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1291 search results for Plant science
(St. Louis Business Journal) Danforth Plant Science Center Elects New Chairman and Expands Board of Trustees
https://www.danforthcenter.org/news-media/in-the-news/in-the-news-item/(st.-louis-business-journal)-danforth-center-elects-new-chairman-and-expands-board-of-trustees
The Center's board has elected John F. McDonnell, a trustee since 2000, to fill the chairman role.
(St. Louis Business Journal) Danforth Plant Science Center Elects New Chairman and Expands Board of Trustees, Dr. William Danforth, a former chancellor ofWashington University, will step down as chairman of the Donald Danforth Plant Science Center, which he founded in 1998. He will take on the title of founding chairman, and will be succeeded by John McDonnell, former chairman of McDonnell, of the Danforth Center since its launch, has played a key role in spurring plant and life sciences in the St
(St. Louis on the Air) How Did The Danforth Plant Science Center Attract European Seed Company KWS To St. Louis?
https://www.danforthcenter.org/news-media/in-the-news/in-the-news-item/(st.-louis-on-the-air)-how-did-the-danforth-plant-science-center-attract-european-seed-company-kws-to-st.-louis-
Out of all possible locations in the United States, German seed company KWS chose St. Louis as the site of its North American headquarters. What made St. Louis stand out from the rest?
(St. Louis on the Air) How Did The Danforth Plant Science Center Attract European Seed Company KWS, ? According to Donald Danforth Plant Science Center President James Carrington and COO Sam Fiorello, in the world. A discussion about new initiatives and research at the Danforth Plant Science, to encourage science and technology education in St. Louis, and current research underway at Danforth, plants that will thrive in brackish water," said Fiorello. In terms of science education, Carrington
(Iowa Corn) Iowa Corn Promotion Board and Donald Danforth Plant Science Center Announce Research Cooperation
https://www.danforthcenter.org/news-media/in-the-news/in-the-news-item/(iowa-corn)-iowa-corn-promotion-board-and-donald-danforth-plant-science-center-announce-research-cooperation
The Iowa Corn Promotion Board (ICPB) and The Donald Danforth Plant Science Center have announced a formal research cooperation to explore opportunities for innovation in nutrient utilization for Iowa's corn farmers.
(Iowa Corn) Iowa Corn Promotion Board and Donald Danforth Plant Science Center Announce Research Cooperation, The Iowa Corn Promotion Board (ICPB) and The Donald Danforth Plant Science Center (Danforth Center), in St. Louis, Missouri, have announced a formal research cooperation to explore opportunities for innovation in nutrient utilization for Iowa's corn farmers. The research cooperation has a goal of developing traits that will be used to improve farmer productivity and manage nutrients
Iowa Corn Promotion Board and Donald Danforth Plant Science Center Announce Research Cooperation
https://www.danforthcenter.org/news-media/news-releases/news-item/iowa-corn-promotion-board-and-donald-danforth-plant-science-center-announce-research-cooperation
The research cooperation has a goal of developing traits that will be used to improve farmer productivity and manage nutrients responsibly, which ICPB has identified as a priority area for research.
Iowa Corn Promotion Board and Donald Danforth Plant Science Center Announce Research Cooperation, Johnston, Jan 6, 2014- The Iowa Corn Promotion Board (ICPB) and The Donald Danforth Plant Science Center (Danforth Center), in St. Louis, Missouri, have announced a formal research cooperation to explore opportunities for innovation in nutrient utilization for Iowa's corn farmers. The research cooperation has a goal of developing traits that will be used to improve farmer productivity and manage
(AlgaeNews) Danforth Plant Science Center's New Renewable Fuels, Algae Researcher
https://www.danforthcenter.org/news-media/in-the-news/in-the-news-item/(AlgaeNews)-Danforth-Plant-Science-Center's-New-Renewable-Fuels-Algae-Researcher
A couple months ago, The Donald Danforth Plant Science Center brought on an addition to their Enterprise Rent-A-Car Institute for Renewable Fuels, Dr. James Umen. He was kind enough to take some time to talk about his research and how it will influen ...
(AlgaeNews) Danforth Plant Science Center's New Renewable Fuels, Algae Researcher, A couple months ago, The Donald Danforth Plant Science Center brought on an addition to their Enterprise Rent-A-Car Institute for Renewable Fuels, Dr. James Umen. He was kind enough to take some time to talk about his research and how it will influence the algae industry. 1) What is your background, /Member Enterprise Rent-A-Car Institute for Renewable Fuels The Donald Danforth Plant Science Center http
Fredbird Enjoying Plant Science
https://www.danforthcenter.org/news-media/roots-shoots-blog/blog-item/Fredbird-Enjoying-Plant-Science
Our favorite bird visited the Danforth Center yesterday.
Fredbird Enjoying Plant Science, Our favorite bird visited the Danforth Center yesterday. , (Collection), (Collection)
Rocking out to Plant Science
https://www.danforthcenter.org/news-media/roots-shoots-blog/blog-item/Rocking-out-to-Plant-Science
A meeting for Africa, For more information visit, http://www.danforthcenter.org/wordpress/?page_id=821&pid=5952 or follow us on Twitter at http://twitter.com/#!/DanforthCenter.
Rocking out to Plant Science, A meeting for Africa, For more information visit, http://www.danforthcenter.org/wordpress/?page_id=821&pid=5952 or follow us on Twitter at http://twitter.com/#!/DanforthCenter. , (Collection), (Collection)
Robots for Plant Science Research
https://www.danforthcenter.org/news-media/roots-shoots-blog/blog-item/Robots-for-Plant-Science-Research-
Understanding how plants work provides the necessary information to improve crops in order to meet the demands of a growing global human population and the challenges of a changing environment. Watch a video of our Robot from its view point- http: ...
Robots for Plant Science Research , Understanding how plants work provides the necessary information to improve crops in order to meet the demands of a growing global human population and the challenges of a changing environment. Watch a video of our Robot from its view point. Learn more about our robots and Dr. Todd Mockler's research here., (Collection), (Collection)
Plant Science is a Team Sport
https://www.danforthcenter.org/news-media/roots-shoots-blog/blog-item/plant-science-is-a-team-sport
Center leadership presented an overview of 2014 accomplishments, and important initiatives slated for 2015 to more than 250 constituents, donors and volunteers.
Plant Science is a Team Sport, On January 29, 2015 the Danforth Center hosted its State of the Center report to the community. During the event, Center leadership presented an overview 2014, , of ending starvation, preserving a livable environment and bringing more science based jobs to our, grants. And science education programs that reached nearly 2000 students in 38 schools. Following, with science, research and recent news. , (Collection), (Collection)
(St. Louis Public Radio) Danforth Science Center Researches Indigo Plant Genes to Make Denim Jeans More Eco-friendly
https://www.danforthcenter.org/news-media/in-the-news/in-the-news-item/(st.-louis-public-radio)-danforth-science-center-researches-indigo-plant-genes-to-make-denim-jeans-more-eco-friendly
The project aims to produce 26,000 acres of indigo crops by 2021 to meet market demand and become cost-competitive with synthetic indigo dye products.
(St. Louis Public Radio) Danforth Science Center Researches Indigo Plant Genes to Make Denim Jeans More Eco-friendly, A collaboration between the Donald Danforth Plant Science Center and a textile, Stony Creek Colors, a company devoted to creating plant-based dyes, is working with the bioinformatics facility at the Danforth Science Center to develop a high-yielding seed to generate a sustainable, was recently funded by a one-year $224,676 grant from the National Science Foundation. "Ultimately, the goal


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Antoine Rudy Bernier (Dinant, 10 september 1997) is een Belgisch voetballer die sinds 2020 uitkomt voor RFC Seraing. Bernier is een vleugelspeler die bij voorkeur wordt uitgespeeld als linksvoor.

Carrière

Jeugd
Bernier begon zijn carrière bij CS Onhaye. Hij stroomde er in het seizoen 2013/14 door naar het eerste elftal in Vierde klasse D, waar ook zijn oudere broer Florent speelde. Bernier trok al gauw de aandacht van een paar eersteklassers: zo ging hij testen bij Club Brugge en kon hij ook testen bij Standard Luik, maar toen zijn broer bij laatstgenoemde club een negatieve ervaring opliep wees hij de Luikenaars af. Het was uiteindelijk RSC Anderlecht dat hem in 2014 binnenhaalde.

In mei 2016 ondertekende Bernier zijn eerste profcontract bij Anderlecht. In het seizoen 2015/16 had hij met Anderlecht de halve finale van de UEFA Youth League gehaald, mede dankzij een doelpunt van hem in de 2-0-zege tegen FC Barcelona in de kwartfinale. Bernier slaagde er echter niet om door te stromen naar het eerste elftal, waarop hij in 2018 de beloften van Anderlecht transfervrij inruilde voor Antwerp FC. Daar speelde hij een half seizoen bij de beloften, waar hij in elf wedstrijden vier keer scoorde.

Lierse Kempenzonen
In januari 2019 mocht Bernier met het eerste elftal van Antwerp mee op winterstage naar Spanje, maar nog in dezelfde maand werd hij voor de rest van het seizoen uitgeleend aan Lierse Kempenzonen. Daar maakte hij op 19 januari 2019 zijn profdebuut in de competitiewedstrijd tegen RFC Seraing (2-1-winst). In zijn tweede officiële wedstrijd droeg hij met twee goals bij aan de 0-4-zege tegen Dessel Sport, twee weken later was hij tegen KSV Oudenaarde opnieuw goed voor een tweeklapper. In de play-offs voor promotie scoorde hij eenmaal: Bernier opende de score in het 2-2-gelijkspel tegen Thes Sport, dat eerste was geëindigd in de reguliere competitie. Het was uiteindelijk niet Lierse Kempenzonen of Thes Sport, maar Excelsior Virton dat promoveerde naar Eerste klasse B.

F91 Dudelange
In de zomer van 2019 volgde een nieuwe uitleenbeurt, ditmaal aan de Luxemburgse eersteklasser F91 Dudelange. Daar speelde hij 28 officiële wedstrijden in het eerste elftal, waarvan 12 Europese: nadat de club in de Champions League-voorrondes (zonder Bernier) werd gewipt door Valletta FC, schakelde het in de Europa Legue-voorrondes achtereenvolgens FK Shkëndija 79 Tetovo, Nõmme Kalju FC en FC Ararat-Armenia uit, waarna het in een groep met APOEL Nicosia, Sevilla FC en FK Qarabağ terechtkwam. Bernier speelde in alle twaalf de Europa League-duels mee en scoorde zowel op de eerste speeldag (in de 3-4-zege tegen APOEL Nicosia) als op de tweede speeldag (1-4-nederlaag tegen Qarabağ).

In de BGL Ligue moest hij voor zijn eerste basisplaats wachten op trainer Bertrand Crasson, die in september 2019 zijn landgenoot Emilio Ferrera was komen vervangen. Dudelange, dat daarvoor vier landstitels op rij had behaald, stond op dat moment in de rechterkolom nadat het onder Ferrera met 4 op 15 aan de competitie was begonnen. Toen de competitie in maart 2020 werd stilgelegd vanwege de coronapandemie stond Dudelange slechts vijfde, het slechtste eindresultaat sinds de negende plaats in het seizoen 1996/97. Bernier scoorde in de competitie slechts één keer, maar deelde wel vier assists uit, waaronder in de 0-1-zege tegen Jeunesse Esch en het 2-2-gelijkspel tegen FC UNA Strassen.

RFC Seraing
Na afloop van zijn uitleenbeurt aan Dudelange ruilde Bernier Antwerp op definitieve basis voor RFC Seraing, waar hij een contract voor een seizoen met optie ondertekende. Samen met hem maakte ook Gaël Kakudji de overstap van Deurne naar Seraing. Bernier, die in het Pairaystadion zijn ex-trainer van bij Dudelange Emilio Ferrera opnieuw tegenkwam, groeide bij Seraing meteen uit tot een vaste waarde. Op het einde van zijn debuutseizoen promoveerde hij met de club naar de Jupiler Pro League. In de terugwedstrijd van de barragewedstrijden tegen Waasland-Beveren, de nummer vijftien uit de Jupiler Pro League, legde hij in de blessuretijd de 2-5-eindscore vast.

Na de promotie naar de Jupiler Pro League kwam Bernier, die in het tussenseizoen zijn contract verlengde tot 2023, minder aan spelen toe. Op de eerste twee competitiespeeldagen kreeg hij nog een basisplaats als linksbuiten, maar daarna posteerde trainer Jordi Condom Aulí daar Gérald Kilota, die in het seizoen daarvoor nog als linksback speelde.

Clubstatistieken

Bijgewerkt op 30 september 2021.

Zie ook
 Lijst van spelers van Antwerp FC
 Lijst van spelers van F91 Dudelange

Bernier,Antoine

redpajama_set_name: RedPajamaWikipedia


The Dublin Village Green Card Club is starting the Cash Game Festival today which will last till October,15. All guests and participants are expecting 120 hours of continuous poker action.
This season the Cash Game Festival has already been held in London's Aspers Casino (February and September), Slovenian Perla Casino (March), Tallinn's Olympic Park Casino (April), Sunborn Casino in Gibraltar (May), Olympic Casino in Malta (June) and in the Platinum Casino in Bulgaria (August).
The stage in Dublin stands out against the background of the rest not only because the capital of Ireland accepts the Cash Game Festival for the first time. Since the city is famous for its nightlife and parties, players have the right to hope that such a relaxed atmosphere will reign during the festival.
This is especially true for the guests who have acquired special hospitality packages that include a lot of interesting outside of poker tables. Unlike tournament festivals, participants will attend all planned events, since they have the opportunity to play when they want.
At the London stage, the premiere of the competition took place at the television table. A participant who won the largest number of big blinds at one of the two television tables during the festival, received an honorable trophy and a hospitality package.
In London, John Kite won this prize at the amount of 853 big blinds during one of the sessions at the £2/£5 TV table.
The Cash Game Festival offers a game for every taste and purse - in addition to unlimited games, participants can try their hand at pot-limit Omaha, Super Dealer Choice and Sviten Special. The minimum limit is set at €1/€2.
If you, for some reason can not visit the festival in Dublin, you can watch the progress of the competition online. Then you can plan a trip to Tallinn, where Olympic Park Casino will host the final stage of the Cash Game Festival on November 15-19.
Although nothing prevents the players from appearing in the right place and start playing, the organizers still advise registering on the site. This is especially important for those who have the desire to compete for a TV table.


text:
\section{Introduction}
	\IEEEPARstart{T}{he} gain in image quality provided by time-of-flight (TOF) in positron emission tomography (PET) is directly linked to the coincidence time resolution (CTR) of the scanner~\cite{conti2011focus,SURTI201612,vandenberghe2016recent}.
	Recently, progress achieved in PET detectors have made it possible to build a clinical scanner approaching a CTR of 200~ps~\cite{van2019performance}.
	Further advances can be expected since a CTR of 58~ps was recently achieved, albeit in a benchmark test using short crystals of LSO:Ce:0.4\%Ca~\cite{gundacker2020experimental}.
	Moreover, the roadmap towards achieving a CTR of 10~ps has been laid out and technological solutions have been discussed extensively~\cite{lecoq2020roadmap}.
	The challenge is huge and many pitfalls remain~\cite{schaart2020achieving}.
	As such, a better understanding of the benefits provided by ultra-fast TOF is of interest.
	For example, it was recently demonstrated that ultra-fast TOF resolution could provide a gain in spatial resolution by mitigating the blur induced by the detectors size~\cite{toussaint2020improvement}.
	Our goal is to investigate how ultra-fast TOF can be exploited in the PET reconstruction scheme to yield further gain in image quality and robustness.

	Low counts acquisition remains a challenge for PET reconstruction~\cite{6878472,lim2018pet}.
	When the correction for random events is applied, the non-negativity constraints of the MLEM reconstruction scheme induces a bias in the evaluation of the projection space correction factors that is propagated in the reconstructed image.
	A solution proposed in~\cite{6878472} consists of replacing the usual Poisson distribution by a Gaussian distribution for projections with a low number of counts.
	The authors of~\cite{lim2018pet} propose a new reconstruction scheme in which the non-negativity constraint is shifted from the image space to the projection space.
	In both cases, negative values in the image space are permitted to circumvent the bias induced by the random estimation included in the projections with low number of counts.
	While one could expect the random coincidences to dwindle with better TOF resolution, the coincidence time window will always be lower bounded by the subject size.
	Another indication of the limitation of the classical PET model for low counts acquisition is highlighted in~\cite{westerwoudt2014advantages}, where the authors showed that the TOF filtered back projection could outperform MLEM in terms of signal-to-noise ratio.

	Since low spatial frequencies converge faster than higher frequencies with the MLEM algorithm, its convergence rate depends on the structures size.
	Over-iteration with the MLEM algorithm also results in noisy images~\cite{qi2006iterative},
	Noise can thus contaminate larger structures before smaller ones can reach their optimal contrast
	This behavior compels users to arbitrarily terminate the reconstruction process early, based on the structures of interest.
	This could be exacerbated with ultra-fast TOF since convergence rate increases with TOF resolution~\cite{SURTI201612}.
	A regularization term can be included to the reconstruction model to mitigate the noise~\cite{qi2006iterative}.
	However, the optimal solution of a low counts reconstruction using a fine image discretization includes high frequency structures, which can impede the efficiency of a regularization scheme.

	In PET models, the physical property of a point source emission following an uniform distribution in the 3D sphere is encoded in the system matrix.
	As such, the forward model attributes a predetermined ratio of the counts in a voxel to all its projections, irrespective of the observed data.
	We propose to extend the parametrization of the reconstruction scheme to also explicitly include the projection domain in order to circumvent the bias induced by statistical noise in low counts reconstruction.
	The resulting number of variables is an order of magnitude larger than in the classical approach.
	Nevertheless, we hypothesize that with ultra-fast TOF, the proposed approach can be well-defined and thus provide a better description of the underlying physical processes for the reconstruction of low counts acquisition.

	An implementation of this new approach was investigated for low counts acquisitions to validate the hypothesis.
	The image quality achieved by this model was studied with a simulated 2D Hot Spot phantom.
	The MLEM algorithm was used as a baseline.
	Overall, the results of this study support the hypothesis that the proposed approach is of interest for low counts reconstruction with ultra-fast TOF.

\section{Parametrization of the Angular Distribution of Emission (PADE) Model}
\label{sec:model}
	In this section, we propose an implementation of this new approach to PET reconstruction.
	Correction factors associated to attenuation, detector efficiency, randoms and scatters are omitted for simplicity.
	The Python/MATLAB convention was used when a subset of the dimension of a matrix/tensor is fixed, e.g., $P_{:,i}^t$ is equivalent to $\{P_{j,i}^t| j \in [1, J]\}$.
	Also, the term pixel was used interchangeably for voxel since a part of the model is described for 2D reconstruction.
	Let $y_j^t$ be the number of coincidences observed in projection $j$ at the TOF bin $t$ and $P$ the TOF system matrix of a scanner.
	The likelihood model consists of solving $y_j^t\sim\textrm{Poisson}( \sum_i P_{j,i}^t \lambda_i), \forall j, t$ with $\lambda_i$ being the number of coincidences originating from the pixel $i$.
	The expected contribution of pixel $i$ to projection $j$ and TOF bin $t$ for a given estimate $\lambda$ is $P_{j,i}^t \lambda_i$.
	To fully exploit ultra-fast TOF resolution, the TOF information needs to be finely discretized.
	This will result in $y$ being sparse and low counts, which makes its approximation with $P_{j,i}^t \lambda_i$ highly prone to bias.

	We propose to extend the parametrization of the reconstruction model to include the projection space.
	Let $\phi_{j, i}$ define the number of coincidences emitted from pixel $i$ and observed in projection $j$.
	In that case, $\lambda_{i} = \sum_{j}{\phi_{j, i}}$ and the expected contribution of $\phi_{j,i}$ to $y_j^t$ is $Q_{j,i}^{t} \phi_{j, i}$, where $Q_{j,i}^{t}$ is the probability of a coincidence originating from pixel $i$ and observed in projection $j$ to be observed in TOF bin $t$.
	Consequently, $Q_{j,i}^{t} R_{j,i} \approx P_{j,i}^t $ where $R$ is the TOF-less system matrix of the scanner.
	Introducing this parameterization in the log-likelihood model results in
	\begin{equation}\label{eq:likelihoodExt}
		\mathcal{L}(\phi) = \sum_{jit} Q_{j, i}^{t} \phi_{j, i} - \sum_{jt} y_j^t \ln\left(\sum_i Q_{j, i}^t \phi_{j, i} \right)
	\end{equation}
	which is the data fit term for the Parametrization of the Angular Distribution of Emission (PADE) model, explicitly introducing the emission angular distribution in projection space.
	$\phi$ can be defined as a sparse matrix along the projection dimension since a given pixel intersects only a very small subset of the projections spanning the entire image domain.
	Thus, the proposed extension does not multiply the number of variables by the total number of projections defined in the scanner but does provide a significant increase in degrees of freedom.
	Also, one could note that the proposed parametrization corresponds to the latent variables used in the MLEM formalism when applied to PET reconstruction.

	A core property of the PET system model is missing in~\eqref{eq:likelihoodExt}: the isotropic nature of its emission that we refer to as the uniform distribution of emission (UDE) property.
	This is usually enforced by the system matrix as $R_{j,i} \lambda_i = \phi_{j,i}, \forall j,i$.
	Let $\mathcal{V}_i\left( \phi \right)$ be a metric that numerically evaluates how closely the pixel $i$ follow the UDE property.
	In this study, the UDE property is enforced as a penalization term defined as
	\begin{equation}\label{eq:geoPenal}
		\mathcal{U}(\phi) = \sum_{i} \omega_i \mathcal{V}_i\left( \phi \right)
	\end{equation}
	where $\omega_i$ is the weight applied to pixel $i$.

	\begin{figure}
		\centering
		\subfloat[Partition of a point source emission angles over projections]{%
			\label{fig:emissionPartInScanner}\includegraphics[width=0.45\linewidth]{emissionPartInScanner.pdf}}
		\quad
		\subfloat[Cones of emission and two examples of $j_i^{\textrm{ref}}$ for the point source]{%
			\label{fig:coneOfEmission}\includegraphics[width=0.45\linewidth]{coneOfEmission.pdf}}\\
		\subfloat[Polar partition of the emission angles relative to the brown $j_i^{\textrm{ref}}$]{%
			\label{fig:vizCircBothPartition}\includegraphics[width=0.45\linewidth]{vizCircBothPartition.pdf}}
		\quad
		\subfloat[Visualization of three counts in the previous partition]{%
			\label{fig:vizCircBothPartitionExample}\includegraphics[width=0.45\linewidth]{vizCircBothPartitionExample.pdf}}
		\caption{%
			Representation of the cyclic nature of PET emission and the impact of $j_i^{\textrm{ref}}$ for an octogonal-shaped scanner with one detector per panel.
			The white circles in \protect\subref{fig:emissionPartInScanner} were added to highlight that the cones of emission in \protect\subref{fig:coneOfEmission} are obtained by extending the lines that connect the detectors extremities to the point source, represented by the dashed green lines.
			The resulting eight cones of emission were colored differently for easier visualization.
			The brown and red lines indicate two possibles $j_i^{\textrm{ref}}$ for ordering the valid projections.
			\protect\subref{fig:vizCircBothPartition} shows the partition of $[0, 2 \pi)$ from the cones of emission of the point source, when ordered using the brown $j_i^{\textrm{ref}}$.
			The partition of $[0, \pi)$ is sufficient to define the cones of emission due to the anti-parallel nature of PET emission.
			\protect\subref{fig:vizCircBothPartitionExample} shows an example of three emission angles that correspond to one counts for $\tilde{\jmath} = \{1, 5, 8\}$ and zero everywhere else for the brown $j_i^{\textrm{ref}}$.
			For the red $j_i^{\textrm{ref}}$, the counts would be in $\tilde{\jmath} = \{1, 4, 5\}$.
		}
		\label{fig:visuUde_geo}
	\end{figure}

	The following implementation of $\mathcal{V}\left( \right)$ was inspired by section 4.4.1 of~\cite{mardia2009directional} where it is pointed out that the uniform distribution is the only cyclic distribution that is invariant under rotation.
	We defined a weighted sum, that we will refer to as momentum, as a numerical characterization of the pixel projection-wise distribution.
	This metric was chosen over the mean since the latter requires a division by the number of elements in the distribution, $\sum_j \phi_{j,i} $, which would make $\mathcal{V}\left( \right)$ more complex and the resulting PADE model harder to solve.
	A visual representation of the key steps behind the computation of the metric are provided in Fig.~\ref{fig:visuUde_geo} and Fig.~\ref{fig:visuUde_num}.
	The goals behind these steps is to define an ordering for the projections, circumvent the discrete sampling of the projection domain and modify the emission angular space of each pixel such that it is centered at zero.
	A partition of the emission angular space is obtained by using the lines that connect the detectors extremities to a pixel, as illustrated in Fig.~\ref{fig:emissionPartInScanner}.
	We refer to a part of that partition as a cone of emission, which is kind-of the dual of the TOF-less tube of response ($R_{j, :}$).
	The cones of emission of the pixel ($R_{:, i}$) in Fig.~\ref{fig:emissionPartInScanner} are highlighted in Fig.~\ref{fig:coneOfEmission}.
	Let $j_i^{\textrm{ref}}$ be a projection of reference for pixel $i$ from which valid projections, i.e. $\{j | R_{j,i} \neq 0.0\}$, can be ordered.
	The choice of $j_i^{\textrm{ref}}$ emulates a rotation over the emission angular space, as shown with the two examples of $j_i^{\textrm{ref}}$ given in Fig.~\ref{fig:coneOfEmission}.
	The resulting polar partition of the emission angular space for the brown $j_i^{\textrm{ref}}$ is shown in Fig.~\ref{fig:vizCircBothPartition}.
	An example of the distribution obtained for three emissions originating from the pixel is illustrated in Fig.~\ref{fig:vizCircBothPartitionExample}.
	The first line of Fig.~\ref{fig:udePenalViz_exA} and~\ref{fig:udePenalViz_exB} show the partition of the emission angular space obtained from the example in Fig.~\ref{fig:visuUde_geo}, respectively for the brown and red $j_i^{\textrm{ref}}$.
	Its discretization was defined as the middle position of the partition resulting from the choice of $j_i^{\textrm{ref}}$.
	Let $D(i, j_i^{\textrm{ref}})$ be a vector that holds that discretization and let $E(i, j_i^{\textrm{ref}}) = D(i, j_i^{\textrm{ref}}) / \pi - 0.5$ be the discretization employed by the metric, illustrated in the second line of Fig.~\ref{fig:udePenalViz_exA} and~\ref{fig:udePenalViz_exB}.
	The subscript $\tilde{\jmath}$ will be used for $E(i, j_i^{\textrm{ref}})$ to specify that the order of the projections differs from $j$ and that only a subset of the projections are defined for a given pixel.
	Let $\mathcal{C}_i(\tilde{\jmath}, j_i^{\textrm{ref}})$ be a function that provides the projection index of the $\tilde{\jmath}$-th projection relative to $j_i^{\textrm{ref}}$ for pixel $i$.
	Thus, the momentum, i.e. a custom weighted sum, of the distribution $\phi_{:, i}$, which is not a mean, is
	\begin{equation}\label{eq:geoPenalMetricInnerLoop}
		\mathcal{W}_i\left( \phi, j_i^{\textrm{ref}} \right) = \sum_{\tilde{\jmath}} \left( [E(i, j_i^{\textrm{ref}})]_{\tilde{\jmath}} ~ \phi_{j,i} \right)
	\end{equation}
	with $j = \mathcal{C}_i(\tilde{\jmath}, j_i^{\textrm{ref}})$.
	This is evaluated over several projections of reference to incorporate its variation over rotations.
	Thus, the UDE metric employed is
	\begin{equation}\label{eq:geoPenalMetric}
		\mathcal{V}_i\left( \phi \right) = B^{-1} \sum_{j_i^{\textrm{ref}}} \left( \mathcal{W}_i\left( \phi, j_i^{\textrm{ref}} \right) \right)^2
	\end{equation}
	where $B$ is the number of $j_i^{\textrm{ref}}$ considered.
	If a distribution follows exactly the UDE property, the momentum will be zero for all projections of reference.
	The example provided in Fig.~\ref{fig:visuUde_num} shows a case where the UDE metric values vary with the choice of $j_i^{\textrm{ref}}$.
	The value being almost zero for the brown $j_i^{\textrm{ref}}$ (Fig.~\ref{fig:udePenalViz_exA}) contrary to the value obtained with the red $j_i^{\textrm{ref}}$ (Fig.~\ref{fig:udePenalViz_exB}).
	\begin{figure}
		\centering
		\subfloat[Computation of $\mathcal{W}_i\left( \phi, j_i^{\textrm{ref}} \right)$ for the brown $j_i^{\textrm{ref}}$]{%
			\label{fig:udePenalViz_exA}\includegraphics{constUnif_exA.pdf}}\\
		\subfloat[Computation of $\mathcal{W}_i\left( \phi, j_i^{\textrm{ref}} \right)$ for the red $j_i^{\textrm{ref}}$]{%
			\label{fig:udePenalViz_exB}\includegraphics{constUnif_exB.pdf}}
		\caption
			Visual representation of the process behind~\eqref{eq:geoPenalMetricInnerLoop} using the example in Fig.~\ref{fig:visuUde_geo}.
			\protect\subref{fig:udePenalViz_exA} represents the case of the brown $j_i^{\textrm{ref}}$ in three steps.
			The first line shows the same partition as Fig.~\ref{fig:vizCircBothPartition} but limited to $[0, \pi)$.
			The second line shows the resulting $E(i, j_i^{\textrm{ref}})$, represented by lines colored to their corresponding projection.
			The third line shows the bins where $\phi_{j,i} = 1$ as green lines and the brown arrow shows the result of $\mathcal{W}_i\left( \phi, j_i^{\textrm{ref}} \right)$.
			\protect\subref{fig:udePenalViz_exB} is the same as previous except with the red $j_i^{\textrm{ref}}$.
			Note that the position of the resulting arrow differs between the two choices of $j_i^{\textrm{ref}}$ and that the position for the red $j_i^{\textrm{ref}}$, which is correctly positioned, illustrates the counter-intuitive aspect of using the momentum instead of the mean in~\eqref{eq:geoPenalMetricInnerLoop}.
		}
		\label{fig:visuUde_num}
	\end{figure}

	One can expect that the UDE penalization term will be more complex for 3D reconstructions since emission angle can no longer be represented over a circle.
	However, most scanners are shaped as a stack of rings and thus their sampled emission space will also be a stack of cylindrical strip along one of the axis of the 3D sphere.
	The resulting sampling scheme can be directly mapped to a 2D uniform space if solid angles are taken into accounts.
	Then, the methodology defined previously should be adequate as long as considerations of a plane domain over a linear domain are taken into account.
	Since PET sampling scheme exclude, most of the time, two pretty large spherical caps, we expect that the cyclic nature of the data might only be usable on the transverse plane.

	One of the convenient property of the MLEM algorithm is the stability of the expected number of coincidences over all iterations~\cite{qi2006iterative}.
	Let $\lambda^k$ be the image obtained after $k$ iterations of MLEM, then $\sum_{t,j,i} P_{j,i}^{t}\lambda_i^k = \sum_{t,j} y_j^t, \forall k > 1$.
	However, this property needs to be incorporated in the reconstruction model for a general solvers.
	It could be enforced as a constraint, with a penalization term or within the solver update scheme.
	We used a penalization term defined as
	\begin{equation}\label{eq:countsPenal}
		\mathcal{H}(\phi) = \left( \sum_{t,j,i} Q_{j,i}^t \phi_{j,i}  - \sum_{t,j} y_j^t \right)^2.
	\end{equation}

	Thus, the general form of the PADE model that was explored was
	\begin{equation}\label{eq:padeModel}
		\begin{aligned}
			&\min_{\phi}       & \qquad & \mathcal{L}\left(\phi\right) + \gamma_1 \mathcal{U}\left(\phi\right) + \gamma_2 \mathcal{H}\left(\phi\right)  \\
			&\text{subject to} &      & \phi \geq 0
		\end{aligned}
	\end{equation}
	where $\gamma_1$ is the weight for the UDE penalization term and $\gamma_2$ the weight for the expected number of coincidences penalization term.
	Both weights need to be positive with the choice of $\mathcal{U}\left(\phi\right)$ and $\mathcal{H}\left(\phi\right)$ presented previously.
	Compared to the classical PET log-likelihood model, this model described in~\eqref{eq:padeModel} relax the interpretation of the UDE property by replacing the relation $R_{j,i} \lambda_i = \phi_{j,i}$ to a penalization term represented by $\mathcal{U}\left(\phi\right)$.
	This new model requires more care to solve than the classical PET log-likelihood model.
	For example, the MLEM inherently imposes non-negativity constraints on $\lambda$.
	This is not the case for all general solvers and it will thus need to be taken into account in the choice of the solver.
	Another example is the calibration of the hyper-parameters $\gamma_1$ and $\gamma_2$.
	The values used for these parameters will affect the quality of the solutions obtained and these values are most likely data-dependent.

\section{ Simulation setup }
\label{sec:meth}
	The goal of this study was to show that the PADE approach is a legitimate candidate for low counts reconstruction.
	Hence, the methodology was built to compare the image quality achieved by the previously proposed PADE implementation to the performance of the MLEM algorithm on low counts acquisition without including further consideration.

	\subsection{ Data simulation }
	\label{subsec:dataSimul}
		The version 8.0 of Geant4 Application for Tomographic Emission (GATE)~\cite{jan2004gate} was used to simulate data acquisitions from a fictive PET ring scanner.
		The sources were defined as back-to-back which means that positron range and annihilation photon acolinearity were not simulated.
		The emission direction of the sources was limited to the 2D plane of the scanner.
		Only photoelectric processes were enabled for the annihilation photons hence the datasets does not have scatter coincidences.
		Also, the emission rate of the sources was chosen such that random coincidences would be negligible.

		The 2-D ring camera was shaped as a regular polygon with 40 sides and an inner diameter of $\sim$80~cm.
		Each panel was 64~mm in size and consisted of 8 detectors of 8~mm in width.
		The scanner thus had 320 detectors, implying that each image pixel was intersected by at least 320 tubes of response (i.e. valid projections).
		The detector length was fixed to 0.1~mm, making the blur induced by depth of interaction negligible.
		The detectors were 4~mm wide in the axial axis and it was assumed that they had a direct readout without light-sharing coding.
		The CTR was fixed to $\sim$13~ps at full width at half maximum (FWHM), resulting in a spatial resolution of 2~mm along projections.

		A custom Hot Spot phantom with background was created for this study.
		Its main body was a cylinder of 136~mm in diameter and 4~mm in height.
		The hot spot diameters were 3.2, 4.8, 6.4, 7.9, 9.5, 11.1~mm.
		The activity in the phantom was defined such that the contrast between the spots and the background would be of four.
		The simulation was repeated ten times, each resulting in a dataset of around 80,000 coincidences.

	\subsection{ Image reconstruction }
	\label{subsec:methRecon}
		The image domain was a $16\times16$~cm$^2$ plane discretized uniformly in $128 \times 128$ pixels, resulting in an in-plane width of 1.25~mm.
		A total of 8,544 projections intersected the image domain.
		The TOF information was discretized uniformly in 128 bins resulting in spatial bins of 1.82~mm in width.
		Thus, the histograms consisted of 1,093,632 elements and most of them had zero coincidences.

		The TOF, $P$, and TOF-less, $R$, system matrices and the pure-TOF matrix, $Q$, were precomputed.
		$R_{j,i}$ was approximated as the geometric probability of a point source centered in the voxel $i$ to emit in the tube of response of projection $j$.
		The TOF response function of a projection was assumed invariant across its tube of response and modeled as a 1D Gaussian of 2~mm FWHM along its tube of response.
		$Q_{j,i}^t$ was approximated as the result at voxel $i$ of the convolution of the TOF response function with the rectangular function associated to the TOF bin $t$.
		$P^t_{j,i}$ was defined as $Q^t_{j,i} P_{j,i}, \forall t,j,i$.
		For all three matrices, the image domain was oversampled three times in both dimensions of the plane and the mean was taken.

		The L-BFGS-B~\cite{2020SciPy-NMeth,zhu1997algorithm} algorithm with non-negativity constraints was employed to solve the PADE model.
		A reduction of the number of variables was applied following the idea that variables that have a null probability of being associated with any coincidences are irrelevant.
		Thus, the constraints were modified from $\phi_{j,i} \geq 0, \forall j,i$ to
		\begin{equation}\label{eq:constraints}
			\begin{cases}
			    \phi_{j,i} = 0 & \text{if } \sum_{t} y_j^t P^t_{j,i} = 0 \\
			    \phi_{j,i} \geq 0              & \text{otherwise}
			\end{cases}
		\end{equation}
		In a ultra-fast TOF and low counts setting, a significant portion of the variables can be deactivated with this approach ($\approx$70\% in this study).
		The $\omega$ were defined in two steps.
		First, it would be detrimental to penalize pixels that have a low value since the UDE property can not be evaluated accurately in those cases.
		Second, the strength of the penalty applied on a pixel should be positively correlated with its value.
		We chose to set the weights at each iteration as the value of the pixels of the previous iteration which was inspired from the approach used in the OSL-MLEM algorithm~\cite{green1990bayesian}.
		Thus, the pixel-dependent weights were defined as
		\begin{equation}\label{eq:omegaWeight}
			\omega_i^k =
			\begin{cases}
			    0 & \text{if } \sum_j \phi_{j,i}^0 < 9.0 \\
			    \sum_j \phi_{j,i}^{k-1}             & \text{otherwise.}
			\end{cases}
		\end{equation}
		Our initial tests had shown that the proposed model did not perform well when it was initialized with an uniform image.
		This might have been due to the update scheme of $\omega$ which results in the objective function being drastically modified at each iterations.
		However, we observed that the MLEM model could produce an adequate initialization for the proposed model, if stopped early.
		As such, a low iteration MLEM reconstruction, $\lambda^k$ with $k$ being the number of iterations, was employed to build an initial estimate.
		Since $\lambda^k$ is only defined in the image domain, the initial estimate, $\phi^0$, was generated using the TOF-less system matrix.
		A modified version of the $R$ matrix was employed in order to satisfy~\eqref{eq:constraints}.
		Let $\widetilde{R}_{j,i}$ be equal to $R_{j,i}$ if $\sum_t y_j^t P^t_{j,i} \neq 0.0$ and 0.0 otherwise.
		The matrix was then normalized such that $\sum_j \widetilde{R}_{j,i} = \sum_j R_{j,i}, \forall i$.
		Thus, the PADE model was initialized with
		\begin{equation}\label{eq:initialization}
			\phi_{j,i}^0 = \widetilde{R}_{j,i} \lambda_i^k, \forall j,i.
		\end{equation}
		The iteration that had the minimum mean squared error with the simulation groundtruth, i.e. the true number of emissions per pixel, was chosen, which was achieved at the 6$^{\textrm{th}}$ iteration when looking at the mean over all repetitions.
		An advantage of using an image obtained from the MLEM for initialization is that it has the correct number of expected coincidences.
		Since the number of valid projections was at least 320 for all pixels, the computation of the UDE metric over all possible $j_i^{\textrm{ref}}$ was computationally expensive.
		For this study, 30 projections of reference were used for each pixel such that they uniformly sampled their respective projection space.

	\subsection{ Comparison of the models }
	\label{subsec:metricComparaison}
		The images obtained with the TOF-PET log-likelihood MLEM reconstruction (\textit{MLEM}), the direct backprojection of the data with TOF Gaussian kernel (\textit{backprojection}) and two versions of the PADE model were compared in term of contrast and noise.
		The first PADE version (\textit{PADE}$_{\textrm{v0}}$) was defined with the weights $(\gamma_1, \gamma_2)$ that offered the best performance given the choice of metrics for this study.
		The second PADE version was defined with $\gamma_1 = 0.0$ and the minimum value of $\gamma_2$ ensuring a divergence in the number of expected coincidences lower than 1\%.
		This version will be referred to as \textit{Extended} since it is the TOF-PET log-likelihood model extended to the new parameterization.

		The four models were compared using contrast recovery coefficient (CRC) and coefficient of variation (COV) for the five smallest spots.
		The background, i.e. body of the phantom excluding the spots, recovery ratio and COV were also studied.
		The true mean value of the spots and the background was extracted from the groundtruth of each simulations.
		The pixels associated to a given region of interest were extracted using the groundtruth, with pixels subjected to significant partial volume effect excluded from the evaluation of the metrics.
		The CRC ratio was computed as $\frac{\mu_{\textrm{spots}}}{\mu_{\textrm{bkg}}} / \textrm{CRC}^{\textrm{true}}$ where $\mu_{\textrm{spots}}$ was the mean value of the pixels extracted from the spots of interest, $\mu_{\textrm{bkg}}$ was the mean value of the pixels extracted from the background and $\textrm{CRC}^{\textrm{true}}$ was the CRC obtained from the simulation groundtruth over the same spots of interest.
		The background recovery ratio was defined as $\mu_{\textrm{bkg}} / \mu_{\textrm{bkg}}^{\textrm{true}}$.
		The COV was defined as $\frac{\sigma_{\textrm{ROI}}}{\mu_{\textrm{ROI}}}$ with $\sigma_{\textrm{ROI}}$ being the standard deviation of the pixels extracted from a region of interest (the spots of a given size or the background).
		The evolution of the metrics over iterations was analyzed since the convergence rate of the MLEM algorithm and the PADE model might differ.

		The weights $(\gamma_1, \gamma_2)$ for the \textit{PADE}$_{\textrm{v0}}$ model were obtained with a grid search, enabled by using the GNU parallel software~\cite{Tange2011a}.
		Values of $10^{-3}$ to $10^{5}$ for $\gamma_1$ and values of $10^{-5}$ to $10^{2}$ for $\gamma_2$ with multiplicative steps of ten were considered.
		For each combination of $(\gamma_1, \gamma_2)$, the solutions obtained over 250 iterations of the solver were registered for the ten simulations.
		The mean CRC and COV values were extracted and the $(\gamma_1, \gamma_2)$ pair yielding the highest CRC ratio for the smallest spots was selected.
		$(\gamma_1, \gamma_2)$ pair were excluded if the CRC ratio of any group of spots were overestimated by more than 10\%, if the mean bias over the background was larger than 0.5 or if the number of expected coincidences deviated by more than 1\%.
		The $(\gamma_1, \gamma_2)$ pair for the \textit{PADE}$_{\textrm{v0}}$ model were (100.0, 10.0).
		As for the \textit{Extended} model, $\gamma_2$ was equal to 0.01.

\section{Results}
\label{sec:results}
	In Fig.~\ref{fig:im_recon_mlemIntuition}, zoomed versions of four images obtained from one of the simulations are shown to provide some insight of the performance provided by classical approaches.
	One of the characteristics of low counts reconstruction is the inherent statistical variations inside regions of interest, as can be observed from the groundtruth shown in Fig.~\ref{fig:im_gt}.
	Fig.~\ref{fig:im_BP} shows the image obtained from the \textit{Backprojection} model.
	Due to the excellent TOF resolution, the greater portion of the spots were resolved albeit with a lower contrast, especially for the smallest spots.
	The spots were better resolved in the image obtained with 6 MLEM iterations (Fig.~\ref{fig:im_mlem_06}) but correlated statistical noise in the background, not present in the groundtruth, were also observed.
	This is an example of the images that were used to initialize the \textit{PADE}$_{\textrm{v0}}$ model, where its spots resolvability allow an efficient initialization of $\omega$ (see~\eqref{eq:omegaWeight}).
	With 10 MLEM iterations (Fig.~\ref{fig:im_mlem_10}) the spots seemed to have a better contrast however the statistical noise is further amplified, both in the spots and the background.
	These observations for the MLEM images are in agreement with the known interplay between the convergence acceleration induced by better TOF, the effect of object size on contrast recovery rate and the noisy nature of the optimal solution for the PET log-likelihood model.
	The images in Fig.~\ref{fig:im_recon_mlemIntuition} illustrate that even with excellent TOF resolution, low counts reconstruction remains a challenge that impede image quality.
	\begin{figure}
		\centering
		\subfloat[Dataset groundtruth]{%
			\label{fig:im_gt}\includegraphics[width=.44\linewidth]{images/groundTruthData.png}}\hfil
		\subfloat[\textit{Backprojection}]{%
			\label{fig:im_BP}\includegraphics[width=.44\linewidth]{images/bpGauss.png}}\\
		\subfloat[\textit{MLEM}, 6 iterations]{%
			\label{fig:im_mlem_06}\includegraphics[width=.44\linewidth]{images/MLEM_ite6.png}}\hfil
		\subfloat[\textit{MLEM}, 10 iterations]{%
			\label{fig:im_mlem_10}\includegraphics[width=.44\linewidth]{images/MLEM_ite10.png}}
		\caption{%
		 	Cropped version of four images built from one of the simulations, shown with the same linear gray scale: \protect\subref{fig:im_gt} true distribution of the coincidences events; \protect\subref{fig:im_BP} image reconstructed from the backprojection of the data using the TOF Gaussian kernel; \protect\subref{fig:im_mlem_06} and \protect\subref{fig:im_mlem_10} images obtained after 6 and 10 iterations, respectively, with the MLEM algorithm.
		}%
		\label{fig:im_recon_mlemIntuition}
	\end{figure}

	Fig.~\ref{fig:crc} compares the CRC ratios of the five smallest spots and the background recovery ratio for the four models.
	Only the first 40 iterations out of 250 are shown since most of them converge towards stable values afterward.
	Overall, the \textit{MLEM} model seems to outperform the other models.
	Optimal values of CRC ratios and background recovery ratio are reached, except for the smallest spot for which an overestimation of around 10\% is observed after 80 iterations (not shown).
	The worst variation over the 10 repetitions were observed with the \textit{MLEM} model for the two smallest spots.
	Furthermore, the image obtained at 10 MLEM iterations, see Fig.~\ref{fig:im_mlem_10}, had already been much affected by the noise, making the progress in CRC ratio afterward less conclusive.
	The \textit{Backprojection} model had the worst CRC ratios and background recovery ratio, as expected from the blurred image in Fig.~\ref{fig:im_BP}.
	However, it was also the most stable which was expected with the choice of TOF kernel.
	The \textit{PADE}$_{\textrm{v0}}$ and \textit{Extended} models both had a good start since they were initialized with the 6$^{\textrm{th}}$ iteration of the MLEM reconstruction.
	For the \textit{Extended} model, the performance metrics worsened with iteration, stabilizing at values a little better than those of the \textit{Backprojection} model.
	The \textit{PADE}$_{\textrm{v0}}$ model achieved some gain in CRC ratio and background recovery ratio for the first few iterations and remained stable afterward.
	While the algorithm converged very rapidly ($<6$ iterations) to stable values, it did not reach the optimal values for the two smallest spots, especially with the smallest one where it did not reach 80\% of the true contrast recovery.
	\begin{figure}
		\centering
		\includegraphics{bias_Metric}
		\caption{%
			The CRC ratio of the five smallest spots and the background recovery ratio (lower right) as a function of the number of iterations are shown for the four models.
			The values for the \textit{Backprojection} model are displayed as horizontal lines since the algorithm is non-iterative.
			Error bars ($\pm2\sigma$) show the variability over the ten repetitions.
			The error bars for the \textit{Backprojection} model are too small to be visible.
		}%
		\label{fig:crc}
	\end{figure}

	Fig.~\ref{fig:cov} compares the COV of the five smallest spots and the background for the four models.
	Only the first 40 iterations of 250 are shown since most of them are stable afterward except for the \textit{MLEM} model where it continued to increase.
	The best model for these metrics was the \textit{Backprojection} model which was most likely due to the smoothing effect of the TOF Gaussian kernel.
	The trends of the \textit{Extended} model differed from what was observed with the CRC metric, here remaining equivalent to the \textit{PADE}$_{\textrm{v0}}$ model.
	The \textit{PADE}$_{\textrm{v0}}$ model remained stable with iterations, suggesting that the gain in CRC was achieved without increasing much the noise.
	The \textit{MLEM} model was notably more unstable than the other models across repetitions.
	At the 10$^{\textrm{th}}$ iteration, the image produced by the \textit{MLEM} model was noisier than the one of the \textit{PADE}$_{\textrm{v0}}$ model, especially in the background.
	\begin{figure}
		\centering
		\includegraphics{variance_Metric}
		\caption{%
			The COV of the five smallest spots and the background as a function of the number of iterations are shown for the four models.
			The values for the \textit{Backprojection} model are displayed as horizontal lines since the algorithm is non-iterative.
			Error bars ($\pm2 \sigma$) show the variability over the ten repetitions.
			The error bars for the \textit{Backprojection} model are too small to be visible.
		}%
		\label{fig:cov}
	\end{figure}

	In Fig.~\ref{fig:im_recon_comp}, a zoomed version of four images obtained from one of the simulation are shown.
	It consists of the groundtruth of the simulation compared to images obtained with the \textit{PADE}$_{\textrm{v0}}$, \textit{Extended} and \textit{MLEM} models.
	We chose the 40$^{\textrm{th}}$ iteration of the \textit{PADE}$_{\textrm{v0}}$ model to display the stability of that model (Fig.~\ref{fig:im_pade_best}).
	We chose the 40$^{\textrm{th}}$ iteration for the \textit{Extended} model, Fig.~\ref{fig:im_pade_ext}, since it was where the CRC ratios stabilized.
	The 10$^{\textrm{th}}$ iteration of the MLEM was chosen since it was where most of the spots CRC ratios were around 1.0.
	The \textit{Extended} image seems to have lower contrast and resolving power then the other models, as shown in Fig.~\ref{fig:crc}.
	This observation indicates that even with excellent TOF resolution, the UDE property remains important to achieve better reconstruction.
	The pattern of the noise in the background of the \textit{PADE}$_{\textrm{v0}}$ and the \textit{MLEM} images, Fig.~\ref{fig:im_pade_best} and Fig.~\ref{fig:im_mlem_10_p2} respectively, were similar except for the intensity.
	This highlight that the initialization of \textit{PADE}$_{\textrm{v0}}$, shown in Fig.~\ref{fig:im_mlem_06}, had a strong impact on the solution of the proposed model.
	The \textit{PADE}$_{\textrm{v0}}$ image seemed less noisy than the \textit{MLEM} image, which seems to enhance the resolving power of the spots in the \textit{PADE}$_{\textrm{v0}}$ image.
	Even with far more iterations, the \textit{PADE}$_{\textrm{v0}}$ image appear less noisy than the \textit{MLEM} image.
	\begin{figure}
		\centering
		\subfloat[Dataset groundtruth]{%
			\label{fig:im_gt_p2}\includegraphics[width=.44\linewidth]{images/groundTruthData.png}}\hfil
		\subfloat[\textit{Extended}, 40 iterations]{%
			\label{fig:im_pade_ext}\includegraphics[width=.44\linewidth]{images/extended_ite40.png}}\\
		\subfloat[\textit{PADE}$_{\textrm{v0}}$, 40 iterations]{%
			\label{fig:im_pade_best}\includegraphics[width=.44\linewidth]{images/padeGeoCyclV1p1_oslT9_mlemIt6V2_ite40.png}}\hfil
		\subfloat[\textit{MLEM}, 10 iterations]{%
			\label{fig:im_mlem_10_p2}\includegraphics[width=.44\linewidth]{images/MLEM_ite10.png}}
		\caption
			Cropped version of four images built from one of the simulations, shown with the same linear gray scale: \protect\subref{fig:im_gt_p2} true distribution of the coincidences events; \protect\subref{fig:im_pade_ext} image reconstructed with the \textit{Extended} model; \protect\subref{fig:im_pade_best} image reconstructed with the \textit{PADE}$_{\textrm{v0}}$ model and \protect\subref{fig:im_mlem_10} image reconstructed with the MLEM algorithm.
		}%
		\label{fig:im_recon_comp}
	\end{figure}

	The projection-wise distribution of the counts inside one pixel is compared in Fig.~\ref{fig:udeAnalysis} for the image obtained with 40 iterations of the \textit{PADE}$_{\textrm{v0}}$ model ($\phi_{:,i}^{40}$) and the groundtruth ($\phi_{:,i}^{*}$) for one of the datasets.
	The pixel compared, $i$, was inside one of the 9.5~mm spots and it had 358 valid projections.
	$\phi_{:,i}^{*}$ was composed of zeros and ones, for a total of 24 counts.
	Fig.~\ref{fig:udeAnalysis_polar} shows their polar distributions, relative to their expected value if they followed exactly the UDE property, for two choices of $j_i^{\textrm{ref}}$.
	$\phi_{:,i}^{*}$ seemed to follow a uniform distribution for both $j_i^{\textrm{ref}}$, see the red and green polar distributions, considering it had only 24 samples distributed in 358 bins.
	$\phi_{:,i}^{40}$ also seemed to follow a uniform distribution for both $j_i^{\textrm{ref}}$, see the cyan and purple polar distributions.
	$\phi_{:,i}^{40}$ was clearly not sparse, contrary to $\phi_{:,i}^{*}$, and we note that its values oscillates around 1.0, which means that $\phi_{j,i}^{40} \approx (\sum_j \phi_{j,i}^{40}) R_{j,i}$.
	These observations suggest that the UDE property was strongly enforced with the \textit{PADE}$_{\textrm{v0}}$ model.
	Fig.~\ref{fig:udeAnalysis_values} shows the histograms of the values of $\mathcal{W}_i(\phi_{:,i}^{40}, j_i^{\textrm{ref}})$ and $\mathcal{W}_i(\phi_{:,i}^{*}, j_i^{\textrm{ref}})$ over the thirty $j_i^{\textrm{ref}}$.
	Note that values outside of the $[-0.5, 0.5]$ range are possible since the metric was defined as a weighted sum (momentum) and not a mean.
	The values of $\mathcal{W}_i()$ for the distributions shown in Fig.~\ref{fig:udeAnalysis_polar} were highlighted to provide a visual intuition of the metric.
	While the two histograms are mostly within the same range, the values associated to $\phi_{:,i}^{*}$ were more dispersed than those of $\phi_{:,i}^{40}$.
	Thus, the $\mathcal{W}_i()$ metric claims that $\phi_{:, i}^{40}$ follow better the UDE property than $\phi_{:, i}^{*}$, which again suggest that the \textit{PADE}$_{\textrm{v0}}$ model strongly enforces the UDE property.
	\begin{figure}
		\centering
		\subfloat[Polar distributions of $\phi_{:,i}^{40}$ and $\phi_{:,i}^*$ for two choices of $j_i^{\textrm{ref}}$]{%
			\label{fig:udeAnalysis_polar}\includegraphics{images/exReconPolarDist.png}}\\
		\subfloat[Value of $\mathcal{W}_i(\phi, j_i^{\textrm{ref}})$ for thirty $j_i^{\textrm{ref}}$ for $\phi_{:,i}^{40}$ and $\phi_{:,i}^*$]{%
			\label{fig:udeAnalysis_values}\includegraphics{exReconMetricDist}}
		\caption{%
			Comparison of $\phi_{:,i}^{40}$ and $\phi_{:,i}^*$ for one of the datasets.
			$\phi^{40}$ is the 40$^{\textrm{th}}$ iteration of the \textit{PADE}$_{\textrm{v0}}$, $\phi^*$ is the dataset groundtruth and $i$ is the index of a pixel inside a 9.5~mm spot.
			$\phi_{:,i}^*$ is composed of ones and zeros and $\sum_j \phi_{j,i}^* = 24$.
			\protect\subref{fig:udeAnalysis_polar} shows their polar distributions, relative to their expected value if they followed exactly the UDE property, for two choices of $j_i^{\textrm{ref}}$, shown as a dashed black line.
			If the $\tilde{\jmath}^{\textrm{th}}$ bar is at 1.0, it means that $\phi_{\tilde{\jmath},i} = (\sum_j \phi_{j,i}) R_{\tilde{\jmath},i}$.
			The cyan and purple distributions are from $\phi_{:,i}^{40}$ while the red and green ones are from $\phi_{:,i}^*$.
			For easier comparison, $\phi_{:,i}^{40}$ and $\phi_{:,i}^*$ are shown in the same graph.
			The parts that exceed 1.5 were shaded to indicate that their full height might not be visible.
			\protect\subref{fig:udeAnalysis_values} shows the values of $\mathcal{W}_i(\phi, j_i^{\textrm{ref}})$ for the thirty $j_i^{\textrm{ref}}$ when applied to $\phi_{:,i}^{40}$ and $\phi_{:,i}^*$.
			The values of $\mathcal{W}_i(\phi, j_i^{\textrm{ref}})$ for the two $j_i^{\textrm{ref}}$ illustrated in \protect\subref{fig:udeAnalysis_polar} were added with their respective color.
			The hatching pattern x was used for $\phi_{:,i}^{40}$ while the slash pattern was used for $\phi_{:,i}^*$.
		}%
		\label{fig:udeAnalysis}
	\end{figure}

\section{Discussion}
\label{sec:disc}
	The goal of this study was to demonstrate the potential of the PADE paradigm for ultra-fast TOF reconstruction of low counts acquisitions.
	The proposed implementation of the PADE approach, \textit{PADE}$_{\textrm{v0}}$, achieved similar CRC ratios to the \textit{MLEM} model in most regions of interest with better noise property and its solutions were more stable.
	However, we can not conclude that it outperforms the classical log-likelihood PET reconstruction model, especially when looking at the CRC ratio obtained on the smallest spots.
	A closer look taken on the solution obtained with the \textit{PADE}$_{\textrm{v0}}$ model showed that the proposed model still enforces strongly the classical interpretation of the UDE property, i.e. $\phi_{j,i} \approx R_{j,i} \lambda_i$.
	Also, the performances of the \textit{Extended} model showed that removing completely the UDE property from the reconstruction scheme is disadvantageous, even if ultra-fast TOF is available.
	These results suggest that the idea behind the PADE model is promising for ultra-fast TOF reconstruction of low counts acquisitions and further investigation will be needed to ascertain its full potential, especially for the UDE metric.

	\subsection{Review of the \textit{PADE}$_{\textrm{v0}}$ model}
	\label{subsec:reviewImplementation}
		The MLEM algorithm, which implicitly enforces non-negativity and expected counts stability, provides quite good results in most cases, if stopped at the correct iteration.
		When combined with its simplicity of use, it is understandable that other candidates for PET reconstruction often remain mostly academic.
		As such, the requirement of finding the appropriate weights $\gamma_1$ and $\gamma_2$, which are most likely data-dependent, make the \textit{PADE}$_{\textrm{v0}}$ model less attractive than the classical log-likelihood model.
		Since $\gamma_2$ is used to enforce expected counts stability, its calibration can be automated by searching the smallest value that enforce this property.
		However, the weight factor, $\gamma_1$, is likely to pose a challenge, as it is the case for PET algorithm that include a regularization scheme~\cite{qi2006iterative}.
		Further investigation is required to understand how critical is the calibration of $\gamma_1$ and its dependence to the data.
		The solution proposed for the maximum \textit{a posteriori} model in~\cite{reader2020bootstrap}, where an automated calibration was proposed, might be applicable for the \textit{PADE}$_{\textrm{v0}}$ model.

		The TOF-less log-likelihood model was underdetermined in this study (8,544 projections v.s. 16,384 pixels).
		While our choice of TOF binning does increases the system sampling well beyond the number of pixels, it does not ensure that the resulting system is overdetermined.
		We expect that the \textit{PADE}$_{\textrm{v0}}$ model would perform better with a scanner having more projections.
		Indeed, the freedom provided by relaxing the UDE property should shine when the number of valid projections is far larger than the number of counts in a voxel.
		However, the computational burden increases with the number of projections, which has limited our capability to calibrate the \textit{PADE}$_{\textrm{v0}}$ model on scanners with more detectors.
		For both the \textit{PADE}$_{\textrm{v0}}$ model and the \textit{MLEM} model, the 3.2~mm spots were mostly resolved even with detectors being 8~mm in width.
		This was expected of the MLEM algorithm~\cite{toussaint2020improvement} and it is reassuring that the PADE approach seems to share that feature.
		Yet, these small structures combined with low counts acquisition have posed a challenge for the \textit{MLEM} model.
		This is highlighted by its CRC ratio, where a value of 1.0 is reached briefly before being overestimated, well after the noise started to significantly spoil the image.
		Thus, comparison of the models using the CRC of the smallest spot is less straightforward and the \textit{MLEM} model might not be an adequate baseline in that case.

		The increase in degrees of freedom provided by the PADE paradigm combined with the interplay between the three metrics in~\eqref{eq:padeModel} also means that the hyperparameters have a significant impact on the optimal solution of the model, which can deviate significantly from the groundtruth.
		Thus, an automated study of several hyperparameters based on one quality metric is misleading and a reduction of the number of unknowns was required.
		We simplified the study by defining a phantom with only two level of concentrations: the background with a low value and the spots with a high value.
		Thus, the threshold in~\eqref{eq:omegaWeight} only needed to be able to distinguish these two.
		As for the value of the $\omega_i$, they were mostly applied to pixels inside the spots, due to the threshold and the initialization, and, as such, their impact is limited to a subset of pixels that should have similar number of counts.
		Even if the optimal $\omega$ was not directly the number of counts per pixels, this was compensated by $\gamma_1$ since it was calibrated to achieve the best model.

		We had observed that having $\omega_i \approx \sum_j \phi^*_{j,i}$, with $\phi^*$ being the groundtruth, provided encouraging results.
		However, $\phi^*$ being unknown, we opted to update $\omega$ with the previous iteration (see~\eqref{eq:omegaWeight}) and use a low iteration MLEM to initialize the reconstruction (see~\eqref{eq:initialization}).
		While this approach makes it possible for $\omega$ to reach the desired value, it also means that the objective function is modified at each iteration.
		Considering that the L-BFGS-B algorithm employs past iterations to create an approximation of the Hessian matrix of the objective function, it is possible that its convergence properties are weakened or lost.
		Nevertheless, the \textit{PADE}$_{\textrm{v0}}$ model was initialized with a pretty good first guess, which might limit the impact of modifying $\omega$ on the solver.
		The stability of the CRC ratios and COV over iterations for the \textit{PADE}$_{\textrm{v0}}$ model goes on longer than the ten iterations that the L-BFGS-B algorithm uses for the Hessian approximation.
		This suggests that the solution obtained with the current iterative scheme is optimal for the \textit{PADE}$_{\textrm{v0}}$ model.
		Moreover, since only a low iteration MLEM is needed with ultra-fast TOF to discern most structures, it might be possible to design an automatic criterion that is independent to the groundtruth.
		Further investigations will be required to evaluate the impact of initialization on the performance of the \textit{PADE}$_{\textrm{v0}}$ model.
		Lastly, another choice of general solver might provide a better behavior.
		For example, the ADMM algorithm breaks the optimization problem in smaller ones that are easier to solve and it might have a better chance at dealing with a model defined as three metrics that compete between each others~\cite{teng2016admm,6825888}.

	\subsection{Potential of the PADE paradigm}
	\label{subsec:futurePade}
		The main novelty of the proposed model is the relaxation of the interpretation of the UDE property from a constraint, i.e. $R_{j,i} \lambda_i = \phi_{j,i}, \forall j,i$, to a penalization term represented by $\mathcal{V}_i()$.
		The goal of this metric is to promote solutions that follow the UDE property without enforcing $R_{j,i} \lambda_i = \phi_{j,i}, \forall j,i$, which is of particular interest when the number of counts per pixel is low.
		The implementation of $\mathcal{V}_i()$ in~\eqref{eq:geoPenalMetric} uses the fact that the momentum of a cyclic uniform distribution should be at the center of its domain for any choice of $j_i^{\textrm{ref}}$.
		The threshold applied on $\omega$ in~\eqref{eq:omegaWeight} is a trick to ensure that $\mathcal{V}_i()$ does not overshadow the  log-likelihood term for pixel with only a few counts.
		It remains to be shown that this implementation of $\mathcal{V}_i()$ is an efficient metric for the PADE paradigm.

		The discrepancy between the groundtruth and the \textit{PADE}$_{\textrm{v0}}$ solution over the pixel projection-wise distributions shown in Fig.~\ref{fig:udeAnalysis} indicates that the proposed implementation of the PADE approach enforced strongly the relation $\phi_{j,i} = R_{j,i} \lambda_i$.
		A better correspondence to the groundtruth could be expected if sparse solutions were enforced, which might be possible with ultra-fast TOF.
		The simplest approach would consists of using a voxel-wise sparsity penalty term, but the calibration would then be an even more complex interplay between the strength of each terms.
		Algorithmic approaches to enforce sparsity, such as FISTA~\cite{beck2009fast}, might be preferable, if it can be adapted to the PADE model.
		Integer optimization is another alternative that might benefit the proposed model.
		The parametrization of the PADE model enables a more accurate use of the integer nature of counts by circumventing the $R_{ji} \lambda_i$ approximation in the log-likelihood term.
		While the number of variables for the PADE model is definitely in the high end for integer programming, which is known as a NP-Hard problem, multiple heuristic methods have been successfully developed for diverse integer optimization problems and an in-depth investigation of its state-of-the-art might provide fruitful solutions~\cite{kumar2010fifty,glover1997general}.
		Other approaches could also be investigated, such as origin ensemble that was already applied to TOF-PET reconstruction~\cite{wulker2015time} or machine learning methods which have already shown their potential for PET reconstruction~\cite{gong2019machine}.

		We expect that the potential of the PADE model would remain for 3D reconstructions and that it would perform even better in this context.
		The histogram being even sparser in 3D, more candidates (i.e. valid projections) could be removed for each voxel.
		Thus, the resulting model should be easier to solve for 3D reconstructions.
		In this study, the mean percentage of valid projections that can be removed for pixels inside the phantom was around 50\% even though the number of detectors was low (320 for one ring of a clinical size scanner).
		If we modify the scanner to have 16 detectors per panel, thus doubling the number of detectors per ring, the mean percentage rises to 80\%, which results in 10\% less candidates then the previous scanner (50\% of $\approx$320 vs 80\% of $\approx$640).

\section{Conclusion}
	We presented the fundamentals of a new paradigm, PADE, to deal with the difficulties associated with low counts in PET reconstruction, particularly in the context of ultra-fast TOF resolution.
	The PADE approach offers greater degrees of freedom than the classical log-likelihood model by relaxing the interpretation of the UDE property, usually encoded in the system matrix.
	This increases the number of variables significantly, which cannot be exploited fully in a classical PET setting.
	Ultra-fast TOF reconstruction with low counts represents a best case scenario for the PADE approach since the number of variables can be reduced by the excellent TOF resolution without loss in degrees of freedom.
	The implementation of the PADE model presented in this paper provides some gains, albeit limited, over the log-likelihood model, which suggests that this new paradigm has potential benefits warranting further investigations.
	The core idea of the PADE approach offers much promise and we conjecture that an efficient and stable implementation of that idea can be achieved.

\section{Acknowledgments}
	The authors gratefully acknowledge Jean-Baptiste Michaud for providing access to his allocated computational cluster ressources and Francis Loignon-Houle for fruitful discussions, for advice on the vulgarization of the PADE model and for proof-reading the paper.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


Mr. Anderson has worked with high school students for over twenty years in and out of the classroom with the last eight years being in school administration. Mr. Anderson taught internationally for several years and is a fluent Spanish speaker. He earned Bachelors and Masters degrees from Northern Arizona University in Flagstaff, Arizona and is currently pursuing a second Masters degree from Grand Canyon University. Prior to assuming the school leader role at Maya High School, Mr. Anderson has worked in five area Leona Group high schools.
If you would like to contact Mr. Anderson, please call 602-242-3442 or email.
If you have any questions contact Mr. Ortiz at 602-242-3442 or email him here.
Mr. Welsh has worked with high school students for over ten years with the last 9 as a Social Studies Teacher. He earned his Bachelor's Degree from Benedictine College in Atchison, KS in Social Science and Secondary Education and his Masters Degree from the University of Mary in Curriculum, Instruction, and Assessment. He is now serving as the Curriculum Coach for Maya High School.
If you would like to contact Mr. Welsh, please call 602-242-3442 or email.


We are in talks for a few exciting things this summer as we plan the DVD release party for early fall. Please make sure you're on Sarah's email list and following along on the G,NA Facebook Page for the most up-to-the-minute news and info.
Can't wait to release this sweet little film to the world!


text:
Андрій Васильович Кондзьолка ( 16 березня 1983, с. Сухівці Підволочиського району Тернопільської області, Україна) — український футболіст, півзахисник.

Клубна кар'єра
Перший тренер — В. Миколайчук.

Виступав за «Збруч» (Підволочиськ), ДЮСШ № 3, ФК «Тернопіль-Нива-2», «Товтри» (Козлів), «Педліцей» (Тернопіль), «Буревісник» (Тернопіль). На професіональному рівні грав за ФК «Тернопіль».

Улітку 2016 року разом з Василем Чорним поїхав до Канади.

Примітки

Посилання

Уродженці Підволочиського району
Українські футболісти
Футболісти «Тернополя»
Футболісти «Юкрейн Юнайтед» (Торонто)


text:
Rumba-Legend
Around 1930, the Cuban sound was renamed rhumba in the United States, under the impulse of Xavier Cugat, and rumba became a ballroom dance, which will be part of the Latin dances in sport dance (despite its name, it is rather danced on Cuban or Mexican boleros).
In its current form, the basic figures keep the old images of the female intentions to dominate the men by their charms.
During a good rumba choreography, one should always see the elements of attraction and rejection between man and woman.
The erotic and sensual movements of women will obtain a response of desire and male domination; it's the man who always wins at the end.
Rumba is danced all over the world today. It is popular in many countries and rumba lessons are available in some major cities.
The rhythm of the "rumba" is counted in 4 steps. The basic step is to make a suspension then a step on each of the following 3 beats. ("nothing [actually a hip sag] -2-3-4"; "nothing, 2,3,4". It takes two measurements to make a full box.
Rumba was born in the patios of the solares and the port docks in Havana (yambù and guaguanco) and in Matanzas (Siguirya and Columbia) during the 1800s in Afro-Cuban circles. The term (perhaps derived from the Spanish rumbo, en route…) designates the nocturnal parties where we gather (often in building courtyards, the "solares") to sing and dance.
It is music made up of songs and percussion. At the very beginning, we used the drawers of the cupboards (cajones) or crates of cod, the crates of the sails of ships, the boxes of cigars struck with bare hands or with small wooden spoons (cucharas), but also the congas (called in Cuba, tumbadoras).
The tumbadoras being drums of Congolese origin used for rituals of Bantu origin (palo, makuta, garabato); transformation of barrels, without bottoms and on which dried animal skins are stretched.
The influence of ethnic groups of Nkua origin (abakua, efi, efo ...) is also predominant in the rhythm, song and dance of rumba. There are four forms:
The oldest and fastest is the siguirya, a term found in the flamenca nomenclature; the rhythm is 6/8, extremely fast and was played on Congo drums. It is a derivative of what is called Palo Congo. Pelladito was one of the few who could still play it. -mime of the slave freeing himself from his shackles. It is originally a dance of virtuoso men, with a fast rhythm. It can be used as a joust, each in turn shows his skill, immediately followed by another who will try to surpass him.
Yambú: the term derives from yambula, the "tierra de les remolinos", land of whirlpools (African lands of the Briyumba hills where aerial whirlpools are not uncommon). Its traditional dance consists of turns on oneself, both of men and women. Undoubtedly, turning on oneself provokes a modified state of consciousness which the African populations interpreted as the possession by the spirit of the ancestors.
This dance, a bit out of fashion, is preserved by the older generations, so their dance is like them, tired! The youngest who dare there therefore imitate the awkwardness of age. It is also mimed on this rhythm the Saint Lazare-Babalu Aye-Coballende, protective deity of the sick and himself affected by leprosy, walking trembling on his crutches.
The yambu begins with a fairly long introduction called "diana", drum call and voice arpeggios, in imitation of the military bugler buzzer sounds and also a souvenir of the lalaeo of the gypsies of Andalusia.
Then, the gallo (the rooster) sings a decima, a poetic form from the Andalusian romance, ten octosyllabic verses, then it is the montuno which progresses until its conclusion by increasingly short choruses and a real acceleration of the tempo , another evocation of African whirlpools.
Guaguancó is the most popular form of rumba today. The narrative texts deal with daily life: politics, love ... The dance revolves around the "vacunao" with erotic meaning, symbolized by a gesture of the dancer or by a scarf that will pursue the dancer, and that this one seeks to avoid it throughout the dance. In the guaguancó, the rhythm is in 2/2.
Rhese last three musical forms are built around the clave, originally in 6/8, then having drifted in 2/2, due to the polyrhythmic "filling" in four flows over three decompositions of time.
In addition and on the contrary, in columbia, the "soloist" discourse of the quinto frequently marks four flows on the ternary decomposition of the pulsations.
Rumba is one of the most Andalusian-African genres in Cuba.
Rumba Flamenca Rumba Catalane Rumba Congolaise Rumba (danse de salon)


text:
A23 Games - Rummy | Fantasy 7.1.0
By Head Digital Works Pvt Ltd
Head Digital Works Pvt Ltd A23 Games - Rummy | Fantasy 7.1.0
Sports Games Card Games Casual Games
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Play rummy the classical Indian style card game only on A23. With an ever-growing community of 45 million players who have trusted us as a gaming platform for more than a decade, explore the world of online rummy on A23 by diving into its diverse game variants which offers both 2-player and 6-player options, along with so much more. Start a game of free rummy or learn how to play the game quickly with Rummy School. Relish the exhilarating ride that is online rummy on the Go – anytime, anywhere.
A23 Carrom is an online version of the famous Indian tabletop game by the name of carrom. It is a cross-platform easy-to-play multiplayer board game that is played by 2 people. In a carrom game, a player needs to pocket all the carrom men/coins before his opponent in order to win.
Play online carrom games against the best players on A23 Carrom, your favourite online carrom app.
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The New York State Thruway Authority (NYSTA) operates the Governor Thomas E. Dewey Thruway comprising 569.83 miles of highway across the state of New York. An estimated 250 million vehicles travel more than eight billion miles on the Thruway each year.
In 1993, NYSTA became the first agency in the Northeast to implement an electronic toll collection system. This form of cashless tolling has greatly reduced congestion, improved safety, and decreased air pollution. Cashless tolling, however, brings one small problem with big costs: uncollected toll payments. While only a small percentage of motorists fail to pay tolls, the aggregate due fees can amount to millions per year – funds that are vital to repairing roads and bridges.
NYSTA enlisted StarStar Mobile to help alleviate toll leakage and improve customer experience. We established a call number, **TBM, an acronym for "Tolls By Mail" that is widely-recognized by commuters. Through road signs with instructions to call **TBM for toll payment info, drivers can pay tolls, create an E-ZPass account, or access travel resources.
Within days of erecting just a handful of **TBM signs, NYSTA saw a 900% increase in online toll transactions, from toll payments to E-ZPass signups.
**TBM increased toll transactions by 900%.


text:
El «Acuerdo para afianzar la unidad en defensa de las libertades y en la lucha contra el terrorismo», también conocido como pacto contra el yihadismo o pacto antiyihadista, es un acuerdo firmado por el presidente del Gobierno de España y del Partido Popular (PP), Mariano Rajoy, y el secretario general del Partido Socialista Obrero Español (PSOE), Pedro Sánchez, tras los atentados terroristas islamistas de enero de 2015 en Francia.

Este Acuerdo hace especial énfasis en la lucha contra el fanatismo radical propagado por Internet, cuya intención sea la de captar y reclutar a terroristas, especialmente en las redes sociales, así como perseguir a quienes enaltecen el terrorismo; también contempla la reforma del Código Penal para que los actos de terrorismo con resultado de muerte sean castigados con la «máxima pena privativa de libertad» contemplada en dicha norma. Tal pena se corresponde con la prisión permanente revisable que, por la fecha de la firma del acuerdo, estaba siendo introducido por la mayoría parlamentaria del PP, y a la que se oponía el PSOE, hasta el punto de presentar un recurso de inconstitucionalidad contra ella. En palabras del líder del PSOE, Pedro Sánchez: «Nos hemos opuesto a la prisión permanente revisable y la suprimiremos cuando tengamos una mayoría suficiente. Pero esto no afecta a lo fundamental, la unidad contra el terrorismo». También se acuerda el reconocimiento de la figura de los «lobos solitarios», esto es, terroristas no vinculados a ninguna organización que actúan de manera individual.

Tras los atentados de París de noviembre de 2015, Ciudadanos, Coalición Canaria, Foro de Ciudadanos, el Partido Aragonés, la Unión Democrática de Cataluña, la Unión del Pueblo Navarro y Unión Progreso y Democracia se adhirieron el 26 de noviembre de 2015 al pacto antiyihadista, mientras que Convergencia Democrática de Cataluña, Esquerra Republicana de Catalunya, Izquierda Unida, el Partido Nacionalista Vasco y Podemos lo rechazaron.

Véase también

 Acuerdo por las Libertades y contra el Terrorismo, también conocido como Pacto antiterrorista.

Referencias

Enlaces externos

  Acuerdo para afianzar la unidad en defensa de las libertades y en la lucha contra el terrorismo, texto del acuerdo.

X Legislatura de España
España en 2015
Antiyihadista
Política en 2015
Terrorismo islámico en España


Summer will not long be with us. Already a dusting of snow has appeared on the mountain ranges around us. So we've squeezed in a few hikes this month…I'll let you guess which was my favorite!
Had we read more closely we would have realized that the elusive teahouse was never completed. This failed enterprise of some tycoon visionary was demolished a few years back. All that remains is the helicopter pad that would have saved the diners an arduous hike!
Climbing three thousand feet in under 2 1/2 miles is difficult but the descent was at least as bad!
My quads complained for days! They are accustomed to pedaling, not climbing and descending.
Well, that was last week. Hoping to 'lock in' these climbing muscles we went for another summit in Banff a couple days ago—Sulphur Mountain.
We once took the gondola but not this time.
and to wait out a passing squall.
Then we hustled down the mountain to dine at McD's and hurry home to get ready for the kids coming for a birthday celebration!
With them we did another sweeter hike the following day.
This time, just 2.8 miles round trip and just 853 feet of rise, but with smaller feet and shorter legs it was a triumph for all!


Cheltenham Borough Councillor Paul McCloskey has been appointed to the board of Publica - the company that delivers shared services to local authorities across Gloucestershire.
Cllr McCloskey replaces his council colleague Wendy Flynn as a non-executive member of the board after the founding member of the board decided to stand down.
With a background in mathematics and engineering, Cllr McCloskey has rich experience in organisational change and development.
He also has IT security experience and can count work for Royal Mail, BT and in the charitable sector on his CV.
As a councillor, he has been vice chair of the borough council's lincensing committee and sat on numerous committees and panels, including planning and treasury management.
He will start in his new role on April 15 and said: "I am very much looking forward to joining the board.
"In these difficult economic times, the success of Publica is pivotal to the success of all four of our partner councils.
"This strategic role well suits my previous experience and is a contrast to my role as an elected member."
Publica is a council-owned employment company who deliver share services to Cotswold and Forest of Dean District Councils and Cheltenham Borough Council.
They also provide services to the Cheltenham Trust, Cheltenham Borough Homes and environmental services local authority company UBICO.
Publica Chairman David Brooks said: "I am delighted to welcome Paul to the board.
"His close connection with residents and long career in industry will offer a fresh view for the board as we move on to the delivery stage of our transformation plan.
"I would also like to take this opportunity to thank Wendy Flynn whom Paul has replaced.
"Wendy was a key part of the Publica set up and her contribution as a founding board member was really important in our successful launch."