This week Poznań will welcome Polish and international upcoming music stars, during the 4th edition of Spring Break Festival. There will be a Scandinavian touch to the event as well!
Spring Break Festival is for Poland what Reeperbahn Festival is for Germany – a showcase event gathering all music lovers and music industry people to present the new trends and upcoming artists.
Mostly focused on presenting Polish artists, last year Spring Break Festival decided to mix it a little bit and invited international acts to play as well (among them – Ida Wenøe and Sherpa, who performed under the wings of Good because Danish). Foreign musicians got a great opportunity to get familiar with Polish music industry and the audience. The experiment of mixing Polish and international music went well and this year it continues. With a special event dedicated to Scandinavian artists.
We will be able to listen to a great selection of Scandinavian rising stars during the Ja Ja Ja showcase and Good because Danish cannot be more thrilled to invite you to check out this particular event during the festival! Sekuoia will be representing Denmark at the showcase and we hope that many of you catch this particular concert!
A few days before the Spring Break Festival begins, we had a chat with Tomek Waśko – one of the organizers of the event – about Polish music scene, the festival and why do Scandinavian musicians should look at Poland with interest. Read the interview below and see you in Poznań starting Thursday, 20. April 2017!
Good because Danish: Promoting young promising artists is a brilliant and noble idea, where did the idea for Spring Break Festival and its format come from?
Tomek Waśko: We're not claiming that we have discovered some secret formula that no one had thought of before. We've been attending showcase festivals all over Europe (Eurosonic, Reeperbahn, The Great Escape) and we decided that it's time for a similar festival in Poland.
In recent years, more and more ambitious music is emerging in Poland, which without the complexes starts to attract fans from outside the country. What do you think about the changes that are clearly visible on the Polish music scene? In which direction do you think Polish music is going?
I think that there's always been good music here, but now it's a good moment for more ambitious music – even industry awards (Fryderyki) recognizes more ambitious projects. And with Spring Break being a good platform for emerging acts we are now more ready to present this music to the audience.
Scandinavian music has not left Spring Break recently. Another year in a row can be presented to a Danish artist at this year's Ja Ja Ja Music showcase with Sekuoia in the line-up. Is mixing Polish and abroad music a proven recipe for organizational success?
We still want Polish music to be the core of Enea Spring Break's line-up, but it's nice to add a little bit of international flavor to make the line-up more exciting and eclectic.
What do you think Polish music market has to offer to the foreign (especially Scandinavian) artists? How important is the role of events like Spring Break Festival in opening the doors of Poland to foreign bands?
Enea Spring Break attracts a lot of industry delegates from labels, festivals and concert agencies. So if you are a member of a young band it's a platform that is a good start to showcase your music to important people of Polish music industry.
If you had to describe Spring Break Festival in one sentence, what would that sentence be?
Spring Break, the biggest Polish showcase festival, a perfect place to start your career in Poland.


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Mourning Grave (; lit. "Girl Ghost Story") is a 2014 South Korean mystery horror film starring Kang Ha-neul and Kim So-eun.

Synopsis
In-soo, a high school student, has a special gift to see ghosts. He transfers to a high school in a rural area outside of Seoul. Plagued by them everywhere he goes and harassed by classmates because of it, he returns to his hometown to live with his uncle and finally put the past to rest. No sooner does he arrive than he sees his first ghost there, a pretty girl; but, just like before, it's not just ghosts that affect his life. School bullies remain a problem, but soon along, the bullies start being attacked by a vengeful ghost wearing a bloody mask, and In-su starts to think that his new friend, the pretty ghost, may have something to do with it.

Cast
Kang Ha-neul as Kang In-soo
Kim So-eun as Jung Se-hee (Ghost girl)
Kim Jung-tae as Seon-il
Han Hye-rin as Park Hyun-ji
Park Doo-shik as Lee Hae-chul
Joo Min-ha as Yoon Na-ra
Joo Da-young as Lee Sung-hee
Lee Bom as Hye-jung
Kwak Jung-wook as Lee Ki-tae
Kim Young-choon as Ho-seop
Lee Ah-hyun as Oh Mi-hee
Oh Yoon-hong as Ah-young's mother
Yoon Chan-young as Kang In-soo (young)
Shin Soo-yeon as Jung Se-hee (young)

Original soundtrack

Box office
Since its domestic release on July 3, 2014, the film has grossed , with 216,000 ticket sales.

International release
At the Cannes Film Market, Mourning Grave was pre-sold to China, Hong Kong, Taiwan, Singapore and Mongolia.

References

External links

South Korean horror films
2014 films
2014 horror films
South Korean mystery films
2010s South Korean films

redpajama_set_name: RedPajamaWikipedia


Barkley Project Group are project managers specializing in renewable energy development and community energy systems. Since 2003, they have provided the capacity and support needed for communities and developers to navigate the entire renewable energy development process, from idea to operation.
Founders Iain Cuthbert and John Ebell made the move from environmental consulting to clean energy after seeing the need for a one-stop-shop in the renewable energy industry in BC. Engineering and consulting firms typically concentrate on one or two aspects of renewable energy development. Barkley Project Group builds and leads project teams with the expertise needed for each stage of development. They are one company that can deliver an entire project.
Barkley Project Group is uniquely positioned – both professionally and geographically – to serve clientele in remote communities on Vancouver Island and the Central Coast. With an office located in Nanaimo, BC, staff have more direct access to remote communities that are only accessible by gravel road, boat or floatplane than firms located on the mainland. In addition, they have attracted highly-skilled and diverse team members from across the country due to the cost of living and lifestyle on Vancouver Island and the burgeoning clean energy industry in BC.


Posted in Climate Sock, Energy sources, Politics on November 23rd, 2015 by Leo – Comments Off on What's the point of UK climate policy?
This was originally published on LabourList.
After tax credits, energy and climate policy are now the Tories' greatest vulnerability and should be a top Labour priority. But while the shadow team have been attacking the Government, their criticisms haven't yet damaged the Tories, allowing them to get away with policies that are killing jobs and unnecessarily increasing bills.
On energy, there's an opportunity for Labour to label the Tories' current approach as incompetent, with recent decisions appearing to be contradictory. One minute, the Government is cutting subsidies for solar and wind: both clean and popular sources of power. The next, it's signing a deal for a new nuclear plant at Hinkley Point that commits to generating electricity for decades at eye-watering costs.
This allows Labour to argue that the government's decisions are directly making life worse for people across the country. The unexpected slashing of support for solar has already cost over 1000 jobs and the industry claims up to 27,000 are at risk as a result of government policy.
At the same time, the nuclear deal is expected to add over £1bn a year to households' energy bills: the equivalent of around £40 per household, every year, for 35 years. While we need new power sources, few outside the government argue this is the best-value way of providing it.
Put these together and you've got a neat criticism of Government policy. We're losing skilled manual jobs in what should a growth industry, while also putting an unnecessary cost on already-stretched families. Both fit with the tax credits frame that the government is undermining work and adding to the burden on poorer families.
The combination of the two is important, as it allows Labour to show it's not just looking for government subsidies to protect jobs and promote growth, but that it also expects public money to be spent well and not wasted on overpriced vanity projects.
To her credit, Lisa Nandy has been attacking the government on this and Labour is developing policies for community energy production. But it's been left to her and the rest of the shadow Energy and Climate Change team to take on the Tories about these issues and they haven't had much attention from those not already interested in the area.
Labour could do more damage if the leadership gave this a higher priority. This is an opportunity to either force a change in policy or do lasting damage to the Tories' reputation: the Hinkley Point contract could be seen as their Millennium Dome, but for now it's not getting enough attention.
Similarly, Labour can force a change in the Government's climate policy.


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Fight Like Hell for the Living: A Year of Struggle in UK Call Centres
After a year of disruption, reorganisation and loss in the UK's call centres, this article surveys ongoing developments in call centre workers' organising and considers the potential for long-term change. This article was first published by Notes from Below.
Letters - Black Flag #219
Letters from Black Flag #219. 2000. On J18 and Bob Black replies to the review of Anarchy After Leftism in a previous issue.
Obituary: Peter Miller 1943-1999
An obituary for anarchist Peter Miller by Phil Ruff, published in Black Flag #219, 2000.
Blood For Oil
Colombian military personnel have invaded the traditional homeland of the U'wa people to make way for the drilling plants of oil giant Occidental.
From Black Flag magazine #219, 2000.
Marxism and politics - Ralph Miliband
Ralph Miliband's out of print introduction to Marxism. "The best primer on Marxism and politics ever written and Miliband's best book." —Leo Panitch, professor of politics, York University
Love & Rage Vol. 2 No. 3, March 1991
Vol 2, Issue 3 of Love & Rage, with letters, Bob McGlynn offering an anarchist critique of "anti-imperialism", an advert for an L&R organizing conference, a report on a black bloc at an anti-Gulf War march, resistance to any possible draft, an introduction to anarcha-feminism and a memorial for victims of the 1989 Montreal massacre, Christopher Day on anarchist organisation, the On Gogol Boulevard column interviewing a Hong Kong anarchist, the ABC column of prisoner news including a report from Leeds ABC and John Perotti launching a hunger strike, and the Notes of Revolt column with miscellaneous news including an invitation to a Class War conference.
Love & Rage Vol. 2 No. 2, February 1991
Volume 2, Issue 2 of Love and Rage, with articles on the Gulf War and resistance, letters, news about L&R's production and an L&R organizing conference in Minneapolis, Wayne Price on different factions in the anti-war movement, anarchist tactics at mass demonstrations, squat evictions in Vancouver, Christopher Day on anarchism and organisation, indigenous resistance to a hydro-power project in Quebec, the On Gogol Boulevard column with news from Hungary, Lithuania, and anti-war Afghanistan veterans in the USSR, prison news including conscientious objectors in Finland, and the Notes of Revolt column with actions across the US and beyond.
Self-Management Marxism and Revolutionary Experiences – Gabriel Teles
To Suffer Thy Comrades: How the revolution decimated its own — Robert Francis B. Garcia
"To Suffer Thy Comrades" is a brutally honest, meticulously researched, and brilliantly written account of one of the CPP-NPA internal anti-infiltration operations—the infamous Oplan Missing Link—written by a former cadre himself who, like his comrades and other purge victims and survivors, seeks healing and justice while striving to move on from the tragedy.
'I Am An Anarchist': Remembering Anarchist Prisoner Brian McCarvill, who Died of COVID-19 in Prison on his 68th Birthday
A biography and obituary of Brian McCarvill, an anarchist prisoner in Oregon who was killed by a Covid-19 outbreak. This story was first published by Perilous Chronicle.
libcom.org is a resource for all people who wish to fight to improve their lives, their communities and their working conditions.
Read more | Introductory guides
Loukanikos, the Greek anarchist dog, photo gallery
Photographs of Loukanikos, "sausage", the legendary stray "riot dog" who was present at nearly every outbreak of mass class struggle and social disorder in Athens up until...
libcom.org further reading guide
libcom.org's reading guides, organised by subject, including other media like film and photographs.
Destruction as a means of struggle - Anton Pannekoek
Prompted by the burning of the Reichstag in 1933 - by Marinus van der Lubbe, a council communist bricklayer and other possible accomplices - Pannekoek debates the value of destroying the products...
Class struggle and revolution from below; the flouting of law; the go-slow and challenging the work ethic; such tactics not only hindered the war effort, they also called into question the social relationships needed for capitalism and the state to function.
Fighting war
Justice For Oscar Grant: A Lost Opportunity?
Vote for change?
First strong points on the last revolts in Arab countries
NATO's secret armies - Daniele Ganser
The Maslakov mutiny and the Makhnovists on the Don, 1921
Thalmann, Clara, 1910-1987

redpajama_set_name: RedPajamaCommonCrawl


Be certain to go through reviews for any vacation property you desire to rent. Determine what thoughts previous tenants have had about the rental and figure out what to expect. If the rental home is popular, you can expect it to have several reviews indicating how excellent it may be.
Features Pick a vacation rental that includes all the features and amenities that you'll need while staying there. Does each condo or villa have enough number of bedrooms, and is the kitchen equipped and furnished adequately for gourmet cooking? Do you need a private swimming pool? Investigate the Surrounding If you're traveling to somewhere far away, a physical examination of the vacation rental before your trip may not be possible. Yet, you may opt to research the neighborhood on the internet or even utilize Google Earth to learn about the surroundings of your chosen vacation rental. Study the surroundings and ascertain that there are no elements or installations that are likely to affect your comfort, safety, or privacy. Neighbors or night clubs that are likely to be noise are not the best for you and your family. Take Access to Public Transport into Account When selecting where you want to stay temporarily during your getaway, be sure to consider access to public transport. If you're going there by air, you need the place to be not very far from the airport. In addition, the accessible mode of transport between the airport and your holiday rental should be known in good time. To be on the safe side, ask about proximity to public transport before closing the deal. If the listing does not say much about your concerns, you may ask your agent to provide an address that you may look up on Google Earth and learn more. Online Connectivity Your vacation rental should offer internet particularly if you depend on it to work or just have fun. Ask for specifics such as speed, download limits, and costs. Internet bandwidth can be very important particularly when you want to be able to make international calls or hold VoIP conversations. Typically, WiFi connectivity is preferred as you won't have to deal with a lot of potentially messy wiring. A vacation rental may be a temporary residence, but it can have an impact on the lasting memories you take back home with you, so pick it very carefully and without haste.


text:
Q: SCCM -Meaing of "microsoft windows nt workstation 10.0 (tablet edition)" Most of our computers registered in SCCM report "microsoft windows nt workstation 10.0 (tablet edition)". We only have a small number of tablet computers, the majority are laptops.
Please can someone advise what this means and what it implies as we are worried that we have done something wrong with the imaging process. We use a custom image build that is based of the installation media that you get from the 365 portal

A: As far as I know this is not really a special edition of windows, it used to be in times of xp but nowadays this just means the service "Tablet PC Input Service" is running. Why this also "renames" the OS Caption I don't know but it is something I noticed as well.
It does however not mean that there is anything missing or wrong with your computers, the only thing where this could lead to a problem is if you use some wmi query for gpos e.g. and wrote them like "name = '%10.0'" or something similar because without a trailing wildcard the query will fail.
As to how this got activated it is a little bit hard to say but we have some Laptops that are conventional form factor but still have a touch panel which could be one reason. There are also certain accessories like styluses or drawing pads that might lead to this service being active. That being said I have seen systems with this active where I could not find any plausible reason so it seems not always given that we are able to understand how the mechanism works.

redpajama_set_name: RedPajamaStackExchange


text:
Apple Watch Series 6/SE review: Buy One for Each of the Family
3 months ago Serena
Under the background of the epidemic in 2020, more and more people start to pay attention to their physical health. Those who used to stay at home and not go out start to move around and pursue a healthier lifestyle.
So, do you need a wrist partner who can monitor your health?
In this September, Apple brought us the Apple Watch Series 6 and the Apple Watch SE. Apple Watch Series 6 adopts the new color match and equipped with the blood oxygen sensor for the first time, which makes up the deficiencies in the field of sports and health. With a brighter screen and a number of new watchbands, it is still quite fashionable.
Apple Watch SE, on the other hand, undertakes the task of popularizing Apple Watch. It has the same design, heart rate monitoring, noise monitoring and other mainstream functions as Apple Watch Series 6, but the price is much cheaper than the Series 6. It is more universal than flagship devices.
The category has more variety, the color is more diverse, the function is more complete and the price is lower. The rich product line of Apple Watch Series 6 and Apple Watch SE is likely to further boost Apple Watch sales and make this the best year for Apple's wearable device sales.
Two watches are coming, did you make up your mind?
The Digital Apple Watch has always been the flagship, as has this year's Apple Watch Series 6. It uses Apple's latest self-developed S6 chip, which performs as well as an A13 processor. It can increase app startup speed by 20%, and the phenomenon of "APP keep loading " will almost never happen again.
And the long-awaited blood oxygen monitoring comes with the new sensor on the Apple Watch Series 6. We can directly monitor the blood oxygen saturation monitoring function through the watch, and then confirm the condition of the body. You can wear an Apple Watch to monitor the blood oxygen level when you go to the gym or go hiking. You can go to the doctor immediately when there is an accident.
In addition to some fitness or outdoor enthusiasts, Apple Watch Series 6 combines blood oxygen monitoring with sleep monitoring, allowing us to control the state of the body 24 hours at any time. The watch's sensor will continue to work during sleep and send our sleep-related information to the health App. Although it cannot be used for medical purposes, it is enough to remind us to take care of our health.
The results of blood oxygen concentration monitoring were retained in the health App
Unlike heart rate, the blood oxygen threshold for the Apple Watch Series 6 is slightly higher. We need to keep the sensor close to the skin, but we also need to keep it as still as possible, because a lot of large movements can affect the accuracy of the detection. I've measured it a few times, and it's between 93% and 99%. It still looks healthy.
While the overall size hasn't changed significantly, the color palette for the Apple Watch Series 6 is still a step forward. In addition to the original silver, space gray and gold watchcase, blue aluminum metal watchcase, red aluminum metal watchcase and other new products are formally launched. And if you're a fan of the stainless-steel case, you can also get a new graphite color version. The bright metal in gray and black also gives the Apple Watch a more textured look.
This year, Apple also offered a quick charge for the Apple Watch Series 6. Officials say it fills 80% of the watch in an hour and the entire watch in 1.5 hours. Personally, the biggest meaning of fast charge is to supplement a certain amount of power for the watch before sleep monitoring, to ensure that it can be used normally. According to the actual measurement, under the condition of 50% power, 15 minutes of bathing can provide 11% power for Apple Watch Series 6, while after one night, sleep monitoring and blood oxygen monitoring consume 10% power. Therefore, sleep monitoring and blood oxygen monitoring do not have too much burden on endurance.
By contrast, Apple Watch SE is a product that is good enough in all aspects. As the official slogan puts it: "Good at everything, easy to get."
The Apple Watch SE features are easy to access, equipped with rich functions and sufficient to use. The body made of 100% recycled aluminum, with a variety of different color watchband, light body enough to make it more design sense of wrist equipment. What's more, it has the same design as Apple Watch Series 6, S5 dual-core SiP encapsulated chip, and supports heart rate monitoring, fall monitoring and noise monitoring. The screen uses the same LTPO screen as the Apple Watch Series 6, which supports up to 1000 nits brightness, but does not support permanent brightness. It's not hard to see that the Watch meets almost all of the Apple Watch's daily needs. You pursue the fashionable appearance, it has the current leading shape; You want all kinds of monitoring, it has all the monitoring protocols except oxygen monitoring. Such a feature-rich smartphone can be purchased for as little as $329, which will also enable more people to experience the Apple Watch SE.
The original intention of Apple Watch SE is to let more consumers have a experience of Apple Watch products and health services provided by Apple through price dropping. In terms of products, it has done its job quite well.
As for the strap of different material, it makes it even better. I personally the first to weave a single ring watchband. It has removed the extra buckle, but also has a certain degree of elasticity, and due to the characteristics of weaving, the breathability of watchband is also very good. Of course, before you buy the strap, I'd still recommend you try it out in the Apple Store to make sure you're buying something that fits the width of your wrist. Of course, the original watchband can also be used with the new watch. Since the debut of the first Apple Watch, the size of the watchband has been consistent. The watchband bought in the past will not become outdated due to the arrival of new products. We can still meet the needs of wearing in different scenes through these watches.
Family sharing has made the Apple Watch more popular
An iPhone plus an Apple Watch is a fixed combination for many users. After the debut of the new Apple Watch, the new "family sharing" function caught my eye. Personally, I think this is a big upgrade for Apple Watch after supporting cellular network and launching independent AppStore. In the future, not only will your iPhone be paired with an Apple Watch, but you'll be able to pair Apple Watches with other family members by sharing them with your family. Even kids and seniors who haven't used an iPhone can enjoy a healthy lifestyle via the AppleWatch.
It's important to note that if a family member hasn't used an Apple device before, they need to register for a new Apple ID.
For children, Apple has designed many optimization schemes in the family sharing function. Instead of dynamic calories, the fitness log tracks the "activity" time. Physical training, such as running, walking and cycling, can also accurately calculate distance and speed. During classes, parents can limit the Apple Watch's capabilities by setting "class time" on the iPhone to keep their children focused on learning.
Before setting up an Apple Watch for children, we need to register an exclusive Apple ID for children. Once the Settings are complete, the child's exclusive Apple ID will be added to the family. With GPS, parents can know where their children are in real time, and we can talk to our children over the cellular network. Of course, we don't have to worry about children's free consumption in the App Store, because parents need to approve any purchase made by children.
For the elderly, Apple has designed a sweet, large text dial for the new Apple Watch, which can also add some sophisticated features. Combined with fall detection and SOS emergency contact, the children can timely know the geographic location and physical health status of the elderly. Moreover, through the cellular network, we can also talk to the elderly directly, most of the children work outside we cannot be with them, a phone call at this time, also let the family affection between the wrist.
Of course, we can also set the SOS emergency contact for the elderly directly in the Settings and turn on the fall detection switch. We can also select "Press and hold side button dialing" from the Settings so that after a long period of pressing the side button, an emergency call can be automatically dialed.
One watch for myself, two watches for parents, and one watch for children. The price of four flagship watches is almost more than $1,500or even $3,000, which is obviously not an average family can afford. At this point, you'll notice that The Apple Watch SE, which Apple launched this year, was almost tailor-made for this feature.
It supports cellular networks and can be used to talk to children or the elderly. It has multiple sensors, as well as features such as fall detection, heart rate monitoring and SOS emergency liaison. Most importantly, it has a lower threshold, with a starting price of $329, 30% less than the flagship model. That's like buying three watches and saving money on one watch.
After using the family sharing function, Apple Watch is no longer an extension of iPhone. It will help some vulnerable groups in the family virtually and enable everyone to enjoy the changes in life brought by technological progress.
Apple Watch will be popularized in the family through family sharing. Please allow me to say the direction is right. Now, the Apple Watch can not only change your life and mine, but also motivate every family member to start taking care of their own health. It's also a great way to strengthen the bond between family members through family sharing, walking with the kids more every day, or teaching the elderly how their heart rate changes.
It is not difficult for us to find that Apple Watch is no longer just an accessory for consumers, but a combination of one iPhone and one Apple Watch that is Shared by family members, which expands Apple's ecological circle and radiates to more people.
New dial upgrade
Every year, Apple creates several new dials for the Apple Watch, and this year is no exception. My favorite, for example, is the artist dial. This dial, with the strong personal style of artist Geoff McFetridge, brings us another kind of surprise through the use of simple graphics and bright colors. The newly designed large text dial also supports more customizable space. In addition to displaying time, it can also be used with altimeter or physical training to achieve more rich functions. The new photo dial offers a different look and feel through the color filter design.
This year, watchOS 7 also gave us a "share dial" feature. You can share it with your friends via iMessage or email. Maybe before using other people's dial also need a long dial design guide, but now just need to share a link. It can let friends use our own dial design, or let us directly use the dial made by others. At this point, when the watch detects an App in the dial that we have not installed, it will also prompt us to install the App before using the new dial, so as to avoid the situation that it cannot be used normally.
As a product that uses the screen as a single interactive form, we can get a lot of information by glancing" at the dial of the Apple Watch. Moreover, the dial can also cover functions such as blood oxygen monitoring and altitude monitoring, and the next operation can be completed by lifting the wrist and clicking the screen. This step by step experience will also further improve the efficiency of use.
Currently, blood oxygen monitoring is the exclusive feature of Apple Watch Series 6, and the dial supporting blood oxygen monitoring only appears in Series 6. In addition, all new watchOS 7-based dials will be available in both the Apple Watch SE and the Apple Watch Series 6. Apple does not restrict certain Watch faces to its flagship model, which makes it a consistent experience for any Apple Watch user.
This in the past required a product to be constantly updated and iterative. This fall, Apple completed the deployment of its Watch product line through the Apple Watch Series 6 and the Apple Watch SE.
Apple Watch SE is a product that subtracts on the Apple Watch Series 6. It doesn't support blood oxygen monitoring, and the screen doesn't support permanent light, but it has the same design as the flagship watch, as well as mainstream monitoring features. With the starting price of $329, the family sharing function can make every family member feel the charm of Apple Watch.
This is apple's way of subtracting the flagship in terms of the appearance that is most easily perceived by users, optimizing some details that are not easily perceived, and finally attaching a more reasonable price to it. Like the iPhone SE and the eighth generation iPad, they cost less and offer no discounts on the experience. What we need to do is to make a choice based on our own needs, and then choose a suitable device for ourselves.
By contrast, the Apple Watch Series 6 as the flagship, is a more complete product. At present, the Apple Watch Series 6 in front of you has the most comprehensive functions, interaction and complete ecology. In addition, functions such as sleep monitoring and fast charging are also subtly changing our habits of using Apple Watch. Even the newly released single-loop wristwatch band is guiding people to accept the partner on the wrist through changes in its shape.
After previous generations of the Apple Watch made its debut, some may still see it as a dispensary, not a necessity. However, with the addition of such situational functions as blood oxygen monitoring and sleep monitoring, the importance of the Apple Watch is also on the rise. For those who are used to the Apple ecosystem, the Apple Watch Series 6 has become irreplaceable. Today, when iPhone, iPad and other product lines are fully launched in the Pro era. Although Pro is not included in the title of Apple Watch Series 6, it has already provided us with pro-level user experience. If you're looking for a full range of monitoring capabilities, the Apple Watch Series 6 is worth it.
Tags: Apple Watch Series 6/SE
Next Huawei Watch's New Wrist ECG Technology Review
The Integration of Traditional Texture and Smart Experience of Zepp Z Smartwatch Experience
3 weeks ago Serena
The Small Square Screen of Redmi Watch is as Light as a Bracelet and Offers Users an Outstanding Wearing Experience
Huawei Watch's New Wrist ECG Technology Review


As can be seen nowadays, the net is being termed as the key source of entertainment for individuals all above the earth. Donchian Channel Moving Average the perfect Way to Guarantee success in the Foreign Exchange trade. The Donchian Channel Moving Average is a kind of oscillating Forex indicator that is virtually utilized as a analysis Forex technical indicator that moves above under a line in the middle. You could discover dizzy searching at the many different forex Forex indicators that are available to utilize.
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Home > News > Maersk to sell Mercosul as part of Hamburg Sud deal
Maersk to sell Mercosul as part of Hamburg Sud deal
DANISH shipping giant, AP Moller-Maersk Group, has confirmed that it's putting Brazilian cabotage subsidiary Mercosul Line up for sale as part of its deal to acquire container carrier Hamburg Sud from the German conglomerate Oetker Group.
The group is selling Mercosul Line in a preemptive move aimed at satisfying any potential competition concerns from Brazil's Conselho Administrativo de Defesa Economica (CADE), American Shipper reported.
Based in Sao Paulo, Brazil, Mercosul Line operates four vessels with 2,500 TEU of capacity each on two services connecting the country's major seaports, according to information on the company's website.
Hamburg Sud subsidiary Alianca Navegacao e Logistica currently controls 59 per cent of the Brazilian cabotage market, while Mercosul controls around 21 per cent, with the remaining share controlled by the companies' sole competitor, Log-In Logistica Intermodal, according to a report from Container Management Magazine.
Multiple media reports said bidders for the firm include CMA CGM of France; Geneva-based Mediterranean Shipping Co. (MSC); China's COSCO Shipping; NYK of Japan; as well as Germany's Hapag-Lloyd, which a few years back bought Chilean north-south specialist CSAV.
In an email to American Shipper, a Maersk spokesperson said: "With the purpose of securing the Brazilian competition authorities' (CADE) swift approval of the Hamburg Sud acquisition, it has been decided to divest Mercosul from AP Moller-Maersk. The divestment will ensure that the cabotage sector in Brazil remains competitive and that customers can benefit from a comprehensive choice of carriers."
Maersk first announced its intentions to acquire Hamburg Sud, the world's seventh largest container shipping line and a leader in the north-south trades, for an undisclosed price back in December 2016.
If completed, the deal would increase Maersk's overall containership fleet from 3.14 million TEU to 3.76 million TEU, growing its share of the world container fleet from 15.7 per cent to 18.6 per cent.


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package br.com.crescer.aula3;

import java.io.IOException;

public class Principal {

    public static void main(String[] args) throws IOException {
        MeuSQLUtils msu = new MeuSQLUtils();
//        PessoaDAO pessoaDAO = new PessoaDAO();
//        pessoaDAO.runExternalSql("instrucoes.sql");

        msu.columnDataAndLineNames("SELECT ID_PESSOA FROM PESSOA");

    }
}

redpajama_set_name: RedPajamaGithub


text:
How to Fight Islamist Terror from the...
How to Fight Islamist Terror from the Missionary Position
How to Fight Islamist Terror from the Missionary Position tells the interlinked stories of three unforgettable men - the flamboyant Ravi, the fundamentalist Karim and the unnamed and pragmatic Pakistani narrator - whose trajectories cross in Denmark. When a 'terrorist attack' takes place in town, all three men find themselves embroiled in doubt, suspicion and, perhaps, danger. An acerbic commentary on the times, How to Fight Islamist Terror from the Missionary Position is also a bittersweet, spell-binding novel about love and life today.
Tabish Khair is the author of various poetry collections, studies and novels. Winner of the All India Poetry Prize and fellowships at Delhi, Cambridge and Hong Kong, his novels - The Bus Stopped (2004), Filming: A Love Story (2007), and The Thing About Thugs (2010) - have been translated into several languages and shortlisted for major prizes in five countries.


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Crown Equity Holdings Inc. (OTCMKTS:CRWE) Announces Changes to Its Board of Directors and Principal Officers
Posted by admin On January 11, 2016 0 Comment
LAS VEGAS, NV / January 11, 2016 – Crown Equity Holdings Inc. (OTCMKTS:CRWE) today announced the resignation of John Scrudato as its Chief Financial Officer and Board member for personal reasons. The company also announced that it has appointed Rudy Chacon as its new CFO and Director, as well as electing Vinoth Sambandam as the company's Chief Technology Officer.
The Board remains at six members.
"As we welcome Mr. Chacon and Mr. Sambandam to the company, I would like to thank Mr. Scrudato for his contributions" stated Mike Zaman, President of Crown Equity Holdings Inc.
Rudy Chacon, brings more than 35 years of financial leadership experience in venture-backed private technology companies. Prior to joining CRWE, he was Chief Financial Officer of Larkspur Technology Solutions Systems Inc, Nech LLC, Gold Coast Construction Group Inc. and Versa Products Inc.
Vinoth Sambandam, brings years of technical (IT) experience to the company. Mr. Sambandam is a graduate of Dhanalakshmi College of Engineering in Chennai, India, where he received his degree in Tech Information Technology.
About Crown Equity Holdings Inc.
Together with its digital network of websites, Crown Equity Holdings Inc. provides and offers advertising branding, marketing solutions and services to boost customer awareness, as well as merchant visibility as a worldwide online multi-media publisher. The company focuses on the distribution of information for the purpose of bringing together its targeted audience and the advertisers that want to reach them. Its advertising services cover and connect a range of marketing specialties, as well as provide search engine optimization for clients interested in online media awareness. Crown Equity Holdings' objective is making its CRWE WORLD ( www.crweworld.com ) endeavor into a global online news and information source, as well as a global one stop shop for various distinct products and services. The company launches, invests and manages select businesses, projects and real estate endeavors. For more information regarding Crown Equity Holdings Inc., please visit: http://www.crownequityholdings.com.
This news release may contains "forward-looking statements" as that term is defined in Section 27A of the United States Securities Act of 1933, as amended and Section 21E of the Securities Exchange Act of 1934, as amended. Statements in this press release which are not purely historical are forward-looking statements and include any statements regarding beliefs, plans, expectations or intentions regarding the future. Such forward-looking statements include, among other things, the development, costs and results of new business opportunities. Actual results could differ from those projected in any forward-looking statements due to numerous factors. Such factors include, among others, the inherent uncertainties associated with new business opportunities and development stage companies. These forward-looking statements are made as of the date of this news release, and we assume no obligation to update the forward-looking statements, or to update the reasons why actual results could differ from those projected in the forward-looking statements. Although we believe that any beliefs, plans, expectations and intentions contained in this press release are reasonable, there can be no assurance that any such beliefs, plans, expectations or intentions will prove to be accurate. Investors should consult all of the information set forth herein and should also refer to the risk factors disclosure outlined in our annual report on Form 10-K for the most recent fiscal year, our quarterly reports on Form 10-Q and other periodic reports filed from time-to-time with the Securities and Exchange Commission.
Mike Zaman, President/CEO
Crown Equity Holdings Inc.
SOURCE: Crown Equity Holdings Inc.
TOPICS Crown Equity HoldingsCRWEOTCMKTS:CRWE
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\section{Introduction}

Relational databases are a common solution to storing large datasets, due to their economical space usage that limits the repetition of duplicate values. A dataset containing $d$ features, represented by columns, is stored in $\tau$ tables $T_1, T_2, \ldots, T_\tau$ that each contain a subset of the features. The design matrix $J$ with all $d$ features is not stored and must be re-constructed by joining the tables, i.e. $J=T_1 \Join T_2 \Join \cdots \Join T_\tau$. This process is considered both time- and space- intensive, but is a necessary step for machine learning algorithms that expect $J$ as input. When training boosted regression trees, the traditional approach is to compute $J$, then train the trees on the data in the design matrix. Relational algorithms\cite{moseley2020relational,abo2021relational} sidestep the need to calculate $J$, which can yield significant time and space complexity improvements. As such, altering the boosted regression trees training algorithm to rely on relational algorithms, instead of $J$, can yield time and space complexity improvements.

Boosted trees build off the classic tree model, known as a decision tree when the label is categorical and as a regression tree when the label is continuous. A decision/regression tree is a rooted binary tree such that each internal node has a condition and each leaf has a prediction. To find the prediction for a given point, we recursively check the condition for each internal node starting from the root. If the point meets the condition, we recurse on the right branch; otherwise we go to the left branch. The boosted regression tree algorithm involves greedily training multiple regression trees, each referred to as a weak regressor. The first tree is trained to predict datapoints' labels and the subsequent trees predict the datapoints' residuals. For some datapoint $x$ and $m$ weak regressors, the residual equals the datapoint's label $x_y$ minus the predictions $\hat{y}_1(x), \hat{y}_2(x), \ldots, \hat{y}_m(x)$ of all previously trained regression trees:
\begin{equation*}
r_x = x_y - \hat{y}_1(x) - \hat{y}_2(x) - \ldots - \hat{y}_m(x).
\end{equation*}
The prediction of the entire boosted regression model for some datapoint $x$ equals the sum of all weak regressors' predictions, i.e. $\hat{y}(x) = \hat{y}_1(x) + \hat{y}_2(x) + \ldots + \hat{y}_m(x)$.

Individual regression trees are commonly trained using a greedy algorithm. Training node $v$ of a regression tree consists of finding a splitting criterion of the form $J_f \leq \alpha$ for some feature $f$ of the dataset $J$ and threshold value $\alpha$ for the values $J_f$. Datapoints at $v$ that fulfill this criterion are assigned to the right child and all other datapoints are assigned to the left child of $v$; and then the algorithm recursively trains each subtree independently. To find this splitting criterion, each possible splitting threshold for each feature of the dataset is evaluated and the candidate splitting criterion yielding the lowest loss is selected\cite{loh2014fifty}. When making predictions in a regression tree, the predicted value of all examples in a leaf $\ell$ equals the average of the labels of all examples in $\ell$. If there are $n_\ell$ examples in the set $J^{(\ell)}$ of examples in leaf $\ell$, and the label of point $x$ is $x_y$, then the prediction for each of these examples will be $\sum_{x \in J^{(\ell)}} \frac{x_y}{n_\ell}$. As such, the goal is to provide a relational adaptation of this greedy algorithm for training regression trees, then to apply this adaptation to boosted regression trees. Section~\ref{sec:onetree} provides an algorithm to train a single regression tree relationally using the inside-out algorithm, a relational algorithm for evaluating SumProd queries~\cite{abo2016faq}.

In the relational setting, the input to a weak regressor consists of all previously trained weak regressors plus the $\tau$ tables $T_1, T_2, \ldots, T_\tau$ that each contain two or more features, which are represented by columns. One of these columns is the label $y$. The goal of the relational boosted regression tree algorithm is to train a set of boosted regression trees to predict $y$ on the basis of the other columns in $J=T_1 \Join \cdots \Join T_\tau$.

While training boosted regression trees on the design matrix can be done using well-known algorithms, there has been no algorithm proposed for training regression trees relationally. We introduce an algorithm in Section~\ref{sec:exactBoosted} for training boosted regression trees based on the algorithm for training individual regression trees as shown in Section~\ref{sec:onetree}. However, the runtime of this algorithm is dominated by the calculation of the sum of the dataset's squared residuals while determining splitting criteria for non-initial weak regressors. As such, the methods used to train a single regression tree do not translate well to training boosted regression trees. To address this issue, we next introduce an algorithm which uses sketching to find the sum of squared residuals in Section~\ref{sec:approx}. Sketching is a powerful dimensionality reduction tool for linear regression and matrix multiplication\cite{rajesh2021indatabase, woodruff2014sketching}. For more details on sketching, see Section~\ref{sec:tensorsketch}.

For acyclic joins, using SumProd queries as explained in Section~\ref{Sec:FAQ} and the inside-out algorithm~\cite{abo2016faq}, the sum of squared residuals can be exactly calculated in time $O(m^3L^2 \tau d^2 n \log n)$ where $m$ weak regressors of $L$ leaves are already trained, there are $\tau$ input tables with a total of $d$ features and the design matrix contains $n$ rows. However, using the sketching technique along with the SumProd query algorithm, an approximation of the sum of squared residuals can be calculated in time $O(m^2 L \tau d^2 n \frac{2+3^\tau}{\epsilon^2 \delta} \log n \log \frac{2+3^\tau}{\epsilon^2 \delta})$. The constant $\delta$ is set according to the desired accuracy guarantee of the sketching. With probability at least $1-\delta$, this algorithm gives a $(1+\epsilon)$ approximation for the sum of squared residuals. This sketching algorithm can then be plugged into the boosted regression trees algorithm. The time complexity of the boosted trees algorithm using sketching is asymptotically better for calculating the sum of squared residuals than the standard exact relational algorithm when $L$ is very big, which signifies that the trees are deep. Heuristically, this algorithm gives a similar result to the standard algorithm.

\subsection{Preliminary}
\subsubsection{FAQs and Relational Algorithms \label{Sec:FAQ}}

A SumProd query $Q$ consists of:
\begin{itemize}
\item A collection $T_1 , . . . , T_\tau$ of tables in which each column has an associated feature. Because all data is numerical in the regression tree setting, assume that all features are numerical. Let $F$ be the collection of all features, and $d = |F |$ be the number of features. The design matrix is $ J = T_1 \Join T_2 \Join \ldots \Join T_\tau$ , the natural join of the tables. Let $n$ denote the number of rows in the largest input table and $|J|$ denote the number of rows in J.
\item A function $q_f : R  \rightarrow S$ for each feature $f \in F$ for some base set $S$. We generally assume each $q_f$ is easy to compute.
\item Binary operations $\oplus$ and $\otimes$ such that $(S, \oplus, \otimes)$ forms a commutative semiring. Most importantly, this means that $\otimes$ distributes over $\oplus$.
\end{itemize}
Evaluating $Q$ results in
\begin{align*}
\oplus_{x \in J} \otimes_{f \in F} q_f(x_f)
\end{align*}
where $x$ is a row in $J$ and $x_f$ is the value for feature $f$ in row $x$. It is also possible for a SumProd query to group $\oplus$ by a table $T_i$. Doing so represents calculating the following term simultaneously for all the rows $r\in T_i$
\begin{align*}
\oplus_{x \in r \Join J} \otimes_{f \in F} q_f(x_f).
\end{align*}

\begin{lemma}[\cite{abo2016faq}]
Any SumProd query can be computed efficiently in time $O(md^2 n^{\text{fhtw}} \log n )$ where fhtw is the fractional hypertree width of the database. For an acyclic join, $\text{fhtw}=1$, so the running time is $O(md^2n \log n )$ which is polynomial.
\end{lemma}
You may find the definition of acyclic joins and fractional hypertree width in Appendix \ref{appendix:agm}.

\subsubsection{Tensor Sketch \label{sec:tensorsketch}}
Tensor sketch~\cite{avron2014subspace} is an approximation technique widely used for linear regression with polynomial kernels and linear regression with matrices that are the result of Kronocker products. Given $\tau$ vectors $v_1,\dots,v_\tau$, where the $i$-th vector is $w_i$ dimensional, and a Kronecker product $v_1 \odot v_2 \odot \cdots \odot v_\tau$, we define $\tau$ 2-wise independent hash functions $h_1(j), h_2(j), \ldots h_\tau(j)$ such that $h_t(j) : [w_t] \rightarrow [k]$. In addition, we define $\tau$ 2-wise independent hash functions $s_1(e), s_2(j), \ldots, s_\tau(j)$ such that $s_t(j) : w_t \rightarrow [0,1]$. Let $S$ be some random matrix of $k$ rows and $m$ columns, where each row has exactly one non-zero entry. The index of the non-zero entry in some row vector $\rho$ is $H(\rho) = \sum^k_{j=1} h_j(\rho_j) \mod m$ and the sign of this entry is $\pi^k_{j=1} s_j(\rho_j)$.

Let $\phi(v_1,\dots,v_\tau) = v_1 \odot v_2 \odot \cdots \odot v_\tau$ where $\odot$ is a Kronecker product which takes the product of all combinations of the coordinates of the input vectors. Next, let $TensorSketch(v_1,\dots,v_\tau)$ equal the result of applying tensor sketch algorithm on vectors $v_1,\dots,v_\tau$ as described in \cite{avron2014subspace} for some random selection of hash functions $h_i(j)$ and $s_i(j)$ where $1 \leq i \leq \tau$.

\begin{theorem}\cite{avron2014subspace} \label{The:tensorsketch}
The result of $TensorSketch(v)$ is the same as $\phi(v) \cdot S$. The matrix $S$ satisfies the Approximate Matrix Product property:

Let $A$ and $B$ be vectors with $d^\tau$ rows. For $k \geq (2 + 3^\tau) / (\epsilon^2 \delta)$, we have
$$Pr[||A^T SS^T B - A^T B||^2_2 \leq \epsilon^2 ||A||^2_2 ||B||^2_2] \geq 1 - \delta.$$

\end{theorem}

As such, the sketched term $A^TSS^TB$ may be calculated more efficiently and used in place of the exact term $A^TB$. Tensor sketch algorithm calculates $A^TS$ and $S^T B$ efficiently, when $A$ and $B$ are the result of a Kronecker product.

\subsection{Related Works}

A few machine learning models have already been adapted for a relational setting. Linear regression and factorization machines are implemented more efficiently by \cite{rendle2013scaling}, through using repeating patterns in the design matrix. \cite{kumar2015learning,schleich2016learning,acdc2018} further improve relational linear regression and factorization machines for specific scenarios. The relational algorithms for linear regression, singular value decomposition, factorization machines, and others are unified by \cite{abo2018database}. The support vector machine training algorithms given by \cite{yang2020towards,abo2021relational} adapt this model to the relational setting. \cite{cheng2019nonlinear} create a relational algorithm for Independent Gaussian Mixture Models, which is experimentally shown to be faster than computing the design matrix. Relational algorithms for $k$-means clustering are provided in \cite{moseley2020relational}.

Section 2 contains the algorithm to train a single regression tree on relational data and the exact algorithm for boosted regression trees on relational data with cubic runtime with respect to $L$. Section 3 describes the approximation algorithm that uses tensor sketching to achieve a quadratic runtime with respect to $L$.

\section{Exact Algorithm}
\subsection{Training a Single Regression Tree (Algorithm 1) \label{sec:onetree}}

For a particular node $v$ in a regression tree, let $J^{(v)}$ be the rows in the design matrix that satisfy all the constraints between node $v$ and the root of the regression tree. For every vertex $v$, the algorithm constructs a criterion of form $J^{(v)}_j \geq \alpha$ where $\alpha$ is a threshold for values of feature $j$ in the dataset. All points satisfying the constraint belong to the right child and all the ones not satisfying the constraint belong to the left child. This means that the training process consists of finding a threshold and a column index for every node in the regression tree. Starting from the root, we build the regression tree from top to bottom in a Breadth First Search order. To choose the splitting criterion at node $v$, the following process is repeated to calculate the mean squared error for each possible feature/column $j$ of in each table $T_i$ and for each possible threshold $\alpha$ for the feature $J_j$:

For every $T_i$, the algorithm performs three SumProd queries grouped by $T_i$ which will be explained shortly in details. Iterating over each row $\rho$ of $T_i$, these queries gather the subset of rows in the design matrix that satisfy all splitting criteria between the root node and $v$, and have the same values as $\rho$ in the columns they share with $\rho$. The first query is $n_v = \sum_{x \in \rho \Join J^{(v)}} 1$, which equals the number of rows in $J^{(v)}$ satisfying the constraints posed by $\rho$. The second is $s_v = \sum_{x \in \rho \Join J^{(v)}} x_y$, which equals the sum of the labels of these such rows and the third is $u_v = \sum_{x \in \rho \Join J^{(v)}} x_y^2$, which equals the sum of the labels squared.

For each feature $j$ in a table $T_i$, the possible threshold values for a splitting criterion on this feature is the domain of column $j$. Let $J_j$ be the domain of column $j$ which can be found in table $T_i$. For each possible splitting threshold $\alpha \in J_j$, the number of points that would satisfy the constraint between $v$ and its left child is
$$n_{v,j,\alpha} = \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} 1.$$
Note that the term $\sum_{x \in \rho \Join J^{(v)}} 1$ for different values of $\rho$ are precomputed using the SumProd queries grouped by table $T_j$. Similarly, the sum of labels of these such points is $$s_{v,j,\alpha} = \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} x_y,$$ and the sum of labels squared is $$u_{v,j,\alpha} = \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} x_y^2.$$ These expressions can each be determined by the SumProd queries that were already performed. All remaining points in $J^{(v)}$ satisfy the constraint between $v$ and the right child. Their number, the sum of their labels and sum of their labels squared can be calculated similarly, i.e. $m_{v,j,\alpha} =\sum_{\rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} 1$ for the number, $z_{v,j,\alpha} = \sum_{\rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} x_y$ for the sum of labels and $w_{v,j,\alpha} = \sum_{\rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} x_y^2$ for the sum of labels squared. For each child, the predicted label for all points in $J^{(v)}$ satisfying the constraint between $v$ and that child is the average label, which is $\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}}$ for the left child and $\frac{z_{v,j,\alpha}}{m_{v,j,\alpha}}$ for the right child.

To evaluate the mean squared error for the threshold $J_j \geq \alpha$, the algorithm calculates the mean squared error at each of the children. For the left child, the MSE is calculated as
$\frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: ,\rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} (\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}} - x_y)^2 =
\frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}}  ((\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}})^2 - 2x_y\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}}  + x_y^2) =  (\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}})^2 - 2s_{v,j,a}\frac{1}{n_{v,j,\alpha}}(\frac{s_{v,j,\alpha}}{n_{v,j,\alpha}}) + \frac{1}{n_{v,j,\alpha}}u_{v,j,a} = -\frac{s^2_{v,j,a}}{n^2_{v,j,a}} + \frac{u_{v,j,a}}{n_{v,j,\alpha}}$

and similarly for the right child as
$\sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} (\frac{z_{v,j,\alpha}}{m_{v,j,\alpha}} - x_y)^2 = -\frac{z^2_{v,j,a}}{m^2_{v,j,a}} + \frac{w_{v,j,a}}{m_{v,j,\alpha}}$. The MSE at $v$ given this splitting threshold is the sum of the MSEs at its children, i.e. $$MSE(v,j,\alpha)=-\frac{s^2_{v,j,a}}{n^2_{v,j,a}} + \frac{u_{v,j,a}}{n_{v,j,\alpha}} -\frac{z^2_{v,j,a}}{m^2_{v,j,a}} + \frac{w_{v,j,a}}{m_{v,j,\alpha}} = -\frac{1}{n_{v}}(\frac{s^2_{v,j,a}}{n_{v,j,a}}  -\frac{z^2_{v,j,a}}{m_{v,j,a}} + u_v).$$

Calculate $MSE(v,j,\alpha)$ for each threshold $\alpha$ to find the best threshold $a$ for each feature $j$, then select the feature $g$ that yields lowest MSE. Finally, add the two new nodes as children of $v$ to the regressor tree.

\begin{theorem}
Algorithm 1 determines the splitting threshold for one node of a regression tree using $O(\tau)$ SumProd queries.
\end{theorem}
\begin{proof}
When selecting a splitting criterion for some node $v$ in the regression tree, it is necessary to find the number of points, the sum of labels and the sum of labels squared for the rows in $J^{(v)}$. These three pieces of information are organized by the rows' values for each of the $d$ features of $J$, which is achieved via grouping by each of the $\tau$ input tables. As such, each of these three pieces of information require $\tau$ SumProd queries, meaning $O(\tau)$ SumProd queries are needed to find the splitting threshold for one node $v$.
\end{proof}

\begin{corollary}
Algorithm 1 trains a single regression tree with $L$ leaves and $\tau$ tables using $O(\tau L)$ SumProd queries.
\end{corollary}
\begin{proof}
Because a tree with $L$ leaves has $O(L)$ nodes and finding the threshold for one node requires $O(\tau)$ SumProd queries, Algorithm 1 requires $O(\tau L)$ SumProd queries.
\end{proof}

\begin{corollary}
Given an acyclic join query, Algorithm 1 trains a single regression tree with $L$ leaves and $\tau$ tables in time $O(\tau L m d^2 n \log n)$.
\end{corollary}
\begin{proof}
Algorithm 1 requires $O(\tau L)$ SumProd queries, the runtime of which is $O(m d^2 n \log n)$. Thus, the runtime of Algorithm 1 is $O(\tau L m d^2 n \log n)$.
\end{proof}

\subsection{Exact Algorithm for Boosted Trees (Algorithm 2) \label{sec:exactBoosted}}

The first weak regressor, $R_1$, is trained using the same method as detailed in Algorithm 1. Assume we have trained regression trees $R_1,\dots, R_m$. The method to construct the regression tree $R_{m+1}$ is similar to Algorithm 1 except that instead of points' labels, the tree must predict the residuals
\begin{align*}
R = Y - \hat{Y}_1 - \hat{Y}_2 - \ldots - \hat{Y}_m.
\end{align*}
Where $Y$ is the vector of labels and $\hat{Y}_t$ is the vector of the $t$-th weak regressor's predictions for the set of points in the design matrix $J$.

As in Algorithm 1, for every vertex $v$, the algorithm constructs a criterion of form $J_j \geq \alpha$ where $\alpha$ is a threshold and all the points satisfying the constraint belong to the right child and all the ones not satisfying the constraint belong to the left child. Starting from the root, we build the regression tree from top to bottom in a Breadth First Search order.

What differs from Algorithm 1 is the need to calculate, for each table $T_i$ and each row $\rho \in T_i$, the values  $\sum_{x \in \rho \Join J^{(v)}} r_x$ and $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$, which respectively equal the sum of the residuals and the sum of the residuals squared for the points that are assigned to node $v$ of the tree $R_{m+1}$ grouped by table $T_i$. To calculate $\sum_{x \in \rho \Join J^{(v)}} r_x$, note that the predicted value for each previously-built regression tree has already been calculated and can be assumed to be available without needing to perform a SumProd query. Instead, for each leaf $\ell$ of each previously built weak regressor $R_t$, let $J^{(\ell)}$ be the set of rows in the design matrix that satisfy all the constraints between node $\ell$ and the root of the regression tree $R_t$ and let $J^{(\ell,v)}$ be the intersection of $J^{(v)}$ and $J^{(\ell)}$. Calculate the SumProd query $\sum_{x \in \rho \Join J^{(\ell,v)} } F(x)$ where $F(x)$ is 1 for all tables except the last table $T_\tau$ and the predicted value of $\ell$ for table $T_\tau$. The result of this query equals the sum of predicted values for all points that are present in $J^{(v)}$ and $J^{(\ell)}$. The sum of repeating this query for each leaf $\ell$ in the set of all leaves $L_t$ in $R_t$ yields $\hat{Y}^{(v)}_t =\sum_{\ell \in L_t} \sum_{x \in \rho \Join J^{(\ell,v)}} F(x)$, the sum of predicted values from $R_t$ for all rows in $J^{(v)}$. Then, calculate the sum of labels for all points in $J^{(v)}$ by the query $J_y^{(v)} =\sum_{x \in \rho \Join J^{(v)}} x_y$ and calculate the sum of residuals for all points in $J^{(v)}$,
\begin{align*}
R^{(v)}  = J_y^{(v)} - \hat{Y}^{(v)}_1  - \hat{Y}^{(v)}_2 - \dots -  \hat{Y}^{(v)}_m.
\end{align*}
Next, let $\hat{y}_t(x)$ be the prediction of weak regressor $R_t$ for some row $x$. To obtain $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$ requires finding the values for
\begin{align}
\sum_{x \in \rho \Join J^{(v)}} (r_x^2) &= \sum_{x \in \rho \Join J^{(v)}} (x_y - \hat{y}_1(x) - \hat{y}_2(x) - \ldots - \hat{y}_m(x))^2 \label{Eq:wantToApprox} \\
&= \sum_{x \in \rho \Join J^{(v)}} (x_y^2 - x_y\sum_{i=1}^m \hat{y}_i(x) + \sum_{i=1}^m \hat{y}_i(x) \sum_{j=1}^m \hat{y}_j(x)) \\
&= \sum_{x \in \rho \Join J^{(v)}} (x_y^2 - x_y\sum_{i=1}^m \hat{y}_i(x) + \sum_{i=1}^m \hat{y}_i(x) \sum_{j=1, j\neq i}^m \hat{y}_j(x)  + \sum_{i=1}^m \hat{y}_i^2(x)).
\end{align}
The first term may be calculated as described in Algorithm 1 and the fourth term (sum of squared regressors' predictions) may be calculated similarly to finding the sum of regressors predictions, i.e. calculate the SumProd query $\sum_{x \in \rho \Join J^{(\ell,v)}} F(x)$ where $F(x)$ is 1 for all tables except the last table $T_\tau$ and the predicted value squared of $\ell$ for table $T_\tau$. The sum of repeating this query for each leaf $\ell$ in the set of all leaves $L_t$ in $R_t$ yields $\sum_{x \in \rho \Join J^{(v)}} \hat{y}^2_t(x) =\sum_{\ell \in L_t} \sum_{x \in \rho \Join J^{(\ell,v)}} F(x)$, the sum of squared predicted values from $R_t$ for all rows in $J^{(v)}$. The second term is merely the product of $\sum_{x \in \rho \Join J^{(v)}}  x_y$ and $\sum_{x \in \rho \Join J^{(v)}}  \sum_{i=1}^m \hat{y}_i(x)$ which were already calculated in order to find the sum of residuals $R^{(v)}$.

However, the fourth term $\sum_{x \in \rho \Join J^{(v)}} \sum_{i=1}^m \hat{y}_i(x) \sum_{j=1, j\neq i}^m \hat{y}_j(x)$ requires finding the product of sums of predictions for any non-matching pair of weak regressors. For any row $x$ in $J^{(v)}$ and any two regressors $R_i$ and $R_j$, $x$ can be in $J^{(\ell_i)}$ for any leaf $\ell_i \in L_i$ of $R_i$ and $J^{(\ell_j)}$ for any leaf $\ell_j \in L_j$ of $R_j$. As such, a separate query must be performed for each pair of leaves $\ell_i$ and $\ell_j$ for every pair of regressors $R_i$ and $R_j$, of the form $\sum_{x \in \rho \Join J^{(v)}} \sum_{x \in \rho \Join J^{(i,j,v)}} F(x)$ where $J^{(i,j,v)}=J^{(\ell_i)} \cap J^{(\ell_j)} \cap J^{(v)}$, the function $F(x)$ equals the product of the predicted values in leaves $\ell_i$ and $\ell_j$ for the last table $T_\tau$ and $F(x)$ is 1 for all other tables. The sum of performing this query $L^2$ times, once for each pair of leaves, equals $\sum_{x \in \rho \Join J^{(v)}} \hat{y}_i(x) \hat{y}_j(x)$ for one pair of weak regressors $R_i$ and $R_j$. This term is computed $m^2-m$ times, once for each non-identical pair of weak regressors.

Let $r_x$ be the residual for a row $x$. After also gathering $n_{v,j,\alpha}$ using the same query as in Algorithm 1, the predicted value for the left child is $p_{v,j,a} = \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} \frac{r_x}{n_{v,j,a}}$ and the predicted value for the right child is $b_{v,j,a} = \sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} \frac{r_x}{m_{v,j,a}}$. Then, the MSE for the left child is

\begin{align*}
\frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} (p_{v,j,a} - r_x)^2 &= \frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} (p_{v,j,a}^2 - 2p_{v,j,a}r_x + r_x^2) \\
&= p_{v,j,a}^2 -2p_{v,j,a}\frac{1}{n_{v,j,\alpha}}(\sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x) + \frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x^2 \\
&= -\frac{(\sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{n^2_{v,j,a}} + \frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} (r_x^2)
\end{align*}
Similarly, the MSE for the right child is $\frac{1}{m_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} (b_{v,j,a}-r_x)^2 = -\frac{(\sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{m^2_{v,j,a}} + \frac{1}{m_{v,j,\alpha}}\sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{i \in J^{(v)}} (r_x^2)$. The MSE for $J^{(v)}$ with splitting criterion $J_j \geq \alpha$ is the sum of the MSEs for the two children of $v$ given this splitting criterion, i.e.

\begin{align*}
MSE(v,j,\alpha) =& -\frac{(\sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{n^2_{v,j,a}} + \frac{1}{n_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} (r_x^2) \\
&-\frac{(\sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{m^2_{v,j,a}} + \frac{1}{m_{v,j,\alpha}} \sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} (r_x^2) \\
=& -\frac{1}{n_{v}} (\frac{(\sum_{\rho \in T_i: \rho_j < \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{n_{v,j,a}} - \frac{(\sum_{\rho \in T_i: \rho_j \geq \alpha} \sum_{x \in \rho \Join J^{(v)}} r_x)^2}{m_{v,j,a}} + \sum_{x \in \rho \Join J^{(v)}} (r_x^2) )
\end{align*}

Calculate $MSE(v,j,\alpha)$ for each threshold $\alpha$ to find the best threshold $a$ for each feature $j$, then select the feature $g$ yields lowest MSE. Finally, add the two new nodes as children of $v$ to the regressor tree.

\begin{theorem} \label{thm:apprsumResids}
Algorithm 2 calculates the sum of squared residuals using $O(m^2L^2 \tau)$ SumProd queries.
\end{theorem}
\begin{proof}
When $m$ weak regressors have already been constructed and the splitting criterion is being selected for some node $v$ of the $(m+1)$-th weak regressor, the sum of residuals squared uses $O(m^2L^2)$ queries because the term $\sum_{x \in \rho \Join J^{(v)}} \sum_{i=1}^m \hat{y}_i(x) \sum_{j=1, j\neq i}^m \hat{y}_j(x)$ iterates over all pairs of leaves of two weak regressors, for all pairs of weak regressors. This process is repeated to group by each of the $\tau$ input tables, so the sum of squared residuals is calculated in $O(m^2L^2 \tau)$ SumProd queries.
\end{proof}

\begin{theorem}
Algorithm 2 calculates the sum of squared residuals in time $O(m^3L^2 \tau d^2 n \log n)$.
\end{theorem}
\begin{proof}
Algorithm 2 requires $O(m^2L^2 \tau)$ SumProd queries to find the sum of residuals squared as shown in \ref{thm:apprsumResids}. The runtime of a SumProd query is $O(m d^2 n \log n)$, so the time to find the sum of squared residuals is $O(m^3L^2 \tau d^2 n \log n)$.
\end{proof}

\begin{theorem}
Algorithm 2 determines the splitting threshold for one node of the $m$-th regression tree using $O(m^2L^2 \tau)$ SumProd querıes.
\end{theorem}
\begin{proof}
When $m$ weak regressors have already been constructed and the splitting criterion is being selected for some node $v$ of the $(m+1)$-th weak regressor, the following items must be gathered for each child of $v$, each feature $j$ of each table $T_t$ and possible splitting threshold $\alpha$ for feature $j$: the number of points, the sum of the residuals and the sum of residuals squared. Grouping by just one input table, the number of points can be gathered with one SumProd query and the sum of residuals requires $O(mL)$ SumProd queries. However, the sum of residuals squared uses $O(m^2L^2)$ queries as shown in Theorem~\ref{thm:apprsumResids}. This process is repeated to group by each of the $\tau$ input tables. As such, Algorithm 2 requires $O(m^2L^2 \tau)$ SumProd queries to find the splitting threshold for one node $v$.
\end{proof}

\begin{theorem}
Algorithm 2 can train the $m$-th regression tree with $L$ leaves using the greedy algorithm using $O(m^2L^3 \tau)$ SumProd querıes.
\end{theorem}
\begin{proof}
This process is repeated at each non-terminal node $v$ of the tree where there are $O(L)$ leaves. As such, Algorithm 2 requires $O(m^2L^3 \tau)$ SumProd queries.
\end{proof}

\begin{corollary}
The runtime of Algorithm 2 is $O(m^3 L^3 \tau d^2 n \log n)$.
\end{corollary}
\begin{proof}
Algorithm 2 requires $O(m^2L^3 \tau)$ SumProd queries. The runtime of a SumProd query is $O(m d^2 n \log n)$.
Hence, the runtime of Algorithm 2 is $O(m^3 L^3 \tau d^2 n \log n)$.
\end{proof}

\section{Approximation Algorithm \label{sec:approx}}
Assume that $m$ weak regressors have already been trained and node $v$ of $R_{m+1}$ is being evaluated to determine its splitting criterion. The time complexity of the boosted algorithm can be improved by approximating the term that dominates the runtime of the exact boosted algorithm, which is
$$\sum_{x \in \rho \Join J^{(v)}} (r_x^2) = \sum_{x \in \rho \Join J^{(v)}} (x_y - \hat{y}_1(x) - \hat{y}_2(x) - \ldots - \hat{y}_m(x))^2$$
as given in Equation~\ref{Eq:wantToApprox}. Let the $i$-th element of some vector $\bar{q}$ be denoted by $\bar{q}_i$. Then, the term $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$ can also be considered the L2 squared norm of vectors, i.e.
$$\sum_{x \in \rho \Join J^{(v)}} (r_x^2) =  || Y - \hat{Y}_1 - \hat{Y}_2 - \ldots - \hat{Y}_m ||^2_2$$
At index $i$, $Y$ contains the label of the $i$-th point and $\hat{Y}_j$ contains the $j$-th regression tree's prediction for the $i$-th point in $J$. Each of these vectors is length $|J|$ and has zeros at the indices corresponding to points in $J$ but not in $J^{(v)}$. To approximate $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$, the vectors $Y, \hat{Y}_1, \hat{Y}_2, \ldots, \hat{Y}_m$ are each sketched to find $Y', \hat{Y}_1', \hat{Y}_2', \ldots, \hat{Y}_m'$. Because sketching is a linear operator, $Y' - \hat{Y}_1' - \hat{Y}_2' - \ldots - \hat{Y}_m'$ is the sketch of $Y - \hat{Y}_1 - \hat{Y}_2 - \ldots - \hat{Y}_m$.

For one weak regressor $R$, the vector $\hat{Y}$ can be sketched as a vector $\hat{Y}'$. For simplicity, consider sketching $\hat{Y}'$ for just one fixed point $x \in \rho \Join J^{(v)}$. Vector $Y$ is the sum of $L$ vectors $p_1, p_2, \ldots, p_L$ of length $|J|$. The vector $p_i$ represents the predictions of the regressor's $i$-th leaf $\ell_i$ for the rows of the design matrix that are assigned to $\ell_i$ and to node $v$. This set of rows can be expressed as $J^{(i,v)} = J^{(\ell_i)} \cap J^{(v)}$. Because each point in $J$ is only in one of the sets $J^{(1,v)}, J^{(2,v)}, \ldots, J^{(L,v)}$, all but one of these vectors consists entirely of zeroes when considering just the fixed point $x$. If $x$ is in set $J^{(i,v)}$, then the vector $p_i$ has only one non-zero element. This element is at the index corresponding to the index of $x$ in the design matrix $J$ and is equal to the prediction at leaf $\ell_i$ of tree $R$.

The vector $p_i$ is the product of $\tau$ vectors, one for each of the tables as explained in the following. The sketching algorithm is applied on these vectors representing tables and is used to approximate the vector $p_k$ representing the predictions of one leaf $\ell_i$ of one regressor $R$.

For each feature $J_j$ represented in the columns of tables $T_1, T_2, \ldots, T_\tau$, assign feature $J_j$ to one of the tables containing this feature. Let $E_t$ be the set of features assigned to table $T_t$ and let $D_t$ be the domain of $E_t$. Let $\pi_t(x)$ be the projection of $x$ onto $T_t$, which is just the features of $x$ that are in $E_t$. Let $w_t(x)$ be the index of $\pi_t(x)$ in $D_t$, assuming some ordering of $D_t$. Let $e_{w_t(x)}$ be a vector of $|D_t|$ elements with 1 in the index $w_t(x)$ and 0 elsewhere. Let $d_i$ be the predicted value at leaf $\ell_i$ of regressor $R$. Then,
$p_{i,x} = d_i ( e_{w_1(x)} \otimes e_{w_2(x)} \otimes \cdots \otimes e_{w_\tau(x)} )$ is representing the prediction of leaf $\ell_i$ for $x$. This vector has the prediction for $x$ at the index corresponding to the index of $x$ in $J$ and zeros at all other indices. Then, $p_i = \sum_{x \in \rho \Join J^{(i,v)}} p_{i,x}$. Calculating and summing together the vectors $p_i$ for all $1 \leq i \leq L$ equals $Y$, the vector of predictions for weak regressor $R$ for all points in $J^{(v)}$.

Sketching a vector $v$ is equivalent to calculating the multiplication $Sv$ for some matrix $S$. Since $S$ is very sparse and has special properties, we do not perform the calculation explicitly. However, the result would be the same as the product. Therefore, the sketch of a summation of vectors is equivalent to the summation of the sketch of those vectors. Therefore, to sketch $Y - \hat{Y}_1 - \hat{Y}_2 - \ldots - \hat{Y}_m$, we can calculate the summation over the sketch of the vectors $p_{k,x}$ which, as we show shortly, can be computed using SumProd queries.

The sketching is applied to the term $e_{w_1(x)} \otimes e_{w_2(x)} \otimes \cdots \otimes e_{w_\tau(x)}$ for some fixed $x \in \rho \Join J^{(i,v)}$ to calculate a smaller vector $p_{i,x}'$. Define $\tau$ 2-wise independent hash functions $h_1(j), h_2(j), \ldots h_\tau(j)$ such that $h_t(j) : |D_t| \rightarrow k$. Also define $\tau$ 2-wise independent hash functions $s_1(e), s_2(j), \ldots, s_\tau(j)$ such that $s_t(j) : |D_t| \rightarrow [0,1]$. Define some integer $k$ depending on the desired accuracy probability and runtime. Let $e_{w_i (x)}(j)$ be the element in the $j$-th index of $e_{w_i (x)}$. Then, for each $t$ where $1 \leq t \leq \tau$ calculate
\begin{align*}
g_t(e_{w_t (x)}) &= \sum^{|D_t|}_{j=1} s_t(j) * e_{w_t (x)}(j) * x^{h_t(j)}  \\
&= s_t(w_t(x)) * z^{h_t(w_t(x))}
\end{align*}
where $z$ is a variable. The degree of $z$ represents the index of its term's coefficient in a vector. The tensor-sketched vector $p_{i,x}'$ of the prediction for one point $x$ in $J^{(i,v)}$ for regressor $R$ may be calculated as $d_i (g_1(e_{w_1 (x)}) * g_2(e_{w_2 (x)}) * \ldots * g_\tau(e_{w_\tau (x)}) )$. Then,  $p_i' = \sum_{x \in \rho \Join J^{(i,v)}} p'_{i,x}$ and $\hat{Y}' = \sum_{i = 1}^L p'_i$. Note that $p'_i$ can be computed using a SumProd query grouped by one of the tables.

Meanwhile, the vector of labels $Y$ can be expressed as the SumProd query $\sum_{x \in \rho \Join J^{(i,v)}} x_y$. This SumProd query is equivalent to $\sum_{x \in \rho \Join J^{(i,v)}} a_1 \otimes a_2 \otimes \cdots \otimes a_\tau$, where $a_t$ corresponds to the $t$-th table $T_t$ and has the same number of elements as $T_t$ has. For some fixed $x \in \rho \Join J^{(v)}$, the elements of vector $a_t$ are all zeroes except at the index corresponding to the index of $\pi_t(x)$ in $T_t$. For $a_1, a_2, \ldots a_{\tau-1}$, the element at this index is equal to $1$. For $a_\tau$, the element at this index is equal to $x_y$. $Y'$ can be found using the sketching technique on $a_1, a_2, \ldots, a_\tau$ for each $x \in \rho \Join J^{(i,v)}$. Using the same $\tau$ 2-wise independent hash functions $h_1(j), h_2(j), \ldots h_\tau(j)$ and the same $\tau$ 2-wise independent hash functions $s_1(e), s_2(j), \ldots, s_\tau(j)$, we can have the tensor sketch of vector $Y$. Let $a_{t}(j)$ be the element in the $t$-th index of $a(i)$. Then, for each $t$ where $1 \leq t \leq \tau$ calculate
\begin{align*}
g_t(a_t) &= \sum^{|D_t|}_{j=1} s_t(j) * a_t(j) * x^{h_t(j)}
\end{align*}
where $*$ is polynomial multiplication modulo $x^k$. Then, $Y' = \sum_{x \in \rho \Join J^{(i,v)}} g_1(a_1) * g_2(a_2) * \ldots * g_\tau(a_\tau) $.

This way, the sketched terms $Y', \hat{Y}_1', \hat{Y}_2', \ldots, \hat{Y}_m'$ need to only be calculated one time for each node $v$ that is being evaluated for a splitting criterion.

\begin{theorem} \label{thm:approxTime}
The tensor sketching technique can approximate $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$ grouped by all tables using $O(mL \tau)$ SumProd queries.
\end{theorem}
\begin{proof}
One query for each leaf of each prior weak regressor, plus one query for Y'.

Each term of the form $p'_i = d_i \sum_{x \in J^{(k,v)}} (g_1(e_{w_1 (x)}) * g_2(e_{w_2 (x)}) * \ldots * g_\tau(e_{w_\tau (x)}) )$ grouped by table $T_i$ can be calculated via one SumProd query, because polynomial multiplication and summation form a semiring. The term $p_i'$ is calculated once for each of the $L$ leaves of the $m$ weak regressors in order to calculate the approximated prediction vectors $\hat{Y}_1', \hat{Y}_2', \ldots, \hat{Y}_m'$ for each weak regressor. It is necessary to repeat this calculation grouped by each of the $\tau$ input tables. As such, the term $p'_i$ is calculated $mL \tau$ times, making for $O(mL \tau)$ SumProd queries. As $Y'$ is found using just one additional SumProd query per input table $\sum_{x \in \rho \Join J^{(k,v)}} g_1(a_1) * g_2(a_2) * \ldots * g_\tau(a_\tau)$ where $\rho \in T_i$ for some input table $T_i$, the number of SumProd queries to find $\sum_{x \in \rho \Join J^{(v)}} (r_x^2)$ is $O(mL \tau)$.
\end{proof}

\begin{theorem} \label{thm:approxTotalTime}
The sketching version of Algorithm 2 can train the $m$-th regression tree with $L$ leaves using the greedy algorithm in  $O(mL^2 \tau)$ SumProd querıes.
\end{theorem}
\begin{proof}
When $m$ weak regressors have already been constructed and the splitting criterion is being selected for some node $v$ of the $(m+1)$-th weak regressor, the sum of residuals squared is now sketched in $O(mL \tau)$ SumProd queries as per Theorem~\ref{thm:approxTime}. Because this process is repeated at each of the $O(L)$ nodes of the $(m+1)$-th weak regressor, the number of required SumProd queries is $O(m L^2 \tau)$.
\end{proof}

\begin{corollary}
The runtime of sketched Algorithm 2 is $O(m^2 L^2 \tau d^2 n k \log n \log k)$.
\end{corollary}
\begin{proof}
Sketched Algorithm 2 requires $O( m L^2 \tau )$ SumProd queries as per \ref{thm:approxTotalTime}. The runtime of a SumProd query is $O(md^2n \log n )$ times the runtime of $\otimes$ which corresponds to Fast Fourier Transform. The Fast Fourier Transform runtime is $O(k \log k)$. Hence, the runtime of Algorithm 2 is $O(m^2 L^2 \tau d^2 n k \log n \log k)$.
\end{proof}

\begin{theorem}
We can obtain $(1\pm \epsilon)$ approximation of $\sum_{x \in \rho \Join J^{(v)}} r_x^2$ for simultaneously for all features and splitting criteria with probability $0.99$ when determining the splitting criterion for node $v$ of regression tree $R_{m+1}$ by setting $k=O(\frac{2+3^\tau}{\epsilon^2 \delta})$.
\end{theorem}
\begin{proof}
To evaluate node $v$ of regressor $R_{m+1}$ for a splitting criterion, it is necessary to evaluate splitting on $O(d)$ features, each at of the $O(n)$ possible thresholds. Thus, there are $O(nd)$ residual squared terms that must be sketched. We use Theorem \ref{The:tensorsketch} and union bound. To apply union-bound, $\delta$ must be set to $O(\frac{1}{n d})$ in order to obtain constant probability for the event that all the approximations are within $1+\epsilon$ accuracy.
\end{proof}

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


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Q: Qual é a relação entre DER e banco de dados relacionais? Qual é a relação entre DER e banco de dados relacionais?

A: DER ou Diagrama Entidade-Relacionamento, como o próprio nome diz, é uma representação gráfica das entidades necessárias em um modelo de dados e seus relacionamentos, portanto é uma forma abstrata.
Bancos de dados relacionais são os mecanismos que concretizam essas representações e produzem uma base de dados com essas entidades e possuem facilidades que permitem que elas sejam acessadas de forma relacionada.
Justamente por ambos terem como base o relacionamento dos dados eles se encaixam bem.
É comum dizermos que o DER é usado para criar um modelo lógico e o banco de dados é o modelo físico. É um pouco mais complicado que isso, mas é uma forma simplificada de entender.
O banco de dados é a implementação do que foi especificado no DER.

A: Um modelo entidade relacionamento (MER) descreve os objetos (entidades) envolvidos em um domínio de negócios, com suas características (atributos) e como elas se relacionam entre si (relacionamentos). Esse modelo conceitual é representado graficamente pelo diagrama de entidade relacionamento (ER ou DER). Esse diagrama facilita a comunicação entre os integrantes da equipe, pois oferece uma linguagem comum utilizada tanto pelo analista, responsável por levantar os requisitos, e os desenvolvedores, responsáveis por implementar aquilo que foi modelado.
Já um banco de dados relacional modela os dados de uma forma que eles sejam percebidos pelo usuário como tabelas, ou mais formalmente relações. A linguagem padrão dos Bancos de Dados Relacionais é a Structured Query Language, ou simplesmente SQL, como é mais conhecida.
A relação entre DER e banco de dados relacionais é que um modelo ER é normalmente implementado como um banco de dados. Nos casos de um banco de dados relacional, que armazena dados em tabelas, as próprias tabelas representam as entidades. Alguns campos de dados nestas tabelas apontam para índices em outras tabelas, que representam relacionamentos.

A: O DER é o diagrama  de entidades e relacionamentos ou seja você vai mostrar a parte dele como as entidades(tabelas) do seu banco de dados estão relacionadas seria uma forma logica de representar esse relacionamento, e o banco de dados relacional uma forma física. De forma geral no DER você coloca varias entidades se relacionando, por exemplo tabela produto com a fornecedor, produto podendo ter apenas um fornecedor e o fornecedor varias coisas, o modelo relacional é a mesma coisa, só que com sua aplicação direta no banco de dados já, através das chaves primárias e estrangeiras.


After that we headed to the Widdler area where both Levi and Isaac got quick sends of the Widdler (see photos below). We then went to the Optimist area where we all tried a bunch of stuff, but I don't think anyone sent anything hard besides Isaac walking up his classic slab problem Willing and Able a couple times. I managed to shake my way up a new problem that I've been looking at ever since I first went to the Optimist area. It's an amazing double hand crack system about 40ft uphill and left of the Green Monster. It's only about 12 ft of V0 climbing, but it's right over the worst landing I've ever bouldered over.
Lastly, Isaac and I went up to Adam's Wall. It's a really cool move up to a horizontal crack, then a couple sketchy moves to the top. I managed to get the first moves, but I couldn't commit to the upper moves. Isaac had done it before, but missed most of the good holds on his top out and made it a little harder. Instead of calling it good, he hopped right back on and sent it again in perfect style.
Also, before I forget, I would like to give credit where credit is due. Jeff Ho, the local Bozeman bouldering legend, took the photo of lichen at Whiskey (with my camera) that I've been egregiously using on top of my website. Without his futuristic vision for lichen photography, this site would only be getting 12 hits a day instead of 14. Thanks Ho!
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Issac, if you do the same problem 15 times, it's not going to inflate your ego anymore! It's already to big, haha. Nice job on the Widdler! Classic.


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I can't prove this of course, just as no one can prove their viewpoint since we can't demonstrate when the spirit leaves the body even though we can often subjectively know for certain when it has happened.
I talk about that in In Light of Eternity when I tell the story of entering the room after my mom had died and being overwhelmed with the sense of her absence, even though she'd barely moved or responded for a few months. The difference wasn't in response, but in the fact that "the glory had departed." She had been in that room every day I had visited her and now was obviously and dramatically gone.
My key text is Hebrews 9:27, "Everyone must die once, and after that be judged by God" (GNT). Obviously it was spoken in a day where giving food and drink and medicines to a person who would otherwise die was about the extent of the intervention, and there was no way to continue someone's breathing by artificial means (beyond breathing oxygen in for a few minutes, which I suppose was rarely done in those days).
But I still believe the essence of Hebrews 9:27 remains true, that while someone may be close to death and appear to die for seconds or minutes or even hours, they actually die only once, at the point God takes their spirit out of their body. And except in miracles, He doesn't put their spirit back in their bodies. I think such miracles are rare. If they were normal, they wouldn't be miracles.
I've been present twice when I believe I knew within seconds when the spirit left the body, once with my friend Jerry Hardin and again when my dad died. They both stopped breathing, and in my dad's case the monitor showed his heart had stopped beating. Death was obvious and I'm convinced it was at that point—not before, though they were both unconscious for days previous—when death actually occurred.
Comas are not death, unconsciousness is not death, "vegetative states" are not death. Death is death. In comas and vegetative states (I hate that term, as it's so dehumanizing) there's evidence of neurological functions. Patients can often breathe on their own, their reflexes still function, and they might respond to light or sound. In those cases, despite inability to communicate, I would surmise death hasn't occurred and their spirits are still present.
But with both Jerry and my dad, efforts could have been made to artificially sustain their breathing and hearts beating. Would those medical efforts have kept their spirits from departing? Part of me says no, God would have taken their spirits at their appointed time; the other part is less sure. Could artificially prolonging physical death actually imprison a spirit in a body it would have left when a person's life would have naturally ended? It's a difficult question and impossible to answer, but it should raise questions for family members of believers who may at some point be "playing God" by not allowing natural death to happen (others, of course, play God by intervening to take the life; I deal with both of these in this article on euthanasia).
Even though I've been told the brain can still function for a few hours after the heart stops, I think a stopped heart that remains stopped may be the most objective way to view death. The brain can't function long without the flow of blood from the beating heart and the oxygen it delivers.
Some people who've told me they've died twice refer to their heart stopping on the operating table, or in the ambulance. But then they're revived. But to say that every time a heart stops a person dies is to say that some people die hundreds or thousands of times, which to me isn't meaningful.
When someone experiences the "irreversible cessation of all functions of the brain," they are considered legally dead. Of course, the operative word is irreversible, meaning that sufficient time must pass for that to be determined. When brain functions return, by definition it hasn't been irreversible, unless this is a miracle such as the raising of Lazarus. I believe in such miracles, of course, but it's easier to measure when no artificial means such as ventilators have kept people alive or appearing to be alive.
Someone who is "brain dead" can appear alive in that they are breathing with the help of a ventilator, and their heart can be kept beating. Many bodily functions can keep going for weeks and months after they're considered medically and legally dead. But that's subjective too because in some cases people considered medically and legally dead "come back to life," which in my opinion means they were never dead (again, unless there's a miracle, and that may be hard to determine).
So I think when someone is restored to life through medical means, or is kept alive by medical means when without them obvious and true death would have occurred, my belief is not that their spirit was RETURNED to the body, but that their spirit never left their body in the first place. Defining death as a permanent cessation of earthly life, only undone in the case of miracles, not a variety of medical interventions, makes most sense to me.
Do We "Go to Sleep" When We Die?
Questions and Answers Related to Near-Death Experiences: Randy and Jim Hendershot speak about the difference between near-death experiences and actual death.
Euthanasia: Mercy or Murder?: This is Randy's long paper on euthanasia which he wrote in seminary, and updated 24 years ago. It has a lot of related thoughts that could be helpful for family members trying to figure out what constitutes death and what doesn't.
Do We "Go to Sleep" When We Die?
Some sincere Christians believe in "soul sleep," the idea that when we die we lose consciousness until the resurrection.