference three days makes.
The Secret Service admitted Thursday that it does, in fact, have information on visitors to President Biden's Wilmington, Del. residence during the time he kept classified records in the home's garage.
Secret Service spokesman Anthony Guglielmi claimed Monday that "we don't independently maintain our own visitor logs because it's a private residence."
But Guglielmi's tune had changed Thursday, when he said that "the Secret Service does generate law enforcement and criminal justice information records for various individuals who may come into contact with Secret Service protected sites."
Meanwhile, Fox News quoted an unnamed source as promising that "the Secret Service is prepared to provide available background information on vetted guests to Biden's residence if requested by Congress."
The Secret Service has changed its tune and now says it does have Delaware visitor records.
President Biden stored classified documents from his vice presidency in Wilmington.
The agency's initial statement that it had no information to provide to journalists or members of Congress caused an uproar, with Republican lawmakers floating subpoenas of Biden's family members and staff to plug the gaps in documentation.
"There are several avenues to obtain information on who had access to classified documents at the Wilmington residence," a spokesman for the House Oversight Committee told The Post, "and the Oversight Committee will pursue those avenues."
Rep. Mike Johnson (R-La.), a member of the House Judiciary Committee, which also is looking into the controversy, had said Monday afternoon that if no records existed, "we'll have to seek it through testimony with family members or those who have been at the residence."
Oversight Committee Chairman James Comer (R-Ky.) and other GOP leaders in Congress had demanded Delaware visitor logs last week as the classified documents scandal grew.
The Secret Service claimed in April that "no records were located" showing logs of Biden's Delaware visitors in response to a Freedom of Information Act request filed by The Post. In late September, the Secret Service denied a FOIA appeal, telling The Post again that "no responsive records" were found after an "additional search of relevant program offices."
On Oct.10, The Post filed a more broadly worded FOIA request asking the Secret Service for "[e]mails that refer to visitors to President Biden's residences" during his time in office. The agency has not yet provided a substantive reply, with a Secret Service FOIA staffer telling The Post Tuesday that "your request is currently being processed."
Some classified documents were found next to Biden's Corvette.
Joe Biden has been at his Wilmington or Rehoboth Beach homes for nearly one-fourth of the days during his two-year presidency.
As vice president and in the years that followed, Joe Biden regularly interacted with his son Hunter and brother James' international business associates — including from China, Kazakhstan, Mexico, Russia and Ukraine — contributing to interest in the Wilmington logs.
Hunter Biden listed the Wilmington home as his own address on a 2018 rental background check form.
A cache of documents was found Dec. 20 in the Wilmington house's garage next to Biden's prized classic Corvette — weeks after the discovery on Nov. 2 of documents dating to his vice presidency in his former offices at the Penn Biden Center in Washington.
Additional classified documents were found as late as last week in other areas of the Wilmington home. The FBI reportedly allowed Biden and his team to conduct its own search of the residences because they were deemed to be cooperative.
Special counsel Robert Hur is reviewing whether Biden or anyone in his orbit violated the law by mishandling records. A different special counsel, Jack Smith, is reviewing whether former President Donald Trump mishandled documents taken to his Florida residence when he left office. The FBI raided Trump's Mar-a-Lago resort on Aug. 8 to retrieve records.


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The text id of the email type is used as the key, while the settings are passed as the value. In our case, template setting is the file of email template.


Well, we made it through the summer. We're still hobbling along with Ellie, but Sam's first day of school is today. She is very excited, but a little nervous too. I know she will do well. That's my girl!
Looks like a star pupil to me!
Previous Previous post: Need to split a multipage PDF into individual files?


text:
Off-duty Garda arrested for drink driving at Tipperary checkpoint
Sources say the officer was arrested at a mandatory checkpoint in Co Tipperary early on Sunday morning and failed the roadside breath test
Michael O'TooleCrime Correspondent
Stock image of a Garda checkpoint (Image: Collins)
A serving Garda is fighting to save his job – after he was arrested on suspicion of drink driving, it has emerged.
The Irish Mirror reports that the officer, who was off duty at the time of the incident, has now been charged and is due to appear in court in the coming weeks.
Sources say the officer was arrested at a mandatory checkpoint in Co Tipperary early on Sunday morning – and failed the roadside breath test.
READ NEXT - Garda investigation underway after woman found dead in 'unexplained circumstances' in Kerry
READ NEXT - New Garda uniform: Gardaí switching to contemporary new look starting today
It's understood he was more than four times over the legal limit, which is currently 22 microgrammes of alcohol per 100 millilitres of breath.
Sources say the officer, who is not involved in roads policing, had a reading of almost 100 microgrammes of alcohol per 100 millilitres of breath.
He was arrested and later charged following the incident and is now facing prosecution.
If convicted, he faces a fine of €400 as well as being put off the road for six months.
But sources have told The Mirror that the officer will also run a serious risk of being sacked from the force if he is convicted.
"He is in real trouble," one source said.
"He will be fighting to keep his job once court is concluded. It is a very serious matter."
Another source said Garda management would take a dim view of the officer's actions - if he is convicted.
"It will be hard for him to stay in the job after this," a source said.
It's understood the officer, who is based in the south of the country, was stopped at a so-called MIT checkpoint in Clonmel on Sunday morning.
Those checkpoints see officers stop random drivers and ask them for a breath specimen. There is no need for officers on the checkpoints to form an opinion the driver is over the limit before asking them for a breath test.
Garda statement
A Garda spokesperson confirmed a member of the force had been arrested at a checkpoint on Sunday morning and was now facing prosecution.
The spokesperson said: "An Garda Siochana can confirm that an off-duty member of An Garda Siochana stationed in the Southern Region was arrested in Clonmel on Sunday morning 14/8/22 on suspicion of driving under the influence of an intoxicant.
"That member was subsequently charged to a future sitting of Clonmel District Court."
READ NEXT - Jail sentences for domestic abuse-related crimes like stalking and non-fatal strangulation to increase
READ NEXT - Nearly 3,000 drivers motorists caught speeding over August bank holiday weekend
READ NEXT - Use of force by An Garda Síochána went up in June
New York taxi driver dies after being 'knocked to ground' by passengers who fled without paying
Dublin Airport reduces recommended arrival times for passengers after 'significant improvement' in queue times


text:
'Spyro Reignited Trilogy' reaches PS4 and Xbox One on September 21st
It's a dramatic remake of the classic dragon adventure.
In this article: activision, av, games, gaming, insomniacgames, ps4, spyro, spyroreignitedtrilogy, spyrothedragon, toysforbob, videogames, xboxone
Activision/Toys for Bob
After years of speculation and more than a little teasing, it's official: the Spyro series is getting a remake. Activision and Toys for Bob have unveiled the Spyro Reignited Trilogy, which reworks the first three Insomniac-made games (Spyro the Dragon, Spyro 2: Ripto's Rage and Spyro: Year of the Dragon) for PS4 and Xbox One. Not surprisingly, the graphics get the biggest upgrade. Toys for Bob has "faithfully" mapped the original levels, but with loads of added detail and flourishes that weren't possible on a PlayStation 20 years ago. And then there's the characters -- much like the Crash Bandicoot overhaul, Spyro and company look better than the original box art (not to mention Spyro's fiercer appearance in Skylanders).
Gallery: Spyro Reignited Trilogy | 14 Photos
Thankfully, the trilogy also catches up with modernized controls (analog stick support in every game!), better cameras, updated cinematics, a 're-imagined' soundtrack and improved reward sequences. Like other remakes, it's more about viewing the games through rose-tinted lenses than maintaining the rough edges in the name of accuracy.
The Reignited Trilogy arrives on September 21st for $40. Yes, it's yet another bid to cash in on nostalgia for gamers whose childhood consoles have long since been sold at garage sales, but it's hard to complain too loudly. Spyro was one of the original PlayStation's definitive series, so it's good to see it rejuvenated after years of both a string of lackluster sequels and a reduced role as a Skylanders character.
Fortnite's latest update adds climbable monsters and brings back Tilted Towers
Cheeky hack-and-slash RPG 'Nobody Saves the World' is available now


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text:
Steven T. Kuhn, D.D.S.
Dr. Steve is originally from a small town in central Illinois called Oreana, but has made Lockport, Illinois his home since 1997. He graduated from the University of Illinois at Urbana-Champaign with his first bachelor's degree in biology in 1992. He then attended the University of Illinois at Chicago College of Dentistry and graduated in 1997. Upon completion, he went to Loyola University Medical Center and spent a year in a General Practice Residency, where he was not only exposed to all fields and forms of dentistry, but also completed rotations in oral surgery, anesthesia and medicine. In 1998, Dr. Steve returned to the University of Illinois at Chicago College of Dentistry after being accepted into the Pediatric Dental program and completed his training in the year 2000.
Dr. Steve currently has two bachelor's degrees and his Doctor of Dental Surgery (DDS) degree. He has a license as a Specialist in Pediatric Dentistry and holds a dental sedation permit in the state of Illinois. He became a Diplomate of the American Board of Pediatric Dentistry in 2006 and he earned the title of Fellow of the American College of Dentistry in 2009. He is a member of the American Dental Association, the American Academy of Pediatric Dentistry, the Chicago Dental Society, the Illinois State Dental Society, the Will County Dental Society and the Illinois Society for Pediatric Dentistry.
Dr. Steve and his wonderful wife, Kathy, have three beautiful children: Beth, Mason and Kyle. He enjoys spending time with his family, fishing, cooking/grilling, gardening and working in his yard. In his spare time, he also enjoys an occasional golf game. Dr. Steve is a rabid University of Illinois fan (Go Illini!). He loves sports (Chicago Bears, St. Louis Cardinals and White Sox) and having fun with family, friends and neighbors.


text:
#ifndef _LINUX_NVHDCP_H_
#define _LINUX_NVHDCP_H_
#include <linux/fb.h>
#include <linux/types.h>
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#include <asm/ioctl.h>
#define TEGRA_NVHDCP_MAX_DEVS 127
#define TEGRA_NVHDCP_FLAG_AN 0x0001
#define TEGRA_NVHDCP_FLAG_AKSV 0x0002
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_FLAG_BKSV 0x0004
#define TEGRA_NVHDCP_FLAG_BSTATUS 0x0008
#define TEGRA_NVHDCP_FLAG_CN 0x0010
#define TEGRA_NVHDCP_FLAG_CKSV 0x0020
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_FLAG_DKSV 0x0040
#define TEGRA_NVHDCP_FLAG_KP 0x0080
#define TEGRA_NVHDCP_FLAG_S 0x0100
#define TEGRA_NVHDCP_FLAG_CS 0x0200
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_FLAG_V 0x0400
#define TEGRA_NVHDCP_FLAG_MP 0x0800
#define TEGRA_NVHDCP_FLAG_BKSVLIST 0x1000
#define TEGRA_NVHDCP_RESULT_SUCCESS 0
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_RESULT_UNSUCCESSFUL 1
#define TEGRA_NVHDCP_RESULT_PENDING 0x103
#define TEGRA_NVHDCP_RESULT_LINK_FAILED 0xc0000013
#define TEGRA_NVHDCP_RESULT_INVALID_PARAMETER 0xc000000d
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_RESULT_INVALID_PARAMETER_MIX 0xc0000030
#define TEGRA_NVHDCP_RESULT_NO_MEMORY 0xc0000017
struct tegra_nvhdcp_packet {
 __u32 value_flags;
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
 __u32 packet_results;
 __u64 c_n;
 __u64 c_ksv;
 __u32 b_status;
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
 __u64 hdcp_status;
 __u64 cs;
 __u64 k_prime;
 __u64 a_n;
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
 __u64 a_ksv;
 __u64 b_ksv;
 __u64 d_ksv;
 __u8 v_prime[20];
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
 __u64 m_prime;
 __u32 num_bksv_list;
 __u64 bksv_list[TEGRA_NVHDCP_MAX_DEVS];
};
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRA_NVHDCP_POLICY_ON_DEMAND 0
#define TEGRA_NVHDCP_POLICY_ALWAYS_ON 1
#define TEGRAIO_NVHDCP_ON _IO('F', 0x70)
#define TEGRAIO_NVHDCP_OFF _IO('F', 0x71)
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#define TEGRAIO_NVHDCP_SET_POLICY _IOW('F', 0x72, __u32)
#define TEGRAIO_NVHDCP_READ_M _IOWR('F', 0x73, struct tegra_nvhdcp_packet)
#define TEGRAIO_NVHDCP_READ_S _IOWR('F', 0x74, struct tegra_nvhdcp_packet)
#define TEGRAIO_NVHDCP_RENEGOTIATE _IO('F', 0x75)
/* WARNING: DO NOT EDIT, AUTO-GENERATED CODE - SEE TOP FOR INSTRUCTIONS */
#endif


text:
Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population
R M McCormack, A P Maxwell, D Carson, C C Patterson, A Bingham, D A Savage
School of Medicine, Dentistry and Biomedical Sciences
Centre for Public Health
Linkage and association has been reported between CTLA4 DNA markers and susceptibility to type 1 diabetes in some populations, but not others. We performed case-control and family-based association studies to assess if the CTLA4 A49G and intron 1 C/T polymorphisms were associated with development of early onset type 1 diabetes in the Northern Ireland population. The distribution of A49G and C/T alleles in cases (n = 144) was similar to those observed in controls (n = 307). In contrast, significant distortions in allele transmissions from informative parents to probands were observed for both the A49G (P = 0.02) and C/T (P = 0.01) polymorphisms employing 297 nuclear families. Our results suggest that the CTLA4 gene may play a minor role in the overall genetic predisposition to type 1 diabetes in this UK population.
Genes and Immunity
https://doi.org/10.1038/sj.gene.6363749
10.1038/sj.gene.6363749
Dive into the research topics of 'Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population'. Together they form a unique fingerprint.
Type 1 Diabetes Mellitus Medicine & Life Sciences 100%
Alleles Medicine & Life Sciences 54%
Northern Ireland Medicine & Life Sciences 50%
Genetic Predisposition to Disease Medicine & Life Sciences 38%
McCormack, R. M., Maxwell, A. P., Carson, D., Patterson, C. C., Bingham, A., & Savage, D. A. (2001). Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population. Genes and Immunity, 2(4), 233-5. https://doi.org/10.1038/sj.gene.6363749
McCormack, R M ; Maxwell, A P ; Carson, D ; Patterson, C C ; Bingham, A ; Savage, D A. / Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population. In: Genes and Immunity. 2001 ; Vol. 2, No. 4. pp. 233-5.
@article{695581dd17c34e4ab00fe6f16d8eaade,
title = "Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population",
abstract = "Linkage and association has been reported between CTLA4 DNA markers and susceptibility to type 1 diabetes in some populations, but not others. We performed case-control and family-based association studies to assess if the CTLA4 A49G and intron 1 C/T polymorphisms were associated with development of early onset type 1 diabetes in the Northern Ireland population. The distribution of A49G and C/T alleles in cases (n = 144) was similar to those observed in controls (n = 307). In contrast, significant distortions in allele transmissions from informative parents to probands were observed for both the A49G (P = 0.02) and C/T (P = 0.01) polymorphisms employing 297 nuclear families. Our results suggest that the CTLA4 gene may play a minor role in the overall genetic predisposition to type 1 diabetes in this UK population.",
author = "McCormack, {R M} and Maxwell, {A P} and D Carson and Patterson, {C C} and A Bingham and Savage, {D A}",
doi = "10.1038/sj.gene.6363749",
journal = "Genes and Immunity",
McCormack, RM, Maxwell, AP, Carson, D, Patterson, CC, Bingham, A & Savage, DA 2001, 'Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population', Genes and Immunity, vol. 2, no. 4, pp. 233-5. https://doi.org/10.1038/sj.gene.6363749
Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population. / McCormack, R M; Maxwell, A P; Carson, D; Patterson, C C; Bingham, A; Savage, D A.
In: Genes and Immunity, Vol. 2, No. 4, 06.2001, p. 233-5.
T1 - Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population
AU - McCormack, R M
AU - Maxwell, A P
AU - Carson, D
AU - Patterson, C C
AU - Bingham, A
AU - Savage, D A
N2 - Linkage and association has been reported between CTLA4 DNA markers and susceptibility to type 1 diabetes in some populations, but not others. We performed case-control and family-based association studies to assess if the CTLA4 A49G and intron 1 C/T polymorphisms were associated with development of early onset type 1 diabetes in the Northern Ireland population. The distribution of A49G and C/T alleles in cases (n = 144) was similar to those observed in controls (n = 307). In contrast, significant distortions in allele transmissions from informative parents to probands were observed for both the A49G (P = 0.02) and C/T (P = 0.01) polymorphisms employing 297 nuclear families. Our results suggest that the CTLA4 gene may play a minor role in the overall genetic predisposition to type 1 diabetes in this UK population.
AB - Linkage and association has been reported between CTLA4 DNA markers and susceptibility to type 1 diabetes in some populations, but not others. We performed case-control and family-based association studies to assess if the CTLA4 A49G and intron 1 C/T polymorphisms were associated with development of early onset type 1 diabetes in the Northern Ireland population. The distribution of A49G and C/T alleles in cases (n = 144) was similar to those observed in controls (n = 307). In contrast, significant distortions in allele transmissions from informative parents to probands were observed for both the A49G (P = 0.02) and C/T (P = 0.01) polymorphisms employing 297 nuclear families. Our results suggest that the CTLA4 gene may play a minor role in the overall genetic predisposition to type 1 diabetes in this UK population.
U2 - 10.1038/sj.gene.6363749
DO - 10.1038/sj.gene.6363749
JO - Genes and Immunity
JF - Genes and Immunity
McCormack RM, Maxwell AP, Carson D, Patterson CC, Bingham A, Savage DA. Possible association between CTLA4 DNA polymorphisms and early onset type 1 diabetes in a UK population. Genes and Immunity. 2001 Jun;2(4):233-5. https://doi.org/10.1038/sj.gene.6363749


An excellent city tour. Famous winery, horse show and cruise through the bay of Cadiz, the best beaches of Andalusia!
Visit of the Williams & Humbert winery.
This day trip is only available on High Season, from April to October 2019.
A local guide will take you through the winery and will explain you the making and ageing of the wine. At the end of the visit, you will have the opportunity to taste two types of wine, accompanied by a snack.


text:
Ipum of Geumgwan Gaya (died 407) (r. 346–407) was the fifth ruler of Geumgwan Gaya, a Gaya state of ancient Korea.  He was the son of King Geojilmi and Queen Aji.

Family
Father: King Geojilmi (거질미왕, 居叱彌王)
Mother: Lady Aji (아지부인, 阿志夫人)
Wife: Lady Jeongsin (정신부인, 貞信夫人)
Son: King Jwaji (좌지왕, 坐知王)

See also
 List of Korean monarchs
 History of Korea
 Gaya confederacy
 Three Kingdoms of Korea

Notes

References

Gaya rulers
407 deaths
4th-century monarchs in Asia
5th-century monarchs in Asia
Year of birth unknown


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Despite growing numbers of family-owned enterprises in India "vying for recognition on the international stage", next-gens were limited to studying a general MBA, Khanna told CampdenFB.
These traditional MBA courses are "not tailor made for asset owners who will very quickly be making decisions, and critically need to have working knowledge of all the functional areas with the skill to effectively structure and delegate function decision making to professionals", he added.
The 18-month IMI programme, starting in September this year, will see students studying for eight months with IMI in Delhi. There is an obligatory international element, with students spending a month at four different leading business schools – the Thunderbird School of Global Management in the US, the Chinese University of Hong Kong, Italy's Bocconi School of Management and the Grenoble Ecole de Management in France.
Students then complete a six-month mentored programme in their respective family businesses, designing and implementing growth and management strategies.
Indian School of Business also launched its a new family business course in December 2012. The Management Programme for Family Business, a part-time 15-month course, will run at ISB's Hyderabad and Mohali campuses with an optional international element.
Deepak Chandra, deputy dean of ISB, said in a statement the course "seeks to address the distinctive challenges that are faced by family business owners".
Elsewhere in Asia, Insead's Asia campus, working with PricewaterhouseCoopers and the Family Business Network Asia, has developed another part-time family business programme.