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Single Market • Briefings • Featured
The Single Market isn't delivering the goods
by David Blake
Written by	David Blake
Professor David Blake examines economic performance in the EU and discovers that trend growth in traded goods actually declined after the Single Market was launched on 1 January 1993
Post Segments
Trend growth in traded goods declined
Trend growth in traded services barely changed
The Single Market is a giant economic non-event
We are told that one of the big attractions of the European Single Market (SM) is that all goods and services produced are required to satisfy a common set of regulatory standards. This ought to make it easier to export to other member states of the European Union. The reality is that the trend growth in traded goods declined, while the trend growth in traded services barely changed after the SM was introduced.
Table 1 provides some surprising evidence. It compares export growth in the 20 years before the introduction of the SM and in the 20 years after. The first row shows that the real growth rate in trade between EU member states actually fell from an average annual rate of 4.71% to 3.05% (or by 35%) after the introduction of the SM. Export growth to the rest of the world (ROW) fell by even more – by 73% from 1.20% to 0.32%. This contrasts dramatically with the growth rate in trade between ROW countries which increased over the same periods from 3.66% to 4.22%. ROW export growth to the EU also increased after the introduction of the SM from 3.29% to 4.11% – so was growing between 1993 and 2012 at a faster rate than trade between EU members. And much of this trade is conducted under World Trade Organization (WTO) rules, while facing the EU's Common External Tariff (CET) – in other words, under what is disparagingly called 'no deal' arrangements. The CET covers more than 13,000 imported goods, with an average tariff of 3-4%, but with much higher tariffs on food, clothing, footwear and cars.
Table1: Export growth 1973-2012
CAGR (%)
Intra-EU export growth (1) 4.71 3.05
Extra-EU export growth (2) 1.20 0.32
World export growth (3) 3.66 4.22
World export growth to EU (4) 3.29 4.11
UK intra-EU export growth (5) 5.38 3.09
UK extra-EU export growth (6) 3.70 3.11
Notes: (1) Exports of EU11 founder members of the EU Single Market to each other, (2) Exports of EU11 to 8 OECD countries (Australia, Canada, Iceland, Japan, Norway, Switzerland, Turkey, and the United States – Iceland, Norway, Switzerland and Turkey have negotiated substantial access to the Single Market), (3) World exports of all developed countries, (4) Exports of eight OECD countries to the EU12, (5) Exports of UK to EU10, (6) Exports of UK to 8 OECD countries. CAGR – cumulative annual growth rate.
Source: Figures 2, 3, 4, 5 and 6 and Table 4 of Michael Burrage (2016) Myth and Paradox of the Single Market: How the trade benefits of EU membership have been mis-sold, Civitas, London; https://www.civitas.org.uk/content/files/mythandparadox.pdf
Even more striking is the decline in the growth rate of UK exports to the EU from 5.38% to 3.09% following the introduction of the SM. UK export growth to the rest of the world also fell, but was still at a marginally higher rate between 1993 and 2012 than for exports to the rest of the EU (3.11% v 3.09%). This helps to explain why UK exports to the EU have fallen from 55% of the total to 46% since the SM was introduced. Further, only 6% of UK companies export to the EU – accounting for around 13% of Gross Domestic Product (GDP) – yet all regulations on product and service standards – including for the 94% of UK companies that do not trade with the EU – are determined in Brussels.
Table 2 shows the growth rate of exports of the top exporting countries to the EU between 1973 and 2012. Although the UK had higher total exports in 2012 than fifteen countries – except the US – they all enjoyed higher average export growth over the period, including China, Russia, Brazil – even Hong Kong. By 2018, China's exports to the EU at $472bn (€400bn) significantly exceeded the UK's at $384bn (£289bn).
Table 2: Growth of exports of selected countries to the EU 1973-2012 compared in 1973US$
% real growth CAGR% Total value in 2012 $bn
China 664 11.3 163.3
Russia 387 8.69 105.7
Brazil 343 8.15 44.7
India 276 7.22 44.3
Turkey 250 6.81 77.0
Korea 199 5.94 43.0
Australia 190 5.76 37.9
Mexico 185 5.66 31.5
S. Africa 165 5.27 26.8
Singapore 145 4.84 35.2
Canada 115 4.11 34.6
US 114 4.09 342.0
Switzerland 102 3.77 148.5
Norway 92 3.49 36.8
Hong Kong 81 3.16 38.6
UK 72 2.90 175.0
EU mean 66 2.71 183.0
Japan 47 2.04 63.2
Iceland 44 1.93 1.5
Israel 37 1.68 30.2
Taiwan 30 1.40 18.6
Source: Table 6 of Michael Burrage (2016) Myth and Paradox of the Single Market: How the trade benefits of EU membership have been mis-sold, Civitas, London; https://www.civitas.org.uk/content/files/mythandparadox.pdf
The result is a £93bn goods deficit with the EU in 2018. The overall trade deficit was £64bn, which is lower due to a £29bn services surplus. The EU is keen for the UK to remain as a captive market in the SM and Customs Union, since we are one of the biggest buyers of its goods. But, as Michael Burrage points out, this could lead to a balance of payments crisis in a few years' time. He estimates if the trend growth rates continue as in Table 1, then by 2030, there will be a goods deficit of £246bn, a services surplus of £58bn, and an overall trade deficit with the EU of £188bn.
The situation is even worse when it comes to services. There is little evidence that the SM has so far helped to develop an integrated EU-wide market in services. In 2015, intra-EU and extra-EU service exports to the EU were 6.9% and 5.9% of EU GDP, respectively, a difference of just 1%. Further, exports of services to the EU by countries outside the EU have grown at a faster rate (0.5% p.a.) than those of EU members to each other. So the 3.05% p.a. increase in intra-EU trade reported in Table 1 must have been mainly in the form of goods. Indeed, over the period 2002-2012, the extra-EU exports of services of 11 of the 12 founder members of the SM, and in particular those of the UK, grew faster than their intra-EU exports. France is the only exception.
Overall, the UK's benefit from the SM in terms of goods and services trade has been negligible. In 2005, an internal Treasury report – which later emerged because of a Freedom of Information request – found that the SM had only a marginal impact on UK trade. UK goods exports to the EU are 49% of total exports, amounting to 8% of GDP. Services account for 80% of the UK economy, but only 40% of the UK's service exports go to the EU, amounting to just 5% of GDP.
Even strong supporters of the EU, like the Financial Times' Wolfgang Münchau, concede that the Single Market is 'not visible in the macro statistics…. the data are telling us a different story – that the Single Market is a giant economic non-event, for both the EU and the UK'.
This makes it all the more curious why so many businesses and politicians in this country insist we have to have unfettered 'access' to the Single Market after we leave the EU. Don't they make any effort to find out the facts? The ignorance in this country about the failings of the Single Market is woeful. The price of that ignorance will turn out to be very high – not only over here, but also over there.
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Professor David Blake is at Cass Business School
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Krakow Hostel | Pictures - Hostel - Backpackers Hostel Krakow - Jagiellonian University Youth Accommodation Center. Hotel-like rooms for cheap hostel price! Budget hostel in Cracow - perfect place for students, backpackers and travelling families. Visit Krakow, Poland!


STARKVILLE, Miss. -- Dee Bost might be missing some teeth. He's definitely found his legs, though.
The Mississippi State junior, playing with his front teeth glued together after taking an elbow to the face earlier in the week, scored 24 points as the Bulldogs beat No. 24 Florida 71-64 on Saturday afternoon at Humphrey Coliseum.
"Our chemistry keeps getting better and better," Bost said. "We just need to keep fighting and getting these wins."
Bost was playing in just his sixth game this season after missing the first 14. He lost five games due to academic issues and then served a nine-game NCAA suspension after failing to pull out of the NBA Draft by the deadline.
The rust was apparent in some of his early games, but the 6-foot-2 point guard was efficient against the Gators, making 8 of 14 shots from the field, including 4 of 8 from 3-point range. He also added five assists and three rebounds.
Kodi Augustus and Renardo Sidney each scored 16. The Bulldogs (11-9, 3-3 Southeastern Conference) have won four of the last five against the Gators.
Only four Mississippi State players scored, but all of them finished in double figures. Ravern Johnson scored 15 points, including 13 in the first half, as the Bulldogs beat a ranked team for the first time this season.
The Bulldogs won despite being outrebounded 43-37 and giving up 17 offensive rebounds.
Florida (16-5, 5-2) trailed 51-42 early in the second half, but went on a 13-1 run to take a 55-52 lead. The game was tight from there, with five lead changes. But the Bulldogs pushed ahead in the final minute, making 6 of 6 free throws to seal the victory.
The clutch play was a stark contrast from barely 36 hours ago, when the Bulldogs led for most of the game before losing to No. 19 Vanderbilt.
"The things that beat us on Thursday night didn't beat us tonight," Stansbury said. "No missed block outs, no turnovers down the stretch."
Florida came into the game with the SEC's best conference record, but was hurt by a 9-of-19 performance (47.4 percent) at the free throw line, including several crucial misses in the final minutes. It's a familiar problem for the Gators, who came into the game 10th in the SEC in free throw shooting at 66.2 percent.
Vernon Macklin made a free throw to tie the game at 64 with 3:32 remaining, but the Gators were held scoreless from that point.
"We had a great opportunity to come out on the road and get a win, and we just shot ourselves in the foot on the foul line," said Florida's Chandler Parsons, who added nine points and 10 rebounds.
Erving Walker led the Gators with 18 points, making 6 of 17 shots from the field. Macklin added 10 points and six rebounds.
"I thought we guarded Florida about as well as you can guard them," Stansbury said.
Florida dominated in the paint, outscoring Mississippi State 38-16 and also held a 17-0 advantage in bench scoring.
Ten different Gators scored at least two points, but combined, they shot just 25 of 63 (39.7 percent) from the field.
"On the road, you want to put yourself in position to win," Florida coach Billy Donovan said. "We felt this was going to be a battle all the way through. We certainly did not make shots or key free throws down the stretch."
Mississippi State had a 40-38 advantage at halftime after leading by as many as 10 in the first half.


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5 Frequently Asked Questions About ACI eManifest | Part 1
As highway carriers struggle with the challenges presented to their business by ACI eManifest regulations and strive to get compliant, we frequently receive inquiries that need clarification. In the coming weeks, we'll feature five frequently asked questions about ACI eManifest. Jan Brock, recently retired Chief of Commercial Operations with Canada Border Services Agency for the Pacific Highway and Abbotsford Huntingdon districts and now a Senior Trade Advisor with Pacific Customs Brokers (Canada) will answer your questions about ACI emanifests and compliance.
So What Are Highway Carriers' Biggest Questions?
1. How Will The ACI eManifest Program Work?
Carriers are now required to electronically transmit cargo and conveyance data to CBSA for all shipments entering Canada. Submissions must be received and validated by the CBSA as early as 30 days in advance but no later than one hour before arrival at the First Port of Arrival (FPOA). All mandatory data elements and conditional elements where applicable must be included in submissions. (See Chapter 4: Electronic Commerce Client Requirements Document ECCRD). A machine-readable barcode must be presented to the Border Services Officer (BSO) at the FPOA. The barcode must either be the Conveyance Reference Number (CRN) or Cargo Control Number (CCN) associated to the trip. If the CCN is provided, the CRN must be hand-written on a document and provided to the BSO.
Carriers have a variety of submission options including utilizing a third-party service provider such as Border Pro for Carriers for eManifest filing services, or CBSA's ACI eManifest portal.
2. Who Has To Provide An eManifest?
With some exceptions, carriers for hire who are transporting commercial goods into Canada, or returning to Canada empty are required to file ACI eManifest.
3. What Is A Conveyance Reference Number?
The first four digits of the Conveyance Reference Number (CRN) must be the carrier code representing the carrier that is physically transporting the goods to Canada and reporting the goods at the First Port of Arrival (FPOA). This statutory obligation cannot be shifted from one carrier to another. The carrier code of the carrier transporting the goods must always be represented in the CRN, regardless of which party transmitted the related cargo data.
4. What Commodities Are Exempt From eManifest Requirements?
At this point, no specific products have been exempted from eManifest requirements. The ACI/eManifest Highway Electronic Commerce Client Requirements Document does provide info on exceptions and exemptions to eManifest filing requirements.
For a list of exceptions and exemptions from the eManifest program, consult the CBSA Electronic Commerce Client Requirements Document - Chapter 4: Advance Commercial Information.
5. Do We Have To Set Up A New eManifest For Every Customs Broker?
No, the ACI eManifest program is not customs broker specific. You are required to transmit advance cargo and conveyance information for each shipment transported into Canada by truck or rail car. These shipments could all be offered for release to CBSA by the same customs broker or by a combination of customs brokers.
Learn more about ACI eManifest
Attend one of our upcoming 90-minute sessions (seminar or webinar) and learn more about ACI eManifest. We will answer your eManifest related questions, offer practical solutions and help you comply with this regulation that is now in effect. For details and to register »
Jan Brock
Canadian Sr. Trade Advisor
PCB Customs Brokers
Jan Brock joined PCB Customs Brokers in 2015 as a Senior Trade Advisor. She retired from Canada Border Services Agency (CBSA) in 2015 after serving more than 37 years. Jan started her career with CBSA as a summer student in 1976 and worked part-time until she graduated from U.B.C. with a Bachelor of Education Degree in 1980 . Shortly after graduating from U.B.C. Jan worked full time as an inspector with CBSA and within three years was promoted to Superintendent. She served some time in the Regional Operations office as an Operations Review Officer before she was promoted to Chief of Operations first at the Customs Mail Centre, then in the Metro District as the Commercial Chief and ending her career as a Chief at Pacific Highway Commercial Operations where she served as Chief from 1992 to 2015. During her career she was a member of the Customs Drug Team and a trainer in the National Enforcement Program. Jan also served as the Regional Coordinator Officer Powers and Use of Force for the Pacific Region. Jan served on many Commercial Program Reviews and committees both national and regional during her career and possesses an expansive knowledge of importing and exporting into and from Canada.
Your Tsawwassen Container Examination Facility Update

redpajama_set_name: RedPajamaCommonCrawl


Want to see how productive your day can get? Read on.
Recently, I've been using Life Graphy, as a tool to keep track of things on a daily basis. It happens to be very helpful especially because I am able to see what I accomplish each day.
Between school, work, photography, family and other things (not on that order specifically), I get overwhelmed easily so I always strive to find tools that allow me to both remember things and keep track of them in the long run. And Life Graphy is a perfect fit for this.
Start by creating tasks to practice and set them up with a long term goal date or even without one. Then assign a day for each task to occur throughout the week and start keeping track. You can also think of these as habits, or any thing that you want to accomplish. For instance, one for me is to "drink 2 bottles of water" every day.
Set the app to remind you at beginning of the day to remind you of what you need to accomplish in that day. Then, tap on each item assigned as if checking them off. You'll see how your day looks like once you've done everything you were supposed to. Finally, jump into the calendar view to see how you did at the end of the week or month (like the picture on the top right). This is a great productivity tool, go check it out.
Do you use Life Graphy, too? Are there any other apps you recommend? Let me know in the comments below.
A capture of what my March month looks like so far.
I am an ePortfolio instructor working in New York City. I am also a student in the MA program in educational psychology at Hunter College. In my current position, I instruct students how to develop and build their ePortfolio to showcase their academic skills. I also collaborate in professional development seminars with faculty members from various departments on building the curriculum to teach the first year seminar experience. Read more about me.
Pablo Avila is a higher education professional, educator, and doctoral student living in New York City.
Do You Have an Online Tattoo?


Phoenix gives us an official early listen of their new "Bankrupt!" album, forthcoming on April 23. The iTunes Music Store hosts the first listen to the new record, featuring the single, "Entertainment" alongside nine new tracks. Listen over on iTunes. Pre-order from Amazon.
Full tracklist on the following page.


We appreciate really good collaboration, and we love the work you do. We think that, with your input and direction, this music could be something great.
To the right, there are demo tracks written and recorded by Jesse over the few days he shut himself up in a Flagstaff, AZ cabin recently. These tracks are rough, some incomplete, and need fleshed out. We hope you hear the magic in them that we do.


16 November will see the clash of two gangs, one in India and the other in South America. The first season of Amazon Prime's Mirzapur and season 4 of Netflix drama Narcos will both premier on their respective platforms on the same day.
Both shows explore similar themes of drugs, violence, power and politics. While Narcos explores the origins of the present day drug war and the rise of cocaine kingpin Pablo Escobar, Mirzapur is the story of the menacing Kaleen Bhaiyya and his cartel set in the small Indian town of Purvanchal.
Speaking about the clash of content on the two OTT platforms, Mirzapur director Karan Anshuman said that he was confident the show will appeal to a global audience. He's sure that while Narcos has a huge fan following, Mirzapur will win Indian hearts considering the story is set closer to home."I don't think the clash will affect views because let's be honest, this is our world, it is our story, by our I mean an Indian thing, and it is very rooted in what our reality is," he says.
. Read more on Hot on Web by The Quint.RSS & BJP's Nehru-Netaji 'Cosplay': Irony Dies a Thousand DeathsIndia vs Windies 5th ODI LIVE: Chasing 104, India 62/1 . Read more on Hot on Web by The Quint.


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The Draughtsman's Contract plus artists' shorts
Sunday 13 November 2016, 14:00 to 18:00
A screening of films specially selected to accompany Daphne Wright's Emotional Archaeology.
The way in which language facilitates (and abstracts) communication; ambiguities inherent within close, personal relationships; intergenerational relationships; domesticity: these films reflect a range of themes explored in Daphne Wright's exhibition.
The Draughtsman's Contract (1982), the first feature film by legendary director Peter Greenaway, is a highly stylised period-drama. Focused on an arrangement between an aristocratic woman and an arrogant young draughtsman, who agrees to exchange sexual favours in return for a series of drawings of her estate, the plot goes on to encompass a murder mystery. Precise narrative resolutions are avoided however, in favour of an arch and witty style which revels in the declamatory vocal delivery of the main characters, and the slight though deliberate skewing of various period details. The score by Michael Nyman, drawing heavily on the music of the 17th century English composer Henry Purcell, testifies to one of the most celebrated creative partnerships in British film making.
Peter Greenaway, UK, 1h 48min, Cert 12.
The screening will be preceded by a selection of artists' short films:
Margaret Tait - A Portrait of Ga
UK, 1952, 5min.
A portrait of the film maker's mother.
Born in 1918 in Kirkwall on Orkney, from 1950 to 1952 she studied film at the Centro Sperimentale di Photographia in Rome. In the 1960's Tait moved back to Orkney where over the following decades she made a series of films inspired by the Orcadian landscape and culture. All but three of her thirty two films were self-financed.
Screenings include National Film Theatre (London), Berlin Film Festival, Centre for Contemporary Art (Warsaw), Arsenal Kino (Berlin), Pacific Film Archives (San Francisco), Knokke le Zoute, Delhi and Riga. Tait was accorded a retrospective at the 1970 Edinburgh Film Festival and has been the subject of profiles on BBC and Channel Four.
The feature length Blue Black Permanent (1993) opened the Edinburgh International Film Festival. Her final film Garden Pieces was completed in 1998. Tait died in Kirkwall in 1999.
Read more about Tait's work by writer Ali Smith here.
Catherine Elwes - The Gunfighters
UK, 1985, 5 min 30.
'Very few artists have tackled the question of masculinity in anything like an accessible way. Cate Elwes' Gunfighters is an exception. The tape is cut so that we see the boys' tenderness and vulnerability before they flip into parody violence. We are left with their fantasy world, hermetic and complete, as well as having questions about its provenance raised in our own minds.' - John Dovey
Co-curator two landmark feminist exhibitions, Women's Images of Men and About Time, (ICA, London, 1980, both of which toured to Arnolfini), Elwes specialises in video and installation exploring gender and identity. She has participated in many international festivals, and her tapes have been shown on Channel 4 as well as on Spanish, Canadian and French television networks. She is Professor of Moving Image at University of the Arts London.
Keren Cytter - Game
2015, 9 min 19. Courtesy of the artist and Pilar Corias Gallery.
Characterised by a non-linear, cyclical logic Cytter's films consist of multiple layers of images, conversation, monologue and narration, systematically composed to undermine conventional linguistic and interpretative conventions. Recalling amateur home movies and video diaries, the artist creates scenes of intensified versions of everyday life, in which the overwhelmingly artificial nature of the situations portrayed is echoed by the very means of their production.
Born in Tel Aviv, 1977, lives and works in New York. Winner of the 2006 Bâloise Art Prize at Art Basel, she has exhibited widely, and had her first major survey show at MCA Chicago last year.
Benjamin A Owen - AcCord: Going along (without a body)
2016, 7 min 48.
Ben is a filmmaker whose work explores politics as it is played out in the everyday and in the commonplace. He often works in film, but his practice encompasses exhibition making, performing music and working in education.
The film shown will consist of new material created as part of his current residency at Cubitt Gallery's Studio 1 at 73 Mildmay Street, an Extra Care home run by Notting Hill Housing Group, where he is developing collaborative work with the residents.
Grace Surman - yournamelitupinneonlights
UK, 2006, 7 min.
yournamelitupinneonlights plunders children's television and picture books, circus animal tamers, Dada and Surrealism, silent films and amateur pantomimes. Surman's work plays with subtleties of appearance and persona. In this stop-motion animated film, she places herself in a world of make-believe, leaving parts of the set unfinished and holding on to a childhood excitement of dressing-up.
Surman is interested in how we live and experience the world through constraints and conditions around us – be it work, gender or age. The drive of the work is to explore and excavate these conditions, drawing on theatrical devices, process-based performance actions, feminist theories and contemporary culture.
Past work has been commissioned by and seen at ICA London, the National Review of Live Art, Kiasma Museum of Contemporary Art, Helsinki, Chelsea Theatre, and Dance Base Edinburgh. Surman lectured at the Royal Scottish Conservatoire until 2007 and was Associate Curator for performance at CCA Glasgow.
This event is part of our Daphne Wright season
Filed under: Screening, DaphneWright
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This event is part of Daphne Wright
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High ideals, upper levels of consciousness. Usually things are stored in the attic like childhood and elders belongings and seasonal decorations. For this reason the attic can also represent forgotten treasures and the examples of squirrel who might make use of your attic too such as storaging for winter. Some other creatures who share the attic are birds like sparrows, rats and bats.
The bathroom most commonly is a place of emotional release. There's the bathtub, shower, toilet and sink, all the representatives of water, cleaning, cleansing, releasing, shedding old for new as well as the sense of privacy. The bathroom can also be communing in a sense, as the symbolism of baptism, cleanliness next to godliness and serious contemplation while on the toilet. It's common for people to escape into the bathroom to cry.
If the pipes are clogged this denotes emotional suppressions while an over flowing toilet or sink denotes the need or desire to fully express. Things are going left unsaid.
Privacy, sleep, intimacy and sexuality. The bedroom best denotes the most private aspects of yourself. The bed represents comfort and security. Where we sleep is the room we rejuvenate, nuture and reconnect with the endless source.
The root cellar, like the attic going into higher levels of consciousness with air, the cellar climbs down into subconscious in connection with the earth. As the attic is hot and airy the cellar is cool, damp and dark. Originally it was used since ancient time as the refrigerator, beginning as a simple hole in the ground, usually inside the home or cave with a slab of rock drawn over it as a means to store such as roots, herbs, foods and more classically, wines. The cellar can also represent the underworld and underworld tunneling such as the railroad system of the escaped slave, catacombs and river ways. It represents deepest subconscious and intuition where shadow self can also be present to represent suppressions. Going down to the basement level is classically used in visualization hypnoses as a means to reach subconscious without inhibition.
Any bones in your closet? Cleaning the closet. Coming out of the closet. Creepy closet. Closet of the self. Hidden things tucked away. In movies and childhood stories the closet, among windows and mirrors, is often a subject of fears of the supernatural.
Doors symbolize a gateway to another side. Inside, outside, beyond side. The door is often referred to in symbolism of unlocking doors in self discovery, new opportunities, to let out the old things for renewal. They can also be a subject of anxiety towards the unknown and used as a means of understanding open portals.
The kitchen is the center piece of preparation, cooking and storing food, washing the dishes. It has come to replace the uses in ancient time for gathering around the center fire as the means to cook, prepare and nourishment within the family bonds. Often it's the center of the family gathering to bond while preparing the meals or also a favorite place to hold the worst arguments where venting can be more easily grounded, cleansed and cleansing. The kitchen is usually also a center of settling ones self in, making themselves at home and finding themselves a place in the family unit or asserting their position by cleaning and cooking, or even occasionally the mothers 'throwing of the pots'. The kitchen best represents in the spiritual sense of bonds, nourishment and perception. Smell, taste, touch and sound.
The living room is sometimes combined as the dining room. The dining room also combines to the kitchen and is best representative as a center point of eating at the table or watching TV It's considered the main 'dwell' or den of the family unit and entertaining guests. It has much the same orientation as the kitchen only is a focal point of resting back for enjoyment and harmony. The cord phone is most likely in this area and arguments are less likely or will wander in transition between kitchen and living room, where living room is more of a place for calm and council.
The reflection of self, consciousness, knowledge and truths. Seeing into the mirror is abstract, noticing what you consider flaws and dislikes. Accept yourself, love and respect yourself. Don't judge so harshly. You've got enough opposition in the world without bringing yourself down.
Rising more popularly as the computer room as well. The study is a private area of meditations and creativity, the studio and the library.
The window of opportunity. Seeing. Perception. Insight, out look, levels of consciousness. A gateway.


A New York Times best seller and librarian favorite that will appeal to shojo and non-shojo fans alike!
The Media Betterment Committee has censored an exhibition at the Museum of Modern Art in Iku's hometown! Iku's top-ranked Library Forces team must train the local troops to defend the freedom of speech using any means necessary...but the librarians there resent her position and aren't shy about making their feelings known. Soon Iku's parents catch wind of her secret life as a member of the Library Forces, with disastrous results!
Releases R to L (Japanese Style) for teen plus audiences.


AG2000 is the brand of a curious and creative designer based in Cardiff, South Wales. I run a design collective of designers and we use our experience to design clean and responsive Websites. AG2000 welcome new challenges with a desire to learn and a passion in creating compelling designs. I love designing, from logos to websites and I take pride in my work to ensure that everything I create is perfect for my clients.
My logo design service will produce a professional logo for all your branding needs.
I create from fast one page HTML5 Websites to WordPress driven CMS with full admin control ready to use.
I am able to provide Social Media Marketing Services and the Marketing of Content through Social Media.
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Q: Apache mod_rewrite Restful api I'm stuck on a problem with correct .htaccess in my restful webapp. My REST api code shall be accessible via the URL-pattern */api/** which should be redirected to index.php in the api folder.
All other URLs (except static files) shall be redirect to index.html in the root folder.
I have following folder structure:

- api
-- application/...
-- vendor/...
-- index.php
- public
-- css/...
-- js/...
- index.html
- .htaccess

And this is my .htaccess content:
Options +FollowSymLinks
RewriteEngine on

# redirect all api calls to /api/index.php
RewriteCond "%{REQUEST_URI}" "^/api"
RewriteRule "^/api/(.+)$" "/api/index.php$" [QSA,L]

# If the request is a file, folder or symlink that exists, serve it up
RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^(.+)$ - [S=1]

# otherwise, serve your index.html app
RewriteRule ^(.+)$ /index.html [L]

I have tried to add another .htaccess to the api folder, to redirect the URLs with /api/* but without any success. So I tried to redirect it with a rule in the .htaccess above.
I think the lower to rules might be correct. Because the redirecting is working as expected. But the /api/ rule does not work. It seems that the requests also redirected to the index.html
What am I missing?

A: Minor tweaks of your regex pattern is what you need:
DirectoryIndex index.php index.html
Options +FollowSymLinks
RewriteEngine on

# redirect all api calls to /api/index.php
RewriteRule ^api/((?!index\.php$).+)$ api/index.php [L,NC]

# If the request is a file, folder or symlink that exists, serve it up
RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]

# otherwise, serve your index.html app
RewriteRule ^(.+)$ index.html [L]

A: Try the following set of rules:
Options +FollowSymLinks
RewriteEngine On

RewriteCond %{REQUEST_URI} !^/api/index\.php$ [NC]
RewriteCond %{REQUEST_URI} ^/api [NC]
RewriteRule ^api/.* /api/index.php$ [QSA,L]

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-l # to check for symbolic links
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule .* /index.html [L]

RewriteRule . - [L]

redpajama_set_name: RedPajamaStackExchange


text:
Broke In Philly
Pa. shortchanged its poorest school districts in giving out federal CARES Act money, report says
by Maddie Hanna, Updated: December 7, 2020
Andrea Evans (left), a first-grade teacher at Mitchell Elementary in Philadelphia, gives a no-contact hug while talking with parent Danielle Johnson, in an April Inquirer file photo. The Philadelphia School District is among those that were shortchanged by Pennsylvania's distribution of federal funding, according to a new report.
JESSICA GRIFFIN / Staff Photographer
Pennsylvania shortchanged its poorest school districts in the distribution of federal relief funding, allocating the most recent round of pandemic aid without accounting for poverty or other needs, according to a new report.
Despite having a formula that directs state aid to districts with greater shares of students in poverty, among other factors, Pennsylvania didn't do so for $175 million in CARES Act funding. Instead, it gave every district the same base amount of aid, then additional money based on enrollment — a process that resulted in the poorest districts receiving less funding than their more affluent counterparts, according to the Keystone Research Center.
The report, released Monday by the left-leaning Harrisburg-based think tank, said the poorest quartile of school districts — based on enrollment — received $36 million of the $175 million, less than each of the three other quartiles.
"Given the nation's heightened awareness in the year 2020 of inequality, especially racial injustice, these are stunning findings," the report said. Had Pennsylvania followed its formula for state education funding increases, the poorest quartile of districts would have received $90 million of the $175 million in aid, according to the analysis. Districts with the highest shares of Black and Latino students also would have received more.
If Pennsylvania receives more federal aid for schools, "we cannot make this mistake again," Stephen Herzenberg, executive director of the research center, said during a news conference Monday.
Prior to the $175 million, Pennsylvania school districts received $400 million in CARES Act funding. Federal rules dictated that the money was awarded based on Title 1, a federal program targeting higher-poverty districts.
Inquirer Morning Newsletter
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The method Pennsylvania used to award the later $175 million was passed by state lawmakers in June as part of a package of revisions to Pennsylvania's school code. The changes were approved by Gov. Tom Wolf.
Lyndsay Kensinger, a spokesperson for Wolf, said the Democratic governor didn't agree with the allocation but approved it "in the spirit of compromise" with the Republican-controlled legislature.
"If we had full control of the remaining CARES Act dollars, we would have allocated it similarly to the first round using Title I, or a similar approach that included an equity lens," Kensinger said.
Neal Lesher, a spokesperson for House Appropriations Committee Chair Stan Saylor (R., York), said lawmakers set a baseline of $120,000 per district "to protect smaller school districts, ensuring that they received a sufficient amount to assist with COVID-19 health and safety mitigation." The rest of the money was based on enrollment, "as the need for cleaning, [personal protective equipment], technology, and other expenses logically grows with the size of the district."
Pennsylvania has recognized that poorer districts need more state aid than wealthier ones. The state enacted a formula in 2016 that distributes school funding based on enrollment, the needs of students, and district wealth.
But the formula only applied to new education spending approved by lawmakers — meaning it isn't used to distribute the vast majority of state aid to districts. Advocates and lawmakers are still locked in a political battle over how the state pays for education, with a court case that alleges deep inequities in the funding system moving toward trial.
» READ MORE: Pennsylvania schools need an additional $4.6 billion to close education gaps, new analysis finds
Stephen Rodriguez, superintendent of the Pottstown School District in Montgomery County, said the way Pennsylvania distributed federal aid was another example of the state's unwillingness to adequately fund poorer districts.
"We've known this has been a problem, yet we've made very little headway into it," Rodriguez said. He acknowledged that the earlier round of federal aid went primarily to higher-poverty districts, but he said those like his were struggling — noting that many urban districts still have families that lack internet access.
» READ MORE: 3 people, 200 square feet: Managing homelessness, remote school, and life in a pandemic
While Pottstown has used federal relief money to buy technology — "thousands and thousands of devices" — and Zoom licenses for teachers, the district hasn't been able to respond as aggressively to the pandemic as some of its peers, Rodriguez said. It hasn't been able to hire extra staff, as Rodriguez said some districts — anticipating shortages brought on by the virus — have done. It hasn't been able to buy more PPE.
"I have 500 masks," said Rodriguez, whose district enrolls 3,400. "We could do with extra of everything."
The Philadelphia Inquirer is one of more than 20 news organizations producing Broke in Philly, a collaborative reporting project on solutions to poverty and the city's push toward economic justice. See all of our reporting at brokeinphilly.org.
Posted: December 7, 2020 - 5:44 PM
Maddie Hanna | @maddiehanna | mhanna@inquirer.com
Joe Biden revokes Donald Trump's '1776 Commission' report promoting 'patriotic education'
Collin Binkley, Associated Press
After inauguration, President Biden extended freeze on student loan payments until Sept. 30
Erin Arvedlund
Camden may have to close some schools, superintendent says
Melanie Burney
Mark Gleason, head of the influential Philadelphia School Partnership, is leaving
Kristen A. Graham
Testing, testing, and more testing on college campuses this spring as coronavirus concerns remain
Susan Snyder
Ted Kirsch, longtime Philadelphia teachers' union chief, dies at 81


There are a lot of reasons to rue the fact that Donald Trump will be our next president. But if you accept the reality of man-made climate change — and are fond of human civilization and/or coral reefs — the president-elect's indifference to the Earth's warming should probably top your list.
Trump's election jeopardizes the Obama administration's entire climate agenda: the Paris climate accords, the Clean Power Plan, new regulations on energy efficiency and coal pollution and various subsidies for green technology. At a time when the North Pole is experiencing record temperatures and sea ice is thinning — and when developed nations need to be slashing emissions by roughly 10 percent a year to keep from eclipsing the two-degree Celsius threshold that triggers self-reinforcing feedback loops of catastrophic warming — the most powerful nation on Earth has elected a man who suspects that climate change is a Chinese hoax.
A source close to Ivanka Trump has told Politico that the soon-to-be first daughter plans to use her new mantle to "speak out" about climate change.
1. Help make a climate-change denier the leader of the free world.
3. Profit (via advocacy that broadens the appeal of her lifestyle brand).
But okay. Bracketing Ivanka's motives and/or strategic reasoning, her opposition to destroying the planet could be of some use. After all, she's probably the most powerful Democrat in the United States right now. If she can convince her father that backing out of the Paris climate treaty is a bad idea — or that he could maximize the number of buildings with his name on them by rolling out Trump-branded solar panels — she could do a lot of good.
But that would require less speaking out, and more speaking up in the company of the president-elect. Which is to say: The fate of humanity may rest on whether Ivanka Trump sees climate change as a catastrophic threat or mere branding opportunity.


Heating, bed linen and towels included. Cot and highchair available. Shared utility room with washer, dryer and freezer. Wifi internet available. Lockable store for bike or a motorbike. Enclosed garden with BBQ and furniture. Hot tub for 4 (private). Parking for up to 1 car.Rose Cottage is a delightful cosy, comfortable cottage, ideally positioned in the picturesque village of Thorpe Bassett near Malton. It is a perfect base for exploring the East Coast, York and the North Yorkshire Moors as it is centrally located and within easy reach of all these areas. The cottage has been tastefully redecorated in soft grey tones giving it a modern feel. The area is a haven for keen ramblers and cyclists and also dog lovers as it is surrounded in glorious open countryside with numerous walks and cycle tracks right outside your door.
Lovely cottage, fully equipped, very comfortable indeed! The hot tub was heavenly and we all enjoyed having this luxury on holiday! Great hosts, some great beaches and towns to explore! Would definitely recommend!
We had a lovely time, despite the poor weather. It was great to come in to a cosy homely cottage!
Response on behalf of the owner; It was lovely to see you again - We're sorry the weather wasn't at its' best but we're pleased you enjoyed your break. Thanks for your lovely comments.
Spent a lovely week at Rose Cottage, cottage itself very comfortable with views overlooking the fields. There is a grass area for exercising the Dog's which was great but not fully enclosed, however there's a nice circular walk that starts just outside the drive gates with a number of bins on route. We were quite central to most of the places of interest we wanted to visit. Our hosts were very approachable which made our stay more enjoyable. Thank you.
Response on behalf of the owner; Many thanks for your lovely comments. We're creating a small enclosed area of private garden to ensure pets are kept safe, and our visitors will still have access to the paddock so hopefully the best of both worlds.
We had a lovey holiday staying at Rose cottage. It wa comfortable, well equipped and the owners were so kind, thoughtful and welcoming. Definitely be back!
Response on behalf of the owner; We appreciate you taking the time to provide feedback - we're happy that you're happy. Your comments are valued.


text:
\section{Introduction}\label{sec:intro}

Clusters of galaxies are the largest self-gravitating objects in the
Universe.  Their ultimate origins must lie in some process of quantum
fluctuations in an expanding universe
\citep{1939Phy.....6..899S,1967RvMP...39..862H,2015PhRvD..91f3505F},
but the earliest observable precursors of galaxy clusters are
fluctuations in the cosmic microwave background.  CMB fluctuations on
the scale of individual clusters would be at $l\sim10^4$, far in the
diffusion-damping tail \citep{1968ApJ...151..459S} and so far barely
accessible observationally \citep{2009ApJ...694.1200R}, but their
subsequent growth through linear gravitational instability is
straightforward.

The early observable proto-clusters
\citep[e.g,][]{2014ApJ...792...15T} are, however, far beyond the baby
fluctuations of the linear regime of gravitational instability --- in
the well-known toy model of spherical collapse, the dynamical outer
boundary of a cluster is at an overdensity of $\simeq 200$ times the
critical density of the Universe.
In this regime some analytical methods based on generalising spherical
collapse are available
\citep{1974ApJ...187..425P,1991ApJ...379..440B,2000MNRAS.318..203S}
but, for the most part, theoretical study depends on numerical
simulations.

With the recent developments in computational resources, it is now possible
to simulate dark matter and gas in cosmological volumes with good
resolution.  In such simulations, it is possible to track the evolution
and mergers of small systems to form large collapsed clusters of
galaxies.  The agreement between simulations and observations have
been improving for various macroscopic properties of galaxies, such as
intergalactic gas, bulge sizes etc.
\citep{2011ApJ...740..102K,2012MNRAS.426.2046A,2012arXiv1206.2838A,
  2014arXiv1407.2600S,2011MNRAS.410.1391A,2013MNRAS.436.3031V,
  2014Natur.509..177V,2014MNRAS.437.1750M,2015MNRAS.446..521S}.  To
study individual objects in more detail, hydrodynamical zoom-in
simulations can be used
\citep{2015MNRAS.446.1939F,2015MNRAS.446.1957F}
in which individual objects are re-simulated at higher resolution
using initial conditions derived from the larger-volume simulation.

A more ambitious comparison between simulations and observations
would be that in terms of the distribution of mass in the clusters.
This is non-trivial for two reasons:

\begin{itemize}
\item First, mass is not an observable; what we observe on the sky is
  light, mass can only be inferred.  Tracing the mass typically
  involves additional assumptions, such as that galaxies sit in the
  potential wells of the dark-matter, light traces mass with some
  scaling parameters, etc.
\item Second, since individual halos, galaxies or clusters of
  galaxies are the outcome of gravitational collapse and various
  baryonic processes of a random field (initial density field), it is
  not possible to compare their mass distribution or clustering
  properties directly. The best one can hope for is to compare them
  statistically.
\end{itemize}

The first problem could be solved with the help of gravitational
lensing, which is sensitive only to the total mass.  Well-known examples of
light not tracing mass, revealed by lensing, are the clusters
ACO~2744 \citep{2011MNRAS.417..333M} and
recently ACO~3827 from \cite{2015MNRAS.449.3393M} \citep[see
  also][]{2011MNRAS.415..448W, 2014MNRAS.439.2651M}.  But simulations of
cluster formation cannot be fitted so as to reproduce detailed
properties of individual clusters.

The second problem could be handled by identifying robust statistical
properties of the clusters.  The simplest quantity is the radial
density profiles.  \cite{2013ApJ...765...24N,2013ApJ...765...25N}
studied the average density profiles of the lensing clusters and
compared them to the simulated clusters. However, this quantity can
only be measured if the cluster is virialised, definitely not for an
ongoing merger.  High-mass clusters in simulations do not usually
virialise until $z\sim0.3$; before that they often show elongation,
multiple cores and many substructures indicating a recent merger, as
do observed lensing clusters.

Another very popular statistic is the mass function; counting the
number of subhalos as a function of their masses
\citep{nat04,nat07,2015ApJ...800...18A}.  However, measuring or even
identifying substructures in lensing clusters has so far been
possible only under the assumption that light traces mass. Without
this assumption, the mass function does not seem a viable statistic
with lensing, especially since lensing gives information about the
sky-projected mass and projection may wash out substructures.

In this work, we propose a different strategy, which is to use a
two-dimensional power spectrum as a basis for comparing lensing
clusters with simulations.  In section \ref{sec:pk}, we define such a
power spectrum, which is normalised differently from the usual
cosmological power spectrum, and has dimensions of mass-squared.  In
section \ref{sec:grale}, we briefly describe GRALE, a
free-form lens-reconstruction technique and code.  In
section~\ref{sec:hff} we apply GRALE to reconstruct the six clusters
of the Hubble Frontier Field from strong-lensing data, and calculate
their power spectra.  Then in section~\ref{sec:comparison} we compare
the clusters with each other and with $\Lambda$CDM simulations, both
dark-matter only and hydrodynamical.  Finally,
section~\ref{sec:discussion} has general discussion and suggestions
for future work.

\section{substructure power spectrum}\label{sec:pk}

Since every cluster is different, comparison of mass maps of observed and simulated clusters is necessarily statistical.  Properties like number of galaxies, 1D density profiles,
concentration, mass function of the structures/substructures, temperature profiles etc.
are useful. However, none of these quantifies the clustering properties of the halo/cluster,
which contains important information about its merging history and evolution.
So it is interesting to study statistically the cluster mass distribution.
The simplest statistic is a two-point function.
Cosmologically, a two-point function gives an excess probability that a local density peak
exists close to another peak, as a function of the separation between the two. It can be well studied
in the Fourier space as the power spectrum. Generally, a power spectrum
$P(k)$ of a 3 dimensional matter density field is defined as:
\begin{equation}
    P(k) = \langle|\tilde{\delta}(k)|^2\rangle
    \label{eqn:pkreal}
\end{equation}
where, $\tilde{\delta}(k)$ is the Fourier transform of the over-density at position corresponding
to the wave-vector $k$.

In this work, we measure the 2D
power spectrum from the projected mass distribution of the halos:
\begin{equation}
    P_{\rm M}(k) = \langle|\tilde{M}_{2D}(k)|^2\rangle
    \label{eqn:pkour}
\end{equation}
where, $\tilde{M}_{2D}(k)$ is the Fourier transform of the 2D projected mass element at position
corresponding to the wave-vector $k$.
\begin{equation}
\tilde M(\vec{k}) = \int \Sigma(\vec{x}) e^{i\vec{k}\cdot\vec{x}} d^2\vec{x}
\end{equation}
This form also gives a natural normalisation of the function
to be the square of the total mass of the halo.

This is not the only way to describe the statistical properties of a density peak, For example,
\cite{2014arXiv1403.2720H}, using the halo model approach, define
\begin{equation}
    P_{\rm 2D}(k) = \int \dfrac{dn}{dM} |\tilde{\kappa}(k)|^2 dM,
\end{equation}
where $P_{\rm 2D}(k)$ is the so-called one-halo term in two dimensions,
$\dfrac{dn}{dM}$ is the differential mass function (number density of halos per unit mass) and
$\tilde{\kappa}(k)$ is the Fourier transform of the convergence (the normalised surface mass density).
The framework is based on the assumptions of virialised halos, and a functional
form for its mass function and radial density profile of each halo. The total contribution to the
power spectrum comes by adding the correlation between different halos (the two-halo term) and
the correlation between matter within the same halo (the one-halo term). Within a halo, there are also
many substructures. If one wants to study the clustering properties of matter within a gravitationally
bound system like a galaxy cluster (or a merging system of galaxies), the two-halo term can be
neglected as all the structures are moving within the gravitational potential of the host and are
indifferent to each other's gravity. However, the one-halo term still exists, and at large scales it
contributes to the Poisson distribution of the substructures which drops at the size of the largest
substructure.
However, this can only apply if the cluster (or the halo) is virialised so that a smooth density
profile can be subtracted in order to see the correlation between the residual field. Now, this is
not a good assumption overall, especially during merging. As most of the massive galaxy
cluster lenses at redshift $>0.3-0.4$ are not virialised systems, this form of the power spectrum
is not intuitive. Therefore, for a general system, including ongoing mergers, recent mergers
and virialised halos, the correlation between the distribution of matter inside the halos
must be studied without such assumptions.

\begin{figure*}
	\centering
	\includegraphics[width=0.32\textwidth]{figures/sim_grid1.eps}
	\includegraphics[width=0.32\textwidth]{figures/sim_grid2.eps}
	\includegraphics[width=0.32\textwidth]{figures/sim_grid3.eps}\\
	\includegraphics[width=0.48\textwidth]{figures/pk_simgrid_abs.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_simgrid.eps}
	\caption{The first three plots (in the top row: Grid1, Grid2, Grid3) are
	the three density map realizations generated
	from the same power spectrum with $k^{-3}$ towards large $k$. The bottom-left panel shows the actual power spectra of each of the grids along with
	the true power spectrum with slope = -3.
	The bottom-right panel shows the
	comparison of the recovered power spectrum from each density grid to the input power.  These maps were only produced to test the numerical computation of the power spectrum, and have no central cluster. While it is possible to generate random fields constrained to have certain features \citep[cf.][]{1991ApJ...380L...5H} these were not needed for this simple test.}
	\label{fig:simgrid}
\end{figure*}

With our definition, if we have a field enclosing only one halo
with its substructures, and we compute $P_{\rm M}(k)$ at scales larger than the size of the halo, for
all those scales one gets the same mass and hence, the power above all those scales will be a constant,
which mimics the Poisson noise of the substructures in the halo model picture. Further this function
drops at scales smaller than the size of the halo,
which is the largest structure in the field, consistent
with the halo model intuition.
For a virialised halo, this function will be smooth and a power law for all scales smaller than
the size of the halo. However, if the halo is not spherically symmetric and in a merging stage
the fluctuations in the function resemble variation in its power at various scales. If one
identifies a large ensemble of halos (let's say in simulations) of nearly the same mass and
the same epoch and averages all the power spectra, one will get an unbiased trend of the clustering
properties of such halos statistically. However, studying individual systems is like studying
a random realisation of a halo which underlies a mean power spectrum and the recovered
power spectrum from such a halo should be statistically consistent with the mean.

To ensure this feature, we performed a test.  We generated three density fields which are the
random realisation of the same power spectrum ($\propto k^{-3}$ at small scales) as shown in figure
\ref{fig:simgrid}. The three density grids enclose structures and some substructures and look very
different morphologically, but as they are generated from the statistics, they should show
a similar power spectrum. In the bottom-right of figure \ref{fig:simgrid} we show the ratio of the
recovered power spectrum from each of the grids to the input power spectrum. The slope
of the recovered power spectrum is calculated by fitting the power law towards the larger
values of $k$, between 0.68 to 4 (in arbitrary units).
All power spectra give nearly the same slope as the input one with an error of about 10-20$\%$.
This test shows that given a density field, the correct mean statistic can be obtained within
a reasonably small error.

For a pure noise field, we expect same power at all scales. We performed this test as well (but we
don't show the result in a figure form), and verified that the power spectrum is flat.

The fluctuations in mass distribution at various scales can be directly inferred as the
presence/absence of substructures. Larger power at small scale indicates the presence of local
density peaks, however, a flat power at all scales indicates similar structures at all scales
or just the noise.  Also, a smoother distribution of the matter gives rise to smaller power whereas
sharp peaks correspond to larger power. Therefore, we expect the power at small scales to
increase as the merger progresses and reach the highest power when the system is virialised.
In other words, one should expect the power on small scales to decrease with redshift.
This form of the power spectrum can be used in order to compare halos statistically, within
simulations or observations or across the two.

\section{Lens reconstruction method}\label{sec:grale}

In GRALE \citep{2007MNRAS.380.1729L,2008MNRAS.389..415L} the mass
distribution is free-form and consists of a superposition of a large
number of adjustable components (several hundred Plummer lenses).  The
distribution of these Plummer lenses is adaptively determined by GRALE
using a multi-objective genetic algorithm, to optimise two fitness
measures.

\begin{enumerate}

\item The {\em overlap fitness\/} quantifies the fractional overlap of
  the projected images of the same source back onto the source plane.
  If all images of a source back-project to exactly the same area on
  the source plane, the source fitness for that image system is
  perfect.  More generally, the larger overlap the better the fitness.
  It is important to use the fractional overlap, as otherwise the
  fitness measure would be biased towards extreme magnifications.

\item The {\em null fitness\/} is a penalty for any spurious images
  implied by a model where none are present in the observations.
  A null space is created at the image plane, subdivided into a number of
  triangles, and the trial solution
  under study is used to project these triangles onto the source plane. Then, the
  amount of overlap between each triangle and the current estimate of the source
  shape is calculated and used to construct a null space fitness measure which
  is the penalty. The
  penalty is applied only in regions where the data make it clear that
  no images are present; extra images are allowed in regions that are
  difficult to observe because, for example, of the presence of nearby
  bright galaxies.  Among lens-modelling techniques, GRALE is unique
  in being able to exploit the {\em absence\/} of images as useful
  information.

\end{enumerate}

Further fitness measures can be defined and incorporated into GRALE,
in particular, time delays
\citep{2009MNRAS.397..341L,2015PASJ...67...21M}.  No information about
the light from the cluster is used --- mass-traces-light assumptions
are completely absent.

While the genetic algorithm optimizes the properties and placement of
the component Plummer lenses, the user still needs to specify a range
for the allowed number of components.  This is, in effect, an overall
resolution of the mass map.  To set this effective resolution, we run
the mass reconstruction process first at coarse resolution, then
finer, and then coarse again, and choose an optimal trade-off between
fitness and resolution --- see \cite{2014MNRAS.439.2651M} for details
and tests of this strategy.  Finally, the entire cycle is repeated 30
times (while using pre-HFF data) or 40 times (while using post-HFF data),
to generate an ensemble of mass reconstructions. In the remainder
of the article, we present the average mass map of 30 (or 40) mass reconstructions
for each cluster lens, unless stated otherwise. The power spectra
for each of the reconstructions were computed, and both average power spectra
as well as the power spectra of the average mass map are presented. For the true
error estimates, the former is more useful.

\section{Hubble Frontier Fields}\label{sec:hff}

Hubble Frontier Fields (HFF) survey (PI: J.Lotz, HST 13498) is a three year
Director's Discretionary Time program that devotes a total of 840 orbits to six
galaxy clusters plus the accompanying parallel fields.  Each field is observed in
three HST optical bands (ACS F435W, F606W and F814W) and four infra-red bands (WFC3-IR
F105W, F125W, F140W, and F160W).
It is the single most ambitious commitment of HST resources to the exploration of
the distant Universe through the power of gravitational lensing by massive galaxy
clusters. All six clusters are early or intermediate stage mergers at $z=0.3$--0.55,
with significant elongation and hence a non-trivial mass distribution. Each had about
10--20 multiply imaged background sources discovered with pre-HFF HST
data. Five independent teams were tasked with making mass and magnification maps for
these six clusters. In the analysis of the present paper, we use mass maps presented
by our team, made with pre-HFF lensing data on six clusters as well as two maps made
with post-HFF data, for clusters MACS0416 and Abell 2744. Table \ref{tbl:HFF} shows the necessary
information about the lensing data in each of the HFF clusters.
In the following figures, the mass maps and the corresponding power spectra are
marked as $\mathtt{v1}$ and $\mathtt{v3}$ indicating pre-HFF and post-HFF data respectively.

\begin{table*}
\centering
\begin{tabular}{ l | l | c | c | c | c  }
  \hline
  Cluster & Data & Redshift & Number of images & Number of sources & Redshift range of sources \\
  \hline
  MACS-J0416 & pre-HFF & 0.396 & 40 & 13 & 1.82-3.25 \\
  MACS-J0416 & post-HFF & 0.396 & 88 & 36 & 1.00-5.90 \\
  Abell 2744 & pre-HFF & 0.308 & 41 & 12 & 2.00-4.00 \\
  Abell 2744 & post-HFF & 0.308 & 55 & 18 & 2.00-4.00 \\
  Abell 370 & pre-HFF & 0.375 & 36 & 11 & 0.73-3.00 \\
  AS-1063 & pre-HFF & 0.348 & 37 & 13 & 1.22-6.09 \\
  MACS-1149 & pre-HFF & 0.543 & 32 & 11 & 1.23-3.80 \\
  MACS-0717 & pre-HFF & 0.545 &  23 & 7 & 1.80-2.91 \\
  \hline
\end{tabular}
\caption{Lensing data from different HFF clusters.}
\label{tbl:HFF}
\end{table*}

\subsection{MACS J0416.1-2403}\label{sec:0416}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/MACS0416-1_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_MACS0416-V1.eps}\\
	\includegraphics[width=0.48\textwidth]{figures/MACS0416-3_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_MACS0416-V3.eps}
	\caption{Left: the density map for MACS0416 cluster using pre-HFF
	data (top row) and HFF data (bottom row). The crosses mark the positions
	of the lensed images.
	Right: the highlighted (black)
	corresponding power spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.}
	\label{fig:density:0416}
\end{figure*}

MACS J0416.1-2403 (MACS0416 henceforth) is a strong gravitational lens at redshift of
nearly 0.396. It is an elongated galaxy cluster, most probably a recent merger or a pre-merger
\citep{ogr15}, and hence has a non-trivial mass distribution. It was first identified by the MAssive
Cluster Survey \citep[MACS;][]{2010MNRAS.407...83E}. Based on its double-
peaked surface brightness in the X-rays \citep{2012MNRAS.420.2120M},
its recent merger stage is confirmed. It is amongst the five high magnification
clusters in the CLASH (Cluster Lensing and Supernovae survey with Hubble) project
\citep{2012ApJS..199...25P}. Detailed mass maps were provided by
\cite{2013ApJ...762L..30Z} using CLASH data, and \cite{2015MNRAS.446.4132J}
and \cite{2015arXiv150708960S} using HFF data.

We made two reconstructions of this lens using GRALE, one with pre-HFF data (total
40 images from 13 sources), using data from \cite{2011MNRAS.417..333M}, as well as data provided by
J. Richard and D. Coe, and one with HFF data (total 88 images from 36 sources)
where we used images that were classified collectively by the HFF teams
being of GOLD and SILVER quality. Many of these images were initially identified by
\cite{2015MNRAS.446.4132J}. The two reconstructed mass models, $\mathtt{v1}$ and
$\mathtt{v3}$---with each being an average
of 30 and 40 realisations respectively---are shown in figure \ref{fig:density:0416} (left column),
each with its respective power spectrum (highlighted in the right column). Both mass models
are very similar at large scales, which is also evident from the power spectrum, and
only differ in the details at small scales. The two mass clumps and the elongation
can be identified in both models. However, the mass models with HFF data (bottom row),
shows larger power or many detailed substructures at small scales. This is
expected as HFF data has many more lensed images than pre-HFF data and hence provides additional
lensing constraints at small scales, which leads to increased power at larger $k$'s.

\subsection{Abell 2744}\label{sec:2744}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/A2744_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_A2744-V1.eps}
  \includegraphics[width=0.48\textwidth]{figures/A2744-3_SL.eps}
  \includegraphics[width=0.48\textwidth]{figures/pk_A2744-V3.eps}
	\caption{Left: the density map for the Abell 2744 cluster using
	 pre-HFF data (top row) and post-HFF data (bottom row).
   The upper left clump could well be an
	 artefact as there
	 are no images there.
	 Right: the highlighted (black) corresponding power
	 spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.}
	\label{fig:density:2744}
\end{figure*}

Abell 2744 is a massive galaxy cluster at redshift 0.308 and an active merger.
It has been studied in various wavelengths, for example, it has an extended radio halo
\citep{1999NewA....4..141G,2001A&A...369..441G}, X-ray emission
\citep{1998MNRAS.296..392A,2010MNRAS.407...83E,2004MNRAS.349..385K,2011ApJ...728...27O}
and various substructures have been identified in the optical observations
\citep{2001ApJ...548...79G,2006A&A...449..461B}.
\cite{2010MNRAS.406.1134S} show a significant offset between the dark-matter
component (from lensing) and baryonic matter (from X-rays observations).
There is also a magnified singly imaged supernova in the background,
at redshift 1.35 \citep{rod15}.
Various lensing analyses have been done
\citep{1997ApJ...479...70S,1998MNRAS.296..392A,2004ApJ...613...95C,
2011MNRAS.417..333M,2014ApJ...797...98L,2014arXiv1409.8663J}.

We present two mass models of Abell 2744 using GRALE, one with pre-HFF data
\citep{2011MNRAS.417..333M,2014MNRAS.444..268R} as well as data provided by J. Richard and D. Coe, for
 a total of 41 images from 12 background sources spread over a redshift range of 2 to 4 and
 another with post-HFF data for a total of 55 images from 18 sources. Figure
\ref{fig:density:2744} shows the reconstructed mass maps and the corresponding
power spectra. It shows two very distinct blobs and an overall
elongated structure, a morphology very likely for a major merger which is in fact confirmed
by previous studies. The post-HFF data contains improved identifications and positions
of the lensing images, and the corresponding map (bottom row of figure \ref{fig:density:2744}) shows fewer spurious structures compared to the pre-HFF map (top row of figure \ref{fig:density:2744}).

Due to very sharp mass peaks, this cluster, like MACS0416, also shows larger power at small scales.

\subsection{Abell 370}\label{sec:370}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/A370_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_A370-V1.eps}
	\caption{Left: the density map for the Abell 370 cluster using
	 pre-HFF data. Right: the highlighted (black) corresponding power
	 spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.}
	\label{fig:density:370}
\end{figure*}

Abell 370 is a strong gravitational lens at redshift 0.375 and hosts a giant
gravitational arc at redshift 0.725. Due to its large Einstein radius, it is
an ideal target to look for high redshift galaxies through its magnification, especially
in high-density regions. There are many published mass models
\citep[for example][]{1987Msngr..50....5S,1998MNRAS.294..734A,ric10}.
We used pre-HFF data from the latter work, as well as data provided by D. Coe and A. Koekemoer,
to reconstruct its mass distribution. Figure \ref{fig:density:370}
shows the resulting mass map. The mass distribution is shallow but shows many
substructures. The resulting power spectrum shows less power on small scales
as compared to other HFF clusters which is reflected in shallower peaks in
its mass distribution.

\subsection{Abell S1063}\label{sec:1063}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/AS1063_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_AS1063-V1.eps}
	\caption{Left: the density map for the AS1063 cluster using
	 pre-HFF data. Right: the highlighted (black) corresponding power
	 spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.
	Note that there are no images in the upper right corner of the map, so the massive
	clump in that region could well be an artefact.
	}
	\label{fig:density:1063}
\end{figure*}

Abell S1063 is a galaxy cluster at redshift 0.348. We used pre-HFF data identified
by \cite{2014MNRAS.444..268R}; our reconstruction used a total of 37 images from 13 background
sources.

Figure \ref{fig:density:1063} shows the reconstructed mass map along with the
corresponding power spectrum. It shows two mass clumps, which lead to
larger power at intermediate scales, but due to the shallowness of the peaks, it loses
power at small scales.

\subsection{MACS J1149.5+2223}\label{sec:1149}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/MACS1149_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_MACS1149-V1.eps}
	\caption{Left: the density map for the MACS1149 cluster using
	 pre-HFF data. Right: the highlighted (black) corresponding power
	 spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.
There are no images beyond X=25'', so the two clumps on the right
could well be artefacts.
        }
	\label{fig:density:1149}
\end{figure*}

MACS J1149+2223 (MACS1149 hereafter) is an X-ray bright cluster at redshift 0.543.
It has been studied by various authors for its rich strong lensing
\citep{2009ApJ...707L.163S,2009ApJ...703L.132Z,2011MNRAS.410.1939Z,2015ApJ...801...44Z,2014MNRAS.443..957R,2014ApJ...797...48J,2015ApJ...800L..26S}.
There is also a multiply imaged supernova
\citep{2014ATel.6729....1K,2015Sci...347.1123K} hosted by a face-on spiral galaxy
at redshift 1.49.

Figure \ref{fig:density:1149} shows the reconstructed mass model of MACS1149 using
GRALE with pre-HFF data (total 32 images from 11 background sources) from
\cite{2009ApJ...707L.163S,2009ApJ...703L.132Z}, and data provided by M. Limousin.
The mass
model favours two dominant peaks and one sub-peak, elongation and many substructures.
The peaks are shallower than those in Abell 2744, also expected as it has nearly the
same mass as Abell 2744 but higher redshift. The corresponding power spectrum is shown
in the right column of the same figure.

\subsection{MACS J0717.5+3745}\label{sec:0717}
\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/MACS0717_SL.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_MACS0717-V1.eps}
	\caption{Left: the density map for the MACS0717 cluster using
	 pre-HFF data. The upper left and bottom right clumps could
	 well be artefacts as there
	 are no images there.
	 Right: the highlighted (black) corresponding power
	 spectrum of the cluster on the left with all other
	HFF clusters' power spectra in the background.}
	\label{fig:density:0717}
\end{figure*}

MACS J0717.5+3745 (MACS0717 hereafter) is a strong gravitational lens at redshift 0.55,
classified as the most dramatic merger in X-ray/optical analysis by
\cite{2012MNRAS.420.2120M}.

We used pre-HFF data from \cite{2012A&A...544A..71L,2014MNRAS.444..268R} and \cite{med13} to reconstruct
its mass distribution using GRALE. Figure \ref{fig:density:0717} shows the resulting
mass map and the corresponding power spectrum. Due to the clear mass peaks and substructures,
the power spectrum shows increased power at intermediate scales, however, due to very shallow peaks the
power spectrum at small scales drops and is amongst the lowest of the HFF clusters.

\section{Comparing the clusters}\label{sec:comparison}

\begin{figure*}
	\centering
  \includegraphics[width=0.48\textwidth]{figures/pk_pkofavgmap.eps}
  \includegraphics[width=0.48\textwidth]{figures/pk_avgofpk.eps}
	\caption{All power spectra: clusters in thick solid lines and
	simulations in thin solid lines.
  Left: showing power spectra calculated for the average mass map of each
  cluster. The error bars are the scatter in different modes at a given $k$
  (or the sample variance).
  Right: each power spectrum is the average of 30 (40 in case of $\mathtt{v3}$) different power
  spectra calculated for each mass map in the ensemble for the respective
  cluster.
  The error bars are the standard deviation of the power spectra,
  including contributions from sample variance, as well as the scatter between different
	reconstructions of the same cluster.}
	\label{fig:pkall}
\end{figure*}

\begin{figure*}
	\centering
	\includegraphics[width=0.48\textwidth]{figures/comparePk_grale_lenstool_v3.eps}
	\includegraphics[width=0.48\textwidth]{figures/pk_simulations_relative.eps}
	\caption{Left: comparing the mean power spectrum for dark-matter only simulations (DMO),
	baryonic simulation (AGN) and different reconstructions using GRALE and LENSTOOL for MACS0416-v3
	(using HFF data only). The vertical lines show the 10 and 1 arc second scales at the cluster's redshift
	$z=0.396$. Right: the relative difference between the
	mean power spectra of DMO and AGN simulations.}
	\label{fig:pk:compare}
\end{figure*}

\begin{figure*}
	\centering
	\includegraphics[width=0.8\textwidth]{figures/pkavgClustersSims.eps}
	\caption{Comparing average power spectrum of HFF clusters to
				that of the simulated clusters.}
	\label{fig:pk:sim}
\end{figure*}

\subsection{Comparing HFF clusters}

We can now compare the clustering properties of HFF clusters
using the lensing power spectrum $P_{\rm M}(k)$ .
The reconstructed mass distributions of the HFF clusters are morphologically different but
show similar statistical structures which is very much evident from comparing the respective
power spectra. Figure \ref{fig:pkall} shows all the power spectra for HFF clusters in
thick lines along with their sample variance, which represents scatter across
all available modes for a given $k$.

Let us first consider two reconstructions for MACS0416, using pre-HFF and HFF data. Both
mass maps are very similar at large scales but differ in detail at small scales. The
same effect can be noticed in the power spectrum (see figure \ref{fig:pkall}): up to
$k \sim 3 \times 10^{-5} \rm{pc}^{-1}$ both look nearly the same, but at smaller scales
the mass map reconstructed with pre-HFF data starts to lose power. This is a
consequence of the fact that HFF data has over two times as many lensed images as pre-HFF
data (see table \ref{tbl:HFF}), allowing for higher resolution in the reconstructed mass maps.
This leads to a higher power at small scales, where the difference in the two power spectra
is almost an order of magnitude. A similar trend can be seen in the two versions
of Abell 2744.

Power spectra for Abell 370 and MACS1149 look very similar to each other. If we look at the corresponding mass maps, both show two dominant peaks with similar width, shallow as compared to the surroundings with similar smoothing.
Similar arguments can be made for Abell 2744 and MACS0416-II clusters.
The clusters show similar power at small scales which is expected from the very steep mass peaks in the two clusters.

It is important to note that the smallest scale (largest $k$) to be trusted depends on the density
of images. For example, MACS0416-v3 has 4 times more images than MACS0717, (assuming
roughly the same area for both in terms of arcsec$^2$), so the typical linear image
spacing is 2 times larger in MACS0717, leading to poorer mass
resolution. And, in fact,
looking at figure \ref{fig:pkall}, the $k$ value where $P_{\rm M}(k)$  of MACS0717 begins to drop
($k\sim 2\times 10^{-5} {\rm pc}^{-1}$) is about a
factor of $\sim 2$ smaller compared to that of MACS0416
($k\sim 4\times 10^{-5} {\rm pc}^{-1}$).

There is also a tendency for low redshift clusters to have higher power at
small scales. Thus, Abell 2744 reconstructed with 41 images has larger power
than MACS0416-v1 (40 images) at small scales.
Similarly, MACS1149 has less power at small scales than A370 and AS1063, again with similar numbers of lensed images.
This is also intuitive as low redshift clusters have had more time to
build small-scale substructures.
Therefore, the power at small scales may be indicative of the age of the cluster.

\subsection{$\Lambda$CDM simulation clusters}

We used 22 clusters of galaxies from dark-matter only (DMO) simulations and
an additional 22 from hydrodynamical simulations which include AGN feedback,
in the mass range  1--3$\times 10^{14} M_{\odot}$ from \cite{2014MNRAS.440.2290M}
using RAMSES \citep{2002A&A...385..337T}.
The mass range is chosen to be comparable to that of the HFF clusters but the
simulated clusters are all at redshift zero. We then projected
them along the three axes, for a total of 66 projected clusters in each case.
Projection does introduce some correlation in the sample, but we assume
such correlations in the sample, but we neglect this effect.
In contrast to HFF clusters, the simulation clusters are virialised but a few show more than one core.
The measured power spectra are shown as thin lines in figure \ref{fig:pkall}.

We also measured the mean power spectrum in each case, DMO and AGN, which is shown in black
in the left panel of figure \ref{fig:pk:compare}.
The error bars show the standard deviation of $P_{\rm M}(k)$, including contributions from
scatter in different modes at a given $k$ as well as the scatter between different clusters.
In the right panel of figure \ref{fig:pk:compare}, we show
the relative difference between the mean power in DMO and AGN simulated clusters.
Comparing the mean power spectra of DMO and AGN, the latter shows a deficit in power
at large scales and a boost at smallest scales. The deficit is nearly $10\%$.
The AGN clusters have the influence of an AGN at the centre that drives the gas
outside the cluster with its feedback process. Losing this mass results in the
deficit of power at those scales. However, these AGN clusters contain a central
stellar component in the form of the brightest cluster galaxy (BCG),
which increases the mass at the very centre of the
cluster resulting in a boost in the power at smallest scales.
The trend is systematically consistent with previous findings.

\subsection{Comparison between HFF clusters and $\Lambda$CDM simulation clusters}

In figure \ref{fig:pkall}, we show $P_{\rm M}(k)$ for all six HFF clusters as
well as both DMO and AGN for all the simulated clusters.
The lensing clusters systematically show less power at small scales
compared to the simulated ones.
We discuss the possible reasons for this in
section \ref{sec:discussion}.

\subsection{Comparison with LTM models}

In the left panel of figure \ref{fig:pk:compare}, we compare the power spectrum measured
from the mass maps reconstructed using GRALE to that made using other methods:
Sharon et al and the CATS group.\footnote{\tt https://archive.stsci.edu/prepds/frontier/lensmodels/}
Both use the LTM method LENSTOOL of \cite{2007NJPh....9..447J} as the reconstruction technique.
Both of these reconstructions show much larger
power at small scales compared to the GRALE reconstruction. This is the result of the fact that LENSTOOL uses
information from the individual cluster galaxies of the lens, and
hence has much steeper density gradients at small scales which results in
larger power. This effect is also seen in the galaxy-mass correlation function of
MACS0416 which shows a sharp peak at zero separation \citep{2015arXiv150708960S}.
The power spectrum of parametrically reconstructed clusters is a mixture
of priors and lensing information, and when the number of images is small, priors
are the dominant contribution.
In contrast, free-form methods like GRALE base the mass
distribution on the lensed images alone, without relying on visible galaxies.

\section{Conclusions and Discussions}\label{sec:discussion}

In this article, we present free-form mass models of six Hubble Frontier Field
clusters using strong gravitational lensing pre-HFF data.
We also studied two of the six clusters, MACS0416 and Abell 2744, using both pre-HFF
and HFF data (with many more lensed images).
For each cluster, a total of 30 mass maps (40 for $\mathtt{v3}$ versions) are made
using a non-parametric lens inversion technique called GRALE, and the
average mass map is presented. All the mass
maps show elongation, multiple cores and many substructures in the mass
distribution implying a recent major merger. The lensing data from
recent HST-HFF observations is rich in lensing images allowing a very
precise identification of substructures to be done with greater
confidence. These mass maps can be used to study various aspects
of the structure formation and merging stages of large collapsed clusters
of galaxies.

We measured the power spectra of these sky-projected mass maps (30 for each cluster),
and presented both average power spectra, as well as the power spectra of the
average mass map for each cluster (figure \ref{fig:pkall}). The error
estimates of the power spectra are either given as the scatter in different modes
at a given $k$, also known as sample variance, or a combination of the sample
variance and the standard deviation of the power spectra for the same cluster.
Power spectra give a statistical description of the clustering properties of the
mass distribution and encode information about the abundance of
substructures  and their contrast with the background.
There are tentative indications that low redshift clusters
have systematically higher power at small scales as compared
to high redshift clusters, presumably because low redshift
clusters are closer to their virial equilibrium than high redshift clusters.
We argue---and illustrate using pre-HFF and HFF maps of MACS0416---that using a
larger number of lensed images in a cluster leads to a better-constrained mass
distribution, and that the power spectrum
can be recovered up to much smaller scales putting stronger constraints
on our understanding of the substructures. On the other hand, parametric
methods that explicitly include cluster galaxies in the models have much larger power on small scales
even with fewer lensed images indicating that the mass maps are dominated
by the priors, especially at small scales.

We compared the power spectra of the HFF clusters with those from $\Lambda$CDM
dark-matter only and hydrodynamical simulations at redshift zero.
Figure \ref{fig:pk:sim} summarizes our comparison between HFF clusters and
$\Lambda$CDM simulation clusters. We average the power spectra of the six HFF
clusters and compare them with the average power spectra of the simulated
clusters. The average power of the clusters is systematically steeper than
that of the simulated clusters and hence have less power at small
scales. This may be due to one or more of the following reasons:

\begin{itemize}
    \item The redshift of the HFF clusters are higher than the simulated clusters.
    We are comparing non-virialised HFF clusters with the virialised
    halos of the simulations. At later times, the mass distribution
    becomes more and more clumpy and the substructures pull
    more mass from the background,
    which results in a higher power at small scales. Therefore, it
    is possible that the lensing clusters in the local Universe may
    show similar power as the simulated clusters
    at redshift zero. Conversely, this can be checked by comparing
    the power spectrum of HFF clusters with that of simulated clusters of similar masses
    in the redshift range 0.3--0.5.

    Another effect of the redshift difference is that the angular resolution is lower for the higher redshift clusters. However, this effect is roughly 20$\%$, too small to account for the observed differences in the power spectrum.

    \item A second possible reason relates to the data and method we are
    using to reconstruct the clusters. A larger number of lensed images gives
    additional constraints on the mass distribution, and this increased resolution leads to a boost
    in the power spectrum. This can be seen in figure \ref{fig:pkall}  where we show the power
    spectrum of MACS0416 using both pre-HFF and HFF data: HFF data shows
    larger power at small scales as compared to pre-HFF data.

    Figure \ref{fig:pk:compare} shows that the power at small scales
    also depends on the assumption of the reconstruction method.
    It is possible that GRALE does not have enough resolution  and hence loses
    power at smallest scales. On the other hand, LENSTOOL maps seem to have
    much more power than expected at those scales and are possibly dominated by priors.

    \item Finally there is the possibility that the simulations are lacking
    some physics that needs to be taken into account in order to simulate
    realistic halos.
\end{itemize}

The second item above can be tested through a more extended pipeline, in which clusters are generated from
state-of-the-art simulations, lensing data are generated from them, and then analysed by independent groups
using different techniques.  Such tests are currently in progress.
It will be interesting to measure the power
spectrum of the original mass distribution and the reconstructed one
using different lens inversion methods.
The current analysis expects that the power spectrum based on GRALE maps
will match the true power spectrum at large scales and ultimately
lose power depending on the density of lensed images, whereas
LTM-based methods may continue having larger power even when the true power
drops. We leave this analysis for future work.

Independent of lensing, it will also be interesting to study the evolution of the power spectrum
as a probe of sub-structures and the merging history of large collapsed objects in simulations.
For example, a cosmological simulation can be set up with a volume large enough to produce
20--50 clusters of galaxies,  in a narrow mass range.  The power spectra can be calculated
for all the clusters in the mass range at different redshifts, and the evolution of the average
power spectrum can be studied. This will give us insight into the evolution of clustering
properties in a merging system. We leave this analysis to future work as well.

\section{Acknowledgement}

We would like to thank Davide Martizzi for providing the projected mass maps of the simulated clusters.
IM would also like to thank Aurel Schneider for
useful discussions about the topic.

LLRW is grateful to the Minnesota Supercomputing Institute for their computational
resources and support.

We are grateful to the numbers of the HFF Map Maker teams, and especially to Dan
Coe, Johan Richard and Anton Koekemoer, who made their image identifications and
redshifts available to us, in some cases prior to publications for the v1 maps. Some
redshifts used were spectroscopic, some photometric and some were predicted by the
lens models. The relevant papers from which image information was taken are cited in
the text.
For v3 models, we are grateful to all those who contributed to the data used here:
members of the CATS team (including Mathilde Jauzac, Johan Richard, Jean-Paul
Kneib), GLAFIC team, Benjamin Clement, Adi Zitrin, Irene Sendra, Claudio Grillo,
Daniel Lam, Jose Diego, Xin Wang, Marusa Bradac, Austin Hoag, Traci Johnson, Brian
Siana, Anahita Alavi, Gabe Brammer, Tomasso Treu, Ryota Kawamata, and especially Dan
Coe and Keren Sharon.

IM is supported by Fermi Research Alliance, LLC under Contract No. De-AC02-07CH11359 with the United States Department of Energy.

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