Another important feature to look for is a lock switch that stops it being operated by anyone who is not supposed to. A stair lift can be a tantalizing possibility for a young child and this system ensures they cannot operate it and potentially hurt themselves. Look also for raises working on 24 volts POWER, meaning that there's no worry more than electric shocks. Which Stairlift? Now you know a little about the features available you can begin taking a look at different models. The internet is a great place to start. You will find comprehensive information on model features on most manufacturer websites.
Stlfamilylife - Floating frost protected slab foundation do it house. Diy floating concrete slab foundation the floating concrete slab foundation is a double steel mesh reinforced slab which does not have frost footings this type of foundation is called a "floating slab" because it "floats" on the soil that slab type can be used in northern climates without any concrete feet which has to extend deep enough to. Frost protected shallow foundations fine homebuilding. Frost protected shallow foundations usually consist of a monolithic thick edged slab wrapped with vertical and horizontal rigid foam insulation there are several benefits to this kind of foundation, but don't make sense everywhere find out if a shallow foundation would make sense for your home. Revised builder's guide to frost protected shallow foundations. A builder's guide to frost protected shallow foundations 1 background a frost protected shallow foundation fpsf is a practical alternative to a deeper, more costly foundation in cold regions with seasonal ground freezing and the potential for frost heave the international residential code � irc includes prescriptive methods for. Concrete foundation three types of concrete foundations. T shaped slab on grade foundation frost protected there are many variations of concrete slabs depending on the purpose of the slab below are some useful links for understanding concrete foundations, along with the three types of concrete foundations building foundation and home foundations. Slabs for colder climates, part 2: installing frost. Related content: slabs for colder climates, part 1: the how and why of frost protected shallow foundations as energy savings and the conservation of resources increasingly drive decision making for homebuilders, frost protected shallow footings offer a good method for constructing slab on grade foundations. Frost protected shallow foundations: common questions and. Question no 7: how energy efficient and comfortable are slab foundations with frost protected footings? the insulation requirements for frost protected footings are minimum requirements to prevent frost damage the requirements will provide a satisfactory level of energy efficiency, comfort, and protection against moisture condensation. Frost protected shallow foundations. Pictured below is a frost protected shallow foundation being used for an on grade concrete slab foundation, but it can also be used for stem wall, floating slab, and unvented crawlspace foundations photo courtesy of home innovation research labs. Frost protected monolithic slab youtube. Subscribe please one of the cold spots on a house is where the edge of a slab is exposed to the outdoors this thermal bridge, is really more like a thermal runway because. Foundations slab on grade insulated publications. Able to successfully construct a frost protected, slab on grade foundation the guide is intended to give builders the knowledge and confidence to design and construct trouble free foundations for design and site conditions that fall within the guidelines set out in this booklet, a frost protected, slab on grade foundation can be designed and. Monolithic or floating slab foundations for garages, sheds. Floating or "alaska" slab foundations can save building cost and time when used on garages, sheds and small barns properly designed monolithic floating slab foundations are approved for use on garages and accessory buildings by many municipalities, north and south, across the u s.


Day 57 of Stanley Quips: A Bridge[stone Arena] Too Far?
And within the span of two games, the tables have turned in this Stanley Cup finals. Honestly, I haven't found this series to be any more enticing as the NBA finals. Sure, all the shenanigans from Nashville's side have been beautiful to watch and a true breath of fresh air to see. But say what you want about agreeing with Charles Barkley: there just hasn't been a single game between Pittsburgh and the Predators that has gone down to the wire from start to finish in this entire series except maybe Game 1. Even that circumstance came after Nashville was down 3-0 coming into the second period. Otherwise, we have seen blowout after blowout with each team hoping that their goalie stands tall when counted upon.
After having Matt Murray save Pittsburgh's bacon in the first two games, Nashville finally broke him when the series was taken to their home rink. In 64 shots in the first two games, Murray gave up only four goals. In the next 59 shots on goal, he gave up nine. These are dark times for someone who should be already considered one of the best goaltenders in the league.
Murray still has just 62 career regular season games under his belt, but he has recorded a career quality start percentage that is still above 60% in both the regular season and postseason and is still just 23-years old. I have explained previously how his relative numbers in junior were a solid enough indication that his current numbers are not a fluke and it would be shocking if he horrifically regresses. At the very least, that's why it will be amazing if Murray continues to be bad throughout the rest of these playoffs. Only a re-aggravation from his injury that he picked up during the very first warm-up of the postseason can explain such a circumstance.
As for Pittsburgh's defense, it has been a known fact all year, even with Kris Letang on the team, that they have been miserable. They were 24th in the NHL in un-adjusted shot attempts against per hour while at even strength at 57.5 and that number has only changed to 59.6 in the playoffs. It's really the offense that has staggeringly worsened as the shot generation has dwindled from an eighth best 57.8 attempts per hour to 51.0 during the postseason.
Evgeni Malkin, in particular, has been an unmitigated disaster. Despite having two goals, he has only been on the ice for an average of 33.8 shot attempts for per hour. This is considering that last Monday, Malkin's most common defense pair that he played with was Olli Maatta and Trevor Daley. When Maatta has played with Malkin this postseason, the two have only seen 46.1% of their shot attempts go in their favor. Meanwhile, Malkin has seen 51.8% of his shot attempts go in his favor when playing with Justin Schultz. More of the Schultz-Cole pair for him please.
Also, it might be time to see a little Mark Streit get some playing time for once. Last time I checked, he was one of Philadelphia's most dependable defensemen before being (eventually) traded to the Pens. Yet somehow, the 38-year old has only played three playoff games this year and was considered a lesser option than pokemon-in-training Chad Ruhwedel. It is beyond obvious how poorly Pittsburgh has struggled getting the puck out of their zone, you would have thought you were seeing the postseason edition of the Washington Capitals instead.
On the other side of things, Nashville's top line of Filip Forsberg, Pontus Aberg and Colton Sissons with P.K. Subban and Mattias Ekholm might as well be the most dominating quintet in the postseason. All five of them are experiencing over 60% puck possession this series and are making players like Malkin, Maatta, Daley and Patric Hornqvist look like Wilkes-Barre Scranton Penguins. Now that the Penguins have last change, I would stop at nothing at having Sidney Crosby attack this group.
During this series, Crosby's most common opponents have amazingly been the Ryan Ellis-Mattias Ekholm pair (over 38 even strength minutes) and Nashville's second line of Viktor Arvidsson, Mike Fisher and James Neal. Meanwhile, you have to look at him playing between 16 and 18 minutes of even strength ice time against Nashville's aforementioned true lineup of death. Why would this ever be acceptable if you're a Penguins fan?!?!? Last time we checked, he's Sidney Crosby. The greatest player of his era should be playing against the best players every single shift under any circumstances.
Pittsburgh's cards are really not on their side thanks to so many players being injured and out of form, but it's not like this is an impossible task for them to win the Stanley Cup. Moneypuck.com has the Penguins trailing in total expected goals 8.6-10.8 while the actual total has been 11-13. They have been slightly snake-bitten on the penalty kill as the Predators have scored on four of their 16 tries when the really should have scored on 2.6 of those occasions. That being said, their power play has been in shackles this series scoring once and 1.8 times in actual and expected goals, respectively, in their 16 attempts.
Streit will be a major help on the man advantage. Play him instead of Maatta, a young defenseman that really has struggled to live up to his massive potential of late, and put Malkin and Crosby in significantly more advantageous situations and the Penguins might see themselves in a different light in these Finals than they have been this past six days.


Moviegoers may or may not stand up and clap to the rhythm of the song when James Cagney starts singing "You're a Grand Old Flag" in the film "Yankee Doodle Dandy," which is what happened when the stage version was performed in Stockton many years ago.
Nonetheless, the Friends of the Fox offering, which screens Friday at 7 p.m. at the Bob Hope Theatre as part of the classic cinema series, is a rousing tribute to George M. Cohan that gets the patriotic juices flowing a week before the Fourth of July, which, incidentally, was the date of Cohan's birth.
"I think that was the last show I did on the old campus at Delta," remembered longtime director Al Muller, who staged the play "George M." in 1976. "I chose it because it's a rousing good piece of theater that would be well-received."
His instincts were correct. An actor from Fresno who had always wanted to play Cohan commuted to Stockton to play the role, and when the flag dropped for the closing number of "You're a Grand Old Flag," everyone in the house was on their feet.
"It's an absolute winner, a great show for families to be a part of and to lose themselves in positive stuff," Muller said.
The film version generates the same reaction.
Some have suggested Cagney, best known for his 1930s tough-guy roles in "Public Enemy" and "Angels With Dirty Faces," among others, won his only best-actor Oscar for the role because of the patriotism of the film released in 1942, when the country was in the midst of fighting World War II.
The suggestion, though, slights the surprise performance by Cagney.
"For Cagney, it's a personal triumph, easily his top cinematic performance," Variety raved upon the movie's release. "He does Cohan like a relative."
Years later, critic Roger Ebert said, "The greatness of the film resides entirely in the Cagney performance."
Fred Astaire turned the role down, and Cagney, who had danced on stage before becoming a film actor, seized the role with Cohan's approval.
The film, and later the stage play "George M." (which starred Joel Gray on Broadway), chronicles Cohan's rise from his vaudeville days with his family, who performed as The Four Cohans, through the days he ruled Broadway as a writer, songwriter, performer, director and producer.
Cagney replicates Cohan's energy and doesn't falter, whether singing, dancing or interacting with the other characters.
The movie glides along with the help of Cohan's most memorable tunes, including "The Yankee Doodle Boy," "Give My Regards to Broadway," and the World War I anthem "Over There."
Cohan was defined by his flag waving, sentiment, rhythm and noisy, brash personality, according to Brooks Atkinson, renowned theater critic for the New York Times from 1925 to 1960 for whom a Broadway theater is named.
He called Cohan a "freak figure in the theater game," in part because of his uncanny ability to succeed on so many levels.
His patriotic fervor, Muller notes, was self-serving.
"But what's wrong with that?" Muller asked. "If you pull back the layers you reveal something that grabs someone else."
The patriotic-tinged film that was released on Memorial Day 1942 was directed by Hungarian-born Michael Curtiz, who directed 173 films during a nearly 50-year career. He was nominated for a best director Oscar for "Yankee Doodle Dandy" but lost to himself: He won the Oscar that year for directing "Casablanca." He later would direct Joan Crawford in her Oscar-winning role in "Mildred Pierce," Bing Crosby in "White Christmas," Elvis Presley in "King Creole" and John Wayne in "The Comancheros."
Before "Yankee Doodle Dandy," he had worked with Cagney in 1938's "Angels With Dirty Faces."
The actor's more familiar gangster roles made his casting in "Yankee Doodle Dandy" so surprising for audiences.
"Cagney was a very well-known entertainer," Muller said. "That's the way those things happen. They put a person in role that had a name everybody knew, and you can teach (him) to dance. In a show like that, you have to be able to sing. The dancing can be slick without being something Baryshnikov would do."
Cagney was credited with nailing Cohan's dance style and memorably ad-libbing a tap dance down a flight a stairs near the movie's end.
Tonight's show is preceded by a pipe organ concert by Tom Thompson beginning at 6:30 p.m. The ticket office opens at 6 p.m.


This morning it was – 30 degrees Celsius and it has not warmed up a lot. However, all athletes are handling the cold very well by now.
Unfortunately, James Innes had to scratch. He got a ride in with our guides. Enrique made it on his on and a long time before cut-off but will likely not continue.
Everybody else is doing well. Florian is now on his way to Pelly Farm and if he does not run into any unexpected difficulties he should win. First on foot is Jan but there is a race now. When Gavan came to Pelly Crossing and realised Jan had just left he did not stop for long. It will be interesting to follow those two guys now.
Bikers Tim and Wolfgang are on their way to Pelly Crossing. 66 year old Wolfgang is amazing. The things he has done in his sporting life are pretty crazy – amongst them a Deca Triathlon (38 km swim, 1,800 km bike, 422 km run). How is that for a start?
Also going strong are Bernadette Benson and Davide Lugato. Both on their way to Pelly Crossing.


To signup for 2018 Kawaga Alumni Fantasy Weekend, Please CLICK HERE.
Whether it's been five years or 50 years since you've spent a summer on the Shores, you'll never forget your first tapping ceremony, running to archery on D2, sitting on sunset dock, or staying up late talking to your cabin mates. We know you can't be a camper forever, but you will always be a member of the Kawaga Nation. One-hundred years and counting! You are indeed part of something special, and there are many ways for you to stay connected.
The Kawaga Spirit is alive and well. Our unique yet shared experience — and the values Kawaga continues to stand for — are something we're so fortunate to have had in our lives. We should continue being connected and being a part of Camp. And, we should do our part to assure that generations more will continue to experience the magic that we know as Kawaga. Be Kawaga!
As part of our Alumni celebration, a tribute video was created that we want to share with all of our Kawaga family.
Now's the time to start planning for Alumni Weekend 2016! Please clear your calendars for June 7-10, 2018. This past summer's event was nothing short of amazing. Let's make Alumni Weekend an ongoing tradition!


Lasers have been used to treat dental problems for more than 2 decades. The FDA has actually approved its use in dentistry, but the American Dental Association has not given its Seal of Acceptance for its use in Orem, Utah, and in the rest of the US. The seal is a way for the association to tell professional dentists and patients that a certain device can be safely and effectively used for dental treatments. The association however, is still optimistic, that one day, they will be able to approve its use for the field of dentistry. It is very important to understand that the lasers used for dental procedures are not like the ones used in phototherapy to deal with pain and inflammation.
Cankers, Biopsy, and Lesions – lasers can be used to remove a small piece of tissue in the body so that it can be examined for cancer, this is also known as a biopsy. Lasers can also be used to get rid of canker sores, and lesions inside the oral cavity.
Gum disease – lasers can be used to remove the damaged areas of the gums during a root canal, it can also be used to reshape the gums.
Teeth Whitening – lasers can activate the peroxide bleach solution so that the in-office whitening treatment will be able to provide you with great results.
Tooth decay – lasers can be used to remove specific areas in the tooth that has been decayed. It can also be used to prepare the tooth prior to filling.
How do lasers work for dentistry treatments?
Lasers can be used in many different ways for dentistry, it can deliver energy in the form of light, and it can act as a cutting instrument that removes tissue that comes into contact with it. Lasers can also be used to strengthen the filling used to treat tooth decay by strengthening the bond between the filling and the tooth. And as mentioned, in whitening treatments, lasers can be used as a heat source to enhance the effects of the whitening chemicals.
What are the advantages and disadvantages of using laser in dentistry procedures?
A dental drill is cheap, where as a laser equipment can cost several thousand dollars, this is why treatments that use lasers will also be expensive.
Although using lasers can make treatments less painful, you should know that it cannot totally eliminate the need for anesthetics.
Although lasers can be used for various procedures, it cannot be used to completely replace the dental drill.
Lasers can only be used on teeth, not on fillings.


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Piano Chord Theory
Home » Piano Chords » Piano Chord Theory
In the next chord piano lesson I'll show you everything you should know about the theory behind piano chords. Learning to play the piano becomes easier when you understand how music is structered.
As far as I'm concerned this is a step further in world of piano harmony. It's not so complicated to follow and anyways, I believe we all should be eager to know more and get to the bottom of music in order to become better musicians.
However, it's also possible to play chords just by reading the symbols and following the songs. Al-right, let's get to business with the basics of piano chord theory.
When we use chords in a song we do it in order to accompany a certain melody.
But where do the chords derive from?
Well, just like the melody of song derives from a certain scale (For example the melody of "Jingle Bells" is based on a major scale) so does the chords.
Let's say we play Jingle Bells in C major. We could assume that the melody will be written out of the notes of C major.
And it really is so:
This is very useful for playing melodies by ear since it helps us to know the logic in a song and limit our notes options. All we have to do is hear if a song derive from a major scale or a minor one, and then trust our ear and intuition to figure the melody out.
But what happens if we would like to find the harmony of a song? Is there some logic in that aspect too? You bet there is! Just like melodies, chords derive from scales. That's the basics of piano chord theory. So if we would like to find the harmony of "Jingle Bells" we would search for chords that belong to C major.
Let's get to know the family of C major. This is quite easy. The members of the family are very friendly. Scales are divided to scale degrees. We state their number in roman letters.
The first chord of C major scale would be C major. We start from C, and then we skip a note in the scale. Then we press on E, then skip a note again and press on G. This is already familiar to you - I'm sure.
The second chord of C major would be D minor. We start from D skip the E, Press on F (we follow the notes of the scale), skip G , and press on A.
We continue this procedure and this is what we get.
Piano Chord Theory Exercise
Find all the chords of C major from the first degree to the seventh degree. Play the chord with the right hand and the bass with the left hand. After you found a chord name its degree and its type (minor, major or diminished).
O.k. now we are familiar with the family of C major. Are the other major chords any different?
Not at all. Since all major scales share the same sequence of tones and half tones then all the chords of a major scale would appear in the same order according to their scale degree. D minor for example, is the second chord on C major. We can say that the chord which is built on the second scale degree of G major (A) would be a minor chord a well (Am).
This next image explains my words clearly.
Later on when we are a bit further with piano chord theory we will learn to transpose songs into different scales. This information of piano chord theory would be very valuable to us then but let's take it one step at the time.
Another Piano Chord Theory Exercise
Find all the chords of these major scales from the first degree to the seventh degree. Play the chord with the right hand and the bass with the left hand. After you found a chord, name its degree and its type (minor, major or diminished). G, D, A, E, B
If you're motivated you could find the chords of all scales. This takes quite some time and isn't always useful for it's a lot of information to process.
Chords in the Minor Scales
The chords in the minor scales are formed at the same way as in the major scale. Since every major scale has its parallel minor scale you can say that the chords of A minor for example are parallel to the chords of C major only starting from the sixth degree.
The only chord which stands as an exception to this rule is the fifth degree. We're going to cover that in our next lesson where we're going to talk about the three triads of the main scale degrees so stay tuned.
Click here if you haven't signed to Piano Playground, our free E-zine yet make sure you do that in order to get the username and password codes for the Trouble piano sheet I provide here under.
Click here for a full printable piano chord chart of both major and minor chord scales degrees.
One of the main reasons to learn the secrets of chord theory is to be able to play piano by ear. It's a big problem to train your ear to identify all the various piano notes but luckily I have found a great solution for you. You can improve your ability to play piano by ear simply by playing the revolutionary new computer game called "Perfect Your Pitch Pro". This great computer game is part of the Rocket Piano Ultimate Piano Learning Kit.
Training your ear by playing "Perfect Your Pitch Pro" is fun and it will fast track you to playing your favourite songs by ear! And Rocket Piano have an amazing method that will get you there like no other piano teacher would. Click here to check out the Rocket Piano Ultimate Piano Learning Kit.

redpajama_set_name: RedPajamaCommonCrawl


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October bountiful for ports on East, Gulf coasts
'Port of Savannah continues to outperform relative to the national market'
Fall has been fruitful for U.S. ports on the East and Gulf coasts but not as bountiful for at least one West Coast gateway.
The Georgia Ports Authority reported Monday that it handled 552,800 twenty-foot equivalent units in October. That's up 9.6% — 48,460 TEUs — from October 2021. Meanwhile, the Port of Long Beach, California, in October moved 658,428 TEUs, a 16.6% decline from the same month last year.
GPA Executive Director Griff Lynch said October was the Port of Savannah's second-busiest month on record, behind only August of this year, when the port handled 575,500 TEUs.
"Customers continue to bring new or expanding business to the Port of Savannah, drawn by our global connectivity and the supply chain network that links Savannah to major U.S. markets," Lynch said in a news release. "We can report that ships at anchor are trending downward, and expanded berth capacity coming online next year will allow us to serve our growing customer base with even greater efficiency."
The port said in the first four months of its fiscal year, 160 importers were either new or existing customers that grew their Savannah trade by 20% or more, resulting in an additional 107,000 TEUs from July through October compared to the previous year.
"There has been downward pressure on the total U.S. container trade related to inflation and a shift in consumer spending toward services such as restaurants and travel," said Joel Wooten, chairman of the GPA board. "However, the Port of Savannah continues to outperform relative to the national market, driving new business for Georgia."
The GPA said recent data showed East Coast ports have increased their market share of the container trade from 47% in July 2021 to 48.4% in July of this year.
October's numbers also showed significant growth at the Port of Brunswick. The GPA said Colonel's Island Terminal handled 70,233 units of roll-on/roll-off cargo in October, a year-over-year increase of 22,045 units — or nearly 46%.
Much of that increase could be attributed to an easing of the semiconductor shortage.
"Greater availability of computer chips has allowed carmakers to increase production," GPA Chief Commercial Officer Cliff Pyron said. "This, combined with manufacturers' traditional end-of-the-year push, yielded strong results for our October auto volumes."
Container volume increases in South Carolina
According to its website, the South Carolina Ports Authority moved a total of 256,879 TEUs last month, up from 226,807 TEUs in September and 234,923 TEUs in October 2021.
As of 2 p.m. EDT Monday, South Carolina Ports had not issued a news release with its October volumes, but its statistics page showed it handled 132,639 TEUs of exports in October and 124,239 TEUs of imports.
Looking at the numbers, it appears last month was the best October on record for South Carolina Ports. The same was true for September.
Export record in Corpus Christi
The Port of Corpus Christi on Texas' Gulf Coast set a monthly crude oil export record of 2.2 million barrels per day in October. That's a more than 60% market share of the national total crude export market, the port said.
The port also set a record in the third quarter, exporting a total of 48.3 million tons, largely crude oil, surpassing the record from just the second quarter of 46.4 million tons, a 4% increase.
"The growth primarily was a result of strong exports of United States-produced crude oil to Western European buyers who have moved away from Russian crude imports," the Port of Corpus Christi said in a news release late last week. "The U.S. and its Western European allies have placed restrictive trade sanctions on Russian crude oil as a result of the Russian invasion of Ukraine. Added strength in exports came from refined petroleum products and liquefied natural gas."
It said additional tonnage records have been achieved this year in renewable energy components as more wind turbines and blades are moved through the Port of Corpus Christi.
The port said crude oil shipments in Q3 totaled 28.7 million tons, up 5% from Q2. Refined products totaled 8.3 million tons, a 4.4% increase. LNG shipments rose 5.8% to 4.2 million tons and the dry bulk cargo volume grew 3.7% to 2.1 million tons.
"The Port of Corpus Christi is a key economics engine, not just for the Texas Coastal Bend region but also the state and the nation," Charles Zahn Jr., chairman of the port commission, said in a statement. "This success also allows the Port of Corpus Christi to reinvest into this great community and plan for future infrastructure improvements that will further the port's commitment to serving not only its existing customer base but also attracting new customers to the region."
Volumes down in Long Beach
In its cargo report late last week, the Port of Long Beach said its volumes "eased up in October following reduced consumer demand and a shift of imported goods toward the Gulf and East coasts."
The port said October imports were down 23.7% year over year to 293,924 TEUs and exports dipped 2% to 119,763 TEUs. Empty containers fell 13.4% from October 2021 to 244,743 TEUs last month.
Putting a positive spin on the declines, Mario Cordero, executive director of the Port of Long Beach, said that the "supply chain is returning back to normal and cargo continues to move, so I am optimistic that store shelves will be stocked and goods will be available for delivery during the holiday season."
The port noted in its news release that in the first 10 months of 2022 it moved 8,000,811 TEUs, a 1.5% increase from the same period in 2021.
"Despite surging inflation and interest rates, economists say consumers still have enough resources to weather economic headwinds," the port said. "Experts feel softening consumer activity will lead to a better balance between supply and demand and reduce stress on the national supply chain."
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T.NETWORK Market News Update Week 4
T.NETWORK-Weekly-Market-Update-Week-4..._Download
Rough start to 2023 for dry bulk, tanker, gas, container shipping
BDI dry bulk shipping index sinks to lowest point since June 2020 "Spot rates are off to a slower start in 2023 across...
Gulf Coast ports see record container volumes in 2022
Houston, Mobile hit all-time container volume highs; Corpus Christi exports more crude oil Ports in both Houston and...


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typedef CLASS RequestHeader* iox_request_header_t;

/// @brief const request header handle
typedef const CLASS RequestHeader* iox_const_request_header_t;

/// @brief extract the request header from a given payload
/// @param[in] payload the pointer to the payload
/// @return a handle to the request header
iox_request_header_t iox_request_header_from_payload(void* const payload);

/// @brief extract the request header from a given payload
/// @param[in] payload the pointer to the payload
/// @return a handle to the request header
iox_const_request_header_t iox_request_header_from_payload_const(const void* const payload);

/// @brief set the sequence id of the request header
/// @param[in] self handle to the request header
/// @param[in] sequenceId the new sequence id value
void iox_request_header_set_sequence_id(iox_request_header_t const self, const int64_t sequenceId);

/// @brief returns the rpc header version
/// @param[in] self handle to the request header
/// @return rpc header version
uint8_t iox_request_header_get_rpc_header_version(iox_request_header_t const self);

/// @brief returns the rpc header version
/// @param[in] self handle to the request header
/// @return rpc header version
uint8_t iox_request_header_get_rpc_header_version_const(iox_const_request_header_t const self);

/// @brief returns the sequence id
/// @param[in] self handle to the request header
/// @return sequence id
int64_t iox_request_header_get_sequence_id(iox_request_header_t const self);

/// @brief returns the sequence id
/// @param[in] self handle to the request header
/// @return sequence id
int64_t iox_request_header_get_sequence_id_const(iox_const_request_header_t const self);

/// @brief returns a pointer to the user payload
/// @param[in] self handle to the request header
/// @return pointer to the payload
void* iox_request_header_get_user_payload(iox_request_header_t const self);

/// @brief returns a pointer to the user payload
/// @param[in] self handle to the request header
/// @return pointer to the payload
const void* iox_request_header_get_user_payload_const(iox_const_request_header_t const self);

/// @brief returns a pointer to the chunk header
/// @param[in] self handle to the request header
/// @return pointer to the chunk header
iox_chunk_header_t* iox_request_header_get_chunk_header(iox_request_header_t const self);

/// @brief returns a pointer to the chunk header
/// @param[in] self handle to the request header
/// @return pointer to the chunk header
const iox_chunk_header_t* iox_request_header_get_chunk_header_const(iox_const_request_header_t const self);

#endif

redpajama_set_name: RedPajamaGithub


Close your eyes and try to imagine this scene: You wake in the morning as the sun peeks above the watery horizon of Lake Erie. In the distance you can hear the rustle of leaves from trees that fill nature preserve nearby. Just ahead you can see the cool waters of a swimming pool where your close friends are relaxing. While this scenario may be fictitious the setting described is real! The scene described is Sawmill Creek Resort, the location for Sing a New Song 2011.
Arriving at Sawmill Creek Resort in Huron/Sandusky, Ohio, you immediately sense something special. Nestled on the shores of Lake Erie, The Lodge, 18-hole Tom Fazio Golf Course, Marina and Shops are set on 235 –acres of affordable luxury. The Lodge features 240 deluxe guest rooms and suites, creative cuisine at Salmon Run Restaurant with patio dining, casual fare in Trappers Deli, indoor and outdoor pools, game room and casual lobby sitting rooms with decor themed to reflect the North American Woodland Indigenous Peoples. Step out of the Lodge to experience the lakefront beach, tennis, and the Sawmill Creek Shops. Stroll down to the marina on Lake Erie or enjoy Sheldon Marsh Nature Preserve, representing some of the last remaining undeveloped stretches of shoreline in the Sandusky Bay region. After a round of golf or lesson with the Pro, enjoy a casual lunch or dinner at Mulligan's Pub covered deck offering views of the pond on the 9th green. Head for the marina to the award winning Mariner's Dockside Restaurant overlooking the Lake and the176-slip marina. The screened patio is a pleasant dining option on a warm summer evening.
Adjacent to the Resort, this preserve and contiguous wetlands comprise some of the last remaining undeveloped stretches of shoreline in the Sandusky Bay region. The main path through the woods, past the wetlands, was the original automobile entrance to Cedar Point Amusement Park in the early 1900's. Walk the trail to the barrier beach for the spectacular view of Lake Erie. This superlative mix of habitats provides for one of Ohio's premiere birding locations.


Experienced Head Of Human Resources with a demonstrated history of working in the building materials industry. Skilled in Negotiation, Budgeting, HR Consulting and Coaching. Strong human resources professional graduated from National College of Ireland.


Hello to everyone and welcome back, back to school!
Welcome back from your summer vacation (for those who did), from summer jobs (inside and outside Athens) and from all kinds of trips. Even for those who did not leave at all, welcome back to the regularity of Athens and the occupations of the new "academic" period.
So what are we waiting for this new year? We hope for a minimal tranquility and optimism in social and economic terms, even a small assumption of the misery that has overwhelmed us in recent years. But in addition to our hopes and wishes, we in Open Space Studio do our best to take a few steps forward. We do everything we can to improve our space, our presence and our organization, always with the limitations – especially financial ones – that make it hard for us to do it on the first day of our venture.
We are offering again quite a few choices of regular classes for you: yoga, capoeira, tai chi (tàijí quán) / chigung, pilates, barre a terre, Indian dance and other.
We will also organize important workshop inviting distinguished teachers from abroad, mainly on weekends, so that they are accessible both in terms of time and cost. We believe that, in the current economic situation, our emphasis on such events is very useful for Greek people who is having difficulty traveling abroad to meet international personalities, as they have done before.
Finally, this year, we will make an effort to add a little more color and liveliness to our space. Without changing our character and style, we will frame our educational activity with more art, entertainment and other social events.
We are expecting your participation, your suggestions and any kind of contribution that can help us to our interesting journey. Welcome back!


text:
es un exfutbolista japonés. Jugaba de delantero y su último club fue el Kataller Toyama de Japón.

Trayectoria

Clubes

Estadística de carrera

J. League

Referencias

Personas de Tokio Metrópoli
Futbolistas de Japón
Futbolistas del FC Gifu
Futbolistas del Kataller Toyama
Futbolistas del Tochigi Soccer Club

redpajama_set_name: RedPajamaWikipedia


Christopher Melillo is the Founder and Managing Partner of Kaye/Bassman's Energy Practice. He manages teams in several areas of the energy industry as well as managing his own team in Oil and Gas Engineering and Geoscience recruitment along with coverage in Energy Commodity Trading. As Practice Leader, Christopher is responsible for the strategic design and development of the practice as a whole. In addition to setting the pace at Kaye/Bassman with his industry leadership, as a committee member of the Kaye/Bassman Foundation, he has been a big part of the growth and success of the Foundation. His passion for helping others has played a key role in the Foundation's milestone accomplishment of donating over $1,000,000 since inception.
Christopher started in the executive search industry in 1990 with PEI then recruited to Rapport Associates Ltd. Six months later, he was promoted to Vice President of Business Development and made Partner where he worked closely with the Interim Management Practice serving Third World development bank consultancies including two large projects for the World Bank – a project with National Housing Corporation in Papua New Guinea and a highway civil engineering project in Sao Paolo, Brazil. Chris was also responsible for production and administrative oversight of all three of Rapport's divisions including the Rapport Temporary Service.
In 1994, Christopher started Global Search, Inc. which was later acquired. He then started MAG Partners, Inc. and ultimately joined Kaye/Bassman in 2004.
Christopher studied Criminal Justice at Winona State University which he attended on a football scholarship. He lettered four years and was the Defensive Captain his Junior and Senior year. Christopher is now a competitive power-lifter and lives with his wife Jodi in Addison, TX.


text:
\section{Introduction}
\label{Intro}
We define a class of problems $H$ that are constrained discrete optimization problems with the objective function (OF) satisfying the principle of optimality (PO) without considering the constraints \cite{Bellman}. The constraint functions are assumed to be neither convex nor linear in their decision variables. Nor are the constraints required to satisfy the linear independence constraint qualification (LICQ) \cite{Nocedal}. These problems, in general, are NP-Hard \cite{NPHard}. Solving $H$ to optimality with reduced computational resources is highly desirable. Popular methods like Dynamic Programming (DP), Branch and Bound (BB), and Lagrangian relaxation methods can solve $H$ to optimality \cite{DynP1,DynP2,Bbound, Kolman, Fisher} as long as we place either linearity or quadratic conditions on the OF or constraints \cite{Bbound,LinShu}, while many others do not ensure optimality \cite{Plancher}.\\
\indent Examples of $H$ include resource allocation (power, ADC bits) in massive Multiple-Input Multiple-Output (MaMIMO) systems with constraints \cite{Zakir2}, constrained network optimization problems used in routing protocols \cite{NetApp}, and Reinforcement Learning (RL) applied to Markov decision processes with constraints \cite{RLbook}, to name a few.\\

\noindent The contributions of this paper are as follows
\begin{itemize}
\item we propose a novel multi-survivor Dynamic Programming (msDP) algorithm to solve $H$ optimally at significantly reduced computational cost, and,
\item we show that Constrained Markov Decision Processes (CMDP) with finite horizons belong to $H$.
\end{itemize}

\textit{Notations:}
The column vectors are represented as boldface small letters. The superscripts $T$ denote transpose. The terms $\mathbb{I}$ and $\mathbb{R}$, indicate space of integers and real numbers respectively. We represent a vector $\bold{x} = [x_1, x_2,\cdots,x_N]^T$ whose entries are constants up to $x_i$ for $i \le m$ as $\bold{x}^{m}$ and call such vectors partial, i.e., $\bold{x}^{m} = [a_1, a_2,\cdots, a_m, x_{m+1},\cdots, x_N]^T$ where $a_i$'s are constants. The $x_i$'s belong to a finite set $\mathcal{X}$ with cardinality $M$. If there are multiple of such partial vectors under consideration, we refer to the $k^{\text{th}}$ such vector as $\bold{x}_{k}^{m}$ and its elements as $\bold{x}_{k}^{m} = \big[a_{1}^{k},a_{2}^k,\cdots,a_{m}^k, x_{m+1}^k,x_{m+2}^k,\cdots,x_N^k \big]^T$.  The $j^{\text{th}}$ element of the set $\mathcal{X}$ is represented as $\{ \mathcal{X} \}_j$. If the $m^{\text{th}}$ element of $\bold{x}_{k}^{m}$ takes a value $\{ \mathcal{X} \}_j$, we represent such partial vector as $\bold{x}_{k}^{mj}$.\\

\indent The rest of this paper is organized as follows. We define the problem $H$ in Section \ref{Prob}. We first show in Section \ref{Cmdp} that the CMDP framework typically used in RL belongs to $H$. In Section \ref{TF} we describe the theoretical foundations that lead to the proposed msDP algorithm. We describe the proposed algorithm and evaluate its worst-case computational complexity in Section \ref{Algo}. We compare the performance and computational complexity of the proposed method with exhaustive search (ES) and the heuristic algorithm in Section \ref{Sim}, followed by the conclusions in Section \ref{Conc}.

\section{Problem Setup}
\label{Prob}
We define $H$ as stated below, where $\bold{x}^*$ is the optimal solution to $\eqref{cdo_1}$ if it exists.
\begin{equation}\label{cdo_1}
\begin{split}
&\underbrace{\text{max}}_{\substack{\bold{x}}} f(\bold{x}),\\
\text{ such that }&c_i(\bold{x}) \le \alpha_i;\text{ for }1 \le i \le Q_{I},\\
&h_j(\bold{x}) = \beta_j;\text{ for }1 \le j \le Q_E,
\end{split}
\end{equation}
where $\bold{x} = [x_1, x_2,\cdots,x_N]^T \in \mathbb{R}^N$. The OF $f(\bold{x})$ satisfies the PO without the constraint functions $c_i(\bold{x})$ and $h_j(\bold{x})$, where $\alpha_i, \beta_j \in \mathbb{R}, \forall i,j$ \cite{Bellman}. Thus, it can be written in the form $f(\bold{x}) = \sum_{i=1}^{N} b_i \phi_i(x_i)$ where $b_i \in \mathbb{R}$ are constants, $x_i \in \mathcal{X}$ can only take values from the set $\mathcal{X}$ whose cardinality is $M$, and, $\phi_i:\mathcal{X} \longrightarrow \mathcal{Y},\text{ for } 1\le i \le N$. The mapping $\phi_i$ need not be known in closed form. The constraint functions $c_i(\bold{x})$ and $h_j(\bold{x})$ are not limited to linear mappings in $x_i$, nor convex and need not satisfy LICQ \cite{Nocedal}. The terms $Q_{I}$ and $Q_E$ represent the number of inequality and equality constraints, respectively.

\section{Finite Horizon CMDP as problem $H$}
\label{Cmdp}
A finite-state Markov decision process is a 5-tuple $(X,A,P,r,\mu)$ where $X$ is the finite set of states, $A$ is the finite set of actions, $P:X \times A \times X^{'} \rightarrow [0,1]$ are the state transition probabilities $p_{x,a}(x^{'})$ that a state $x^{'}$ is attained when an action $a \in A$ is taken in state $x$. Both $x, x^{'} \in X$. A reward $r:X \times A \rightarrow \mathbb{R}$ is associated with an $a \in A$ from a state $x \in X$. The map $\mu : X \rightarrow [0,1]$ is the starting state distribution \cite{RL2}.\\
\indent A policy $\pi = (D_1, D_2,\cdots,D_{N-1})$ is defined as a set of decisions taken by an agent over states that maximize a certain cumulative reward. A stationary deterministic policy has a decision rule $D_i:X \rightarrow A$ that maps states to actions. In case of randomized policies, the decision rule $D_i$ is a random variable and described using state dependent distributions on possible actions. Hence, $D_i$ is described as $D_i:X \rightarrow \mathcal{P}(A)$ where $\mathcal{P}(A)$ is the probability distribution over actions defined by $q_i(a|x) = \mbox{Prob}[D_i=a|x_i]$ for every action $a \in A$.\\
\indent The cumulative reward is defined as $R = \sum_{i=1}^N \gamma^i r_i$ where $r_i$ is a reward accrued at $i^{\text{th}}$ time instance when the agent uses a policy $\pi$. The discount factor $\gamma \in [0,1]$. We can write the expected sum of discounted rewards as a function of a given policy and an initial state $x$ as $V^{\pi}(x) = \mathbb{E}[R \mid x_1=x] $\cite{RL2}, which can be rewritten as
\begin{equation}\label{cdo_3}
\begin{split}
&V^{\pi}(x) = \mathbb{E}\bigg[ \sum_{i=1}^N \gamma^i r_i\big(x_i,D_i(x_i)\big) \mid x_1=x\bigg],\\
&= \sum_{i=1}^N \gamma^i \hat{r_i}(x_i),\text{ where }\hat{r_i}(x_i) =  \sum_{a \in A} q_i(a|x_i)r_i(x_i,a),
\end{split}
\end{equation}
assuming a random stationary policy. Considering an initial distribution $\mu$ on all the possible starting states on set $X$, we can define the value of the policy as \cite{RL2}
\begin{equation}\label{cdo_5}
\begin{split}
J(\pi) &= \mathbb{E}_{x \sim \mu}\bigg[ V^{\pi}(x)\bigg] = \sum_{x \in X} \mu(x)V^{\pi}(x).\\
&= \sum_{x \in X} \mu(x) \sum_{i=1}^N \gamma^i \hat{r_i}(x_i) = \sum_{i=1}^N \gamma^i \phi_i(x_i),\\
\end{split}
\end{equation}
where $\phi_i(x_i) = \sum_{x \in X} \mu(x)\hat{r_i}(x_i)$, which is obtained by substituting $V^{\pi}(x)$ from \eqref{cdo_3}. We see that with $b_i = \gamma^i$ the OF $J(\pi)$ of \eqref{cdo_5} is similar to the OF $f(\bold{x}) = \sum_{i=1}^{N} b_i \phi_i(x_i)$ of $H$ in \eqref{cdo_1}.\\
\indent For the CMDP case, we have constraint functions that could be either secondary reward functions or penalty functions. The constraint functions $c$ defined as $c:X \times A \rightarrow \mathbb{R}$ such that $c^{\pi}(x) \le d$. The whole optimization problem is written as \cite{RL2}
\begin{equation}\label{cdo_6}
\underbrace{\text{max}}_{\substack{\pi}} J(\pi),\text{ such that }c(\pi) \le d.
\end{equation}
In \eqref{cdo_6}, $c(\pi) = \mathbb{E}[c^{\pi}(x)] = \mathbb{E} \big[ \sum_{i=1}^N \gamma^i c_i(x_i,a_i) \big]$.

\section{Theoretical Foundations of msDP}\label{TF}
In this section, we construct the theoretical foundations for the proposed msDP. We first define the Constraint Satisfaction Function (CSF).
We define a boolean function $A:\bold{x} \rightarrow \{0,1\}$ such that
\begin{equation}\label{cdo_8}
    A(\bold{x})=
\begin{cases}
    1,& \text{if } \bold{x} \text{ satisfies all the constraints }\\
    &c_i(\bold{x}), h_j(\bold{x}) \text{ of H; for all } i,j.\\
    0,              & \text{otherwise.}
\end{cases}
\end{equation}
We also define $A(\cdot)$ on a partially assigned vector $\bold{x}_{k}^{m}$ as $A(\bold{x}_{k}^{m}) = 1$ for $1 \le m < N$ if there exists at least one vector ${\bold{b}_k} = [b_{m+1}^k,b_{m+2}^k,\cdots,b_{N}^k]^T$ such that $b_i \in \mathcal{X}$ for $i > m$ that satisfies all the constraints. This is represented as
\begin{equation}\label{cdo_9}
    A(\bold{x}_{k}^{m})=
\begin{cases}
    1,& \text{if there exists at least one } \bold{b}_k \text{ defined}\\
    &\text{ above, that satisfies all the constraints }\\
    &c_i(\bold{x}_{k}^{m}), h_j(\bold{x}_{k}^{m}) \text{ for all } i,j.\\
    0,              & \text{otherwise.}
\end{cases}
\end{equation}

\subsection{Principle of Optimality}
We define a partially computed OF of $H$ as $\lambda(\bold{x}_{k}^{m}) = \sum_{i=1}^{m} b_i \phi_i(a_i)$ for $1 \le m < N$. It is to be noted that $A(\bold{x}) = A(\bold{x}^N)$ and $\lambda(\bold{x}^{N}) = f(\bold{x})$. Here $\bold{x}^N$ is a completely known vector.\\
\indent Now we show that $H$ does not satisfy the PO. We then introduce a multi-valued function $\mbox{max}_l\{\cdot\}$ that returns $l$ maximum values from its domain. Adopting $\mbox{max}_l\{\cdot\}$, we reformulate $H$ to satisfy the PO.\\

\newtheorem{thrm}{Theorem}
\begin{thrm}\label{thrm1}
If $\bold{x}^*$ is the optimal solution to $H$ described in \eqref{cdo_1} and if there exists at least one infeasible solution $\bold{x}_1$ to $H$ such that $f(\bold{x}_1) > f(\bold{x}^*)$ with constraint satisfaction function being true at some intermediate stage $l$ in the recursion $A(\bold{x}_1^l) > 0$, then it can be shown that $J = \underbrace{\max}_{\bold{x},A(\bold{x}) > 0}f(\bold{x})$ does not obey the PO.
\end{thrm}
\begin{proof}
We say that \eqref{cdo_1} satisfies the PO if we can express it as a value function \cite{Bellman}. That is, given
\begin{equation}\label{cdo_10}
\begin{split}
J &= f(\bold{x}^*) = J(x_1) = \underbrace{\text{max}}_{\substack{\{x_i\}_{i=1}^N,\\A(\bold{x}) > 0}}\Big\{\sum_{i=1}^{N} b_i \phi_i(x_i)\Big\},\text{ then}\\
J(x_i) &= \underbrace{\text{max}}_{\substack{x_i;\\A(\bold{x}^{i})>0}}\Bigg\{ b_i\phi_i(x_i) +  \underbrace{\text{max}}_{\substack{\{x_j\}_{j={i+1}}^N;\\{A(\bold{x}^{i+1}) > 0}}} \sum_{j={i+1}}^{N} b_j \phi_i(x_j) \Bigg\},\\
J(x_i) &= \underbrace{\text{max}}_{\substack x_i;A(\bold{x}^{i})>0}\Bigg\{ b_i\phi_i(x_i) +  J(x_{i+1}) \Bigg\}.
\end{split}
\end{equation}
\indent Let $\bold{x}_1$ be an infeasible solution to $H$ such that
\begin{equation}\label{cdo_10a}
\begin{split}
f(\bold{x}_1) &> f(\bold{x}^{*}),\text{ where}\\
A(\bold{x}_1) &= 0\text{ and }A(\bold{x}^*) > 0.
\end{split}
\end{equation}
However, at some intermediate stage $l < N$ in the recursion, the condition depicted below would arise as a consequence of no conditions placed on the constraints \cite{Nocedal, Boyd}.\\
As $\lambda(\bold{x}_1^l) > \lambda(\bold{x}^{*l}),\text{ such that }A(\bold{x}_1^l) > 0\text{ and }A(\bold{x}^{*l}) > 0: \lambda(\bold{x}_1^l) = \underbrace{\text{max}}_{\substack x_l;A(\bold{x}^{l})>0}\bigg\{ \lambda(\bold{x}_1^l), \lambda(\bold{x}^{*l}), \cdots \bigg\}$.
Thus, we can write the recursion at stage $l$ in \eqref{cdo_10} as $J = \lambda(\bold{x}_1^l) +  J(x_{l+1})$.
As a result, we see that the optimal solution $\bold{x}^{*l}$ is dropped against $\bold{x}_1^{l}$ at stage $l$. However, in the subsequent stage $r$, where $l < r \le N$, another candidate solution $\bold{x}_2^r$ is picked against $\bold{x}_1^r$ because the infeasibility of $\bold{x}_1^{r}$ shows up as $A(\bold{x}_2^r) > 0,\text{ and }A(\bold{x}_1^r) = 0$.
Consequently, $\bold{x}_1^{r}$ is dropped and we have the recursion equation at stage $r \le N$ as
\begin{equation}\label{cdo_14}
\begin{split}
J &= \lambda(\bold{x}_2^r) +  J(x_{r+1}).
\end{split}
\end{equation}
Extending the result to stage $N$, we can see that
\begin{equation}\label{cdo_14}
\begin{split}
J &= f(\bold{x}_2) = \lambda(\bold{x}_2^N) = \underbrace{\text{max}}_{\substack{\bold{x};A(\bold{x}) > 0}}\sum_{i=1}^{N} b_i\phi_i(x_i).
\end{split}
\end{equation}
However, by definition we have
\begin{equation}\label{cdo_14}
J = f(\bold{x}^*) = \lambda(\bold{x}^{*N}) = \underbrace{\text{max}}_{\substack{\bold{x};A(\bold{x}) > 0}}\sum_{i=1}^{N} b_i\phi_i(x_i),
\end{equation}
where $\bold{x}^{*} \ne \bold{x}_2$, hence, $H$ defined in \eqref{cdo_1} does not satisfy the PO.
\end{proof}
We now define a multi-valued function $\mbox{max}_{N_e}:\mathbb{R}^m \rightarrow \mathbb{R}^{N_e}$ such that it returns at-most $N_e$ maximum values over a combination of $m$ variables in its domain. We now rewrite $H$ in \eqref{cdo_1} using $\Gamma$ as defined below
\begin{equation}\label{cdo_15}
\begin{split}
&\underbrace{\text{max}}_{\substack {\bold{x}};A(\bold{x})>0} f(\bold{x}) = J = \text{max}\Big\{ \Gamma(x_1) \Big\},\text{ where}\\
&\Gamma(x_1) = \boldsymbol{\lambda}(\bold{\vec{x}}) = \underbrace{\mbox{max}_{N_e}}_{\substack \{x_j\}_{j=1}^{N};A(\bold{\vec{x}})>0}\Big\{\sum_{i=1}^{N} b_i \phi_i(x_i)\Big\},
\end{split}
\end{equation}
where $\boldsymbol{\lambda}(\bold{\vec{x}})$ is a vector of $N_e$ maximum values. That is, $\boldsymbol{\lambda}(\bold{\vec{x}}) = [\lambda(\bold{x}_1), \lambda(\bold{x}_2),\cdots,\lambda(\bold{x}_{N_e})]^T$ that corresponds to the $N_e$ solutions $\bold{\vec{x}} = [\bold{x}_1,\bold{x}_2,\cdots,\bold{x}_{N_e}]^T$. It is also to be noted that the CSF $A(\bold{\vec{x}})>0$ is true iff $A(\bold{x}_i)>0$ is satisfied for all  $\bold{x}_i \in \bold{\vec{x}}$.\\
\indent We also define the partially evaluated objective at stage $m \le N$ as $\boldsymbol{\lambda}(\bold{\vec{x}}^m) = [\lambda(\bold{x}_1^m), \lambda(\bold{x}_2^m),\cdots,\lambda(\bold{x}_{N_e}^m)]^T = \underbrace{\text{max}_{N_e}}_{\substack \{x_j\}_{j=1}^{m};A(\bold{\vec{x}}^m)>0}\Big\{\sum_{i=1}^{m} b_i \phi_i(x_i)\Big\}$. As before, the CSF  $A(\bold{\vec{x}}^m)>0$ is true iff $A(\bold{x}_i^m)>0$ is satisfied for all  $\bold{x}_i^m \in \bold{\vec{x}}^m$.\\
Given the optimal solution $\bold{x}^*$, we say that the value function $\Gamma(\cdot)$ in \eqref{cdo_15} satisfies the PO if we can write
\begin{equation}\label{cdo_16}
\begin{split}
\Gamma(x_i) &= \underbrace{\mbox{max}_{N_e}}_{\substack x_i;A(\bold{\vec{x}}^{i})>0}\Big\{b_i\phi_i(x_i) + \Gamma(x_{i+1})\Big\},\text{ where}\\
J &= f(\bold{x}^*) = \text{max}\Big\{ \Gamma(x_1) \Big\}.
\end{split}
\end{equation}
That is, the optimal solution is maintained at every stage of the recursion in $\Gamma(x_i)$.
\begin{thrm}\label{thrm2}
If $\bold{x}^*$ is the optimal solution to $H$ described in \eqref{cdo_1}, then with an appropriate choice of $N_e$ that is dependent on the constraint satisfaction function $A(\cdot)$, it can be shown that $\Gamma(x_1) = \underbrace{\max_{N_e}}_{\substack \{x_j\}_{j=1}^{N};A(\bold{\vec{x}})>0}\Big\{\sum_{i=1}^{N} b_i \phi_i(x_i)\Big\}$ always satisfies the PO.
\end{thrm}
\begin{proof}
Let $\bold{x}_1$ be an infeasible solution to $H$ as described in \eqref{cdo_10a} in Theorem \ref{thrm1}. Let the PO \eqref{cdo_16} hold true; we can then write the same at recursion $l \le N$ as
\begin{equation}\label{cdo_17}
\begin{split}
\Gamma(x_1) &= \underbrace{\mbox{max}_{N_e}}_{\substack x_l;A(\bold{\vec{x}}^l)>0}\Big\{b_l \phi_l(x_l)  + \Gamma(x_{l+1})\Big\},\\
&= \boldsymbol{\lambda}(\bold{\vec{x}}^l) + \Gamma(x_{l+1}).
\end{split}
\end{equation}
We now let $N_e$ be large enough such that $\boldsymbol{\lambda}(\bold{\vec{x}}^l) = [\lambda(\bold{x}_1^l), \lambda(\bold{x}^{*l}),\cdots]^T$. That is $(\bold{x}_1^l, \bold{x}^{*l}) \in \bold{\vec{x}}^l$.\\
\indent However, at some later stage $r$ where $l < r \le N$, we can write the recursion as
\begin{equation}\label{cdo_18}
\begin{split}
\Gamma(x_1) &= \underbrace{\mbox{max}_{N_e}}_{\substack x_r;A(\bold{\vec{x}}^r)>0}\Big\{b_r \phi_l(x_r)  + \Gamma(x_{r+1})\Big\},\\
&= \boldsymbol{\lambda}(\bold{\vec{x}}^r) + \Gamma(x_{r+1}).
\end{split}
\end{equation}
Now we note that $\lambda(\bold{x}_2^r) \in \boldsymbol{\lambda}(\bold{\vec{x}}^r)$ and $\lambda(\bold{x}_1^r) \not\in \boldsymbol{\lambda}(\bold{\vec{x}}^l)$. This is because, at this stage in the recursion, the infeasibility of the candidate solution $\bold{x}_1^r$ becomes known as indicated by $A(\bold{x}_1^r) = 0$. Thus the solution $\bold{x}_1^r$ is not part of $\bold{\vec{x}}^r$.\\
With the appropriate choice of $N_e$, it can be ensured that $(\bold{x}_2^r, \bold{x}^{*r}) \in \bold{\vec{x}}^r$. The determination of $N_e$ is discussed in Lemmas \ref{lemma3} and \ref{lemma4} in section \ref{TF}. Extending $r$ to $N$, we have $(\bold{x}_2^N, \bold{x}^{*N}) \in \bold{\vec{x}}^N$. Hence, we can write
\begin{equation}\label{cdo_19}
\begin{split}
\Gamma(x_1) &= \boldsymbol{\lambda}(\bold{\vec{x}}^N) =  \underbrace{\mbox{max}_{N_e}}_{\substack \{x_j\}_{j=1}^{N};A(\bold{\vec{x}}^N)>0}\Big\{\sum_{i=1}^{N} b_i \phi_i(x_i)\Big\},\\
&\text{with }\bold{x}^{*} \in \bold{\vec{x}}^N;\text{ Thus, }f(\bold{x}^*) = \text{max}\Big\{ \Gamma(x_1) \Big\}.
\end{split}
\end{equation}
Thus, with an appropriate choice of $N_e$, we see that the PO for \eqref{cdo_15} is always satisfied.
\end{proof}

\subsection{Trellis for H}\label{graph}
We define a graph $G(V,E,A)$ with nodes $V$, edges $E$, and edge label $A$ as
\begin{equation}\label{mlba_4}
\begin{split}
V_i &= \Big\{ x_{ij} \mid x_{ij} = \{ \mathcal{X} \}_j; 1 \le i \le N; 1 \le j \le M \Big\} \cup S \cup F,\\
E &=\Big\{(x_{ij},x_{{i+1}m}) \mid x_{ij} = \{ \mathcal{X} \}_j; x_{{i+1}m} = \{ \mathcal{X} \}_m;\\
&1 \le j,m \le M; 1 \le i \le N-1; (S,x_{1j}),  (x_{Nm},F) \Big\},\\
A &= \Big\{ \psi_i(x_{i+1} \mid x_{i}) =  \phi_i(x_i) \leftarrow (x_{i},x_{i+1}) \mid \forall x_i \in \mathcal{X};\\
&1 \le i \le N; \phi_N(x_N) \leftarrow (x_N,F) \mid \forall x_N \in \mathcal{X}; \\
& 0  \leftarrow (S,x_1) \mid \forall x_1 \in \mathcal{X} \Big\}.
\end{split}
\end{equation}
The nodes $S$ and $F$ are the starting and terminal nodes, respectively. The optimal solution $\bold{x}^* = [x_{1j},x_{2j},\cdots,x_{Nj}]^T$ can be thought of as a walk through this graph starting at node $S$ and ending at the destination node $F$ passing through the nodes $x_{ij} \in V_i$ from stage $i=1$ to $i=N$, along the edges $(x_{ij},x_{{i+1}m}) \in E$ accruing a reward $\psi_i(x_{{i+1}m} \mid x_{ij}) = \phi_i(x_{ij}) \in A$ that results in the maximum total accumulated reward $f(\bold{x}^*)$ such that all the constraints are satisfied. That is  $A(\bold{x}^*) > 0$. It can also be noted that this graph $G(V,E,A)$ can be qualified as a trellis  $T(V,E,A)$ \cite{Kolman}. An example $T(V,E,A)$ with $M=4$ is shown in Fig \ref{Fig2_mlba}.\\
\begin{figure*}[http]
\centering
\resizebox{.7\textwidth}{!}{
\input{Fig1_ICML2020_t.eps}
}
\caption{An example trellis $T(V,E,A)$ for $M=4$.}
\label{Fig2_mlba}
\end{figure*}
\indent A DP approach can not be used to obtain $\bold{x}^*$ as shown using Theorem \ref{thrm1}. We note from Theorem \ref{thrm2} that the PO is satisfied by using the multi-valued function $\mbox{max}_{N_e}$. Thus, maintaining multiple survivor paths $(N_e)$ at each stage of the trellis ensures optimality if $N_e$ is picked properly. An appropriate choice of  $N_e$ is discussed in the next subsection. Thus the DP algorithm is modified to perform Add, Compare, and Multiple Select (ACMS) as basic operation at each node in the trellis as opposed to Add, Compare, and Select (ACS). The algorithm is described in section \ref{Algo}.

\subsection{Determination of $N_e$}\label{SecNe}
In the Lemmas below, we establish a relationship between the number of survivors $N_e$ and CSF $A(\cdot)$ to ensure optimality. Due to the page limitation, the proofs are omitted.
\newtheorem{lemm}{Lemma}
\begin{lemm}\label{lemma3}
The number of survivor paths (or partial solutions) that need to be maintained at a given node $x_{ij}$ in trellis $T(V,A,E)$ to obtain optimal solution to $H$ is dependent on the constraint satisfaction function $A(\bold{x}^{ij})$ at the node $x_{ij}$ in the trellis. It can be shown that
\end{lemm}
\begin{equation}\label{cdo_lem1}
B(x_{ij}) \triangleq \sum_{k=1}^{L_{ij}} A(\bold{x}^{ij}_k),
\end{equation}
where $L_{ij}$ is the number of paths incident on the node $x_{ij}$, out of which $B(x_{ij})$ paths satisfy all the constraints as per the definition of CSF in \eqref{cdo_9}.

\begin{lemm}\label{lemma4}
The minimum number of maximum paths $N_e$ that need to be maintained in \eqref{cdo_16} at each stage in the recursion for optimality of $H$ can be expressed as a lower bound:
\end{lemm}
\begin{equation}\label{cdo_lem4_3}
N_e \ge \underbrace{\text{max}}_{\substack i} \sum_{j=1}^M \sum_{k=1}^{L_{ij}} A(\bold{x}^{ij}_k).
\end{equation}

\section{Multi-survivor Dynamic Programming Algorithm}
\label{Algo}
\begin{algorithm}[h!]
  \caption{Multi-survivor Dynamic Programming.}\label{AlgoMVA}
  \begin{algorithmic}
    \small
    \State {\bfseries Input:}{$M$,$N$,$A(\cdot)$,$\mathcal{X}$}
      \State $M\gets \text{Cardinality of sets }\mathcal{X}$
      \State $N\gets \text{Number of stages or variables of }f(\cdot)\text{ of problem H}$
      \State $A(\cdot) \gets \text{Constraint satisfaction function of H}$
      \State $\mathcal{X} \gets \text{Set of discrete values that }x_i\text{'s can take }$
      \State \text{Determine the path valency $E(x_{ir})$ for all nodes}
      \State \text{Initialize paths and its associated costs}
      \State $\scriptstyle \bold{x}^{1,1} = \{\mathcal{X}\}_1, \bold{x}^{1,2} = \{\mathcal{X}\}_2, \cdots, \bold{x}^{1,M} = \{\mathcal{X}\}_M$
      \State $\scriptstyle \lambda(\bold{x}^{1,1})=b_1\phi_1(\{\mathcal{X}\}_1), \lambda(\bold{x}^{1,2})=b_1\phi_1(\{\mathcal{X}\}_2), \cdots,$
      \State $\scriptstyle \lambda(\bold{x}^{1,M})=b_1\phi_1(\{\mathcal{X}\}_M)$
      \For{$i=2:N$}
           \For{$r=1:M$}
           \State{$m \gets 1$}
           	\For{$b=1:M$}
		   \If {$(x_{{i-1}b},x_{ir}) \in T(A)$}
			\For{$k=1:E(x_{ir})$}
			   \If {$A(\bold{x}_k^{ir}) > 0$}
			       \State{$x_{ir} =  \{\mathcal{X}\}_r$}
			       \State{$\bold{x}^{i,r}_k = [(\bold{x}^{i-1,b}_k)^T, x_{ir}]^T$}
    			       \State{$\lambda(\bold{x}^{i,r}_k) = \lambda(\bold{x}^{i-1,b}_k) + b_i\phi_i(x_{ir})$}
			   \EndIf
			\EndFor
		   \EndIf
		\EndFor
		\State{\text{Keep only $\{\bold{x}_m^{i,r}\}_{m=1,\cdots,E(x_{i,r})}$ paths, that }
		\State{$\text{ correspond to }E(x_{ir})$ maximum values of}
		\State{$\scriptstyle \Big\{\lambda(\bold{x}_m^{i,r})\Big\}_{m=1,\cdots,E(x_{ir})}$ and ignore the rest!}}
           \EndFor
     \EndFor
     \State{Process the termial node "F"}
     \State{$m \gets 1$}
     \For{$b=1:M$}
		\For{$k=1:L_{T}\text{ All paths incident on terminal node F}$}
			\State{$\scriptstyle \lambda(\bold{x}_m^F) = \lambda(\bold{x}^{N-1,b}_k)+b_N\phi_N(x_{Nb})$}
			\State{$\scriptstyle m \gets m+1$}
		\EndFor
     \EndFor
     \State{\text{Pick $\bold{x}^*$ that has maximum of $\Big\{\lambda(\bold{x}^F_k)\Big\}_{k=1,\cdots,m-1}$ }}
     \State{$\textbf{return }\bold{x}^* \text{ Optimal Solution}$}
  \end{algorithmic}
\end{algorithm}

\subsection{Evaluation of CSF}\label{const}
It can be shown that the $A(\bold{x}^m)$ can be evaluated at any intermediate stage $m \le N$ by posing it as an unconstrained discrete optimization (UDO) problem. The UDO problems can be solved in polynomial time using graph structures like Depth-First-Search (DFS), Breadth-First-Search (BFS), or BB algorithms \cite{Bbound, Ndale}.

\subsection{Computational Complexity Analysis}
\label{CCA}
The computational blocks of the msDP involve (i) evaluating the CSF $A(x^{ij}_k)$, and (ii) performing the ACMS operation on the $E(x_{ij})$ paths incident on a given node $x_{ij}$ of the trellis. For (i), a BFS or DFS can be used in such cases which has complexity of $O(E + V)$, where $E$ and $V$ are the numbers of edges and vertices of the trellis \cite{Ndale}. In the worst case of a fully connected trellis, $E = (N-1)M^2,$ and $V = NM$. Also, in the worst case scenario of $N_e^{'} = \frac{N_e}{M}$ incident on all the nodes in the given trellis, the net complexity of CSF evaluation $T_{CSF}$ can be expressed as
\begin{equation}\label{cdo_cca1}
T_{CSF} = N_e\Big((N-1)NM^2+N^2M\Big)\text{ for all the }NM\text{ nodes}.
\end{equation}
In case of (ii), the total number of ACMS evaluations for the trellis in the worst case is $T_{ACMS} = \frac{N_e}{M}NM = N_eN$. Thus, the complexity of msDP is $O(N_eN^2M^2)$ or in general $O(N_eN^{l})$, where $l \in \mathbb{R}$. On the other hand, the ES requires an evaluation of the CSF and OF for $M^N$ solutions. Hence its complexity is $O(M^N)$. In the case of learning techniques like RL, to guarantee an optimal solution, the complexity required is $\approx O(M^N)$ \cite{Watkins}.

\section{Simulations}
\label{Sim}
In this section, we apply the proposed msDP to solve (i) Analog to Digital Converter (ADC) Bit-Allocation (BA) problem for MaMIMO receiver, and (ii) DNA fragment assembly (DFA) problem that is a part of DNA sequencing \cite{Maria,DFA2}. We evaluate the performance and compare the number of computations\footnote{Number of computations = Actual number of CSF evaluations + ACMS operations.} against the ES and the heuristic suboptimal simulated annealing (SA) algorithms\footnote{The optimality is compromised against complexity with heuristic algorithms like SA.} \cite{SimAn2}.

\subsection{ADC Bit Allocation for MaMIMO}
The ADC BA problem is to assign the number of bits to be used by Variable-Resolution ADCs on different Radio Frequency (RF) paths of the MaMIMO receivers. An optimal BA ensures that the performance, of the receiver is maximized under a non-linear power constraint. It is to be noted that the OF is non-linear. In \cite{Zakir2}, the authors reduce this to a problem in $H$, which is described as
\begin{equation}\label{cdo_sim_ba1}
J = \underbrace{\text{max}}_{\substack{\{x_i\}_{i=1}^N;A(\bold{x}) > 0}}\Big\{\sum_{i=1}^{N} \frac{a_i^2}{b_i^2+d_i2^{x_i}}\Big\},
\end{equation}
where $a_i$, $b_i$, and $d_i$ are constants $\in \mathbb{R}$ that represent channel singular value, noise power, and coefficient of quantization noise due to bit allocation $x_i$ on the $i^{th}$ RF path, respectively. Here $N$ is the number of RF paths in the receiver. The CSF $A(\bold{x}) > 0$ iff the power constraint $\sum_{i=1}^{N} 2^{x_i} \le P_t$, and bit-ordering  constraint $x_1 \ge x_2  \ge \cdots  \ge x_N$ are satisfied. The total ADC power budget is $P_t$. Hence we have
\begin{equation}\label{cdo_sim3}
    A(\bold{x}) =
\begin{cases}
    1,\text{ if } &\sum_{i=1}^{N} 2^{x_i} \le P_t,\\
       &x_1 \ge x_2  \ge \cdots  \ge x_N.\\
    0, &\text{ Otherwise}.\\
\end{cases}
\end{equation}
We perform simulations considering the parameters used by the authors in \cite{Zakir2}. They consider a maximum bit resolution of $M=4$, such that $x_i$'s (bits) take values from the set $\mathcal{X} = \{1,2,3,4\}$ for $1 \le i \le N$. We assume the number of RF paths in the receiver as $N=12$ and the power budget of $P_t=48$. For this case, we achieve $N_e \ge 13$. The number of computations with msDP, ES, and SA algorithms are shown in Table \ref{tab2}. Both the brute-force and msDP methods obtain the optimal solution of $\bold{x}^* = [4,2,2,2,2,2,1,1,1,1,1,1]^T$ \cite{Zakir5}.

\subsection{DNA Fragment Assembly}
We apply our proposed formalism to the DFA problem, which has equivalence to the TSP \cite{Maria, boundTSP}. DFA is the challenging process of the DNA sequencing \cite{Jay}. DNA sequencing's main problem is that the current technology can not read an entire genome in one shot, sometimes not even more than 1000 bases. Even the simplest organisms, like bacteria and viruses, have much longer genome lengths. Consequently, the genomes are broken down into smaller readable fragments and sequenced \cite{Sanger}. In this step, $N$ copies of DNA are created.  A short fragment is derived from each of the replicated DNA at some random location. These short fragments are sequenced. The final and challenging step is to assemble these sequenced fragments to obtain the original DNA sequence. This step is called the DFA, which is illustrated through an example below \cite{Maria}.\\
\indent We assume the DNA sequence to be $TTACCGTGC$, and the fragments sequenced using 4 DNA copies being $F_1 = ACCGT$, $F_2 = CGTGC$, $F_3 = TTAC$, and $F_4 = TACCGT$. The overlap of each fragment with the other three fragments are computed using similarity measure. Based on this similarity measure, the order of fragments are determined which in the case of this example is $F_3F_4F_1F_2$.\\
\indent The DFA problem is posed as a maximization problem where the sum of the similarity measures\footnote{The similarity scores between different pairs of fragments are derived using the Smith-Waterman algorithm \cite{Maria, Smith}.} between two adjacent DNA fragments is maximized. This is subject to the constraint that there is no repetition of the fragments in the sequence. Formally, this problem is defined as \cite{Maria}
\begin{equation}\label{cdo_sim1}
J = \underbrace{\text{max}}_{\substack{\{F_{\sigma_i}\}_{i=1}^N;A(\mathcal{F}) > 0}}\Big\{\sum_{i=1}^{N-1} \phi(F_{\sigma_i},F_{\sigma_{i+1}})\Big\},
\end{equation}
where $\mathcal{F} = \{ F_{\sigma_1}, F_{\sigma_2},\cdots,F_{\sigma_N} \}$ is the optimal solution indicating the original DNA sequence, $\sigma_i$ is the fragment index, and $\phi(F_{\sigma_i},F_{\sigma_{i+1}})$ is the similarity measure between the fragments $F_{\sigma_i}$ and $F_{\sigma_{i+1}}$. Here, the set $\mathcal{X}$ is collection of DNA fragments $\{F_{\sigma_j}\}_{j=1}^{N}$, where $N$ is the number of fragments. In this example we have $M=N$. For this problem the CSF $A:\mathcal{F} \rightarrow \{0,1\}$ is defined on the set $\mathcal{F}$ as $A(\mathcal{F}) > 0$ iff all the fragments in $\mathcal{F}$ are unique. The CSF denoted as
\begin{equation}\label{cdo_sim3}
    A(\mathcal{F}) =
\begin{cases}
    1,&\text{ if }\bigcap\limits_{i=1}^{N} F_{\sigma_i} = \varnothing,\\
    0, &\text{ Otherwise}.\\
\end{cases}
\end{equation}
We perform the DFA of a small section of the DNA sequence of bacterium \textit{Escherihia Coli (E. coli)} \cite{Maria}. The original section of the DNA is represented as  $TACTAGCAATACGCTTGCGTTCGGT$. We consider $N=10$ fragments each with 8 bases, as follows: $F_1 = \textit{ACGCTTGC}$, $F_2 = \textit{TTGCGTTC}$, $F_3 = \textit{ACTAGCAA}$, $F_4 = \textit{CGTTCGGT}$, $F_5 = \textit{AGCAATAC}$, $F_6 = \textit{TACTAGCA}$, $F_7 = \textit{AATACGCT}$, $F_8 = \textit{CTTGCGTT}$, $F_9 = \textit{ATACGCTT}$, and $F_{10} = \textit{CTAGCAAT}$.
Using the proposed method, we obtain the optimal solution $\mathcal{F} = \{F_6 F_3 F_{10} F_5 F_7 F_9 F_1 F_8 F_2 F_4 \}$. It can be shown that by imposing a second constraint using an upper bound \cite{boundTSP}, we achieve $N_e \ge 454$. Solving the DFA problem to optimality with the imposition of these additional constraints is not possible using the traditional DP. The results are shown in Table \ref{tab3}.

\begin{table}[t]
\caption{Comparison of the total actual number of computations $^\mathsection$ required for msDP, ES, and SA algorithms.}
\label{tab2}
\begin{center}
\begin{sc}
\resizebox{\columnwidth}{!}{%
\begin{tabular}{ |c|c|c|c|}
\hline
& \small Proposed & \small Exhaustive & \small Simulated \\
& \small Method  & \small Search & \small annealing \\
& \tiny $O(N_eN^2M^2)$  & \tiny $O(M^N),O(N!)$ & \tiny $\approx O(M^N),O(N!)^{\ddagger}$ \\
\hline
\small ADC BA  & \small 6912 $(N_e = 13)$ & \small $16.7 \times 10^6$ & \small 5220 \\
\hline
\small DFA-1{$^{\dagger}$} & \small 83890 $(N_e = 434)$ & \small $3.62 \times10^6$ & \small 380 \\
\hline
\end{tabular}%
}
\end{sc}
\tiny{$^{\dagger}$} DFA with a second constraint. \tiny{$\mathsection$ Number of computations = Actual number of CSF evaluations + ACMS operations}. \tiny{$^{\ddagger}$} To guarantee optimal solution.
\end{center}
\vskip -0.1in
\end{table}

\begin{table}[h!]
\caption{Comparison of performance of the msDP, ES, and SA algorithms.}
\label{tab3}
\begin{center}
\begin{sc}
\resizebox{\columnwidth}{!}{%
\begin{tabular}{ |c|c|c|c|}
\hline
& \small Proposed & \small Exhaustive & \small Simulated \\
& \small Algorithm  & \small Search & \small annealing\\
& \small \textbf{\textcolor{blue}{Optimal}}  & \small \textbf{\textcolor{blue}{Optimal}} & \small \textbf{\textcolor{red}{Suboptimal}} \\
\hline
\small ADC BA  & \small \textcolor{blue}{$[4,2,2,2,2,2,1,1,1,1,1,1]^T$}  & \small \textcolor{blue}{$[4,2,2,2,2,2,1,1,1,1,1,1]^T$} & \small \textcolor{red}{$[4,4,2,2,1,1,1,1,1,1,1,1]^T$} \\
\hline
\small DFA-1 \small{$^{\dagger}$} & \small \textcolor{blue}{$[6,3,10,5,7,9,1,8,2,4]^T$} & \small \textcolor{blue}{$[6,3,10,5,7,9,1,8,2,4]^T$} & \small \textcolor{red}{$[6,3,10,5,2,8,4,7,9,1]^T$} \\
\hline
\end{tabular}%
}
\end{sc}
\end{center}
\vskip -0.1in
\end{table}

\section{Conclusion}
\label{Conc}
Constrained discrete optimization problems with the objective function that satisfies the optimality principle and place no conditions on the constraints are NP-Hard. In general, such problems arise in many areas of science, engineering, finance, and management. We propose a multi-survivor dynamic programming framework that solves these problems to optimality with worst-case complexity reduction from either $O(K^N)$ or $O(N!)$ to $O(N_eN^l)$, where $N_e$ and $l$ are constants that depend on the constraints.

\section*{Acknowledgment}
The authors would like to thank National Instruments for the financial support extended for this work.
\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


Some projects will be very private, and others will be public. Allow users to find public projects that match their interests and skill set.
Changed the title from "[v1.4] Project Ecosystem: allow users to browse/search through public projects" to "[v1.3] Allow users to browse/search through public projects"


An elegant name with a repeating 'ah' sound. Possible uses: A paving company. A skincare line. A jewelry brand. A research firm. An app.
The following are business names for sale with similar qualities to Pavara.com.


text:
News archiveCurrently selected
The Recipe for ecosystem overviews in ICES
"How do we transfer our improved understanding of human interactions with the marine ecosystem into our operational advice?" This was the central question addressed by ICES Workshop on Ecosystem Overviews (WKECOVER).
WKECOVER was designed to carry forward the development of ecosystem overviews, with a focus on identifying a structure that would meet ICES needs and feed into ICES advice. Thewords "application" and "concise" were emphasised as key in the construction of overviews.
According to discussions at WKECOVER, ecocsystem overviews have four key purposes:
to describe the location, scale, management, and assessment boundaries of eco-regions;
to alert ICES expert groups to situations within the environment and ecosystems that are expected to significantly influence their advice;
to describe the distribution of human activity and resultant pressure on the environment and ecosystem;
to describe the state of the ecosystem and to comment on pressures accounting for changes in state.
Expected audiences and users of the overviews include regional commissions (e.g. OSPAR, HELCOM etc), ICES expert groups, and the wider ICES community and network. Owing to this range of audience, the workshop recognised that the overviews will be evolving documents, driven by both top-down (advisory requests and ICES decisions about strategic direction) and bottom-up processes (information streams highlighting new issues from the ICES community and network). It is also foreseen that the overviews will highlight ICES capacity to provide integrated advice, which is expected to meet the future needs of advice on the environmental status of the marine ecosystem.
The workshop output is, in effect, a recipe book for developing and updating ecosystem overviews, which will be based on the following sections:
Ecoregion description;
Key signals within the environment and ecosystem;
Activity and pressure;
The workshop group defined the contents of each of the sections of the overview and partially developed overviews for three example ecoregions, while proposing update frequencies, responsibilities for updates, and quality control of the contents. It was important to highlight how the overviews could be operationally maintained and also the criteria for including information in the overviews.
Incorporating material into the overviews and progressively improving them will require the engagement of many parts of the ICES community. WKECOVER proposed that sections 1 and 2 of the overview should be prioritised for short-term development and should appear in the 2013 advice, with sections 3 and 4 developed in the longer-term. Encouragingly, ICES Data centre and spatial facility made significant progress developing section 1, Ecoregion description, during the workshop. Lively discussions suggested that there was a risk that sections 3 and 4 might become repositories for all known information on "pressure" and "state" in each ecoregion - something that wouldn't help the ICES advisory process - and workshop participants concluded that it was most important to focus on indicators of direct relevance to the advisory and management process in these sections.
Key signals in the environment and ecosystem that would feature in section 2 were defined as those environmental, biotic, or human influences that are expected to significantly influence advice developed by expert groups. Expert groups, and in particular the regional integrated assessment groups, can play an important role in identifying key signals, by screening the wide range of environmental and ecosystem signals in eco-regions and identifying those that have a significant effect on the way in which other expert groups would develop advice. This requires integration with the assessment benchmark process to account for key signals in the environment and ecosystem. Where existing assessment models could readily be modified to account for key signals in the environment and ecosystem then this could be done as part of the normal assessment cycle.
To best support their purposes and ICES advisory needs, the workshop concluded that the overviews must be living documents. Overviews will need to be regularly reviewed in the context of other sections of the ICES advice to ensure that inconsistencies are identified and rectified and that incompatibilities are addressed. Ultimately, it would be the ICES community, drawing on their scientific and advisory expertise, that would need to guide the users' interpretation of the overview contents, and thus workshop participants were keen to stress that contents of the overview should always be supported by interpretive narrative. The structure of the overviews will now be discussed by various ICES groups and the integrated ecosystem assessment groups will further develop and populate the documents. It is hoped that WKECOVER has kicked off a process that will lead to integration of advice on human interactions with the marine environment. So the recipe, whilst not resulting in a tasty dessert, will hopefully lead to a better blend of our scientific research with the advisory process in ICES.
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WKECOVER met at the ICES Secretariat in Copenhagen in January.
View WKECOVER report


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text:
Stephen Carpenter
Director, Center for Limnology and
Stephen Alfred Forbes Professor of Zoology
Eric Booth
Assistant Research Scientist
Agronomy and Civil & Environmental Engineering
Xi Chen
Melissa Motew
Agriculture in the Yahara Watershed
The Yahara lakes are among the world's most studied bodies of freshwater. Changes in climate and land use are impacting their health and could continue to do so into the future. An impact of particular concern is phosphorus pollution from agricultural and urban areas.
While essential for life, phosphorus is harmful when in excess in soil and water. Erosion and surface runoff transport phosphorus from farmland and urban areas into the lakes, which results in eutrophication, or a surplus of nutrients in the water. Algal blooms are the most visible sign of eutrophication and are a frequent occurrence in the Yahara lakes in the summer. They disrupt natural ecological processes in freshwater and can be harmful to animals and humans.
Our water quality research improves our understanding of how current and future climate and land-use changes could affect phosphorus pollution levels and subsequent lake health, pointing to ways we could improve water quality in the region and beyond.
How have changes in climate, land use, and land management affected lake water quality over the past several decades? What has been the effect of water quality initiatives over this time period, including the adoption of agricultural best management practices (BMPs)?
What could lake water quality be like in the year 2070 under certain conditions of social and environmental change, especially those outlined in the Yahara 2070 scenarios?
How would different phosphorus management strategies affect lake water quality under future climate change?
Despite significant efforts to improve lake water quality in the last several decades, several factors have resulted in no significant change in the amount of phosphorus entering the lakes. Our research shows more frequent heavy rain events, urban expansion, larger livestock herds on smaller parcels of land, and more row crops have hindered progress. Addressing these factors will be critical for reducing phosphorus loads and improving water quality. That said, beneficial factors such as better farming practices, urban runoff management, improved cow diets, and decreased fertilizer use are helping and may be the reason lake water quality has not gotten worse.
Our research shows a powerful determinant of water quality is legacy phosphorus, or the buildup of phosphorus in soils, streams, wetlands, and lakes from historical land management practices. To improve water quality, it will be necessary to develop and implement practices that reduce the amount of legacy phosphorous stored in the watershed's soils, in addition to continuing practices that reduce the transport of phosphorus from land to water, such as stream buffers.
Substantial land-use changes such as those that occur in the Yahara 2070 scenarios - for example, more grass grown for biofuels and the elimination of manure - could improve lake water clarity by one foot, as measured by a secchi disk, by 2070.
Even with significant land-use changes, aquatic invasive species could be game changers in efforts to clean up the lakes. Invasive species like the spiny water flea, which is already established in Lake Mendota, could make it more difficult to improve water quality, because they eat Daphnia, a zooplankton that eats algae. Protecting Daphnia and preventing or controlling invasive species will be critical to continue making progress.
Study quantifies role of 'legacy phosphorus' in reduced water quality
A quarter of Wisconsin's lakes are getting murkier but study shows hope for improvement
Improving Water Quality: An "Upstream" Battle (infographic)
Wisconsin's lakes need stronger management to tolerate climate change
New study: Bursts of phosphorus to blame for Lake Mendota's water quality problems
Good news and bad news for reducing phosphorus in the lakes
Extreme daily loads: role in annual phosphorus input to a north temperate lake
Phosphorus loading, transport and concentrations in a lake chain: a probabilistic model to compare management options
Regime Shift in Fertilizer Commodities Indicates More Turbulence Ahead for Food Security
Water quality implications from three decades of phosphorus loads and trophic dynamics in the Yahara chain of lakes
What is the influence on water quality in temperate eutrophic lakes of a reduction of planktivorous and benthivorous fish? A systematic review protocol
Creating a safe operating space for iconic ecosystems
Planetary boundaries: Guiding human development on a changing planet
Invasive species triggers a massive loss of ecosystem services through a trophic cascade
Reducing Phosphorus to Curb Lake Eutrophication is a Success
Annual precipitation regulates spatial and temporal drivers of lake water clarity
The Influence of Legacy P on Lake Water Quality in a Midwestern Agricultural Watershed


text:
Home > Companies & Markets
SGX heads for arbitration with NSE over Nifty dispute
Tue, May 29, 2018 - 7:36 PM
Jamie Lee leejamie@sph.com.sg@JamieLeeBT
THE Singapore Exchange (SGX) on Tuesday said the Bombay High Court has ordered for the lawsuit filed against SGX by a unit of the National Stock Exchange of India (NSE) to be settled through arbitration. The decision on the injunction is expected by June 16.
NSE's subsidiary, the India Index Services and Products Ltd (IISL), on May 21 filed an interim injunction against the upcoming launch of SGX's new India derivatives products. SGX said it had been unable to contest this injunction as it was not given notice of its application for the injunction.
"SGX will contest the interim injunction and reserves all rights in respect of damages caused by IISL's action," it said.
SGX noted that given the "uncertainty" that was caused by the interim injunction, it will "reschedule" the launch of its new India derivatives products, pending the outcome of the arbitration. The products were meant to be launched next week, on June 4.
SGX will also continue listing SGX Nifty contracts until August 2018, as contractually provided for under its licence agreement.
SEE ALSO: SGX considers volatility controls for pre-open and pre-close trading
It added that IISL's action has adversely affected international investors who rely on SGX's platform to manage the risks of their exposures to the Indian market, and significantly diminishes access to, and interest in, the capital markets in India. "SGX remains open to a collaborative long-term solution that will benefit Indian markets."
Singapore Exchange
Nifty Futures
SBF launches joint platform with Vietnam counterpart to strengthen business ties
Memtech's proposed delisting gets SGX nod; EGM not required
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Can you believe that a neo-Nazi website gets a million more visitors a month than we do, due to Google's penalty against this site? And a Google employee lied about the penalty. November update: I've started naming names. Read the details here.
Can you believe that a neo-Nazi website gets a million more visitors a month than we do, due to Google's penalty against this site? And a Google employee lied about it. But I'm naming names. Read more here.
There's a neo-Nazi website that gets a million more visitors a month than we do, due to Google's penalty against this site. And a Google employee lied about it. Read the details here.
A neo-Nazi website gets a million more visitors a month than we do, due to Google's penalty against this site. A Google employee lied about it. Read more here.
A neo-Nazi website gets a million more visitors a month than we do, due to Google's penalty against this site. And Google lied about it. More here.
N O P Q R S T U V W X Y Z #
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Browsing page 142 of "S" words
snack boy
a handsome but unintelligent young man with whom one would like to have a casual sexual relationship. The opposite of a full-meal deal.
I'm not really interested in anything but a snack boy right now.
This definition is questionable and is pending deletion. It will be saved from deletion if legitimate citations are found.
Last edited on Aug 18 2017. Submitted by Anonymous from Austin, TX, USA on Sep 26 1997.
+ Add a definition for this slang term
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annoying; rude.
That is one snacky-ass bitch.
Some girls are snacky with guys.
Last edited on Aug 17 2011. Submitted by Kathy A. from Dallas, TX, USA on Jan 09 2002.
snippy, irritable, Maybe from southern Ohio? I learned this one from my Mom.
The child got snacky with me when I asked him to take out the trash.
Last edited on Feb 22 2003. Submitted by Holly C. on Feb 22 2003.
SNAF
a derogatory term, implies an unpleasant individual or a low-life. Acronym for sub-normal and fucking stupid. Allegedly used extensively in the middle of England.
Look over there, another snaf just walked in.
See more words with the same meaning: uncool person, jerk, asshole (general insults - list of).
Last edited on May 18 2011. Submitted by Louise D. from Derby, Derby, UK on Oct 23 1999.
snaffle
To borrow. Usually applied to a small and/or insignificant item. The implication is sometimes that the item may not be returned for the foreseeable future, e.g. "He's got a new stapler wasn't using his old one, so I snaffled it."
Can I snaffle that, please?
Last edited on Feb 06 2003. Submitted by Ceri from Surrey, UK on Feb 06 2003.
messed up as usual.
Well, that's typical, they're just snafu!
See more words with the same meaning: a mess.
See more words with the same meaning: acronyms (list of).
Last edited on Feb 23 1998. Submitted by Wayne C. from San Mateo, CA, USA on Feb 23 1998.
a mistake.
There was a little SNAFU with your car, Mrs. Reynolds.
See more words with the same meaning: a mistake, bad idea, wrong, inappropriate.
Last edited on Jul 14 2004. Submitted by C.G. from Iowa, USA on Jul 14 2004.
Acronym for "situation normal, all fucked up."
Acronym for "simultaneous Navy / Army fuck-up."
See more words with the same meaning: military (related to).
Last edited on Sep 07 2006. Submitted by Mike S. on Sep 07 2006.
a problem, especially one causing a delay.
See more words with the same meaning: hard, confusing, difficult, a problem.
Last edited on Sep 14 2009. Submitted by Walter Rader (Editor) from Sacramento, CA, USA on Sep 14 2009.
acronym for "sensitive new-age guy".
Last edited on May 19 2010. Submitted by Walter Rader (Editor) from Sacramento, CA, USA on May 19 2010.
A powwow hook up.
Him? Oh, he's my old snag from '97 powwow season.
Last edited on Jun 27 2017. Submitted by Anonymous on Jun 27 2017.
verb - intransitive
To get a snag
We snagging at the powwow or bringing the kids?
verb - transitive
to acquire.
I snagged this jacket from the Buckle yesterday.
He snagged the money from his mom's wallet.
Citation from "Chapter 8", Eastbound & Down (TV), Season 2 Episode 2 (2010) censored in hope of resolving Google's penalty against this site.
See more words with the same meaning: to have, take, get.
Last edited on Dec 15 2011. Submitted by Anonymous on Oct 01 2001.
See also snags.
snaggle tooth
teeth that are very crooked.
That girl is cute but she has bad snaggle tooth.
Last edited on Nov 14 2005. Submitted by matt w. from Orlando, FL, USA on Nov 14 2005.
snag out
They were really "snagging out.
Last edited on Jan 11 2004. Submitted by Terry T. from Lukachukai, AZ, USA on Jan 11 2004.
snags
sausage. Australian slang.
something slow.
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text:
LSU hangs on, Louisiana Tech earns sweep to highlight Saturday's College Basketball action
Adebayo, Dragic leave with injuries as Heat routed in Game 1
by: BRIAN MAHONEY, Associated Press
Miami Heat's Jimmy Butler (22) pauses after an apparent injury during the first half of Game 1 of basketball's NBA Finals Wednesday, Sept. 30, 2020, in Lake Buena Vista, Fla. (AP Photo/Mark J. Terrill)
The Miami Heat were not only badly beaten. They were beaten up.
Bam Adebayo (left shoulder strain) and Goran Dragic (left foot) departed with injuries and Jimmy Butler played through one in Game 1 of the NBA Finals. A series that started so impressively for the Heat could be a short one if their three best players are out or limited.
They were blown out 116-98 by the Los Angeles Lakerson Wednesday night, but their concerns go far beyond how can they compete.
The bigger question might be: Who can?
Dragic didn't play in the second half because of a torn left plantar fascia, a person with knowledge of the details told The Associated Press. The person spoke on condition of anonymity because no official announcement was made.
It was unclear how or when the veteran guard was hurt, or if he will be able to play in the remainder of the series.
"We know how much he wants to win, how much he wants to go to war and battle with us," Butler said. "Obviously we love him for that and we want him out there with us. But whatever the doc tells him to do, that's what he's got to do."
The Slovenian is a veteran leader for the Heat, who acquired him in 2015, the season after their last NBA Finals appearance. He played as a reserve during the regular season but has been starting in the playoffs, and his six-point finish to Game 1 ended a streak of 33 consecutive postseason games in double figures.
"We're still expecting to win. We still know that we can," Butler said. "Like I said earlier, we want that guy out there with us. He's a big part of what we're trying to do, but until we can have him back, we got to go out there and we got to fight even harder."
Just before halftime, Butler turned his left ankle on a drive to the basket. He was able to stay on the floor after a timeout for the final seconds, but the injury still appeared to be bothering him in the second half. The star swingman appeared to be hobbling when he landed after scoring while being fouled 13 seconds into the third quarter.
He said he felt some soreness after the game but would be OK with treatment.
"I've got to be ready to go, so we'll see how it feels tomorrow but I'll be fine," he said.
Adebayo's shoulder crashed hard into Dwight Howard as he drove into the lane with 7:03 left in the third quarter. Adebayo, Miami's All-Defensive team center, is already wearing a sleeve on his left arm and was clearly hurting during the Eastern Conference finals against Boston.
The Heat said X-rays taken at the arena were negative. Coach Eric Spoelstra said he wasn't sure if Adebayo had a lingering injury from the previous series.
"I don't have that answer right now," Spoelstra said. "We'll reevaluate him tomorrow and see where we are."
Adebayo overcame the injury to finish with 32 points and 14 rebounds in the Heat's victory in Game 6 to eliminate Boston, but he couldn't keep going Wednesday. He appeared to bang the arm again on a rebound attempt shortly after Howard fouled him and soon left the floor for treatment.
In case things weren't bad enough by then, Butler appeared to be hobbling again after going back into the game in the fourth quarter.
Dragic averaged 22.8 points to lead the Heat in their first-round sweep of Indiana in the first round. Butler paced Miami with 23.4 per game when it knocked out top-seeded Milwaukee in the Eastern Conference semifinals and Adebayo scored 21.8 per game in the East finals, making the Heat the first team since the 1999 San Antonio Spurs to reach the NBA Finals with three leading scorers in each of the first three rounds.
That trio powered the No. 5 Heat to the finals as the lowest-seeded team since that year, when the Spurs beat the No. 8 New York Knicks.
The Heat then jumped on LeBron James and the Lakers with a quick 13-0 run — all but three points coming from Adebayo, Butler and Dragic — to open a 23-10 lead. But Los Angeles closed the quarter with a 21-5 finish to take a three-point lead to the second, when things quickly fell apart for Miami.
The Heat will try to bounce back Friday in Game 2. They just don't know yet who can help them try to do it.
AP Basketball Writer Tim Reynolds in Lake Buena Vista, Florida contributed to this report.
by John Sartori / Jan 16, 2021
BUFFALO, Ny (KTAL/KMSS) - For the first time since 1993 the Buffalo Bills are headed to the AFC Championship game. Buffalo will face the winner of tomorrow's Cleveland-Kansas City matchup.
As the Bills advance to the AFC title game, Shreveport native and Green Oaks High School alumni Tre'Davious White advances as well. White made 6 tackles and deflected a pass as the Bill defense allowed just 3 points to Baltimore on Saturday night.