From the introduction to a lecture presented at the Gregorian University in Rome on the occasion of the fiftieth anniversary of the Second Vatican Council's Decree on Ecumenism, 21 November 2014.
The obstacles to church unity loom, I think, larger than ever—but not larger than our hopes. We are started on a long journey for which some of the legislation now signed, sealed, and delivered by the Council will serve as passport and guide. I have never before been a party to undertaking a task quite so specific, which I knew in advance could not be accomplished in my lifetime. It has been good to be in at the start of it—and every fifty years or so I intend to look back on this terrestrial scene, if the looking is good from where I am, to see how the work is getting on.
Pope—now Saint—John XXIII has been rightly called "the spiritual father of the Decree on Ecumenism." It was he, of course, who convened Vatican II and made sure that ecumenism was central to its deliberations by creating the new Secretariat of Christian Unity and engrafting it into the structure of the Council. At the pope's insistence, both Protestant and Orthodox observers were invited to the Council. Although an early draft of the Decree on Ecumenism was shown to Papa Giovanni shortly before his death in 1963, by the time it was finally accepted, he had left this world for a better place. He wrote these words in his diary: "Shall it be given me to see the end of the Council? Then God be praised! Shall it not be given? Then in that case I shall experience the blessed conclusion of the Council from heaven, to which the divine mercy shall have called me." Without transgressing the limits of what we know about the state of the blessed departed, could we perhaps think that not only St. John XXIII and Douglas Horton but also a host of others within the company of the redeemed have some special interest in our gathering today?
I am honored by the invitation to speak as a Protestant on this occasion, but I speak as a Protestant who is also an evangelical and a Baptist, both latecomers to the ecumenical conversation. This itself is some indication of how far we have come for, although the Baptist World Alliance was invited to send official observers to the Council in 1962, the leaders of the BWA decided, after a full day of deliberations, that it would cause too much division within their own ranks to do so. In recent decades, however, the Baptist World Alliance has completed two phases of bilateral dialogues with the Pontifical Council for Promoting Christian Unity. The most recent dialogue, "The Word of God in the Life of the Church," dealt with communion and covenant, with the authority of Christ in Scripture and tradition, with baptism and the Lord's Supper as the visible words of God in the koinonia of the Church, with Mary—affirmed for the first time in a Baptist document as Theotokos—as a model of discipleship in the communion of the Church, and with oversight as a gift of Christ to the Church to enable the ministry of the whole people of God.
What the Holy Father was hoping to stir up—or rather to pray down—was a new Pentecost. But less discerning souls, especially many in the media, found other ways to frame what by Catholic reckoning would be the twenty-first ecumenical council in the history of the Church. These included existentialism, closely linked to individualism, a philosophy stressing subjective self-realization and rejecting any generally valid truth as totalizing and repressive; others invoked internationalism, with the demise of colonialism and the rise of new nation-states; still others spoke of universalism, not so much in Origen's sense of apokatastasis but rather as a denial of particularity, tradition, and history that could in any sense claim to be privileged.
In its own way, of course, the Council would attend to these issues—conscience and freedom, especially religious freedom, are among its great concepts. And during the fourth session Pope Paul VI would become the first reigning pontiff to address the General Assembly of the United Nations. But the historic significance of Vatican II is this: It was the first ecumenical council in twenty centuries to address as its main theme the doctrine of the Church and to do so not in response to an external crisis such as the Protestant Reformation (Trent) or the French Revolution (Vatican I) but rather in terms of its own internal and spiritual renewal.
At Vatican II the Catholic Church entered the ecumenical movement and by doing so transformed it. The Council was not called to address the problem of Christian disunity as such, but it soon became clear that the kind of reform that was required ad intra could not be carried forward without serious attention to the scandalous divisions among the people of God. Thus, chapter one of Unitatis Redintegratio cites what has become the locus classicus of all ecumenical endeavors for the Orthodox, Catholics, and Protestants alike, namely, the prayer Jesus offered to his heavenly Father for all who believe in him "that they may all be one. As you, Father, are in me and I am in you, may they also be in us, so that the world may believe that you have sent me" (John 17:21).
The fact that Christians today are divided—most outrageously at the Table of the Lord—contradicts the prayer of Christ and countermands the Church's missionary task to communicate and display the love of God to all peoples. Today, even more urgently than in 1964, the quest for Christian unity and the task of world evangelization are inseparable.
Timothy George is the dean of Beeson Divinity School of Samford University (Birmingham, Alabama, USA) and chair of the Doctrine and Christian Unity Commission of the Baptist World Alliance. His email address is tfgeorge@samford.edu.


text:
Home News Kerry Washington makes a rare appearance with husband Nnamdi Asomugha after...
Kerry Washington makes a rare appearance with husband Nnamdi Asomugha after the birth of her son
Kerry Washington makes a rare appearance with husband Nnamdi Asomugha after the birth of her child
The Olivia Pope of Scandal is finally Free like a Bird once again after the Birth of her Second Child with Husband and former NFL Player Nnamdi Asomugha.
The Two where seen in Public together for the First time in while since rumors about a Possible Split come on the web some months ago while Kerry was still pregnant with their second child.
The Parents of two wonderful babies left their cuties at home to attend the Ambassadors for Humanity Gala Benefiting USC Shoah Foundation in Hollywood, Los Angeles on Thursday.
Her husband was all smiles as they mingled with Hollywood finest directors Steven Spielberg and honoree George Lucas at the event.
Prior to giving birth, the 39-year-old actress said at this year's Emmy Awards that she was nervous about having two children in the house. She said:
"I'm an only child so every time the family grows it uh… it brings up a little bit of anxiety," she explained. "But it's fantastic. I'm really happy."
The the 39-year-old actress gave birth to their second child, a son, Caleb Kelechi Asomugha. This marks the Scandal star's first public appearance since giving birth to their son in October.
SO SAD! Emirates Female Crew Member Dies After Falling Off Plane (See How It Happened)
Previous articleTaylor Swift and Zayn Malik release New song tilted 'I don't wanna live forever' for Fifty Shades darker soundtrack
Next articleMila Kunis and husband Ashton Kutcher step out for the first time since they welcomed a baby boy
Idia Aisien celebrates birthday in a different way as she clocks a new age...
One of the all time model, Idia takes to her social media page to celebrate her birthday in grand style. It has always become the...
Curvy Sister Of Ooni's Wife, Similoluwa 'Steals Show' With Her Backside At Royal Event...
Johnson Olumide - July 20, 2021 0
A trending video has shown the moment Similoluwa, the sister of Olori Moronke Naomi Silekunola, wife of the Ooni of Ife, Oba Enitan Adeyeye...
Serena Williams Shows of Her Nude Side Boob in Photoshoot for Harper's Bazaar
34-year-old Serena Williams Displayed her Nude Side Boobs in a Photoshoot for Harper's Bazaar February Edition. (adsbygoogle = window.adsbygoogle || ).push({}); The 21 time Grand Slam winner uploaded...
'Dont Send my Future Husband Away' – Bbnaija's Koko reacts to the pregnancy rumor...
Johnson Olumide - June 10, 2020 0
Nigerian Business woman, Fashion designer, content creator and reality star Abiri Oluwabusayomi aka Koko or Khloe has finally reacted to rumors of her been...
Timaya and his 3rd baby mama, Dunnie, celebrates their daughter 1st birthday (Photo)
Veteran singer and songwriter, Timaya and his third baby mama, Dunnie, have taken to social media to celebrate their daughter, Maya, on her 1st...

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to keep text and image in a single line inside a div? I am trying to put title and content in a div vertically parallel to image div,
My jsfiddle . But when ever the text content length in increasing the image is coming in next line.

.archive .woocommerce-product-page .grid {
    padding-left: 0;
    padding-right: 0;
    margin-bottom: 20px;
}
.card--sub-category.card--product-sub-cat {
    /* display: table; */
    margin: 30px 10px 30px 10px;
    /* background: #ffffff; */
    /* width: 100%; */
    padding-bottom: 30px;
    border-bottom: 1px solid rgba(0, 0, 0, 0.075);
}
.sub-category-content {
    /* height: 100%; */
    overflow: auto;
}
.sub_category_card__content {
    /* padding-left: 10px; */
    padding-left: 0;
    font-weight: normal;
    /* float: left; */
}
.sub-cat-description .category-desc {
    margin-bottom: 0;
    font-weight: normal;
    text-align: left;
    display: block;
    font-size: small;
    color: #919191;
}
.product_post__thumbnail {
    float: right;
}
.product_post__thumbnail img {
    height: 75px;
    width: 75px;
    border-radius: 3px;
    vertical-align: bottom;
    border: 1px solid rgba(0, 0, 0, 0.075);
}

                            Contracts and Agreements

Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs

I want the text to take all the sapce when there is no image.

A: U can try add 'width' and 'float: left' on
 tag, something like this:
.sub-cat-description .category-desc {

    float: left;
    width: 200px;

    margin-bottom: 0;
    font-weight: normal;
    text-align: left;
    display: block;
    font-size: small;
    color: #919191;

}

if u want to make it responsive, you should change your html structure and apply something like this:

#img_container{
  position: relative;
  float: right;
  width: 150px;
  height: 135px;
  padding: 0px 0px 12px 12px;
}

 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Pellentesque vehicula erat augue, non mattis enim pretium non. Morbi sed purus a erat condimentum finibus et a diam. Quisque eleifend felis a pretium lobortis. Aenean eu porta libero. Donec nec ante in felis condimentum dapibus. Nam tincidunt mauris imperdiet posuere ullamcorper. Nam suscipit ex nulla, et ullamcorper ligula lacinia et. Nunc et nulla nunc. Sed vestibulum mi mauris, ut commodo urna porttitor id. Sed quis maximus elit.

A: I believe that using display: flex would be the best approach here.
Here is a great article on flex -> https://css-tricks.com/snippets/css/a-guide-to-flexbox/
Find bellow your html code with 2 lines of css. :)

.sub-category-content{
   display: flex;
   align-items: flex-start;
}

.sub_category_card__content{
    margin-right: 10px
}

.sub_category_card__content h2 {
    margin: 0;
}

.product_post__thumbnail > img {
    height:  75px;
    width: 75px;
}

Contracts and Agreements

Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs

A: This can be achieved generally by simply placing the image inside of the paragraph tags.

Hello, this is some text.

https://jsfiddle.net/vnnf7yxz/

A: Try to get your divs to float left or right.
For example:
`

 link

Title

Pic

Text

`

A: Finally achieve it.

                            Contracts and Agreements

Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs Review or create business contracts, review of employment contracts, consulting agreements and NDAs

and css-
   .card--sub-category.card--product-sub-cat {
    margin: 30px 10px 30px 10px;
    padding-bottom: 30px;
    border-bottom: 1px solid rgba(0, 0, 0, 0.075);
}
.sub-category-content {
    overflow: auto;
    padding-left: 0;
    font-weight: normal;
}
.product_post__thumbnail {
    float: right;
}
.product_post__thumbnail img {
    height: 75px;
    width: 75px;
    border-radius: 3px;
    vertical-align: bottom;
    border: 1px solid rgba(0, 0, 0, 0.075);
}
.sub-category-title {
    font-size: 1rem;
    font-weight: bold;
    color: #484848;
    margin-bottom: 4px;
    padding: 0;
}
.sub-cat-description .category-desc {
    margin-bottom: 0;
    font-weight: normal;
    text-align: left;
    display: block;
    font-size: small;
    color: #919191;
}

jsfiddle of my working version

redpajama_set_name: RedPajamaStackExchange


text:
Here's the robotic vehicle that will carry equipment for US troops
The Army has picked an eight-wheel drive version of the MUTT for its SMET program. ( Lance Cpl. Rhita Daniel/U.S. Marine Corps)
WASHINGTON — The U.S. Army has selected General Dynamics Land Systems' Multi-Utility Tactical Transport, or MUTT, for its Squad Multipurpose Equipment Transport unmanned ground system program of record.
The initial contract for the eight-wheel drive robotic vehicle totals $162.4 million and includes support hardware, user training and technical support. The contract will wrap up at the end of October 2024, according to an Oct. 30 Defense Department announcement.
GDLS will produce 624 systems for the Squad Multipurpose Equipment Transport, or SMET, program under the contract and will begin delivery in the second quarter of fiscal 2021, an Army spokesperson confirmed to Defense News.
Four companies were chosen at the end of 2017 to compete to build the robotic vehicle that will help troops carry equipment on the battlefield.
Dirty work: Robots take on complex obstacles in US Army exercise
Learning by doing, the Army is assessing how robots can be an asset on the battlefield.
A team of Applied Research Associates and Polaris Defense; General Dynamics Land Systems; HDT Expeditionary Systems and Howe & Howe were selected to build 20 platforms each that were issued to two infantry brigade combat teams for testing and analysis of utility in the field.
Polaris' MRZR X was evaluated as well as HDT's six-wheel drive Global Hunter WOLF, or Wheeled Offload Logistics Follower. Textron-owned Howe & Howe offered its Grizzly unmanned vehicle, which is powered by an electric engine.
HDT's Global Hunter WOLF was recently picked, along with three other teams to include Textron and QinetiQ North America, to compete to build vehicles for the Robotic Combat Vehicle-Light effort.
The Army selected those teams from an array of companies chosen to participate in a demonstration event in the fall of 2017 at Fort Benning, Georgia. Other companies that participated in that demonstration included American Robot Company; Lockheed Martin; AM General; Robo-Team NA; and QinetiQ North America.
For the SMET program, the Army was looking for a vehicle that can carry about 1,000 pounds worth of soldier equipment. This equates to lightening the load of nine soldiers across an infantry squad. The Army wanted the robots to be able to travel 60 miles over three days and to be able to provide a spare kilowatt hour of power while moving and at least 3 kilowatt hours while stationary.
US agency forecasts cost for missile defense plans over next decade
Lebanese military to receive 100 armored vehicles from UK to secure borders
Australia selects Boeing Apache as next armed reconnaissance helicopter
Why America needs a layered homeland missile defense
Pentagon weapons tester wants to delay fielding of new Army tactical network tools


Abstract. This study examines the factors that influence resistance to change in a business organization. Four factors were selected to test the possibility of having a simple but comprehensive model that can predict resistance to change.... It considers the phenomenon of resistance to change in nursing academia, which has created obstacles to revising pedagogical processes, resulting in ongoing difficulties in creating change in the practice setting. A model based on transdisciplinary practices for creative change in nursing is described.
1/10/2008�� change; possible resistance to change among governors, parents and the local community. Successful innovation was linked principally to strong leadership at all levels.
Abstract. The aim of this research is investigating the relationship between big five personality traits and resistance to change. Extraversion, agreeableness, conscientiousness, emotional stability and openness to experience are five traits hypothesised to have a significant and negative relationship with resistance to change.


text:
SuperPower 2 Download (2004 Strategy Game)
Strategy Games:
Download full SuperPower 2:
Download (1.16 GB)
SuperPower 2 screenshots:
This political simulation sequel gives players control of their favorite world-power country to pursue political, economic, and military goals, in cooperation or competition with other nations of the world. As in the original SuperPower, this follow-up runs on a complicated model of dynamic, interrelated factors, and AI that has each computer-controlled opponent analyzing from its own perspective and making decisions in its own best interests. New features in SuperPower 2 include multiplayer capabilities, over a LAN or the Internet, and the availability of editing tools and developer support to encourage creative modding of the core game.
The original SuperPower was one of the most unintentionally hilarious games you could ever hope to play. Bhutan might suddenly decide to invade Uruguay. A border clash might erupt between Lithuania and Botswana, regardless of the minor detail that they don't share a border. Poland might pick a fight with Mexico for no good reason, sending troops overseas faster than you could say "Bush Doctrine." It was like a wacky sitcom except with crazy countries slapping each other instead of mismatched roommates. Nations Behaving Badly.
Unfortunately, everything beyond the unintentional hilarity was tedious and obscure. SuperPower 2 addresses this problem by removing the unintentional hilarity, giving nations preset relationships that keep them from engaging in trans-global slapfights. Which leaves only the tedium and obscurity of the original SuperPower.
At first glance, the game appears to be an epic undertaking, along the lines of Paradox Software's challenging but manageable Europa Universalis titles. When you boot up SuperPower 2, you're greeted with a colorful globe, rotating slowly under a wispy coat of clouds. When you look closer, you'll notice the entire world is divided into its component countries and provinces, with major roads and rivers visible if you zoom in close enough. When you start a game, you can select any country and choose your own the victory conditions (although most of the victory conditions mentioned in the manual are missing). Alternatively, you can lend the proceedings a bit more focus by choosing one of nine scenarios. Try to invade Iraq, lead France into economic health, or lift the trade embargo on Cuba. Most of these are little more than tutorials, however; SuperPower 2 would have fared better with more developed scenarios.
Once you're situated in the game proper, it still looks promising. There are overlays to give you a good overview of the globe, which you can spin adroitly under your fingertips. When you click on a country, there are three buttons to peer into its economic, military, and political conditions. And here's where anyone who tried to play Master of Orion 3 might start to feel a little queasy. Once you've opened these windows, you'll find yourself in a Russian nesting doll of windows, tabs, and displays, invariably tucked behind tiny buttons without hotkeys or cross-links, all crammed with information you might never figure out even if you read the moderately helpful manual. All the while, messages are constantly scrolling past a one-line window, alerting you that four people died in a flood in Lithuania, that Albania has increased its tax rate .5%, and that Surinam just had a bountiful harvest. Occasionally you'll get a terse and marginally helpful warning from one of your advisors.
This sort of complexity and detail can work, as the aforementioned Europa Universalis demonstrated. But SuperPower 2 carries over from its predecessor one of the cardinal sins of game design: it consists almost entirely of making choices whose effects are unclear and miniscule. So much of what's going on is hidden under the surface, with very little feedback about why or even whether something happens, even once you've digested the manual. For instance, you can proscribe languages and religions, which the manual says will increase instability in your country. But in the same paragraph, the manual tells you that allowing multiple languages and religions can also increase stability. So when that stability bar inches oh-so-imperceptibly from 30.6% to 30.7%, not only do you not know why, but you probably won't even notice.
Nor will you care. There's nothing by way of a hook to grab your imagination. Playing Iran's mullahs doesn't feel any different from playing the U.S.'s Republicans. Researching and building a new tank doesn't do anything to flesh out battles beyond a bunch of numbers ticking down for some unknown reason. The new treaty options could have given injected a bit of personality, but instead just provide another thick tangled list that might nudge a slider bar a pixel to the left or perhaps add a few million dollars to a multi-trillion dollar sum. There is no attempt to hide the fact that every country is nothing more than a collection of bald data driven by inscrutable formulae.
And because the game is so devoid of personality, it's not even engaging as a way of experimenting with nightmare scenarios. There's nothing satisfying about taking control of the U.S. and changing it to a military dictatorship without freedom of speech or women's suffrage, only to see your political standing inch to the right and maybe your approval rating dip for a while.
SuperPower 2 has pretty slick multiplayer support in that you just start a multiplayer game just like a normal game, with the difference being that anyone can jump into any country that isn't taken by a human player. But for all intents and purposes, it's not very different from a single-player game since there's not much meaningful interaction among countries. You're left with little to do but cobble together a few treaties to boost your economies. In fact, most online multiplayer games have been plagued with bored newcomers randomly invading other countries or lobbing nukes around just for the hell of it. To add insult to injury, if the host loses an election or if his country is eliminated, he has to leave the game running with nothing to look at but a window that says: "You've been eliminated but don't close this window or you'll shut down the server!" It's hard to imagine that SuperPower 2 will develop much of a multiplayer community.
Finally, it doesn't help that the military element of the game is utterly ludicrous. When the shooting starts in SuperPower 2, any pretense it had towards being a serious simulation goes right out the window. In one of SuperPower 2's most outrageous misrepresentations, it's a simple matter to nuke Iraq's military out of existence and then just roll a few men in afterwards to annex the country. Tiny army icons can shuffle around the globe at supersonic speeds, without any concern for crucial real-world issues like logistics, supply, or interdiction. When armies butt heads, they just tick down their counters like battling cells in a spreadsheet.
In fact, that's pretty much SuperPower 2 in a nutshell: a bunch of pointless hand-waving in a half-hearted attempt to pawn off a ponderous spreadsheet as a game.
People who downloaded SuperPower 2 have also downloaded:
SuperPower, Supreme Ruler 2010, Stronghold: Crusader, Sudden Strike 2, Theatre of War, Sudden Strike: Resource War, Sudden Strike, Stronghold Legends


In the world of Digital TV, Multi-System Operators (MSO's) are facing the challenges of a continuously changing experience of broadcasting. In this heavily competitive market consumers are using more and more bandwidth, forcing MSO's to innovate and facilitate these demands.
What if MSO's want to add a series concept to their set-top box in order to provide a 'watch next episode' functionality? When the back-office doesn't support this concept and the vendor is not capable to extend the back-office within time and money constraints, the operator needs to go for an external customization based upon the current supported back-office functionality. With the SeriesSoftLinker application, Hightech ICT and Divverence specialists have developed a solution that removes these barriers.
The SeriesSoftLinker is a 24/7 running application that monitors an ingest folder for new TVA file ingests. On startup it requests a Content Management System for a full TVA file drop, so that after processing this full TVA file the SeriesSoftLinker is aware of the complete catalog structure.
After each ingested file is processed by the SeriesSoftLinker, it analyses the changes and determines the desired 'state' for each title (i.e. whether it should have a series softlink or not). For each title the actual 'state' is retrieved via the OnlineApi and transformed via OnlineApi call to the desired 'state'.


duchess fare: Nancy Braithwaite ~ "Simplicity"
Something to look forward to with Fall.... Seasoned interior designer Nancy Braithwaite's (written previously about here + here) long awaited premier design book, Simplicity, will be hitting bookshelves October 21 (cover above). Atlanta based for over 40 years, Nancy's design aesthetic translates a signature style that seamlessly blends modern with craft through scale, color, and selected furnishings. Included below are images of Nancy's custom designed (exterior & interior) Kiawah Island, SC home, featured in Veranda's March 2011 issue.... Her home's living room serves as inspiration for the book's cover.


This category combines all articles with unsourced statements from November 2012 (2012-11) to enable us to work through the backlog more systematically. It is a member of Category:Articles with unsourced statements.
Pages in category "Articles with unsourced statements from November 2012"
This page was last changed on 26 March 2013, at 04:32.


text:
interview | john paul fauves
Baslisa (Mixed Media, 2017)
Grabbing my soul (Mixed Media, 2018)
Nothing escapes John Paul Fauves' scope. From Trump to Disney, this Costa Rican contemporary artist takes pop culture critiques to new levels with his "disorienting" collaging techniques. Full of colour and commentary, Fauves' work questions our attachment to social media and takes shots at mainstream culture. Taking his name from the Fauvist art movement, his pieces have been exhibited in cities like New York, LA, Miami and Madrid — among many others. His solo exhibitions, A Loss of Innocence and The Mickey Me Collection, are a clear example of Fauves' pervasively poignant style. Schön! caught up with the masked-artist to talk about his upcoming exhibition at Scope, his Costa Rican roots and pop-expressionism.
You live and work in San José. Does living in Costa Rica affect your craft in any way?
I'm very comfortable in my studio and home. The city can absorb you if you let it. Also, nature, in particular the beach, plays an important factor in my life. However, I feel that there is not as much opportunity to emerge as an artist in this country. So, before social media became such a game changer for artists, I had to work in a different field. But, in this day and age, the world has become pretty flat (not conspiracy-wise) in globalizing every country. The internet has connected humanity so now it's easier to be further away from big cities and still be aware of what is going on in the world.
Jaguar Pizza Mouth (Mixed Media, 2017)
Mickey and friends (Mixed Media, 2017)
Most "contemporary artists" cave to societal pressure and resort to the city living. Being born in Costa Rica, why have you decided to stay?
Actually, I used to live in Madrid and had lots of fun back in the day… maybe a bit too much fun. So I definitely don't need big cities anymore. I think they live inside of me. Luckily, as an artist, I have been given many opportunities to exhibit my work on an international level. This has presented me with an amazing "excuse" to travel. As a matter of fact, I just got back from my latest trip to LA. I worked in this spectacular pop up event alongside some distinguished international artists at La Peer Hotel in West Hollywood. My frequent travel to big cities gives me enough of a dose of the city life. I wouldn't trade the cosmos of Costa Rica, my life at my studio and the fact that I can stay close to my 3-year-old son, for anything.
Gucci in Wonderland (Mixed Media, 2018)
You trained in business but never stopped painting and after "a period of hedonistic self-destruction," you made art your priority. What did that hedonistic self-destruction entail?
At that time, I thought that the right way to be an artist was to die like one and I was very close to death several times due to my substance abuse. I had a lot of resentment and hadn't found my place in life. I always loved to paint, but at that point, I didn't have the confidence to pursue a career in art properly. Environmental factors also played a major factor in my scepticism, I never had a support system. Also, people here made me believe I was not good enough to succeed in art. So, I found art and the hedonist lifestyle a perfect escape from my "nine to five" job. I felt like a superhero or an actor living a double life. During the day I wore the normal office mask and then at night, the wild beast would come out with paint and drugs and crazy adventures that I don't think I can write down here…
Gucci Savage (Mixed Media, 2018)
Alice Land (Mixed Media, 2017)
Fauvism inspires your art greatly, as seen in the vivid colours and lack of classical order. What precise aspects of this movement attracted you so much that you even named your art persona after it?
Several aspects actually: starting with the wild beast meaning behind it since it was all that represented my life. And in certain aspects, it was the only thing that could tame the beast. Art actually saved my life. I was also inspired by the use of colours and the technique of painting directly from the tube. I always did that as a young child and can still remember my art teacher complaining that I wasn't mixing the colours on the pallet properly. Plus there is the fact that this movement went against the odds and the tradition and became transgressive for their time, something I'm very passionate about today.
IKEA (Mixed Media, 2018)
Saturday (Mixed Media, 2017)
Do you feel like John Paul Fauves is a Warholian-like art persona or is it purely yourself?
Definitely Warholian, Basqiolian, Picassolian, Liveolian, Mickeyolian, Godolian… [laughs] and the list goes on. I'm the product of my life experiences, influences and of the people and actions that have inspired me.
Some people describe your work as neo pop-expressionism. Would you agree? How do you describe it?
I do like that term and think it's well related. However, if I had the option, I would like to describe it as "transgressive art", since that is what inspires me the most. I'm in constant search of uniqueness and originality.
In the morning (Mixed Media, 2018)
Coyboy II (Mixed Media, 2018)
Your work questions identity and our infatuation as a society with mainstream culture and social media. Is there a specific reaction you hope to cause with your paintings?
Yes, that specific reaction is to break the illusion of self and the idea that the world rotates around us. There is so much noise and propaganda that people want to solely build and consume in an external need for satisfaction. We are looking the wrong way. It's actually in silence and in an inward journey where we find peace and true happiness.
Are you still working on your series No Profile Picture? What inspired you to start it?
I'm working on it in parallel to Micasso, which is part of the Mickey series. The main inspiration is very similar in all my collections. As I mentioned before, it is about the detachment of ego. As we grow, we are bombarded by information and experiences that mould our personality, but sometimes [they] also make us forget who we are and why we are here, on this planet. My No Profile Picture series is based on the icon "no display picture" you find in WhatsApp, Facebook and Instagram. It is the global icon representing "no image". In a certain way, this icon makes your social media seem uncool or scary. Posting selfies and photos of trips and achievements are the norm we have grown accustomed to. I'm trying to give this no profile concept a place in the established phenomenon that represents your true self, or your soul, to put in other words. In other words, we are not how we think we are, we are much more than a name, a career, a parent or property owner. We are spiritual beings having a human experience.
Thrift shop Mickey (Mixed Media, 2018)
NO Mickey (Mixed Media, 2018)
Your art is a take on capitalism and the self-inflicted pains and pleasures our society goes through via external distractions and social media, specifically. Knowing you have to promote yourself via the mediums you critique, how do you escape falling into hypocrisy?
Well, there is no better seller than the one that knows his product. I represent all this hedonism. I'm proud and embrace my past because it helped me to wake up my own personal fight of the bondage of self.
Now, regarding promoting myself through social media, I don't see it that way. I use it as a platform for expression to the outside world; not as an egocentric need. It can be tricky and addictive so it's a daily effort not to fall into the narcissism of ego-boosting traps. I'm not critiquing the platform as I am no stranger to it, I'm just pointing out that there is another way to use it rather than what we are customary to. In general, criticizing is not a word I feel comfortable with since everybody has their own level of understanding in life and I do respect that.
Fight Club (Mixed Media, 2018)
I read that you are focussing on "the mass-production of the individual". What do you mean when you say?
I don't remember saying that [laughs] but well, just like art, words also come from sporadic inspirations. What it means is that we are all one energy, yet we don't even know ourselves. We have to make more effort in searching within us rather than in external possessions.
You are showing at Scope Basel shortly. What can people expect?
There is a Buddhist quote that says "expect nothing and accept everything and you will never be disappointed". No, but really, I'm very excited about Scope. I'm exhibiting with an exciting new Milan-based gallery called One Arts Club alongside CB Hoyo and Roberto Del Rio, whom I consider to be good friends and visionary artists. All I can say is that every single painting is like a picture of one's soul. So, they can see a soul if they know how to look.
John Paul Fauves' artwork will be exhibited at One Arts Club, Scope Basel, from June 12 to 17. Check out a full portfolio of his work here.
words. Sara Delgado
All images courtesy of the artist and Julia Mozheyko @ JM Art Management.
Discover the latest issue of Schön!.
Now available in print, as an ebook, online and on any mobile device.
by Schön! Magazine / June 11th, 2018
Tags: Art, Basel, John Paul Fauves, Sara Delgado, Scope Basel
take me to jupiter | k-swiss' new collaboration features lil jupiter and luisaviaroma
Sportshoes have taken over the…
review | protest! at the irish museum of modern art
In the closing minutes of…
interview | madison iseman
Despite hailing from Myrtle Beach,…
luo yang's "new generation" explores china's youth
A follow-up from her ongoing GIRLS…
anton yelchin's provocative beauty | interview with curator alessio de'navasques
A leader in culture, born to…


The new costing module evaluates economics based on Icarus technology. The approach used in the technology doesn't rely on capacity-factored curves for equipment sizing, nor does it rely on factors to estimate installation quantities and installed cost from bare equipment cost. Instead, it follows industry-standard design codes and procedures to represent equipment with associated plant bulks, and cost modeling and scheduling methods to estimate the cost of project.
The Mapping and Sizing steps can be individually performed or can be skipped in favor of an "Auto Evaluation" based on default-assigned mappings and sizing algorithms.
The costing engine is Aspen Process Economic Analyzer (APEA). By activating the economic module, the Aspen HYSYS simulation results automatically transfer to APEA. The module develops estimates based on a "standard basis file" which includes company-standardized, project-standardized, and the geographic cost basis (US Gulf Coast, Europe, Middle East, UK, and Japan) information.
A key step in economic evaluation with the new integrated evaluation feature is the mapping of each simulator model (unit operation) to one or more process equipment. For example, a distillation column in Aspen HYSYS might be mapped into several items such as a trayed tower, a kettle-type reboiler, an overhead condenser, a reflux pump, and a horizontal drum (Figure 2). The new workflow has both the ability to automatically establish "default" mappings as well as the capability to over-ride these mappings and substitute the user's own mappings. The user can change, remove, and add equipment during the mapping process.
Sizing of the equipment is performed using the available simulation data and the default sizing procedure; missing data is estimated by the system. The default material of construction for all equipment is carbon steel. Users can review the sizing and materials of construction and override estimated sizes, revise material of construction, and enter values for unsized equipment.
Construction expenses - Fringe benefits, Burdens, Insurance, Scaffolding, Equipment Rental, Field services, temporary constructions, etc.
The utility cost of a project is determined by the Economic module based on the appropriate process utility fluids selected either by the user or by the Sizing Expert from the list of 21 default utility streams already present in the system. Once the utility resources are selected, the utility cost for every utility resource used in the project is determined during the operating cost evaluation.
The results of the economic evaluation and the equipment summaries can be created in Excel format as a complete project economic report. The summary and detailed results can be reviewed in order to study the feasibility of the design and to compare process alternatives.
Contingency (defined based on specified process description, process complexity, and project type), process control, location, engineering start date, soil conditions, vessel design code, and level of instrumentation are the general specifications affecting capital and operating costs. The costing scenario created by Aspen HYSYS can be opened directly by Aspen Process Economic Analyze (APEA) or by Aspen Capital Cost Estimator (ACCE) for further development, define a custom model for sizing equipment or tuning of the cost estimate.
In general, the new feature will be of interest to many HYSYS users due to its functionality in reasonable cost estimation of a project through a simple system and in providing a way to study process alternatives from an economic point of view early in the process design. However, it should be noted that the sizing and the cost evaluation of a project are performed using default methods and procedures and missing data is estimated by system. So, if the user enters more detailed information in the system based on the design criteria and the scope of the project, the estimated cost of the project would be more accurate.
1. "Aspen Process Economic Analyzer V7.0 User Guide", Aspen Technology Industry (July 2008).
2. D. McCarthy, R. Beck, and G. Dissinger, "Getting Started with Relative Economics in Aspen HYSYS", Aspen Technology Inc. (2011).


text:
\section{Introduction}

The goal of unsupervised semantic image segmentation is to divide an image into semantically distinct coherent regions, \emph{i.e.}, regions corresponding to objects or parts of objects. It plays an important role in a wide range of computer vision applications, such as object recognition and tracking and image retrieval \cite{zhao:2010,shi:2000,comaniciu:2002, felzenszwalb:2004}.  Yet, in many images, widely used image segmentation methods fail to perform.  Specifically, imagery in which there are smooth gradients and transition regions are poorly-addressed with the many crisp image segmentation methods in the literature.    For example, consider the photograph in Fig. \ref{fig:afog} where the gradually thinning fog blurs the boundary between the foggy sky and the mountain, a sharp boundary between the ``fog'' and ``mountain'' topics does not exist. Similarly, in Fig. \ref{fig:bsun} consider the gradually fading sunlight or in Fig. \ref{fig:csonar} consider the gradually vanishing sand ripples shown in the Synthetic Aperture SONAR image of the sea floor.  In both of these cases, sharp boundaries between the ``sun'' and ``sky'' topics or ``sand ripple'' and ``flat sand'' topics do not exist.  In this paper, we present a Partial Membership Latent Dirichlet Allocation (PM-LDA) to address image segmentation in the case of gradients and regions of transition.

\begin{figure}[!htb]
\centering
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1\linewidth,height=0.8\linewidth]{fog1_1.pdf}
\captionsetup{labelformat=empty,,skip=0pt}
\caption{(a)}
\label{fig:afog}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1\linewidth,height=0.8\linewidth]{sun.jpg}
\captionsetup{labelformat=empty,skip=0pt}
\caption{(b)}
\label{fig:bsun}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1\linewidth,height=0.8\linewidth]{sonar2.pdf}
\captionsetup{labelformat=empty,skip=0pt}
\caption{(c)}
\label{fig:csonar}
\end{subfigure}
\caption{Imagery with regions of gradual transition. (a) Image with gradual transition from fog to mountain.
(b) Sunset image with gradual transition from sun to sky.
(c) SONAR image with gradually vanishing sand ripples. }
\label{fig:sunset}
\vspace{-4mm}
\end{figure}

Inspired by the success of Latent Dirichlet Allocation (LDA) \cite{blei:2003} in discovering semantically meaningful topics from document collections, many have successfully applied LDA or its variants to image segmentation \cite{russell:2006, cao:2007, wang:2008, zhao:2010,andreetto:2012}.  These unsupervised semantic image segmentation methods differ from traditional (\emph{i.e.}, non-hierarchical/flat) segmentation methods  (\emph{e.g.}, normalized cuts algorithm \cite{shi:2000}) by estimating and describing additional inter-segment relationships. Namely, unsupervised semantic image segmentation methods over-segment imagery and then group these ``visual words'' into topic clusters such that small segments from the same object class can be combined into a complete object and provide a comprehensive organization of the larger scene.   In other words, unsupervised semantic image segmentation methods cluster imagery hierarchically in which the lower level corresponds to an over-segmentation of the imagery and the higher level groups the over-segmented pieces into topic clusters.

\begin{figure*}[htb!]
  \begin{subfigure}{0.3\textwidth}
     \centering
     \includegraphics[width=0.8\linewidth]{bpm-h.pdf}
     \captionsetup{skip=0pt}
     \caption{BPM}
     \label{fig:bmp}
  \end{subfigure}
  \begin{subfigure}{0.3\textwidth}
     \centering
     \includegraphics[width=0.8\linewidth]{lda-h.pdf}
    \captionsetup{skip=0pt}
     \caption{LDA}
     \label{fig:lda}
  \end{subfigure}
  \begin{subfigure}{0.3\textwidth}
     \centering
     \includegraphics[width=0.8\linewidth]{pm-lda-h.pdf}
    \captionsetup{skip=0pt}
     \caption{PM-LDA}
     \label{fig:pmlda}
  \end{subfigure}
  \caption{(a) Graphical model for BPM. (b) Graphical model for LDA. (c) Graphical model for PM-LDA}
\end{figure*}

However, under these existing topic models, a visual word is only assigned to one topic (\emph{i.e.}, the word-topic assignment is a binary indicator).   Yet, in many images, it is impossible to assign a crisp boundary between topics.  In this paper, we generalize LDA to allow for partial memberships.

Partial membership models and algorithms have been previously developed in the literature.  One prevalent partial membership approach is the Fuzzy C-means algorithm (FCM) \cite{bezdek:1984}.
More recently, Heller \emph{et al.} \cite{heller:2008} and Glenn \emph{et al.} \cite{GlennZare:2014} proposed Bayesian partial membership models (\emph{i.e.}, probabilistic interpretations of FCM) along with their associated generative processes. Glenn \emph{et al.} \cite{GlennZare:2014} proposed a Bayesian Fuzzy Clustering (BFC) model and associated algorithms to bridge and extend  probabilistic clustering and fuzzy clustering methods.
Heller \emph{et al.} \cite{heller:2008} derived a Bayesian partial membership model (BPM) by extending the standard mixture model. The generative processes for both the BFC and BPM models are similar. The main difference between the BPM and BFC models is that the BFC uses both a fixed \emph{fuzzifier} parameter and a scaling parameter to control the degree of mixing between topics.  In contrast, in the BPM, the degree of mixing between topics is controlled only through a scaling hyper-parameter, $s$, found in the prior distribution on partial membership values.
These existing partial membership methods are non-hierarchical approaches.  The proposed PM-LDA extends these to hierarchical approaches to allow for semantic image segmentation. PM-LDA is an extension of both the LDA model proposed by Blei \emph{et al.} \cite{blei:2003} and the partial membership model proposed by Heller \emph{et al.} \cite{heller:2008}.

\section{Bayesian Partial Membership Model} \label{sec:heller}

In a finite mixture model, the data likelihood of $\mathbf{x}_n$,  is
\begin{equation}
p(\mathbf{x}_n|\boldsymbol{\beta})=\sum_{k=1}^{K}\pi_kp_k(\mathbf{x}_n|\beta_k),
\end{equation}
where $\left\{ \pi_k \right\}_{k=1}^K$  are the mixture weights and ${\boldsymbol{\beta}}=\{{\beta}_1, {\beta}_2, ..., {\beta}_K\}$ are the mixture component parameters. $p_k(\mathbf{x}_n|\beta_k)$ is the $k^{th}$ mixture component with parameters ${\beta}_k$. In this model, a data point is assumed to come from one (and only one) of the $K$ mixture components. Thus, given its component assignment, $\mathbf{z}_n$, the probability of a data point, $\mathbf{x}_n$,  is defined as $p(\mathbf{x}_n|\mathbf{z}_n,\boldsymbol{\beta})=\prod_{k=1}^{K}p_k(\mathbf{x}_n|\beta_k)^{z_{nk}}$ where $
z_{nk} \in \{0,1\}$, $\sum_{k=1}^{K}z_{nk}=1$,
and $\mathbf{z}_n=[z_{n1}, z_{n2}, ..., z_{nK}]$ is the binary membership vector.   If $z_{nk}=1$, the data point $\mathbf{x}_n$ is assumed to have been drawn from mixture component $k$.

 In order to obtain a model allowing multiple cluster memberships for a data point, the constraint $z_{nk} \in \{0, 1\}$ is relaxed to $z_{nk} \in [0,1]$.

The modified constraints and the inclusion of prior distributions for several  key parameters results in the Bayesian Partial Membership model \cite{heller:2008},
\begin{eqnarray}
p(\boldsymbol{\pi},s,\mathbf{z}_n, \mathbf{x}_n|\boldsymbol{\alpha},\lambda,\boldsymbol{\beta})&=&p(\boldsymbol{\pi}|\boldsymbol{\alpha})p(s|\lambda)p(\mathbf{z}_n|\boldsymbol{\pi} s) \nonumber \\
&&\prod_{k=1}^{K}p_k(\mathbf{x}_n|\beta_k)^{z_{nk}},
\label{eqn:bpm}
\end{eqnarray}
where $z_{nk}\in[0,1]$, $\sum_{k=1}^{K}z_{nk}=1$, and $\boldsymbol{\pi}$ is the cluster mixing proportion assumed to be distributed according to a Dirichlet distribution with parameter $\boldsymbol{\alpha}$, \emph{i.e.,} $\boldsymbol{\pi} \sim \text{Dir}(\boldsymbol{\alpha})$.
 The scaling factor, $s$, determines the level of cluster mixing and is distributed according to an exponential distribution with mean $1/\lambda$, $s \sim \text{exp}(\lambda)$, and
$\mathbf{z}_n \sim \text{Dir}(\boldsymbol{\pi} s)$ is the membership vector for data point $\mathbf{x}_n$.

As shown in \cite{heller:2008}, if each of the mixture components are exponential family distributions of the same type, then $p(\mathbf{x}_n|\mathbf{z}_n,\boldsymbol{\beta})=\prod_{k=1}^{K}p_k(\mathbf{x}_n|\beta_k)^{z_{nk}}$ with $z_{nk} \in [0,1]$ and $\sum_{k=1}^{K}z_{nk}=1$, can be written as:
\begin{equation}
p(\mathbf{x}_n|\mathbf{z}_n,\boldsymbol{\beta}) = \text{Expon}\left(\sum_k z_{nk}{\eta}_k\right).
\label{eqn:expfamprod}
\end{equation}
This indicates that the data generating distribution for $\mathbf{x}_n$ is of the same exponential family distribution as the original $K$ clusters, but with new natural parameters $\sum_k z_{nk}{\eta}_k$.  The new parameters are a convex combination of the natural parameters, $\eta_k$, of the original clusters weighted by $z_{nk}$. This provides the powerful (and convenient) ability to sample directly from the unique mixture distribution for each data point if the natural parameters of the original clusters and the membership vector for the data point are known. A graphical model of BPM is shown in Fig. \ref{fig:bmp}.

\section{Partial Membership LDA}  \label{sec:PMLDA}

In the BPM,  data points are organized at only one level, where each data point is indexed by its corresponding component distribution. In our proposed model, PM-LDA, (and in LDA) data is organized at two levels: the word level and the document level as illustrated in Fig. \ref{fig:lda} and \ref{fig:pmlda}.  In the proposed PM-LDA model, the random variable associated with a data point is assumed to be distributed according to multiple topics with a continuous partial membership in each topic. Specifically, the PM-LDA model is
\begin{eqnarray}
p(\boldsymbol{\pi}^d,s^d, \mathbf{z}^d_n,\mathbf{x}^d_n|\boldsymbol{\alpha},\lambda,\boldsymbol{\beta})&=&p(\boldsymbol{\pi}^d|\boldsymbol{\alpha})p(s^d|\lambda)p(\mathbf{z}^d_n|\boldsymbol{\pi}^ds^d)\nonumber \\
&& \prod_{k=1}^{K}p_k(\mathbf{x}_n^d|\beta_k)^{{z}^d_{nk}}
\label{eqn:pmlda}
\end{eqnarray}
where $\mathbf{x}^d_n$ is the $n$th word in document $d$, $\mathbf{z}^d_n$ is the partial membership vector of $\mathbf{x}^d_n$, $\boldsymbol{\pi}^d \sim \text{Dir}(\boldsymbol{\alpha})$ and $s^d \sim \text{exp}(\lambda)$ are the topic proportion and  the level of topic mixing in document $d$, respectively. The parameter $\boldsymbol{\alpha}$ gives the topic composition across a document. For example, in  Fig. \ref{fig:csonar}, the image may be composed of $40\%$ ``sand ripple'' topic and $60\%$ ``flat sand'' topic (\emph{i.e.}, $\boldsymbol{\alpha} = [0.4, 0.6]$).  The  parameter $\lambda$ controls how similar the partial membership vector of each word is expected to be to the topic distribution of the document. For example, a small $\lambda$ would correspond to most words in an document to have partial membership vectors very close to $\boldsymbol{\pi}^{d}$. During image segmentation, a small $\lambda$ generally corresponds to large transition regions (\emph{e.g.}, transition from ``flat sand'' to ``sand ripple'' comprises most of the image). For a large $\lambda$, the partial membership vectors for each word can vary significantly from the document mixing proportions.  In general, a large $\lambda$ corresponds to very narrow (tending towards crisp) transition regions during image segmentation (\emph{e.g.}, the SAS image may have $39\%$ of the visual words as pure ``sand ripple'', $59\%$ as pure ``flat sand'', and only $2\%$ mixed).

The vector  $\mathbf{z}^d_{n} \sim \text{Dir}(\boldsymbol{\pi}^{d} s^{d})$ represents the partial memberships of data point $\mathbf{x}^{d}_{n}$ in each of the $K$ topics.
If each topic distribution is assumed to be of the exponential family, $p_k(\cdot|\beta_k) = \text{Expon}(\eta_k)$, then using the result in \eqref{eqn:expfamprod}, $p(\mathbf{x}_n^d|\mathbf{z}_n^d,\boldsymbol{\beta}) = \text{Expon}(\sum_k z_{nk}^d{\eta}_k)$. The  graphical model  for PM-LDA is shown in Fig. \ref{fig:pmlda}.

 In PM-LDA, the membership $\mathbf{z}^d_{n}$ is drawn from a Dirichlet distribution which is in contrast to a multinomial distribution as used in LDA. With the infinite number of possible values for $\mathbf{z}^{d}_n$, the word generating distributions in PM-LDA are expanded from only $K$ generating distributions (as in LDA) to infinitely many. Fig. \ref{fig:topics}  illustrates this using two Gaussian topic distributions, where the membership value to one topic is varied from $0$ to $1$ with an increment $0.1$. The two original topics are shown as the Gaussian distributions at either end. In LDA,  words are generated from only the two original topic distributions. In PM-LDA, words can be generated from any (of the infinitely many) convex combinations of the topic distributions.  As the scaling factor $s \rightarrow 0$, the PM-LDA model will degrade to the LDA model.

\begin{figure}[!tb]
\centering
 \begin{subfigure}[b]{0.22\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{rings.pdf}
\captionsetup{labelformat=empty,skip=0pt}
\caption{(a)}
\end{subfigure}
 \begin{subfigure}[b]{0.22\textwidth}
\centering
\includegraphics[width=0.8\linewidth]{rings1.pdf}
\captionsetup{labelformat=empty,skip=0pt}
\caption{(b)}
\end{subfigure}
\caption{Partial membership data generating distributions. In (a), two Gaussian topics with $\mu_1=[-4, -4]; \mu_2=[6, 6]$, $\Sigma_1=\Sigma_2=\mathbf{I}$. In (b), two Gaussian topics with  $\mu_1=[-4,-4]; \mu_2=[6, 6]$, $\Sigma_1=[4, 0; 0, 1],\Sigma_2=[1, 0; 0, 4]$ \cite{heller:2008}.}
\vspace{-4mm}
\label{fig:topics}
\end{figure}

Given the hyperparameters $\boldsymbol{\Psi}=\{\boldsymbol{\alpha},\lambda,\boldsymbol{\beta}\}$, the full PM-LDA model over all words in the $d^{th}$ document is:
\begin{eqnarray}
\label{eqn:joint}
&&p(\boldsymbol{\pi}^d,s^d,\mathbf{Z}^d,\mathbf{X}^d|\boldsymbol{\alpha},\lambda,\boldsymbol{\beta})   \\ \nonumber
&=&p(\boldsymbol{\pi}^d|\boldsymbol{\alpha}) p(s^d|\lambda) \prod_{n=1}^{N^d}p(\mathbf{x}^{d}_{n}|\mathbf{z}^{d}_{n},\boldsymbol{\beta})p(\mathbf{z}^{d}_{n}|\boldsymbol{\pi}^ds^d). \nonumber
\end{eqnarray}
where $\boldsymbol{\pi}^d$ are the topic proportions, scaling factor $s^d$, partial membership vectors $\mathbf{Z}^d=\{\mathbf{z}^{d}_{n}\}_{n=1}^{N^d}$ and a set of $N^d$  words $\mathbf{X}^d$ for document $d$.
The log of \eqref{eqn:joint} when considering the specific forms chosen in our model, is shown in \eqref{eqn:onedocument}.
\begin{figure*}[ht!]
\begin{eqnarray}  \label{eqn:onedocument}
\pazocal{L}^{d} &=& \ln(p(\boldsymbol{\pi}^d,s^d,\mathbf{Z}^d,\mathbf{X}^d|\boldsymbol{\alpha},\lambda,\boldsymbol{\beta}) ) =  \ln \Gamma \left(\sum_{k=1}^{K}\alpha_k\right)-\sum_{k=1}^{K}\ln\Gamma \left(\alpha_k \right) + \sum_{k=1}^{K}(\alpha_k-1)\ln \pi^d_k +\ln \lambda - \lambda s^d \nonumber \\
&+&\sum_{n=1}^{N^d}\ln p(\mathbf{x}^{d}_{n}|\mathbf{z}^{d}_{n},\boldsymbol{\beta}) +\sum_{n=1}^{N^d}\bigg\{\ln \Gamma \left(\sum_{k=1}^{K}s^d\pi^{d}_{k}\right) -\sum_{k=1}^{K}\ln\Gamma(s^d\pi^{d}_{k})+\sum_{k=1}^{K}(s^d\pi^{d}_{k}-1)\ln z^{d}_{nk}\bigg\}
\end{eqnarray}
\end{figure*}
During parameter estimation, our goal is to maximize $\pazocal{L}=\sum_{d=1}^{D}\pazocal{L}^{d}$ by estimating all the model parameters ${\boldsymbol{\pi}^{d},s^{d}, \mathbf{z}^{d}_n, \boldsymbol{\beta}}$.
In this paper, we employ an Metropolis within Gibbs  \cite{robert:2013, GlennZare:2014} sampling approach.

\section{Parameter Estimation for PM-LDA}
The goal of parameter estimation is to maximize the following  posterior distribution,
\begin{equation}
p(\boldsymbol{\Pi},\mathbf{S},\mathbf{M},\boldsymbol{\beta}|\mathbf{D},\boldsymbol{\alpha},\lambda) \propto p({\boldsymbol{\Pi},\mathbf{S},\mathbf{M},\mathbf{D}|\boldsymbol{\alpha},\lambda,\boldsymbol{\beta})},
\label{eqn:post}
\end{equation}
where $\mathbf{D} =\left\{\mathbf{X}^1, \mathbf{X}^2, ..., \mathbf{X}^D \right\}$ includes all training documents and $\boldsymbol{\Pi}, \mathbf{S}, \mathbf{M}$ include all of the topic proportions, scaling factors and membership vectors, respectively.

A Metropolis within Gibbs sampler is employed to perform the MAP inference which can generate samples from the posterior distribution in \eqref{eqn:post}, \cite{robert:2013,GlennZare:2014}. An outline of the sampler is provided in Alg. \ref{alg:clustercenter}. The sampler is simple and straight-forward implement composed only of a series of draws from candidate distributions for each parameter and then evaluation of the candidate in the appropriate acceptance ratio. Our implementation of the sampler has been posted online.\footnote[1]{Code can be found at: https://github.com/TigerSense/PMLDA}   In our current implementation, we consider the topic distributions to be Gaussian with different means, $\mu_k$, but identical diagonal and isotropic covariance matrices, $\Sigma_k = \sigma^2\mathbf{I}$.

\begin{algorithm}[ht]
\begin{algorithmic}[1]
\REQUIRE{A corpus $\mathbf{D}$, the number of topics $K$, and the number of sampling iterations $T$}
\ENSURE{Collection of all samples: $\boldsymbol{\Pi}^{(t)}, \mathbf{S}^{(t)}, \mathbf{M}^{(t)}$,  $\boldsymbol{\beta}^{(t)}=\left\{\mu^{(t)}_1, \Sigma^{(t)}_1, \mu^{(t)}_2, \Sigma^{(t)}_2..., \mu^{(t)}_K, \Sigma^{(t)}_K\right\}$.
\FOR{$t=1:T$}
\FOR{$d=1:D$}
\STATE \underline{Sample $\boldsymbol{\pi}^d$:} Draw candidate: $\boldsymbol{\pi}^\dagger \sim \text{Dir}(\boldsymbol{\alpha})$ \\
 Accept candidate with probability:\\ $a_{\boldsymbol{\pi}}=\min \left \{ 1, \frac{p(\boldsymbol{\pi}^{\dagger}, s^{(t-1)}, \mathbf{Z}^{(t-1)}, \mathbf{X}|\boldsymbol{\Psi}) p(\boldsymbol{\pi}^{(t-1)}|\boldsymbol{\alpha})}{ p(\boldsymbol{\pi}^{(t-1)}, s^{(t-1)}, \mathbf{Z}^{(t-1)}, \mathbf{X}|\boldsymbol{\Psi}) p(\boldsymbol{\pi}^\dagger|\boldsymbol{\alpha})}\right \}$

\STATE \underline{Sample $s^d$:} Draw candidate: $s^\dagger \sim \text{exp}(\lambda)$\\
Accept candidate with probability:\\
$a_s=\min \left \{ 1, \frac{p(\boldsymbol{\pi}^{(t)}, s^{\dagger}, \mathbf{Z}^{(t-1)}, \mathbf{X}|\boldsymbol{\Psi})p(s^{(t-1)}|\lambda)}{p(\boldsymbol{\pi}^{(t)}, s^{(t-1)}, \mathbf{Z}^{(t-1)}, \mathbf{X}|\boldsymbol{\Psi})p(s^{\dagger}|\lambda)}\right \}$

\FOR{$n=1:N^d$}
\STATE \underline{Sample $\mathbf{z}^d_n$:} Draw candidate: $\mathbf{z}_n^\dagger \sim \text{Dir}(\mathbf{1}_K)$\\
Accept candidate with probability:\\
$a_{\mathbf{z}}=\min \left\{1, \frac{p(\boldsymbol{\pi}^{(t)}, s^{(t)}, \mathbf{z}_n^\dagger, \mathbf{x}_n|\boldsymbol{\Psi})}{p(\boldsymbol{\pi}^{(t)}, s^{(t)}, \mathbf{z}_n^{(t-1)}, \mathbf{x}_n|\boldsymbol{\Psi})}\right\} $
\ENDFOR
\ENDFOR

\FOR{$k=1:K$}
\STATE \underline{Sample $\mu_k$:} Draw proposal: ${\mu}_k^{\dagger}\sim\mathcal{N}(\cdot|{\mu}_{\mathbf{D}},f{\Sigma}_{\mathbf{D}})$\\
${\mu}_{\mathbf{D}}$ and ${\Sigma}_{\mathbf{D}}$ are  mean and covariance of the data\\
Accept candidate with probability:\\
$a_k=\small{\min\left\{1, \frac{p\left(\boldsymbol{\Pi}^{(t)}, \mathbf{S}^{(t)}, \mathbf{M}^{(t)}, \mathbf{D}|{\mu}_k^{\dagger}\right)\mathcal{N}(\mu_k^{(t-1)}|\mu_\mathbf{D}, \Sigma_\mathbf{D})}{p\left(\boldsymbol{\Pi}^{(t)}, \mathbf{S}^{(t)}, \mathbf{M}^{(t)}, \mathbf{D}|\boldsymbol{\mu}_k^{(t-1)}\right)\mathcal{N}(\mu_k^{\dagger}|\mu_\mathbf{D}, \Sigma_\mathbf{D})} \right\}}$

\ENDFOR
\STATE \underline{Sample covariance matrices $\boldsymbol{\Sigma}= \sigma^2\mathbf{I}$:}\\
Draw candidate from:\\ $\sigma^2 = \frac{1}{2}\left\{\max_{\mathbf{x}_n}d^2(\mathbf{x}_n-{\mu}_{\mathbf{D}})-\min_{\mathbf{x}_n}d^2(\mathbf{x}_n-{\mu}_{\mathbf{D}}) \right\}$\\
Accept candidate with probability: \\
$a_{\boldsymbol{\Sigma}}= \min\left\{1, \frac{p\left(\boldsymbol{\Pi}^{(t)}, \mathbf{S}^{(t)}, \mathbf{M}^{(t)}, \mathbf{D}|\boldsymbol{\Sigma}^\dagger\right)}{p\left(\boldsymbol{\Pi}^{(t)}, \mathbf{S}^{(t)}, \mathbf{M}^{(t)}, \mathbf{D}|\boldsymbol{\Sigma}^{(t-1)}\right)} \right\}.$

\ENDFOR}
\end{algorithmic}
\caption{Metropolis-within-Gibbs Sampling Method for Parameter Estimation}
\label{alg:clustercenter}
\end{algorithm}

The proposed Metropolis within Gibbs scheme will return the full distribution of parameter values given the desired posterior. We use the MAP sample (i.e., the sample with the largest log posterior value) as the final estimate, $\left\{\boldsymbol{\Pi}^{*}, \mathbf{S}^{*},\mathbf{M}^{*},\boldsymbol{\mu}^{*}, \boldsymbol{\Sigma}^{*}\right\}$.

\section{Data \& Experimental Results}
In this section, we show  results of image segmentation on three datasets: (i) Synthetic Aperture SONAR (SAS) imagery, (ii) Sunset imagery, and the (iii) MSRC dataset \cite{v1:2004}.

\paragraph{Synthetic Aperture Sonar (SAS) Imagery Dataset}  From our SAS image dataset, we selected 4 images (shown in the first column in Fig. \ref{fig:all}) and compute the average intensity value and entropy within a 21 $\times$ 21 window as feature values. The average intensity value is scaled ($\times 10$) to roughly the same magnitude of the average entropy value. Each image is divided into multiple documents using a sliding window approach. A document consists of all of the feature vectors associated with each pixel (\emph{i.e.}, visual words) in the window. The number of topics in this dataset is set to $3$. For LDA, a dictionary of size $100$ is built by clustering all the computed feature values using the K-means.  FCM results with $m=1.5$. Parameters for LDA and FCM were selected manually to provide the best results. Due to the lack of ground-truth, qualitative segmentation results in Fig. \ref{fig:all} is provided. In the first row, Subfigures (b), (c), and (d) show the partial membership maps in the ``dark flat sand" , ``sand ripple" , and  ``bright flat sand'' topics using PM-LDA, respectively.  Subfigures (f), (g), and (h) show the partial membership maps in each of the three clusters using FCM, respectively.  In (b) - (d) and (f) - (h), the color indicates the degree of membership of a visual word in a topic where red corresponds to a full membership of $1$ and dark blue color corresponds to a membership value of $0$. The LDA result is shown in (e) where color indicates topic assignment. Subfigures in Row 2-4 follow the same subfigure captions in Row 1.

From the experimental results,  we can see that PM-LDA achieves much better results than FCM and LDA. As shown in Fig. \ref{fig:1c} and \ref{fig:2c}, the segmentation results of PM-LDA show a gradual change from ``sand ripple" to ``dark flat sand".   FCM captures the gradual transition to some extent but is not able to clearly differentiate between clusters. For example, as shown in Fig. \ref{fig:2g} - \ref{fig:2h} and Fig. \ref{fig:3g} - \ref{fig:3h},  using FCM, the rippled region in Images 2 and 3 is assigned to 2 clusters with nearly equal partial memberships.  As LDA cannot generate partial memberships, in Fig. \ref{fig:1e} and \ref{fig:2e}, Image 1 and 2 are simply partitioned into different topics using LDA. Yet, by comparing Fig. \ref{fig:3e} with \ref{fig:3d} and Fig. \ref{fig:4e} with \ref{fig:4d}, we can see that on Image 3 and 4 that do not contain transition regions, LDA achieves similar segmentation result to PM-LDA.

\begin{figure*}
\centering
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing1.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
    \caption{{(a) Image 1}} \label{fig:c1}
 \end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing1_1_color.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
    \caption{{(b) PM-LDA:1}}
    \end{subfigure}
     \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing1_2_color.pdf}
    \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
    \caption{{(c) PM-LDA:2}} \label{fig:1c}
    \end{subfigure}
     \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing1_3_color.pdf}
     \captionsetup{labelformat=empty,width=1.1\linewidth,justification=centering,skip=-5pt}
    \caption{{(d) PM-LDA:3}}
 \end{subfigure}
\begin{subfigure}[t]{0.015\textwidth}
   \centering
     \includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=-5pt}
     \caption{}
\end{subfigure}
\setcounter{subfigure}{4}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{lda1_100.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
    \caption{{(e) LDA}} \label{fig:1e}
    \end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{FCM15_mixing1_1_color.pdf}
    \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
      \caption{{(f) FCM:1}}
 \end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{FCM15_mixing1_2_color.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
        \caption{{(g) FCM:2}}
    \end{subfigure}
     \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing1_3_color.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
        \caption{{(h) FCM:3}}
    \end{subfigure}
    \begin{subfigure}[t]{0.015\textwidth}
   \centering
     \includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
     \captionsetup{labelformat=empty,width=1\linewidth,justification=centering,skip=0pt}
\end{subfigure}
\setcounter{subfigure}{8}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing3.pdf}
			 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(i) Image 2} \label{fig:c2}
 \end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing3_1_color.pdf}
				 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(j) PM-LDA:1}
		\end{subfigure}
		 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing3_2_color.pdf}
				 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(k) PM-LDA:2} \label{fig:2c}
		\end{subfigure}
		 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{mixing3_3_color.pdf}
				 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(l) PM-LDA:3}
 \end{subfigure}
\begin{subfigure}[t]{0.015\textwidth}
   \centering
     \includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
				 \captionsetup{labelformat=empty,skip=0pt}
				 \caption{}
\end{subfigure}
\setcounter{subfigure}{12}
\begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{lda3_100.pdf}
					 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(m) LDA} \label{fig:2e}
		\end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{FCM15_mixing3_1_color.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(n) FCM:1}
 \end{subfigure}
 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{FCM15_mixing3_2_color.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(o) FCM:2} \label{fig:2g}
		\end{subfigure}
		 \begin{subfigure}[t]{0.11\textwidth}
     \centering
     \includegraphics[width=1\linewidth,,height=0.8\linewidth]{FCM15_mixing3_3_color.pdf}
		 \captionsetup{labelformat=empty,skip=0pt}
		\caption{(p) FCM:3} \label{fig:2h}
 \end{subfigure}
\begin{subfigure}[t]{0.015\textwidth}
   \centering
     \includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
		 \captionsetup{labelformat=empty,skip=0pt}
\end{subfigure}
\setcounter{subfigure}{16}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing12.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(q) Image 3} \label{fig:c3}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing12_1_color_smooth1.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(r) PM-LDA:1}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing12_2_color_smooth1.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(s) PM-LDA:2}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing12_3_color_smooth1.pdf}
	\centering
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(t) PM-LDA:3}\label{fig:3d}
\end{subfigure}
\begin{subfigure}[t]{0.015\textwidth}
	\centering
	\includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
\end{subfigure}
\setcounter{subfigure}{20}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{lda12_100.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(u) LDA} \label{fig:3e}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing12_1_color.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(v) FCM:1}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing12_2_color.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(w) FCM:2} \label{fig:3g}
\end{subfigure}
\begin{subfigure}[t]{0.11\textwidth}
	\centering
	\includegraphics[width=1\linewidth,height=0.81\linewidth]{FCM15_mixing12_3_color.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
	\caption{(x) FCM:3}	\label{fig:3h}
\end{subfigure}
\begin{subfigure}[t]{0.015\textwidth}
	\centering
	\includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
	\captionsetup{labelformat=empty,skip=0pt}
\end{subfigure}
	\setcounter{subfigure}{24}

\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing22.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(y) Image 4} \label{fig:c4}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing22_1_color_smooth.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(z) PM-LDA:1}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing22_2_color_smooth.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(aa) PM-LDA:2}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{mixing22_3_color_smooth.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(ab) PM-LDA:3} \label{fig:4d}
	\end{subfigure}
	\begin{subfigure}[t]{0.015\textwidth}
		\centering
		\includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
	\end{subfigure}
	\setcounter{subfigure}{28}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{lda22_100.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(ac) LDA}\label{fig:4e}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing22_1_color.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(ad) FCM:1}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing22_2_color.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(ae) FCM:2}
	\end{subfigure}
	\begin{subfigure}[t]{0.11\textwidth}
		\centering
		\includegraphics[width=1\linewidth,height=0.8\linewidth]{FCM15_mixing22_3_color.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(af) FCM:3}
	\end{subfigure}
	\begin{subfigure}[t]{0.015\textwidth}
		\centering
		\includegraphics[width=0.91\linewidth]{jetcolorbar.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
	\end{subfigure}

	\caption{Segmentation results of Image 1 - 4 using PM-LDA, FCM and LDA. (a): SAS Image. (b)-(d): PM-LDA partial membership map in the ``dark flat sand,'' ``sand ripple,'' ``bright flat sand'' topics, respectively. (e): LDA result where color indicates topic label. (f)-(h): FCM  partial membership map in the first, second, and third cluster, respectively. Subfigure captions in Row 2 - 4 follow those in Row 1. In PM-LDA and FCM results,  color indicates the degree of membership of a visual word in a topic or cluster. }
	\label{fig:all}
\end{figure*}

As discussed in Section \ref{sec:PMLDA}, the scaling factor $s^d$ determines the similarity of the partial membership vector of each word, $\mathbf{z}_n^d$, to the topic proportion $\boldsymbol{\pi}^d$.  In this experiment, we investigated the effect of $s$ by estimating the memberships and topics with fixed topic proportion. A subregion consisting of three superpixels \cite{cobb:2013multi} are used in this experiment and shown in Fig. \ref{fig:3sup}. Each superpixel is treated as a document. The topic proportion $\boldsymbol{\pi}^d$ is set to be $[1,1,1]/3$ and the scaling factor $s$ is varied to be $3, 10, 300, 30000$. The membership estimation results are shown in Figure \ref{fig:varyings}. As can be seen, as the scaling factor $s$ increases, the partial memberships gradually approach the topic proportion $[1,1,1]/3$ and become more smooth.
\begin{figure}[htb]
	\centering
	\includegraphics[height=0.18\linewidth]{threesuperpixels.pdf}
	\caption{A subregion of three superpixels}
	\label{fig:3sup}
	\vspace{-2mm}
\end{figure}

\begin{figure}[!htb]
	\centering
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s3_1.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) $s=3$}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s3_2.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(b) }
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s3_3.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c) }
	\end{subfigure}

	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s10_1.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) $s=10$}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s10_2.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(b)}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s10_3.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c)}
	\end{subfigure}

	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s300_1.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) $s=300$}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s300_2.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(b) }
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s300_3.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c) }
	\end{subfigure}

	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s30000_1.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) $s=30000$}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s30000_2.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(b)}
	\end{subfigure}
	\begin{subfigure}[t]{0.12\textwidth}
		\centering
		\includegraphics[height=0.5\linewidth]{s30000_3.jpg}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c) }
	\end{subfigure}

	\caption[Partial membership maps  with varying $s$]{Partial membership maps  with varying $s$. Each row shows the estimated membership maps of the three estimated topics. The black contour indicates the superpixel boundary. The superpixels are results published in \cite{cobb:2013multi}.}
	\label{fig:varyings}
	\vspace{-4mm}
\end{figure}

\paragraph{Sunset Dataset} Experimental results on Sunset dataset show the ability of PM-LDA to perform partial membership segmentation given visual natural imagery. Two sunset themed images from Flickr (with the necessary permissions)\footnote[2]{\scriptsize{Photo can be found at: https://www.flickr.com/photos/aoa-/6104409480/}}  \footnote[3]{\scriptsize{Photo can be found at: https://www.flickr.com/photos/frenchdave/8482336933/}} were used in this experiment. For each visual word, the first order Gaussian gradient ($\sigma=2$)  with respect to $y$-axis and R and B channels are used as the feature vectors. The number of topics is set to be $3$. Experiments are run on each image individually and results are shown in Fig. \ref{fig:sunset}. Columns 2-4 show the segmentation results of PM-LDA.  Column 5 is the LDA results with $3$ topics.  Comparing Column 3 and Column 5 in Fig. \ref{fig:sunset}, we can see that PM-LDA can generate continuous partial membership according to the extent to which the sky is colored by sunlight. The partial membership map illustrates how the topic gradually shift from one to the other. In contrast, LDA can only produce $0$-$1$ segmentation.

\begin{figure}[!htb]
	\centering
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun1.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun11.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun12.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun13.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun1_lda.pdf}
		\caption{}
	\end{subfigure}

	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun2.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun21.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun22.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun23.pdf}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[b]{0.09\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{sun2_lda.pdf}
		\caption{}
	\end{subfigure}
	\caption{Examples of segmentation result on Sunset dataset. (a): Sunset Image 1. (f): Sunset Image 2. (b)-(d) and (g)-(i) are the PM-LDA partial membership maps in the estimated three topics for Sunset Image 1 and Sunset Image 2, respectively. The color indicates the degree of membership of a visual word in a topic or cluster. (e) and (j) are the LDA results where color indicates the topic.}
	\label{fig:sunset}
\end{figure}

\begin{figure*}[!htb]
	\centering
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) cow1}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1_1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(b) ``grass''}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1_2.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c) ``sky''}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1_3.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(d) ``cow''}
	\end{subfigure}
	\hspace{-0.2cm}
	\begin{subfigure}[t]{0.029\textwidth}
		\centering
		\includegraphics[width=0.58\linewidth]{colorbar1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{allEdge1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(e) transition}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1_max.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(f) max}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow1_LDA_jet.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(g) LDA}
	\end{subfigure}

	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(a) cow2}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9_1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(t) ``grass''}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9_2.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(c) ``sky''}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9_3.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(d) ``cow''}
	\end{subfigure}
	\hspace{-0.2cm}
	\begin{subfigure}[t]{0.029\textwidth}
		\centering
		\includegraphics[width=0.58\linewidth]{colorbar1.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{allEdge9.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(e) transition}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9_max.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(f) max}
	\end{subfigure}
	\begin{subfigure}[t]{0.13\textwidth}
		\centering
		\includegraphics[width=1\linewidth]{cow9_LDA_jet.pdf}
		\captionsetup{labelformat=empty,skip=0pt}
		\caption{(g) LDA}
	\end{subfigure}

	\caption{Example of PM-LDA and LDA results. (a) Original image. (b)-(d) Results of PM-LDA,  the partial membership maps in ``grass'', ``sky'', and ``cow'' topics, respectively. The color indicates the degree of membership in a topic. (e) Transition regions consisting of visual words with at lease one partial membership value in range $[0.4, 0.6]$ (f) Modified segmentation result of PM-LDA by assigning each visual word to the topic with the largest membership. The colors indicate topics. (g) Result of LDA. The colors indicate topics. }
	\label{fig:cow1}
\end{figure*}

\begin{figure}[!htb]
	\centering
	\includegraphics[height=0.4\linewidth,width=0.5\linewidth]{roc.pdf}
	\caption{ROC curve of PM-LDA for cow detection evaluated at the pixel level. The red star represents the LDA cow detection results. }
	\label{fig:roc}
	\vspace{-2mm}
\end{figure}

\paragraph{Microsoft Research Cambridge data set version one (MSRCv1)} The MSRCv1 database consists of 240, $213\times320$ pixel images. A subset from this database consisting of all images that include the ``grass'', ``cow'', and ``sky'' topics was used in this experiment. The local descriptors proposed in \cite{winn:2005}, the output of a set of filter bank responses made of 3 Gaussians, 4 Laplacian of Gaussians (LoG) and 4 first order derivatives of Gaussians were used as the feature vectors. The filter window size used was $15\times 15$.  In this experiment, instead of using each image as a document, we apply normalized cuts method to get $40$ super-pixel segments from each image and treat each super-pixel as a document. The topic number is set to be $3$, and for LDA, we densely sample the filter bank output and build a dictionary of size 200. Quantitative comparison results on accurate detection of the ``cow'' class are shown in Fig. \ref{fig:roc}. ROC curve analysis of PM-LDA using the ``cow'' membership map was conducted. The red star indicates the quantitative LDA result (a ROC curve cannot be generated due to the crisp segmentation of the LDA method).  Example results are shown in Fig. \ref{fig:cow1}.  In Subfigure (e), transition regions are highlighted by indicating the pixels with at least one membership value in range $[0.4, 0.6]$. As shown in (e), these partial membership values mostly occur at the boundary between two topics. Thus, PM-LDA is able to identify when the feature vector contains information from multiple topics (as the feature vector is being computed over a window that contains more than one topic).  This is a powerful result showing the effectiveness of PM-LDA to provide semantic image understanding.  For comparison with LDA, we modified the segmentation result of PM-LDA by assigning each visual word to the topic with the largest membership. As shown in (f) and (g), PM-LDA can achieve similar results to LDA. So on these images with crisp boundaries, PM-LDA can generate binary membership values, and learn the three semantic topics comparable to LDA. Thus, PM-LDA also is effective for use in crisp labeling problems.

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redpajama_set_name: RedPajamaArXiv


text:
Сергі́й Па́влович Дерка́ч (1973—2014) — підполковник (посмертно) Збройних сил України, учасник російсько-української війни.

Життєпис
Народився 1973 року в Івано-Франківську, в родині військовослужбовця. Закінчив 9 класів середньої школи (у 1989 р.) та Прилуцьке медичне училище (у 1993 р.). Від 1993 року в лавах Збройних сил України. 1998 року закінчив Харківський військовий університет за спеціальністю «метеорологічне забезпечення систем та комплексів». З червня 1998-го проходив службу на офіцерських посадах, у тому числі в 38-му об'єднаному навчальному центрі Повітряних сил ЗСУ.

З грудня 2013 року — заступник командира 3-го танкового батальйону по роботі з особовим складом 1-ї окремої гвардійської танкової бригади. З червня 2014-го брав участь у боях на сході України. 30 липня 2014-го біля села Шишкове під Луганськом машина, в якій перебував Сергій Деркач, підірвалася на фугасній міні. Внаслідок підриву здетонували боєзапаси, які перевозили в автомобілі. Сергій загинув на місці разом із водієм Володимиром Моісеєнком (родом з Ічнянського району).

1 серпня 2014 року похований в Прилуках.

Вдома залишилась дружина Віта й діти — восьмирічна Аліна та чотирирічна Діана. Сім'я полеглого мешкає в гуртожитку військової частини у смт Гончарівське.

Нагороди та вшанування
 8 вересня 2014 року — за особисту мужність і героїзм, виявлені у захисті державного суверенітету та територіальної цілісності України, вірність військовій присязі під час російсько-української війни, відзначений — нагороджений орденом «За мужність» III ступеня (посмертно).
 26 жовтня 2016 року встановлено меморіальну дошку на фасаді Прилуцького медичного училища
 11 травня 2016 року наказом Міністра оборони України присвоєно чергове військове звання — підполковник (посмертно).

Примітки

Джерела
 Указ Президента № 708/2014
 Деркач Сергій Павлович
 В Прилуках поховали Сергія Деркача, що загинув на Луганщині
 Чернігівська ОДА
 Книга пам'яті
 Український Меморіал

Уродженці Івано-Франківська
Померли в Шишковому
Поховані в Прилуках

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