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Perfect Daily Grind > Roastery Management > How Have Roasters Adapted During Covid-19?
How Have Roasters Adapted During Covid-19?
The full long-term effects of Covid-19 on the coffee industry will not be known for some time. However, as time goes on, we see more and more businesses in all sectors close their doors either temporarily or permanently.
Much of the focus around Covid-19 in the coffee sector has been on how cafés and baristas have coped. However, with the decrease in demand from many of their regular customers, roasters have also faced difficulties throughout 2020. Café closures mean less business for roasters, in turn affecting cashflow along the rest of the supply chain.
To look at how roasters have adapted and diversified to survive through the pandemic, we spoke to Jolene Zehnder and Michelle Dunaway from Mercon Specialty, a member of the Mercon Coffee Group, as well as Jill Killen from Cloud City Coffee.
Lee este artículo en español ¿Cómo se Han Adaptado Los Tostadores Durante el Covid-19?
The Issues And Impact
When buying coffee, roasters want their green beans to be as fresh as possible. This allows them to offer customers the full range of flavours that the beans hold.
Roasters will look at their sales to determine where and when demand peaks, to make sure they don't overbuy (leaving them with too much green coffee that starts to lose its freshness) or underbuy (leaving them without enough coffee to fulfil customer demand).
With this in mind, roasters generally buy precise quantities of beans to maximise quality for the consumer. However, when Covid-19 spread rapidly and countries across the world went into lockdown in early 2020, roasters faced an issue.
Many of them found that they were unable to guarantee the sales they had relied on when cafés and other hospitality sector customers closed their doors. Furthermore, demand shrunk so quickly during the first surge of the pandemic, and roasters didn't have the time to anticipate and change their green coffee orders. In fact, many had even already pre-signed sales contracts with their green coffee suppliers.
Michelle Dunaway is a coffee trader at Mercon Specialty in Seattle, Washington. As a green coffee importer, Mercon Specialty's client base is predominantly made up of roasters. Michelle says that at the beginning of the pandemic, she saw that roasters were not at all able to use the amount of coffee they had already purchased, let alone commit to buying more.
"I would say that maybe 80 to 90% of the customer base that we have has been impacted," Michelle says. "Small roasters that, for instance, operate a coffee shop or sell at a farmer's market… for them, that all stopped. Then [you have to consider] restaurants and shops being closed for a month or two."
It's important to note that this doesn't just impact roasters and coffee shops. The knock-on effects impact everyone across the supply chain. For example, green coffee importers like Mercon often have close relationships with producers at origin. The money brought in from coffee sales boosts the economy in producing regions, which improves infrastructure, education, and healthcare in these areas.
You might also like How Does Technical Assistance Affect Coffee Producers?
How Roasters Have Diversified
With demand and sales down in a totally unprecedented way, roasters had to look beyond major supply contracts to secure new income streams. Even today, as restrictions are being eased in many areas around the world, uncertainty still remains.
Jill Killen is the owner of Cloud City Coffee in Seattle, Washington. She tells me that her business, like many others, was affected when pandemic regulations came into play. "I was forced to close one business that was too big to sustain other sales. Plus, my smaller business is down by 40%, as we do not allow customers inside."
To adapt, Jill explains that she made some quick changes in areas she felt would benefit the business as much as possible. "We've made online and mobile ordering more robust, and expanded our social media presence. We also started offering coffee subscriptions."
Even though some areas of the business have seen huge drops in sales, Jill says there were signs of how the market was changing and that Cloud City adapted in kind. She explains that while sales went down in some areas of her business, others grew. "Grab and go and wholebean sales have exploded," she says. "We've also sold more retail [equipment], such as pour over coffee brewers."
This change in the market appears to be here to stay. Roasters all across the world adapted during Covid-19 to offer online sales and subscription services. Earlier this year, it was reported that by the end of March 2020, packaged coffee sales were up by as much as 70%.
The Importance Of Supplier Flexibility
However, while diversifying and adapting have helped in some aspects, for many roasters, this isn't enough to make up for a massive fall in sales.
Jolene Zehnder is Mercon Specialty's Director of Sales. She explains that when Covid-19 hit, the company realised that it needed to change the way it was dealing with existing customers. Jolene says that by being more flexible and empathetic, they were able to support customers while also strengthening their customer-buyer relationship for the future.
"Typically, when importers sell green coffee, we sell on 'spread contracts' over long periods of time," Jolene explains. "This is because cafés and roasters know their business, and know how much green coffee they'll use. All of a sudden, they weren't picking up their contracts at the warehouse."
So, as many cafés had to close their doors to sit-in customers, there was a huge drop in demand for wholesale coffee. What did suppliers do to respond?
Jolene says: "We changed our sales technique. We said we were willing to let these customers out of contracts to ease business and to make them feel better.
"That's because we know once the pandemic is over and businesses come back up, they will feel more comfortable coming back to suppliers that have helped them during this time."
Jill explains that when she worked with Mercon, they were understanding and ultimately flexible. She tells me that it was beneficial to work with a supplier who understands that supporting their customers throughout a tough time will eventually lead to a stronger buying relationship.
"Mercon specifically helped me to find a home for some of the coffees I was over-contracted for, and also supported me in purchasing coffee from another company that they were overstocked on."
A Flexible Future?
Across all steps of the supply chain, coffee businesses continue to struggle with the impact of Covid-19. At present, nobody really knows what will change for sure in the next few months. However, both green coffee suppliers and roasters have adapted to the need for increased flexibility across the supply chain.
Michelle explains to me that going forward, Mercon Specialty will look at ways to be more flexible with existing and prospective customers. When the year started, our minimum order was one bag," she says. "People would order anything from one bag to 10 containers." However, with a need for more flexibility across the supply chain, this has changed dramatically.
"One of our latest innovations has been selling 25lb and 50lb boxes," Michelle explains. "We ship these via UPS directly to the customer's door." She says that this allows them to "take care of the micro roasters that might have cash constraints", as well as their larger customers.
It's not an understatement to say that Covid-19 has changed things for the coffee industry. We're no longer able to predict what the market will do with any certainty, and large parts of the supply chain have had to adapt in order to survive.
Without the ability to predict what the next week, month, or year's sales might hold, both green coffee suppliers and roasters are benefiting from increased flexibility.
But could this new structure could be here to stay? A more flexible supply of green coffee will surely open more doors than it will close, and improve access for aspiring roasters looking to get started somewhere.
Enjoyed this? Then read How Can Roasters Market Sustainable Coffee?
Photo credits: Cloud City Coffee, Miguel Regalado, Marco Verch, David Chau
Please note: Mercon Specialty is a sponsor of Perfect Daily Grind.
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Josef Mott
Barista, mestre de torra, e treinador SCA. O café me leva ao redor do mundo e eu quero compartilhar minhas experiências com todos.
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Martini 3 open-beta release
Last Updated: Tuesday, 31 July 2018 16:20
We gladly announce the release of the open beta version of MARTINI 3. This first glance of the new MARTINI includes all the necessary files to perform CG simulations of phospholipid bilayers and proteins. In the near future, new models for other molecules will also be included in this open beta. So, continue visiting our website to be updated with the news. The main goal of this release is to get feedback from the scientific community. Reporting problems in our forum will help us in the improvement of the force field, which also increase the chances of your favorite system be properly working in the near future. Good feedback is also welcome for the sake of the developers. Be aware, the parametrization is still on-the-fly, which means that the CG models used (from the interaction between beads to the bonded parameters) can/will change until the release and publication of the definitive version.
You can find the open-beta input parameters here.
"A man must defend his home, his wife, his children, and his martini." - Jackie Gleason

redpajama_set_name: RedPajamaCommonCrawl


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News Sports Life Opinion Nation / World Obituaries E-Edition Legals
The Louisville gym where Muhammad Ali's 'whole life' started now has a historical marker
Ben Tobin
The red bike glistened atop Columbia Gym Thursday morning in downtown Louisville as city officials and Muhammad Ali's family gathered to honor the champ and the venue where he first started boxing.
Ali, who died in June 2016 and would have been 78 years old Friday, learned how to box at the building at 824 S. Fourth St. Someone stole the future world heavy champion's bike outside of that building in 1954 — and the 12-year-old Cassius Clay proceeded to tell police officer Joe Martin that he was going to "whup" whoever took the bike.
Martin told Clay that to accomplish that goal, he would have to learn how to fight. Clay then started training at Columbia Gym, and the rest was history.
The building, now housing several sports teams as well as athletic department offices for Spalding University, received a historical marker Thursday. There are more than 2,400 historical markers across the commonwealth.
'Sitting with greatness':Why this man spent 9 hours at Muhammad Ali's grave
Danielle Lavender, the strength and conditioning coach for Spalding athletics, was one of several speakers at the historical marker dedication ceremony. She said it is "immensely important to honor those who came before us."
"I''m thankful for all the efforts that have been made to ensure that the life and work of the world's greatest are never forgotten," Lavender said. "Muhammad Ali may not be present with us today, but his legacy lives on."
Spalding President Tori Murden McClure said she "got to work pretty closely with Muhammad" when she was a full-time employee at the Muhammad Ali Center in downtown Louisville. According to McClure, Ali was a major influence in her decision to row solo across the Atlantic Ocean in 1999.
One special guest who helped unveil the marker was Rahman Ali, the 76-year-old younger brother of Muhammad Ali. The younger Ali said that his brother's "whole life" started at Columbia Gym.
"Being here today — it's like being in paradise with my brother," Rahman Ali said.
Muhammad Ali: The inside stories behind these memorable photos of 'The Greatest'
Events at the Muhammad Ali Center on Friday for Ali's birthday
The Muhammad Ali Center and Metro United Way are partnering on Friday, which would have been Ali's 78th birthday, on a service imitative titled "The Greatest Give." Here are the events:
The Greatest Confidence: 9 a.m. to 11 a.m. — Volunteers will assemble 780 personal care packages for neighbors in need of hygiene items.
The Greatest Care: noon to 2 p.m. — Volunteers will decorate and fill 780 healthy packs to keep youth and seniors strong, active and encouraged.
The Greatest Comfort: 3 p.m. to 5 p.m. — Volunteers will work together to make 78 tie-knot blankets to help keep children and families warm.
Contact Ben Tobin at bjtobin@gannett.com and 502-582-4181 or follow on Twitter @TobinBen. Support strong local journalism by subscribing today: subscribe.courier-journal.com.


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A World Without Sex: Identity without the Intercourse
by D. M. Domosea
In this month's column, we focus our thought experiment on the influence of sex on identity and imagine how a world without sexual reproduction might shape the way we negotiate social and personal labels.
Trigger Warning: This article discusses sexual violence in the context of colonization and racial identity.
Speculative writers with an eye (and patience!) for detail tend to build lush worlds filled with fully-developed civilizations. They spend time crafting rich identities for their characters and the societies from which they come, but social identity for inhabitants of egalitarian or matriarchal worlds won't necessarily replicate those of the patriarchal one we are used to. Writers must consider how identity might be informed in such worlds if they choose to write them. Imagining our own world without the male-preferenced aspect of sexual reproduction–an aspect that both influences and is influenced by identity–might help.
Sexual reproduction of course has a significant impact on our definitions of sexual preference and gendering identities. Our modern world is only now awakening to a wider understanding of gender identity and sexuality spectra, though universal acceptance is still far from our collective grasp. Some countries persecute non-cis/het citizens and relationships as a matter of law while others tolerate LGBTQ+ identities without embracing true and full equality. While such treatment is ostensibly tied to religious beliefs and the moral demands of such, those beliefs themselves have long been interpreted and enforced by heterosexual men to serve their desires.
Does sex shape other forms of identity, such as race, ethnicity, religion or class? Not in the way they are defined. Rather, perception of these identities shape the way women within those identity groups are approached when it comes to sex, often to their detriment. Black women, for example, have long been the most victimized group when it comes to sexual violence. Not only do they suffer attacks from within their own communities in the way all women do, but historically they have been subjected to assault from colonizers and slavers who claimed ownership of, and thus privilege to, their bodies. Today, black women, and especially black trans women, continue to experience higher degrees of sexual harassment and violence than other populations. They are less likely to report incidents—having no safe and effective way to do so—and are unlikely to receive justice or rightful compensation when they do.
Other identities outside of white or Western European ones are also often exoticized and harmfully fetishized when it comes to sex. Consider the recent uproar over Kim Kardashian's "kimono" shapeware line. The online rebuke wasn't simply culturally-protective finger-wagging. The disapproval stems from the historical sexual objectification of Japanese women (and Asian women in general) by non-Asian societies. The use of "kimono"—a sophisticated traditional gown designed for formal events—by a privileged American entrepreneur to sensualize her shapeware line ignores, and even capitalizes on, that harmful stereotype.
Native American women haven't escaped white colonial objectification, either. As recently as last year, companies continued to sell sexy "Native American" princess costumes, despite the protests of actual Native American women who explained the dangers of sexualizing their already at-risk communities. (The company cited in the linked article seems to have removed all products categorized as "Native American," from their 2019 catalog.)
The patriarchal legacy of sexual reproduction also creates stumbling blocks when it comes to class identity. In India, a nation plagued by an illegal yet persistent caste system, class identity can define a woman's sexual status. Girls from lower castes are often forced into prostitution to support their families. The opportunity for education is rare, and marriage is a tentative escape at best.
Patriarchal attitudes surrounding sex have also influenced religious identity, much of which can be culled from the combination of my two previous posts on clothing and religion. Suffice to say, ideas on who can claim the title of a "true practitioner" of one's faith are often tied to clothing choices (either too little or not enough when it comes to women), sexual status (piety and purity reign supreme) and—tying back to our opening topic—sexual preference. Those who don't fall in line must leave the religion or claim it with caveats. (Membership with caveats is NOT full membership.)
Now, in the context of our thought experiment, let's neuter the human race to remove sexual reproduction with its contrivances and complications. Shamefully, "othering" and the resulting persecution would likely not cease, as humanity with its need to conquer seems to excel at both. However, asexualizing humanity would remove a source of deep trauma for victims of identity-based sexual violence in that it removes a tool of oppression and terror. Identities of class, religion, race and ethnicity would remain in a sexless world, but presumed authority wouldn't involve sexual degradation and humiliation, and women wouldn't be pointedly targeted. Keep this in mind when describing the fears and realities of women in mixed-identity societies.
Without incentive to compete for sexual mating rites, masculinity and femininity as "biological indicators" become unimportant. They instead morph into fluid descriptors found on a wider gender spectrum. A baby might be identified at birth as having male, female or even intersex genitals (remember, we still utilize sperm, eggs, and the uterus in our thought experiment), but without any further implication of what that means for personality, interactions and preferences as the child grows. In other words, we wouldn't simply tag a child born with sperm-producing genitalia with the "masculine" label and raise them as such.
Today, increasing numbers of progressive-minded families take this tact with their children. And many adults, once forced into ill-fitting gender and sexuality identities based solely on biology, are now recognizing and reclaiming their true selves. Inequality and even persecution remains, but possibility is there where it wasn't before. The way they redefine their identities, ejecting restrictive binary pronouns and labels, provides positive inspiration for building characters in egalitarian or matriarchal worlds. Imagine mastering the skill to create a character who is compelling and relatable without being explicit—through pronouns, names or actions—about where they fall on the gender spectrum.
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Surveillance and Human Rights
13 Principles: A Legal Toolkit for Global Surveillance Reform:
In 2013, EFF and a coalition of hundreds of experts and human rights activists put the finishing touches on the Necessary and Proportionate Principles. These 13 Principles articulate how international human rights law should be applied to government surveillance. National and local activists from Mexico to Egypt have used the Principles to push for stronger protections against digital surveillance. We've seen them used in litigation, legislation, administrative work, and advocacy campaigns, as well as debated in both regional and international policy venues. As part of our work to assist lawmakers, activists and judges in creating modern, effective surveillance law that are respectful of human rights, EFF and our partners are working to build a complete legal toolkit around the Principles, starting with a detailed legal backgrounder and analysis, explaining their basis in international human rights law.
Reviews of Local Surveillance Law:
In 2015, EFF collaborated with Latin American groups and individuals to compile local country reports aimed at analyzing state communications surveillance and the protection of fundamental rights in Latin America. The reports explain the concept of communications surveillance, according to the definition set by international human rights standards, and discuss how state surveillance activities are often at odds with certain fundamental rights recognized in constitutions, regulations, and law. The reports analyze local surveillance activities vis-à-vis the 13 Principles, a set of international standards that articulate the duties and obligations of states when engaging in communications surveillance, and provide public policy recommendations as the basis for future law reform.
State Communications Surveillance and Protection of Fundamental Rights in Peru
State Communications Surveillance and the Protection of Fundamental Rights in Chile
State Communications Surveillance and the Protection of Fundamental Rights in Colombia
State Communications Surveillance and the Protection of Fundamental Rights in Mexico
State Surveillance of Communications in Brazil and the Protection of Fundamental Rights
Vigilancia Estatal de las Comunicaciones en Brasil y la Protección de los Derechos Fundamentales
Vigilancia Estatal de las Comunicaciones y Protección de los Derechos Fundamentales en Argentina
Vigilancia Estatal de las Comunicaciones y Protección de los Derechos Fundamentales en Chile
Vigilancia Estatal de las Comunicaciones y Protección de los Derechos Fundamentales en Colombia
Vigilancia Estatal de las Comunicaciones y Protección de los Derechos Fundamentales en México
Vigilancia estatal de las comunicaciones y derechos fundamentales en Paraguay
Vigilancia Estatal de las Comunicaciones y Derechos Fundamentales en Perú
Vigilancia Estatal de las Comunicaciones y Protección de los Derechos Fundamentales en Uruguay
Advocacy Strategies:
All around the world, people are taking on the surveillance machine -- and winning. EFF has been working in tandem with successful advocates in Colombia, Zimbabwe, Egypt and beyond to identify some of the best strategies for challenging proposals and surveillance practices which erode civil liberties. We have gathered counter-surveillance success stories to share with a global coalition of advocates who are encountering problematic proposals in their own countries. We're sure that this list of examples will continue to grow.
Success story: Protecting privacy of web commenter (Chile)
Success story: Breaking news about data retention (Argentina)
Success story: Turning the tide against online spying (Canada)
Success story: Dismantling UK's biometric ID database (UK)
Success story: Mobilizing netizens to stop cyber spying (US)
Success story: An Effective Protester is a Secure Protester (Brazil)
Success story: How Brazilian Activists Took Charge When Public Demand For Internet Security Intensified (Brazil)
Success story: CriptoRally in Mexico City: A creative approach to fighting the Ley Telecom (Mexico)
Success story: Blogging Under Surveillance (Germany)
Success story: Why Metadata Matters: The Dangers and Revealing Nature of Data Retention (Germany)
Success story: How Digital Rights Ireland Litigated Against the EU Data Retention Directive and Won (Ireland)
Success story: Ameliorating the Implementation of the Polish Data Retention Mandates Law (Poland)
Success story: Who Has Your Back - Protecting Your Data From Governmental Request (US)
Success story: The Dutch Transparency Battle: Data Requests and a User's Right to Know (Amsterdam)
Success story: Mapping The Canadian Government's Telecommunications Surveillance (Canada)
Success story: Fighting Against Extraterritorial Powers in the US FISA Amendment Act of 2008 and Similar Legislation (Belgium)
Success story: Rallying to End Subscriber Registration Regulations in Zimbabwe (Zimbabwe)
Success story: Defeating the Draft Communications Data Bill (UK)
Through our Global Surveillance and Human Rights Project, advocates will learn how to effectively fight overreaching government surveillance proposals around the world. By working together with advocates, lawyers, journalists, bloggers, and security experts on the ground, we built a Surveillance and Human Rights Camp in which we mapped specific problems posed by invasive surveillance infrastructure and devise regional and national solutions, strategies, and tactics. Together, we share knowledge on existing legislative initiatives, international fora, and other venues where we can make an impact, and devise strong legal safeguards, based on a realistic understanding of the technological threats, against government access to people's communications and data.
EFF Related Content: Surveillance and Human Rights
Written Submission for the Hearing at the Inter-American Commission on Human Rights on Global NSA Surveillance
Inter-American Commission on Human Rights: 149th ordinary period of sessions.
The Electronic Frontier Foundation, Asociación por los Derechos Civiles, Access, ARTICLE 19 - Mexico and Central America office,...
Read more about Written Submission for the Hearing at the Inter-American Commission on Human Rights on Global NSA Surveillance
Deeplinks Blog by Katitza Rodriguez | October 10, 2013
More Than 30 Organizations Unite To Safeguard Canadians' Privacy Rights Amid Spy Agency Scandal
EFF is joining more than 30 major Canadian organizations to form the largest pro-privacy coalition in Canadian history. With the Canadian Parliament set to resume, the Protect Our Privacy Coalition has banded together to ensure Canadians get effective legal measures to protect their privacy against government...
Read more about More Than 30 Organizations Unite To Safeguard Canadians' Privacy Rights Amid Spy Agency Scandal
Deeplinks Blog by Cindy Cohn | October 4, 2013
EFF Gives Expert Testimony on NSA Spying in Challenge to British Surveillance Program
Three major British privacy organizations on Thursday launched an important legal challenge to the United Kingdom's participation in the massive global surveillance scandal. To support the case as an expert witness, I submitted a 32-page statement laying out much that is publicly known about the National Security Agency's...
Read more about EFF Gives Expert Testimony on NSA Spying in Challenge to British Surveillance Program
Press Release | September 20, 2013
Thirteen Principles Against Unchecked Surveillance Launched at United Nations
Geneva - At the 24th Session of the United Nations Human Rights Council on Friday, six major privacy NGOs, including the Electronic Frontier Foundation (EFF), warned nations of the urgent need comply with international human rights law to protect their citizens from the dangers posed by mass digital surveillance.The groups...
Read more about Thirteen Principles Against Unchecked Surveillance Launched at United Nations
Deeplinks Blog by Danny O'Brien | September 20, 2013
The United Nations Meets 13 Principles Against Unchecked Surveillance
In a Geneva room full of representatives from nations around the world, some of the world's largest privacy organizations, including EFF, today warned the United Nations of the dangers of the mass Internet spying being conducted by its own members. We used the side-event on privacy to officially launch...
Read more about The United Nations Meets 13 Principles Against Unchecked Surveillance


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https://www.wsj.com/articles/BL-TB-24352
AT&T Could Lose 40% Of iPhone Subs To Verizon, Davenport Says
Eric Savitz
AT&T (T) could lose as many as 40% of current subscribers who use the Apple (AAPL) iPhone once Verizon (VZ) starts selling a version of the phone, according to Davenport & Co. analyst F. Drake Johnstone.
Johnstone thinks as many as 6 million of its current 15 million iPhone customers at AT&T could defect. He notes that AT&T recently said it will raise its early termination fee for customers that buy new smart phones from $175 to $325 - a sign that "AT&T is clearly worried that it will lose customers once a competing carrier...
AT&T (T) could lose as many as 40% of current subscribers who use the Apple (AAPL) iPhone once Verizon (VZ) starts selling a version of the phone, according to Davenport & Co.


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Billy Graham's grandson to play him in 'Unbroken' sequel
Rachel Cruz	 28 February, 2018 2:48 PM
Evangelist Billy Graham's grandson, Will Graham, is going to play his grandfather on the big screen in the sequel to "Unbroken." The follow-up movie, which is titled "Unbroken: Path to Redemption," will pick up from where war hero Louis Zamperini discovered God.
(REUTERS/Shannon Stapleton)Billy Graham speaks during his New York Crusade at Flushing Meadows Park in New York in 2005.
The younger Graham, 43, spoke with CBN News about the role he was playing in the faith-based film. He stated that he was not trying to fill his grandfather's shoes, who recently died of natural causes at 99 years old, but said there was a bigger reason why he agreed to the role.
"Knowing how God used Billy Graham in Louie Zamperini's life, I couldn't pass the opportunity to portray him in this inspiring story," Graham said. "If I just please the Lord, the Lord will take care of the rest."
Like his elders, Graham is also an evangelist and works in the organization that his departed grandfather established decades ago, which is now being managed by his father, Franklin. The younger Graham has traveled across America, as well as India, Australia, Asia and South America to preach the Gospel.
"Unbroken: Path to Redemption" follows the 2014 film that Angelina Jolie directed based on the book that Laura Hillenbrand wrote about Zamperini. Towards the end of the movie, Zamperini recovered from alcoholism and post-traumatic stress disorder because of the war, and he began listening to the Word of God through the elder Graham.
The sequel will attempt to put more focus on Zamperini's relationship with the famous evangelist. Apparently, viewers became disappointed that the first movie did not highlight the impact of Graham's evangelism in Zamperini's life.
Harold Cronk, the director of "God's Not Dead" will also helm "Unbroken: Path to Redemption." Pure Flix, Universal Pictures and the WTA Group, a faith-based marketing firm, will produce the sequel. The movie has no projected release date for now.
"The details of [Zamperini's] post-war struggles and ultimate redemption are so stirring," producer Matt Baer said. "They deserve to be told in a stand-alone project."
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Christians speak out as migrant children are detained without soap, hygiene needs
19 killed by gunmen in Burkina Faso: 'There's no Christian anymore in this town
Chinese Christians memorize entire Bible in prison: Gov't 'can't take what's hidden in your heart'
Pope Francis approves change to the Lord's Prayer despite opposition: 'It's deeply problematic'


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Q: fine-tuning a CNN from a lower fc layer I've noticed that most fine-tuning of CNN over new dataset is done only on the "last" fully connected (fc) layer.
I'm interested in fine-tuning from the "first" fully connected layer: that is, I want to use mid-level features from convolution and pooling layers as they are, (supposing it's trained on ImageNet) but then fit all fc layers to my new dataset.
Theoretically and in practice, what is the supposed effect of this? Is it likely to learn a more proper set of parameters for my new dataset?

A: Theoretically, the deeper you fine-tune, the better your model fits your data. So, if you could fine-tune the whole model - the better.
So, what's the catch, you must be asking, why don't everyone fine-tune the whole model?
First, fine-tuning the whole model involves lots and lots of parameters, in order to train properly millions of parameters without the risk of overfitting, you must have a LOT of new training examples. In most cases, when fine-tuning you only have a very few annotated samples for the new task and therefore you are unable to afford fine-tuning of the whole model.
Second, fine-tuning the whole model takes much longer than training just the top fc layer. Thus, if you have little time and budget you only fine-tune the top fc layer.
In your case, if you have enough samples you may fine-tune the top two fc layers. From my experience it is better to fine tune the top layer first and then fine-tune the top two together after some iterations are done on the top layer alone.

A: The purpose of FC layers in a ConvNet is only to perform classification for your problem. You could just use the final flattened output from your last Conv/Pooling layer as engineered features and put it in another machine learning model and it would have the same effect.
This implies that the parameters learned by FC layers in most cases are very problem specific (depends on the data) and, in most cases not transferable.
So whenever people fine tune on a pre-trained model they almost always dump the FC layers on the top.
Now you can go 2 ways from here.

*

*Use the final flattened output from the last Conv/Pooling layer as extracted features for your problem and train a ML model on it. This method is commonly used if your data set is small or not similar to the pre-trained model.

*Get the extracted features using the above method and then use them to train a FC neural network. Once you achieved a decent accuracy stack it on top of last conv/pooling layer of the pre-trained model (dont forget to remove the orignal FC layers). Now freeze(parameters are made constant and dont change on training) most of the pre-trained model and only allow the last few conv layers to be trained. Now train the entire network to train with a very small learning rate.

The whole point of freezing most of the model is that we assume that the model already knows basic stuff like edge detection and color from the earlier conv layers. Now we fine tune the last few layers for the our problem. We chose a small learning rate so that we don't end up messing up what the model has already learned.
The reason we train the FC layers before we fit them on to the pre-trained model is just to save training time and more importantly to ensure that we don't make to much changes to the Conv layers and end up over fitting.

redpajama_set_name: RedPajamaStackExchange


Today I had my final thesis presentation. Before the presentation I went shopping in Amsterdam. I bought a very cool dotted jumpsuit. But more about this jumpsuit and my shopping spree will be in the upcoming 'New In' post!
So off to the outfit: I wore my new Primark dress and combined it with black and white details. Hope you'll like it!
I love the silhouette of the dress!
Was that your outfit on your thesis defense? Well, it would certainly give you confidence while defending your thesis ideas. It can certainly help to avoid mistake and problems that came with being nervous.


text:
\section{Introduction}

A phospholipid membrane can be easily deformed and exhibits appreciable fluctuations  due to its small elastic constant \cite{helfrich1973,helfrich1978,lipowskysackmann1995, smith2006b,monzel2012,marx2002}. While  occurring on time scales between $10^{-9}$ and $10^{-5}$ s \cite{monzel2016a,fenz2012, betz2012,schmidt2014}, the fluctuations are overdamped by the  surrounding fluid \cite{brochard1975,kramer1971,seifert1993, atzberger2011}. Nonetheless,  mean fluctuation amplitudes of up to $\unit[100]{nm}$ have been observed experimentally \cite{monzel2016b}. In a vicinity of a substrate, these fluctuations are known to contribute to an effective potential which prevents the membrane from non-specifically adhering to the underlying scaffold \cite{helfrich1973, helfrich1984, evans1986, israelachvili1992, raedler1995,lipowskysackmann1995, seifert1997, lorz2007, schmidt2014}. The scaffold in turn affects the hydrodynamic damping of the membrane reflected in changes of the time dependent correlation function and the associated power spectrum, the so-called power spectral density (PSD) \cite{safran2005, betz2009,monzel2015, monzel2016b}. Moreover, in the cellular environment, active processes couple with the membrane fluctuations \cite{prost1998, ramaswamy2000, manneville2001, girard2005, gov2005, lin2006, betz2009, loubet2012, Hanlumyuang2014, alert2015, monzel2015}, resulting in the violation of the fluctuation-dissipation theorem in the activated state of the cell \cite{mizuno2007, ben-isaac2011, turlier2016}.

Over the last two decades, models for the fluctuations of free membranes, based on the Helfrich energetics and Stokes fluid dynamics, were experimentally confirmed, either by measuring the PSD or its Fourier transform, the time dependent correlation function (for reviews see \cite{monzel2016a,monzel2016b} and references therein). This body of work confirmed the appropriateness of the models based on the Helfrich Hamiltonian \cite{helfrich1973} to capture the equilibrium dynamics of free membranes. However, the presence of the pinning introduces a challenge, which is often circumvented by homogenising the effects of interactions with the scaffold \cite{gov2004b,turlier2016}.
Alternative approaches, where the local pinnings remain explicit, commonly involved simulations \cite{lin2005, reister2011, hu2013, bihr2015}, while the theoretical modelling focused on the static properties of the membrane shape and fluctuations \cite{bruinsma1994, gov2004b, janes2018}. On the other hand, analytic treatments of the membrane-dynamics, even in the context of equilibrium, remained an open problem up to now. First quasi-analytical predictions were obtained for infinitely strong pinnings \cite{lin2004b}, while the more realistic case, where the membrane is attached by proteins which themselves maintain a certain flexibility has not been considered so far.

In this paper we address this open issue by analytically solving the integro-differential equation governing the motion of a pre-tensed membrane pinned by a single flexible construct. We describe in detail the effect of the pinning on the membrane's equilibrium dynamics. At last, we provide an exact analytical method for calculating the pinning stiffness from the experimentally measured PSD, accounting for the finite resolution of the setup. While constructed in the context of biological membranes, the obtained result can be applied more generally, in the context of bending fluctuations of thin sheets.

\begin{figure*}[tbp]
 \centering
 \includegraphics[width=0.7\linewidth]{fig1.pdf}
 \caption{Snapshot from the Langevin simulation of locally pinned membrane fluctuating in a non-specific potential (Left). Sketch of the system (Right). Membrane is residing in a harmonic potential of strength $\gamma$ at $h_0$ separation from a flat substrate and pinned by an elastic spring of stiffness $\lambda$ and rest length $l_0$ positioned at ${\bf r}=0$.
}
 \label{fig:sketch}
\end{figure*}

\section{Equation of motion}

The system consists of one flexible attachment (harmonic spring of an elastic constant $\lambda$ and rest length $l_0$) that pins a tensed membrane (bending rigidity $\kappa$, tension $\sigma$). The later fluctuates in a harmonic non-specific potential (strength $\gamma$) positioned at the distance $h_0$ above the substrate (Fig. \ref{fig:sketch}). Placing the origin of the coordinate system at the pinning site and into the minimum of the non-specific potential sets the form of the energy functional  \cite{schmidt2012, janes2018} as
\begin{align}
 \mathcal H = \int\limits_A \mathrm{d}{\bf r} &\Bigg[ \frac{\kappa}{2} \left ( \nabla^2u({\bf r},t) \right )^2 + \frac{\sigma}{2} \left ( \nabla u({\bf r},t) \right )^2 + \frac{\gamma}{2} \left ( u({\bf r},t) \right )^2  \nonumber
 \\
 &+  \frac{1}{2} \lambda\left ( u({\bf r},t) - (l_0-h_0) \right )^2 \delta ({\bf r})\Bigg].
 \label{eq:Translated_Hamiltonian}
\end{align}
Here and throughout the paper, the energy scale $k_\text{B}T$ is set to unity, with Boltzmann constant denoted as $k_\text{B}$ and absolute temperature $T$.

Dynamics of an overdamped membrane in a hydrodynamic surrounding is captured by the Langevin equation \cite{doi1988, seifert1997, granek1997, lin2006b, reister2008, sigurdsson2013, reister2011, bihr2015}
\begin{align}
\frac{\partial u({\bf r},t)}{\partial t} &= \int d{\bf r}' \Lambda({\bf r}-{\bf r}') \left( -\frac{\delta  \mathcal H}{\delta u({\bf r}',t)} + f({\bf r}',t) \right) \nonumber
\\
&\equiv \Lambda({\bf r}) * \left( -\frac{\delta  \mathcal H}{\delta u({\bf r},t)} + f({\bf r},t) \right),
\label{eq:Hydrodynamic_equation_for_a_pinned_membrane}
\end{align}
which states that the velocity of the membrane profile $u({\bf r},t)$ is given by a convolution of the hydrodynamic kernel $\Lambda({\bf r})$, the Oseen tensor, with the forces acting on the membrane. External forces on the system are denoted by $f({\bf r},t)$, while the internal forces acting to minimize the Hamiltonian (eq. (\ref{eq:Translated_Hamiltonian})) are given by the first variation \cite{janes2018}
\begin{align}
\frac{\delta  \mathcal H}{\delta u({\bf r},t)} = &\left(\kappa \nabla^4 - \sigma\nabla^2 + \gamma + \lambda \delta ({\bf r})\right) u({\bf r},t) \nonumber \\
- &\lambda (l_0-h_0) \delta ({\bf r}).
\end{align}
Together with eq. (\ref{eq:Hydrodynamic_equation_for_a_pinned_membrane}), this leads to the equation for the dynamics of an overdamped pinned membrane
\begin{align}
\mathcal D \left[u({\bf r},t)\right] = \Lambda({\bf r})* \left[ f({\bf r},t) + \lambda (l_0-h_0) \delta ({\bf r}) \right],
\label{eq:Hydrodynamic_equation_for_a_pinned_membrane_explicit}
\end{align}
with the operator $\mathcal D $ set as
\begin{align}
 \mathcal D = \frac{\partial}{\partial t} + \Lambda({\bf r})*\left(\kappa \nabla^4 - \sigma\nabla^2 + \gamma + \lambda \delta ({\bf r})\right).
\label{eq:Dynamical_operator}
\end{align}

\section{Time-dependent Green's function}

The solution of eq. (\ref{eq:Hydrodynamic_equation_for_a_pinned_membrane_explicit}) provides the evolution of the membrane profile $u({\bf r},t)$. It is obtained by the integration of forces acting on the membrane, the latter accounted for by the  dynamic Green's function $g({\bf r},t\vert{\bf r}',t')$
\begin{align}
u({\bf r},t) = &\int_{\mathbb{R}^2}\mathrm{d {\bf r}'} \int_{\mathbb{R}}\mathrm{d t}'\  g({\bf r},t\vert{\bf r}',t') \times \nonumber \\
&\times \left( f({\bf r}',t') + \lambda (l_0-h_0) \delta ({\bf r}')\right).
\label{eq:Pinned_membrane_profile_as_aconvolution_of_force_with_the_dynamical_greens_fucntion}
\end{align}
Here the Green's function is defined by
\begin{align}
\mathcal D \left[g({\bf r},t\vert{\bf r}',t')\right] = &\Lambda({\bf r})* \left[ \delta({\bf r}-{\bf r}')\delta(t-t') \right].
\label{eq:Dynamical_Green's_function_of_apinned_membrane_definition}
\end{align}
Besides imposing causality, this equation is subject to homogeneous spatial boundary conditions forcing the membrane in the minimum of the non-specific potential far from the pinning.

\subsection{Free membrane ($\lambda=0$)}

Recognizing spatio-temporal translational invariance of the free membrane system, the corresponding Green's function $g_f({\bf r},t\vert{\bf r}',t') $ can be written in terms of variables $\tilde{t}=t-t'$ and $\tilde{{\bf r}} = {\bf r}-{\bf r}'$ as
\begin{align}
g_f({\bf r},t\vert{\bf r}',t') = g_f({\bf r}-{\bf r}',t-t')\equiv g_f(\tilde{{\bf r}},\tilde{t}).
\label{eq:Green_spatio_temporal_trans_invariance}
\end{align}
Consequently, for the free membrane eq. (\ref{eq:Dynamical_Green's_function_of_apinned_membrane_definition}) becomes
\begin{align}
& \left[ \frac{\partial}{\partial \tilde{t}} + \Lambda(\tilde{{\bf r}})*\left(\kappa \nabla_{\tilde{{\bf r}}}^4 - \sigma\nabla_{\tilde{{\bf r}}}^2 + \gamma \right) \right] g_f(\tilde{{\bf r}},\tilde{t}) \nonumber \\
&= \Lambda(\tilde{{\bf r}})* \left[ \delta(\tilde{{\bf r}})\delta(\tilde{t}) \right].
\label{eq:Trans_invar_free_dynamical_equation}
\end{align}
Fourier transforming eq. (\ref{eq:Trans_invar_free_dynamical_equation}) ($\tilde{{\bf r}}\to {\bf k}$ and $\tilde{t} \to \omega$) upon rearranging yields
\begin{align}
g_f({\bf k},\omega) = \frac{1}{i\omega / \Lambda_k + E_k},
\label{eq:k_omega_Hydrodynamic_equation_for_a_pinned_membrane_greens_fucntion}
\end{align}
where $\Lambda_k$ is the spatial Fourier transform of $\Lambda(\tilde{{\bf r}}$) and
\begin{align}
E_k = \kappa k^4 + \sigma k^2 + \gamma.
\label{eq:eigenvalues}
\end{align}
Finally, transforming back to the spatio-temporal domain (${\bf k}\to \tilde{{\bf r}}$ and $\omega \to \tilde{t}$) provides the spatio-temporal Green's function for the free membrane
\begin{align}
g_f(\tilde{{\bf r}},\tilde{t})=\int_{\mathbb{R}^2} \frac{d{\bf k}}{(2\pi)^{2}} \int_{\mathbb{R}} \frac{d\omega}{2\pi} \frac{ e^{i{\bf k}\tilde{{\bf r}}}e^{i \omega \tilde{t}}}{i\omega/\Lambda_k + E_k}.
\label{eq:Free_Green_spatio_temporal_trans_invariance}
\end{align}
Integrating over the frequencies gives
\begin{align}
g_f(\tilde{{\bf r}},\tilde{t})&= \int\frac{d{\bf k}}{(2\pi)^{2}} \, \Lambda_k e^{i{\bf k}\tilde{{\bf r}}}e^{-\Lambda_kE_k\tilde{t}} \Theta(\tilde{t})\nonumber
\\
&=\int^{\infty}_0 \frac{dk}{2\pi}\, \Lambda_k k J_0(k\vert\tilde{{\bf r}}\vert) e^{-\Lambda_kE_k\tilde{t}} \Theta(\tilde{t}),
\label{eq:Free_Green_spatio_temporal_trans_invariance_causality}
\end{align}
where $\Theta$ is the Heaviside step function appearing as a consequence of causality. Moreover, $g_f(\tilde{{\bf r}},\tilde{t})$ depends only on the absolute value of $\tilde{{\bf r}}$, as expected.

For $\omega = 0$, the Green's function $g_f(\tilde{{\bf r}},\omega)$ reduces to the static correlation function \cite{janes2018}. Consequently,
\begin{align}
 g_f(\tilde{{\bf r}}=0,\omega=0)  \equiv \frac{1}{\lambda_m} = \frac{\text{arctan}\left(\sqrt{\left(\frac{\lambda_m^{0}}{4\sigma}\right)^{2}-1}\right)}{2\pi\sigma\sqrt{\left(\frac{\lambda_m^{0}}{4\sigma}\right)^{2}-1}}
\label{eq:Free_membrane_fluctuation_amplitude}
\end{align}
represents the fluctuation amplitude, which in the tensionless case reduces to
\begin{align}
 g_f(\tilde{{\bf r}}=0,\omega=0;\sigma=0) \equiv \frac{1}{\lambda^{0}_m} = \frac{1}{8\sqrt{\kappa \gamma}}.
\label{eq:Free_membrane_fluctuation_amplitude}
\end{align}

\subsection{Pinned membrane}

Permanent pinning breaks the spatial, but keeps the temporal translational invariance. Therefore, the Green's function of the pinned membrane must be described by two spatial variables ${\bf r}$ and ${\bf r}'$ and one temporal variable $\tilde{t}=t-t'$
\begin{align}
g({\bf r},t\vert{\bf r}',t') = g({\bf r},t-t'\vert {\bf r}')\equiv g({\bf r},\tilde{t}\vert {\bf r}').
\label{eq:Pinned_Green_temporal_trans_invariance}
\end{align}
In this notation, eq. (\ref{eq:Dynamical_Green's_function_of_apinned_membrane_definition}) for the pinned membrane Green's function becomes
\begin{align}
\left[ \frac{\partial}{\partial \tilde{t}} + \Lambda({\bf r})*\left(\kappa \nabla^4 - \sigma\nabla^2 + \gamma + \lambda \delta ({\bf r})\right) \right] g({\bf r} ,\tilde{t}\vert {\bf r}' )  \nonumber \\
= \Lambda({\bf r})* \left[ \delta({\bf r}-{\bf r}')\delta(\tilde{t}) \right].
\label{eq:Trans_invar_pinned_dynamical_equation}
\end{align}
Fourier transforming (${\bf r}\to {\bf k}$ and $\tilde{t} \to \omega$) and rearranging eq. (\ref{eq:Trans_invar_pinned_dynamical_equation}) gives
\begin{align}
g({\bf k},\omega \vert {\bf r}') = \frac{e^{-i{\bf k}{\bf r}'}}{i\omega / \Lambda_k + E_k} - \lambda g({\bf r}=0,\omega \vert {\bf r}')\frac{1}{i\omega / \Lambda_k + E_k}.
\label{eq:k_omega_Hydrodynamic_equation_for_a_pinned_membrane_greens_fucntion}
\end{align}
Transforming back to the spatial domain (${\bf k}\to {\bf r}$) gives
\begin{align}
g({\bf r},\omega \vert {\bf r}') = & g_f({\bf r}- {\bf r}',\omega) - \lambda g({\bf r}=0,\omega \vert {\bf r}')g_f({\bf r},\omega).
\label{eq:r_omega_Hydrodynamic_equation_for_a_pinned_membrane_greens_fucntion}
\end{align}
For ${\bf r}=0$ in eq. (\ref{eq:r_omega_Hydrodynamic_equation_for_a_pinned_membrane_greens_fucntion}) we find
\begin{align}
g({\bf r},\omega \vert {\bf r}') = \frac{g_f({\bf r}',\omega)}{1+\lambda g_f({\bf r}=0,\omega)},
\label{eq:Green_r_omega_pinning_site}
\end{align}
which upon inserting into (\ref{eq:r_omega_Hydrodynamic_equation_for_a_pinned_membrane_greens_fucntion}) yields the Green's function for the pinned membrane in the spatio-frequency domain
\begin{align}
g({\bf r},\omega \vert {\bf r}') = g_f({\bf r}- {\bf r}',\omega) - \lambda \frac{g_f({\bf r},\omega) g_f({\bf r}',\omega)}{1+\lambda g_f({\bf r}=0,\omega)}.
\label{eq:Pinned_Green}
\end{align}
Fourier transforming eq. (\ref{eq:Pinned_Green}) (${\bf r}\to{\bf k}$ and ${\bf r}'\to{\bf k}'$) results in
\begin{align}
g({\bf k},\omega \vert {\bf k}') = (2\pi)^{2} \delta ({\bf k}+{\bf k}') g_f({\bf k},\omega) - \lambda \frac{g_f({\bf k},\omega) g_f({\bf k}',\omega)}{1+\lambda g_f({\bf r}=0,\omega)},
\label{eq:Pinned_Green_k_space}
\end{align}
which is the representation of the Green's function in the Fourier space.

\section{Dynamics of thermal fluctuations}

\subsection{Oseen tensor}

In thermal equilibrium $f({\bf r},t)$ is associated with the stochastic thermal noise characterized by a vanishing mean
\begin{align}
\langle f ({\bf r},t) \rangle =0
\label{eq:Thermal_noise_mean}
\end{align}
and spatio-temporal correlations obeying the fluctuation-dissipation theorem
\begin{align}
\langle f({\bf r},t) f({\bf r}',t^\prime) \rangle = 2\Lambda^{-1}({\bf r}-{\bf r}') \delta (t-t^\prime).
\label{eq:Thermal_noise_variance}
\end{align}
Here $\Lambda^{-1}({\bf r})$ is defined by
\begin{align}
\Lambda({\bf r})*\Lambda^{-1}({\bf r})=\delta({\bf r}).
\end{align}
To model damping of the membrane due to hydrodynamic interactions with the surrounding fluid close to a wall \cite{doi1988, lin2006b}, we will use the Fourier transform of the Oseen tensor $\Lambda_k$
\begin{align}
\Lambda_k=(4\eta k)^{-1},
\label{eq:Oseen_coefficients}
\end{align}
where $\eta$ is the viscosity of the surrounding fluid. Eq. (\ref{eq:Oseen_coefficients}) is appropriate when the wall is permeable to the fluid. In the presence of an impermeable wall, damping coefficients are modified  \cite{seifert1994a, gov2003}, which in the case of protein mediated adhesion, typically has an effect only on the amplitude of the first few membrane modes \cite{reister2008}.
Furthermore, if the membrane is surrounded by two different fluids with viscosities $\eta_1$ and $\eta_2$, the viscosity $\eta$ in the damping coefficients is replaced by the arithmetic mean  $\eta=(\eta_1 + \eta_2)/2$ \cite{monzel2016b}.

\subsection{Simulation methods}
Eq. (\ref{eq:Hydrodynamic_equation_for_a_pinned_membrane_explicit}) for the membrane dynamics, subject to thermal noise defined with eqs. (\ref{eq:Thermal_noise_mean})-(\ref{eq:Oseen_coefficients}), is the foundation of our Langevin dynamics simulations of the membrane, described previously in full detail \cite{bihr2015}. In the current case, one pinning site is placed in a middle of the simulation box (periodic boundary conditions) of a size of $640\times640$ nm for a tensionless membrane, and a size of $5120 \times  5120$ nm at finite tensions. The simulations are performed with a temporal and lateral resolution of $10^{-9}$ s and $10$ nm, respectively. The membrane height profile is recorded as a function of time and analyzed to extract the membrane shape and correlation functions.

\subsection{Power Spectral Density}

\begin{figure*}[t]
 \centering
 \includegraphics[width=\linewidth]{fig2.pdf}
 \caption{Dynamical properties of a membrane at the pinning site. Comparison of modelling (lines) and simulations (symbols) shows excellent agreement across the entire parameter range. a) Power spectral density of a free membrane (eq. (\ref{eq:PSDu})) (red) and a pinned tensionless membrane eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning}) (blue dashed curves for $\lambda/\lambda_m^0=1,3,10$, increasing in the direction of the arrows). The high-frequency regime of the PSD is unaffected by the pinning and the free-membrane behaviour ($\omega^{-5/3}$) is recovered.
b) Low frequency limit of the PSD (eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning_omega_zero})) as a function of the membrane tension $\sigma$ for different pinning strengths ($\lambda/\lambda_m^0=1,3,10$). For large tensions, a $\sigma^{-3/2}$ dependence is recovered irrespective of $\lambda$.
c) Low frequency limit as a function of the pinning strength for different membrane tensions ($8\sigma/\lambda_m^{0}=1,3,10$).  For large bond stiffness, a $\lambda^{-2}$ dependence is displayed. All curves are plotted for $\kappa=20 k_\text{B}T$, $\gamma=3\times 10^{-7}  k_\text{B}T/$nm$^{4}$ and $\eta=1$ mPas.
 }
 \label{fig:Exact}
\end{figure*}

We complement the simulations of thermally fluctuating membrane with the analytic calculations based on the Green's function approach (eq. (\ref{eq:Pinned_membrane_profile_as_aconvolution_of_force_with_the_dynamical_greens_fucntion})). We start with   rewriting  eq. (\ref{eq:Pinned_membrane_profile_as_aconvolution_of_force_with_the_dynamical_greens_fucntion}) as
\begin{align}
 u({\bf r},t) =  \langle u({\bf r}) \rangle +  v({\bf r},t),
\label{eq:mean_plus_fluctuations}
\end{align}
where
\begin{align}
v({\bf r},t) = &\int_{\mathbb{R}^2}\mathrm{d {\bf r}'} \int_{\mathbb{R}}\mathrm{d t}'\  g({\bf r},t-t'\vert{\bf r}') f({\bf r}',t')
\label{eq:Fluctuations_Green}
\end{align}
are the fluctuations around the ensemble averaged static profile \cite{janes2018}
\begin{align}
\langle u({\bf r}) \rangle = &\int_{\mathbb{R}^2}\mathrm{d {\bf r}'} \int_{\mathbb{R}}\mathrm{d t}'\  g({\bf r},t-t'\vert{\bf r}')  \lambda (l_0-h_0) \delta ({\bf r}').
\label{eq:Mean_shape_Green}
\end{align}

Transforming ($t\to\omega$) eq. (\ref{eq:Fluctuations_Green}) gives
\begin{align}
v({\bf r},\omega) &= \int_{\mathbb{R}^2}\mathrm{d {\bf r}'}\  g({\bf r},\omega\vert{\bf r}') f({\bf r}',\omega)
\label{eq:Fluctuation_of_omega_space_profile}
\end{align}
from which the PSD $\langle \vert v({\bf r},\omega)\vert ^{2} \rangle$ can be calculated as (see Supplementary Information)
\begin{align}
\langle \vert v({\bf r},\omega) \vert ^{2} \rangle =&\frac{1}{(2\pi)^2}\int_{\mathbb{R}^2}\mathrm{d{\bf k}}\frac{2\Lambda_k^{-1}}{ (\omega/\Lambda_k)^2 + E^2_k} \times \nonumber \\
 & \times \left\vert 1 - \frac{\lambda g_f({\bf r},\omega)}{1+\lambda g_f({\bf r}=0,\omega)} e^{-i{\bf k}{\bf r}} \right\vert ^2.
\label{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning}
\end{align}

With the hydrodynamic coefficients specified as in eq. (\ref{eq:Oseen_coefficients}), eq. (\ref{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning}) becomes
\begin{align}
\langle \vert v({\bf r},\omega) \vert ^{2} \rangle =&\frac{4\eta}{\pi} \int\limits_0^\infty \mathrm d k \frac{k^2}{(4 \eta k \omega)^2 + (\kappa k^4 + \sigma k^2 + \gamma)^2} \times \nonumber \\
 & \times \left\vert 1 - \frac{\lambda g_f({\bf r},\omega)}{1+\lambda g_f({\bf r}=0,\omega)} e^{-i{\bf k}{\bf r}} \right\vert ^2.
\label{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning_hydrodynamic_coeffitients_specified}
\end{align}

In the absence of the pinning ($\lambda =0$), eq. (\ref{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning_hydrodynamic_coeffitients_specified}) becomes homogeneous in space and reduces to the well-known result
\begin{align}
\left\langle \vert v_f(\omega) \vert ^2\right\rangle &= \frac{4\eta}{\pi} \int\limits_0^\infty \mathrm d k \frac{k^2}{(4 \eta k \omega)^2 + (\kappa k^4 + \sigma k^2 + \gamma)^2},
 \label{eq:PSDu}
\end{align}
which for small and large $\omega$  has the limiting behaviour  \cite{brochard1975, helfer2000, betz2009, betz2012}
\begin{align}
\langle |v_f(\omega)|^2 \rangle =\begin{cases}
	\frac{\eta}{\sqrt{\gamma (\lambda_m^{0}/4 +\sigma)^3 }}, & \omega \ll \omega_0 \\
 	\frac{1}{6\sqrt[3]{2\eta^2 \kappa }} \omega^{-5/3}, & \omega \gg \omega_0.
 	\end{cases}
 \label{eq:PSD_free_limits}
\end{align}
Here,  $\omega_0\equiv \sqrt[4]{\kappa\gamma^3}/\eta$ is a cross-over frequency, defined as the intersection of the lines fitting the low- and high-frequency limits of the spectrum. The low-frequency limit decays with $\sigma^{-3/2}$ for tensions $\sigma \gg \lambda_m^{0}$  (Fig. \ref{fig:Exact}b).

It is clear from Eq. (\ref{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning_hydrodynamic_coeffitients_specified}) that the PSD at the pinning site ${\bf r}=0$  can be recast into
\begin{align}
\langle \vert v({\bf r}=0,\omega)\vert ^{2} \rangle &=\left\vert \frac{1}{1+\lambda g_f({\bf r}=0,\omega)} \right\rvert ^{2} \langle \vert v_f(\omega)\vert ^{2} \rangle.
\label{eq:Single_bond_Power_spectral_density_at_the_pinning}
\end{align}

In agreement with simulations based on eqs. (\ref{eq:Hydrodynamic_equation_for_a_pinned_membrane_explicit}), (\ref{eq:Thermal_noise_mean}) and (\ref{eq:Thermal_noise_variance}) \cite{bihr2015}, eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning}) shows that only the pinning stiffness, and not its length, has an effect on the PSD and that the pinning affects only the low-frequency regime (Fig. \ref{fig:Exact}a). The low-frequency behaviour can be obtained upon combining eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning}) for $\omega=0$ with eq. (\ref{eq:PSD_free_limits}) to yield
\begin{align}
 & \langle \vert v({\bf r}=0,\omega =0)\vert ^{2}  \rangle =  \left( \frac{1}{1+\lambda/\lambda_m}\right) ^{2} \frac{\eta}{\sqrt{\gamma (\lambda_m^{0}/4 +\sigma)^3 }}\nonumber  \\
 = & \begin{cases}
	\left( \frac{1}{1+\lambda/\lambda^{0}_m}\right) ^{2}  \frac{\eta}{\sqrt{\gamma (\lambda^{0}_m/4)^3 }}, &\quad 4\sigma/\lambda_m^{0} \ll 1  \\
 	\left( \frac{1}{1+\lambda\ln(\sigma)/(2\pi\sigma)}\right) ^{2}  \frac{\eta}{\sqrt{\gamma \sigma^3 }}, &\quad 4\sigma/\lambda_m^{0} \gg 1.
 	\end{cases}
\label{eq:Single_bond_Power_spectral_density_at_the_pinning_omega_zero}
\end{align}

Eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning_omega_zero}) shows that the low-frequency spectrum is independent of membrane tension for $ 4\sigma/\lambda_m^{0} \ll 1$ and it decays with $\sigma ^{-3/2}$ for membrane tensions large enough to diminish the effect of the pinning ($\lambda\ln(\sigma)/(2\pi\sigma)\ll 1$) (Fig. \ref{fig:Exact}b). For stiff pinnings ($\lambda/\lambda_m \gg 1 $) the low-frequency limit falls off as $\lambda^{-2}$ (Fig. \ref{fig:Exact}c). On the other hand, for  $\lambda/\lambda_m \ll 1 $, pinning effects vanish even in the low-frequency limit. Interestingly, the cross-over frequency $\tilde{\omega}_0$ for the pinned membrane
\begin{align}
 \tilde{\omega}_0 & = \left [ 6\sqrt[3]{2\eta^2\kappa}\ \langle \vert v({\bf r}=0,\omega =0)\vert ^{2} \rangle \right ]^{-3/5},
 \label{eq:cross_over_frequency}
\end{align}
defined analogously to the one for the free membrane, becomes sensitive to the elastic properties of the pinning as $\tilde{\omega}_0 \sim \lambda^{6/5}$ and as such increases with the pinning stiffness.

\section{Effect of the finite experimental resolution on the fluctuation spectrum}

In order to compare with experiments, it is necessary to account for the finite temporal and spatial resolutions of the set-up \cite{pecreaux2004,monzel2016b}. Averaging the true membrane profile $ u({\bf r},t) $ over a spatial domain $A$ and a time interval ${\tau}$, gives rise the so-called apparent membrane profile $u^{A}_{\tau} ({\bf r},t) $
\begin{equation}
 u^{A}_{\tau} ({\bf r},t) = \int\limits_0^{\tau} \frac{\mathrm d t^\prime}{{\tau}} \int\limits_A \frac{\mathrm d {\bf r}^\prime}{A} u({\bf r} + {\bf r}^\prime, t+t^\prime),
 \label{eq:h_finres}
\end{equation}
from which it is straightforward to derive the apparent PSD (Supplementary Information, section I. A)
\begin{align}
\langle \vert &v^{A}_{\tau}({\bf r},\omega) \vert ^{2} \rangle = \left(\frac{\sin(\omega {\tau}/2)}{\omega {\tau}/2}\right)^{2}  \frac{2}{(2\pi)^2} \times
\nonumber \\
&\times \int_{\mathbb{R}^2}\mathrm{d{\bf k}}\ \frac{\Lambda_k^{-1}}{ (\omega/\Lambda_k)^2 + E^2_k} \left\vert \int\limits_A \frac{\mathrm d {\bf r}'}{A} e^{i{\bf k}({\bf r}+{\bf r}')}\right. \times
\nonumber \\
& \times \left. \left(1 - \frac{\lambda g_f({\bf r}+{\bf r}',\omega)}{1+\lambda g_f(0,\omega)} e^{-i{\bf k}({\bf r}+{\bf r}')}\right) \right\vert ^2.
 \label{eq:apperent_PSD}
\end{align}
The PSD measured around the pinning placed centrally in a circle of radius $R$ is (Supplementary Information, section I. A.1.)
\begin{align}
&\langle \vert v^{R^{2}\pi}_{\tau}({\bf r}=0,\omega)\vert ^{2} \rangle =\left(\frac{\sin(\omega {\tau}/2)}{\omega {\tau}/2}\right)^{2}  \frac{1}{\pi} \times
\nonumber \\
\times &\int\limits^{\infty}_0\mathrm{dk}\ \frac{k \Lambda_k^{-1}}{ (\omega/\Lambda_k)^2 + E^2_k} \rule{0cm}{0.8cm} \frac{4}{R^2}  \nonumber \\
\times & \rule{0cm}{0.8cm}  \left\vert  \frac{J_1(kR)}{k} -  \frac{\lambda}{1+\lambda g_f(0,\omega)}\frac{1}{2\pi} \int\limits^{\infty}_0\mathrm{d k'}\frac{J_1(k'R)}{i\omega/\Lambda_{k'}+E_{k'}}  \right\vert ^2.
 \label{eq:apperent_PSD_at_the_pinning}
\end{align}
Eq. (\ref{eq:apperent_PSD_at_the_pinning}) reduces to eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning}) in the limit ${\tau},R\to 0$.

The high frequency regime of the averaged PSD recovers the averaging behaviour of the free membrane - spatial averaging changes the decay from  $\omega^{-5/3}$ to $ \omega^{-2}$ as previously reported \cite{betz2012}, while finite temporal resolution induces an additional attenuation of $ \omega^{-2}$. Hence, the PSD which is subject to both temporal and spatial averaging decays as $\omega^{-4}$.

\begin{figure*}[t]
 \centering
 \includegraphics[width=1 \linewidth]{fig3.pdf}
 \caption{Effect of the finite resolution (averaging over a circle of radius $R$ and a time interval $\tau$) on the PSD at the pinning (eq. (\ref{eq:apperent_PSD_at_the_pinning})). a) Averaging decreases the difference between the free and pinned PSD's, therefore reducing the effect of the pinning on the PSD. Pinning has no effect on the high-frequency part of the spectrum, for both the averaged and the unaveraged spectrum. b) The low-frequency part of the PSD is a non-monotone function of the spatial averaging area. On the other hand, increasing the averaging area always attenuates the high-frequency components, which in this case fall as $\sim \omega^{-2}$ instead of $\sim \omega^{-5/3}$. c) Time averaging introduces oscillatory behaviour of the PSD for which only the envelope of the PSD is shown. The combined effect of the spatial and temporal averaging gives a $\sim \omega^{-4}$ behaviour of the high-frequency regime . Parameters $\kappa=20 k_\text{B}T$, $\sigma = 10^{-20}  k_\text{B}T/\text{nm}^{2}$ and $\gamma=3\times 10^{-7}  k_\text{B}T/$nm$^{4}$, $\lambda /\lambda^{0}_m$=10 and $\eta=\unit[1]{mPas}$.}
 \label{fig:Spatial_averaging}
\end{figure*}

In the low frequency regime, temporal averaging plays no role for $\omega<1/{\tau}$, while the finite spatial resolution has a more complex effect. Due to the interplay with the effects of the pinning, the low frequency amplitude is not a monotone function of the averaging area (Fig. \ref{fig:Spatial_averaging}). Increasing the averaging area up to some critical size (which is approximately the area affected by the pinning) amplifies the low-frequency components, but further increase of the averaging area starts to attenuate them. This can be understood as a competition of two effects; averaging has the effect of attenuating the low frequency components, as can be seen for the free membrane, but at the same time, averaging reduces the effect of the pinning on the PSD, which amplifies the low-frequency components. Obviously, the later effect is stronger up to the critical averaging area size, after which the first effect dominates. Specifically, for $\omega = 0$ we obtain (Supplementary Information, section I.A.1)
\begin{align}
 &\langle \vert v^{R^{2}\pi}_{\tau}({\bf r}=0,0)\vert ^{2} \rangle = \nonumber \\
&= \frac{4\eta}{\pi}\int\limits^{\infty}_0\mathrm{dk}\ \frac{k^2 }{E^2_k} \left\vert  \frac{J_1(kR)}{kR/2} -  \frac{\lambda}{1+\lambda /\lambda_m}s(R) \right\vert ^2,
 \label{eq:single_bond_averaged_PSD_r_zero_omega_zero}
\end{align}
where for brevity purposes we introduce a reduced coefficient $s(R)$
\begin{align}
s(R)&=\frac{1}{R^2\pi\sqrt{\sigma-4\kappa\gamma}} \times
\nonumber \\
\times &\left(\frac{1-a_-RK_1(a_-R)}{a^2_-}-\frac{1-a_+RK_1(a_+R)}{a^2_+}\right),
 \label{eq:coeff_s_R}
\end{align}
with $a_\pm$
\begin{align}
a_{\pm}&=\left[\frac{\sigma}{2\kappa}\left(1\pm\sqrt{1-\left(\frac{\lambda_m^{0}}{4\sigma}\right)^{2}}\right)\right]^{1/2}.
\label{eq:Free_membrane_Greens_function_coeffitients}
\end{align}

In order to calculate the pinning stiffness $\lambda$ from the PSD, eq. (\ref{eq:single_bond_averaged_PSD_r_zero_omega_zero}) can be inverted,  which upon introduction of coefficients $L$, $a$, $b$ and $c$, yields
\begin{align}
\lambda=\left( \dfrac{1}{L}-\frac{1}{\lambda_m} \right)^{-1},
 \label{eq:lambda}
\end{align}
with
\begin{align}
L=\frac{b}{2a}-\sqrt{\left(\frac{b}{2a}\right)^2-\frac{c}{a}}
 \label{eq:L}
\end{align}
and
\begin{align}
a=&\frac{\pi s^2(R)}{4\sqrt{\gamma(\lambda_m^{0}/4+\sigma)^3}}, \nonumber \\
b=&\frac{4s(R)}{R} \left(\int\limits^{\infty}_0\mathrm{d k}\frac{k J_1(kR)}{E^2_{k}}\right), \nonumber \\
c=&\left(\frac{2}{R}\right)^2\int\limits^{\infty}_0\mathrm{dk}\frac{J_1^2(kR)}{E^2_k} - \frac{\pi}{4\eta} \langle \vert v^{R^{2}\pi}_{\tau}({\bf r}=0,0)\vert ^{2} \rangle .
 \label{eq:coefficients_lambda}
\end{align}
The averaged spectrum is contained in the coefficient $c$. When implemented numerically, eqs. (\ref{eq:lambda}-\ref{eq:coefficients_lambda}) represent a fast and exact method for obtaining information about the pinning stiffness from the experimentally measured PSD. Here we note that the deconvolution of the noise associated with the experimental setting should be performed prior to the extraction of the pinning stiffness.

\section{Discussion and Conclusion}

Our calculation of the Green's function (eq. (\ref{eq:Pinned_Green})) fully resolves the dynamics of an overdamped, permanently pinned membrane in a hydrodynamic surrounding (eq. (\ref{eq:Hydrodynamic_equation_for_a_pinned_membrane})). The solution is general in a sense that it works for any forces acting on the membrane and enables one to study the membrane dynamics in the presence of both non-thermal and thermal perturbations. The later case is resolved in this paper by the calculation of the thermal equilibrium power spectral density (eq. (\ref{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning})). For the specific case of hydrodynamic damping close to a permeable wall, our analytical calculation (eq. (\ref{eq:Power_spectral_density_of_a_membrane_with_a_single_pinning_hydrodynamic_coeffitients_specified})) is verified with Langevin simulations in a broad range of parameters, such as the pinning stiffness, membrane tension, and strength of the non-specific potential, which were allowed to independently vary for several orders of magnitude (Fig. \ref{fig:Exact}). It is shown that the pinning decreases the low-frequency amplitudes of the spectrum and pushes the cross-over frequency (eq. (\ref{eq:cross_over_frequency})) to higher values, while the high-frequency amplitudes remain unaffected (Fig. \ref{fig:Exact}).

Interestingly, the pinned-membrane PSD at the pinning site is given by a product of a free-membrane PSD and a $\lambda$-dependent prefactor (eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning})). Assuming knowledge of the pinning stiffness $\lambda$, this enables inference of the pinned-membrane PSD at the pinning site directly from the free-membrane PSD. This approach has a clear advantage over a direct measurement of the pinned-PSD, as it replaces the pinned-membrane measurement, with a well-established free membrane measurement. On the other hand, if $\lambda$ is not known, it can be easily determined by comparing the pinned- and free-membranes PSDs. The low-frequency limit of the PSD at the pinning site (eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning_omega_zero})) is particularly useful for getting a better understanding of the interplay of the system parameters and shows a $\lambda ^{-2}$ decay.

These relationships, however, may not be observed experimentally due to the finite resolution of the measurements. Specifically, while the effects of the temporal averaging are simple, significant spatial averaging introduces nontrivial modulations of the spectrum and breaks the relation between the free- and the pinned-membrane PSD given by eq. (\ref{eq:Single_bond_Power_spectral_density_at_the_pinning}). In this regime the pinning stiffness can be inferred from the measured PSD with the use of the spatially averaged spectrum (eqs. (\ref{eq:lambda}-\ref{eq:coefficients_lambda})).

A deep understanding of the mechanics of the pinned membrane is crucial for elucidating the role of more complex pinnings, which under typical biological conditions stochastically bind and unbind from the membrane. The stochasticity of this attachment will have additional effects on fluctuations of the membrane which could not be resolved prior to this investigation, and will be subject to a future study.  The results presented in this paper will thus help establishing the connection between functioning of the protein assembly and the properties of the elastic fluctuating membrane, which is important for understanding of the formation of adhesions. Namely, there is a growing body of evidence that the membrane affects the affinity \cite{huppa2010} and the kinetic rates for protein binding \cite{bihr2015, fenz2017}, which in turn affect the fluctuations and the early stage signalling in developing junctions between cells \cite{perez2008}.

The model presented here can be used to measure the elasticity of the bond from membrane fluctuations. Hitherto, it was not possible to interpret these measurements accurately, a task that is enabled now by our current work. Such measurements could then be compared to AFM measurements, which are commonly used to study elastic properties of the linkers.

\emph{Acknowledgments:}
A.-S.S and J.A.J. thank ERCStg MembranesAct for support as well as the Croatian Science Foundation research project CompSoLs MolFlex 8238. A.-S.S and D.S. were supported by the Research Training Group 1962 at the Friedrich-Alexander-Universität Erlangen-N\"urnberg.

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