text:
Roof mounting – jobs 2019
Roof mounting
114 requests from category Roof mounting
I would like to assemble a complete roof, Spruce Grove
...of the contract: Recommended by the experts Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): I'm not sure Roofing: Tile (clay, concrete) Roof...
Looking for a company for roof construction, Chatham-Kent
...contract: Install Exchange, a new roof cladding/coating on the old roof Reason for renovation: Transformation of the building Roof area (in square meters): 50-100 Roofing: Tile (clay, concrete)...
Looking for a company for roof construction, Sarnia
Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof sags Roof area (in square meters): I'm not sure Roofing: Wood shingles Roof age: 31-40 years...
The work in the construction of the roof, Saint John
...experts Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): 0-50 Roofing: Metal Roof age: 31-40 years Roof description: Steep...
Looking for a company for roof construction, Prince Albert
...of the contract: Install Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof sags Roof area...
Roof mounting – see costs and prices
Do you you want to know, what are the costs in the services in the range of Roof mounting? Wait no longer! Send a quote request. You can get and compare price quotes and Preisverzeichnisen. Give what you need. Try to give as much details. For example: the needed services or the date of order. Write, who should get the necessary materials. Add everything that is particularly important for you. Describe your requirements. The payment methods, the run time of the job, the guarantee and the experience of the Executive in this area. Keep in mind that the prices can vary depending on the delivery area, manufacturer, quantity ordered, and distance. That is why it is important to detail your inquiry as far as possible. If you need advice, ask for a talking to. Don't forget also to give the full contact information. Choose the preferred contact method - by phone or e-mail. The companies will offer you their own products. As a result, you get only practical offerings.
The services on our Web site are free of charge and the surviving quotations - non-binding. Look, how quickly and conveniently you can find the provider – without leaving the House
The work in the construction of the roof, Surrey
...contract: Recommended by the experts Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): I'm not sure...
Looking for a company for roof construction, Barrie
...by the experts Reason for renovation: Transformation of the building Roof area (in square meters): 100-200 Roofing: Slate Roof age: 11-20 years Roof description: Completely...
The work in the construction of the roof, Hamilton
...experts Reason for renovation: Transformation of the building Roof area (in square meters): 0-50 Roofing: Asphalt shingles Roof age: 31-40 years Roof...
Looking for a company for roof construction, Brampton
...of the contract: Install Exchange, a new roof cladding/coating on the old roof Reason for renovation: Transformation of the building Roof...
I would like to assemble a complete roof, Saguenay
...contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is leaking or has water damage...
Advice and ratings of professionals and services
It is worth to compare the ratings and reviews of companies in Oferteo. In this way, you can quickly verify the companies from the category Roof mounting. The Internet profiles of specialists are very helpful. You can read more information about the provider. You should look on the reviews from other buyers one. The customers make the statements about the company: about the work performed through the contact with the company and quality of services. This is very important if you want to select a reliable Pro. Also the descriptions that are published by the company are helpful. Here you can check the information about the company's experience, scope of services, privileges and powers. If you're looking for advice, send a message to professionals. The company will send you cancellation recommendations. To do this, they describe the services. Our experts are always at your disposal.
Via Oferteo, you can really just compare reviews of service providers. You will get also the detailed advice. Now, you can compare the offers and services and find out - a company without cost and without obligation.
I would like to assemble a complete roof, Wetaskiwin
Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): 50-100 Roofing: Asphalt shingles Roof age:...
Looking for a company for roof construction, Stephenville
...new roof cladding/coating on the old roof Reason for renovation: Roof is cracked or damaged Roof area (in square meters): 0-50 Roofing: I'm not sure Roof age: 11-20...
The work in the construction of the roof, Victoria
...of the contract: Replacing the old roof was removed and a new will is mounted Reason for renovation: Roof is moldy Roof area (in square meters): 100-200 Roofing: Metal...
I would like to assemble a complete roof, Nanaimo
...contract: Replacing the old roof was removed and a new will is mounted Reason for renovation: Roof is moldy Roof area (in square meters): I'm not...
Looking for a company for roof construction, Kingston
...the old roof was removed and a new will is mounted Reason for renovation: Life span of a roof is...
Roof mounting – Current jobs
Oferteo makes it easy, the new jobs of finds. Here, you can discover very quickly the latest jobs in your area. This is easy! Oferteo makes you accessible new tools, thanks to their contact with a customer and sales even easier are. The customer requests are verified by us by telephone and extended. Then, we will send you notification of the new orders. You collect only the tested contacts. The rest is in your hands! Contact with the customers and make him the best offer. Worry that it is thoroughly and according to the requirements of the customer. Call with the customer as quickly as possible after receiving the notice. The farms which immediately answer and immediate respond to request more successfully attract the customers. Take a free, professional company profile in claims. Give to the company description and note what assignments you are looking for. So imagine the future customers and leave a good impression behind. The striking profile helps you to make credibility and good image in the Internet.
Oferteo providers are now. Get a new jobs from the category Roof mounting directly to your mail box.
The work in the construction of the roof, Windsor
...experts Reason for renovation: Roof is moldy Roof area (in square meters): 0-50 Roofing: Tile (clay, concrete) Roof age: 31-40 years Roof description:...
Looking for a company for roof construction, Kamloops
...of the contract: Recommended by the experts Reason for renovation: Life span of a roof is over Roof area (in square meters): 0-50 Roofing: Asphalt...
Looking for a company for roof construction, Whitehorse
...contract: Recommended by the experts Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): 50-100 Roofing:...
The work in the construction of the roof, Charlottetown
...by the experts Reason for renovation: Roof is moldy Roof area (in square meters): 100-200 Roofing: Wood shingles Roof age: 31-40...
Looking for a company for roof construction, London
...new roof cladding/coating on the old roof Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): I'm not...
Looking for a company for roof construction, Brooks
...of the contract: Recommended by the experts Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): I'm not sure Roofing: Wood shingles Roof age:...
Looking for a company for roof construction, Melfort
...contract: Install Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof is cracked or damaged Roof area (in square meters): 50-100 Roofing: Slate Roof...
I would like to assemble a complete roof, Cambridge
...by the experts Reason for renovation: Roof sags Roof area (in square meters): 100-200 Roofing: Wood shingles Roof age: 0-10 years Roof description: Steep and difficult to commit Needed...
I would like to assemble a complete roof, Canmore
...roof was removed and a new will is mounted Reason for renovation: Transformation of the building Roof area (in square meters): I'm not sure Roofing: I'm...
I would like to assemble a complete roof, Sydney
...of the contract: Recommended by the experts Reason for renovation: Transformation of the building Roof area (in square meters): I'm...
The work in the construction of the roof, Prince George
...contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is leaking or has water...
The work in the construction of the roof, Bathurst
...the old roof was removed and a new will is mounted Reason for renovation: Life span of a roof is over Roof area (in square...
I would like to assemble a complete roof, Uxbridge
...roof was removed and a new will is mounted Reason for renovation: Life span of a roof is over Roof area (in...
I would like to assemble a complete roof, St. Albert
...of the contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is...
Looking for a company for roof construction, Sherbrooke
...contract: Replacing the old roof was removed and a new will is mounted Reason for renovation: Roof is cracked or damaged Roof area (in...
Looking for a company for roof construction, Fredericton
Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof is leaking or has water damage Roof area (in square meters): I'm not sure Roofing: Asphalt shingles...
I would like to assemble a complete roof, Brandon
...experts Reason for renovation: Life span of a roof is over Roof area (in square meters): 0-50 Roofing: Asphalt shingles Roof age: 0-10 years Roof description: Mostly flat...
I would like to assemble a complete roof, Richmond
...of the contract: Recommended by the experts Reason for renovation: Transformation of the building Roof area (in square meters): 50-100 Roofing: I'm not sure Roof age: 31-40 years Roof...
I would like to assemble a complete roof, Longueuil
...contract: Recommended by the experts Reason for renovation: Life span of a roof is over Roof area (in square meters): I'm not sure Roofing: Slate Roof...
Looking for a company for roof construction, Summerside
...a new roof on a building, which is still without a roof Reason for renovation: Roof is cracked or damaged...
Looking for a company for roof construction, Sault Ste. Marie
...roof on a building, which is still without a roof Reason for renovation: Life span of a roof is over Roof area (in...
The work in the construction of the roof, Clarenville
Clarenville
...of the contract: Recommended by the experts Reason for renovation: Roof is moldy Roof area (in square meters): 0-50 Roofing: Tile (clay, concrete) Roof age:...
Looking for a company for roof construction, Medicine Hat
...contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is moldy Roof area...
The work in the construction of the roof, Fort Saskatchewan
Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof is leaking or has water damage Roof area...
I would like to assemble a complete roof, Calgary
...roof on a building, which is still without a roof Reason for renovation: Transformation of the building Roof area (in square meters): 100-200 Roofing:...
I would like to assemble a complete roof, Swift Current
...of the contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is cracked or damaged Roof area (in square meters): 50-100...
I would like to assemble a complete roof, Melville
...contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof is cracked or damaged Roof area (in square meters): I'm...
The work in the construction of the roof, Levis
Exchange, a new roof cladding/coating on the old roof Reason for renovation: Roof sags Roof area (in square meters): I'm not sure Roofing: Wood shingles Roof age: 0-10 years...
The work in the construction of the roof, Estevan
...experts Reason for renovation: Roof sags Roof area (in square meters): 0-50 Roofing: Slate Roof age: 11-20 years Roof description: Completely flat and accessible Needed roofs...
The work in the construction of the roof, Sudbury
...of the contract: Install a new roof on a building, which is still without a roof Reason for renovation: Roof...
Looking for a company for roof construction, Leduc
...contract: Recommended by the experts Reason for renovation: Transformation of the building Roof area (in square meters): 50-100 Roofing: I'm not sure Roof...
Looking for a company for roof construction, Banff
...the old roof was removed and a new will is mounted Reason for renovation: Roof is moldy Roof area (in square meters): 0-50 Roofing: Wood...
I would like to assemble a complete roof, Selkirk
...roof was removed and a new will is mounted Reason for renovation: Transformation of the building Roof area (in square meters): 50-100...
I would like to assemble a complete roof, Montreal
Looking for a company for roof construction, Happy Valley-Goose Bay
...contract: Recommended by the experts Reason for renovation: Roof sags Roof area (in square meters): I'm not sure Roofing: Metal Roof age: 21-30 years...


text:
Sandra L. Worms
By Editor | March 26, 2021 | 0
Sandra L. Worms, 67, of O'Fallon, IL, passed away on Friday, March 19, 2021 at her residence in O'Fallon, IL.
Sandra was born August 30, 1953 in East St. Louis, IL. She graduated from O'Fallon Township High School in 1972 before continuing her education and graduating from the Coiffure School of Beauty Culture. She was a beautician for Donna Mae's in Mascoutah, IL, Nina's Beauty Salon in O'Fallon, IL, and Kut n' Kurl in O'Fallon, IL. Was a member of Caseyville United Methodist Church, was a believer in Jesus Christ and her life reflected her love and walked with him. Sandra enjoyed driving around the countryside seeing nature, and she loved her dog, Sicily.
Sandra was preceded in death by her parents; Joseph Rupprecht and Laverne Rupprecht (nee Thereon), and her niece; Kathy Rupprecht.
Surviving is her loving husband; Gerald Kent Worms of O'Fallon, IL, one brother; Clarence (Linda) Rupprecht of Caseyville, IL, two nieces; Andrea (Brad) Buskirk of Highland, IL and Kelly (Ron) Sneed of Fairview Heights, IL, six great-nieces and nephews; Adam Buskirk, Aaron (Kayla) Buskirk, Kelsey (Jacob) Burns, Ronnie (Steffinie) Sneed, Brittany Sneed, and Jessica Sneed, and four great-great-nieces.
Memorials can be made to the Belleville Humane Society https://bahspets.org/donate, Caseyville United Methodist Church http://www.disciplewalk.com/CasyevilleChurch.html, or donor's choice.
Condolences may be extended to the family online at www.schildknechtfh.com.
Visitation will be held from 3:00 P.M. – 7:00 P.M. on Tuesday, March 23, 2021 at Schildknecht Funeral Home, 301 S. Lincoln Ave., O'Fallon, IL 62269.
Funeral Services will be held at 2:00 P.M. on Wednesday, March 24, 2021 at Schildknecht Funeral Home, 301 S. Lincoln Ave., O'Fallon, IL 62269. Burial will follow at the Mascoutah City Cemetery in Mascoutah, IL.
Arrangements have been entrusted to Schildknecht Funeral Home.

redpajama_set_name: RedPajamaCommonCrawl


text:
Home / ALIEN/UFO / Archetype of the UFO
View cart "Archetype of the UFO" has been added to your cart.
Archetype of the UFO
Archetype of the UFO quantity
Directed by O.H. Krill
The world of UFO's and Aliens is filled with controversy, speculation and mystery. What are the UFO's? Do they exist in reality or are they drawn from somewhere within the mind of man? Do they they emanate from another dimension altogether or are they ancient archetypes that we have forgotten with the sands of time?
The Archetype of the UFO tackles these dilemmas head on, going where few UFO documentaries have dared to go before. As we near 2012, we now need to abandon any previous notions about this phenomenon and delve deeper into this fascinating realm that lures the entire human race toward its future destiny.
Be prepared to think again, outside of standardized reasoning and journey with us into a new paradigm on this controversial and mounting subject.
Joining O. H. Krill and Philip Gardiner in this search is Nick Pope, the real-life Fox Mulder with his incredible and unique insight from his days leading the British Ministry of Defense UFO Project.
Click Here for Trailer
Be the first to review "Archetype of the UFO" Cancel reply
UFO Chronicles: Aliens and War
Reality UFO Series Volume 2
Reality Entertainment presents the Reality UFO Series V2, the second in a unique series in conjunction with Hard Evidence and Ufologist Magazines. Featuring the most compelling and well documented cases in UFO and Paranormal History.
Reality UFO Series Volume 2 includes:
Dr. Richard Boylan Ph.D., B.A.
Dr. Boylan is a Researcher, Behavioral Scientist, Exo Anthropologist, emeritus University Associate Professor of Psychology, Certified Clinical Hypnotherapist, author, consultant, and researcher. Dr. Boylan provides hypnotherapy for recalling full details of partially-remembered close encounters with alien beings, and for exploring previous life experiences stored in subconscious memory. Reality UFO V2 includes his presentation of "Star Kids and Star Seeds, their origin, identity and mission".
Freddy Silva is one of the world's leading experts on UFO's, crop circles and sacred sites, and a highly regarded researcher into the interaction between temples and consciousness. As a best-selling author and filmmaker he frequently lectures internationally, and has made keynote presentations at the International Science and Consciousness Conference, and the International Society For The Study Of Subtle Energies & Energy Medicine, in addition to appearances on The History Channel, Discovery Channel, BBC, numerous video documentaries, and radio shows.
Peter's first UFO Abduction experience was in 1988, Peter has a mark on his head where a needle was inserted by the beings. He also has a scoop mark on his right leg where a sample was taken. His 1992 Abduction Experience which involved two alien females, a blonde and an Asian, became the world's first UFO abduction case with biological evidence. The two hair samples, were DNA tested using the PCR method. The investigation is still on going.
Keith has been involved in the area of UFO research for over two decades. In 1981 his book on Australian UFO reports "Close Encounters of an Australian Kind", was published, followed in 1997 with a revised version of "UFOs: A Report on Australian Encounters". An active member of the UFO community, Keith Basterfield has lectured around the world and been involved in many of the UFO organizations.
UPC: TBD
Aliens from Outer Space UFO's Do Not Exist!
You're viewing: Archetype of the UFO $12.49


text:
Q: Using Forge to Insert into database but not getting an insert ID I'm new to Fuel...
got my script inserting a record using the following code:
             $address =  Model_Address::forge(array(
                    'street1' => $step1_data['street1'],
                    'street2' => $step1_data['street2'],
                    'suburb' => $step1_data['street2'],
                    'city' => $step1_data['city'],
                    'region' => $step1_data['region'],
                    'country' => $step1_data['country'],
                    'postcode' => $step1_data['postcode'],
            ));

            $address->save();

I think I should be able to get the insert id via $address->id but it's empty.
I'm not sure what I'm doing wrong?
We are using pg_swl not sure if that makes any difference.

redpajama_set_name: RedPajamaStackExchange


alt="Moulin Roty Stack Up Cubes"
Moulin Roty's Grand Family stacking cubes are great way to introduce your child to counting, colours and spatial awareness as well as another language!
A 10 piece set, made from sturdy cardboard, each cube features a colour and a number (in written as well as in diagrammatic form to encourage your child to visualise the number). Beautifully illustrated by French artist Camille Jourdy, the cubes also feature a scene from everyday life, an illustrated phrase in both English and French and a single illustrated item, also written in English and French.
The cubes can be stacked or nestled into each other, encouraging spatial skills. When play is finished, the cubes pack away neatly into the lovely presentation box. A great gift idea.


text:
Israel prevents massive multiple-bombing attack
1,000-year-old Jerusalem Old City moat, carved handprint discovered
Israel's attorney general reportedly considers naming Netanyahu unfit for PM
Netanyahu faces new public trial over judicial reforms
Turkish ambassador presents credentials to Israeli President Herzog
The terror cell's plans were at an advanced stage with a large bomb already built and ready to be deployed
All Israel News Staff | December 27, 2022
Israeli troops operate in the West Bank, Dec. 26, 2022. (Photo: Israel Defense Forces)
The Israeli Security Agency, Shin Bet, revealed on Monday that it stopped an extensive terror attack in Israel on Dec. 14, which was to involve a massive bombing, as well as several suicide bombings.
The authorities said they nabbed a four-man terror cell in the West Bank, but that the complex terror operation being planned appeared to be have been initiated from the Hamas-ruled Gaza Strip. The Shin Bet revealed that the terror cell received instructions from Ahmed Omar Hajaj, a Gaza-based explosives expert.
The four Arab suspects reportedly are affiliated with both the "Resistance Committees" and the Al Aqsa Martyrs' Brigades, a terrorist organization affiliated with the Fatah party – formerly, the Palestinian National Liberation Movement.
The terror cell's plans were at an advanced stage with a large bomb already built and ready to be deployed. The bomb reportedly was similar to the sophisticated bomb used in November in a lethal terror attack targeting a Jerusalem bus. The terror plot reportedly also involved other Gaza-based terrorists.
The Shin Bet announced that the successful anti-terror operation was the result of cooperation with the Israeli Defense Forces and the Israel Police.
"The actions that were carried out and that thwarted the planned attacks are part of a continuous campaign that the Shin Bet, the IDF and the police have been undertaking together to prevent terror in Israel using a diverse range of tools and tactics," stated the Israeli Security Agency.
Israeli Prime Minister Yair Lapid praised the security forces for preventing the attack and promised that Israel would continue its efforts to "reach anyone who tries to hurt the citizens of Israel."
The Israeli premier stressed that Israel's fight against terrorism is a long-term effort that requires constant alertness and coordination.
"The war against terror infrastructures and terrorists continues every day, in all arenas. Security forces continue to act, constantly, to thwart any attempt to harm us," Lapid stated.
In its assessment, Shin Bet blamed Hamas for the spread of terrorism from Gaza into Israel and the West Bank.
"Israel views the terror activity directed from the Gaza Strip toward the West Bank and Israel with severity, and works to thwart any threat ahead of time, and considers Hamas to be responsible for all terror activity emanating from the Gaza Strip," Shin Bet stated.
Israeli authorities recently arrested Aslam Farouk, an Arab resident of Jerusalem who is believed to be a member of the Islamic State [ISIS] and to be behind November's terror attack.
The Shin Bet reported that 2022 was one of the most lethal years for both Israelis and Arabs in Israel and the adjacent disputed territories, with Arab terrorists killing 31 Israelis and injuring an additional 129 people. The report also registered more than 2,200 terrorist attacks this year in Israel and the West Bank.
While most of the terror attacks were carried out by non-Israeli Arab residents in the West Bank and Jerusalem, some Israeli Arabs were also involved. The IDF also confirmed that 151 Arabs were killed during security operations – the overwhelming majority were armed terrorist combatants.
The increase in terror attacks targeting Israel is believed to be linked to the ongoing smuggling of weapons, including arms stolen from IDF army bases and smuggled from Jordan and other countries.
Israeli security officials tasked with monitoring the Jordan Valley, along the Jordanian border, told the Times of Israel that it foiled about 80% of all weapons-smuggling attempts from Jordan in 2022. All in all, Israeli authorities captured some 500 guns that could have ended up in the hands of terrorists or criminals inside the Arab Israeli community.
Read more: TERRORISM


2 Bedroom End of Terrace House For Sale in Stratford-upon-Avon for Guide Price £182,500.
A great two bedroom home with a fantastic plot to the front, rear and side. Ideal for enlargement subject to the necessary planning permission. Positioned The accommodation allows; entrance hall, sitting room, breakfast kitchen with access to the garden, two double bedrooms and a bathroom. There is a mature rear garden that extends to the side and front. Potential for extension and parking to be created. Viewing is advised.
Double glazed window to the front elevation. Storage cupboard.
Range of matching wall and base units including roll edge work surfaces incorporating a stainless steel sink and drainer unit. Space for a cooker, washing machine and fridge freezer. Tiling to the walls and vinyl to the floor. Radiator. Double glazed window to the rear and side elevations. UPVC door to the outside. Pantry cupboard.
White suite allowing a low level w.c, wash hand basin and bath with shower over. Tiling to the walls and vinyl to the floor. Radiator. Double glazed obscure window to the rear elevation.
Lawned garden with fencing and side gated access. There is a right of way across the rear for the neighbouring property.


text:
News | Entertainment
Home > News > Entertainment
Daisy Edgar-Jones has won the first ever Rose d'Or Emerging Talent Award
The 'Normal People' star feels "so lucky" to have played the role of Marianne on the hit BBC One show, as she thanked the Rose d'Or judges for the "special" award
Speaking about the accolade, she said: "Normal People really was a dream job. I just feel so lucky to have played Marianne and it's done so much for me. To be acknowledged as an Emerging Talent by Rose d'Or for it is so special. Thank you so, so much. I'm very proud and very chuffed."
And 'Sex Education's Ncuti Gatwa is also to receive Performance of the Year Award for his portrayal of Eric in the his Netflix show, with the actor admitting it was a huge "honour".
He said: "What an honour to receive the Performance of the Year Award! It's such a joy playing Eric, someone who is so fun but has real depth to him. The fact that people can see themselves in him and relate to the issues we cover in the show is really inspiring and incredibly important to me as an actor."
The 2020 Rose d'Or Awards will be hosted this year by comedian Nish Kumar, and will be held virtually at 3pm on Wednesday, December 9 amid the coronavirus pandemic.
Mark Rowland, chair of the 2020 judges, added:?"Daisy and Ncuti's authentic character portrayals stood out for the judges and audiences alike, we are delighted to be able to recognise their outstanding performances. The Rose d'Or would also like to congratulate Daisy on being the inaugural winner of the Emerging Talent Award, which we've instituted to recognise great new talent this year and every year."
The 2020 Rose d'Or Awards will take place on Wednesday December 9.
>> More Entertainment News
© 2021 Bang Showbiz, NZCity
Other Entertainment News
17 Jan: Mary-Kate Olsen has finalised her divorce from Olivier Sarkozy
17 Jan: The 2021 SAG Awards have been moved to April 4 after the Grammy Awards were rescheduled to the same date as their ceremony
17 Jan: Paloma Faith has vowed to not "step outside" her house again until she's given birth
17 Jan: Ellen DeGeneres slept for 16 hours a day when she was battling coronavirus
17 Jan: Tom Hanks will lead a primetime special celebrating President Joe Biden's inauguration
17 Jan: Katy Perry is teaming up with Pokemon for a new music programme
17 Jan: Wendy Williams doesn't "regret" anything about her marriage
Entertainment NZ News NewsLinks NZ Web


text:
\section{Introduction}
\OnlyInFull{
With the wide popularity of social media and social network sites such as Facebook, Twitter, WeChat, etc.,
social networks have become a powerful platform for spreading information among individuals.
Thus, influential users always play important role in a social network.
Motivated by this background, influence diffusion in social networks has been extensively studied
 \cite{domingos2001mining,kempe2003maximizing,chen2013information}.}
\OnlyInShort{Influence diffusion in social networks has been extensively studied
	\cite{domingos2001mining,kempe2003maximizing,chen2013information}.}
Most of previous works focus on exploring influential nodes.
To the best of our knowledge, there is no study about the ``stability'' of influential nodes (seed set) when they are treated as a coalition.

Consider the following scenario.
A group of influential people in a social network are considering forming
	a coalition so that they can better serve many advertisers through
	viral marketing in the social network.
To make the coalition stable, we need to design a fair profit allocation
	scheme among the members of the coalition, such that
	no individual or a subset of people have incentive to deviate
	from this coalition, thinking that the allocation to them is unfair and
	they could earn more by the deviation and forming an alliance by
	themselves.
A useful and mature framework of studying such incentives for stable coalition
	formation is the cooperative game theory, and in particular
	the coreness (core and its related concepts) of the cooperative games \cite{Gabrielle2004groupstability,reshef2011ijcai}.

	First we will motivate our consideration of the truncated submodular
	functions here.
In the above social influence scenario, the typical way of measuring the
	contribution of any set $S$ of influential people is by its
	influence spread function $\sigma(S)$, which measures the expected number
	of people in the social network that could be influenced by
	$S$ under some stochastic diffusion model.
Extensive researches have been done on stochastic diffusion models, and
	it has been shown that under a large class of models $\sigma(S)$
	is both monotone and submodular\footnote{A set function
	$f$ is monotone if $f(S) \le f(T)$ for all $S\subseteq T$, and is
	submodular if $f(S\cup \{u\}) - f(S) \ge f(T\cup \{u\}) - f(T)$ for
	all $S\subseteq T$ and $u \not\in T$.
	}
	\cite{kempe2003maximizing,mossel10,chen2013information}.
However, the advertisers would only be interested in the coalition as
	a viral marketing platform when the influence spread reaches certain
	scale level.
In other words, the coalition can only receive profit after the influence
	spread is above a certain scale threshold $\eta$.
Therefore, the true profit function for the coalition is
	$f(S) = \sigma(S)$ when $\sigma(S) \ge \eta$, and $f(S) = 0$ otherwise.
We call such $f$ truncated submodular functions.

Both submodularity and scale effect are common in economic behaviors beyond
	the above example of viral marketing in social networks.
Therefore, considering truncated submodular functions
	as the profit functions is reasonable.
In this paper, we study the computational issues related to the coreness
	of cooperative games with truncated submodular profit functions.

\textbf{Solution Concepts in Cooperative Games.}
A cooperative game $\Gamma=(V, \gamma)$ consists of a player set $V=\{1,2,\cdots,n\}$
and a profit function $\gamma: 2^V\rightarrow \mathbb{R}$
with $\gamma(\emptyset)=0$.
A subset of players $S\subseteq V$ is called a \emph{coalition} and $V$ is called the \emph{grand coalition}.
For each coalition $S$, $\gamma(S)$ represents the profit obtained by $S$ without help of other players.
An allocation over the players is denoted by a vector $x=(x_1,x_2,\cdots,x_n)\in \mathbb{R}^{|V|}$ whose components are one-to-one associated with players in $V$, where $x_i\in \mathbb{R}$ is the value received by player $i\in V$ under allocation $x$.
For any player set $S\subseteq V$, we use the shorthand notation $x(S)=\sum_{i\in S}x_i$.
A set of all allocations satisfying some specific requirements is called a \emph{solution concept}.

The \emph{core} \cite{gillies1953core,shapley1955core} is one of the earliest and most attractive solution concepts
	that directly addresses the issue of stability.
The core of a game is the set of allocations ensuring that no coalition would have an incentive
    to split from the grand coalition, and do better on its own.
More precisely, the core of a game $\Gamma$ (denoted by ${\cal C}(\Gamma)$), is the following set of allocations:
${\cal C}(\Gamma)$=$\{x\in \mathbb{R}^{|V|}: x(V)=\gamma(V), x(S)\geq\gamma(S),~ \forall~S\subseteq V\}$.
In practice, core is very strict and may be even empty in some cases.
When ${\cal C}(\Gamma)$ is empty, there must be some coalitions becoming dissatisfaction since they can obtain more benefits
    if they leave the grand coalition and work as a separated team.
In this case, we use the dissatisfaction degree
	(or dissatisfaction value), defined as $dv(S,x) = \max\{\gamma(S)-x(S),0\}$,
	to capture the instability of player set $S$ with respect to
	the allocation $x$.
Then, the overall stability of the game can be measured as either the
	worst-case or average-case dissatisfaction degree, for
	which we consider the following three versions.

The first one is the \textit{relative least-core value} (${\cal RLCV}$) \cite{faigle1993relativeleastcore}, which reflects the relative stability,
i.e. the minimum value of the maximum proportional difference between the profits and the payoffs among all coalitions.
\begin{definition}
	Given a cooperative game $\Gamma$,
	the {\em relative least-core value} of $\Gamma$ (${\cal RLCV}(\Gamma)$\xspace) is $\min_x\max_S \frac{dv(S,x)}{\gamma(S)}$. Technically, ${\cal RLCV}(\Gamma)$\xspace is the optimal solution of the following linear programming:
	\begin{equation}
	\OnlyInShort{\small}
	\begin{array}{ll}

    \min & \ r\\
	\mbox{s.t.}&\left\{
	\begin{array}{ll}
	x(V)=\gamma(V)\\
	x(S)\geq (1-r)\gamma(S)  & \quad \forall~S\subseteq V\\
	x(\{i\}) \ge 0 & \quad \forall~i\in V
	\end{array}\right.
	\end{array}
	\end{equation}
\end{definition}

The second one is the \textit{absolute least-core value} (${\cal ALCV})$ \cite{Maschler1979leastcore} which reflects the absolute stability,
    i.e. the minimum value of the maximum difference between the profits and the payoffs among all coalitions.
The formal definition is as following.
\begin{definition}
Given an cooperative game $\Gamma$,
the {\em absolute least-core value} of $\Gamma$ (${\cal ALCV}(\Gamma)$\xspace) is $\min_x\max_Sdv(S,x)$. Technically, ${\cal ALCV}(\Gamma)$\xspace is the optimal solution of the following linear programming:
 \begin{equation}
 \OnlyInShort{\small}
 \begin{array}{ll}
\min & \ \varepsilon\\
 \mbox{s.t.}&\left\{
 \begin{array}{ll}
 x(V)=\gamma(V)\\
 x(S)\geq\gamma(S)-\varepsilon  & \quad \forall~S\subseteq V\\
 	x(\{i\}) \ge 0 & \quad \forall~i\in V
 \end{array}\right.
 \end{array}
 \end{equation}
\end{definition}

The above two classical least-core values capture the stability from the perspective of the most dissatisfied coalition i.e. the worst case of stability.
Sometimes the worst case is too extreme to reflect the real stability.
Thus, we introduce the \textit{least average dissatisfaction value} (${\cal LADV}$) which reflects the minimum value of average dissatisfaction degree among all coalitions.

\begin{definition}\label{def:acv}
	Given a cooperative game $\Gamma$, the
	{\em least average dissatisfaction value} of $\Gamma$ (${\cal LADV}(\Gamma)$\xspace) is

$\min_x \mathbb{E}_S(dv(S,x))$.
 Technically, ${\cal LADV}(\Gamma)$\xspace is the optimal value of
	the following linear programming:
	\begin{equation}
	\OnlyInShort{\small}
	\begin{array}{ll}
	\min & \frac{1}{2^n}\sum_{S\subseteq V}\max \{\gamma(S)-x(S), 0\}\\
	\mbox{s.t.}&\left\{
	\begin{array}{ll}
	x(V)=\gamma(V)\\
	x(\{i\}) \ge 0 & \quad \forall~i\in V\\
	\end{array}\right.
	\end{array}
	\end{equation}
\end{definition}

In this paper, we consider the following computational problems in the context
	of truncated submodular functions:
(a) Whether the core of a given cooperative game is empty?
(b) How to find an allocation in core if the core is not empty?
(c) If the core is empty, how
	to compute the relative least-core value, the absolute least-core value and the least average dissatisfaction value of a cooperative game?

\textbf{Contributions.}
We study coreness (solution concepts related to core) of truncated submodular profit cooperative game $\Gamma_{f}$\xspace.
We consider computational properties of the core, the relative least-core value, the absolute least-core value and the least average dissatisfaction value of $\Gamma_{f}$\xspace, which are denoted by ${\cal C}(\Gamma_{f})$\xspace, ${\cal RLCV}(\Gamma_{f})$\xspace, ${\cal ALCV}(\Gamma_{f})$\xspace and ${\cal LADV}(\Gamma_{f})$\xspace, respectively.

We first prove that checking the non-emptiness of ${\cal C}(\Gamma_{f})$\xspace can be done in polynomial time.
Moreover, we can find an allocation in the core if the core is not empty.
Next, we consider the case when the core is empty.
For the problem of computing the relative least-core value (${\cal RLCV}(\Gamma_{f})$\xspace),
	we show that it is in general NP-hard, but
	when truncation threshold $\eta=0$, there is a polynomial time
	algorithm.
Along the way, we also find an interesting partial result showing that
	there is no polynomial time separation oracle for the ${\cal RLCV}(\Gamma_{f})$\xspace's
	linear program unless P=NP, which is of independent interest since
	it reveals close connections with a new class of combinatorial problems.
For the absolute least-core value problem ${\cal ALCV}(\Gamma_{f})$\xspace, we prove that
	finding ${\cal ALCV}(\Gamma_{f})$\xspace is APX-hard even when $\sigma(\cdot)$ is defined as the influence spread under the classical independent cascade
	(IC) model in social network.
We also prove that there exists a polynomial time algorithm which can guarantee an additive term approximation.
Finally, for the least average dissatisfaction value problem ${\cal LADV}(\Gamma_{f})$\xspace,
	we show that we can use the stochastic gradient descent algorithm to compute ${\cal LADV}(\Gamma_{f})$\xspace to an arbitrary small additive error.

\textbf{Related Work.}
Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements between agents are possible \cite{chalkiadakis2011computational}.
Numerous classical studies about cooperative game provide rich mathematical framework to solve issues related to cooperation in multi-agent systems \cite{deng1994complexity,ieong2005marginal,conitzer2006complexity}.
\cite{schulz2013approximating} studies the approximation of the absolute least core value of supermodular cost cooperative games, the results in this paper can be generalized to submodular profit cooperative games.
An important application of our study is to analyze the stability of influential people in social networks.

Almost all the existing studies focus on selecting seed set \cite{ChenWY09efficientinfluence,goyal2012minimizing,tang2015rrset}.
To the best of our knowledge, there is no literature considering the stability of the selected seed set.
We utilize cooperative game theory to analyse the stability of seed set,
	and generalize it to a generic cooperative game with truncated submodular functions.
	The truncated operation represents the  ``threshold effect'' which has been studied widely in literature\cite{Mark1978threshold,Albert1984}.

\section{Model and Problems}
\subsection{Cooperative Games with Truncated Submodular Profit Functions}
A truncated submodular profit cooperative game is denoted by $\Gamma_{f}$\xspace$=(V, f(\cdot))$.
\OnlyInShort{In $\Gamma_{f}$\xspace, $V$ is the player set and $f(\cdot)$ is the profit function which is defined as $f(S)=\sigma(S)$ if $\sigma(S)\geq \eta$ and $f(S)=0$ if $\sigma(S)< \eta$.}
In $\Gamma_{f}$\xspace, $V$ is the player set and $f(\cdot)$ is the profit function which is defined as follows:
\begin{equation*}
\OnlyInShort{\small}
f(S)=
\begin{cases}
\sigma(S), & \text{if $\sigma(S)\geq \eta$}\\
0, & \text{if $\sigma(S)< \eta$}
\end{cases}
\end{equation*}
Note that $\sigma(\cdot)$ is a nonnegative monotone increasing submodular function with $\sigma(\emptyset)=0$ and $0\leq\eta\leq\sigma(V)$ is a nonnegative threshold.
To express clearly, in the left of this paper, a truncated submodular profit cooperative game is denoted by a triple form $(V, \sigma(\cdot), \eta)$.

Note that the explicit representation of $\sigma(\cdot)$ might be exponential in the size of $V$.
The standard way to bypass this difficulty is to assume that
 $\sigma(\cdot)$ is given by a value oracle.

\subsection{Computational Problems on the Coreness}\label{sec:problemdefinition}
Given an truncated submodular profit cooperative game $\Gamma_{f}$\xspace, we focus on the following problems:\\
CORE\xspace: Is ${\cal C}(\Gamma_{f})$\xspace $\neq\emptyset$ and how to find an allocation in ${\cal C}(\Gamma_{f})$\xspace when ${\cal C}(\Gamma_{f})$\xspace$\neq\emptyset$?\\
ALCV\xspace: When ${\cal C}(\Gamma_{f})$\xspace$=\emptyset$, how to compute ${\cal ALCV}(\Gamma_{f})$\xspace?\\
RLCV\xspace: When ${\cal C}(\Gamma_{f})$\xspace$=\emptyset$, how to compute ${\cal RLCV}(\Gamma_{f})$\xspace?\\
LADV\xspace: When ${\cal C}(\Gamma_{f})$\xspace$=\emptyset$, how to compute ${\cal LADV}(\Gamma_{f})$\xspace?

Before we analyze the above problems, we introduce a specific instance of truncated submodular profit cooperative game (see Section \ref{sec:infgame}).

\subsection{Influence Cooperative Game ($\Gamma_{\rm inf}$\xspace)}\label{sec:infgame}
As the description in our introduction, an important motivation of our model is influence in social networks.
In this section, we introduce a specific instance of truncated submodular profit cooperative game, {\em influence cooperative game}.

{\bf Social graph.} A social graph is a directed graph $G=(V\cup U,E; P)$, where $V\cup U$ is the vertex set and $E$ is the edge set.
$P=\{p_e\}_{e\in E}$ and $p_e$ is the influence probability on each edge $e\in E$.
Note that, $V$ and $U$ denote the vertex set of influential people and target people in $G$, respectively.

{\bf Influence diffusion model.} The information diffusion process follows the independent cascade (IC) model proposed by \cite{kempe2003maximizing}.
\OnlyInFull{
In the IC model, discrete time steps $t=0, 1, 2, \cdots$ are used to model the diffusion process. Each node in $G$ has two states:
inactive or active.
 At step 0,
nodes in seed set $S$ are active and other nodes are inactive.
For any step $t\ge 1$, if a node $u$ is newly active at step $t-1$,
 $u$ has a single chance to influence each of its inactive out-neighbor $v$ with independent probability $p_{uv}$
to make $v$ active.
Once a node becomes active, it will never return to the inactive state.
The diffusion process stops when there is no new active nodes at a time step.
}
For any $S\subseteq V$, we use ${\sigma^{\rm IC}}(S)$ to denote the influence spread of $S$,
	the expected number of activated nodes in $U$ from seed set $S\subseteq V$, at the end of an IC diffusion.
According to \cite{kempe2003maximizing}, ${\sigma^{\rm IC}}(\cdot)$ is a monotone submodular function.

\begin{definition}
An {\em influence cooperative game} $\Gamma_{\rm inf}$\xspace$=(V, {\sigma^{\rm IC}}(\cdot), \eta)$ is a special form of the truncated cooperative
	game, with $V$ as the player set,
	and the truncation of influence spread function ${\sigma^{\rm IC}}(\cdot)$ as the profit function.
\end{definition}

In the rest of this paper, we analyze problems defined in Section \ref{sec:problemdefinition} one by one.
Note that our positive results (properties and algorithms) could apply to all truncated submodular profit cooperative games including influence cooperative game.
Our hardness results are established for the influence
	cooperative games, so it is stronger than the hardness results
	for general truncated submodular cooperative games.

\section{Computing Core}\label{sec:core}
We start by considering the core of $\Gamma_{f}$\xspace (${\cal C}(\Gamma_{f})$\xspace).
In $\Gamma_{f}$\xspace, we say a player $i\in V$ is a \emph{veto player}
    if $\sigma(S)<\eta$ for any $S\subseteq V\setminus\{i\}$.
That is to say, a successful coalition must include all veto players.
\begin{lemma}\label{lem:coreiff}
${\cal C}(\Gamma_{f})$\xspace $\neq \emptyset$ if and only if:\\
   (i) There exists at least one veto player in $\Gamma_{f}$\xspace, or\\
   (ii) $\sigma(S)=\sum_{i\in S}\sigma(\{i\})$, for any $S\subseteq V$.\\
\end{lemma}

\begin{proof}
Suppose the player set of $\Gamma_{f}$\xspace is $V=\{1,2,\cdots, n\}$. We first prove the sufficiency of Lemma \ref{lem:coreiff}.
On one hand, suppose $i$ is a veto player of $\Gamma_{f}$\xspace, then we can find a trivial allocation $x$ in ${\cal C}(\Gamma_{f})$\xspace:
    $x(\{i\})=\sigma(V)$ and $x(\{j\})=0$, $\forall~j\in V\setminus \{i\}$.
On the other hand, $x(\{i\})=\sigma(\{i\})$ ( $\forall i \in V$) is an allocation in ${\cal C}(\Gamma_{f})$\xspace if $\sigma(S)=\sum_{i\in S}\sigma(\{i\})$.

Now we prove the necessity.
Suppose ${\cal C}(\Gamma_{f})$\xspace$\neq\emptyset$ and $x\in$${\cal C}(\Gamma_{f})$\xspace.
Let $\sigma(V)=\sum_{i=1}^n M_i$, where $M_i=\sigma(\{1,2,\cdots,i\})-\sigma(\{1,2,\cdots,i-1\})$
    is the marginal increasing of player $i$.
If there is no veto player, then for any $i\in V$, $\sigma(V\setminus\{i\})\geq\eta$
    since $\sigma(S)$ is monotone.
Thus, $f(V\setminus\{i\})=\sigma(V\setminus\{i\})$, $\forall~i\in V$.
Suppose $\sigma(V\setminus\{i\})=\sum_{j=1}^{i-1}M_j+\sum_{j=i+1}^{n}M'_{ij}$,
    where $M'_{ij}=\sigma(\{1,2,\cdots,i-1,i+1,\cdots,j\})-\sigma(\{1,2,\cdots,i-1,i+1,\cdots,j-1\})$.
Note that $M'_{ij}\geq M_j$ since $\sigma(S)$ is submodular.
By the definition of the core, for any $i\in\{1,2,\cdots,n\}$, we have:
$x(V\setminus\{i\})\geq f(V\setminus\{i\})=\sigma(\{V\setminus\{i\}\})$.
That is,$x(V)-x(\{i\})\geq \sum_{j=1}^{i-1}M_j+\sum_{j=i+1}^{n}M'_{ij}$, $\forall i \in V$.

Summing up these inequalities for all $i\in V$, we have,
$(n-1)\sum_{i=1}^n x(\{i\})\geq\sum_{i=1 }^n (\sum_{j=1}^{i-1}M_j+\sum_{j=i+1}^{n}M'_{ij})
	\geq \sum_{i=1 }^n(\sum_{j=1}^{i-1}M_j+\sum_{j=i+1}^{n}M_j)
	=\sum_{i=1 }^n(\sigma(V)-M_i)
	=(n-1)\sigma(V)$.

We have known that $\sum_{i=1}^n x(\{i\})=\sum_{j=1}^{n}M_j=\sigma(V)$ and then
    $M_j=M'_{ij}$, $\forall i,j\in V$.
Thus, $\sigma(S)=\sum_{i\in S}\sigma(\{i\})$.
\end{proof}
An important application of Lemma \ref{lem:coreiff} is Theorem \ref{thm:core_polysolvable}.
\begin{theorem}\label{thm:core_polysolvable}
Deciding whether ${\cal C}(\Gamma_{f})$\xspace is empty can be done in polynomial time and
 an allocation in ${\cal C}(\Gamma_{f})$\xspace can be computed in polynomial time if ${\cal C}(\Gamma_{f})$\xspace is not empty.
\end{theorem}
\begin{proof}[Sketch]
	First, it takes polynomial time to check the non-emptiness of ${\cal C}(\Gamma_{f})$\xspace. When ${\cal C}(\Gamma_{f})$\xspace is not empty, then $(x_j=\sigma(V), \textbf{0}_{\{i:i\neq j\}})$ $\in$ ${\cal C}(\Gamma_{f})$\xspace when $j$ is a veto player and $(\sigma(\{1\}), \cdots, \sigma(\{n\}))$ $\in$ ${\cal C}(\Gamma_{f})$\xspace when $(ii)$ satisfies.
\end{proof}
The detail proof of Theorem \ref{thm:core_polysolvable} is shown in the appendix.

\section{Computing Relative Least-Core Value}
\label{sec:relativeleastcorevalue}
From Lemma \ref{lem:coreiff}, ${\cal C}(\Gamma_{f})$\xspace may be empty in many cases.
It is obvious that ${\cal RLCV}(\Gamma_{f})$\xspace$>0$ if ${\cal C}(\Gamma_{f})$\xspace$=\emptyset$ and ${\cal RLCV}(\Gamma_{f})$\xspace$=0$ otherwise.
In this section, we study computational properties of RLCV\xspace  problem.
The linear programming corresponding to ${\cal RLCV}(\Gamma_{f})$\xspace (LP-RLCV\xspace) is as follows:
\begin{equation}
\OnlyInShort{\small}
\begin{array}{ll}
\min& r\\
\mbox{s.t.}&\left\{
\begin{array}{ll}
x(V)=\sigma(V)\\
x(S)\ge (1-r)\sigma(S)  & \forall~S\subseteq V,~ \sigma(S)\geq \eta\\
x(\{i\}) \ge 0 & \forall~i\in V\\
\end{array}\right.
\end{array}
\end{equation}

A special case of computing ${\cal RLCV}(\Gamma_{f})$\xspace is when $\eta=0$.
It captures the scenario that the profit of any coalition exactly equals to its influence spread under influence cooperative game.
In Theorem~\ref{thm:existseparationoracle} we show that, although there are exponential number of constraints, LP-RLCV\xspace can be solved in polynomial time by
providing a polynomial time separation oracle when $\eta=0$.
A separation oracle for a linear program is an algorithm that, given a putative feasible solution, checks whether it is indeed feasible, and if not, outputs a violated constraint.
It is known that a linear program can be solved in polynomial time by the ellipsoid method as long as it has a polynomial time separation oracle \cite{grotschel2012geometric}.
\begin{theorem}\label{thm:existseparationoracle}
	There exists a polynomial time separation oracle of LP-RLCV\xspace when $\eta=0$.
Therefore, RLCV\xspace can be solved in polynomial time when $\eta=0$.
\end{theorem}

\begin{proof}
	Given any solution candidate of LP-RLCV\xspace $(x',r')$, we need to either assert $(x',r')$ is a feasible solution or
	find a constraint in LP-RLCV\xspace such that $(x',r')$ violates it.
	Note that, checking $x'(V)=\sigma(V)$ and $x'(\{i\})\ge 0$ ($\forall~ i\in V$) can be done
	in polynomial time.
	Thus, we only need to check whether $g(S)\triangleq 1-x'(S)/\sigma(S)\leq r',~ \forall S\subseteq V$.

	An important property is

	 $g(S)$ achieves its maximum value when $S$ contains only one single player.
This is because
 $g(S)=1-\frac{x'(S)}{\sigma(S)}\leq 1-\frac{\sum_{i\in S}x'_i}{\sum_{i\in S}\sigma(\{i\})}\leq 1-\min_{i:i\in S}\{\frac{x'_i}{\sigma(\{i\})}\}=\max_{i:i\in S}\{g(\{i\})\}$.
	The first inequality is due to the submodularity of $\sigma(S)$ and the second inequality is due to
	$\min_{i:i\in[n]}\{\frac{a_i}{b_i}\}\leq \frac{\sum_{i=1}^n a_i}{\sum_{i=1}^n b_i}$, $\forall a_i, b_i \in \mathbb{R}$.
	Thus, the exponential number of constraints can be simplified to $n$ constraints on all single players.
	Then, we can find a polynomial time separation oracle of LP-RLCV\xspace directly.

\end{proof}

When $\eta=0$, RLCV\xspace can be solved in polynomial time is mainly because the most dissatisfaction coalition is a single player.
However, when $\eta\neq 0$, it becomes intractable to find the most dissatisfaction coalition.

\begin{theorem}\label{thm:oraclehard}
	There is no polynomial time separation oracle of LP-RLCV\xspace for some $\eta>0$, unless P=NP.
\end{theorem}

Theorem \ref{thm:oraclehard} can not imply the NP-hardness of RLCV\xspace.
However, the proof of Theorem \ref{thm:oraclehard} reveals an interesting connection between RLCV\xspace problem and a series of well defined combinatorial problems.
We will report the proof of Theorem \ref{thm:oraclehard} and the generalized combinatorial problems in the appendix.

In the left of this section, we prove the NP-hardness of RLCV\xspace, a stronger hardness result than which in Theorem \ref{thm:oraclehard}.
\begin{theorem}\label{thm:rleastcorenphard}
	It is NP-hard to compute ${\cal RLCV}(\Gamma_{f})$\xspace, even under influence cooperative game.
\end{theorem}

\begin{proof}[Sketch]
	We construct a reduction from the SAT problem.
	A boolean formula is in conjunctive normal form (CNF) if it is expressed as an AND of clauses,
	each of which is the OR of one or more literals.
	The SAT problem is defined as follows:
	given a CNF formula $F$, determine whether $F$ has a satisfiable assignment.
	Let $F$ be a CNF formula with $m$ clauses $C_1, C_2, \cdots, C_m$, over $n$ literals $z_1, z_2, \cdots, z_n$.
	Without loss of generality, we set $m>4n$.

	We construct a social graph $G$ as follows:
	\begin{figure}[t]
		\centering

		\includegraphics[width=0.6\textwidth]{reduction-sat.png}\\
		\caption{The reduction from SAT to ${\cal RLCV}(\Gamma_{f})$\xspace}\label{fig:reduction-sat}
	\end{figure}
	$G=(V_1\cup V_2\cup V_3, E)$ is a tripartite graph (see the sketch graph in Figure \ref{fig:reduction-sat}).
	In the first layer ($V_1$), there are two nodes $S_i$ and $T_i$ corresponding to each $i\in \{1, 2, \cdots, n\}$,
	$n+1$ dummy nodes labeled as $u_1, u_2, \cdots, u_{n+1}$ and $n$ dummy nodes labeled as $v_1, v_2, \cdots, v_n$.
	In the second layer ($V_2$), there are two nodes $x_i$ and $\overline{x}_i$ corresponding to each $i\in \{1, 2, \cdots, n\}$, one node $c_j$ for each $j\in\{1, 2, \cdots, m\}$ and a dummy node $w$.
	The third layer ($V_3$) contains only node $Q$.
	Edges exist only between the adjacent layers.
	For each $i\in \{1, 2, \cdots, n\}$, $S_i$ sends an edge to every node in
	$\{x_i, \overline{x}_i\}\cup\{c_j:$ clause $C_j$ contains literal $z_i, j\in\{1, 2, \cdots, m\}\}$.
	Similarly, for each $i\in \{1, 2, \cdots, n\}$, $T_i$ sends an edge to every node in
	$\{x_i, \overline{x}_i\}\cup\{c_j:$ clause $C_j$ contains literal $\overline{z}_i, j\in\{1, 2, \cdots, m\}\}$.
	The probabilities on edges sent form $S_i$ and $T_i$ are 1.
	There is an edge with influence probability 1 from $u_i$ to $c_i$ for any $i\in \{1, 2, \cdots, n\}$ and $m-n$ edges form $u_{n+1}$ to $c_{n+1}, c_{n+2}, \cdots, c_m$.
	There is an edge from $u_i$ to $w$ with influence probability $1-\sqrt[n+1]{1/2}$ for any $i\in \{1, 2, \cdots, n+1\}$.
	There is also exists an edge from $v_i$ to $w$ with influence probability $1-\sqrt[n]{1/2}$ for any $i\in \{1, 2, \cdots, n\}$.
	The left edges are  from $Q$ to all nodes in the second layer.
	The influence probability on edge $(Q, w)$ is $1/2$ and all other probabilities on edges sent from $Q$ is 1.
	The influence cooperative game defined on $G$ is $\Gamma(G)=(V=V_1\cup V_3, {\sigma^{\rm IC}}(\cdot), \eta=2n+m+1/2)$.
	For convenient, we set $N=2n+m$.

	Suppose $r^*$ is the optimal solution of the relative least-core value of  $\Gamma(G)$
	We can prove that $r^*\geq 1-\frac{1}{3}(N+\frac{7}{8})/(N+\frac{1}{2})$  if $F$ is satisfiable and $r<1-\frac{1}{3}(N+\frac{7}{8})/(N+\frac{1}{2})$ if $F$ is un-satisfiable.
	The proof of this part is shown in the appendix.
\end{proof}

\section{Computing Absolute Least-Core Value}\label{sec:leastcorevalue}

\subsection{Hardness of ALCV\xspace}\label{sec:hardnessofleastcorevalue}
\begin{theorem}\label{thm:alcvhardness}
ALCV\xspace problem of influence cooperative game cannot be approximated within 1.139 under the unique games conjecture.
\end{theorem}

\begin{proof}[Sketch]
	We construct a reduction from MAX-CUT problem. Under our construction, for any instance of MAX-CUT problem, we can construct an instance of  ALCV\xspace problem such that the optimal solution of these two instances are equal. The detail proof is shown in our appendix.
\end{proof}

\subsection{Approximating ${\cal ALCV}(\Gamma_{f})$\xspace}\label{sec:approximateleastcorevalue}

In this section, we approximate ${\cal ALCV}(\Gamma_{f})$\xspace by approximating the following linear programming (LP-PRIME\xspace):

\begin{equation*}\label{equ:lpprime}
\OnlyInShort{\small}
\begin{array}{ll}
\mbox{min}& \ \varepsilon\\
\mbox{s.t.}&\left\{
\begin{array}{ll}
 x(V)=\sigma(V)\\
 x(\{S\})\ge \sigma(\{S\})-\varepsilon  & \quad \forall S\subseteq V, \sigma(S)\geq \eta\\
 x(\{u\}) \ge 0 & \quad \forall u\in V\\
\end{array}\right.
\end{array}
\end{equation*}

The intractability of LP-PRIME\xspace lies on the exponential number of constraints and
    the hardness of identifying all successful coalitions.
We use a relaxed version LP-RE\xspace and a strengthen version LP-STR\xspace of LP-PRIME\xspace to
    design an approximation algorithm of ${\cal ALCV}(\Gamma_{f})$\xspace.
(\ref{equ:lprelax}) and (\ref{equ:lpstrengthen}) are formal definitions of LP-RE\xspace and LP-STR\xspace, respectively.

\begin{equation}\label{equ:lprelax}
\OnlyInShort{\small}
\begin{array}{ll}
\mbox{min}& \ \varepsilon\\
\mbox{s.t.}&\left\{
\begin{array}{ll}
 x(V)=\sigma(V)\\
 x(S)\ge \eta-\varepsilon  & \quad \forall~S\subseteq V, \sigma(S)\geq \eta\\
 x(\{u\}) \ge 0 & \quad \forall~u\in V\\
\end{array}\right.
\end{array}
\end{equation}

\begin{equation}\label{equ:lpstrengthen}
\OnlyInShort{\small}
\begin{array}{ll}
\mbox{min}& \ \varepsilon\\
\mbox{s.t.}&\left\{
\begin{array}{ll}
 x(V)=\sigma(V)\\
 x(S)\ge \sigma(S)-\varepsilon  & \quad \forall~S\subseteq V\\
 x(\{u\}) \ge 0 & \quad \forall~u\in V\\
\end{array}\right.
\end{array}
\end{equation}

	Intuitively, LP-RE\xspace and LP-STR\xspace denote absolute least-core values of two cooperative games with new profit functions.
	Specifically, LP-RE\xspace relaxes the constraints in LP-PRIME\xspace
	by reducing the profits of all successful coalitions excepting $V$ to $\eta$.
Formally, the profit function in LP-RE\xspace is $g(S)$:
$g(V)=\sigma(V)$, $\forall~S\subset V$,  $g(S)=\eta$ if $\sigma(S)\geq\eta$ and $g(S)=0$ otherwise.
The profit function in LP-STR\xspace is $h(S)=\sigma(S)$, $\forall S\subseteq V$.
Clearly, LP-STR\xspace strengthens LP-PRIME\xspace by increasing the profits of all unsuccessful coalitions.

Our main result in this section is shown in Theorem \ref{thm:approxmate_alcv}.

\begin{theorem}\label{thm:approxmate_alcv}
	$\forall~\delta>0$, there exists an approximate algorithm ${\cal A}$ of the ${\cal ALCV}(\Gamma_{f})$\xspace problem  with running time in $poly(n, 1/\delta, \log\sigma(V))$,
	${\cal A}$ outputs $\varepsilon'_p$ such that $\varepsilon^*_p\leq \varepsilon_p'\leq\min\{\varepsilon^*_p+\sigma(V)-\eta+2\delta,~\max\{3\varepsilon^*_p,\eta\}\}$,.

\end{theorem}

We prove Theorem \ref{thm:approxmate_alcv} by show Lemma \ref{lem:lpplprlps}, Lemma \ref{lem:lpstrengthen} and Lemma \ref{lem:lprelax} in order.
\begin{lemma}\label{lem:lpplprlps}
	Suppose the optimal value of LP-PRIME\xspace, LP-RE\xspace and LP-STR\xspace are $\varepsilon_p^*$, $\varepsilon_r^*$ and $\varepsilon_s^*$, respectively.
	Then, we have
	\begin{equation}\label{eq:lprandlpp}
	\varepsilon_p^*\leq \varepsilon_r^*+(\sigma(V)-\eta)\leq \varepsilon_p^*+(\sigma(V)-\eta),
	\end{equation}
	\begin{equation}\label{eq:lpsandlpp}
	\varepsilon_p^*\leq \varepsilon_s^*\leq \max\{\varepsilon_p^*,\eta\}.
\end{equation}
\end{lemma}

\begin{lemma}\label{lem:lpstrengthen}
	There exists a polynomial time approximate algorithm of LP-STR\xspace outputting $\varepsilon_s'$ such that $\varepsilon_s^*\leq\varepsilon_s'\leq 3\varepsilon_s^*$.
\end{lemma}

\begin{lemma}\label{lem:lprelax}
	$\forall~\delta>0$, there exists an algorithm of LP-RE\xspace outputting $\varepsilon_r'$
	such that $\varepsilon_r^*\leq\varepsilon_r'\leq\varepsilon^*_r+2\delta$, with runs time in $poly(n, 1/\delta, \log \sigma(V))$.
\end{lemma}
The proofs of Lemma \ref{lem:lpplprlps} to Lemma \ref{lem:lprelax} rely heavily on mathematical computation and we report them in the appendix.

\section{Computing Least Average Dissatisfaction Value}\label{sec:ladv}
Based on Definition \ref{def:acv}, ${\cal LADV}(\Gamma_{f})$\xspace equals the optimal value of
    the following linear programming:
\begin{equation}\label{equ:ladv}
\OnlyInShort{\small}
\begin{array}{ll}
\mbox{min}& F(x)=\frac{1}{2^n}\sum_{S\subseteq V}\max \{f(S)-x(S), 0\}\\
\mbox{s.t.}&\left\{
\begin{array}{ll}
 x(V)=\sigma(V)\\
 x(\{i\}) \ge 0 & \quad \forall~i\in V\\
\end{array}\right.
\end{array}
\end{equation}
Where $f(S)=\sigma(S)$ if $\sigma(S)\geq \eta$ and $f(S)=0$ otherwise.
There are exponential terms in $F(x)$, however, we can utilize stochastic gradient algorithm to approximate the optimal solution of (\ref{equ:ladv}).
This is because the object function $F(x)$ is a convex function (Lemma \ref{lem:gsubmodular}) and the feasible solution area in (\ref{equ:ladv}) is a convex set.

\begin{lemma}\label{lem:gsubmodular}
	$F(x)$ is a convex function.
\end{lemma}
The proof of Lemma \ref{lem:gsubmodular} is shown in our appendix.
The stochastic gradient descent algorithm
	(cf. \cite{shalev2014understanding}) can be used to compute ${\cal LADV}(\Gamma_{f})$\xspace (see Algorithm \ref{alg:sgd}).

\begin{algorithm}[h]
	\OnlyInShort{\small}
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand\algorithmicensure {\textbf{Output:}}
\caption{Stochastic gradient descent for LADV\xspace}\label{alg:acv}
\begin{algorithmic}[1]\label{alg:sgd}
\STATE	\textbf{Parameters:} Scaler $\alpha>0$, integer $T>0$
\STATE  \textbf{Initialize:} $\textbf{X}^1=\textbf{0}$, $t=0$.\\
\STATE  Set $D=\{\textbf{X}:\textbf{X}_i\geq 0 (\forall~i\in V),~\sum_{i\in V}\textbf{X}_i= \sigma(V)\}$.\\
\FOR {$t=1$ to $T$}
	\STATE  /*choose a random $\textbf{Y}^t$ such that $\mathbb{E}[\textbf{Y}^t|\textbf{X}^t]$ is a subgradient of $F$.*/
	\STATE	Uniformly at random choose a set $S\in 2^V$.\\ \label{line:beginchoose}
	\IF {$f(S)\geq\textbf{X}^t(S)$}
		\STATE Set $\textbf{Y}^t=(-\textbf{1}_S, \textbf{0}_{V\setminus S})$.\\
	\ELSE
			\STATE Set $\textbf{Y}^t=\textbf{0}$.
	\ENDIF \label{line:endchoose}
    \STATE  update $\textbf{X}^{t+\frac{1}{2}}=\textbf{X}^t-\alpha \textbf{Y}^t$.\\
    \STATE  /*Project $\textbf{X}^{t+\frac{1}{2}}$ to D*/
    \STATE  $\textbf{X}^{t+1}=\arg\min_{\textbf{X}\in D} \|\textbf{X}-\textbf{X}^{t+\frac{1}{2}}\|^2 $.\\
\ENDFOR
\RETURN $\hat{F}=\min \{F(\textbf{X}^t)\}_{t\in \{1,2,\cdots, T\}}$.
\end{algorithmic}
\end{algorithm}

Let $F^*$ be the optimal solution of ${\cal LADV}(\Gamma_{f})$\xspace, $\hat {F}$ be the output of Algorithm \ref{alg:sgd} and the profit of grand coalition $\sigma(V)=V$. Then, the performance of Algorithm \ref{alg:sgd} can be formalized in the following theorem.
\begin{theorem}\label{thm:sgd}
	$\forall$ $\varepsilon>0$, $\mathbb{E}[\hat {F}]-F^*\leq \varepsilon$ if $T\geq\frac{\sigma(V)^4n^4}{\varepsilon^2}$ and $\alpha=\sqrt{\frac{\sigma(V)^4}{Tn^4}}$ in Algorithm \ref{alg:acv}.
\end{theorem}
Following  the analysis in Chapter 14 of \cite{shalev2014understanding},
Theorem \ref{thm:sgd} holds since it is easy to check that $\mathbb{E}[\textbf{Y}^t|\textbf{X}^t]$ is a subgradient of $F(\textbf{X})$ at node $\textbf{X}^t$, for any $t\in [T]$ (line \ref{line:beginchoose} - line\ref{line:endchoose} in Algorithm \ref{alg:sgd}).
\section{Conclusion and future work}
In this paper, we study the core related solution concepts of truncated submodular profit cooperative game.
One possible future work is to change the way of truncating a function.
For example, we can set $f(S)=\sigma(S)$ if $|S|\geq k$ and $f(S)=0$ otherwise.
This setting is a special case of the setting in our paper and maybe we can try to design algorithms for it.
In this paper, we prove that computing the relative least-core value is NP-hard.
We also prove that the relative least-core value can be solved in polynomial time in a special case.
A directly future work is to design an approximate algorithm of RLCV\xspace under general case.

\newpage

redpajama_set_name: RedPajamaArXiv


text:
Molly Solomon: Taking Big Swings at Golf Channel
In 2012, Molly Solomon became the first woman to serve as executive producer for a national sports network when she was named executive producer and senior vice president, production and operations for Golf Channel.
Our sister site, NBCUniversal.com caught up with Golf Channel Executive Producer Molly Solomon (a 10-time Emmy Award-winner and longtime NBC Olympics producer) as she reflected on NBC Sports' most exciting golf schedule ever in 2016, including its inaugural coverage of The Open and golf's return to the Olympics after more than 100 years.
Q: First year with a men's major (The Open), the Rio Olympics, huge ratings and now the upcoming Ryder Cup. Can you talk about a huge 2016 at Golf Channel?
Molly Solomon: We couldn't wait for the "summer of golf" to begin. Golf Channel televising its first-ever men's major at Royal Troon in July; golf returning to the Olympics for the first time in more than a century in August followed by September's PGA TOUR FedExCup Playoffs; four LPGA Tour major championships and what many term the greatest event in golf – the Ryder Cup returning to American soil. Every week was "major" as we often say at Golf Channel. Our production, technical and announce teams have worked incredibly hard, alongside everyone at Golf Channel, and we expect this to be one of the highest-rated years in our 21 year history. But we need to now carry our tremendous momentum through the end of the year and continue to serve our viewers this fall with Tiger Woods' return to professional golf, our new original series Driver vs. Driver, our World Long Drive Championship and our position as the exclusive home to live golf from around the globe.
Q: You are the first female executive producer of a national sports network. What does that mean to you and to women coming up in this business?
Solomon: I never realized how meaningful it was until after I took the job. I heard from dozens of women about why it was important. I kept those notes, and it was humbling that women took the time to reach out. The best part of being "the first" is that tag will never be used again – and that's a good thing. Now we get to celebrate women attaining executive jobs in sports as their own personal accomplishments. The challenge now is to sponsor more women so they are offered executive opportunities.
Q: So not only are you an executive at Golf Channel but your husband, Geoff Russell, is the Executive Editor. How did that happen? And how is it working together?
Solomon: Geoff was a magazine editor for Golf Digest's news weekly, Golf World, for 12 years and he was approached to work for Golf Channel before I was! As the print industry was increasingly challenged, it was a terrific opportunity for Geoff to take on the role of Executive Editor, molding Golf Channel's editorial direction. As for working together, I don't recommend it for any marriage! Just kidding...we knew our relationship could handle it, but there have been more trying times in the last 4½ years than there were in the first 16! He's an incredible people person and I admire him even more after having the opportunity to work together at NBCUniversal.
Q: How's your golf game?
Solomon: I worked with someone at NBC Sports who made sure he added a few whimsical accomplishments and goals to his year-end review. Inspired by his sense of humor, I've added a golf handicap goal to my EMS report since moving to Florida. I'm at a career-low 14 and came within two shots of breaking 80. So I'm headed in the right direction, but playing in pro-ams and with business partners is a whole different kind of pressure than weekend games with my friends and kids.
Q: You started as an Olympic researcher in 1992 in Barcelona. With golf back at the Olympics in Rio you got to work another Olympics. How was that?
Solomon: Rio was my 10th Olympics and I saw it through two completely different lenses; both the golf community including the PGA TOUR and LPGA Tour professionals, as well as our Golf Channel team working at an Olympics for the first time. They were amazed by the experience and being a part of the world's biggest sporting event. To steal a line from one of the reporters covering the Games, "It wasn't 'Olympic Golf,' it was 'Golf in the Olympics.'" Many of our Golf Channel employees also worked for the Olympics Division in Rio and at the Stamford, Conn., headquarters. We had a "Lunch and Learn" panel after Rio for our Orlando-based employees, and to hear them rave about this professional experience was everything we hoped for as part of the NBC Sports Group.
Q: What is your advice to women who are trying to break into the sports TV business?
Solomon: The advice is the same for both genders; observe, listen intently and work harder than what's required. I always tried to learn something new every day – a fact, a skill, a takeaway. Leave work daily with one accomplishment. Feel like you got smarter in your craft.
Q: You have a big job at the office, but at home you are the mother to 13-year-old triplets. How do you do it?
Solomon: Mom to 13-year-old triplets is a lot easier than 2-, 3- and 4-year triplets. Like every working family we have good days and challenging ones, but in the end organized chaos is exhilarating, be it in the control room or at home.
Q: Guilty TV pleasure?
Solomon: "The Real Housewives of..." any city is my coast-to-coast airplane indulgence.
Q: Three life mentors?
Solomon: I always used to list my Dad who made me aim high and "leave it all on the track." As I raise children, I am in awe of my mother who dreamed of leaving a farm town in rural Illinois to see the world as an army nurse in the 1960s, raised three kids and went back to work to give her kids' debt-free college educations. Now she cares for my father who is suffering from Parkinson's disease. I can't say enough about her strength and faith. It's inspiring every single day. And Dick Ebersol, former Chairman of the NBC Sports Group, mentored me by giving me challenges and opportunities before I ever knew or believed I was ready. You need someone who believes in you, almost more than you do.


April 21, 2016 April 22, 2016 Writing your first novel-Some things you should knowHow can I make my story move faster?, How do I regulate the tempo of my novel?, How to make your novel more exciting., I need to pick up the pace, Pacing in Novels, Why does my novel move so slow?
The pacing in your story is only one of many things you must consider. People who love to read but have never written books are cognizant of the pacing. I have read many a good book that I skipped portions of because I was tired of reading about the duchesses frilly dress or the description of the inner hull of a slave ship. I'm glad the author did their homework and provided historical information but sometimes it can be a bit much and totally bog down your story. there has to be a balance.
I love fast paced novels. Slow dragging stories full of description put me to sleep. They can't hold my attention. However with this being said there has to be a balance. I will discuss this more in my next blog.


Yesterday afternoon, I walked from the Mid-City Mall back to Kroger down the East side of Bardstown Rd and I was shocked by how miserable an experience it was.
First I want to thank the business that did make the effort to clear the entire sidewalk in front of their buildings.
Sadly, very few businesses have shoveled at all. And, of those that did, most just shoveled from their parking lot to the front door leaving huge sections of the sidewalk impassable.
Here's a long list of businesses that didn't shovel on the East side of Bardstown Rd.
PNC Bank at Longest Ave.


text:
King & Wood Mallesons news, updates and analysis | Page 1 of 19
Posted on 17 January 2020 13:14pm | Muna Abdi
US King & Wood MallesonsMishcon de Reya
Mishcon de Reya has called it quits in Manhattan after ten years as the firm's three remaining partners jumped ship for the New York office of King & Wood Mallesons.
Dispute resolution partners Mark Raskin, Robert Whiteman and Vincent Filardo have joined the global disputes practice at KWM along with six senior counsel and one paralegal.
Raskin is an IP litigator experienced in patent, trademark, trade secret and copyright litigation with a focus on life sciences, biotechnology and pharmaceuticals. Whiteman is a trial lawyer who is experienced in patent cases in federal courts and focuses on electrical patent disputes. Filardo is a commercial litigator and trial lawyer dealing in commercial disputes, trade secrets and unfair competition, business tort, defamation, employment disputes and white-collar crime.
Raskin commented: 'With KWM's unique international platform and client base, together with our local capability and experience, we are very excited about the growth opportunities this move presents. We look forward to joining the global KWM network and leveraging our shared strengths to enhance the offering we provide to our clients in the US and around the world.'
Senior counsel Eric Berger, Michael DeVincenzo, Elizabeth Long, Andrea Pacelli, John Petrsoric and Charles Wizenfeld have also joined KWM from Mishcon.
Managing partner of Mishcon Kevin Gold said: 'After much deliberation, we have agreed with the partners of Mishcon de Reya New York to withdraw from that business.
'Mishcon de Reya New York was always a separate business to Mishcon de Reya in London, with different partners and a different structure. Over the last number of years, the New York office had focused its practice on contingency patent cases. This type of practice was no longer consistent with our business in London.
'This will not affect the many relationships we have with other law firms based in the USA,' added Gold.
Mishcon opened its New York office in 2010 and at one point had eight partners and 25 attorneys with capabilities in complex civil litigation, IP and patent litigation, family, international arbitration, internal investigations, white-collar criminal and regulatory defense, fraud and asset recovery, hedge and mutual funds and employment litigation.
In July last year Mishcon confirmed that it was considering all options for raising funds as part of its 'ambitious plans' for growth, including either an IPO or partnering with a private equity investor.
Apathy and a multimillion-pound shortfall define beleaguered KWM Europe insolvency
Posted on 8 April 2019 09:30am 5 April 2019 15:39pm | Thomas Alan
Financial management King & Wood Mallesons Focus
Thomas Alan finds reality setting in for creditors and former partners more than two years on
'My immediate thought was: "Can't we just move on?" I can't be bothered with it,' says one former King & Wood Mallesons (KWM) Europe and Middle East partner when asked for their thoughts on the firm's latest administration report. Indeed, it is hard not to share some of the sentiment. Two years after the collapse of KWM EUME, the saga continues to limp forward in a fashion considered onerous even by law firm insolvency standards.
KWM administration report shows £18.3m hole for creditors as former staff set for payouts
Posted on 7 March 2019 10:10am 7 March 2019 11:46am | Thomas Alan
Financial management King & Wood Mallesons
Two years after the collapse of King & Wood Mallesons (KWM) the saga rumbles on, with administrators primed to pay former staff as an £18.3m funding deficit leaves unsecured creditors out of pocket.
A progress report filed last week details how some former employees of the firm have been ranked as preferential creditors following KWM's 2017 insolvency. These employees will now be eligible for successful claims on failing to consult on the redundancy process, as well as payouts on wages and holiday pay.
Though among former partners there is a lingering sense of apathy regarding the latest report, with one former KWM partner telling Legal Business: 'I've not actually read the latest report or been sent it. In truth I've not been following any updates on it for a while.'
The firm's unsecured creditors will likely be more concerned, however. Quantuma, who received a 12-month extension to its role as administrators of KWM in January last year, has set aside £600,000 for unsecured creditors, the maximum possible based on the collapsed firm's assets.
However, the 159 claims received from unsecured creditors totals £18.9m, leaving a multimillion-pound shortfall. The firm's sole secured creditor is banking giant Barclays, who to date has received £6.5m, with £500,000 paid between 17 June 2018 and 16 January this year.
Having first begun in January 2017, the administration was extended by 12 months in January 2018, while in January of this year it was extended once more as KWM's dispute with Standard Chartered over unpaid fees held up the process.
Meanwhile, former partners of the firm are still wrestling with tax issues following the collapse of its European arm, meaning further delays to rebate payments. Despite this, none of the former partners Legal Business approached had seen the most recent report.
In September 2017, 288 former KWM employees were awarded over £1m by an employment tribunal which settled claims after the collapse, as it was deemed KWM failed to properly engage in a formal redundancy consultation. The latest report states the administrators are currently calculating and distributing the money owed to other former employees, with the KWM story set to continue for some time.
thomas.alan@legalbusiness.co.uk
'A clear cut case' – Ex-KWM employees win £1m pay-out from employment tribunal
Posted on 22 September 2017 13:19pm 22 September 2017 13:36pm | Tom Baker
Litigation King & Wood Mallesons
After being on the verge of accepting a six-figure sum last month, a group of 288 former King & Wood Mallesons (KWM) employees have been awarded over £1m by an employment tribunal to settle claims from the collapse of the firm's European arm.
The ex-staffers received the compensation award this week (20 September) following the failure of KWM to properly engage in a formal redundancy consultation during its much-publicised European insolvency.
The pay-out represents a significant uplift in compensation for the claimant group, which had considered accepting a near-£800,000 settlement offer from the firm's administrators made in August. Quantuma, KWM's administrators, made the offer after conceding that a 'technical breach' had taken place during the required UK redundancy consultation period. The earlier proposed settlement constituted eight weeks' pay, capped at £479 per week per person.
The claimants, however, rejected the settlement, taking the case to employment tribunal, which handed down its judgment this week.
The claimants were represented by Wokingham law firm Herrington Carmichael, with a team led by partner and head of employment Alistair McArthur. In a statement, McArthur thanked Quantuma 'for being amenable and helpful throughout the process' and described the case as 'a very unfortunate situation for all involved'. McArthur went on to label the claim as 'a clear cut legal case' and stated the firm was 'confident that the former employees had a strong case for compensation through the employment tribunal'.
The pay-out is the latest episode in the lengthy saga of KWM's European collapse. The firm filed for administration in December 2016 with debts of over £30m after senior figures had left the firm in droves. It was the largest failure to ever hit the European legal market. The practice was largely made up of the legacy SJ Berwin practice, which merged with Asia-Pacific giant KWM in 2013. Despite the union, the firm remained structured as individual partnerships leaving the rest of KWM unaffected by the insolvency.
A report filed earlier this month by Quantuma at Companies House revealed the costs associated with the firm's European administration, including CMS Cameron McKenna receiving a total of £826,740 for 'assistance in attending to the complex legal issues which have arisen both in the pre and post-administration periods.'
tom.baker@legalease.co.uk
Click here for the definitive account of the collapse of KWM (£)
KWM insolvency report reveals cost of everything from artwork to legal fees as ex-staff agree payout
Posted on 8 September 2017 15:22pm 22 February 2018 09:55am | Kathryn McCann
Eight months on and the King & Wood Mallesons (KWM) saga continues, with a progress report filed this week revealing the cost of the firm's European administration amid confirmation that ex-staff are set to receive a payout.
According to a report filed by administrator Quantuma at Companies House on 5 September, CMS Cameron McKenna received a total of £826,740 for 'assistance in attending to the complex legal issues which have arisen both in the pre and post administration periods'. This figure also includes costs of £235,544 incurred by the firm in dealing with KWM's German offices while additional legal fees of £186,318 go to Pinsent Masons for advising the administrators as well as £70,000 to iLaw Legal Services.
The report also shows the amount paid to Barclays, KWM's main secured creditor. The report states: 'The joint administrators instructed their legal advisers to conduct a review of the bank's security… valued at £16,557,222.' A total of £4,473,767 has been paid to Barclays so far in three separate instalments.
Included by Quantuma are the costs owed by numerous law firms including KWM 2.0, DLA Piper and Baker McKenzie. KWM 2.0 paid £75,000 for numerous assets in January – however, the firm still owes £881,250. DLA Piper still owes £521,000 after making a payment of £419,000 in May this year while Baker McKenzie made a full payment of £103,603 in January.
Additionally the report lists numerous miscellaneous costs including everything from artwork to mobile phones. It is revealed that the firm's mobile phones have been sold for a total of £5,780; £4,000 has been paid to Hector Patterson & Co in regards to the valuation of KWM's artwork displayed throughout their premises and a total of £26,515 was paid to Clear it Solutions for clearance of KWM's offices.
Tim Bednall, KWM's former managing partner, was paid £25,380 to be 'instructed as the joint administrators' agent in order to advise and assist' due to his knowledge of the firm's clients. This was agreed on a fixed-fee basis.
News of the administration's progress comes as KWM's staff have accepted a financial settlement offered by Quantuma after conceding a 'technical breach' occurred in the required UK redundancy consolation period.
The proposed settlement constitutes eight weeks' pay, capped at £479 per week per person. An email sent to around 200 staff from the group's solicitors Herrington Carmichael said that following discussions with the Redundancy Payment Office, the firm would apply to the Employment Tribunal for the judgement by consent agreed between the parties. The email added: 'We were delighted to receive full acceptance of the proposal from all claimants and, therefore, have now made the required application.'
This week's news is the latest update in the acrimonious collapse of the European practice of KWM, which is formed by the legacy SJ Berwin. The SJ Berwin business, which remained a separate partnership after combining with KWM in 2013, collapsed in December 2016 with debts of over £30m after a string of senior departures. It was the largest failure to ever hit Europe's legal market.
kathryn.mccann@legalease.co.uk
KWM Germany plans to double Chinese-German deals capability by mid-2018 in focus shift
Posted on 28 July 2017 14:36pm 7 August 2017 11:50am | Georgiana Tudor
Strategic recruitment King & Wood Mallesons
Asia-headquartered firm King & Wood Mallesons (KWM) has made a strategic commitment to its German practice with the hire of two new partners in Frankfurt to strengthen its Sino-German deals capability, following the collapse of its European arm in January.
With four corporate partners in Germany, all based in its Frankfurt office, the firm told Legal Business that it plans to grow around 50% in the region by mid-2018.
'We want to implement our global strategy, and due to the activity in Germany we have decided to enlarge our corporate finance element here,' said corporate partner Christian Cornett.
According to Cornett, KWM's German practice is currently engaged in 40% local German work and 60% international transactions work, stemming from the Asia-Pacific region.
'Germany currently has the strongest economy in Europe, so our international network naturally has a strong focus on Germany now,' he added.
Corporate partners Hui Zhao and Daniel Ehret will join the firm on 1 October bringing additional corporate finance expertise including clients involved in Sino-German investments.
Cornett said that the firm had approached 'a few select people' to join the German practice, with Zhao and Ehret as the first to join, with two or three more due to come on board by the end of the year.
Based in Frankfurt, Zhao joins from Noerr and is a corporate lawyer specialising in Chinese M&A in Germany and worked to develop Noerr's China practice over the last decade. Ehret is a finance and restructuring specialist who joined from Latham & Watkins. He has represented investors, lenders and distressed companies on restructurings.
'The strategy is to build two strong pillars in this practice – one international platform servicing work from our Asia Pacific network, and the other to have a strong local German practice. With additional private equity (PE) capability we can now build these,' Frankfurt Corporate partner Sandra Link said.
'Outbound investment of Chinese investors has increased in general based on various factors including scarcity of attractive domestic assets in China and a supportive financing and political environment,' she added.
'Chinese investors are in particular interested in technology and industrial know-how and "Made in Germany" has a high reputation,' Link said.
Link cited an rise in Chinese M&A transactions in Germany over the past five years, counting 39 in 2015 and 68 in 2016.
In 2016, in KWM Germany's mandates included advising Techcent Entrepreneur Family Deng on its joint venture with ALBA Group, and Chinese fertilizer company Kingenta Ecological Engineering Group on its acquisition of Compo Consumer Business from PE investor Triton.
After the firm's European practice broke down over the last year, EUME senior partner Michael Cziesla, based in Frankfurt, joined McDermott Will & Emery earlier this year. Cziesla had only been elected senior partner of the firm in October last year.
In January, DLA Piper also recruited KWM Germany real estate head Lars Reubekeul and real estate partner Florian Biesalski, along with their teams, to DLA's Frankfurt and Munich offices.
When Reed Smith confirmed the hire of 50 KWM lawyers across Europe, adding 10% to its European headcount, it also hired two partners in Germany. These were competition and antitrust partner Tilman Siebert in Munich and litigation partner Francis Bellen in Frankfurt.
Georgiana.tudor@legalease.co.uk
Ex-KWM real estate duo exits Ashurst for Fried Frank after one year
Posted on 20 June 2017 11:12am 7 November 2018 13:27pm | Madeleine Farman
Strategic recruitment AshurstFried, Frank, Harris, Shriver & JacobsonKing & Wood Mallesons Property
Real estate duo Darren Rogers and Patrick Williams has resigned from Ashurst to join Fried, Frank, Harris, Shriver & Jacobson's London office just over a year after joining the City firm from King & Wood Mallesons (KWM).
Rogers was made up to partner at legacy SJ Berwin in 2010, where he started as an associate 16 years ago. Ashurst announced he was set to join the real estate team as a partner in April last year together with Williams, who was promoted to partner in 2015 when KWM made up only two London lawyers as part of a 36-strong round.
The pair counts British Land as a longstanding client, alongside Invesco Real Estate, CBRE Global Investors and Battersea Power Station Development Company among others.
The hire is the first Fried Frank's London office has made for over a year, with the US firm bringing in Mayer Brown co-head of restructuring Ashley Katz in February 2016.
Fried Frank's corporate real estate co-head Fiona Kelly said Rogers and Williams 'have a strong reputation, both within the UK and internationally, for providing preeminent counsel in this sector.'
She added that the duo's broad experience in commercial real estate law and corporate law would add strength to the firm's clients 'in all facets of high value commercial real estate investment'.
An Ashurst spokesperson said the real estate group, which has 21 London based partners, will continue to focus on high end work: 'We do not anticipate these departures as having any significant impact on the real estate practice and they are likely to increase our profitability.'
Earlier this June, Ashurst lost a four-partner team from its Paris arm to Gibson, Dunn & Crutcher, which came just four months after it emerged a group of five Ashurst corporate partners in Paris to Freshfields, collectively responsible for a book of business worth £8m.
The firm's London head of pensions Marcus Fink also departed to PwC earlier this year.
Conversely, in March Ashurst launched a European high-yield offering, bringing in Allen & Overy senior associate Tamer Bahgat, who was made up to partner at Ashurst, and Linklaters counsel Natalia Sokolova.
The firm has also hired Linklaters leveraged finance senior associate Pierre Roux and PwC tax director Emmanuelle Pontnau-Faure in Paris, who will both be made up to partner in the move.
In March, Fried Frank confirmed London managing partner and City veteran Graham White would leave private practice at the end of May. Asset management partner Mark Mifsud stepped into the role following his departure.
Georgiana.tudor@legalease.co.uk and Madeleine.farman@legalease.co.uk
'Cementing KWM': Australian chief exec Kench elected as new global managing partner
Posted on 10 May 2017 08:01am 14 February 2018 15:56pm | Georgiana Tudor
Leadership King & Wood Mallesons
After going months without a global managing partner, King & Wood Mallesons (KWM) has appointed Australia chief executive partner Sue Kench to the role, effective 1 June 2017.
Kench succeeds Stuart Fuller, who stepped down from the role at the end of 2016 during the collapse of the firm's European arm, and has since returned to full time practice.
Kench has been chief executive partner in Australia since 2013. She is also currently a member of the firm's global executive committee and the international management committee. In her new role, she will work with recently-appointed global chairman Wang Jungfeng.
Kench joined legacy Mallesons in 1996 and held leadership positions such as managing partner of the real estate and construction practice, sector lead in real estate and construction and board member.
KWM said in a release that Kench will lead the firm's global strategy and operations 'with a focus on cementing KWM as leading international firm in Asia'.
Speaking to Legal Business, Kench said: 'The key for us really is to bring the firm closer together, integrate the businesses better and harness the opportunities that are out there for us. When coming into Asia, we should be the first firm that people recognise. And if Asia clients want work done outside the region, our other capabilities should be capturing that work as well.'
'We will have a stronger focus on all of the component parts that make up integration, and what work should we be attracting beyond Australia and China. There's no other firm like us in the world. That's the differentiator, and we have to use that to the maximum.'
The firm has also announced the appointment of Rupert Li as global chief operating officer (COO) and Berkeley Cox as Kench's replacement, as chief executive partner in Australia. Li was international partner within China and Hong Kong, and is also a current member of the international management committee and the China management committee. Cox was deputy managing partner for Australia.
Last month Legal Business revealed KWM Europe partners who took out personal loans from Barclays for their capital contributions had received payment ultimatums. Former KWM staff have also come together earlier this year to take legal action over the way redundancies were handled, as the administrators' investigation into the collapse of the legacy SJ Berwin business.
Read more: 'Shattered – The final days of 'SJ Berwin'
Posted on 9 May 2017 08:30am 18 January 2018 13:17pm | Legal Business
Addleshaw GoddardKing & Wood MallesonsPinsent MasonsReed Smith EuropeHong KongMiddle East and AfricaUS
PINSENTS LAUNCHES IN MADRID
Pinsent Masons has launched in Madrid, the firm's third international office in less than a year. The new office comprises six partners, four from local Madrid firm Ramón y Cajal Abogados. The firm has also hired from contractor OHL and promoted a Pinsents associate to partner.
Barclays deadline looms for KWM partners who took personal loans for capital
Posted on 21 April 2017 09:33am 14 February 2018 15:56pm | Georgiana Tudor
Financial management BarclaysKing & Wood Mallesons
Former King & Wood Mallesons (KWM) partners who took out personal loans from Barclays for their capital contributions have received payment ultimatums as the bank is demanding repayment by the end of April.
Lawyers often take out loans for working capital at law firms when they are elevated to partners. As at 30 April 2016 KWM comprised of 163 partners, and according to one former partner, at least 50 of these owed six-figure sums to Barclays, which is also the largest creditor of the now defunct European arm.
'The point scale was 20 to 60 – by the time you got to 30 points you'd be over £160,000 debt. I estimate Barclays will recover at least £8m from these loans,' he said.
The bank started sending letters asking for the money back in February after legacy SJ Berwin went into administration, but partners argue they have not received any response to their emails in February. Instead, the bank followed with a demand for repayment, asking partners to avoid default notices and pay by the end of April.
'The guy who sent out the letters initially has since been ill and nobody has been getting any responses,' a former partner said.
'Barclays cocked it up internally with these loans, and did not respond to our letters asking for payment schedules. Instead they sent a demand straight away. Not to mention they were incompetent enough to pump tens of millions into a firm who clearly couldn't pay it back' says another former partner who owes a six-figure sum.
However, it is understood that since the second set of letters demanding repayment arrived in March, the bank has had someone in place to respond to communication from former partners.
Another former partner added: 'This is quite personal for me. I understand they're asking for it rationally but [Barclays] should have known back then that the finances were not what they appeared to be, and they were still lending people like me money to put into the business.'
Other former partners are more pragmatic about the situation, with one adding: 'These are regular business loans that happen in all law firms. I don't want to undermine the positions of the others but they don't have a leg to stand on. However most partners will have taken out these loans, they were so easy to get.'
Other events some junior partners have criticised are the billing practices in the last few months of 2016, as the legacy SJ Berwin practice was collapsing.
'The billing practices going on towards the end of last year were very dodgy. People stockpiled WIP, they got their new firms to buy it and made a shedload of cash and used that to help them repay their loans – no skin off their nose,' one said.
'When people were moving it was well known that some would move to protect those loans,' another added.
Some partners have looked into challenging the loans using the Consumer Credit Act, however previous cases around the collapse of Dewey & LeBoeuf or Halliwells suggest a successful challenge is unlikely.
In both cases, Barclays was involved. With Dewey, the bank had $56m worth of outstanding loans to 220 partners when the firm collapsed in 2012. In 2015 the bank won a High Court lawsuit in a long running battle to secure repayment of a $540,000 loan from former Dewey partner Londell McMillan. The case was closely watched by the industry.
As is typical with any insolvency, KWM administrators Andrew Hosking and Sean Bucknall of Quantuma are investigating all elements of the collapse of the legacy practice. This includes management, how the firm's finances were run and other circumstances that led to the failure. In January when they released their first report, the administrators concluded partner exits had 'accelerated the ultimate demise' of the firm.
Read more in: 'Shattered – The final days of 'SJ Berwin'