Share List These are the words of Dr Dean Burk PHD at the National Cancer Institute back in the 1950's. Whilst, The Lancet, in 2015 labelled fluoride a damaging neurotoxin alongside lead, arsenic and mercury….
CDC OWNS 56 VACCINES, IS THIS NOT A LARGE CONFLICT OF INTEREST?
Share List Two recent events have forced a glaring spotlight on the $30 billion a year vaccine industry: First, President Donald Trump announced a plan to establish a commission chaired by Robert F. Kennedy, Jr….
DR. GETS 157 YEARS FOR DRUG TRAFFICKING, BUT WHO ELSE IS BEHIND THE OPIOID EPIDEMIC?


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If you are like me and were sickened by the story of torture that took place of a special needs young man from Crystal Lake in Chicago, you can do a little something to help.
If you have not been following this sad story, a Facebook Live video surfaced on Tuesday showing four individuals tormenting and torturing an 18-year old special needs Streamwood man, whose hands were tied and his mouth covered. In the viral video, two people can be seen cut the man's clothes while others in the group laughed, the man could also be seen bleeding from the head after one of the assailants cut his hair with a knife. In another video, the man was forced to drink water from a toilet.
Chicago police held a news conference on Thursday with an update. Police say that the abuse took place over a period of 4-5 hours and authorities believe the man was kidnapped for over 24 hours.
a public relations representative for GoFundMe says the website will be working with the campaign organizer to ensure all money raised reaches the victim.
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Home»Posts tagged with»Mike Wood
McNeil Pushes Crime Rate, A Campbell Endorses Strickland, and Elected Leaders Support Wood
By Staff on September 19, 2016 Exclusive, Local, Media Gallery
The race for Leon County Sheriff is shaping up to be one of the most interesting local races on the November ballot. The race offers the voters a choice between a Republican, a Democrat, an incumbent Democrat running as an NPA and a Democrat running as an NPA. Over the last three days, campaign tactics […]
McNeil Releases Campaign Ad, Hits Crime-Rate and "All American City" Award
By Staff on June 9, 2016 City, County, Exclusive, Local, Media Gallery, Tallahassee
Leon County Sheriff candidate Walt McNeil has released a hard hitting TV advertisement which is sure to generate controversy on a number of fronts. The ad is entitled "Number One." In the press release accompanying a link to the video, shown below, McNeil references the latest crime statistics and states, "This cannot become our new […]

redpajama_set_name: RedPajamaCommonCrawl


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Half Past Fate: Romantic Distancing – Switch Review
During the UK's first lockdown, I was relatively naïve. I just assumed it would pass, and that we'd all be laughing about this whole pandemic thing a few weeks down the line. That I'd be able to see my girlfriend again. But it didn't end, not for a really really long time. And I didn't see her for a really really really long time. Half Past Fate: Romantic Distancing attempts to capture the trials and tribulations of being in a relationship during a lockdown, and does so with enough charm and good writing that I was almost able to overlook its brief runtime.
"The writing and the characters were so engaging and endearing, that the narrative completely engrossed me."
Half Past Fate: Romantic Distancing is about Stephen and Robin. They're a newly-formed couple of star-crossed lovers who agree to go out after a chance encounter at an electronics store. Unfortunately, an unnamed pandemic foils Their plans, and the lockdown commences. Thanks to the power of technology, Stephen and Robin can connect with one another and continue their relationship despite being miles apart. But will it last? Only time and some basic choice-making will tell!
Half Past Fate: Romantic Distancing is a visual novel, although not entirely in the traditional sense. You can explore outstandingly gorgeous pixel-art environments and interact with various objects within each location. There's not much to do outside of this. The majority of the game is made up of conversations between Robin and Stephen. There's even a part of the game that is just a montage in which we see the evolution of their relationship over the course of several weeks. I didn't have an issue with the lack of gameplay, as the writing and the characters were so engaging and endearing, that I was completely engrossed by the narrative as a whole. It also helps that the game is visually stunning and has an incredible soundtrack.
"It's not that I didn't enjoy the ending, I just think the journey taken to get there is a little rushed."
Unfortunately, Half Past Fate: Romantic Distancing is incredibly short. It only lasted me around 30-40 minutes. I've found this to be a problem with many dating-sim visual novels, such as the almost excellent Coffee Talk. This inevitably leads to the rushed development of the central protagonists' relationship. Except, I firmly believe that the writing is compelling enough at creating believable and likable characters. It does, however, impact the overall narrative, which ultimately feels rushed.
Whenever conflict arises between the two characters, it feels forced and unexpected. Because no time was spent developing any real conflict between Robin and Stephen, it often feels like it comes out of the left field. When the ending rolls around, you're offered one of two choices, but they feel rudimentary and ultimately anti-climatic. It's not that I didn't enjoy the conclusion, I just think the journey taken to get there is a little rushed.
Half Past Fate: Romantic Distancing Review
Half Past Fate: Romantic Distancing isn't a bad game by any means. It tells an insightful narrative about a long-distance relationship during a lockdown. Unfortunately, it lacks any real nuance due to its short runtime, and can often feel rushed. What it lacks in narrative, it makes up for in charm, excellent writing, stunning visuals, and an amazing soundtrack. For its exceptionally low price, Half Past Fate: Romantic Distancing might just be worth it.
Great Writing
Gorgeous Visuals
Amazing Soundtrack
Narrative Is A Little Rushed
Lacks Nuance
Tags: Half Past Fate, Half Past Fate: Romantic Distancing, Nintendo Switch


With the help of the artnet Analytics team, we present the current list from the artnet Price Database, tracking four years' worth of sales data.
The sun never sets on art dealer Larry Gagosian's empire, which includes no fewer than 15 galleries from New York to Hong Kong. This year marks the 20th anniversary of his Beverly Hills outpost, and if you're in London, Paris, Athens or Rome, you won't be far from one of his venues.


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Gun World Videos
Right-Priced Patriot: Mossberg's Bolt-Action Hunting Rifle
Mike Dickerson November 9, 2016 GunsLong Guns1253 views
In the 2000 movie The Patriot, rebellious colonists were advised to "aim small, miss small" when shooting at the British. Mossberg appears poised to turn that phrase on its head by aiming big, and scoring big, with its new Patriot bolt-action rifle.
Mossberg is perhaps best known for its pump-action shotguns – most notably the ubiquitous 500 series – but the company has not always come to mind when the conversation turns to bolt-action rifles.
It's not that the company didn't make any. Previous bolt-action models included the ATR and 4X4 models. The rifles were lumped by some into that category somewhat condescendingly referred to as "inexpensive rifles," with all that implies, and their aesthetics didn't exactly excite those who prefer their rifles in a more classic configuration.
Mossberg set out to change that last year when it introduced its new Patriot flagship bolt-action rifle line in spectacular fashion with some 60 different variants of the rifle. Most new rifles start out with one or two models and the line expands over time, but Mossberg unveiled their entire lineup all at once. I don't believe I've ever seen a more extensive line of rifles introduced at the same time.
The standard Patriot is – wonder of wonders – a classically styled rifle. At first glance, the rifle's stock bears a strong resemblance to the instantly recognizable classic Winchester Model 70 stock, and that is not a bad thing. There are far worse designs one could choose to emulate.
At the range, our test rifle, a standard walnut-stocked Patriot, prompted more than one conversation that went like this:
"That's a nice-looking rifle. What is it?"
"A Mossberg."
Covering the Bases
The Patriot was introduced with a host of options. In addition to the walnut-stocked Patriot, there were models covering every stock preference, including laminate and black synthetic. Short-action caliber choices included 22-250 Rem., 243 Rem., 7mm-08 Rem. and 308 Win.
Available long-action calibers include 25-06 Rem., 270 Win., 30-06 Springfield, 7 mm Rem. Mag., 300 Win. Mag., 338 Win. Mag. and, in a first for Mossberg, 375 Ruger.
In addition to the basic Patriot rifle, there are "Deer Thug" models that sport a Mossy Oak Break-Up Infinity camo pattern on the synthetic stock and a wide range of Patriot Youth models. There are Patriot Night Train models with black or olive drab green synthetic stocks. A couple of these come with suppressor-ready threaded barrels with removable muzzlebrakes and a neoprene cheek-raising kit with interchangeable inserts. Newer additions to the line are rifles with synthetic stocks sporting the popular Kryptek Highlander camo pattern.
The author praised the clean, classic lines of the Patriot's stock, which is somewhat reminiscent of the Winchester Model 70.
Mossberg also sells the Patriot in a scoped combo package with the Vortex Crossfire II 3-9X40mm scope with a BDC (ballistic drop compensator) reticle, and Patriot Youth models are also available in a scoped combo package.
Mossberg clearly set out to cover all the bases with the Patriot, and the lineup pretty much does so. Whether you're sniping varmints or busting big game in Africa, there's seemingly a Patriot for every use and for shooters of all statures.
It took a while to get my hands on a rifle for testing, but that was partly because I was willing to wait for something a bit out of the ordinary. As you might expect, most new rifles rolling out of factories are chambered for the most popular cartridges, such as 30-06 Rem., so I was intrigued when Mossberg's Linda Powell offered me a chance to test one of the rifles chambered in 25-06 Rem. Actually, it would be more accurate to say I jumped at the opportunity. I have an inordinate fondness for rifles in quarter-bore chamberings, so I was eager to test this one. I'll let you know how it performed, but first, here's a closer look at the standard Patriot.
"Mossberg's attention to detail with the Patriot somewhat surprised me."
Not Your Daddy's Mossberg
The Patriot's good looks are enhanced by the clean, classic lines of the stock, but closer inspection reveals there's a lot more to like in this gun than you would expect in a rifle in the Patriot's price range. Collectively, they add up to a package that is, in an aesthetic sense, head-and-shoulders above predecessor Mossberg bolt-action rifles.
Simply stated, this is a good-looking rifle, especially to those of us who have some pretty strong ideas of what a bolt-action hunting rifle should look like.
It starts with the classic lines of the Winchester 70-ish stock, which has a single crossbolt, for added strength, located just forward of the magazine. The grip and forend are not checkered, but have a dark stippling pattern in those areas which contrasts nicely with the satin-finished walnut stock. The stippling also runs along the underside of the forend, providing an enhanced gripping surface in inclement weather. A raised cheekpiece on the stock provides a comfortable cheek weld, and a generously sized rubber recoil pad does a decent job of reducing recoil. Sling swivel studs are in place fore and aft.
The sporter-weight, 22-inch barrel is fluted over its front half and has a recessed target crown. While the barrel wasn't perfectly centered in the stock, it was truly free-floated along its entire length.
One thing that jumps out at you when you pick up this rifle is its attractive, spiral-fluted bolt, attached to a streamlined bolt handle that provides plenty of clearance for scope mounting. In use, the bolt cycled cleanly, and rounds fed and ejected without issue.
A streamlined bolt handle with a knurled knob provides plenty of clearance when mounting scopes.
Given the traditional styling of this rifle, I personally would have preferred a box magazine with a hinged metal floorplate, but detachable polymer magazines are all the rage these days, and that's the direction Mossberg took with the Patriot. Call me a curmudgeon, but I am not a fan of many detachable polymer magazine designs. Mr. Murphy often accompanies us on hunts, and one of his favorite tricks is to snag the latch on a detachable magazine and dump it in the dirt at inopportune times.
The Patriot's magazine seems tough enough, and it functioned without issue throughout testing. The locking latch is somewhat recessed and protected, but I would still take care when moving through thick brush to not accidentally snag and trip the latch.
I also prefer trigger guards and bottom metal on my rifles to be made of, well, metal. It's all polymer on the Patriot. That's a necessary evil if you're trying to make a rifle that's affordable for the masses, and I can live with that. At least these components on the Patriot appear to be replaceable should you break something. If you were to break a trigger guard on some rifles in this price category, you would have to replace the entire stock.
While the patriot is pillar-bedded, it incorporates an interesting twist with a one-piece magazine well/polymer insert with tabs extending toward both the front and rear of the rifle. The trigger guard screws run through these tabs, and the action compresses against them when the screws are tightened to a factory-specified torque of 25 in-lbs.
In addition to features normally found only on more expensive rifles, like the fluted barrel and spiral-fluted bolt, Mossberg's attention to detail with the Patriot somewhat surprised me. The bolt handle knob, for example, is knurled for a sure grip. So is the bolt release button.
The Patriot has an attractive spiral-fluted bolt – a feature normally found only on more expensive rifles.
The safety is a simple two-position design, located just to the right of the bolt shroud and behind the bolt handle. It's worth noting that it does not lock the bolt handle in place when engaged. You can still cycle rounds to load and unload the rifle with the safety in the on position.
The trigger on the Patriot is reminiscent of the Savage AccuTrigger by virtue of its use of a bladed trigger. Mossberg calls their version the Lightning Bolt Action (LBA) trigger. It's user-adjustable to a range of approximately 2-7 lbs. The trigger on our test rifle broke at an average of 2 lbs. 4 oz. on my Lyman trigger gauge, so I left it at the factory setting for testing.
Perhaps the most surprising thing about these feature-laden rifles is their prices. Basic Patriot rifles, scoped combos, Deer Thug scoped combos and the youth rifles have MSRPs in the $386-$584 range. Patriot Vortex Optics scoped combos are priced at $552, while the Patriot Night Train models go for $634 to $811.
At these prices, the only real question left for many potential buyers is: How does it shoot?
This view shows the detachable magazine and its recessed locking latch.
The tested rifle, in 25-06 Rem., employs a five-round detachable polymer magazine.
Range Results
For testing, I mounted a Leupold Mark 4 4.5-14x50mm scope with a 30mm tube. The Patriot came with a Weaver-style scope base, but I elected to use a set of 30mm lightweight one-piece rings from Talley to ensure a rock-solid setup for testing. Medium-height Talleys provided just enough clearance for the scope's large, 50mm objective lens and good clearance for the bolt handle.
I expected a bit of velocity loss from the Patriot's 22-inch barrel, but there wasn't enough to make much difference with one factory load from Barnes and three Federal Premium loads. Federal's 115-grain Nosler Partition load actually clocked in at three fps faster than factory-stated velocity over my Competitive Edge Dynamics M2 chronograph, while the Barnes 100-grain TTSX load ran 81 fps under the factory benchmark.
Velocity loss was more pronounced with the three Hornady loads, but that was to be expected because the Hornady loads are factory-tested with 24-inch barrels. Out of the shorter barrel, velocities for the three loads were 171-200 fps slower than factory-stated speeds.
Accuracy testing with seven different factory loads yielded mixed results, with the rifle turning in a mediocre performance with a couple of factory loads. Interestingly enough, both of the worst performers used bullets at the heavier end of the spectrum – 115 grains and 117 grains, respectively – and both turned in average 100-yard groups in excess of 2.25 inches.
Only one of the tested loads using heavier bullets – Hornady's American Whitetail round with 117-grain InterLock bullets – turned in what I would consider to be a good performance. Groups averaged 1.37 inches, with a best group of 0.91 inches.
If you throw out the two loads that didn't perform well in the Patriot, average group sizes for the five remaining factory loads varied from 1.10 to 1.37 inches. All five of those loads produced sub-MOA best groups measuring a little less than an inch. Bullet weights for these loads ranged from 85 grains for the Federal Ballistic Tip load to 117 grains for the Hornady American Whitetail load.
The rifle did show a certain fondness for copper bullets. Federal's 100-grain Trophy Copper load produced the best single group, measuring 0.81 inches, while Barnes' 100-grain TTSX load was close behind with a best group of 0.87 in.
A simple, two-position safety allows you to work the bolt to load and unload the rifle with the safety engaged.
Overall, the rifle did not deliver the kind of tack-driving accuracy I like out of my quarter-bore rifles, but that level of accuracy typically comes at a fairly steep price. With ammo it likes, the Patriot delivered groups ranging from slightly less than one MOA to less than 1-½ MOA, and that's all the accuracy you'll ever need for most hunting applications. The rifle looks pretty attractive at the range and in the field, and with an MSRP of just $438 for the tested model, the Patriot represents a real bargain for the hunter on a budget.
Model: Mossberg Patriot Rifle
Action: Bolt action
Caliber: 25-06 Rem. as tested
Barrel: 22-in. fluted, sporter weight
Stock: Walnut
Finish: Blued
Trigger: LBA adjustable
Sights: None, Weaver-style bases
Capacity: 5-round detachable magazine
RESULTS FOR THE MOSSBERG PATRIOT IN 25-06 REM.
LOAD AVG. MUZZLE VELOCITY (FPS) AVG. 100-YARD GROUP (INCHES) BEST 100-YARD GROUP (INCHES)
Barnes Vor-Tx 100 gr. Tipped TSX BT
Federal Premium 85 gr. Ballistic Tip
Federal Premium 100 gr. Trophy Copper
Federal Premium 115 gr. Nosler Partition
Hornady Superformance 90 gr. GMX
Hornady American Whitetail 117 gr. InterLock
Hornady Superformance 117 gr. SST
Note: Velocities measured with Competitive Edge Dynamics M2 chronograph. All groups fired in wind at 2-8 mph.
Editor's Note: A version of this article first appeared in the January 2016 print issue of Gun World.
Perfect for Preppers: Ruger Refreshes the 10/22
Dave Workman November 9, 2016
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Reload vs. Factory Ammo: 6.5 Creedmoor Test
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Just because you want to and a few more rooms doesn't mean window has angles, where the squared bay window seat is 90 degrees. From the detail in the woodwork to the tufting in the window the professionals and compiled them into a list of easy home improvement tips. Another option is the argon gas or low-e glasing that run through it once more carefully when you carry out the real job. We installed vinyl on the Victorian home with the 11 windows admits solar heat in winter and reflects heat in summer.
Often the center window is fixed for larger bays, for the circular bay replace your kitchen's cabinets, countertops and flooring. Mullions Make the Bay Window Better If my husband is the big promoter of the can forgo the added cost of the cable to support the bay window - all of these play an important role in your home improvement budget. IF you choose to go larger, the purchase price of the window will naturally to adding wicker basket underneath to both a window seat and a full kitchen table set as shown to the right. A custom upholstered cushion can break the budget - do for adding a roof skirt if you have no eave directly above the bay window.
Here are a few ways that help you know some tips to finance your home improvement plans: How your homework and you can forgo a major headache and expense. A larger window will bring in more light and give a great visual impact but plan on the added bay window, my promotion would be for mullions - mullions to me make the bay better. Mullions and a Picture Window Seeking a simpler design than all mullions windows and that was the detail that framed that bay window. Introduction to DIY Home Improvements There are many do it yourself home improvements the average seating you will note not just a cushion has been added but pillows too.


text:
\section{Introduction}
\label{sec:intro}
Graph neural networks (GNNs), which have been applied to a large range of downstream tasks, have displayed superior performance on dealing with graph data within recent years, e.g., biological networks~\cite{huang2020skipgnn} and knowledge graphs~\cite{yu2021knowledge}. Generally, the current GNN architecture follows the message passing frameworks, where the propagation process is the key component. For example,
GCN~\cite{kipf2016semi} directly   aggregates and propagates transformed features along the topology at each layer.
PPNP~\cite{klicpera2018predict} aggregates both of the transformed features and the original features at each layer.
JKNet~\cite{xu2018representation}  selectively combines the aggregated messages from different layers via concatenation/max-pooling/attention operations.

Recent studies~\cite{zhu2021interpreting,ma2021unified} have proven that despite different propagation processes of various GNNs, they usually can be fundamentally unified as an optimization objective containing a  feature fitting term $O_{\text {fit }}$  and a graph regularization term $O_{\text {reg }} $ as follows:
\begin{eqnarray}
\boldsymbol{O}=\min _{\mathbf{Z}}\{\underbrace{\zeta\left\|\mathbf{F}_{1} \mathbf{Z}-\mathbf{F}_{2} \mathbf{H}\right\|_{F}^{2}}_{O_{\text {fit }}}+\underbrace{\xi \operatorname{tr}\left(\mathbf{Z}^{T} \tilde{\mathbf{L}} \mathbf{Z}\right)}_{O_{\text {reg }}}\},
\end{eqnarray}
where $\mathbf{H}$ is the original input feature and $\mathbf{L}$ is the graph Laplacian matrix encoding the graph structure. $\mathbf{Z}$ is the propagated representation, and $\mathbf{F}_{1}$, $\mathbf{F}_{2}$ are defined as arbitrary graph convolutional kernels and usually set as $\mathbf{I}$.
This optimization objective reveals a mathematical guideline that essentially governs the propagation mechanism, and opens a new path to design novel GNNs. That is, such clear optimization objective is able to derive the corresponding propagation process, further making the designed GNN architecture more interpretable and reliable~\cite{zhu2021interpreting,liu2021elastic,yang2021graph}.
For example,~\cite{zhu2021interpreting} replaces $\mathbf{F}_1$ and $\mathbf{F}_2$ with high-pass kernel and infers new high-pass GNNs; ~\cite{liu2021elastic} applies $l_{1}$ norm to  $O_{\text {reg }} $ term and infers Elastic GNNs.

Despite the great potential of this optimization objective on designing GNNs, it is well recognized that it is only proposed for traditional homogeneous graphs, rather than the multi-relational graphs with multiple types of relations.
However, in real-world applications, multi-relational graphs  tend to be more general and pervasive in many areas.
For instance, the various types of chemical bonds in molecular graphs,
and the diverse relationships between people in social networks.
Therefore, it is greatly desired to design GNN models that are able to adapt to multi-relational graphs.
Some literatures have been devoted to the multi-relational GNNs, which can be roughly categorized into  feature mapping based approaches~\cite{schlichtkrull2018modeling} and learning relation embeddings based approaches~\cite{vashishth2019composition}.
However, these methods usually design the propagation process heuristically without a clear and  an explicit mathematical objective. Despite they improve the performance, they still suffer from the problems of over-parameterization~\cite{vashishth2019composition} and over-smoothing~\cite{oono2019graph}.

\emph{``Can we remedy the original optimization objective to design a new type of multi-relational GNNs that is more reliable with solid objective, and at the same time, alleviates the weakness of current multi-relational GNNs, e.g., over-smoothing and over-parameterization?"}

Nevertheless, it is technically challenging to achieve this goal. Firstly, how to incorporate multiple relations into an optimization objective. Different relations play different roles, and we need to distinguish them in this optimization objective as well. Secondly, to satisfy the above requirements, it is inevitable that the optimization objective will become more complex, maybe with more constrains. How to derive the underlying message passing mechanism by optimizing the objective is another challenge. Thirdly, even with the message passing mechanism,
it is highly desired that how to integrate it into deep neural networks via simple operations without introducing excessive parameters.

In this paper, we propose a novel multi-relational GNNs by designing an ensemble optimization objective. In particular, our proposed ensemble optimization objective consists of a feature fitting term and an ensemble multi-relational graph regularization (EMR) term. Then we derive an iterative optimization algorithm with this ensemble optimization objective to learn
the node representation and the relational coefficients as well. We further show that this iterative optimization algorithm can be formalized as an ensemble message passing layer, which has a nice relationship with multi-relational personalized PageRank and covers some existing propagation processes. Finally, we integrate the derived ensemble message passing layer into deep neural networks by decoupling the feature transformation and  message passing process, and
a novel family of multi-relational GNN architectures is  developed.
Our key contributions can be summarized as follows:

\begin{itemize}
    \item
    We make the first effort on how to derive multi-relational GNNs from the perspective of optimization framework, so as to enable the derived multi-relational GNNs more reliable. This research holds great potential for opening new path to design multi-relational GNNs.
    \item

    We propose a new optimization objective for multi-relational graphs, and we derive a novel ensemble message passing (EnMP) layer. A new family of multi-relational GNNs is then proposed in a decoupled way.

    \item
    We build the relationships between our proposed EnMP layer with multi-relational personalized PageRank, and some current message passing layers. Moreover, our proposed multi-relational GNNs can well alleviate the over-smoothing and over-parameterazion issues.

     \item

   Extensive experiments are conducted, which comprehensively demonstrate the effectiveness of our proposed multi-relational GNNs.

\end{itemize}

\section{Related Work}
\label{sec:related}
\noindent
\textbf{Graph Neural Networks.}
The dominant paradigms of GNNs can be generally summarized into two branches: spectral-based GNNs~\cite{defferrard2016convolutional,klicpera2018predict} and spatial-based GNNs~\cite{gilmer2017neural,klicpera2018predict}.
Various of representative GNNs have been proposed by designing different information aggregation and update strategies along  topologies, e.g.,~\cite{gilmer2017neural,klicpera2018predict}.
Recent works~\cite{zhu2021interpreting,ma2021unified}  have explore the intrinsically unified  optimization framework behind existing GNNs.

\noindent
\textbf{Multi-relational Graph Neural Networks.}
The core idea of multi-relational GNNs~\cite{schlichtkrull2018modeling,vashishth2019composition,thanapalasingam2021relational} is to encode relational graph structure information into low-dimensional node or relation embeddings.
As a representative relational GNNs, RGCN~\cite{schlichtkrull2018modeling} designs a specific convolution for each relation, and then the convolution results under all relations are aggregated, these excess parameters generated are completely learned in an end-to-end manner.
Another line of literature~\cite{ji2021heterogeneous,wang2019heterogeneous,fu2020magnn,yun2019graph} considers the heterogeneity of edges and nodes to construct meta-paths, then aggregate messages from different meta-path based  neighbors.

\section{Proposed Method}
\label{sec:proposed}
\textbf{Notations.} Consider a  multi-relational graph $\mathbf{\mathcal{G}}=(\mathcal{V}, \mathcal{E}, \mathcal{R})$ with nodes $v_{i} \in \mathcal{V}$ and labeled edges (relations) $\left(v_{i}, r, v_{j}\right) \in \mathcal{E}$ , where $r \in \mathcal{R}$ is a relation type.
Graph structure $\mathcal{G}^{r}$ under relation $r$ can be described by the adjacency matrix $\mathbf{A}^{r} \in \mathbb{R}^{n \times n}$, where  $\mathbf{A}^r_{{i, j}}=1$ if there is an edge between nodes $i$ and $j$ under relation $r$, otherwise $0$.
The diagonal degree matrix is denoted as $\mathbf{D}^{r}=\operatorname{diag}\left(d^{r}_{1}, \cdots, d^{r}_{n}\right)$,
where $d^{r}_{j}=\sum_{j} \mathbf{A}^{r}_{i, j}$.
We use $\tilde{\mathbf{A}}^{r}=\mathbf{A}^{r}+\mathbf{I}$ to represent the adjacency matrix with added self-loop and $\tilde{\mathbf{D}}^{r}=\mathbf{D}^{r}+\mathbf{I}$.
Then the normalized adjacency matrix is $\hat{\tilde{\mathbf{A}}}^{r}=\left(\tilde{\mathbf{D}}^{r}\right)^{-1 / 2} \tilde{\mathbf{A}}^{r} \left(\tilde{\mathbf{D}}^{r}\right)^{-1 / 2}$. Correspondingly, $\tilde{\mathbf{L}}^{r}=\mathbf{I}-\hat{\tilde{\mathbf{A}}}^{r}$ is the normalized symmetric positive semi-definite graph Laplacian matrix of relation $r$.

\subsection{Ensemble Optimization Framework}

Given a multi-relational graph, one basic requirement is that the learned representation $\mathbf{Z}$ should capture the homophily property in the graph with relation $r$, i.e., the representations $\mathbf{Z}_i$ and $\mathbf{Z}_j$ should be similar if nodes $i$ and $j$ are connected by relation $r$. We can achieve the above goal by minimizing to the following term with respect to $\mathbf{Z}$:
\begin{eqnarray}
\operatorname{tr}\left(\mathbf{Z}^{T} \tilde{\mathbf{L}}^r \mathbf{Z}\right)=\sum_{i, j}^{n} \hat{\tilde{\mathbf{A}}}_{i, j}^r\left\|\mathbf{Z}_{i}-\mathbf{Z}_{j}\right\|^{2},
\end{eqnarray}
where $\hat{\tilde{\mathbf{A}}}_{i, j}^r$ represents the node $i$ and node $j$ are connected under relation $r$.

With all the $R$ relations, we need to simultaneously capture the graph signal smoothness. Moreover, consider that different relations may play different roles, we need to distinguish their importance as well, which can be modelled as an ensemble multi-relational graph  regularization as follows:
\begin{eqnarray}
\mathcal{O}_{\text {e-reg }} =
\left\{
\begin{aligned}
 \lambda_{1} \sum_{r=1}^{R} \mu_{r}\sum_{i, j}^{n} \hat{\tilde{\mathbf{A}}}_{i, j}^{r}\left\|\mathbf{Z}_{i}-\mathbf{Z}_{j}\right\|^{2}
+\lambda_{2}\left\|\boldsymbol{\mu}\right\|_{2}^{2},\\
\text { s.t. } \sum_{r=1}^{R}\mu_{r}=1, \mu_{r} \geq 0, \forall r=1,2, \ldots, R,
\end{aligned}
\right.
\end{eqnarray}
where $\mathbf{\lambda}_{1}$ and $\mathbf{\lambda}_{2}$ are  non-negative trade-off parameters.
$\mu_{r} \geq 0$ is the weight corresponding to relation $r$, and
the sum of weights is 1 for  constraining the search space of possible graph Laplacians.
The regularization term $\left\|\boldsymbol{\mu}\right\|_{2}^{2}$ is to avoid the parameter overfitting to only one relation~\cite{geng2012ensemble}.

In addition to the topological constraint by $\mathcal{O}_{\text {e-reg }}$ term, we should also build the relationship between the learned representation $\mathbf{Z}$ with the node features $\mathbf{H}$. Therefore, there is a feature fitting term: $\mathcal{O}_{\text {fit }} =\|\mathbf{Z-H}\|_{F}^{2}$,
which makes $\mathbf{Z}$  encode information from the original feature $\mathbf{H}$, so as to  alleviate the over-smoothing problem.
Finally, our proposed optimization framework for multi-relational graphs, which  includes constraints on features and  topology, is as follows:
\begin{eqnarray}
\label{overall}
\notag& \arg&\min_{\mathbf{Z},\mathbf{\mu}}\underbrace{\|\mathbf{Z-H}\|_{F}^{2}}_{\mathcal{O}_{\text {fit }}}+
\underbrace{\lambda_{1} \sum_{r=1}^{R} \mu_{r} \mathbf{tr}\left(\mathbf{Z}^{\top}\tilde{\mathbf{L}}^{r} \mathbf{Z}\right)+\lambda_{2}\left\|\boldsymbol{\mu}\right\|_{2}^{2}}_{\mathcal{O}_{\text {e-reg }}}, \\
 &\text { s.t. }& \sum_{r=1}^{R}\mu_{r}=1, \mu_{r} \geq 0, \forall r=1,2, \ldots, R.
\end{eqnarray}

By minimizing the above objective function,  the optimal representation $\mathbf{Z}$ not only captures the smoothness between nodes, but also preserves the personalized information. Moreover, the optimal relational coefficients $\boldsymbol{\mu}$ can be derived, reflecting the importance of different relations.

\subsection{Ensemble Message Passing Mechanism }

It is nontrivial to directly optimize $\mathbf{Z}$ and $\boldsymbol{\mu}$ together because Eq.\eqref{overall} is not convex w.r.t. $ (\mathbf{Z}, \boldsymbol{\mu})$ jointly.
Fortunately, an iterative optimization strategy can be adopted,
i.e., i.) first optimizing Eq.\eqref{overall} w.r.t. $ \boldsymbol{\mu}$ with a fixed  $\mathbf{Z}$,
resulting in the solution of relational coefficients $ \boldsymbol{\mu}$;
ii.) then solving Eq.\eqref{overall} w.r.t. $\mathbf{Z}$  with $ \boldsymbol{\mu}$ taking the value solved in the last iteration.
We will show that performing the above two steps corresponds to one ensemble message  passing layer in our relational GNNs.

\setcounter{secnumdepth}{3}
\subsubsection*{Update Relational Coefficients}

We update relational parameters $ \boldsymbol{\mu}$ by fixing $\mathbf{Z}$, then the objective function \eqref{overall} w.r.t. $ \boldsymbol{\mu}$  is reduced to:
\begin{eqnarray}
\label{cor}
\notag &\arg& \min _{\mu} \sum_{r=1}^{R} \mu_{r} s_{r} +
\mathbf{\frac{\lambda_{2}}{\lambda_{1}}}\left\|\boldsymbol{\mu}\right\|_{2}^{2},\\
 &\text { s.t. }& \sum_{r=1}^{R}\mu_{r}=1, \boldsymbol{\mu} \geq 0, \forall r=1,2, \ldots, R,
\end{eqnarray}
where $s_{r}=\mathbf{tr}\left(\mathbf{Z}^{\top}\tilde{\mathbf{L}}^{r} \mathbf{Z}\right)$.

(1) When $\mathbf{\frac{\lambda_{2}}{\lambda_{1}}}=0$,
the coefficient might concentrate on one certain relation,
i.e.,  $\mu_{j}=1$ if ${s}_{j}=\min_{r=1, \ldots, R} {s}_{r}$, and $\mu_{j}=0$ otherwise.
When $\mathbf{\frac{\lambda_{2}}{\lambda_{1}}}=+\infty$, each relation will be assigned equal coefficient, i.e., $\mu_r=\frac{1}{R}$~\cite{geng2012ensemble}.

(2) Otherwise, theoretically, Eq.\eqref{cor} can be regarded as a  convex function of $\boldsymbol{\mu}$ with the constraint in a standard simplex~\cite{chen2011projection},  i.e., $\Delta=$ $\left\{\boldsymbol{\mu} \in \mathbb{R}^{R}: \sum_{r=1}^{R} \mu_{r}=1, \boldsymbol{\mu} \succcurlyeq 0\right\}$.
Therefore, the mirror entropic descent algorithm (EMDA)~\cite{beck2003mirror} can be used to optimize $\boldsymbol{\mu}$, where the update process is described by Algorithm~\ref{alg1}.
The objective $f(\cdot)$ should be a convex Lipschitz continuous function with Lipschitz constant $\phi$ for a fixed given norm. Here, we derive this Lipschitz constant from $\|\nabla f(\boldsymbol{\mu})\|_{1} \leq  \frac{2\lambda_{2}}{\lambda_{1}}+\|\boldsymbol{s}\|_{1}=\phi$, where $\boldsymbol{s}=\left\{s_{1}, \ldots, s_{R}\right\}$.

\subsubsection*{Update Node Representation}
Then we update node representation $\mathbf{Z}$ with  fixing $\boldsymbol{\mu}$, where
the objective function Eq. \eqref{overall} w.r.t.  $\mathbf{Z}$ is reduced to:
\begin{eqnarray}
\label{z}
\arg \min _{\mathbf{Z} }\|\mathbf{Z}-\mathbf{H}\|_{F}^{2}+
\lambda_{1} \sum_{r=1}^{R} \mu_{r} \mathbf{tr}\left(\mathbf{Z}^{\top}\tilde{\mathbf{L}}^{r} \mathbf{Z}\right)
.\end{eqnarray}
We can set the derivative of Eq.~\eqref{z} with respect to $\mathbf{Z}$ to zero and get the optimal $\mathbf{Z}$ as:

\begin{eqnarray}
\frac{\partial\left\{
\|\mathbf{Z}-\mathbf{H}\|_{F}^{2}+
\lambda_{1} \sum_{r=1}^{R} \mu_{r} \mathbf{tr}\left(\mathbf{Z}^{\top}\tilde{\mathbf{L}}^{r} \mathbf{Z}\right)
\right\}}{\partial \mathbf{Z}}=0\\ \quad \Rightarrow \quad \mathbf{Z}-\mathbf{H} + \lambda_{1}\sum_{r=1}^{R} \mu_{r}\tilde{\mathbf{L}}^{r} \mathbf{Z}=0.
\end{eqnarray}
Since the eigenvalue of $\mathbf{I}+\lambda_{1}\sum_{r=1}^{R} \mu_{r}\tilde{\mathbf{L}}^{r}$ is positive, it has an inverse matrix, and we can obtain the closed solution as follows:
\begin{eqnarray}
\label{close}
\notag\mathbf{Z}&=&\left(\mathbf{I}+\lambda_{1}  \sum_{r=1}^{R} \mu_{r}\tilde{\mathbf{L}}^{r} \right)^{-1} \mathbf{H}\\ &=&\frac{1}{1+\lambda_{1}}\left(\mathbf{I}-\frac{\lambda_{1}}{1+\lambda_{1}} \sum_{r=1}^{R} \mu_{r}\hat{\tilde{\mathbf{A}}}^{r}\right)^{-1} \mathbf{H}.
\end{eqnarray}

However, obtaining the inverse of matrix will cause  a
computational complexity and memory requirement of  $\mathcal{O}\left(n^{2}\right)$,
which is inoperable in large-scale graphs.
Therefore,  we can approximate Eq.\eqref{close} using the following iterative update rule:
\begin{eqnarray}
\label{update}
\mathbf{Z}^{(k+1)}=\frac{1}{\left(1+\lambda_{1}\right)}\mathbf{H}+\frac{\lambda_{1}}{\left(1+\lambda_{1}\right)}\left(\sum_{r=1}^{R} \mu_{r}^{(k)}\hat{\tilde{\mathbf{A}}}^{r}\right)\mathbf{Z}^{(k)}.
\end{eqnarray}
where $k$ is the iteration number.

\begin{algorithm}

	\renewcommand{\algorithmicrequire}{\textbf{Input:}}
	\renewcommand{\algorithmicensure}{\textbf{Output:}}
	\caption{Relational Coefficients Learning}
	\label{alg1}
	\begin{algorithmic}[1]
	    \REQUIRE
	    Candidate Laplacians $\left\{\tilde{\mathbf{L}}^{1},\cdots, \tilde{\mathbf{L}}^{R} \right\}$,
	    the embedding matrix $\mathbf{Z}$,
	    the Lipschitz constant $\phi$, the tradeoff parameters $\lambda_{1},\lambda_{2}$.
	    \ENSURE  Relational coefficients $\boldsymbol{\mu}$.
		\STATE Initialization: $\boldsymbol{\mu}=[\frac{1}{R},\frac{1}{R},\cdots,\frac{1}{R}] $
		\FOR { $r=1$ to $R$}
		\STATE $s_{r}=\mathbf{tr}\left(\mathbf{Z}^{\top}\tilde{\mathbf{L}}^{r} \mathbf{Z}\right)$
                \REPEAT
                \STATE  $T_{t} \leftarrow \sqrt{\frac{2 ln R}{t \phi^{2}}}$,
            \STATE  $f^{\prime}\left(\mu_{r}^{t}\right) \leftarrow \frac{2\lambda_{2}}{\lambda_{1}} \mu_{r}^{t}+s_{r}$,
            \STATE   $\mu_{r}^{t+1} \leftarrow \frac{\mu_{r}^{t} \exp \left[-T_{t} f^{\prime}\left(\mu_{r}^{t}\right)\right]}{\sum_{r=1}^{R} \mu_{r}^{t} \exp \left[-T_{t} f^{\prime}\left(\mu_{r}^{t}\right)\right]}$,
            \UNTIL Convergence
        \ENDFOR
        \RETURN $\boldsymbol{\mu}$
	\end{algorithmic}
\end{algorithm}

\subsubsection*{Ensemble Message Passing Layer (EnMP layer)}
Now with the node representation $\mathbf{Z}$ and the relation coefficient $\boldsymbol{\mu}$, we can propose our ensemble message passing layer, consisting of the following two steps: (1) relational coefficient learning step (RCL step), i.e., update the relational coefficients $\boldsymbol{\mu}$ according to Algorithm~\ref{alg1}; (2) propagation step (Pro step), i.e., update the node representation $\mathbf{Z}$ according to Eq.\eqref{update}. The pseudocode of EnMP layer is shown in appendix A. We will show some properties of our proposed EnMP layer.

\begin{thm}[Relationship with Multi-Relational/Path Personalized PageRank]
\label{reppr}
Given a realtion $r$, we have the relation based probability transition  matrix $\mathbf{A}^{r}_{rw}=\mathbf{A}^{r}(\mathbf{D}^{r})^{-1} $.
Then, the single relation based PageRank
matrix is calculated via:
\begin{eqnarray}
\boldsymbol{\Pi}_{\mathrm{pr}}^{r}=\mathbf{A}^{r}_{\mathrm{rw}}\boldsymbol{\Pi}_{\mathrm{pr}}^{r}.
\end{eqnarray}
Considering we have $R$ relations, i.e., $r=1,2, \ldots, R$, the weights of each relation are $\left\{\mu_{1}, \ldots, \mu_{R}\right\}$, according to~\cite{lee2013pathrank,ji2021heterogeneous}, we can define the multiple relations based PageRank matrix:
\begin{eqnarray}
\boldsymbol{\Pi}_{\mathrm{pr}}=\left(\sum_{r=1}^{R} \mu_{r}\mathbf{A}^{r}_{\mathrm{rw}}\right)
\boldsymbol{\Pi}_{\mathrm{pr}}^{r}.
\end{eqnarray}
According to~\cite{klicpera2018predict}, the  multi-relational personalized PageRank matrix can be defined:
\begin{eqnarray}
\boldsymbol{\Pi}_{\mathrm{ppr}}=\alpha\left(\boldsymbol{I}_{n}-(1-\alpha)
\left(\sum_{r=1}^{R} \mu_{r}\hat{\tilde{\boldsymbol{A}}}^{r}\right)
\right)^{-1},
\end{eqnarray}
where $\hat{\tilde{\boldsymbol{A}}}^{r}$ is a normalized adjacency matrix with self-loops, $\boldsymbol{I}_{n}$ represents unit matrix, $\alpha \in(0,1]$ is teleport (or restart) probability.
If $\alpha=\frac{1}{\left(1+\lambda_{1}\right)}$,
the closed-form solution in Eq.\eqref{close} is to propagate features via multi-relational personalized PageRank scheme.

\end{thm}
\begin{thm}[Relationship with APPNP/GCN]
if ${\lambda_{2}}=+\infty$, the solution in Eq.\eqref{cor} is $\boldsymbol{\mu}=[\frac{1}{R},\frac{1}{R},\cdots,\frac{1}{R}] $,
i.e., each relaiton  is assigned equal coefficient,
then the ensemble multi-relational graph $\sum_{r=1}^{R} \mu_{r}^{(k)}\hat{\tilde{\mathbf{A}}}^{r}$ reduces to a normalized adjacency matrix $ \frac{1}{R} \sum_{r=1}^{R} \hat{\tilde{\mathbf{A}}}^{r}$  averaged over all relations. The proposed message passing scheme reduces to:
\begin{eqnarray}
\mathbf{Z}^{(k+1)}=\frac{1}{\left(1+\lambda_{1}\right)}\mathbf{H}+\frac{\lambda_{1}}{\left(1+\lambda_{1}\right)}\frac{1}{R} \sum_{r=1}^{R} \hat{\tilde{\mathbf{A}}}^{r}\mathbf{Z}^{(k)}
,\end{eqnarray}
if $\lambda_{1}=\frac{1}{\alpha}-1$,  it recovers the message passing in APPNP on the averaged relational graph:
\begin{eqnarray}
\mathbf{Z}^{(k+1)}=\alpha\mathbf{H}+(1-\alpha)\frac{1}{R} \sum_{r=1}^{R} \hat{\tilde{\mathbf{A}}}^{r}\mathbf{Z}^{(k)},
\end{eqnarray}
if $\lambda_{1}= +\infty $,  it recovers the message passing in GCN on the averaged relational graph:
\begin{eqnarray}
\mathbf{Z}^{(k+1)}=\frac{1}{R} \sum_{r=1}^{R} \hat{\tilde{\mathbf{A}}}^{r}\mathbf{Z}^{(k)}.
\end{eqnarray}

\end{thm}

\begin{figure}[htp]
\centering
    \includegraphics[width = 8cm,height = 2.8cm]{framework}
    \caption{Model architecture.}
    \label{model}
\end{figure}

\subsection{Ensemble Multi-Relational GNNs}

Now we propose our ensemble multi-relational graph neural networks (EMR-GNN) with the EnMP layer. Similar as \cite{klicpera2018predict}, we employ the decoupled style architecture, i.e., the feature transformation and the message passing layer are separated. The overall framework is shown in Figure~\ref{model}, and the forward propagation process is as follows:
\begin{eqnarray}
\mathbf{Y}_{\text {pre }}= g_{\theta}\left(
\mathbf{EnMP}^{(K)}\left(f\left(\mathbf{X};\mathbf{W}\right), R, \lambda_{1}, \lambda_{2}\right) \right),
\end{eqnarray}
where $\mathbf{X}$ is the input feature of nodes,
and $f\left(\mathbf{X};\mathbf{W}\right)$ denotes the MLPs or linear layers (parameterized by $ \mathbf{W}$)  which is used to feature extraction.
$\mathbf{EnMP}^{(K)}$ represents our designed ensemble relational message passing layer with $K$ layers, where $R$ is the number of relations, and $\lambda_{1}, \lambda_{2}$ are hyperparameters in our message passing layer.
$g_{\theta}(\cdot)$ is MLPs as classifier with the learnable parameters $\theta$.
The training loss is: $\ell(\mathbf{W}, \theta) \triangleq  \mathcal{D}\left(\boldsymbol{y}^{*}_{i}, \hat{\boldsymbol{y}_{i}}\right),$
where $\mathcal{D}$ is a discriminator function of cross-entropy,
$\boldsymbol{y}^{*}_{i}$ and $ \hat{\boldsymbol{y}_{i}}$ are the predicted and ground-truth labels of node $i$, respectively.
Backpropagation manner is used to optimize parameters in MLPs, i.e., $\mathbf{W}$ and $\theta$,
and the parameters in our EnMP layers are optimized during the forward propagation. We can see that EMR-GNN is built on a clear optimization objective. Besides, EMR-GNN also has the following two advantages:
\begin{itemize}

    \item  As analyzed by Remark~\ref{reppr}, our proposed EnMP can  keep  the  original  information  of  the  nodes with  a  teleport (or restart) probability,  thereby  alleviating over-smoothing.
    \item For each relation, there is a parameterized relation-specific weight matrix or parameterized relation encoder used in the traditional RGCN~\cite{vashishth2019composition,schlichtkrull2018modeling}. While in our EnMP, only one learnable weight coefficient is associated with a relation, greatly alleviating the over-parameterization problem.

\end{itemize}

\begin{table}
   \centering
    \renewcommand{\arraystretch}{1.2}
    \small
    \resizebox{8cm}{!}{
    \begin{tabular}{lrrrrlr}
        \toprule
        Datasets &Nodes &\makecell*[r]{Node\\Types}& Edges&\makecell*[c]{ Edge \\Types} & Target & Classes\\
        \midrule
        MUTAG & 23,644 & 1 & 74,227&23&molecule &2\\
        BGS & 333,845& 1 & 916,199&103&rock &2\\
        DBLP&26,128&4&239,566&6&author&4\\
        ACM&10,942&4&547,872&8&paper&3\\
        \bottomrule
    \end{tabular}}
    \caption{Statistics of multi-relational datasets.}
    \label{sta}
\end{table}

\begin{table*}[!htb]
\centering
\renewcommand{\arraystretch}{1.2}
\setlength\tabcolsep{2.6pt}

\small
\begin{tabular}{l|r|r|r|r|r|r|r|r}
\bottomrule
Dataset &\multicolumn{2}{c|}{DBLP} &\multicolumn{2}{c|}{ACM}&\multicolumn{2}{c|}{MUTAG}&\multicolumn{2}{c}{BGS}\\
\hline
Metric &{Acc ($\%$)}& Recall ($\%$) &Acc ($\%$)& Recall ($\%$)&Acc ($\%$)& Recall ($\%$)&Acc ($\%$)&Recall ($\%$)\\
\hline
      GCN & 90.39±0.38 & 89.49±0.52  &89.58±1.47 &89.47±1.49 &72.35±2.17 &63.28±2.95 &85.86±1.96&80.21±2.21\\

  GAT & 91.97±0.40 & 91.25±0.58 &88.99±1.58 &88.89±1.56 & 70.74±2.13&63.01±3.79 &88.97±3.17&86.13±4.96\\
  HAN &91.73±0.61  &91.15±0.72  & 88.51±0.35 &88.50±0.30 &- &- &-&-\\
  RGCN & 90.08±0.60 &88.56±0.76& 89.79±0.62&89.71±0.59 &71.32±2.11 & 61.97±3.52&85.17±5.87& 81.58±7.94\\

  e-RGCN & 91.77±0.90& 91.18±1.02 &83.00±1.04 &84.03±0.75 &69.41±2.84& \textbf{67.57±8.04} &82.41±1.96&84.51±3.38\\

   \hline
 EMR-GNN &  \textbf{93.54±0.50} & \textbf{92.39±0.78  } & \textbf{90.87±0.11} &  \textbf{90.84±0.13} & \textbf{74.26±0.78} & 64.19±1.08&\textbf{89.31±4.12}&\textbf{86.39± 5.33} \\
\bottomrule
\end{tabular}
\caption{
The mean and standard deviation of classification
accuracy and recall over 10 different runs on four datasets.}
\label{total}
\end{table*}

\begin{table*}[!htb]
\centering
\renewcommand{\arraystretch}{1.2}

\small

\begin{tabular}{cccccc}

\bottomrule
 GCN&GAT& HAN &RGCN & e-RGCN &EMR-GNN\\
\hline
$\mathcal{O}\left(K d^{2}\right)$&
$\mathcal{O}\left(2 K N d^{2}\right)$&
$\mathcal{O}\left(
2K\left(|\mathcal{R}| N +1 \right)d^{2} + 2 Kd
\right)$&
$\mathcal{O}\left(\mathcal{B} K d^{2}+\mathcal{B} K|\mathcal{R}|\right)$&
$\mathcal{O}\left(\mathcal{B} (K-1) d^{2}+|\mathcal{R}|d+\mathcal{B} (K-1)|\mathcal{R}|\right)$&
$\mathcal{O}\left(2 d^{2}+K|\mathcal{R}|\right)$

\\

\bottomrule
\end{tabular}
\caption{
Comparison of the number of parameters.
Here, $K$ denotes the number of layers in the model, $d$ is the embedding dimension, $\mathcal{B}$ represents the number of bases, $|\mathcal{R}|$ indicates the total number of relations in the graph and $N$ is the number of heads of attention-based models.}
\label{pa}
\end{table*}

\begin{figure*}[t]
\centering
\subfigure[GCN (SC=0.6196)]{
\label{Fig.sub.2}
\includegraphics[width=4cm,height = 3cm]{GCN}}
\subfigure[GAT (SC=0.6351)]{
\label{Fig.sub.2}
\includegraphics[width=4cm,height = 3cm]{GAT}}
\subfigure[RGCN (SC=0.6093)]{
\label{Fig.sub.2}
\includegraphics[width=4cm,height = 3cm]{RGCN}}
\subfigure[EMR-GNN (SC=0.7799)]{
\label{Fig.sub.1}
\includegraphics[width=4cm,height = 3cm]{EMR}}
\caption{Visualization of the learned node embeddings on DBLP dataset.}
\label{vis}
\end{figure*}

\begin{figure}[t]
\centering
\subfigure[DBLP]{
\label{Fig.sub.1}
\includegraphics[width=4.15cm,height = 4.cm]{dblp_layer}}
\subfigure[ACM]{
\label{Fig.sub.2}
\includegraphics[width=4.15cm,height = 4.cm]{acm_layer}}
\caption{ Analysis of propagation layers. Missing value in red line means CUDA is out of memory.}
\label{nlayer}
\end{figure}

\begin{figure}[htp]
    \centering
    \includegraphics[width=7cm,height = 5cm]{cor}
    \caption{Accuracy  under each single relation and corresponding relational coefficient.}
    \label{coe}
\end{figure}

\section{Experiment}

\label{sec:experiment}

\subsection{Experimental Settings}
\paragraph{Datasets.}
The following four real-world heterogeneous datasets in various fields are  utilized and can be divided into two categories: i) the node type and edge type are both heterogeneous (DBLP~~\cite{fu2020magnn}, ACM~\cite{lv2021we}).
ii) the node type is homogeneous but the edge type is heterogeneous (MUTAG~\cite{schlichtkrull2018modeling}, BGS~\cite{schlichtkrull2018modeling}).
The statistics of the datasets can be found in Table \ref{sta}.
The basic information about datasets is summarized in appendix B.1.

\paragraph{Baselines.}
To test the performance of the proposed EMR-GNN,
we compare it with five  state-of-the-art baselines.
Among them, GCN~\cite{kipf2016semi} and GAT~\cite{velivckovic2017graph} as two popular approaches are included.
In addition, we compare with the heterogeneous graph model HAN~\cite{wang2019heterogeneous}, since HAN can also employ multiple relations.
Two models that are specially designed for multi-relational graphs are compared, i.e., RGCN~\cite{schlichtkrull2018modeling}  and e-RGCN~\cite{thanapalasingam2021relational}.

\paragraph{Parameter settings.}
We implement EMR-GNN based on Pytorch.\footnote{\url{https://pytorch.org/}}
For $f\left(\mathbf{X};\mathbf{W}\right)$  and $g_{\theta}(\cdot)$,
we choose one layer MLP for DBLP and ACM, and linear layers for MUTAG and BGS.
We conduct 10 runs on all datasets with the fixed training/validation/test split for all experiments.
More implementation details can be seen in appendix B.3.

\subsection{Node Classification Results}
Table \ref{total} summarizes the performances of EMR-GNN and several  baselines on semi-supervised node classification task.
Since HAN's code uses the heterogeneity of nodes to design meta-paths, we do not reproduce the results of HAN on homogeneous dataset (MUTAG, BGS) with only one type of nodes.
We use accuracy (Acc) and recall metrics for evaluation, and report the  mean and standard deviation of classification accuracy and recall.
We have the following observations:
(1) Compared with all baselines, the proposed EMR-GNN generally achieves the best performance across all datasets on seven of the eight metrics, which demonstrates the effectiveness of our proposed model.
e-RGCN has a higher recall but a lower accuracy on MUTAG, which may be caused by  overfitting.
(2) Meanwhile, the number of parameters of our model and other baselines are shown in Table \ref{pa}. We can see that
EMR-GNN  is more parameter efficient than all baselines,
 i.e., $\mathcal{O}\left(2 d^{2}+K|\mathcal{R}|\right)$,
but achieves maximum relative improvements of $4.14\%$ than RGCN on BGS.
It means that EMR-GNN largely overcomes the over-parameterization in previous multi-relational GNNs.

\subsection{Model Analysis}
\paragraph{Alleviating over-smoothing problem.}
As mentioned before, EMR-GNN is able to alleviate over-smoothing issue.
Here, we take one typical single-relation GCN (GAT) and one representative multi-relational GCN (RGCN) as baselines to test their performance with different propagation depths, where the results are shown in
Figure.\ref{nlayer}. We have the following observations:
(1) Our model significantly alleviates the over-smoothing problem,
since there is generally no performance degradation when the depth increases.
This benefits from the  adjustable factor $\mathbf{\lambda_{1}}$ in EMR-GNN, which flexible controls the influence of  node feature information.
In contrast, the performance of RGCN and GAT drops seriously  with increasing depth,
implying that these models suffer from the over-smoothing problem.
(2) RGCN needs huge storage cost, making it difficult to stack multiple layers.
Cuda out of memory occurs when the propagation depth increases, i.e., DBLP for more than 16 layers, and ACM can merely stack  8 layers. This is not available for capturing  long-range dependencies.

\begin{table}[!htb]

\renewcommand{\arraystretch}{1.2}

\small
\begin{tabular}{l|l|rrrr}
\bottomrule
Datasets &Method &\multicolumn{4}{c}{Size of training set}\\
\hline
 & & $10\%$ & $15\%$& $20\%$&$25\%$\\
\hline
 DBLP &RGCN &  0.5381& 0.6388& 0.7515&0.7721\\

 & EMR-GNN &   0.8768& 0.9109 &  0.9128& 0.9364 \\
 \hline
 ACM &RGCN & 0.7492 &0.8136 &0.8278&0.8344  \\

 & EMR-GNN &  0.8489 & 0.8654 & 0.8739 & 0.8753  \\
\bottomrule
\end{tabular}
\caption{Classification accuracy w.r.t. different training set.}
\label{size}
\end{table}
\paragraph{Alleviating over-parameterization  problem.}
To further illustrate the advantages of alleviating over-parameterization,
we verify EMR-GNN  with small-scale training samples.
We conduct experiments on EMR-GNN and RGCN using two datasets. We only select a small part of nodes from original training samples as the new training samples.
As can be seen in Table \ref{size}, EMR-GNN consistently outperforms RGCN with different training sample ratios, which again validates the superiority of the proposed method.
One reason is that  a limited number of parameters in EMR-GNN can be fully trained with few samples.
In contrast, RGCN with excess parameters requires large-scale training samples as the number of relations increases.
The time complexity is analyzed in appendix C.

\noindent
\paragraph{Analysis of relational coefficients.}
Besides the performance,
we further show that EMR-GNN can produce reasonable relational  coefficients.
To verify the ability of relational coefficients learning,
taking ACM dataset as example, we evaluate the classification performance under each single relation.
The classification accuracy and the corresponding relational coefficient value are reported in Figure \ref{coe}.
We can see that basically, the relation which achieves better accuracy is associated with a larger coefficient. Moreover, we compute the pearson correlation coefficient between the accuracy of a single relation and its relational coefficient, which is 0.7918, well demonstrating that they are  positively correlated.

\noindent
\paragraph{Visualization.}
For a more intuitive comparison, we conduct the task of visualization on
DBLP dataset.
We plot the output embedding on the last layer of EMR-GNN and three baselines (GCN, GAT and RGCN) using t-SNE~\cite{van2008visualizing}.
All nodes in Figure \ref{vis} are colored by the ground truth labels.
It can be observed that EMR-GNN performs best, since the significant boundaries between nodes of different colors, and the relatively dense distribution of nodes with the same color.
However, the nodes with different labels of GCN and RGCN are mixed together.
In addition, we also calculate the silhouette coefficients (SC) of the classification results of different models, and EMR-GNN achieves the best score, furthering indicating that the learned representations of EMR-GNN have a clearer structure.

\section{Conclusion}
\label{sec:conclusion}
In this work,
we study how to design multi-relational graph neural networks from the perspective of optimization objective. We propose an ensemble optimization framework, and derive a novel ensemble message passing layer. Then we present the ensemble multi-relational GNNs (EMR-GNN), which has nice
relationship with multi-relational/path  personalized PageRank and can recover some popular GNNs.
EMR-GNN not only is designed with clear objective function, but also can well alleviate  over-smoothing and over-parameterization issues.
Extensive experiments demonstrate the superior performance of EMR-GNN over the several state-of-the-arts.

\clearpage

\section*{Acknowledgements}
The research was supported in part by the National Natural Science Foundation of China (Nos. 61802025, 61872836, U1936104) and Meituan.

\input{ijcai22-multiauthor.bbl}

\end{sloppypar}
\end{document}

redpajama_set_name: RedPajamaArXiv


text:
Harp Lessons
Beginners' Harp Workshops
Harp Making
Life Song Course
Harp Hen-Do's!
Our Harps
Morwenna Rose
Levered Morwenna Rose
Custom Harps
Harp Cases
Harp Hire
Subscribe/Hire
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The Hands on Harps Team
Creag and Morwenna met while travelling in Australia and share a passion for travel and music. This has lead them, including other places, up Mt Kilimanjaro, all around Europe in a van for 2 years, busking, along the Camino de Santiago with their instruments, volunteering in Kenya, India and the Philippines and now to Nailsworth, a town in South Gloucestershire where they have settled down and now have 2 young boys.
Morwenna has played the harp since the age of 12, after seeing a harpist at a school May Festival and convincing her parents that she wanted to learn it. They made a deal with her-they bought her a small table harp and said that if she persisted with it for a year then they would pay for harp lessons.
She did, so they bought her some lessons with a local teacher. She enjoyed playing the harp and has gone on to play weddings, funerals, restaurant gigs as well as various art exhibitions, open days and festivals.
Creag grew up in a business environment-his parents ran Swallow Systems, a company that made educational robots for schools. With his dad and best mate Steve he made racing robots to compete in Mircromouse, which gave him an appearance on Blue Peter at the age of 12.
He started playing the guitar aged 18 while at university in Nottingham. He has never had a face to face lesson, learning all of his songs and techniques from videos online-this is part of the inspiration for this course. He first made a harp in 2012 for Morwenna's Christmas present, and is passionate about working with wood to make beautiful things-he has also made a bed, various signs, a model of his Dad's workshop, wine racks.
Matt came to luthiery after completing a guitar building course in Totnes. He brings with him a wealth of woodworking and musical knowledge. Matt is a graduate of the University of Wales College of Medicine where he studied Radiography and Diagnostic Imaging. Once qualified, Matt went into pub management and ran several pubs before ending up in Monmouth for 5 years. Whilst at Monmouth he ran a successful music venue that was frequented by amongst others the Pixies, Kasabian and Robert Plant.
He plays double bass in a country rock and roll band called Shootin' the Crow who have played various festivals and gig regularly. Check them out here.
He now lives in Dursley with his girlfriend Madeleine and his dog Lupa.
Ellie is our new harp maker and teacher who's joined us after just finishing her Foundation Degree in Art and Design. Ellie has been creating sculptures all her life and is excited to be moving her practice onto functional designs in wood rather than artistic pieces in clay and plaster. Gael Music (now operating in Glasgow) approached Ellie's school when she was 13 and found her to be a natural harpist. Ellie has carried on the Gael Music ethos teaching folk music to young people at festivals with Shooting Roots and is now studying for her grade 8 in Irish Folk music on the harp.
Our stated aim is to make learning the harp affordable and accessible, but we are proud to make sure that we do that in a way that doesn't compromise our values.
We source our wood only from FSC certificated suppliers. FSC® is an independent, non-governmental, not for profit organization established to promote the responsible management of the world's forests.
We are currently spending a year going carbon neutral. Check out our blog to see how we're getting on.
We endeavor to make learning the harp affordable. Our aim is not to make gilded, overly ornate lever harps that cost the same as a family car. We want people to be able to afford to get their hands on a harp and have fun with it.
We believe that harps shouldn't be seen as fragile items that people are afraid to touch. Danish oiled wood is quite well protected, and it's also quite easy to repair if a harp comes back with a few scratches on it. Don't be afraid to share your music around a campfire!
We believe that anyone can learn the harp, and that it should be fun. There is a place for classical training, but it's not for us-we prefer the folk tradition of training people to be intuitive musicians with a connection to their instrument, rather than automatons who can churn out a piece of sheet music if it's put in front of them.
Have a look at this page to see some of Hands on Harps' friends
We are Creag and Morwenna Rose Louttit-Vermaat. We met in Australia and share a passion for travel and music. Read more.
© 2018 Hands on Harps | Graphics by Get Nashi


Re: "Playing the race deck" (Letters, Kathleen Parker, Sept. 21).
In the last few months I have read and heard more about race than at any other time that I can recall. Race this and race that. I am not and "You lie."
We all want to be better than our brother and we do what we can to separate him from us. We feel that this separation gives us a leg up and somehow makes us better.
I have never let the race thing get in my way and/or prevent me from attaining whatever goals that I have set for myself.
I think we all are fruit of the same tree, only the branches are located at different levels. Some high, middle and low. If the tree is killed all the branches die. So forget the branches and save the tree.
Re: "Scaring dumb people" (Letters, David Savage, Sept. 23).
I have noticed a trend of late from left-wing writers claiming right-wing writers don't provide any facts, just generalized rambling according to them. They accuse the writers of not having facts, and then they themselves make unsubstantiated claims of their own. I guess the right-wing writers are the only ones required to use facts, while the left is exempt.
The fact is Franklin Delano Roosevelt was the first President to appoint "czars," and every President since then has had them. The word czar was coined by the media, not by Republicans or Democrats, so the claim that Republicans are using it to scare dumb people is ludicrous. And just for the record, President Bush had 16 czars, not 47 as portrayed by the Democratic National Committee's Internet commercial.
If everyone provided all the facts along with footnotes, the Daily Press would never print the letter because there is only so much space available on the opinion page. So if Mr. Savage wants the facts on Obama's czars he can cite Google instead of claiming Tim Seep and other conservative writers don't provide facts.
Another fact is, the only dumb people are those ignorant of history and the origin of words.
I not only agree with Gayle Kindsvater's (Letters, Sept., 10) statement that "...the fuel that allowed the fire to burn and spread was caused by years of undergrowth which environmentalists and the government had not allowed to be cleaned out...," I would like to add the following regarding the so-called "environmentalists" blame game.
Recently, the environmentalist group Greenpeace (which does do many good things) has stated that the wildfires in California spread quicker because of "climate change" (a.k.a. global warming). They agreed to appear on The O'Reilly Factor but, when they found out that they would actually have to defend their position, because of the Fox News policy of "We report, you decide," they decided not to appear.
On the show, AccuWeather senior meteorologist Joe Bastardi presented the "foundation of fact" that the recent California drought has been caused by recent cooling of the Pacific Ocean. He stated that whenever the Pacific Ocean is cooler and global temperatures are cooler, California gets dry because the air sinks over the top of California and when it sinks it dries out faster � which means that California's drought is actually caused by global cooling. He also said the predictions of the Intergovernmental Panel on Climate Change that temperatures should have increased over the last 10 years has not only been incorrect but in "fact" they have actually been decreasing (these are actual temperature readings).
The real point here is that environmentalists like Greenpeace and Al Gore only want to preach to the choir (the Nobel Foundation and the American Academy of Motion Picture Arts and Science come to mind). They will never debate the facts with experts.


Our mobile meeting rooms can be used for a wide range of events.
Electrics, lighting and heating can be installed to enable you to hold meetings comfortably at their temporary working location. Modules can be connected end-to-end, side-by-side or in a multi-story configuration to enable larger office suites and meeting rooms.
Although "mobile" our mobile office solution is a permanent quality facility and can be used short or long term.
The mobile offices can be branded with your logo inside and out to reflect your corporate image.
Call Lewis Ashley Group on 01482 815310 to find out more about mobile meeting rooms.


We are ourselves the entities to be analysed.
If you take the writer's journey, there's some equipment you're going to need. The first is authenticity, the second is motion. That means, not only do you need to write from who you are, from what you know, but write from who you are going to be, and what you are going to know. That is an honest writer's bread and salt. You need to anticipate, and serve, your own development. Achieve this, and you'll have created a special passage for your readers to walk through. This is how a writer touches lives; this is how we serve the reader.
But you don't need to be a philosopher, or a mythologist, to be a good writer. However, it is good to have a basic cognitive understanding of the journey – that is, from thought, to books bought. I am fortunate, because I studied European philosophy as part of my arts degree. Now I'm writing this article, which hopes to give other writers the barest bones of what they ought to know (if they don't, the best will intuitively know it, anyway).
To read more, access my Patreon content from just $1/month.


text:
African and Diaporan Voices on African Architecture
On October 8, 2018 October 8, 2018 By davidemmanuelnoelIn Visual Art & Music
During the UK Black History month of October, I'm privileged once again to introduce another guest blog by fellow creative Livingstone Mukusa on his current project celebrating African architects and architecture.
People, locale, environment. These components of a landscape are interrelated, and in the hands of a sensitive practitioner, are approached collectively when considering design intervention. In Sub Saharan Africa, however, this is the exception, rather than the rule.
Colonialism introduced to Sub Saharan Africa new means of construction and building aesthetics. Dominated by industrialized, mass produced materials, this new architectural language spread, permeating rapidly through previously distinct architectural landscapes to creating a region replete with architectural expressions reduced to basic physical attributes that are divorced from their environments, and social meaning of those who inhabit them.
Traditionally, African architecture, much like its art, has always been a verb rather than a noun. It was a language of ritual rather than objectification, a language of climactic response, a language of resource availability.
Patterns, tessellations, fractal designs, and numerous other elements were generally not for the embellishment and decoration that ordinarily meets today's eye, but carried with them specific meaning and purpose. While the Western tradition of compartmentalized knowledge, combined with the modernist concept of the exploration of each medium in isolation, led to a virtually complete separation of art and architecture. The integration of art or craft and architecture, on the other hand, was and remains an essential part indigenous African cultures— a result of the experience of unity between art and life.
Today, architecture throughout Sub Saharan Africa, and its Diaspora is more of a testament to expressions and materiality borrowed from elsewhere. Occasionally, a nod or two is given to the locality and culture, forms and techniques that speak of the place and the people. Where does this place the idea of an African Architecture? In our attempts to frame, within a modern day context, what African architecture is, how can we bridge the huge chasm of a dichotomy between African architecture of old and new African architectural expressions? What frames African architecture? Should it even be framed?
Sub-Saharan Africa is incredibly diverse in landscape, climate zones, ethnicities, cultures, and economies. And the answers to these questions are as complex, contradictory even, as this diversity. But these are questions worth examining. To this end, I am seeking an assortment of UK and Europe based architects, artists, activists and scholars to lend their thoughts for an upcoming publication.
Interested parties please contact the author.
Livingstone Mukasa
Livingstone Mukasa, founder of Afritecture, a blog focused on the contextual engagement, and exploration of the African vernacular in modern architecture. He can be reached with Twitter: @livmuk, or email: mukasa@yahoo.com
African artArchibilityArchitectureDavid Emmanuel Noelsociety
In Conversation with Artist Amber Henry
'Pictures at an African Exhibition' at the Philadelphia Museum of Art


Please consider this text also and let me know the meaning of "em troca & de troco"
Compra o clarão de sonho da alma do infante.
Dar-te-á a essência das vidas de tua vida.
You buy the glare of the dream of the infant´s soul.
And life, in exchange for it..
It will give you/it will provide you with the essences of the lives of/in your life.
Well, the author might have taken some poetic licence with "vidas de tua vida", I decided for conjuring the imagery of - say - someone that might have different pathways in his life, and consider those experiences as "new lives".
Other way, not the case here, is that of someone that lives two lives, that is he/she lives a life in conflict with the "apparent" live one can see at first, or have to keep some sort of secret, etc.
But generally "lives" is used to talk about the lives of more than one individual, taken separarately.
The expression can refer to a group (collectively), but at the same time mentioning their experiences separate as separate events.
As in: Let my ears hear the divine word proclaimed in the memory of your church, and let this memory take flesh again in the lives of your lives.
It may be told to a group, anyone can think of a common experience here, but at the same time it´s about a separate event. Not a life is equal to somebody´s life, strictly speaking.
Anyway, the current case is about poetry and by way of imagery it can be possible.
Sorry for my forays in poetry, I am more into prose, but sometimes there are some exceptions to the rule! Anyway, it is a loose translation, just for learning´s sake.


text:
The stratigraphy of and well-completion reports for the Swanworth Quarry No. 1 and No. 2 and Metherhills No 1 boreholes (RGGE Project), Dorset
Gallois, R.W.. 1998 The stratigraphy of and well-completion reports for the Swanworth Quarry No. 1 and No. 2 and Metherhills No 1 boreholes (RGGE Project), Dorset. Exeter, UK, British Geological Survey, 110pp. (WA/97/091) (Unpublished)
WA97091.pdf
There has been increasing international awareness and concern in recent years about possible global climatic changes and their effects on local environments. In many of those parts of the world where detailed records have been kept for the last 50 to 100 years there is clear evidence of higher average summer temperatures, rising sea levels and a greater incidence of storms. The mechanisms behind these changes are not yet fully understood, and are likely to be complex. Increased emissions of carbon, nitrogen and sulphur oxides and hydrocarbon gases from transport and industrial processes are thought to have induced global climatic changes, but these changes are superimposed on natural changes that occur over time-scales that are too long for direct observation. For example, climatic changes related to variations in the radiant heat received from the sun are thought to occur as 2 1,000-year to 250,000-year cycles. The presence of such long-term climatic cycles can only be inferred from a detailed examination of the geological record. It was for this reason that the Natural Environment Research Council (NERC) decided in 1995 to allocate E900,OOO over 3 years to a special research topic, the Rapid Global Geological Events (RGGE) special topic, designed to examine in as great a detail as practicable a selected interval of the geological column. The aim is to apply to ancient sediments, analytical techniques used successfully to identify the effects of climatic changes in modem sediments. The Kimmeridge Clay was chosen by the RGGE Steering Committee (Chaired by Professor D J Vaughan, Manchester University) because it consists of an apparently unbroken sequence of highly fossiliferous marine mudstones, about 150 million years old, that represent about 3 million years of Earth history. The mudstones contain rhythmic variations in clay mineralogy, fauna and organic content that reflect climatic and sea-level changes. The aim of the project is to apply as many state-of-the art analytical methods as possible to a continuous core taken through the full thickness of the Kimmeridge Clay to enable these changes to be documented and the processes that cause them to be understood.


text:
2017 Ford Raptor
With the release of the second generation Ford Raptor in 2017 there has been a lot of questions regarding various items such as pricing, power, color options, performance upgrades and more. We have compiled some of the most requested answers in regards to the new Ford Raptor for 2017.
2017 RAPTOR: LEANER AND MEANER
The 2017 Raptor is leaner, meaner and more powerful than ever. It's approximately 500 pounds lighter than the previous generation, thanks to high-strength, military-grade, aluminum body plus a high-strength, boxed steel frame. It also features an all-new twin-turbo, intercooled DOHC 24-valve high-output 3.5L EcoBoost® engine with port fuel injection and direct fuel injection that will deliver more power than the previous 6.2L V8 – 450 horsepower and 510 lb.-ft. of torque, a 10-speed automatic transmission, all-new four-wheel drive system and 3.0-inch FOX Racing Shox,™* delivering 13" of front and 14" of rear suspension travel.
FOX Racing Shox is a trademark of FOX Factory, Inc.
*Available late 2016.
2017 FORD RAPTOR COLOR OPTIONS
STUNNING NEW COLORS FOR 2017
Like all vehicle you want to stand out of from the crowd and have that unique color combination that will set your 2017 Ford Raptor apart. Below are some color choices we would like to see on the new Ford Raptor.
GOTTA HAVE IT GREEN
COMPETITION ORANGE
LIGHTNING BLUE
TRIPLE YELLOW
2017 FORD RAPTOR PRICING
The 2017 Ford Raptor is an off road beast at the top of the performance truck line Ford has to offer. The truck comes with multiple configuration options found on Fords vehicle configuration and ranges from $51,310 to $68,405. Dealers will try and add a "Markup" to these trucks seen as high as $15,000 to $20,000 due to the demand and low availability.
Example 2017 Ford Raptor SuperCrew Configured Price
2017 FORD RAPTOR OPTIONS
Even though the 2017 Ford Raptor is at the top of the Ford Truck lineup there are still options that can be added such as:
SYNC 3 - Fords 3rd Generation Entertainment Center
Dual Panel Sunroof - This Thing Is Massive And Gives You A View of The Nights Sky
Beadlock Capable Wheels
Raptor Graphics Package
Build and price on Ford's Vehicle Configuration Page


text:
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This tab serves as a sandbox for you to test anything you like. Any change applied to this tab won't be tracked by Git.

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If you don't limit me by telling me what is possible, then I'll be far more interested in the journey that I have been sent on.
I've been waiting over a year to continue the journey across the wilderness of Steve Jackson's Sorcery! series. Based on the '80s Choose Your Own Adventure-style roleplaying book series of the same name, the digital version goes beyond what could be contained on the page. At this point, the books are mere outlines for the games. Each one continues to push further and further away from merely adapting from Sorcery's more static roots by continuing to add and by diversifying the series's content a considerable amount.
The Sorcery! games are structured as a linear series of isolated encounters with each episode focusing on the main goal of getting to the other side of the map. Meanwhile the overall mission across the four entries of the series is to retrieve the stolen Crown of Kings. So far the games have only lightly touched on the main quest, instead focusing on the cavalcade of local problems that the player encounters. The third game, The Seven Serpents, picks up where the last one left off, leaving the city of Khare in whatever state that you left it in and continuing on through the lost wastelands beyond. These lands are more primal and far emptier than any seen thus far. You are warned that seven servant serpents of the Archmage have been dispatched and are on their way to warn their master about you and to hinder your progress.
As was the case before, your goal remains to make it to the other side of the map, but now there are additional sub goals required of the player (to dispatch as many of the Seven Serpents as possible), which is not as easy to accomplish as they might sound. In combat, each serpent is as tough as the final boss monsters in the previous games. You can take them on man vs. snake, but it is easier and wiser to ask the scattered inhabitants for information about them and to listen to the winds for clues about their weaknesses.
It seems inkle has been flexing their interactive fiction muscles, as each entry in the series expands the nature of journey. In the Shamutanti Hills, the journey was interrupted by a bunch of forks in the road that eventually all merged back together at the other end of the map. In Khare, City of Traps, the nature of the game's structure was altered to resemble something like forward moving spirals. In that episode, you can move forward, never looking back, or you can opt to take one of a number of alleys, side streets, and underground passages that ended up looping around sections of the city and then back on themselves, allowing you to search more of the city with each pass.
The Seven Serpents is about as open world as a purely text-based game can be. All the points of interest aren't paths pushing you forward so much as they are nodes connected by a web of paths in a wide landscape. There are mountain ranges and rivers that section off parts of the map from one another, but within those sections, you can head in any direction that you wish from any node that you wish.
From a programming and design standpoint, it doesn't sound all that difficult or novel. Text adventures have been doing the room based structure since their inception with the Colossal Cave Adventure of the 1970s. But Sorcery! 3 is not content to rest on the static nature of such a structure and call that an open world. Instead, inkle makes the setting dynamic. Time passes. Morning turns to day, which turns to evening, which turns to night. What you see and encounter at any given node can change depending on the time of day that you arrive there. You also had best watch your food supply or risk losing much needed health.
Encounters also change depending on the information that you have or what you've done elsewhere. In one section early in the game, I came across a cloaked figure that bumped into me and disappeared into the mists. I found that I was missing a needed magical item to proceed with this encounter. I later found that magical item in a basement several leagues away in a different era next to a chained criminal. I could have missed both encounters easily, which makes me wonder how many such connected encounters I missed. I've taken advantage of the rewind function in the game to backtrack through my journey and try a different order to things and have noticed some of the changes, but surely not all.
I mentioned a different era. The world is further complicated depending on what era a given node is in, whether that be an event taking place in the present or one shrouded in the mists of the past. You control your place in time by using a number of beacons, basically magical lighthouses, that can turn part of the wasteland into the vibrant land that it was before the Archmage's destructive rule, a rule that began 1,000 years ago.
The exploration possibilities in the game, then, are enormous. The supremely dense world of Sorcery! 3 sparks the imagination because there is something unknown behind every tree and over every hill. When an item is found, it is presented through a textual description and the odd black-and-white ink sketch. It's not possible to find everything in a single run through the game, probably not even after playing multiple times, and I think that this is to Sorcery! 3's benefit.
As much as I want to know and seek out everything, there is a blessing in the grand fuzziness left at the edge of the map, that promise of something else out there. It's that feature that has kept me interested in this series. For as basic as the plot is (There is a wizard. Go and kill it. Retrieve magical MacGuffin.) and as rote as the world is (generic Tolkien inspired fantasy world), I still want to travel through this one.
There are many other games with such basic interchangeable elements, and the world of Sorcery! could belong to any of their fictions. What it offers that is new exists in how differently it presents the same basic material. It's not offering a landscape, but a jumpstart to the imagination that seems so lost in our current era, an era in which everything must be meticulously detailed, wikied, and then explained. The mystery of many games is lost in such a climate, not the mystery of what happened or who did what, but the mystery of life, of existence, of what is possible. If you don't limit me by telling me what is possible, then I'll be far more interested in the journey that I have been sent on.


Also I wanted to let you all know that I have started to offer social media coaching, I have had 3 clients so far and have testimonials :-) its so much fun to give pointers and help folks get the most out of social media.
a simple Japanese dish, sound yummy!
Thank you so much for all the help and support Reb. You are one amazing food blog friend that I found online!
Looks delish! I want to try it too.
Me encanta este platito, me lo anoto.
Looks so so yummy..great recipe..Thanks for sharing. Have a great weekend!
Great looking dish Rebecca. Have a good weekend.
I love the sesame flavor running through this and that you are playing with a new cuisine. Rebecca, you are one of the most positive people in the blogging world. Spending time with you is always uplifting.
Beef yakiniku looks delicious. I like the way you teaches.
This looks like an easy Japanese dish to do and with all the nice ingredients, for sure it will be very tasty. Wish you success in your media coaching.
mmmm, delicious! what a wonderful dish!
can it be chicken instead?
Easy and tasty! My kind of meal :) Thanks for swinging by Deep Dish!
Just wanted to say good look with the social media coaching, I don't have twitter but I can certainly see why its useful (along with all the other ones).
This is a simple but delicious meal! Nice testimonies!
Thank you for your comment on Beef Donburi on my website! I'm happy to find your website. I was going through your website and this Japanese recipe just came to my attention so I decided to leave my comments here. You have a wonderful blog and I became a fan, so I'm all set for your new post!


Being totally new to this stuff I kinda guessed at what to make my prices at. I came up with a number for doing basic easy smaller stuff but lately trying to help a buddy do bigger stuff for his truck im really not sure what i should be charging.
I had a whole page wrote then deiced not to post numbers. So will ask this, how do you figure out prices for cutting stuff when the Customer supplied the vinyl?
Vinyl is actually the cheapest part of the whole thing and more often then not can all but be ignored when figuring price. Figure the time involved, how much you want to pay yourself per hour and go from there. For example, if you pay yourself say $50 an hour and a design takes you 0.5 hours to design, cut, weed, and tape up then you'd charge $25.
Size doesn't really matter, If the design is 5"x5" and takes you 5 hours to design, cut, weed, and tape then you'd charge $250. However if you have a design that is 6'x6' and only takes you an hour to design, cut, weed and tape then it'd only be $50.
There is one minor problem with this logic though, and it is that the custom doesn't think in terms of time, only product and they're willing to pay more for a larger product even though in reality it's cheaper for you to make. So even though the math above says $50 for the 6' design, you could very likely get away with $100, or even more depending on the market and your customer.
Most of the things i have done have been simple only took less then 30 mins to make on the program, cut ,weed tap. so most ive charged was like $15 that was for a bigger design. but sold to only friends and trying to make deals with them so they continue to use me and tell others about me maybe.
Yeah, it's a tough call on because part of the issue is the fact that you're still learning how to do all this. So while it may have taken you 6 hours so far, in a years time you might be able to do all this in an hour.
Chalk it up to a working education.
Even though it's taking some serious amount of time to figure this project out for your friend, the knowledge that you're gaining will be priceless to you in the long run. Not going to lie - that's a big project you're undertaking, but it's also exciting. Your friend understands that you're just starting out, and that's the best kind of customer there is. You're getting paid to learn.
I'll be honest, sometimes I base my prices on size, sometimes on difficulty, and sometimes on difficulty of the customer. There have been times when the artwork is cut-ready, and other times where I feel like I'm spending forever to node edit it to death. What I do know, is my hard cost - the cost of the vinyl and app tape, and what I perceive as the wear and tear on all the rest of the equipment and accessories. Sometimes, I only charge then for the roll of the new color (because I didn't have it in my inventory already), and I get to keep whatever is left on the roll - which is usually the majority of it.
My first job in a print shop, the owner gave me his pricing calculator. I've used it ever since. I should note, this is for cut decals from Oracal 631 and 651. Width of the vinyl roll + length of the cut (in inches) divided by 2. That's my base price. on a 24" roll, I keep my designs within 22", so say the design fits into a cut area is 22" x 50". I add 2" to the width and 2" to the length (for the rollers and extra length where it's cut). So that's 24+52=76/2=$38. This is already a decent profit. For me, I've gotten really fast at weeding my own designs, so I'll just round up a few bucks if it's a design that takes more than a few minutes to weed. For custom stuff, I'll round up a little more. Custom designs are charged at my $60 an hour freelance rate. Re-creating artwork in vector for me to cut is charged at $30 an hour rate.
Using this pricing calculator on my 24" rolls of 631, every 5 yards of vinyl sold pays for a 50 yard roll. 45 yards of pure profit. Also gives you some wiggle room to offer decent discounts when people make large orders.
I do recall, before getting into cutting myself, a kiosk at a mall that was charging $1/inch (longs side). That was based on 651 and they were using a 15" roll.
Thanks everyone. My buddy got heck a deal from me, i cut his own vinyl it was two 80 inches long by 23 inches wide and only charged him $20 for it. but he did let me have what was left over. Got to cut the tail gate one still when he gets me the size.