text:
Vincent Asaro Found Not Guilty In Lufthansa Mob Heist Trial
CrimeBy Joe Levin November 12, 2015 Leave a comment
An ageing mobster has been acquitted of charges that he helped plan and pull off the 1978 Lufthansa heist in New York that was retold in the hit Mafia movie Goodfellas.
Boca Raton, FL – Jewish Family ID'd As Those Killed In Ohio Plane Crash, Investigators Say Wreckage, Records, Video May Hold Clues
INVESTIGATIONSBy Joe Levin November 12, 2015 Leave a comment
Boca Raton – The identities of eight of the nine people killed in Tuesday's Ohio plane crash are being revealed by family members.
At Least 41 Dead In Blast At Hezbollah Stronghold In Beirut
Two explosions in a predominantly Shi'ite area of southern Beirut have killed at least 41 people, according to the Lebanese Health Ministry as cited by Al Jazeera. At least 200 are said to be injured.
Driven To Hospital, Virginia Man Tased, Shackled and Dies In Police Custody
Police CrimeBy Joe Levin November 12, 2015 Leave a comment
Police in South Boston repeatedly fired their stun guns on a Richmond man before he died in 2013, a network news program revealed Wednesday.
Facebook Says Governments Demanding More User Data
Facebook has said government requests for data and demands for content to be taken down surged in the first half of 2015, which the social network has seen continually increase since it began publicly releasing such data two years ago.
Inside Job? Clues Suggest Lois Colley Murder Wasn't Random
Crime, INVESTIGATIONSBy Joe Levin November 12, 2015 Leave a comment
Investigators are questioning relatives and current and ex-employees of Westchester socialite Lois Colley to see if anyone had a beef with her that might have led to her murder, sources said Wednesday.
Florida Police officer Faces Charges After Argument With Wounded Vet Over Parking Space
RIVIERA BEACH — A 20-year city police officer was placed on administrative leave Tuesday night while authorities investigate an incident caught on film of him knocking a smartphone out of a 28-year-old Army veteran's hands during an argument over the legitimacy of his handicapped tag.
Ukrainian – Vadim Rabinovich Accuses Kiev of 'Flirting With Radicals'
One of Ukraine's most prominent Jews on Tuesday voiced concerns over Kiev's use of far-right radical nationalist groups in the battle against Russian-backed separatists, warning that the police have lost their "monopoly on the use of force."
Watch: Israeli Agents Pose As Arab Family In Daring Operation
GeneralBy Joe Levin November 12, 2015 Leave a comment
The IDF's undercover unit performed a daring operation at the Alhali Hospital in Hevron early Thursday morning.
Venezuelan First Lady's Nephews Arrested In US Drug Case
US authorities have arrested two relatives of Venezuelan President Nicolas Maduro for allegedly trying to smuggle 800 kilograms of cocaine into New York.
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We have been supplying new, original (manufacturers own) inkjet and laser toner cartridges for almost twenty years and carry one of the largest stocks of original inks in the area.
We offer a wide selection of top quality compatible inks and factory re-manufactured (not refilled) laser toner cartridges. If we haven't got one in stock we can usually get one the following day.


At Clayhall Dental Care we are happy to accept new patients on the NHS. Healthy gums, teeth and good oral hygiene are important and everyone should have access to good quality, NHS dental care.
It is important to understand, however, that there are differences between NHS dentistry and Private dental treatment. NHS is a health service with limited resources, not a cosmetic service. Private dentistry offers a wider range of treatments, materials and advanced dental techniques and equipment. Cosmetic dentistry such as white fillings, veneers and teeth whitening are not available on the NHS.
The choice between NHS and private dental treatment is yours but please ask your dentist to explain the differences in detail. This will allow you to make an informed decision and be happy with the choice you make.


MINSK, 3 April (BelTA-TASS) - Russia will resume oil supplies to Belarus in full, Russian Vice Premier Arkady Dvorkovich told the media.
"Some intergovernmental documents regarding mutual relations in the gas and oil sector will be adjusted. Once they are initialed, Belarus will pay its debt to Gazprom, i.e. Gazprom Transgaz Belarus to the Gazprom subsidiary, and we will resume oil supplies at the full volume of 24 million tonnes," said Arkady Dvorkovich.
He added that Gazprom would offer Belarus a discount with a decreasing coefficient for the oil price formula for the period from 2018 to 2019. The relations between the countries after that period will depend on further negotiations, Arkady Dvorkovich added.
The Vice Premier also said that oil supplies might be resumed in April.
"Oil supplies will soon resume, perhaps in April. This will depend on the technical capabilities of the companies," said Arkady Dvorkovich.


Uniforms will be available to order at the two Registration Days.
Check the sizing guide below and download the order form.
Nippers must wear a club skull cap and a HI-VIS Pink vest at all club events, training and carnivals. These items of clothing are compulsory; this allows us to safely identify and organise our nippers. To compete in team events at SLS carnivals all nippers must be in the same uniform and must wear a Carnival Tshirt, available to purchase at the club.
All swimwear will be available to try on for sizing and purchase on both registration days. Orders can also be made by downloading the Uniform Order form and emailing to uniforms@sandonpointsurfclub.org.au. and paid through the SLS Member Portal.
The Uniforms are still supplied by SLIX Australia but are now managed by the Club. All inquiries are to be emailed to the above email address.
We receive your return/exchange back within 14 days from date of pickup.
SLS Member Portal, Cash, EFTPOS and Credit Card. Payment is to be made at the time of ordering. Orders will not be placed until payment has been received.
Please ensure you order early to avoid disappointment. Orders made on both registrations will be available for pickup on the 14 October 2018.
Pickup date and time to be advised by email to those who have ordered as above.


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text:
By David O'Rourke
A toddler has become the youngest person to receive a bioengineered organ, receiving a life-saving windpipe transplant made from her own stem cells.
Hannah is two-and-a-half years old and was born with a rare congenital abnormality in which her trachea failed to develop. When she was born, a tube was inserted into her mouth so she could breathe on a ventilator.
The operation to transplant a windpipe into Hannah's chest took nine hours and was performed by an international team of surgeons at the Children's Hospital of Illinois, US, headed by Dr. Paolo Macchiarini of the Karolinska Institutet, Stockholm.
The team employed a two-step process to create the 'bioartificial' windpipe. Firstly, they engineered a 1.3 centimetre diameter synthetic scaffold out of plastic fibres using scans of Hannah's chest as a template. This polymer tube had many tiny pores designed to support the growth of Hannah's cells, promote a blood supply to the new organ and to degrade over time.
Secondly, the pores in and around the scaffold were filled with stem cells taken from Hannah's bone marrow. This was achieved by mixing her stem cells with a supportive growth media in a bioreactor, where they could attach to the scaffold. Over approximately two days, the cells connected to the polymer, filling the pores and creating an organ.
'The transplant crosses frontiers by eliminating the need for a human donor and a lifetime of immunosuppressant drugs', said Dr Macchiarini. This is the sixth operation of this kind to be carried out by this international team (reported in 162874" title="162874" target="_blank" class="">BioNews 667). They now believe that this approach to building organs may work best with children, as it harnesses their natural ability to grow and heal.
It is hoped that regenerative medicine will one day be able to create more complex multi-tissue organs such as kidneys and lungs, but so far it has only been possible to grow and transplant basic, hollow organs such as bladders, bones and windpipes.
Hannah continues to recover and with the help of pulmonologists, respiratory therapists, and speech therapists, her future looks promising. 'Hannah's case is a great example of how the international community can work together to save a child's life', said Dr. Mark Holterman, co-surgeon and professor of surgery and pediatrics at the University of Illinois College of Medicine.
First child in the world to receive tissue-engineered bioartificial trachea (press release)
Karolinska Institutet, Stockholm | 30 April 2013
Groundbreaking Surgery for Girl Born Without Windpipe
New York Times | 30 April 2013
Hannah's Story – From Seoul to Peoria (press release)
Children's Hospital of Illinois | 30 April 2013
Toddler Born Without a Windpipe Gets Artificial Trachea
ABC News | 30 April 2013
Toddler given life-saving windpipe transplant using her stem cells
Daily Telegraph | 2 May 2013
Young Girl Receives Lifesaving Windpipe Transplant Made From Her Stem Cells
Time | 30 April 2013
Stem-cell controversy unfolds in Sweden
15 February 2016 - by Kirsty Oswald
The world-renowned Karolinska Institute is at the centre of a scandal surrounding the conduct of stem-cell surgeon Paulo Macchiarini...
14 April 2014 - by Dr Nicola Davis
A lab in London where scientists grow human noses and windpipes has opened its doors to the press...
Lung cells grown from stem cells for first time
9 December 2013 - by Dr Greg Ball
Human induced pluripotent stem cells (iPS cells) have been transformed into lung and airway cells for the first time...
Tooth grown from human gum and mouse stem cells
18 March 2013 - by Dr Rosie Morley
For the first time, teeth have been grown from human gum cells, in combination with stem cells from mouse embryos...
Human kidney tissue successfully grown from stem cells
28 January 2013 - by Michelle Downes
In what is thought to be a first, stem cells have been used to generate human kidney tissue...
Girl receives first ever transplant of stem cell-treated vein
18 June 2012 - by Dr Lucy Freem
A ten-year-old Swedish girl has become the first recipient of a donor vein treated with a patient's own stem cells...

redpajama_set_name: RedPajamaCommonCrawl


text:
HANOVER, GERMANY - JUNE 12: The Huawei logo is displayed at the 2018 CeBIT technology trade fair on June 12, 2018 in Hanover, Germany. The 2018 CeBIT is running from June 11-15. (Photo by Alexander Koerner/Getty Images)
Design>Networks
U.S. Urges Allies to Avoid Using Huawei Equipment, WSJ Says
Scrutiny of Huawei has increased since Donald Trump became U.S. President as trade tensions between Washington and Beijing escalate.
Bloomberg | Nov 23, 2018
(Bloomberg) -- The U.S. government is contacting key allies to get them to persuade telecommunications companies in their countries to avoid using equipment from China's Huawei Technologies Co., the Wall Street Journal reported.
Officials from the U.S. have reached out to counterparts and executives in countries including Germany, Italy and Japan about perceived cybersecurity risks, the Journal said, citing unidentified people familiar with the matter. The U.S. may boost aid for telecommunications development in countries that shun Huawei equipment, some of the people said.
Huawei has long been labeled a security risk by U.S. lawmakers because of alleged links to the Chinese government, in part because it was founded by former military engineer Ren Zhengfei. While the Shenzhen-based company has denied any inappropriate connections, it's been banned in Australia from supplying fifth-generation wireless equipment, faced scrutiny in the U.K. and found itself largely shut out from the U.S. market.
Scrutiny of Huawei has increased since Donald Trump became U.S. President as trade tensions between Washington and Beijing escalate. The closely held company is now the world's second-largest maker of smartphones and is one of the biggest producers of equipment for running phone networks.
Huawei said customers around the world choose its products because they trust the company.
"Huawei is surprised by the behaviors of the US government detailed in the article," the company said in an email. "If a government's behavior extends beyond its jurisdiction, such activity should not be encouraged."
The spread on Huawei's 3.25 percent dollar bonds due in 2022 widened, with investors demanding the biggest yield premium since early July, according to data compiled by Bloomberg. Analysts cited the story as adding to weak sentiment in Chinese and Hong Kong equity markets, which led regional losses.
American officials are concerned about the use of the Chinese equipment in countries that host U.S. military bases such as Germany, Japan and Italy, the Journal reported. There is concern about China's ability to force companies to comply with government requests, it said.
A number of major telecommunications companies directed more than 5 percent of their capital expenditure to Huawei, according to Bloomberg supply chain data. That includes Telecom Italia SpA and Japan's NTT Docomo Inc. and KDDI Corp., the data shows.
Huawei has been pouring billions into developing 5G technology and its potential to become the global leader in the space is said to be a reason why Trump blocked the biggest ever chip deal earlier this year.
Chinese Spies Accused of Using Huawei in Secret Australia Telecom Hack
Executive at Swiss Tech Company Said to Operate Secret Surveillance Operation
First Submarine Cable Between Europe and South America Goes Live
SASE Model Proving Value Beyond Remote Work Scenarios


POLICE are urging the public to help the police tackle terrorism and save lives by reporting suspicious behaviour and activity.
In the UK, 82 per cent of adults have said they would report suspicious activity to the police.
Police want to keep this figure high and make sure people have the confidence to talk to officers if they notice anything that they believe could be terrorist-related.
Hampshire police We will be supporting the campaign efforts of their colleagues at the National Counter Terrorism Police.
Detective chief superintendent Kath Barnes, head of Counter Terrorism Policing South East, said: 'It's vital for the public to know that no matter how small the matter might be, if they think it is suspicious and have concerns, report it.
'Counter Terrorism Policing South East will take all information seriously, any piece of information could be important, it is better to be safe and report.
'Communities are the key to defeating terrorism and people can help us prevent terrorism and save lives through their actions.
More than a fifth of reports from the public produce intelligence which is helpful to police.
Now, he is launching the second phase of the 'ACT –Action Counters Terrorism' campaign, featuring a new 60-second film based on real-life foiled plots, which will show examples of terrorist-related suspicious activity and behaviour, as well as attack planning methodology.
ASCO Basu added: 'We need help to exploit opportunities for police and the security services to discover and stop these attacks before they happen.
'That could be someone buying or storing chemicals, fertilisers or gas cylinders for no obvious reasons, or receiving deliveries for unusual items, it could be someone embracing extremist ideology, or searching for such material online.
'This new film has been made to try and help people understand recent terrorist attack-planning methods, but also to demonstrate that each report from the public can be one vital piece of a much larger picture.
Report anything unusual or suspicious at gov.uk/ACT.


text:
\section{Introduction}\label{sec:intro}

The Kalman Filter (KF)~\cite{Kalman1960Kalman} is a cornerstone in control theory. Its elegance and optimality has motivated its extension to distributed setups, with several promising applications such as cooperative tracking~\cite{Morbidi2012Active}
or monitoring~\cite{Khan2008Monitoring}.
However, the optimal fusion of estimates in DKF requires tracking of the whole network covariance~\cite{Olfati2009DKF}. This is impractical in terms of memory and communication.
The alternative is to consider unknown correlations, solving the estimation fusion sub-optimally or via an NP-hard optimisation problem.
The latest relies on convex relaxations, trading off formal guarantees of finding the original optimum.
This is where \textit{certification} is of key importance, verifying if the relaxed solution is that of the original problem~\cite{Yang2020Teaser}.

Exploiting this idea, our main contribution is the Certifiable Optimal Distributed Kalman Filter (CO-DKF), the \textit{first DKF with certifiability guarantees}.
If the certification is positive, then CO-DKF is \textit{optimal in the Mean Square Error (MSE) sense under unknown correlations}.
Otherwise, it is still globally asymptotically stable.
Besides, nodes can check optimality locally and online, enabling security mechanisms to be exploited in applications where the estimator is embedded in the control structure~\cite{Talebi2019Distributed}.
In addition, CO-DKF is \textit{fully distributed}, has \textit{small communication burden} and works with \textit{heterogeneous} sensor models.

\section{Related work}\label{sec:SA}

The seminal works by Olfati-Saber~\cite{Olfati2005DKF,Olfati2007DKF} opened an era of consensus-based DKFs. The optimal gains in the MSE sense for the DKF proposed in~\cite{Olfati2007DKF} are found in~\cite{Olfati2009DKF}, but it is also proved that their computation is not scalable.
Since then, several works have searched for an Optimal DKF.
In~\cite{Das2016Consensus} the authors propose a DKF composed by a dynamic consensus and a filtering step, where each agent knows the communication topology and sensor models. Two other DKFs are~\cite{Kamal2013Information,Battistelli2014Consensus}, where the consensus over information and measurements is exploited to improve the performance. The solution in~\cite{Kamal2013Information} converges to the centralised KF but reaching average consensus at each time step. These papers track the network error covariance matrix or do not consider the information in the error covariances to define optimality.

The absence of optimal \textit{scalable} solutions motivated the Diffusion KFs (DfKF). They assume \textit{unknown correlations} so that only local error covariances are leveraged, where the most popular approach is the Covariance Intersection (CI) method~\cite{Julier1997CI}. The work in~\cite{Reinhardt2015CI} shows that CI provides the optimal bound for two nodes, but for a greater number the CI method is generally not optimal, arising a necessity of certification.
The authors of~\cite{Cattivelli2010Diffusion} proposed the DfKF suggesting a general convex optimisation. The CI method in DfKF was first applied in~\cite{Hu2011Diffusion}; however, arguing on its computational complexity, they study an approximation using only the estimate associated with the smaller error covariance trace. The work in~\cite{Deng2012sequential} proposes a sequential algorithm where each node performs a CI optimisation of two covariances, reducing the computation but increasing the communication burden. Two other CI-based DKFs are~\cite{wang2017convergence,he2018consistent}. The former provides novel proofs of stability for general time-varying and non-detectable scenarios, while the latter proposes an adaptive CI which decreases the conservativeness and preserves consistency. However, they do not guarantee optimality nor certifiability.

Inspired by the DfKF solutions, CO-DKF gathers the benefits of all the aforementioned solutions and adds the \textit{certifiability and optimality} properties, which come from a reformulation of the CI method based on the outer Löwner-John ellipsoid intersection method~\cite{Boyd1994LMI} and a SDP relaxation. Moreover, by proving the equivalence between CO-DKF and the optimal consensus over estimates we can demonstrate global asymptotic stability. An interesting consequence is an improved robustness against high levels of noise in the sensor measurements and sparse networks, validated in simulations that compare CO-DKF to other state-of-the-art filters.

\section{Problem formulation}\label{sec:preliminaries}

The target system is described by linear dynamics\footnote{For simplicity we do not consider external inputs and no matrix multiplying $\mathbf{w}(k)$. However, the results of the paper are directly generalisable.}
\begin{equation}\label{eq:system}
    \mathbf{x}(k+1) = \mathbf{A}\mathbf{x}(k) + \mathbf{w}(k),
\end{equation}
where $k \in \mathbb{N}_{\ge 0}$ is the discrete time, $\mathbf{x} \in \mathbb{R}^{n}$ is the state, $\mathbf{A} \in \mathbb{R}^{n} \times \mathbb{R}^{n}$ is a matrix comprising the target system dynamics, and $\mathbf{w}(k) \sim \mathcal{N}(\mathbf{0},\mathbf{Q}(k))$ with $\hbox{E}[\mathbf{w}(a)\mathbf{w}^T(b)] := \mathbf{Q}(k) \delta_{ab}$ is the Zero Gaussian Mean (ZGM) state noise, where $\delta_{ab} = 1$ if $a=b$ and $\delta_{ab} = 0$ otherwise.

To track the system, there is a network of sensors with a communication graph $G = (V,E)$. The number of nodes is $N=|V|$. Moreover, $\mathcal{N}_i = \{j|(i,j)\in E \}$ is the set of neighbours of node $i$ and $\mathcal{J}_i = \mathcal{N}_i \cup i$ with $p = |\mathcal{J}_i|$ its cardinality. Each sensor is described by a linear model
\begin{equation}\label{eq:distributedSensorModel}
    \mathbf{z}_i(k) = \mathbf{H}_i\mathbf{x}(k) + \mathbf{v}_i(k).
\end{equation}
Here, $\mathbf{z}_i \in \mathbb{R}^{m_i}$ is the measurement of node $i$, $\mathbf{H}_i \in \mathbb{R}^{m_i} \times \mathbb{R}^{n}$ is the (unbiased) sensor model of node $i$, $m_i$ is the dimension of $\mathbf{z}_i$ and $\mathbf{v}_i(k) \sim \mathcal{N}(\mathbf{0},\mathbf{R}_i(k))$ with $\hbox{E}[\mathbf{v}_i(a)\mathbf{v}_i^T(b)] := \mathbf{R}_i(k) \delta_{ab}$ is the ZGM measurement noise, where $\delta_{ab} = 1$ if $a=b$ and $\delta_{ab} = 0$ otherwise. We consider independent measurements. Notice that by using $m_i$ we are considering heterogeneous and/or incomplete, as long as the system is observable by at least one node.

The objective of the network is to cooperatively estimate $\mathbf{x}$. To do so, each node runs a local estimation algorithm, composed by a prediction step of the state ($\bar{\mathbf{x}}_i$), and an update of the prediction ($\hat{\mathbf{x}}_i$).
Associated with the prediction there is an error covariance matrix $\mathbf{P}_i := \hbox{E}\{(\bar{\mathbf{x}}_i-\mathbf{x})(\bar{\mathbf{x}}_i-\mathbf{x})^T\} $. Since this matrix is not known, each node has a predicted ($\bar{\mathbf{P}}_{i}$) and an updated ($\hat{\mathbf{P}}_{i}$) version. Unless it is essential, in the paper we will omit the dependencies with $k$ for clearness.

Given complete knowledge of the network, the optimal fusion of these terms is
\begin{align}
    \bar{\mathbf{S}}^*_{i} &= (\bar{\mathbf{P}}_{i}^*)^{-1} = (\mathbf{1} \otimes \mathbf{I}_{n}) \bar{\mathbf{P}}_{c}^{-1} (\mathbf{1} \otimes \mathbf{I}_{n})^T, \label{eq:optimal1}
    \\
    \bar{\mathbf{x}}_{i}^* &= \bar{\mathbf{P}}^*_{i} (\mathbf{1} \otimes \mathbf{I}_{n}) \bar{\mathbf{P}}_{c}^{-1} [\bar{\mathbf{x}}_1^T, \hdots, \bar{\mathbf{x}}_N^T]^T,\label{eq:optimal2}
\end{align}
where $(\cdot)^*$ denotes optimality, $\mathbf{1}$ is the row vector of $N$ ones, $\mathbf{I}_{n}$ is the identity matrix of order $n$, $\otimes$ is the Kronecker product, and $\bar{\mathbf{P}}_{c}$ is the full covariance matrix of the network that includes the self-correlations $\bar{\mathbf{P}}_i$ and the cross-correlations $\bar{\mathbf{P}}_{ij}$. The optimality of~\eqref{eq:optimal1}-\eqref{eq:optimal2} is in terms of the MSE, defined as follows:
\begin{definition}[\textbf{Mean Square Error}]\label{definition:MSE}
The Mean-Square Error (MSE) is $\hbox{MSE} := \sum_{i=1}^{N} \hbox{E}[||\hat{\mathbf{x}}_i-\mathbf{x}||^2].$
\end{definition}
The optimal fusion in Eqs.~\eqref{eq:optimal1}-\eqref{eq:optimal2} is not scalable because it needs to track every $\bar{\mathbf{P}}_{ij},  \bar{\mathbf{P}}_{i}$ and $\bar{\mathbf{x}}_i$. This has a strong computational and memory burden, and requires communication with second order neighbours~\cite{Olfati2009DKF}.

A typical alternative is to consider that the off-diagonal terms on $\bar{\mathbf{P}}_{c}$ are unknown and disregard non-neighbouring error covariances. Then, the optimal fusion can be achieved through optimisation, using the neighbouring predictions and predicted error covariances to produce an optimal bound of $\bar{\mathbf{P}}^*_i$ and the corresponding prediction.
We rely on a bit abuse of notation and also denote this optimal bound by $\bar{\mathbf{P}}^*_i$, since it is the best result given unknown correlations and non-neighbouring error covariances.

This optimisation problem is intractable (Section~\ref{sec:solution}), which forces the use of convex relaxations to solve it. Despite enabling tractability, the relaxed solution is not guaranteed to be the original optimum. This motivates the need of certifiability on the optimisation, formally defined as follows:
\begin{definition}[\textbf{Certifiable Algorithms, from Definition 19 on~\cite{Yang2020Teaser}}]\label{definition:certifiability}
Given an optimization problem $\mathbb{O}(\mathbb{D})$ that depends on input data $\mathbb{D}$, we say that an algorithm $\mathbb{A}$ is certifiable if, after solving $\mathbb{O}(\mathbb{D})$, algorithm $\mathbb{A}$ either provides a certificate for the quality of its solution or declares failure otherwise.
\end{definition}

Now, we formulate the problem addressed in the paper.

\begin{problem}[\textbf{Certifiable optimal DKF under unknown correlations}]\label{problem:CO-DKF}
Find a stable algorithm that certificates locally and in real time if the estimation of system~\eqref{eq:system} carried out by each node is being optimal, i.e, at each $k$, each node $i$ minimises the MSE, under the following restrictions:
\begin{enumerate}
    \item \textbf{Unknown correlations}: The correlation terms $\mathbf{P_{ij}}(k)$ $\forall i \neq j$ are unknown $\forall i$ and $\forall k$.
    \item \textbf{Locality}: At instant $k$ and $\forall i$, node $i$ only uses $\mathbf{A}$, $\mathbf{H}_i$, $\mathbf{Q}(k)$, and $\mathbf{R}_i(k)$ as parameters.
    \item \textbf{One-hop communication}: At instant $k$ and $\forall i$, node $i$ only communicates once with its neighbours $j \in \mathcal{N}_i$.
\end{enumerate}
\end{problem}

\section{CO-DKF Algorithm}\label{sec:algorithm}

The proposed solution for Problem~\ref{problem:CO-DKF} is CO-DKF. We first offer an overview the algorithm and then, in Sections~\ref{sec:solution} and~\ref{sec:stability}, we formally study its main properties.

At a given iteration of the algorithm, each node first sends and receives the prediction (with its covariance) and measurement (with its covariance) in information form to avoid the propagation of sensor models and unnecessary inversions of matrices,
\begin{equation*}
    \begin{aligned}
    \mathbf{u}_i &= \mathbf{H}_i^T\mathbf{R}_i^{-1}\mathbf{z}_i, &
    \mathbf{U}_i &= \mathbf{H}_i^T\mathbf{R}_i^{-1}\mathbf{H}_i,
    \\
    \bar{\mathbf{s}}_i &= \bar{\mathbf{P}}_i^{-1}\bar{\mathbf{x}}_i, & \bar{\mathbf{S}}_i &= \bar{\mathbf{P}}_i^{-1}.
    \end{aligned}
\end{equation*}
These quantities are aggregated using the information provided by the covariances. In the case of the measurements, this is direct because they are independent
\begin{flalign}
    \mathbf{y}_i = \frac{1}{p}\sum_{j\in \mathcal{J}_i} \mathbf{u}_j \hbox{ and }
    \mathbf{Y}_i = \frac{1}{p}\sum_{j\in \mathcal{J}_i} \mathbf{U}_j\label{eq:KF1}.
\end{flalign}
On the other hand, the aggregation of predictions is harder due to the correlations among them. Even if these correlations are unknown, they need to be taken into account into the fusion.
To solve it, we propose to use the outer Löwner-John (LJ) method~\cite{John2014Ellipsoid}, which gives the following relaxed optimisation problem
\begin{subequations}\label{eq:outerLJellipse}
\begin{alignat}{2}
\bar{\mathbf{S}}_i^*, \lambda^* =  \:\:\: &\underset{\bar{\mathbf{S}},\lambda}{\arg\max}         \:\:\:\:\:\:\:\:\hbox{Tr}(\bar{\mathbf{S}})  \label{eq:optProb3}
\\
   \:\:\:\:\:\: s.t.  \:\:\:\:\:&\mathbf{0}  \prec \bar{\mathbf{S}} \preceq \sum_{j\in \mathcal{J}_i} \lambda_j \bar{\mathbf{S}}_j ,\label{eq:constraint31}
\\
&\sum_{j\in \mathcal{J}_i} \lambda_j   \leq 1 \hbox{ , } \lambda_j  \geq 0, \:\:\:\forall j \in \mathcal{J}_i \label{eq:constraint32}
\end{alignat}
\end{subequations}
where Tr$(\cdot)$ is the trace of a matrix, and $\prec$ and $\preceq$ denote definiteness and semidefiniteness. We recall that $\bar{\mathbf{P}}_i^{-1} = \bar{\mathbf{S}}_i$. The selection of the trace as the optimisation cost function follows from the definition of optimality, demonstrated later in the proof of Theorem~\ref{theorem:optimality}. The output of~\eqref{eq:outerLJellipse} is used to aggregate the predictions as follows
\begin{flalign}
    \bar{\mathbf{P}}^*_{i} = (\bar{\mathbf{S}}_i^*)^{-1} \hbox{ , }\:\:\:\:\:
    \bar{\mathbf{x}}_{i}^* = \bar{\mathbf{P}}_{i}^* \sum_{j\in \mathcal{J}_i} \lambda_j^*\bar{\mathbf{s}}_j\label{eq:KF_o1}.
\end{flalign}
The formal results over this aggregation are developed in Section~\ref{sec:solution}.
To the best of our knowledge, this is the first time optimisation problem~\eqref{eq:outerLJellipse} is applied to calculate $\bar{\mathbf{P}}^*_i$ and $\bar{\mathbf{x}}^*_i$ in a DKF. Furthermore, it enables the optimality certification of the CO-DKF.
With the data aggregated, each node calculates $\mathbf{M}_i:= \hbox{E}\{(\hat{\mathbf{x}}_i-\mathbf{x})(\hat{\mathbf{x}}_i-\mathbf{x})^T\}$ as
\begin{equation}
    \mathbf{M}_i = \left(\bar{\mathbf{S}}_i^* + \mathbf{Y}_i\right)^{-1}\label{eq:KF3}
\end{equation}
and then they correct the result of the predictions' aggregation by doing the following update
\begin{equation}\label{eq:CODKF_estimation}
    \hat{\mathbf{x}}_i^* = \bar{\mathbf{x}}_i^* + \mathbf{M}_i(\mathbf{y}_i - \mathbf{Y}_i\bar{\mathbf{x}}_i^*).
\end{equation}
It is noteworthy that the structure of Eq.~\eqref{eq:CODKF_estimation} is similar to
\begin{equation}
    \label{eq:KF4}
    \hat{\mathbf{x}}_i =
        \bar{\mathbf{x}}_i + \mathbf{M}_i\left(\mathbf{y}_i - \mathbf{Y}_i\bar{\mathbf{x}}_i\right) +\gamma \mathbf{M}_i \sum_{j\in \mathcal{N}_i} (\bar{\mathbf{x}}_j - \bar{\mathbf{x}}_i),
\end{equation}
which comes from the consensus-based distributed Kalman filter in~\cite{Olfati2007DKF}. However, in CO-DKF the consensus is implicit in the optimisation, relaxing the dependence for stability on parameter $\gamma$.
Finally, nodes predict for the next time-step,
\begin{flalign}
    \bar{\mathbf{P}}_i(k+1) &= \mathbf{A}\mathbf{M}_i(k)\mathbf{A}^T + \mathbf{Q}(k)\label{eq:KF5},
    \\
    \bar{\mathbf{x}}_i(k+1) &= \mathbf{A}\hat{\mathbf{x}}_i^*(k)\label{eq:KF6}.
\end{flalign}

We briefly discuss the communication and computational burden of this algorithm. Regarding communication, each node sends $\mathbf{U}_i, \mathbf{u}_i, \bar{\mathbf{S}}_i$ and $\bar{\mathbf{s}}_i.$
The size of the message is constant in the number of nodes, confirming the communication scalability of the proposal. Another advantage of CO-DKF is that nodes do not need any global knowledge of the topology nor sensor models of neighbours. Regarding computational cost, the bottleneck is the computation of~\eqref{eq:outerLJellipse}. The current hardware is able to solve large instances of this optimisation problem in real-time.
This is discussed in more details in Section~\ref{sec:examples}.

In summary, CO-DKF is described by Algorithm~\ref{al:CO-DKF}.

\begin{algorithm}
\caption{CO-DKF in node $i$}\label{al:CO-DKF}
\begin{algorithmic}[1]
\STATE Initialisation: $\bar{\mathbf{P}}_i = \mathbf{P}_0$, $\bar{\mathbf{x}}_i = \mathbf{x}_0$
\WHILE{True}
    \STATE  Get $\mathbf{z}_i$, send $\{ \mathbf{U}_i, \mathbf{u}_i, \bar{\mathbf{S}}_i, \bar{\mathbf{s}}_i  \}$ and receive $\{ \mathbf{U}_j, \mathbf{u}_j, \bar{\mathbf{S}}_j, \bar{\mathbf{s}}_j  \}$ from neighbours.
    \STATE Aggregate measurements' data:
           \begin{itemize}
               \item[] $\mathbf{Y}_i = \frac{1}{p}\sum_{j\in \mathcal{J}_i} \mathbf{U}_j$
               \item[] $\mathbf{y}_i \:= \frac{1}{p}\sum_{j\in \mathcal{J}_i}  \mathbf{u}_j$
           \end{itemize}
    \STATE Aggregate predictions' data:
            \begin{itemize}
               \item[] \:$\bar{\mathbf{S}}_i^*$,$\mathbf{\lambda}^*$ $\leftarrow$ Solution of ~\eqref{eq:outerLJellipse}
               \item[] \:\:\:\:\:\:\:\:\:\:\:\:\:$\bar{\mathbf{P}}_{i}^* = (\bar{\mathbf{S}}_i^*)^{-1}$
               \item[] \:\:\:\:\:\:\:\:\:\:\:\:\:$\bar{\mathbf{x}}_{i}^* \:= \bar{\mathbf{P}}_{i}^* \sum_{j\in \mathcal{J}_i} \lambda_j^*\bar{\mathbf{s}}_j$
           \end{itemize}
    \STATE CO-DKF estimation update:
            \begin{itemize}
               \item[] $\mathbf{M}_i = (\bar{\mathbf{S}}^*_i + \mathbf{Y}_i)^{-1}$
               \item[] \:\:$\hat{\mathbf{x}}_i^* = \bar{\mathbf{x}}_{i}^* + \mathbf{M}_i(\mathbf{y}_i - \mathbf{Y}_i\bar{\mathbf{x}}_{i}^*)$
           \end{itemize}
    \STATE Compute the next-step prediction:
            \begin{itemize}
               \item[] $\bar{\mathbf{P}}_i(k+1) = \mathbf{A}\mathbf{M}_i(k)\mathbf{A}^T + \mathbf{Q}(k)$
               \item[] \:$\bar{\mathbf{x}}_i(k+1) = \mathbf{A}\hat{\mathbf{x}}_i^*(k)$
           \end{itemize}
\ENDWHILE
\end{algorithmic}
\end{algorithm}

\section{Certifiable Covariance Bounding}\label{sec:solution}

To achieve optimality it is necessary to optimally aggregate the neighbouring predictions under unknown correlations. This fusion can be described as finding the minimum volume ellipsoid containing the intersection of the $p$ ellipsoids~\cite{Boyd1994LMI} formed by the matrices $\bar{\mathbf{P}}_j$ in $\mathcal{J}_i$.
Thus, we first define the concept of ellipsoid and intersection of ellipsoids.
\begin{definition}[\textbf{Ellipsoid}]\label{definition:ellipsoid}
Given $\bar{\mathbf{S}}_i = (\bar{\mathbf{P}}_i)^{-1}$ and assuming unbiased sensors, the ellipsoid $\varepsilon_i$ is $\varepsilon_i := \{\,\mathbf{x} \,| \,\mathbf{x}^T \bar{\mathbf{S}}_i \mathbf{x} \leq 1 \, \}.$
\end{definition}
\begin{definition}[\textbf{Intersection of ellipsoids}]\label{definition:intersection}
The intersection of $p$ ellipsoids is the polytope
$\mathcal{F} := \varepsilon_1 \cap \hdots \cap \varepsilon_p$.
\end{definition}

From Definitions~\ref{definition:ellipsoid}-\ref{definition:intersection}, minimising the volume can be transformed into a maximisation over the information matrices. In particular, since the MSE is equivalent to the trace of $\mathbf{M}_i,$ the objective of CO-DKF is to optimise this metric.

\begin{problem}[\textbf{Optimal intersection of ellipsoids}, adapted from~\cite{Boyd1994LMI}]\label{problem:intersection}
Find $\varepsilon^{*}_i$ such that contains $\mathcal{F}_i$ and \emph{Tr}$(\bar{\mathbf{S}}_i^*)$ is maximised.
\end{problem}
The solution of Problem~\ref{problem:intersection} is given by~\cite{Henrion2001LMI}
\begin{subequations}\label{eq:traceProblem}
\begin{alignat}{2}
\underset{\mathbf{X}}{\max} & \:\:\:\:\:\:\:\hbox{Tr}(\mathbf{X}) \label{eq:optProb4}
\\
s.t. & \:\:\:\:\:\:\:    \hbox{Tr}(\mathbf{X} \bar{\mathbf{S}}_j)  \leq 1 \:\:\: \forall j \in \mathcal{J}_i,\label{eq:constraint41}
\\
&   \:\:\:\:\:\:\:   \mathbf{X}    \succeq \mathbf{0} \label{eq:constraint42}
\\
&   \:\:\:\:\:\:\:   \hbox{rank}(\mathbf{X})  = 1 \label{eq:constraint43}
\end{alignat}
\end{subequations}
Unfortunately, this problem is NP-hard because of constraint~\eqref{eq:constraint43}. Thus, it is necessary to find a convex relaxation.
The simplest solution is to drop the non-convex constraint,
\begin{subequations}\label{eq:traceRelax}
\begin{alignat}{2}
\underset{\mathbf{X}}{\max} & \:\:\:\:\:\:\: \hbox{Tr}(\mathbf{X}) \label{eq:optProb5}
\\
s.t. & \:\:\:\:\:\:\:     \hbox{Tr}(\mathbf{X}\bar{\mathbf{S}}_j)  \leq 1 \:\:\: \forall j \in \mathcal{J}_i,\label{eq:constraint51}
\\
& \:\:\:\:\:\:\:\mathbf{X}    \succeq \mathbf{0} \label{eq:constraint52}
\end{alignat}
\end{subequations}
However, once again it is not possible to use~\eqref{eq:traceRelax} in CO-DKF because it does not provide $\bar{\mathbf{S}}_i^*$ nor $\bar{\mathbf{x}}^*_i$, as is the case of the outer LJ relaxation in~\eqref{eq:outerLJellipse}.
Nevertheless, problem~\eqref{eq:traceRelax} is important because it enables the certification of optimality. This is formally stated in the next Proposition.

\begin{proposition}[\textbf{Certifiability}]\label{proposition:certifiability}
Let $\mathbf{X}^*$ be the solution of~\eqref{eq:traceRelax}.
Define
\begin{flalign}
    \mathbb{C}_i := \emph{rank}\left(\mathbf{X}^*\right) \hbox{ and }
    \rho_i &:= \emph{Tr}(\mathbf{X}^*) \vartheta(\bar{\mathbf{S}}_i^*)\in [0,1],
\end{flalign}
where $\vartheta(\bar{\mathbf{S}}_i^*)$ denotes the minimum eigenvalue of $\bar{\mathbf{S}}_i^*$, obtained solving~\eqref{eq:outerLJellipse}.
If $\mathbb{C}_i=\rho_i=1$, then the solution of~\eqref{eq:outerLJellipse} is the optimum of the original non-relaxed problem~\eqref{eq:traceProblem}.
\end{proposition}
\begin{proof}
If constraint~\eqref{eq:constraint43} holds for $\mathbf{X}^*$, then it is also the optimum of~\eqref{eq:traceProblem}. This can be demonstrated by contradiction. Consequently, $\mathbb{C}_i=1$ is a certificate of this equivalence.

The next part is to show that the optimums of~\eqref{eq:traceRelax} and~\eqref{eq:outerLJellipse} are equivalent. This is described in detail in Section 2 of~\cite{Henrion2001LMI}, so we only sketch here the procedure. Obtained the Lagrangian of~\eqref{eq:traceRelax} and assuming that $\mathcal{F}$ does not reduce to zero, by Slater's condition both dual and primal have the same optimum. Then, by the S-procedure,~\eqref{eq:outerLJellipse} is equivalent to the dual and hence equivalent to~\eqref{eq:traceRelax}.

If it is the case, then outputs of~\eqref{eq:traceRelax} and~\eqref{eq:outerLJellipse} can be compared to see how close is the solution of~\eqref{eq:outerLJellipse} to the solution of Problem~\ref{eq:traceProblem}. To do so, Theorem 4 of~\cite{Henrion2001LMI} states that the optimal value of~\eqref{eq:outerLJellipse} is bounded by $1/\vartheta(\bar{\mathbf{S}}^*_i)$, where $\bar{\mathbf{S}}^*_i$ is the output of the optimisation in~\eqref{eq:outerLJellipse}. Therefore, $\rho_i$ assesses the output of~\eqref{eq:outerLJellipse} comparing it with the optimal value certified by the constraint~\eqref{eq:constraint43}. If $\mathbb{C}_i=1$ and $\rho_i=1$, then the solution of~\eqref{eq:outerLJellipse} is the optimum of the original Problem~\ref{problem:intersection}.
\end{proof}

Thus, the proposition gives a procedure to check, locally and online, the optimisation process by finding the optimal value for Problem~\ref{problem:intersection}.

\section{Stability and Optimality}\label{sec:stability}

In this Section we analyse the global properties of CO-DKF. To this end, we define the update error as $\eta_i = \hat{\mathbf{x}}_i-{\mathbf{x}}$,
\begin{equation*}
    \begin{aligned}
        \eta :=& [\eta_1^T, \hdots, \eta_{N}^T]^T,  & \mathbf{H} :=& \hbox{block-diag}(\mathbf{H}_1, \hdots, \mathbf{H}_{N})
        \\
        \mathbf{z} :=& [\mathbf{z}_1^T, \hdots, \mathbf{z}_N^T]^T, &\mathbf{R} :=& \hbox{block-diag}(\mathbf{R}_1, \hdots, \mathbf{R}_{N}),
        \\
        \mathbf{y} :=& [\mathbf{y}_1^T, \hdots, \mathbf{y}_N^T]^T,&\mathbf{U} :=& \hbox{block-diag}(\mathbf{U}_1, \hdots, \mathbf{U}_{N}),
        \\
        \mathbf{\mathcal{A}} :=& \mathbf{I} \otimes \mathbf{A}, &\mathbf{M} :=& \hbox{block-diag}(\mathbf{M}_1, \hdots, \mathbf{M}_{N}),
        \\
        \mathbf{\mathcal{Q}} :=& \mathbf{I} \otimes \mathbf{Q},&\bar{\mathbf{P}}^* :=& \hbox{block-diag}(\bar{\mathbf{P}}_{1}^*, \hdots, \bar{\mathbf{P}}_{N}^*),
    \end{aligned}
\end{equation*}
and
\begin{equation}\label{eq:nw}
\begin{aligned}
    \mathbf{Y} \overset{Eq.~\eqref{eq:KF1}}{=} \mathbf{N}_w \mathbf{U} \Rightarrow &
    \left. \begin{array}{ll}
         |\mathbf{N}_w|_{ij} = \frac{1}{p}*\mathbf{I}  \hbox{ if } j\in \mathcal{J}_i  \\
         |\mathbf{N}_w|_{ij} = 0*\mathbf{I} \hbox{ otherwise}
    \end{array}\right..
\end{aligned}
\end{equation}

To demonstrate the global asymptotic stability of CO-DKF, we adapt two Lemmas from~\cite{Olfati2009DKF} and derive a novel one which will support our main result.
\begin{lemma}[\textbf{Adapted from Lemma 2 from~\cite{Olfati2009DKF}}]\label{lemma:matrices}
Given Eqs.~\eqref{eq:KF3}-\eqref{eq:CODKF_estimation}, the following holds:
\begin{enumerate}
    \item $\mathbf{F} = \mathbf{I} - \mathbf{M}\mathbf{Y}=\mathbf{M}(\bar{\mathbf{P}}^*)^{-1}$.
    \item $\mathbf{M} = \mathbf{F}\mathbf{G}\mathbf{F}^T$ with $\mathbf{G} = \mathbf{\mathcal{A}}\mathbf{M}\mathbf{\mathcal{A}}^T + \mathbf{\mathcal{Q}} + \mathbf{T}\mathbf{R}^{-1}\mathbf{T}^T$ and $\mathbf{T} = \bar{\mathbf{P}}^* \mathbf{N}_w \mathbf{H}^T$.
\end{enumerate}
\end{lemma}
\begin{proof}
Let $\mathbf{F} = \mathbf{I} - \mathbf{M}\mathbf{Y}$, by Eq.~\eqref{eq:KF3} we can write $\mathbf{M} = ((\bar{\mathbf{P}}^*)^{-1} + \mathbf{Y})^{-1}$. Then,
\begin{equation}
  \mathbf{M}((\bar{\mathbf{P}}^*)^{-1} + \mathbf{Y}) = \mathbf{I} \Rightarrow \mathbf{I} - \mathbf{M}\mathbf{Y}=\mathbf{M}(\bar{\mathbf{P}}^*)^{-1}
\end{equation}
and the first statement is proved. Regarding the second statement, notice that Eq.~\eqref{eq:CODKF_estimation} can be stacked as follows
\begin{equation}\label{eq:CODKF_estimation_stacked}
    \hat{\mathbf{x}}^* = \bar{\mathbf{x}}^* + \mathbf{M}(\mathbf{y} - \mathbf{Y}\bar{\mathbf{x}}^*).
\end{equation}
Then, taking into account that $\mathbf{y}=\mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}\mathbf{z}$ and $\mathbf{Y}=\mathbf{N}_w\mathbf{U} = \mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}\mathbf{H}$, Eq.~\eqref{eq:CODKF_estimation_stacked} is rewritten from its information form as
\begin{equation}\label{eq:CODKF_estimation_standard}
    \hat{\mathbf{x}}^* = \bar{\mathbf{x}}^* + \mathbf{M}\mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}(\mathbf{z} - \mathbf{H}\bar{\mathbf{x}}^*) = \bar{\mathbf{x}}^* + \mathbf{K}(\mathbf{z} - \mathbf{H}\bar{\mathbf{x}}^*)
\end{equation}
with $\mathbf{K}=\mathbf{M}\mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}$ the Kalman Gain of the standard KF formulation. Let now consider the update of $\mathbf{M}$ as
\begin{equation}\label{eq:standard}
    \mathbf{M}^{+} = \mathbf{F}\mathbf{P}^+\mathbf{F}^T + \mathbf{K}\mathbf{R}\mathbf{K}^T,
\end{equation}
where $(\cdot)^+$ is the update operator. This expression comes from the standard KF~\cite{Olfati2009DKF}. Therefore, substituting $\mathbf{K}$ we obtain
\begin{equation}\label{eq:standard2}
    \mathbf{M}^{+} = \mathbf{F}(\mathbf{\mathcal{A}}\mathbf{M}\mathbf{\mathcal{A}}^T + \mathbf{\mathcal{Q}})\mathbf{F}^T + \mathbf{M}\mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}\mathbf{H}\mathbf{N}_w^T\mathbf{M}^T.
\end{equation}
Given statement 1 of the Lemma,
\begin{equation}\label{eq:standard3}
    \mathbf{M}^{+} = \mathbf{F}(\mathbf{\mathcal{A}}\mathbf{M}\mathbf{\mathcal{A}}^T + \mathbf{\mathcal{Q}} + \bar{\mathbf{P}}^*\mathbf{N}_w\mathbf{H}^T\mathbf{R}^{-1}\mathbf{H}\mathbf{N}_w^T(\bar{\mathbf{P}}^*)^T)\mathbf{F}^T,
\end{equation}
and statement 2 is proved.
\end{proof}
\begin{lemma}[\textbf{Adapted from Lemma 3 from~\cite{Olfati2009DKF}}]\label{lemma:stability}
Suppose that the error dynamics without noise are $\eta^+ = \mathbf{F}\mathbf{\mathcal{A}}\eta$ with $\mathbf{F}$ defined as in Lemma~\ref{lemma:matrices}. Then, the error dynamics is globally asymptotically stable system with a Lyapunov function $V(\eta) = \eta^T \mathbf{M}^{-1} \eta$ and $\Lambda = \mathbf{M}^{-1} - \mathbf{\mathcal{A}}^T\mathbf{G}^{-1} \mathbf{\mathcal{A}} \succ \mathbf{0}$.
\end{lemma}
\begin{proof}
Given $V(\eta) = \eta^T \mathbf{M}^{-1} \eta$ as Lyapunov function candidate,
\begin{equation}
\begin{aligned}
    \delta V =& (\eta^+)^T (\mathbf{M}^+)^{-1} \eta^+ - \eta^T \mathbf{M}^{-1} \eta =\\
              & \eta^T\left.(\mathbf{\mathcal{A}}^T\mathbf{F}^T (\mathbf{M}^+)^{-1} \mathbf{F} \mathbf{\mathcal{A}} - \mathbf{M}^{-1})\right. \eta = \\
              & \eta^T\left.(\mathbf{\mathcal{A}}^T\mathbf{G}^{-1} \mathbf{\mathcal{A}} - \mathbf{M}^{-1})\right. \eta = \\
              & -\eta^T\left.(\mathbf{M}^{-1} - \mathbf{\mathcal{A}}^T(\mathbf{\mathcal{A}}\mathbf{M}\mathbf{\mathcal{A}}^T + \mathbf{W})^{-1} \mathbf{\mathcal{A}})\right. \eta = \\
              & -\eta^T \Lambda \eta,
\end{aligned}
\end{equation}
with $\mathbf{W} = \mathbf{\mathcal{Q}} + \mathbf{T}\mathbf{R}^{-1}\mathbf{T}^T \succ \mathbf{0}$ and $\Lambda = \mathbf{M}^{-1} - \mathbf{\mathcal{A}}^T(\mathbf{\mathcal{A}}\mathbf{M}\mathbf{\mathcal{A}}^T + \mathbf{W})^{-1}\mathbf{\mathcal{A}}$. The rest of the proof directly follows from Lemma 3 of~\cite{Olfati2009DKF}, showing that $\Lambda \succ \mathbf{0}$. Therefore, the error dynamics is globally asymptotically stable.
\end{proof}
Finally, to prove stability of CO-DKF we provide a Lemma associated to~\eqref{eq:outerLJellipse}.
show that, if the predicted covariance matrices converge to a constant value, then  constraint~\eqref{eq:constraint31} in an strict equality.
\begin{lemma}[\textbf{Strong equalities}]
\label{lemma:convergence}
Given optimisation problem~\eqref{eq:outerLJellipse}, $\bar{\mathbf{S}}^*_i = \sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j$ with $j \in \mathcal{J}_i$, for all $i$.
\end{lemma}
\begin{proof}
Problem~\eqref{eq:outerLJellipse} is a convex maximisation with respect to $\bar{\mathbf{S}}$ and $\lambda$, which means that its optimum is unique. Notice that the cost function is the trace of $\bar{\mathbf{S}}$. Therefore, maximisation of Tr$(\bar{\mathbf{S}})$ with respect to $\lambda$ implies that the maximum is found when constraint~\eqref{eq:constraint32} is an equality and $\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j$ is the convex combination of $\bar{\mathbf{S}}_j$ with maximum trace. This can be demonstrated by contradiction: if $\sum_{j=1}^p \lambda_j < 1$ then there exists another convex combination of $\bar{\mathbf{S}}_j$ with a higher trace, which means that the optimum is with $\sum_{j=1}^p \lambda_j = 1$; in addition, the values of $\lambda_j$ must be such that $\sum_{j=1}^p \lambda_j \bar{\mathbf{S}}_j$ is maximised, otherwise there exists a different convex combination of $\bar{\mathbf{S}}_j$ with a higher trace.

Now, notice that $\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j$ is in constraint~\eqref{eq:constraint31} bounding the value of $\bar{\mathbf{S}}$ such that matrix $\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j - \bar{\mathbf{S}}$ must be positive semidefinite. Therefore, the optimal value of problem~\eqref{eq:outerLJellipse} must be the supremum of constraint~\eqref{eq:constraint31} and the optimal value of $\bar{\mathbf{S}}$ must share eigenvalues with $\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j$. Since they share eigenvalues, the trace of both quantities are equal and $\hbox{Tr}(\bar{\mathbf{S}}^*_i) = \hbox{Tr}(\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j)$ holds. Given the uniqueness of optimum, the optimal value of $\bar{\mathbf{S}}$ is $\sum_{j=1}^p \lambda_j^* \bar{\mathbf{S}}_j$ and the statement of the Lemma is proved.

\end{proof}

In essence, Lemma~\ref{lemma:convergence} says that the optimisation in~\eqref{eq:outerLJellipse} becomes a standard discrete-time consensus protocol tuned to optimise the trace of the final consensus value of each node. Interestingly, from~\eqref{eq:KF3} we can expect that the optimisation will ponder more the nodes equipped with better sensors, which is a positive side effect of CO-DKF when compared with the widely used update equation in~\eqref{eq:KF4}.

We can now demonstrate the stability of the estimator.
\begin{theorem}[\textbf{Stability}]\label{theorem:stability}
CO-DKF is a globally asymptotically stable estimator.
\end{theorem}
\begin{proof}
The first step is to rewrite Eq.~\eqref{eq:CODKF_estimation} like Eq.~\eqref{eq:KF4}. The aggregated prediction $\bar{\mathbf{x}}^*_{i}$ in Eq.~\eqref{eq:CODKF_estimation} is obtained by
\begin{equation}\label{eq:xfusiones}
     \bar{\mathbf{x}}_{i}^* = \bar{\mathbf{P}}_{i}^* \sum_{j\in \mathcal{J}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}\bar{\mathbf{x}}_{j}.
\end{equation}
This expression can be rewritten as
\begin{equation}\label{eq:xfusiones3}
     \bar{\mathbf{x}}_{i}^* = \bar{\mathbf{P}}_{i}^*\sum_{j\in \mathcal{J}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}  \bar{\mathbf{x}}_{i}  +
     \bar{\mathbf{P}}^*_{i} \sum_{j\in \mathcal{N}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}(\bar{\mathbf{x}}_{j}-\bar{\mathbf{x}}_{i}).
\end{equation}
From Lemma~\ref{lemma:convergence} we have that $\bar{\mathbf{P}}_{i}^*\sum_{j\in \mathcal{J}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1} = \mathbf{I}$. Thus, plugging~\eqref{eq:xfusiones3} into~\eqref{eq:CODKF_estimation} gives
\begin{equation}\label{eq:rewrite_sta}
\begin{aligned}
     \hat{\mathbf{x}}_{i} =& \bar{\mathbf{x}}_{i} + \mathbf{M}_i(\mathbf{y}_i - \mathbf{Y}_i\bar{\mathbf{x}}_{i})  +
     \\&
     (\mathbf{I}-\mathbf{M}_i\mathbf{Y}_i)\bar{\mathbf{P}}_{i}^*
     \sum_{j\in \mathcal{N}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}(\bar{\mathbf{x}}_{j}-\bar{\mathbf{x}}_{i}).
\end{aligned}
\end{equation}
The last expression is equivalent to Eq.~\eqref{eq:KF4} but weighting each term with the result of optimising~\eqref{eq:outerLJellipse}.
Given this equivalence, the noiseless dynamics of $\eta_i$ is
\begin{equation}\label{eq:error_dynamics}
     \eta_{i}^+ = (\mathbf{I}-\mathbf{M}_i\mathbf{Y}_i)(\mathbf{A}\eta_{i} +
     \bar{\mathbf{P}}_{i}^*\sum_{j\in \mathcal{N}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}\mathbf{A}(\eta_{j}-\eta_{i})),
\end{equation}
which can be written in compact form as $\eta^+ = \mathbf{F}\left.\mathbf{L}_w\right. \mathbf{\mathcal{A}}\eta.$ Here, $(\cdot)^+$ is the update operator, $\mathbf{F}$ is defined as in Lemma~\ref{lemma:matrices}, and $\mathbf{L}_w$ is such that $|\mathbf{L}_w|_{ij} = \bar{\mathbf{P}}_{i}^*\lambda_j^*\bar{\mathbf{P}}_j^{-1}$ for all $j\in \mathcal{J}_i$ and $\mathbf{0}$ otherwise. The latest is similar to the error dynamics proved as globally asymptotically stable in Lemma~\ref{lemma:stability}, but with $\mathbf{L}_w$ in between. Lemma~\ref{lemma:stability} states that $\Lambda = \mathbf{M}^{-1} - \mathbf{\mathcal{A}}^T\mathbf{G}^{-1} \mathbf{\mathcal{A}} \succ \mathbf{0}$
but, since the error dynamics is $\eta^+$, we instead have $\Lambda^{'} = \mathbf{M}^{-1} - \mathbf{\mathcal{A}}^T\mathbf{L}_w^T\mathbf{G}^{-1}\mathbf{L}_w\mathbf{\mathcal{A}}.$ If
\begin{equation}\label{eq:statement1}
 \mathbf{\mathcal{A}}^T\mathbf{G}^{-1} \mathbf{\mathcal{A}} \succeq \mathbf{\mathcal{A}}^T\mathbf{L}_w^T\mathbf{G}^{-1}\mathbf{L}_w\mathbf{\mathcal{A}},
\end{equation}
then $\Lambda^{'} \succ \mathbf{0}$ and global asymptotic stability of the error dynamics is proved. The statement in~\eqref{eq:statement1} is equivalent to $\mathbf{I} \succeq \mathbf{L}_w$. Given Lemma~\ref{lemma:convergence}, $\mathbf{L}_w$ is a row-stochastic matrix. Therefore, by linear algebra results, the absolute value of any eigenvalue of $\mathbf{L}_w$ is less than or equal to $1$. This means that the eigenvalues of matrix $\mathbf{L}_w - \mathbf{I}$ are all negative or equal to $0$ (is negative semidefinite) and, then, $\mathbf{0} \succeq \mathbf{L}_w - \mathbf{I}$.

Thus, the statement $\mathbf{I} \succeq \mathbf{L}_w$ holds and $\Lambda^{'} \succ \mathbf{0}$.
\end{proof}

As a remark, notice that the stability result applies to CO-DKF independently of the certification.
The next step is to demonstrate that CO-DKF is optimal when it is certified.

\begin{theorem}[\textbf{Optimality}]\label{theorem:optimality}
Assume that the solution of~\eqref{eq:outerLJellipse} is certified as optimal. Then, it provides the optimal consensus gains of Eq.~\eqref{eq:KF4}, under the restrictions of Problem~\ref{problem:CO-DKF}.
\end{theorem}
\begin{proof}
The expression in Eq.~\eqref{eq:rewrite_sta} can be reformulated as
\begin{equation}\label{eq:rewrite}
     \hat{\mathbf{x}}_{i}^* = \bar{\mathbf{x}}_{i} + \mathbf{M}_i(\mathbf{y}_i - \mathbf{Y}_i\bar{\mathbf{x}}_{i})  +
     \gamma\mathbf{M}_i\sum_{j\in \mathcal{N}_i} \lambda_j^*\bar{\mathbf{P}}_j^{-1}(\bar{\mathbf{x}}_{j}-\bar{\mathbf{x}}_{i})
\end{equation}
with $\gamma = (\mathbf{I}-\mathbf{M}_i\mathbf{Y}_i)\bar{\mathbf{P}}_{i}^*\mathbf{M}_i^{-1}$. The latest is equivalent to Eq.~\eqref{eq:KF4} but weighting each term with the result of optimising~\eqref{eq:outerLJellipse}. Recalling Definition~\ref{definition:MSE}, the MSE is $\sum_i^{N}\hbox{E}[||\hat{\mathbf{x}}_i-\mathbf{x}||^2]$, which can be rewritten as $\sum_i^{N}\hbox{Tr}(\mathbf{M}_i)$. Since $\mathbf{M}_i = (\bar{\mathbf{S}}_{i}^{*} + \mathbf{Y}_i)^{-1}$ and $\bar{\mathbf{S}}_{i}^{*}$ comes from the optimisation in~\eqref{eq:outerLJellipse} which optimises over the trace of $\bar{\mathbf{S}}_{i}$, and this solution is certified as optimal, then the solution of~\eqref{eq:outerLJellipse} is equivalent to finding the optimal consensus gains of Eq.~\eqref{eq:KF4}.
\end{proof}

This result means that the optimisation carried on to fuse the neighbouring predictions is equivalent to finding the optimal consensus gains in the MSE sense. Thus, if the node certifies its optimality at instant $k$, then the estimation at instant $k$ is optimal.

It is interesting to note the differences of CO-DKF with~\cite{wang2017convergence,he2018consistent}. Despite taking a similar approach for the fusion of estimates, they both omit, implicitly or explicitly, the consensus over estimates and/or measurements. Moreover, the optimisation problem for the fusion of estimates is the common CI (the adaptive CI in~\cite{he2018consistent} is another optimisation problem over the original one). These two aspects are key differential because (i) our reformulation allows to certify optimality in the weights' election and therefore, (ii) in conjunction with the  explicit consensus over measurements and implicit consensus over estimates, we can proof optimality.

\section{Simulations}\label{sec:examples}

To validate CO-DKF we compare the performance of different estimators: (i) \textit{CO-DKF}, our proposal, (ii) \textit{CDFK}, Algorithm 3 from~\cite{Olfati2007DKF} with consensus gain $\gamma_i = 1/(||\mathbf{M}_i||_{F} + 1)$ and $||\cdot||_F$ the Frobenius norm, (iii) \textit{HDfKF}, complete algorithm in~\cite{Hu2011Diffusion}, (iv) \textit{HADfKF}, simplified algorithm in~\cite{Hu2011Diffusion}, (v) \textit{CKF}, centralised equivalent KF. The target system is a 2D particle described by
\begin{align}
    \mathbf{x} &= \begin{pmatrix}
    x & y & v_x & v_y
    \end{pmatrix}^T
    \\
    \mathbf{A} &=
    \begin{pmatrix}
    1 & 0 & \sin{w_p T} &  \cos{w_p T} - 1
    \\
    0 & 1 & 1-\cos{w_p f T} & \sin{w_p T}
    \\
    0 & 0 & \cos{w_p T} & \sin{w_p T}
    \\
    0 & 0 & \sin{w_p T}  & \cos{w_p T}
    \end{pmatrix}
\end{align}
with $w_p=0.5$rad/s, $T=0.1$s and $\mathbf{Q}=2\times 10^{-6}\mathbf{I}_4$.

To do the comparison, we analyse two scenarios. Experiment $1$ instantiates a random Laplacian to produce a random sensor network, with appropriate parameters to obtain a sparse connected topology. Then, we uniformly randomly decide the quantities each sensors measures, selecting among measuring $x$, measuring $y$ or measuring $x$ and $y$. Notice that we never measure $v_x$ nor $v_y$. Besides, the values of each $\mathbf{H}_i$ come from a uniform distribution in the range $[1,3]$. After that, a $p=0.5$ Bernoulli distribution decides if the diagonal values of $\mathbf{R}_i$ are in the range $[3,5]\times 10^{-2}$ or $[3,5]$, i.e., if the sensor has high or low quality. This process is done 100 times, computing the MSE and doing the average over the experiments, which is the same procedure in~\cite{Cattivelli2010Diffusion} and~\cite{Hu2011Diffusion}. Experiment $2$ is more challenging and aims at validating the robustness and performance of CO-DKF. We repeat the initialisation process of Experiment $1$ but only one sensor is of high quality. An instance is shown in Fig.~\ref{fig:topology}.
\begin{figure}[!ht]
\centering
\includegraphics[width=0.8\columnwidth]{Topology.pdf}
\caption{Example of random sensor network generated in Experiment $2$.}
\label{fig:topology}
\end{figure}

In the case of the CDKF, we have computed the average over the successful experiments, which is a $42\%$ in Experiment $1$ and a $15\%$ in Experiment $2$. This is reasonable since the CDKF needs a sufficiently small consensus gain to be stable~\cite{Olfati2009DKF}, subject to the quality and density of the measurements. For the rest of the estimators, all the experiments converged.

The results of Experiment $1$ are shown in the first column of Fig.~\ref{fig:RMSEvsREAL_transient}. The best performance is obtained by CO-DKF, with a difference of an order of magnitude with HDfKF and HADfKF, and of several orders of magnitude with CDKF. Indeed, the trace of the CDKF only appears in the zoomed pannel in Fig.~\ref{fig:RMSEvsREAL_transient}. Focusing near the steady-state, we can see that CO-DKF is also the best, with the fastest convergence to the CKF and with a difference of an order of magnitude with HDfKF/HADfKF. The CDKF improves its performance, without surpassing CO-DKF, but we recall that it corresponds to a $42\%$ of success rate.

The differences are greater in Experiment $2$, as it is shown in the second column of Fig.~\ref{fig:RMSEvsREAL_transient}, where the HADfKF diverges and HDfKF exhibits a much worse transient response. Therefore, CO-DKF obtains the best performance, coming with certifiability, optimality and stability guarantees, and with no need of tuning even with only a single high-quality sensor.

\begin{figure}[!ht]
\centering
\begin{tabular}{cc}
    {\footnotesize Experiment 1}
    &
    {\footnotesize Experiment 2}
    \\
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{RMSE_TOTAL_good.pdf}
    &
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{RMSE_TOTAL.pdf}
    \\
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{RMSE_TOTAL_SS_good.pdf}
    &
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{RMSE_TOTAL_SS.pdf}
    \\
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{RatiosGood.pdf}
    &
    \includegraphics[width=0.45\columnwidth,height=0.4\columnwidth]{Ratios.pdf}
\end{tabular}
\caption{Simulation results. First row depicts the MSE for the different estimators during the transient. Second row is a zoom of the previous in the proximity of steady-state. The third row shows the certification results, plotting the ratio achieved by the sensors over time and assigning an arbitrary colour to each sensor. CO-DKF is successful in certifying the estimation in a: (left) $96.062\%$, (right)  $93.473\%$.}
\label{fig:RMSEvsREAL_transient}
\end{figure}

The last row of Fig.~\ref{fig:RMSEvsREAL_transient} shows the value of $\rho$ in both Experiments. We see that the solution of~\eqref{eq:outerLJellipse} rapidly converges to $1$. Since in Experiment $1$ there are more high-quality sensors, the transient converges quicker than in Experiment $2$. The lower values of $\rho$ are at $0.65$, and this is only in the initialisation. We have also calculated the percentage of times that the nodes can certificate Problem~\ref{problem:intersection}, i.e.,  Constraint~\eqref{eq:constraint43} holds. This is a $96.062\%$ in Experiment $1$ and $93.473\%$ in Experiment $2$, so, along with the rapid convergence towards $\rho=1$, we can assure that our SDP relaxation is \textit{tight} and therefore CO-DKF optimality is tight.

The computation of~\eqref{eq:outerLJellipse} and~\eqref{eq:traceRelax} takes about $50$ms using CVXPY~\cite{cvxpy}, MOSEK~\cite{mosek} and an standard laptop, which can be speed up by an ad hoc implementation and consistent with $T=100$ms.

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

This paper has presented CO-DKF, the first certifiable optimal distributed Kalman Filter under unknown correlations. The use of the outer Löwner-John ellipsoid method allows us to fusion the neighbouring estimates with certifiable guarantees of optimality, which comes from a tight relaxation of the original SDP problem. The optimisation is integrated in an information DKF, achieving a robust CO-DKF over heterogeneous sensor networks, with minimal communication burden and no tuning. We have also proved global asymptotic stability of the estimator and the equivalence between CO-DKF and a consensus DKF with optimal gains in the MSE sense. Two experiments have validated all the aforementioned features, returning remarkable results in sparse, highly noisy scenarios.

\balance

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


What is the Omise GO Cryptocurrency?
OmiseGo (OMG) is a Cryptocurrency founded in 2013 and built on the Ethereum platform and it's based in Thailand, Japan, Singapore, and Indonesia. It's CEO Jun Hasegawa is an entrepreneur from Japan with an expertise in e-commerce and mobile payments. The company had initially raised $50 Million through private investors and an Initial Coin offering in 2017. Astonishingly, they now have a valuation of nearly $1 Billion. The project was advised and backed by Ethereum creator Vitalik Buterin which gave the company a massive boost forward. OmiseGO is described as the answer to a fundamental coordination problem amongst payment processors, gateways and financial institutions.
As a Cryptocurrency it is encouraging to see a real world use case such as McDonald's online orders. Investors should expect to see OMG rise much further in the coming 6 months. They plan to expand into neighboring asian countries and this could mean OMG will be one of the most widely used Cryptocurrencies in the continent.


text:
Q: Parse and get specific part from sting I have an ugly string:
a1a5021a96188bbfa7d\" alt=\"\" \/>\u003C\/a>\u003Cdiv class=\"_8u _42ef\">\u003Cdiv class=\"_6a _5u5j\">\u003Cdiv class=\"_6a _6b\" style=\"height:100px\">\u003C\/div>\u003Cdiv class=\"_6a _5u5j _6b\">\u003Cdiv class=\"fsl fwb fcb\">\u003Ca href=\"https:\/\/www.facebook.com\/username.ivn?fref=grp_mmbr_list\" data-hovercard=\"\/ajax\/hovercard\/user.php?id=100002759468783&extragetparams=\u00257B\u002522fref\u002522\u00253A\u002522grp_mmbr_list\u002522\u00257D\">Mamu Ivaniadze\u003C\/a>\u003C\/div>

How to get the part of user.php?id=100002759468783  from it. In reality it's a big string and I need to get all ids  user.php?id=someId.

A: You can use this regular expression:
(user\.php\?id=[0-9]+)

It will always get you the user URL part and the id out. Use Regex.Match or Regex.Matches (in case of multiple possible results) to match the input string and use the capture(s) to get the URL out.

A: You don't parse HTML using regular expressions.

*

*Parse the HTML using HtmlAgilityPack.

*Obtain all a tags that have an data-hovercard attribute, and select that attribute value.

*Now you have a list of strings, representing relative URIs.

*Parse the URIs and obtain the query string.

*Parse the query string and obtain the value of the id key.

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WEEKLY VLOG: Registering Baby's Birth After 2 Months+ Huge B&M Haul!!
What I Eat In A Day WHILE BREASTFEEDING!
StoryTime: MY EMERGENCY C-SECTION, NATURAL VS C-SEC+ BABY'S NAME REVEAL!
WEEKLY VLOG; Life With A Newborn, Breastfeeding Chat+ My New Pram!
WHAT'S IN MINE AND BABY'S HOSPITAL BAG| INDUCTION AT 40 WEEKS PREGNANT!
Come Homewear Shopping With me +Haul! |Zeinah Nur.
Flying Long Distance At 8 Months Pregnant!
Weekly Vlog: I'VE GOT SOMETHING TO TELL YOU!


text:
Q: Using Q_Property to display properties I have a GUI displaying a tree architecture as shown here.

Each of those nodes are separate classes that are derived from the node above them. All of them inherit QObject for their implementation.
Now I need to add a few properties to be displayed when the user selects Properties under the Right-Click menu of Implicit. Selecting this opens a window with the properties.
I added these properties in the header file of Implicit like so :
#ifndef FCIMPLICIT_H
#define FCIMPLICIT_H
#include <QObject>
#include "Interface.h"
#include "ResourceItem.h"
#include "MonWindow.h"
#include "FCTab.h"
#include "ResourceItem.h"
#include "FCAbstract.h"
#include "FCInterface.h"
#include "FCConnections.h"
class CFCImplicit: public CResourceItem
{

    Q_OBJECT
    Q_PROPERTY(int FCPortID READ getPortID )
    Q_PROPERTY(QString Type READ getType )
    Q_PROPERTY(QString Status READ getStat )
    Q_PROPERTY(int WWNodeNumber READ getNodeNo )
    Q_PROPERTY(int WWPortNumber READ getPortNo )
    Q_PROPERTY(bool AutoActive READ getAuto )
public:
    CFCImplicit(QObject*);
    ~CFCImplicit();

    QString                 getType();
    QString                 getStat();
    int                     getPortID();
    int                     getPortNo();
    int                     getNodeNo();
    bool                    getAuto();

};

FCinterface.h is the header of the FCASM node.
The issue is that only the first property is displayed, as seen in the second picture. Is there a reason why this is happening? Am I supposed to add something to the constructor or a new function?
The constructor for the Implicit class is
CFCImplicit::CFCImplicit(QObject* parent) : CResourceItem(parent)
{

    fnSetProperty("objectName", QString("Implicit"));
    ((CResourceItem*)parent)->fnAddResources(this);

}

EDIT:
This is the code for all the READ functions
QString CFCImplicit::getType()
{
QString a;
a="Implicit";
return a;
}

QString CFCImplicit::getStat()
{QString a;
a="Idle";
return a;}

int CFCImplicit::getPortID()
{int a;
a=1;
return a;}

int CFCImplicit::getPortNo()
{int a;
a=2;
return a;}

int CFCImplicit::getNodeNo()
{int a;
a=2;
return a;}

bool CFCImplicit::getAuto()
{bool a;
a=true;
return a;}

A: I found out what I was doing wrong. I assumed that since the properties were read only, I only needed a READ accessor function. By adding the WRITE accessor and adding the required WRITE functions, the properties were displayed. I don't exactly understand why this condition is required (maybe having just READ just makes the properties available for introspection), but it worked! So there you go.
Happy coding everyone!

A: No need to add the READ and the function, you can use the MEMBER to have direct access to the variable.


text:
Q: Mvc4 Ajax Call Opens New Page I've looked at what must be 100 posts and can't get this to work in my new project. I've got all the scripts, its seems like the simplist of tests and unobtrusive is set in the webconfig, still no luck getting the actionlink to replace the text in the div. Firebug reports all scripts loaded successfully and code is below. If anyone can help it would be much appreciated and I'd get you a virtual beer!
Controller:
public ActionResult AjaxTest()
{
return Content("Ajax Test Successful");
}

View:
@{
ViewBag.Title = "User";
}

Users

@Html.ActionLink("Ajax Test", "AjaxTest", "Admin", new AjaxOptions() { InsertionMode = InsertionMode.Replace, UpdateTargetId = "ajaxtest" })

Layout:
<!DOCTYPE html>

<meta charset="utf-8" />
<title>@ViewBag.Title - My ASP.NET MVC Application</title>
<link href="~/favicon.ico" rel="shortcut icon" type="image/x-icon" />
<meta name="viewport" content="width=device-width" />
@Styles.Render("~/Content/css")
@Scripts.Render("~/bundles/modernizr")

@Html.Partial("_LoginPartial")

@Html.ActionLink("Home", "Index", "Home")

@Html.ActionLink("Upload Files", "UploadFiles", "Upload")

@Html.ActionLink("Upload History", "UploadHistory", "Upload")

@Html.ActionLink("Help", "Help", "Home")

@Html.ActionLink("Admin", "Home", "Admin")

@RenderSection("featured", required: false)

@RenderBody()

© @DateTime.Now.Year - My ASP.NET MVC Application

@Scripts.Render("~/bundles/jquery")
@Scripts.Render("~/bundles/jqueryval")

@RenderSection("scripts", required: false)

Html of rendered page:
<!DOCTYPE html>

    <meta charset="utf-8" />
    <title>User - My ASP.NET MVC Application</title>
    <link href="/favicon.ico" rel="shortcut icon" type="image/x-icon" />
    <meta name="viewport" content="width=device-width" />
    <link href="/Content/site.css" rel="stylesheet"/>
<link href="/Content/buttons.css" rel="stylesheet"/>

Register

Log in

Home

Upload Files

Upload History

Help

Admin

Users

Ajax Test

© 2013 - My ASP.NET MVC Application

Web config:
<add key="ClientValidationEnabled" value="true" />
<add key="UnobtrusiveJavaScriptEnabled" value="true" />

A: You should be using Ajax.ActionLink not Html.ActionLink and also you should make sure that MicrosoftAjax.js and MicrosoftMvcAjax.js scripts are loaded in your page if you are using MVC 2 or older (your rendered html does not show them).
You're looking for an output like this:
Ajax Test


One of New York's funnest street fairs of the year actually isn't in New York, it's in Hoboken. This afternoon at 2:30 PM, Boo Reiners and Elena Skye – the brain trust of pioneering NYC urban C&W group Demolition String Band – are the main attraction at this year's Hoboken Arts & Music Festival. It's not the first time they've been the stars of this show and it probably won't be the last. The stage is on the town's main drag, Washington Street at 8th Street, just a short ten-minute walk from the Hoboken Path train station.
Elena and Boo also have a new album out, I Wait for the Light, streaming at Bandcamp. It's the second one they've released under their own names, after four with Demolition String Band, and it's notable for being their most rocking one so far. The lineup on this one is much the same as the original unit: Reiners wailing and flatpicking up a storm on Telecaster and banjo, Skye on mandolin, guitar and baritone guitar, with Kenny Soule on drums, Winston Roye and Mike Santoro sharing bass duties.
The album kicks off with the highway rock anthem I Don't Know, I Can't Say. With her forceful, soulful, twangy delivery, Skye has never sung better: this song is like vintage 90s Wilco with a woman out front. The second track, Sea of Pleasure has a dynamic the BoDeans used to work all the time – hushed and muted, then richly clangy, with a tantalizingly brief, biting Reiners Tele solo out.
The tender ballad Red For You has a hushed vintage 50s Kitty Wells sway with 21st century production values, and a rich web of guitars that build to an achingly sunbaked peak. The album's mightiest track, the big anthem She's Nobody's Girl is the kind of snarling guitar rocker that someone like Miranda Lambert could only wish she'd written. The band follows with the lingering ballad Deep Cool Green Ravine, which wouldn't be out of place in the Emmylou Harris catalog.
Then they pick up the pace with the burning acoustic-electric Every Day An Angel and its subtle Beatlesque tinges. The duo reinvent Elegant Wind, a familiar number to Demolition String Band fans, as spare Gillian Welch-style folk. By contrast, the blazing Sailor Girl is a mashup of Revolver-era Beatles and shuffling vintage 60s honkytonk.
"Jesus was a peace freak, he took care of the weak," Skye reminds in the Ramones-influenced Jesus Was a Liberal, the album's most ferocious and arguably best track. "if Jesus had a radio show, or a tv show, he'd been on after Randi Rhodes, or Rachel Maddow," Slye asserts, something you might expect from a singer who in the past decade would make it a point to dedicate Demolition String Band's snarling version of Creedence's Fortunate Son to George W. Bush.
The lush blend of banjo, mando and guitar textures throughout the wounded ballad Scar on My Heart are among the album's tastiest moments. They wind it up on an upbeat note with You Keep Me Up, which draws a straight line back to the Emmylou Harris/Rodney Crowell collaborations of about ten years ago.


text:
A referendum on the Federation of Arab Republics (Arabic: استفتاء اتحاد الجمهوريات العربية السوري 1971) was held in Syria on 1 September 1971, alongside simultaneous referendums in Egypt and Libya. It was approved by 96.4% of voters, with a turnout of 89.7%.

Results

References

1971 in Syria
1971 referendums
Federation of Arab Republics
Referendums in Syria

redpajama_set_name: RedPajamaWikipedia


text:
Home/delighted
Braverman's battling performance delighted supporters but she's not out of trouble yet | Jon Craig
So it's all a "political witch-hunt", is it? That was the claim made by the embattled Suella Braverman on Halloween.…
Rishi Sunak says he's 'delighted to welcome her back' as he stands by rehire of Suella Braverman at Prime Minister's Questions
Rishi Sunak has stood by his decision to re-appoint Suella Braverman as home secretary, despite calls for an investigation into…


Birch Crest Resort is a family owned and operated resort on Horn Lake in Burk's Falls. We offer beautiful 1 and 2 bedroom fully furnished housekeeping cabins which sleep 4-6 people. All cottages are steps from the water and are fully equipped; kitchens with appliances, living room, microwave, TV, coffee maker, kettle and 3 piece bathroom. Enjoy the sunsets from your deck or private campfire, and enjoy ample space between cottages for privacy.
Birch Crest Resort also offers a variety of amenities and adventure opportunities for everyone of all ages to enjoy. Swim or make sand castles at our beautiful sandy beach, enjoy free use of our canoes, kayaks and pedal boats, swim out to the floating raft, or use the basketball hoop, horseshoe pits, children's playground, and of course hundreds of miles of hiking and nature for you to explore. For the fisherman (or fisherwoman) we offer a boat launch ramp, docking, and a marina gas pump. We are also pet friendly so bring along your whole family!


text:
Lyric Theories
[ Lyric Theories index | Submit a theory ]
We just finished a "spring cleaning" of the Lyric Theories section which we do periodically. However do to the current large and ever-growing size of this section, we decided to post information about this procedure here instead of just in our newsletter.
First and foremost we NEVER delete because we don't like or agree with them. The idea of this section is for people to express their opinions, and we do not censor it. However there are certain things that are not appropriate for this area. They basic guidelines we use when cleaning up are as follows:
Submissions that are not theories on lyrics are not appropriate. Saying that you like the song, or you dislike the song, or the song makes you happy is not a theory on what the lyrics mean and therefore does not belong here.
Message board style posts often times get deleted. Why? Because we have message boards, and because emails are included in each post so that you may write back to that person. This is NOT a set-in-stone rule. A submission that says "I agree that this song is about ______, but I also think that..." will most likely stay in the database, however a submission like "Joe, you're a moron, it's not..." is likely to be removed. If you'd like to post what you think do so, if you've already done that, then please don't feel the need to respond to everyone who thinks something different. However, feel free to bring such a discussion to our message boards.
Blank submissions will be removed.
Submissions that are mostly flame (i.e., 90% flame, 10% theory) have a good chance of being removed, depending on my (Phil) mood.
Cleaning is done by the IPOM Staff, but final decision is made by Phil, so if you have questions, wanna bitch, or anything else, send them to here.
© 1997 - present Phil Dibowitz
Please read our Copyright Info


US Ambassador, Mr Stephen Beecroft and Luxor Governor, Mr Mohamed Badr, participated in a groundbreaking ceremony on March 6 for the expansion of Luxor's wastewater treatment plant.
When complete, the expansion will nearly double the capacity of the system to provide wastewater treatment to residents of Luxor and El Bayadeya.
Funded by the United States Agency for International Development (USAID) and carried out in partnership with the Luxor Potable Water and Sanitation Company, the expansion will provide improved wastewater treatment for Luxor and El Bayadeya to meet projected population growth for the next two decades.
Since 1978, the U.S. government, through USAID, has invested nearly $30 billion in Egypt. Over $3.5 billion dollars has been used to help construct or upgrade water and wastewater facilities that serve more than 25 million Egyptians.


Kinto is a mobile app for individuals and families caring for an aging loved one. We have experienced the many challenges, and rewards, that come along with this very important responsibility. We are here for you -- to make it easier.


text:
Meanwhile, in Iraq and Afghanistan….
Washington, DC, Bureau ChiefBio | Follow
Kevin is off for a few days–and not in Argentina. He'll be back and ready to blog on Tuesday. In the meantime, I will be your pilot.
Under usual circumstances, the withdrawal of US troops from a theater of war would be considered a big deal.
Not these days.
The United States has begun to pull troops out of Iraq, and there's not much attention being paid–even with the explosion of violence in Iraq this week. (Insert gratuitous Michael Jackson reference here.) And there are other milestones to look ahead to within Iraq. Reuters notes:
Many observers see Iraq's most crucial milestone being the parliamentary election next January, rather than the withdrawal of U.S. soldiers from town and cities by the end of this month.
That vote will be a defining test of whether the country's feuding factions can live together after the years of sectarian bloodshed unleashed by the 2003 U.S. invasion.
"Security gains in a narrow sense will be of limited value unless the … election is turned into a thoroughly inclusive affair where Iraqis get the opportunity to discuss fundamental issues of national reconciliation in an open atmosphere," said Reidar Visser of the Norwegian Institute of International Affairs and editor of Iraq-focused website www.historiae.org
This is something else to look forward to being insufficiently covered within the American media.
Just like the Afghanistan presidential election campaign now in process. From Politico:
Without strong preemptive action by the Obama administration and the international community, Afghanistan's impending elections could be just as suspect — and have just as dire consequences — as Iran's, a top opponent to Afghan President Hamid Karzai claimed on Tuesday.
"The possibility of a Kenya or a Zimbabwe or an Iran looms large," said Ashraf Ghani Ahmadzai, a former World Bank official and Karzai adviser now challenging him for president in the Aug. 20 election.
Well, what would you expect a Karzai challenger to say? But what if he's right? A bad election in Afghanistan would truly undermine the US operation there. The International Crisis Group, a savvy NGO, has put out a report outlining the election challenges in Afghanistan. The group's South Asia project director, Samina Ahmed, notes:
Ultimately, it is the perception of the Afghan population that will measure electoral success. If they are to be encouraged to vote, they must be confident that their ballots will count. But if perceived to be unfairly conducted, elections could provide a potential flashpoint.
Isn't Afghanistan already a flashpoint? Ugh.
You can follow David Corn's postings and media appearances via Twitter.


text:
var util = require('util'),
	request = require('request'),
	events = require('events'),
	cheerio = require('cheerio'),
	URI = require('uri-js');

module.exports = function() {

  var _my = null;

  var debug;

  if (/\bmetainspector\b/.test(process.env.NODE_DEBUG)) {
    debug = function() {
      console.error('METAINSPECTOR %s', util.format.apply(util, arguments));
    };
  } else {
    debug = function() {};
  }

  function parseFeeds(format)
  {
  	var self = this;

  	var feeds = this.parsedDocument("link[type='application/" + format + "+xml']").map(function(i ,elem){
  		return self.parsedDocument(this).attr('href');
  	});

  	return feeds;
  }

  function withDefaultScheme(url){
  	return URI.parse(url).scheme ? url : "http://" + url;
  }

  var MetaInspector = function(url, body){
    _my = {};
    if(url){
    	this.url = URI.normalize(withDefaultScheme(url));
    	this.parsedUrl = URI.parse(this.url);
    	this.scheme = this.parsedUrl.scheme;
    	this.host = this.parsedUrl.host;
    	this.rootUrl = this.scheme + "://" + this.host;
    } else {
        this.body = body;
        this.parsedUrl = '';
    	this.scheme = '';
    	this.host = '';
    	this.rootUrl = '';
    }
  };

  MetaInspector.prototype = new events.EventEmitter();

  function getTitle()
  {
  	debug("Parsing page title");

  	if(_my.title === undefined)
  	{
  		_my.title = this.parsedDocument('title').text();
  	}

  	return _my.title;
  }

  function getOgTitle()
  {
  	debug("Parsing page Open Graph title");

  	if(_my.ogTitle === undefined)
  	{
  		_my.ogTitle = this.parsedDocument("meta[property='og:title']").attr("content");
  	}

  	return _my.ogTitle;
  }

  function getLinks()
  {
  	debug("Parsing page links");

  	var self = this;

  	if(_my.links === undefined)
  	{
  		_my.links = self.parsedDocument('a').map(function(i ,elem){
  			return self.parsedDocument(this).attr('href');
  		});
  	}

  	return _my.links;
  }

  function getMetaDescription()
  {
  	debug("Parsing page description based on meta elements");

  	if(_my.metaDescription === undefined)
  	{
  		_my.metaDescription = this.parsedDocument("meta[name='description']").attr("content");
  	}

  	return _my.metaDescription;
  }

  function getSecondaryDescription()
  {
  	debug("Parsing page secondary description");

  	var self = this;

  	if(_my.metaDescription === undefined)
  	{
  		var minimumPLength = 120;

  		self.parsedDocument("p").each(function(i, elem){
  			if(_my.metaDescription !== undefined){
  				return;
  			}

  			var text = self.parsedDocument(this).text();

  			// If we found a paragraph with more than
  			if(text.length >= minimumPLength)
  			{
  				_my.metaDescription = text;
  			}
  		});
  	}

  	return _my.metaDescription;
  }

  function getDescription()
  {
  	debug("Parsing page description based on meta description or secondary description");
  	return getMetaDescription.apply(this) || getSecondaryDescription.apply(this);
  }

  function getKeywords()
  {
  	debug("Parsing page keywords from apropriate metatag");

  	var self = this;

  	if(_my.metaKeywords === undefined)
  	{
  		var keywordsString = self.parsedDocument("meta[name='keywords']").attr("content");

  		if(keywordsString !== undefined) {
  			_my.metaKeywords = keywordsString.split(',');
  		}
  	}

  	return _my.metaKeywords;
  }

  function getAuthor()
  {
  	debug("Parsing page author from apropriate metatag");

  	var self = this;

  	if(_my.metaAuthor === undefined)
  	{
  		_my.metaAuthor = self.parsedDocument("meta[name='author']").attr("content");
  	}

  	return _my.metaAuthor;
  }

  function getCharset()
  {
  	debug("Parsing page charset from apropriate metatag");

  	var self = this;

  	if(_my.metaCharset === undefined)
  	{
  		_my.metaCharset = self.parsedDocument("meta[charset]").attr("charset");
  	}

  	return _my.metaCharset;
  }

  function getImage()
  {
  	debug("Parsing page image based on the Open Graph image");

  	if(_my.metaImage === undefined)
  	{
  		_my.metaImage = this.parsedDocument("meta[property='og:image']").attr("content");
  	}

  	return _my.metaImage;
  }

  function getImages()
  {
  	debug("Parsing page body images");

  	var self = this;

  	if(_my.images === undefined)
  	{
  		_my.images = self.parsedDocument('img').map(function(i ,elem){
  			var src = self.parsedDocument(this).attr('src');
  			return self.getAbsolutePath(src);
  		});
  	}
  	return _my.images;
  }

  function getFeeds()
  {
  	debug("Parsing page feeds based on rss or atom feeds");

  	if(_my.feeds === undefined)
  	{
  		_my.feeds = parseFeeds.apply(this, ["rss"]) || parseFeeds.apply(this, ["atom"]);
  	}

  	return _my.feeds;
  }

  function initAllProperties()
  {
  	// title of the page, as string
  	this.title = getTitle.bind(this);

  	// author name from metatag, as string
  	this.author = getAuthor.bind(this);

  	// charset from metatag, as string
  	this.charset = getCharset.bind(this);

    // array of strings, with every keyword from keywords metatag
  	this.keywords = getKeywords.bind(this);

  	// array of strings, with every link found on the page
  	this.links = getLinks.bind(this);

  	// meta description, as string
  	this.metaDescription = getMetaDescription.bind(this);

  	// returns the meta description, or the first long paragraph if no meta description is found
  	this.description = getDescription.bind(this);

  	// Most relevant image, if defined with og:image
  	this.image = getImage.bind(this);

  	// array of strings, with every image path on the page, relative links are converted to absolute paths
  	this.images = getImages.bind(this);

  	// Get rss or atom links in meta data fields as array
  	this.feeds = getFeeds.bind(this);

  	// opengraph title
  	this.ogTitle = getOgTitle.bind(this);
  }

  MetaInspector.prototype.getAbsolutePath = function(href){
  	if((/^(http:|https:)?\/\//i).test(href)) { return href; }
  	if(!(/^\//).test(href)){ href = '/' + href; }
  	return this.rootUrl + href;
  };

  MetaInspector.prototype.fetch = function(){
  	var self = this;
    if(!self.url){
  		return self.emit("error", new Error('function not available'));
    }
  	request({uri : this.url}, function(error, response, body){
  		if(!error && response.statusCode === 200){
  			self.document = body;
  			self.parsedDocument = cheerio.load(body);
  			self.response = response;

  			initAllProperties.apply(self);

  			self.emit("fetch");
  		}
  		else{
  			self.emit("error", error);
  		}
  	});
  };

  // Additional function added for LinkProcessingServer

  MetaInspector.prototype.parse = function(){
  	var self = this;
    if(!self.body){
  		return self.emit("error", new Error('function not available'));
    }
    self.document = text;
    self.parsedDocument = cheerio.load(body);
    initAllProperties.apply(self);
  	self.emit("fetch");
  };

  return MetaInspector;
}

redpajama_set_name: RedPajamaGithub


text:
ウェブツール
学術情報
(¥) JPY
Version: 1 Revision Date: 11/30/2015
PE/Dazzle™ 594 anti-human CD45RO Antibody
UCHL1 (See other available formats)
IV N31
CD45RO
Mouse IgG2a, κ
Human peripheral blood lymphocytes were stained with CD45RA APC and CD45RO (clone UCHL1) PE/Dazzle™ 594 (top) or mouse IgG2a, κ PE/Dazzle™ 594 isotype control (bottom).
Compare all formats See PE/Dazzle™ 594 spectral data
304247 25 tests ¥24,000
304248 100 tests ¥59,000
CD45RO is a 180 kD single chain membrane glycoprotein. It is a splice variant of tyrosine phosphatase CD45, lacking the A, B, and C determinants. The CD45RO isoform is expressed on activated and memory T cells, some B cell subsets, activated monocytes/macrophages, and granulocytes. CD45RO enhances both T cell receptor and B cell receptor signaling mediated activation. CD45 and its isoforms non-covalently associate with lymphocyte phosphatase-associated phosphoprotein (LPAP) on T and B lymphocytes. CD45 has been reported to be associated with several other cell surface antigens including CD1, CD2, CD3, and CD4. CD45 has also been reported to bind galectin-1 and CD22. CD45 isoform expression can change in response to cytokines.
Human, Chimpanzee, Cynomolgus, Common Marmoset
IL-2 dependent T cell line, CA1
Phosphate-buffered solution, pH 7.2, containing 0.09% sodium azide and 0.2% (w/v) BSA (origin USA).
The antibody was purified by affinity chromatography and conjugated with PE/Dazzle™ 594 under optimal conditions.
Lot-specific (please contact technical support for concentration and total µg amount, or use our Lookup tool if you have a lot number.)
Each lot of this antibody is quality control tested by immunofluorescent staining with flow cytometric analysis. For flow cytometric staining, the suggested use of this reagent is 5 µl per million cells in 100 µl staining volume or 5 µl per 100 µl of whole blood.
* PE/Dazzle™ 594 has a maximum excitation of 566 nm and a maximum emission of 610 nm.
Blue Laser (488 nm)
Green Laser (532 nm)/Yellow-Green Laser (561 nm)
The UCHL1 antibody is commonly used in combination with antibodies against CD45RA to discern memory and naïve T cells. Additional reported applications (for the relevant formats) include: immunohistochemical staining of acetone-fixed frozen tissue sections5 and formalin-fixed paraffin-embedded tissue sections4, Western blotting2, and immunoprecipitation3.
Knapp W, et al. Eds. 1989. Leucocyte Typing IV. Oxford University Press. New York. (FC)
Ishii T, et al. 2001. P. Natl. Acad. Sci. USA 98:12138. (WB)
Ponsford M, et al. 2001. Clin. Exp. Immunol. 124:315. (IP)
Yamada M, et al. 1996. Stroke 27:1155. (IHC)
Sakkas LI, et al. 1998. Clin. Diagn. Lab. Immunol. 5:430. (IHC)
Baba N, et al. 2010. Int. Immunol. 22:237. PubMed
Thakral D, et al. 2008. J. Immunol. 180:7431. (FC) PubMed
Weiss L, et al. 2010. P. Natl. Acad. Sci. USA 107:10632. PubMed
Wu YY, et al. 2007. Infect. Immun. 75:4357. PubMed
Mozaffarian N, et al. 2008. Rheumatology 47:1335. PubMed
Roque S, et al. 2007. J. Immunol. 178:8028. PubMed
Yoshino N, et al. 2000. Exp. Anim. (Tokyo) 49:97. (FC)
Smith SH, et al. 1986. Immunology 58:63. (Immunogen)
Peterson VM, et al. 2017. Nat. Biotechnol. 35:936. (PG)
Tyrosine phosphatases, type I transmembrane, 180 kD (isoform of CD45 containing none of the A, B, or C determinants)
Activated and memory T cells, B cell subsets, monocytes, macrophages, granulocytes
Enhances TCR and BCR signaling
B cells, Granulocytes, Macrophages, Mesenchymal Stem Cells, Monocytes, T cells, Tregs
Cell Biology, Immunology, Inhibitory Molecules, Neuroscience, Neuroscience Cell Markers, Stem Cells
CD Molecules
1. Thomas M. 1989. Annu. Rev. Immunol. 7:339.
2. Trowbridge I, et al. 1994. Annu. Rev. Immunol. 12:85.
5788 View all products for this Gene ID
View information about CD45RO on UniProt.org
PE/Dazzle™ 594 Conjugates
The Tandem
The Tandem Mobile Application
View All CD45RO Reagents Request Custom Conjugation
Alexa Fluor® 700 anti-human HLA-DR
Clone: L243
FITC anti-human CD197 (CCR7)
Clone: G043H7
PE/Cyanine7 anti-human CD107a (LAMP-1)
Clone: H4A3
PE anti-human TNF-α
Clone: MAb11
Go To Top Version: 1 Revision Date: 11/30/2015
日本版法規制関連情報


text:
Police pull pilot from plane moments before train crash
LOS ANGELES (AP) — A pilot who crashed a small plane onto railroad tracks was pulled alive from the wreck by a group of Los Angeles Police officers just moments before a commuter train roared through, authorities said.
Video of the harrowing rescue shows the officers pulling the bloodied man to safety seconds before the commuter train, blaring its horn, smashed the Cessna 172 into pieces.
The plane crashed around 2:10 p.m. Sunday, shortly after takeoff from Whiteman Airport in the San Fernando Valley community of Pacoima, according to the Federal Aviation Administration. The timestamp on a police officer's body camera shows the train smashing the plane at 2:15 p.m.
The plane had landed on the tracks at a railroad crossing just blocks from the LAPD's Foothills Division station, and officers were on the scene almost immediately.
CBSN Los Angeles said four officers managed to extricate the pilot and drag him onto the pavement. The station identified them as Damien Castro, Christopher Aboyte, Robert Sherock and Sgt. Joseph Cavestany.
It's unclear how much time passed before authorities realized the plane was on the tracks, or exactly when police notified the railroad, but the officers realized there was no time to spare.
"I had requested Metrolink to cease all train activity, but apparently that didn't happen," Cavestany said.
The pilot, the only person on board, was transported in unknown condition, the Los Angeles Fire Department said. No other injuries were reported.
"Seeing what happened, I'm grateful to be alive. I'm grateful the pilot survived as well," Sherock said.
Metrolink subsequently halted train service and road traffic was detoured in the area about 20 miles (32 kilometers) northwest of downtown Los Angeles. The FAA and the National Transportation Safety Board will investigate.
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St. Lawrence River lake sturgeon populations continue …


Telekom Srbija ltd is the national telecommunications company, in which the Republic of Serbia has a majority stake. The company is engaged in mobile and landline telephony services, acts as an internet and IPTV provider.
Telekom Srbija is the owner of Telekom Srpske Banja Luka from Bosnia-Herzegovina, m:tel doo Podgorica from Montenegro and TS:Net BV Amsterdam from the Netherlands.
All financial and employment data are from 2015, the most recent available year. An average exchange rate of 108.8543 RSD to the US dollar for 2015 was used to convert financial figures from Serbian dinars into dollars. Information on the Executive Board and Supervisory Board comes from Telekom Srbija's website and the Serbian Business Registers Agency.