Program in Integrative Nutrition and Complex Diseases, Texas A&M University, College Station, Texas.Department of Nutrition and Food Science, Texas A&M University, College Station, Texas.
Department of Veterinary Pathobiology, College Station, Texas.
Department of Nutrition and Food Science, Texas A&M University, College Station, Texas.Center for Translational Environmental Health Research, Texas A&M University, College Station, Texas.
Program in Integrative Nutrition and Complex Diseases, Texas A&M University, College Station, Texas.Department of Nutrition and Food Science, Texas A&M University, College Station, Texas.Center for Translational Environmental Health Research, Texas A&M University, College Station, Texas.
p53 has been shown to mediate cancer stem–like cell function by suppressing pluripotency and cellular dedifferentiation. However, there have been no studies to date that have addressed the specific effects of p53 loss in colonic adult stem cells. In this study, we investigated the consequences of conditionally ablating p53 in the highly relevant Lgr5+ stem cell population on tumor initiation and progression in the colon. In a mouse model of carcinogen (AOM)-induced colon cancer, tamoxifen-inducible Lgr5-driven deletion of p53 reduced apoptosis and increased proliferation of crypt stem cells, but had no effect on tumor incidence or size. Conversely, in a mouse model of colitis-associated cancer, in which mice are exposed to AOM and the potent inflammation inducer DSS, stem cell–specific p53 deletion greatly enhanced tumor size and incidence in the colon. These novel findings suggest that the loss of p53 function in stem cells enables colonic tumor formation only when combined with DNA damage and chronic inflammation. Furthermore, we propose that stem cell targeting approaches are valuable for interrogating prevention and therapeutic strategies that aim to specifically eradicate genetically compromised stem cells. Cancer Res; 75(24); 1–6. ©2015 AACR.


There was a lot of hype going on when Chef Hung opened up in Aberdeen. There were long lineups just to try out his dishes! I wasn't interested enough to wait in line, so I never got to try it until now. Now that the lines are gone, the hype is over. The place was fairly empty when Rose and I arrived there for dinner on a Wednesday night.
Upon entering the place, we were greeted and promptly seated. I noticed there was a lot of servers working in a place that was pretty empty. There must've been 2 hostesses and another 6 waitresses in a place where there were only 2 tables occupied.
So, I found the place to be fairly clean. The menu looks like it's written on a takeout menu pamphlet. You are also given a sheet where you 'check' off your order. I thought this was a waste of paper, hopefully they recycle/reuse it. I'd understand if it a table of 10 doing an order, but if you're just 1 or 2 people, I just think that's a waste.
The first dish to arrive was the Cold Mixed Bean Curd Noodle.
Next up was the Marinated Beef Wrapped in Crispy Pancake. This was extremely dry and flavourless. The wrap was much too doughy. This was a complete miss. We even asked for more sauce, and that didn't help this dish.
Rose went with the Braised Beef with 5 kinds of vegetables in clear soup(above left).
I went with the Beef Shank with noodle in soup. I did not enjoy the beef, it was tough and too chewy. The soup was flavourful, but was slightly hotter than warm. I did enjoy the handcut noodles. It was not overcooked and still chewy.


The USA Outdoor Track & Field Championships for open and junior (ages 20 & under) athletes began Thursday on the campus of the University of Oregon in Eugene, Oregon and will run through Sunday. Thirteen (13) open athletes and five (5) junior athletes from Indiana are entered in the championships.
The Indiana highlights on day 2 of the championships included Molly Ludlow (Indianapolis / Saucony) winning her semi-final heat in the open 800m and advancing to Sunday's finals and Adriana Brown (Indianapolis / Kentucky) placing 4th in the Junior shot put .
Geoffery Davis (Indianapolis, Ind.) finished 10th in the men's high jump with a leap of 2.15 meters, seven places ahead of his initial seed.
Morgan Uceny (Plymouth, Ind.) faded over the last few meters of her heat in the women's 1500m and failed to qualify for the finals. Uceny finished in 22nd place with a time of 4 minutes, 21.20 seconds.
Patrick Freeney (South Bend, Ind.) and Kind Butler (Indianapolis, Ind.) both competed in the 400m semi-finals but did not advance to the finals.. Freeney finished 12th overal in a time of 45.80 seconds and Butler placed 15th in 46.73 seconds.
Brown, a 2014 Lawerence Central High School alum who holds the #5 all-time Indiana high school mark, finished 4th in the junior women's shot put with a throw of 15.21 meters (49' 11"). Brown entered the competition with the #3 seed (15.89m) in the competition. On Thursday, Brown finished 6th in the Discus Throw with a throw of 47.91m (157-2).
In the women's 400m semi-finals, Ayiana Gaines (South Bend, IN / Western Michigan) ran the third fastest time of the sixteen competitors, running 53.97 seconds. Finals are set for today at 4:30 PM.
Grant Stamm (Linton, IN / Indiana State) finished 12th in the 110m hurdles with a time of 14.17 seconds and Lorenzo Wells (Portage, IN / Central Michigan) finished 14th in the 100m dash in 10.84 seconds.
Today Indiana State's Katie Wise (Morgantown, IN) and Adarius Washington (Indianapolis, IN) are set to compete in the women's 200m and men's 110m hurdles, respectively.
High school national record holder, Deakin Volz (Bloomington, IN) will seek to win his first USA outdoor championship today in the men's pole vault. Volz heads into the competition with the #2 seed, just weeks after winning the Indiana high school state championship and breaking the state met records.
Lorenzo Wells (Portage, IN / Central Michigan) plans to compete in his second event of the week as he heads into the men's 200m with the 14th seed.
Ayiana Gaines (South Bend, IN / Western Michigan) will head into the women's 400m finals with the third fastest qualifying time, 53.97 seconds. Finals are set for today at 4:30 PM PT.


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DeKalb Commissioner Ted Terry: 'We're taking action now' to address gun safety
Metro ATL Trending
DeKalb County Commissioner Ted Terry. Image provided to Decaturish
By Logan C. Ritchie, contributor
DeKalb County, GA — Julvonnia McDowell's voice quivered as she described wanting to hear the voice of her son one more time, a sound she will never experience again. Her son, 14-year-old Jajuan McDowell was accidentally shot and killed with an unsecured firearm while visiting his family in Savannah in 2016.
McDowell's son never attended high school, danced at the prom or walked across a stage for graduation.
"It left a gaping hole in my heart that asphalt cannot fill," said McDowell, a volunteer with Moms Demand Action and member of Everytown Survivor Network. "As the holidays draw near, it is very, very important that gun owners … take the time to secure your firearms."
McDowell spoke on Dec. 7 at a press conference sponsored by elected officials who are taking a stand on gun safety. An unsecured gun was used in the shooting at Oxford High School in Oxford Township, Mich., on Nov. 30. Four students were killed, and seven people were injured.
The month of November saw multiple accidental gun deaths of children in metro Atlanta. Victims include 14-year-old Kyra Scott who died when a ghost gun made by her 13-year-old brother was fired, 8-year-old Kayden Jones who was shot at an apartment complex, and 5-year-old Khalis Eberhart who was killed on Thanksgiving by her 3-year-old family member.
State Sen. Elena Parent filed Senate Bill 146 this year which would allow for the owner of a gun to be charged if a minor gained access to the gun that the owner failed to secure, with harsher penalties if the child discharges the firearm and causes death or serious harm. She said her legislation has been blocked by Republicans at the General Assembly and the gun lobby.
In 2020, there were 22 firearm accidents in Georgia involving children, 11 of which were fatal. These accidents are not merely a statistic, Parent said.
"Children as young as 2 and as old as 17 have shot their siblings, friends, their parents, neighbors, classmates and thousands of times, themselves," said Parent. "If we fail to act, unsecured firearms in the hands of children will continue to wreak havoc on families, communities and our kids."
Jason Esteves, board of education chair of Atlanta Public Schools, announced a resolution to promote safe and responsible gun storage. The school board can't pass gun legislation, Esteves said, but it can educate stakeholders that guns must be stored responsibly.
DeKalb County Commissioner Ted Terry is introducing legislation to require safe storage of firearms. The legislation states: "It shall be unlawful for any person to store a firearm in any place where the person know, or reasonably should know, that a minor, at-risk person or prohibited person may gain access to the firearm, and the minor, at-risk person or prohibited person obtains access to and discharges the firearm," unless the firearm is secured.
Terry spoke with county commissioners and local leaders in Columbus, Macon, Savannah, Chatham, Athens, Clayton, Cobb, Gwinnett, Newton, Rockdale – all leaders who are interested in taking action in the absence of action at the state and federal level, he said.
"This is an opportunity for us to not only save children's lives at home, to reduce gun violence and to reduce school shootings," said Terry. "We're not waiting. We're taking action now."

redpajama_set_name: RedPajamaCommonCrawl


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With over three decades in the region, Paul, Weiss has long been recognized as a leader and legal innovator among international law firms in Asia. Our Asia based partners have been consistently ranked in the top tier of practitioners in their areas of expertise.
Prosus Conducts Accelerated Offering of Tencent Shares for $14.6 Billion
Paul, Weiss advised Prosus N.V. in its disposal and placing of approximately 2% of the issued shares of Tencent Holdings Limited, a Chinese technology conglomerate listed on the Hong Kong Stock Exchange.
L Catterton Asia Invests in Nebula Brands
Judie Ng Shortell
Paul, Weiss advised L Catterton Asia as the lead investor in a series B financing round of over $50 million in Nebula Brands, a leading Chinese Amazon vendors aggregator.
General Atlantic and Buyer Consortium Acquire 58.com in $8.7 Billion Deal
Paul, Weiss advised General Atlantic, a lead member of an investor consortium, in its acquisition of 58.com, China's largest online classifieds marketplace.
China's State Grid Acquires Chilean Utility Company Compania General de Electricidad for $3.04 Billion
Paul, Weiss advised China-based utilities company State Grid International Development Limited in its $3.04 billion acquisition of Compania General de Electricidad S.A. (CGE), a publicly traded corporation, from Spain's Naturgy Energy Group S.A.
Funds Managed by Affiliates of Apollo to Acquire Mitsubishi Chemical's Thermal and Emission Control Materials Business
Paul, Weiss is advising funds managed by affiliates of Apollo Global Management, Inc. in their acquisition of the thermal and emission control materials (MAFTEC) business from Mitsubishi Chemical Corporation and Mitsubishi Chemical High-Technica (MCHT).
DCP Acquires Stake in Datong Insurance Sales & Services
Paul, Weiss advised DCP Capital, in its purchase, alongside China Merchants Venture, ZWC Ventures and Huagai Capital, of a 32.98% stake in Datong Insurance Sales & Service Co., Ltd. from Anxin Trust.
KPS Capital Completes Sale of TaylorMade to Centroid Investment Partners
Paul, Weiss advised KPS Capital Partners, LP in the sale of its portfolio company TaylorMade Golf Company, Inc. to Centroid Investment Partners, a Seoul, Korea-based private equity firm.
DCP Capital to Acquire China's 51job in Take-Private Deal Valued at $5.7 Billion
Paul, Weiss is advising a DCP Capital Partners-led group of investors in their take-private acquisition of 51job, Inc., a leading U.S.-listed, China-based provider of integrated human resource services.
Didi Chuxing Carves Out $1.5 Billion Freight Business
Paul, Weiss is representing Didi Chuxing Technology Co., a leading app-based mobile transportation platform, in the carve-out and subsequent $1.5 billion fundraising of its freight business Didi Freight, an on-demand freight logistics and delivery services provider.
KKR and DCP Co-Invest in Adopt A Cow
Paul, Weiss advised KKR and DCP Capital in their investment in Adopt A Cow, a technology-enabled, direct-to-consumer dairy company in China.
Tarena to Merge With Kidedu in Take-Private Deal
Paul, Weiss is representing KKR as a rollover shareholder in Tarena International, Inc.'s buyout by Kidedu Holdings Limited
Paul, Weiss in Beijing: A New Chapter
Jerome A. Cohen
Xiaoyu Greg Liu
In August 2018, Paul, Weiss's Beijing office moved to Fortune Financial Center, the second-tallest office tower in the metropolis. The firm's relocation provided an opportunity to reflect on the office's storied history and future plans.
Chris Frey Interviewed on Enforcement Trends as Part of ALB Japan In-House Legal Summit
Litigation partner Chris Frey shared insights on recent cross-border enforcement and significant global cases as part of ALB's Virtual Japan In-House Legal Summit 2021.
Jack Lange Interviewed by Legal 500 Asia Pacific Hall of Fame
Corporate partner Jack Lange was recognized in The Legal 500 Asia Pacific Hall of Fame for his achievements in private equity work in Hong Kong.
Update for Chinese SEC Reporting Companies: President's Working Group Issues Mandated Report on Listings
On August 6, the President's Working Group on Financial Markets released its report in response to President Trump's mandate that it set forth recommendations to address the continued constraints on access by the Public Company…
Paul, Weiss Panel: Recent Development in the U.S. Affecting U.S.-Listed Chinese Companies
Paul, Weiss will host a webinar presentation, "Recent Developments in the United States Affecting U.S.-Listed Chinese Companies," featuring corporate partners Mark Bergman and Xiaoyu Greg Liu, and litigation partners Christopher…
Update for Chinese SEC Reporting Companies: President Trump Mandates Report on PCAOB Access and Investor Protections
In response to the political impasse over access by U.S. regulators to information relating to U.S.-listed Chinese companies and, in particular, access by the Public Company Accounting Oversight Board to work papers relating to the…
Disclosure and Other Considerations: an Update for Chinese SEC Reporting Companies
As many Chinese companies with SEC reporting obligations have taken advantage of the relief provided by the U.S. Securities and Exchange Commission to delay the filings of their annual reports on Form 20-F, we outline key disclosure…
U.S. State Department Issues Unprecedented Global Travel Advisory
The State Department has issued a Level 4 (Do Not Travel) advisory for all travel outside the United States. It advises U.S. citizens not to travel abroad and U.S. citizens abroad who reside in the United States to return home if…
Force Majeure in the Wake of the Coronavirus (COVID-19)
The coming months are likely to bring many assertions of force majeure—contract provisions that excuse a party's nonperformance when "acts of God" or other extraordinary events prevent a party from fulfilling its contractual…
M&A Perspectives: Japan - Focus on Activism
There is no question that activism is gaining traction in Japan. Reports indicate that as of the end of the 2019 proxy season, a record 54 Japanese companies received shareholder proposals for the 2019 annual meetings – a 29% increase …
Senior DOJ Antitrust Official Rejoins Paul, Weiss
Andrew Finch has returned to the firm as Co-Chair of the Antitrust Practice Group.
Paul, Weiss Recognized at ALB China Law Awards 2021
Paul, Weiss won Asian Legal Business's "M&A Deal of the Year – Premium" award presented at ALB's annual China Law Awards.
Paul, Weiss Wins Six China Business Law Awards
Paul, Weiss was recognized by the China Business Law Journal as an international law firm winner in the categories of "M&A (Inbound & Domestic)," "M&A (Outbound)," "Private Equity & Venture Capital," "Consumer and…
Paul, Weiss Recognized by IFLR Asia-Pacific Awards With Two "Deals of the Year"
Paul, Weiss was recognized by International Financial Law Review's 2021 Asia-Pacific Awards with a "Private Equity Deal of the Year" and a "Restructuring Deal of the Year."
Three Paul, Weiss Transactions Named Deals of the Year by China Business Law Journal
Three Paul, Weiss transactions have been named 2020 "Deals of the Year" by the China Business Law Journal.
Judie Ng Shortell Named to China Business Law Journal's 2020 "A-List"
Corporate partner Judie Ng Shortell has been included in China Business Law Journal's "The A-List 2020: China's Elite 100 Lawyers (Foreign Firms)."
Paul, Weiss Recognized by FinanceAsia in Its 2020 Achievement Awards
Paul, Weiss was recognized by FinanceAsia with a "Venture Capital/Private Equity Deal of the Year" award for our representation of General Atlantic LLC as lead member of an investor consortium in the $9.68 billion take-private…
Paul, Weiss Recognized at ALB Hong Kong Law Awards 2020
Asian Legal Business recognized two Paul, Weiss transactions as "M&A Deal of the Year" and "Finance Deal of the Year."
Paul, Weiss Named "Cross-border M&A Legal Adviser of the Year," "Consumer M&A Deal of the Year " and "Private Equity Deal of the Year" by Mergermarket for Chinese M&A
Paul, Weiss was named "Cross-border M&A Legal Adviser of the Year" by Mergermarket at its annual China M&A Awards.
Of Counsel Jerome Cohen Awarded Honorary Doctorate of Law from Yale University
On May 18, corporate of counsel Jerome Cohen, a pioneering scholar of Chinese business and human rights law, was presented with his third degree from Yale University: an honorary Doctor of Law.
Jack Lange Highlighted in Legal 500 Asia Pacific Hall of Fame
Corporate partner Jack Lange was recognized in The Legal 500 Asia Pacific Hall of Fame for their excellent achievement in private equity work in Hong Kong.


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Portfolio » National Arts Program Venue Map
National Arts Program Venue Map
4x3 has revamped not only the NAP with an entirely new responsive website, but also added value with new ways to track our artists, engage our users and use social media to our advantage and benefit. In today's tough philanthropic times, staying fresh, dynamic and keeping your mission relevant is critical to our future. They have been a great asset to our organization.
Jackie Szafara
The National Art Program hosts several annual exhibits featuring the visual artworks across the United States. As such, it is necessary to integrate custom Google Maps to highlight exhibit venues for members.
4x3 built and integrated custom Google maps and other location-based assets into mobile and desktop redesign. Our Drupal-based web platform allows for sophisticated multi-layer, interactive map that enhances the website's usability, social integration and local SEO.
View More from The National Arts Program »
New Year, New Look: NAP Website Redesign
It's important that a website always reflects the company's current strategy and communicates it's brand values. Design and development are crucial when thinking about website redesign. By working closely with The National Arts Program, 4x3 was able to do a full web redesign in coordination with the launch of their new logo and new brand from J2 Design.
© 2022 4x3, LLC Design and Development | Suburban Philadelphia Site Design and Programming 4x3


If you want to authorize anyone or any organization to properly handle your affairs while you are unable to do so or while you are unavailable, you should get a power of attorney. It is a document that summarizes and proves your agreement to give your appointed person (the agent or attorney-in-fact) the authority to act on your behalf.
There are four main types of power of attorney that you could choose from. These types may be functional and useful depending on your need and requirements. They are: general, special, healthcare, and durable power of attorney.
A general power of attorney is a document that gives your agent a broad authority in handling your affairs. This authority usually includes handling of your banking transactions, purchasing and disposing properties, settling claims, exercising stock rights, entering into deals or contracts, filing tax returns, and buying life insurance. It is usually used to enable your appointed agent the power to handle your important transactions within a specified period when you are practically unable to do them personally.
The special power of attorney provides your agent specific powers. You would decide on those specifics. Unlike the general power of attorney, the special power attorney does not give the agent a broad range of coverage. It only specifies how he/she should act. The document should specify which activities the agent should do. Transactions that are not included in the provisions could not in any way be managed or handled by the person.
The healthcare power of attorney designates the agent as a person who should make proper healthcare decisions for you if you get mentally incompetent or unconscious. If you would not be able to make logical decisions due to health reasons, the agent would be authorized to do so in your behalf. However, take note that the healthcare power of attorney is not the same as a living will, which is a document to express your personal wishes in case you would need life-sustaining procedures.
The durable power of attorney could be a general, healthcare or special power of attorney containing specific durability provisions. In case you suddenly get mentally incapacitated while any of the three kinds of power of attorney is in effect, the durability provision of the document would allow the agent to stay as your attorney-in-fact indefinitely. In the durable power of attorney, you are acknowledging the possibility that you could become mentally or totally incompetent because of any accident or illness. For this power of attorney to take effect there has to be a genuine certification from a doctor to prove the incompetence.
In every power of attorney you would get into, it is always important to make sure you are choosing and agent or an attorney-in-fact who is very trustworthy and reliable. He/She should be able to uphold only your best interest when doing transactions and making decisions on your behalf. You may fully entrust into him/her the authority and power to handle and manage your money or assets.


An image from a peripheral blood smear showing red blood cell agglutination, spherocytes, and polychromasia (50X oil immersion).
An image from a peripheral blood smear showing numerous small mature lymphocytes and smudge cells seen in a patient with CLL (50X oil immersion). Numerous spherocytes and increased polychromasia is also noted, indicating an auto-immune hemolytic process.
An image from a peripheral blood smear showing numerous small mature lymphocytes and smudge cells seen in a patient with CLL (100X oil immersion). Numerous spherocytes and increased polychromasia is also noted (out of focus), indicating an auto-immune hemolytic process.
An image from a peripheral blood smear showing numerous small mature lymphocytes and a smudge cell seen in a patient with CLL (100X oil immersion). Numerous spherocytes and increased polychromasia is also noted, indicating an auto-immune hemolytic process.
An image from a peripheral blood smear showing numerous small mature lymphocytes and a smudge cell seen in a patient with CLL (100X oil immersion). Numerous spherocytes and increased polychromasia is also noted (out of focus), indicating an auto-immune hemolytic process.
An image from a peripheral blood smear demonstrating marked spherocytosis and polychromasia in hereditary spherocytosis (100X oil immersion). A stippled nucleated red blood cell (center) can also be seen.
This image from a peripheral blood smear demonstrates increased spherocytosis, polychromasia, and a Howell-Jolly body seen in either hereditary spherocytosis or autoimmune hemolytic anemia (AIHA).
An image from a peripheral blood smear demonstrating marked spherocytosis and polychromasia in hereditary spherocytosis (50X oil immersion). A nucleated red blood cell (center) and normal leukocytes can also be seen.


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Karen Kelser
Karen Kelser (Meritorious Service) - Inducted 2021
Karen Kelser is currently the Grassroots Director at FCV Ashburn under the umbrella of The St James. She has been the Director of Coaching Education and a head coach at Arlington Soccer. She worked 17 years at DC Stoddert, where she earned Coach of the Year. She worked there in Coaching Education, as an Age Group Director, coaching and developing players. She instructed the first all-women's coaching license for the state. Many players spent their formative years in that program and later advanced to NCAA DI and DIII, and moved on to national pools and teams. She earned the US Soccer Grassroots Coaching Instructor License. She has a BS in Exercise Science, and holds a current US Soccer National A Level Coaching License and National Youth License, KNVB Dutch Youth Coaching Diploma, and the NSCAA Advanced National Coaching License. She has been a Virginia State Coaching Education Instructor for VYSA since 1997. She has been a Director for the girls' North District Development-ODP program. She has also worked with West Central District D-ODP and ODP, and North District and State ODP programs. She was also a Regional Director for Coerver Coaching of Virginia. She played NCAA DI soccer at GWU, has head coached collegiately at Marymount University.
© Virginia-DC Soccer Hall of Fame. All rights reserved.


Eureka College baseball head coach Jerry Rashid picked up his first collegiate win on Sunday, defeating Elmhurst 5-4. Rashid, who has over 800 wins in high school baseball throughout central Illinois, is in his first season as the Red Devils head coach.
Courtney Kedroski was named to the NFCA Division III Leadoff Classic All-Tournament team for the Griffins softball squad. Kedroski hit .277 on the week with three doubles and one triple, driving in four and scoring four times. On the season Kedroski is hitting .296 with four RBI and six runs scored.
The Greenville men's basketball team put a scare into #9 ranked Augustana (Ill.) in the opening round of the NCAA Division III Tournament, jumping out to a 24-6 lead and leading by 20 points into the second-half. However, the Panthers hot hand, which knocked down 11 three-pointers in the first half, went cold with just four in the second-half and falling 123-111 to the host Vikings.
Iowa Wesleyan's Joseph Belarde took home NCBWA Division III Hitter of the Week honors last week. Belarde hit .538 with two home runs and nine runs batted in. He also picked up SLIAC Hitter of the Week honors and was named to the d3baseball.com Team of the Week.
The MacMurray baseball team is coming off a 9-6 win over Lawrence on Sunday. Each of the first seven hitters in the Highlanders line up notched a hit with Nathan Luft leading the way with three hits. Trevor Knipe picked up the win, going six innings and allowing two earned runs while striking out four.
Principia freshman Wyatt Dale was named the SLIAC Men's Tennis Player of the Week. Dale went 3-1 last week, winning both of his singles matches. Playing at the #1 spot for the Panthers he defeated Grinnell 6-2, 7-5; notching his teams only point of the afternoon. He also added a 7-5, 6-2 win over Division II Truman State and a doubles win.
Jimi Keating was named the NCBWA Division III Pitcher of the Week last week. This was after Keating earned SLIAC Pitcher of the Week honors and was named to the d3baseball.com Team of the Week. Keating is currently 2-0 with 34 strikeouts in 22 1/3 innings and has not allowed an earned run this season.
The Webster University women's basketball season came to a close last Friday night with an 86-45 loss to #2 ranked Wartburg College. Webster, playing in their first national tournament game since 2011, was unable to get their offense going against the undefeated and host Knights shooting just 29-percent from the floor in the game.
Katie Price was named the SLIAC Softball Hitter of the Week after her opening weekend performance against Wisconsin-Platteville. Price recorded three hits and five runs batted in during the doubleheader. She finished with a .600 average and a .714 on-base percentage.


Rocket and Fennel Salad with Sumac dressing – Ready in just minutes and the perfect accompaniment to any meal.
This rocket and fennel salad with sumac was something I thought I would try after a suggestion from my naturopath to introduce more bitter leaf salads into my diet. It is a salad I make regularly now because I just love it so much. It goes with pretty much everything and bitter leaves with the citrus sumac works so well. The salad is easy to put together and enjoyed by all. It is also the perfect salad to make ahead. You can always keep the dressing separate and make a big enough batch to take with you to work daily in the knowledge that bitter foods are so good for you. Why so?
I was apprehensive to introduce bitter foods into my diet. Not many people like the thought of eating bitter things, especially me. Like anyone else, I steer clear of anything that will make me want to heave and that is a lot of things because I have such a weak stomach!
However this salad is a delicious way to incorporate bitters into the diet! Promise.
One of the most important elements in overall health is balance. Unani Tibb (Greek Medicine), Prophetic Medicine, Chinese Medicine, Ayurveda and Traditional Medicine emphasises the need for balance in our diets. In our diets we often neglect bitter flavours in favour of salty or sweet flavours. Imbalances in the diet but also in other areas causes problems to overall health. Therefore slowly implementing changes is much more beneficial for the body, then making sudden drastic changes.
Bitter foods are specifically good for cleaning/detoxing/healing. As some of you are aware, that is a journey I have started recently. Rocket and fennel Salad with Sumac is one of the salads I really enjoy and eating it doesn't feel like a chore. That is to say it doesn't feel like I have to force myself to eat it in order to achieve balance.
So if rocket isn't your thing, you could use lettuce instead? Or Watercress? Or Dark Chocolate? Haha just kidding. That really won't work. Although I do make a salad at the moment with a dark chocolate dressing. It will be on le blog soon. Fennel and chocolate..hmm. I am seriously thinking about this now.
In a medium, large bowl combine the fennel , rocket leaves and red onion.
In a separate small bowl, whisk together the oil, sumac, lemon juice, salt and pepper.
Just before serving add the dressing to the salad leaves and top with toasted mixed seeds.
In Lunch, Recipes, Salads and Bowls, Sides. Bookmark the permalink.


It is common practice to monitor via screen, but being present in the workspace can bring advantages such as a swifter resolution.
In a previous article, we defined the concept of nano management as the real-time management of issues that can affect the quality, safety and yield of processed chickens. In that article, we also emphasized the need to remain vigilant for "hidden costs."
Hanging on the shackles: Are all shackles full? Has the processing speed been established?
Exit from the pluckers: Have all chickens been properly plucked?
Dispatch: Are trucks being loaded on time to ship clients' orders?
We also noted that one of the great challenges that processing plant managers face is to ensure, with their teams and simple tools, the successful operation of the plant.
If we look at successes in maximizing efficiency in vehicle production, there are two basic monitoring approaches: Muda, or total waste control, and Gemba, or real place.
These management models can also be successfully applied to poultry processing plants.
The seven classes of waste in operational processes were defined by Taiichi Ohno, who designed the Toyota production system. Similarly, classes of waste can be identified along the final part of the broiler production process, for example, at pre-slaughter, catching, transportation, in waiting time, during processing, through overproduction, reprocessing, and storage.
Failure to recognize human potential; studies have shown that the failure to address this small but significant detail can make all the difference between success and failure.
This Japanese term means that in order to successfully monitor in real time, those responsible for the task must be physically present, so that they can observe, evaluate and take corrective action as quickly as possible.
This workplace management concept can also be applied to poultry processing to improve the competitiveness of the company.
But why are these specific points so important?
By monitoring the birds entering the stunner, any pre-shock problems can be identified and remedied. Problems at this point can have serious implications for the automatic slaughter of the bird and carcass quality. If birds are leaving the stunner still conscious with a raised or shrunken neck, they will not pass through the machine guides to be slaughtered.
At the stunner exit, the success of the operation can be evaluated. Birds must be unconscious, have dilated pupils, a slight curve to the neck, their wings held close to the body and be totally calm.
On exit from the plucker, wing veins should be dilated, and there should be a widening of the vein near the thigh joint, which should have a bluish tinge.
Wing tips should not have accumulated blood and there must be no tonality. Any trauma pre-slaughter will present as hematomas, which are dark in color.
Chickens should be completely free from feathers and the skin should be intact. There should be no scratches or breaks to the skin, particularly around the wings, where the humerus may emerge.
As a check, make a statistically established selection of birds and cut the skin to examine the breast. This should show the natural color of muscle and subcutaneous fat should be attached to the skin.
Is the abdominal fat intact? It should weigh some 40 grams.
Is the neck cut of sufficient length?
Is the head cut flush with the first vertebra?
With regard to processing the gizzard, does the automatic system cut, wash, clean and completely remove the cuticle?
Is the percentage of lost meat known? Sampling should be carried out.
What percentage needs to be reprocessed to completely remove the cuticle?
Are chicken carcasses completely and uniformly submerged?
Is there foam - subcutaneous fat - on the water? Visually estimate how much foam may be present. It there too little, is the amount about right, or is there too much?
To sum up, following the Gemba philosophy will keep the various operations performed during the processing of chickens thoroughly under control.
On exit from the plucker, wing veins should be dilated.
Abdominal fat should be intact.
Foam levels pre-chilling should be evaluated visually.


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\section{Introduction}

Let $p , q \in \mathbb{N}-\{0\}$;
a    $p \times q$  interval matrix is a  $p \times q$  matrix
whose entries are closed bounded  nonempty intervals in $\mathbb{R}$.
We say that a  $p \times q$  matrix $A$  with entries in $\mathbb{R}$ is contained in $\mu$ if and only if, for every $i,j$, we have that $A_{i,j} \in \mu_{i,j}$.

 On the other side, for any field
 $K$, a partial matrix over $K$ is defined to be  a
matrix where only some of the entries are given and they are elements of
$K$;
a completion of a partial  matrix is a specification in $K$ of the unspecified entries.
We say that a submatrix of a partial matrix is specified if all its entries are specified.

There are several papers both on interval matrices and
on partial matrices.
On partial matrices, there is a wide literature about
the problem of determining the maximal and the minimal rank of the completions of a partial matrix.
 We quote, for instance, the papers  \cite{CD},  \cite{Woe} and
\cite{CJRW}. In the last, Cohen,  Johnson,  Rodman and Woerdeman determined
the maximal rank of the completions of a partial
matrix in terms of the ranks and the sizes of its maximal
specified submatrices; see also \cite{CD}
for the proof.
 The problem of determining the minimal rank of   the completions of a partial matrix seems more difficult  and it has been solved only in some particular cases,
  see for example  \cite{Woe1} for the case of triangular matrices.

 Also  interval matrices have been widely studied and in particular
there are several papers studying when a $p \times q $ interval  matrix $\mu$ has full rank, that is when all the matrices contained in $\mu$ have rank equal to $\min\{p,q\}$.
For any  $p \times q $ interval matrix $\mu = ( [m_{i,j}, M_{i,j}])_{i,j}$ with $m_{i,j} \leq M_{i,j}$,
let $C^{\mu}$,$\Delta^{\mu}$ and $|\mu|$ be
 the  $p \times q$   matrices such that $$ C^{\mu}_{i,j}= \frac{m_{i,j}+ M_{i,j}}{2}, \hspace*{1cm} \Delta^{\mu}_{i,j}= \frac{M_{i,j}- m_{i,j}}{2}, \hspace*{1cm}
|\mu|_{i,j} = \max\{|m_{i,j}|,| M_{i,j}|\} $$ for any $i,j$.
The following theorem
characterizes full-rank square interval matrices:

\begin{thm} {\bf (Rohn, \cite{Rohn})}
Let   $\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be  a  $p \times p$  interval matrix, where
 $m_{i,j} \leq M_{i,j}$  for any $i,j$.
Let $Y_p=\{-1,1\}^p$ and, for any $x
 \in Y_p$, denote by $T_x$ the diagonal matrix whose diagonal is $x$; moreover
 define
  $$C^{\mu}_{x,y} = C^{\mu} - T_x \, \Delta^{\mu} \, T_y.$$

Then  $\mu$ is a full-rank interval matrix
if and only if,  for each
$x,y ,x',y'\in Y_p$,  $$det(C^{\mu}_{x,y}) \,det(C^{\mu}_{x',y'})>0. $$
\end{thm}

See  \cite{Rohn} and  \cite{Rohn2} for other characterizations. Finally, as to interval matrices, we want to quote also the paper \cite{JR}, where
 an algorithm for checking regularity of interval matrices is presented, and
the following theorem characterizing
full-rank $p \times q$ interval matrices, see
\cite{Rohn3}, \cite{Rohn4}, \cite{Shary}:

\begin{thm}  {\bf (Rohn)}
A $p \times q$ interval matrix $\mu$ with $p \geq q$ has full rank if and only if the system
of inequalities $$\hspace*{2cm} |C^{\mu} x| \leq \Delta^{\mu}
|x|, \hspace*{1.5cm} x \in \mathbb{R}^q$$ has only the trivial solution $x=0$.
\end{thm}

  Obviously the problem of partial matrices in the real case and the one of interval matrices are connected; in fact  we can consider matrices whose entries
   are closed connected subsets of $\mathbb{R}$;  these matrices generalize both the interval matrices and the partial matrices.
   We call a matrix
 whose entries are closed connected subsets of $\mathbb{R}$
  a ``general closed interval matrix''.

  In this paper we generalize Rhon's result
  on full-rank square interval matrices
  to
general closed interval matrices, see Theorem \ref{gen} for the precise statement.

\section{Notation and some recalls}

$\bullet$  Let $\mathbb{R}_{>0}$ be the set $\{x \in \mathbb{R} | \; x >0\}$ and
let $\mathbb{R}_{\geq 0}$ be the set $\{x \in \mathbb{R} | \; x  \geq 0\}$; we define analogously $\mathbb{R}_{<0}$ and $\mathbb{R}_{ \leq 0}$.

$\bullet $ Throughout the paper  let $p , q \in \mathbb{N}-\{0\}$.

$\bullet $ Let $\Sigma_p$ be the set of the permutations on $\{1,....,p\}$.

$\bullet$ Let $M(p \times q, \mathbb{R}) $ denote the set of the $p \times q $  matrices
with entries in $\mathbb{R}$. For any $A
\in M(p \times q, \mathbb{R})$, let $rk(A) $ denote the rank of $A$
and let $A^{(j)}$ be the $j$-th column of $A$.

$\bullet$ For any $p \times q$ general closed interval matrix $\mu$, any $\{i_1, \ldots, i_s\} \subset \{1, \ldots , p\}$ and any $\{j_1, \ldots, j_r\} \subset \{1, \ldots , q\}$, we denote by $\mu_{\widehat{i_1,\ldots , i_s}, \widehat{j_1, \ldots , j_s}} $ the matrix obtained from $\mu$  by deleting the rows $i_1, \ldots , i_s$ and the columns  $j_1, \ldots , j_r$.

\begin{defin} A {\bf general  interval matrix} is a matrix
 whose entries are connected nonempty subsets of $\mathbb{R}$.

 A {\bf general closed interval matrix} is a matrix
 whose entries are closed connected  nonempty subsets of $\mathbb{R}$.

 An {\bf interval matrix} is a matrix
 whose entries are closed bounded nonempty intervals of $\mathbb{R}$.

 Let   $\mu $ be  a $p \times q $  general interval matrix.
 As we have already said,
 given a matrix $A \in M(p \times q, \mathbb{R}) $, we say that  $ A \in \mu $ if and only if  $a_{i,j} \in  \mu_{i,j} $ for any $i,j$.

      We define
$$mrk(\mu) = min\{rk(A)   | \; A \in \mu     \},$$
$$Mrk(\mu) = max\{rk(A) | \; A \in \mu     \}.$$
We call them respectively {\bf minimal rank} and {\bf maximal rank} of $\mu$.
Moreover, we define
$$rkRange (\mu) =  \{ rk(A)  | \; A \in \mu \};$$
we call the set above the {\bf rank range} of $\mu$.

We say that the  entry $i,j$ of $\mu$ is a {\bf constant}
 if $ \mu_{i,j}$ is a subset of $\mathbb{R}$ given by only one element.

We say that the  entry $i,j$ of $\mu$ is {\bf bounded}
 if $ \mu_{i,j}=[a,b]$ for some $a,b \in \mathbb{R}$; we say that  the  entry $i,j$ of $\mu$ is  {\bf half-bounded}
 if either  $ \mu_{i,j}=[a,+ \infty ) $ ({\bf left-bounded}) or
  $ \mu_{i,j}=(- \infty ,a] $  ({\bf right-bounded})
 for some $a \in \mathbb{R}$.
\end{defin}

\begin{rem}
Let $\mu$ be an interval matrix. Observe that  $$rkRange(\mu) =
  [mrk(\mu)  , Mrk(\mu)] \cap \mathbb{N}.$$
\end{rem}

See \cite{Rub} for a proof.

\begin{defin}
Given a $p \times p $ interval  matrix, $\nu$, a {\bf partial generalized
diagonal} ({\bf pg-diagonal} for short) of length $k$ of $\nu$ is a $k$-uple of the kind $$
(\nu_{i_1, j_1},\dots, \nu_{i_k, j_k})$$
for some  $\{i_1, \dots i_k\}$ and $ \{j_1, \dots, j_k\} $ subsets of $ \{1,\dots ,p\}$.

Its {\bf complementary matrix} is defined to be the submatrix of $\mu$ given by the rows and columns whose indices are respectively in  $\{1,\ldots , p\}- \{i_1, \ldots , i_k\}$ and
in  $\{1,\ldots , p\}- \{j_1, \ldots , j_k\}$.

We say that a pg-diagonal is {\bf
totally nonconstant} if and only if all its entries are not constant.

We define $det^c(\mu) $ as follows:
$$ det^c(\mu) = \sum_{\sigma \in \Sigma_p \; s.t. \; \mu_{1, \sigma(1)}, \dots, \mu_{p, \sigma(p)} \;  are \; constant} \epsilon (\sigma) \,
\mu_{1, \sigma(1)} \cdot \ldots  \cdot\mu_{p, \sigma(p)} ,$$
where $ \epsilon (\sigma)$ denotes the sign of the permutation $ \sigma$.
\end{defin}

The following theorem and corollary were proved in \cite{Rub} for interval matrices; the same
proof yields the results for general closed interval matrices:

\begin{thm} \label{Mrkquadrate}
Let $\mu $ be a $p \times p $ general closed interval matrix. Then $Mrk(\mu) < p$ if and only if the following conditions hold:

(1) in $\mu$ there is no totally nonconstant pg-diagonal of length $p$,

(2) the complementary matrix of every  totally nonconstant pg-diagonal of  length between $0$ and $p-1$ has $det^c $ equal to $0$.

\end{thm}

\begin{cor} \label{Mrk}
Let $\mu $ be a general closed  interval matrix. Then $Mrk(\mu)$
is the maximum of the natural numbers $t$ such that there is a $ t \times t $ submatrix  of
 $\mu$ either with a totally nonconstant pg-diagonal of  length
 $t$ or with a totally nonconstant
 pg-diagonal of length between $0$ and $t-1$ whose complementary matrix has $det^c  \neq 0$.
 \end{cor}

 \begin{nota} Let  $\mu$ be a general closed interval matrix.

$\bullet $
We denote by $\tilde{\mu}$ the matrix obtained from $\mu$ by replacing the entries $(-\infty , + \infty)$ with $0$.

 $\bullet$
 We denote by $ \overline{\mu}$
 the matrix obtained from $\mu$ by replacing every  entry of kind  $[a, + \infty)$, for some $a \in \mathbb{R}$,  with $a$ and every entry of kind $(-\infty, b]$, for some $b \in \mathbb{R}$, with $b$.

 $\bullet $
 We denote by $\mu_l$
  the matrix obtained from $\mu$ by replacing every entry of kind  $[a, b] $, for some $a ,b \in \mathbb{R}$ with $a \leq b$,  with $a$.
 We denote by $\mu_r$
  the matrix obtained from $\mu$ by replacing  every entry  of kind  $[a, b] $, for some $a ,b \in \mathbb{R}$ with $a \leq b$,  with $b$.

\end{nota}

 \begin{defin} \label{vertexmatrix}
Let $\mu $ be a  general closed interval matrix.

We say that $\gamma $ is  a {\bf vertex matrix} of $\mu$ if  $\gamma_{i,j} \in \{m_{i,j}, M_{i,j}\}$ for any $i,j$ such that $\mu_{i,j}$ is a bounded interval and $\gamma_{i,j}= \mu_{i,j}$ otherwise.

We say that a  vertex matrix $\gamma$ of $\mu$ is {\bf of even type} if,
for every  $2 \times 2$ submatrix of $\mu$ such that all its entries are bounded intervals,
either  the number of the entries of the corresponding submatrix of $\gamma$ that are equal to the minimum of the corresponding  entries of $\mu$ is even or some of its entries are constant.
We say that it is {\bf of odd type} if it is not of even type.  \end{defin}

  {\bf Example.} Let $$\mu=\begin{pmatrix}
[1,2] & [2,3] & [2,+\infty] \\
[-3,4] & [-1, 5] & [1,4]
  \end{pmatrix}.$$ Then $\gamma=\begin{pmatrix}
1 & 2 & [2,+\infty] \\
4 &  5 & 1
  \end{pmatrix}$ is a vertex matrix of $\mu $ of even type, while $\delta=\begin{pmatrix}
1 & 3 & [2 , -\infty)\\
4 &  5 & 1
  \end{pmatrix}$ is a  vertex matrix of $\mu$ of odd type.

\bigskip

Observe that, by using Definition \ref{vertexmatrix}, we can restate Rohn's theorem as follows:

\begin{thm} {\bf (Rohn, \cite{Rohn})}  \label{Rohnbis}
Let   $\mu$ be  a  $p \times p$  interval matrix.
Then  $\mu$ is a full-rank interval matrix
if and only if,  for any vertex matrices $A_1, A_2$ of even type of $\mu$, $$det(A_1) \,det(A_2)>0. $$
\end{thm}

\section{The main result}

\begin{rem} \label{polin}
Let $p(x_1,\ldots, x_n)$ be a polynomial
with coefficients in $\mathbb{R}$ of degree $1$ in every variable. Let $\overline{x} \in \mathbb{R}^n$.
Then $p(x) \geq 0 $ (respectively $p(x)>0$)  for every $x \in \overline{x} + \mathbb{R}^n_{\geq 0}$ if and only if
$p(\overline{x}) \geq 0$ (respectively $p(\overline{x})>0$)
and $\frac{ \partial \,p }{\partial x_i} (x) \geq 0 $     for every $x
 \in \overline{x} + \mathbb{R}^n_{\geq 0}$ and for every $i=1, \ldots, n$.

\end{rem}

\begin{lem} \label{lem1}
Let $\mu $ be a general closed interval $p \times p$ matrix.
Then $\mu $ is full-rank if and only if
$\tilde{\mu}$ is full-rank and for every
$i,j$ such that $ \mu_{i,j}= (-\infty, + \infty)$
we have that $ Mrk( \mu_{\hat{i}, \hat{j}})
 < p-1$.
\end{lem}

\begin{proof} Suppose
 $\mu $ is full-rank. Then  obviously
$\tilde{\mu}$ is full-rank.  Moreover, let
$i,j$ be such that $ \mu_{i,j}= (-\infty, + \infty)$. Then the  determinant of every $A \in  \mu_{\hat{i}, \hat{j}}$ must be zero; otherwise, suppose there  exists  $A \in  \mu_{\hat{i}, \hat{j}}$ with $det(A) \neq 0$; then,
for any choice of
 $x_{i,s}$ in  $\mu_{i,s}$ for any $s \in \{1, \ldots , p\}-\{j\}$
  and $x_{r,j}$ in  $\mu_{r,j}$ for any $r \in \{1, \ldots , p\}-\{i\}$,
we can choose $x_{i,j} \in  \mu_{i,j}$ such that, if we define $X$ to be the matrix
such that   $X_{r,s}= x_{r,s}$ for $(r,s)$ such that
either $r=i$ or $s=j$   and
$X_{\hat{i}, \hat{j}}=A$, we have that
the determinant of $X$  is zero, which is absurd since
$\mu$ is full-rank.
So $ Mrk( \mu_{\hat{i}, \hat{j}})
 < p-1$ and we have proved the right-handed implication.

 On the other side, let $(i_1,j_1), \ldots,
 (i_s, j_s) $ be the indices of the entries of $\mu $ equal to $ (-\infty, + \infty)$ and suppose that $\tilde{\mu}$ is full-rank and that $ Mrk( \mu_{\hat{i_k}, \hat{j_k}})< p-1$
 for every $k=1, \ldots ,s$.
 Let  $B \in M(p \times p, \mathbb{R})$ be such that
$B \in   \mu$. For every  $k=1, \ldots, s$, let $B_k$ be the matrix obtained from $B$ by
 replacing the  entries $(i_1,j_1), \ldots , (i_k, j_k) $  with $0$. Then
 $det (B)= det (B_1)= \ldots =det(B_s)  $
 since $ Mrk( \mu_{\hat{i_k}, \hat{j_k}})< p-1$ for every $k=1, \ldots ,s$.
Obviously $B_s \in \tilde{\mu}$, so $det (B_s)$ is nonzero  since $\tilde{\mu}$ is full-rank; hence $det(B)$ is nonzero  and
we conclude.
\end{proof}

\begin{lem}  \label{lem2}
Let $\nu $ be  a general closed interval $p \times p $ matrix with only bounded or half-bounded entries. Then $\nu $ is full-rank
 if and only if, for any $\gamma $ vertex matrix of $\nu$ of even type, we have that $\gamma $  is full-rank and  $det(\overline{\gamma})$ has the same sign as $det( \overline{\nu}_l)$.
\end{lem}

\begin{proof} $\Longrightarrow$
Obviously if $\nu$ has full-rank, then the determinant of all
the matrices contained in $\nu $ must have the same sign (since the determinant is a continous function and the image by a continous function of a connected subset is connected), in particular
 $det(\overline{\gamma})$ must have the same sign as $det( \overline{\nu}_l)$.

 $\Longleftarrow$
Let $A \in M(p \times p, \mathbb{R}) $ be such that $A \in \nu$; define
$\alpha $ to be the interval matrix such that
$\alpha_{i,j} = \nu_{i,j}$ if $\nu_{i,j}$  is bounded and $\alpha_{i,j} = a_{i,j}$ if $\nu_{i,j}$  is half-bounded.

 To prove that $A$ has full-rank, obviously it is sufficient to prove that $\alpha$ is full-rank.
 By Rohn's theorem (see Theorem \ref{Rohnbis}), to prove that $\alpha$ is full-rank, it is sufficient to prove that  any two
 vertex matrices $A_1,A_2$   of even type of $\alpha$  are  full-rank and the sign of  their determinant is the same.
Obviously, for $i=1,2$, the matrix  $A_i$ is contained in a vertex matrix $\gamma_i$ of even type of $\nu$;  by assumption,  for $i=1,2$, the matrix $\gamma_i$ is full-rank, so the matrix $A_i$ is full-rank
and its determinant has the same sign
as  $det(\overline{\gamma}_i)$.
Moreover,   by assumption the sign of
$det(\overline{\gamma}_i)$ is equal to the
sign of $det( \overline{\nu}_l)$ for $i=1,2$;
 in particular $det(\overline{\gamma}_1)$
 and $det(\overline{\gamma}_2)$ have the same sign, so $det(A_1)$ and $det (A_2)$
 have the same sign, as we wanted to prove.
\end{proof}

\begin{nota}
Let $\rho$ be a square general closed interval matrix. We say that $DET(\rho)$ is
greater than $0$ (respectively less than $0$, equal to $0$...) if and only if,  for any $A \in \rho$, we have that
$det(A)$ is greater than $0$ (respectively less than $0$, equal to $0$...).
\end{nota}

\begin{lem}  \label{lem3}
Let $\rho $ be  a general closed interval $p \times p $ matrix with only constant or half-bounded entries. Then $\rho $ is full-rank
 if and only if $det(\overline{\rho}) \neq 0$ and,
 for any $(i_1,j_1), \ldots,
 (i_s,j_s) \in \{1,\ldots , p \} \times   \{1,\ldots , p \} $ such that $i_1, \ldots , i_s$ are distinct and $j_1, \ldots , j_s$ are distinct and $\rho_{i_1,j_1}, \ldots , \rho_{i_s,j_s} $ are half-bounded,
$$ (-1)^{i_1+j_1+ \widetilde{i_2} + \widetilde{j_2}+ \ldots + \widetilde{i_s}+ \widetilde{j_s}+ \chi((i_1,j_1),
\ldots, (i_s, j_s) ) }  det (\overline{\rho}) \,det (\overline{\rho}_{\widehat{i_1,\ldots, i_s}, \widehat{j_1, \ldots, j_s}} )  \geq 0, $$
where:

$\bullet $ the determinant of a $0 \times 0 $ matrix is defined to be $1$,

$\bullet$
$\chi((i_1,j_1),
\ldots, (i_s, j_s) )$ is defined to be  the number of the  right-bounded intervals in
$\rho_{i_1,j_1}, \ldots, \rho_{i_s,j_s}$,

$\bullet$
 for $t=2, \ldots, s$, we define
$\widetilde{i_t}$ to be  $i_t$ minus the number of the elements among $i_1, \ldots i_{t-1}$ smaller than
$i_t$ and  $\widetilde{j_t}$ to be  $j_t$ minus the number of the elements among $j_1, \ldots j_{t-1}$ smaller than  $j_t$.

\end{lem}

\begin{proof}
By Remark \ref{polin}, the matrix $\rho $ is full-rank if and only if   $det(\overline{\rho}) \neq 0$ and,
for any $i_1, j_1$ such that $\rho_{i_1,j_1}$ is half-bounded,
$$ (-1)^{i_1+ j_1 + \chi(i_1,j_1)} \, det (\overline{\rho} ) \,DET (\rho_{\hat{i_1},\hat{j_1}} ) \geq 0 $$
and, again by  Remark \ref{polin}, the last condition holds  if and only if,
for any $i_1, j_1$ such that $\rho_{i_1,j_1}$ is half-bounded, we have that
$$ (-1)^{i_1+ j_1 + \chi(i_1,j_1)} \, det (\overline{\rho} ) \,det (\overline{\rho}_{\hat{i_1},\hat{j_1}} ) \geq 0 $$
and, for any  $i_2, j_2$ such that $i_1 \neq i_2$ and $j_1
\neq j_2$ and
$\rho_{i_2,j_2}$ is half-bounded, we have that
$$ (-1)^{i_1+ j_1 +\widetilde{i_2} + \widetilde{j_2} + \chi((i_1,j_1), (i_2,j_2))} \, det (\overline{\rho} ) \,DET (\rho_{\widehat{i_1,i_2},\widehat{j_1,j_2}} ) \geq 0 $$
and so on.
\end{proof}

\begin{thm} \label{gen}
Let $\mu $ be a general closed interval matrix.
Then $\mu $ is full-rank if and only if the following conditions hold:

(1) for every  $i,j$ such that  $\mu_{i,j} = (- \infty, +\infty) $ we have that in  $\mu_{\hat{i}, \hat{j}} $
 there are no totally nonconstant pg-diagonal of  length
 $p-1$ and the complementary matrix of every   totally nonconstant
 pg-diagonal in  $\mu_{\hat{i}, \hat{j}} $ of  length between $0$ and $p-2$  has $det^c $ equal to $0$.

(2) the product of the determinant every  vertex matrix of  $\overline{\tilde{\mu}}$ of even type and the determinant of $\overline{\tilde{\mu}}_l$
is positive,

(3)  for every vertex matrix $\gamma$ of $\tilde{\mu}$ of even type and every $(i_1,j_1),\ldots, (i_s, j_s)
\in \{1,\ldots , p \} \times   \{1,\ldots , p \} $ such that $i_1, \ldots , i_s$ are distinct and $j_1, \ldots , j_s$ are distinct and
$\mu_{i_1,j_1}, \ldots , \mu_{i_s,j_s} $ are half-bounded, we have:
$$ (-1)^{i_1+j_1+ \widetilde{i_2}+ \widetilde{j_2}+\ldots + \widetilde{i_s}+ \widetilde{j_s}+ \chi((i_1,j_1),
\ldots, (i_s, j_s) ) }
det (\overline{\tilde{\mu}}_l) \,
det (\overline{\gamma}_{\widehat{i_1,\ldots, i_s}, \widehat{j_1, \ldots, j_s}} )  \geq 0 ,$$
where:

$\bullet $  the determinant of a $0 \times 0 $ matrix is defined to be $1$,

$\bullet$  the number $\chi((i_1,j_1),
\ldots, (i_s, j_s) )$ is defined to be the number of right-bounded
intervals  in
$\mu_{i_1,j_1}, \ldots, \mu_{i_s,j_s}$,

$\bullet $
 for $t=2, \ldots, s$,  we define
$$\widetilde{i_t} := i_t - \sharp \{i_r\; \mbox{\em for} \; r=1, \dots,  t-1 | \; i_r <i_t   \}$$
$$\widetilde{j_t} := j_t - \sharp \{j_r\; \mbox{\em for} \; r=1, \dots,  t-1 | \; j_r <j_t   \}.$$
\end{thm}

\begin{proof} By Lemma \ref{lem1},
the matrix  $\mu $ is full-rank if and only if
$\tilde{\mu}$ is full-rank and for every
$i,j$ such that $ \mu_{i,j}= (-\infty, + \infty)$
we have that $ Mrk( \mu_{\hat{i}, \hat{j}})
 < p-1$. By Theorem \ref{Mrkquadrate}
this is true if and only if $\tilde{\mu}$ is full-rank and for every
$i,j$ such that $ \mu_{i,j}= (-\infty, + \infty)$
we have that
 in  $\mu_{\hat{i}, \hat{j}} $
 there are no totally nonconstant pg-diagonal of  length
 $p-1$ and the complementary matrix of every   totally nonconstant
 pg-diagonal in  $\mu_{\hat{i}, \hat{j}} $ of  length between $0$ and $p-2$  has $det^c $ equal to $ 0$.

 Moreover, by Lemma \ref{lem2}
(with $\nu= \tilde{\mu}$), we have that $\tilde{\mu}$ is full-rank
 if and only if, for any $\gamma $ vertex matrix of $\tilde{\mu}$ of even type, we have that $\gamma $  is full-rank and  $det(\overline{\gamma})$ has the same sign as $det( \overline{\tilde{\mu}}_l)$.

 Finally,
 this is true if and only if (2) holds and,
 by Lemma \ref{lem3}, for any $\gamma$ vertex matrix of $\tilde{\mu}$,
 for any $(i_1,j_1), \ldots,
 (i_s,j_s) \in \{1,\ldots , p \} \times   \{1,\ldots , p \} $ such that $i_1, \ldots , i_s$ are distinct and $j_1, \ldots , j_s$ are distinct and $\gamma_{i_1,j_1}, \ldots , \gamma_{i_s,j_s} $ are half-bounded, we have that  $det(\overline{\gamma}) \neq 0$
and
$$ (-1)^{i_1+j_1+ \widetilde{i_2} + \widetilde{j_2} \ldots +\widetilde{i_s}+ \widetilde{j_s}+ \chi((i_1,j_1),
\ldots, (i_s, j_s) ) } \, det (\overline{\gamma})  \,det (\overline{\gamma}_{\widehat{i_1,\ldots, i_s}, \widehat{j_1, \ldots, j_s}} )
  \geq 0, $$
which, by condition (2), is equivalent to condition (3).
\end{proof}

{\bf Examples.}
1) Let $$\alpha= \begin{pmatrix}
(-\infty , +\infty ) & [1, + \infty ) & 1 & 1 & 4 \\
1 & [2,3] & 6 & 2 & 4 \\
(-\infty ,2] & 0 & [1,4] & 0 & [3,6]\\
0 & [-1, 2] & 3 & 1 & 2 \\
3 & 0  & 3 & 1 & 2
\end{pmatrix}.$$
We can easily that $\alpha$ does not satisfy
condition (2) of Theorem \ref{gen}, in fact
$\overline{\tilde{\alpha}}_l =  \begin{pmatrix}
0 & 1 & 1 & 1 & 4 \\
1 & 2 & 6 & 2 & 4 \\
2 & 0 & 1 & 0 & 3\\
0 & -1 & 3 & 1 & 2 \\
3 & 0  & 3 & 1 & 2
\end{pmatrix}$ has negative determinant, while the following vertex matrix of even type of $ \overline{\tilde{\alpha}}$ has positive determinant:
$$  \begin{pmatrix}
0 & 1 & 1 & 1 & 4 \\
1 & 2 & 6 & 2 & 4 \\
2 & 0 & 1 & 0 & 3\\
0 & 2 & 3 & 1 & 2 \\
3 & 0  & 3 & 1 & 2
\end{pmatrix}$$
So $\alpha$  is not full-rank. In fact it contains the matrix  $$ \begin{pmatrix}
0 & 1 & 1 & 1 & 4 \\
1 & 2 & 6 & 2 & 4 \\
2 & 0 & 1 & 0 & 3\\
0 & 6/5 & 3 & 1 & 2 \\
3 & 0  & 3 & 1 & 2
\end{pmatrix},$$ which is not invertible.

2) Let $$\beta =\begin{pmatrix} [2, +\infty) & 1 & 2 & (-\infty, +\infty) \\ [1,2] & 0 & 3 & 2 \\
3 & [3,7] & 5 & 3 \\ 0 & 0 & 0 & [1, +\infty)
\end{pmatrix}.$$ We can easily see that $\beta $ satisfies conditions (1),(2),(3) of Theorem
\ref{gen}, so it is full-rank.

3) Let $$\delta =\begin{pmatrix} (-\infty, +\infty) & 1 & 2 & (-\infty, +\infty) \\ [1,2]
&[1,2] & 9 & 2 \\ 3 & [1,5] & 4 & 0 \\
2 & [1,2] & [-1,+ \infty] & 3 \\
\end{pmatrix}.$$
Obviously it does not satisfy  condition (1) of Theorem \ref{gen}, in fact
$\delta_{\hat{1},\hat{1}}$ contains
totally nonconstant pg-diagonal whose complementary matrix has $det^c \neq 0$.
So $\delta $ is not full-rank.
\bigskip

{\bf Open problem.} A problem that naturally arises is
the one of the characterization of full-rank matrices whose entries are (not necessarily closed)
connected subsets of $\mathbb{R}$.

\bigskip

{\bf Acknowledgments.}
This work was supported by the National Group for Algebraic and Geometric Structures, and their  Applications (GNSAGA-INdAM).

{\small

redpajama_set_name: RedPajamaArXiv


text:
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William Longo is the Director of the Music Technology and Production program at Providence College, where he also teaches courses in jazz studies, music theory, and composition.
A versatile composer and arranger, Longo's works have been performed and recorded by notable jazz and popular artists, including Bruce Hornsby, Steve Miller, Jon Secada, Cyrille Aimée, and Nicole Henry. In 2014, Longo received the USAFB Sammy Nestico Award for his composition, New Day, which was premiered by The Airmen of Note, the premier jazz ensemble of the United States Air Force. In addition to his work as a composer, Longo also works as a conductor, recording and mixing engineer, and producer. Please visit williamlongomusic.com to learn more about his latest projects.
Prior to his appointment at Providence College, Dr. Longo served on the faculty at the University of Rhode Island, where he taught courses in Jazz History and Applied Jazz and Contemporary Composition. In addition, Dr. Longo was previously an instructor at the University of Miami, where he taught courses in the departments of Studio Music and Jazz, and Music Theory and Composition. An active educator during his eight years in South Florida, Dr. Longo also taught courses in Media Writing and Technology at Florida International University and Miami Dade College.
Dr. Longo completed his D.M.A. in Jazz Composition at the University of Miami and has earned degrees from the University of Connecticut (B.A.), Queens College (M.A.), and the University of Miami (M.M.). In addition, Dr. Longo is an Avid Certified Pro Tools Instructor and is authorized to teach official Avid courses and administer Avid certification exams at Providence College.
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Endoscopic Resection of a Pedunculated Brunner's Gland Hamartoma of the Duodenum.
Iwamuro M, Tanaka T, Ando S, Gotoda T, Kanzaki H, Kawano S, Kawahara Y, Okada H.
Case Rep Gastrointest Med. 2016;2016:6707235. doi: 10.1155/2016/6707235. Epub 2016 Aug 8.
Diagnosing Pancreatic Tumors Using Contrast-enhanced Harmonic Endoscopic Ultrasonography with Sonazoid.
Yamamoto N, Kato H, Mizukawa S, Muro S, Akimoto Y, Uchida D, Tomoda T, Matsumoto K, Horiguchi S, Tsutsumi K, Okada H.
Efficacy and Safety of Endoscopic Ultrasound-guided Ethanol Ablation Therapy for Pancreatic Neuroendocrine Tumors.
Matsumoto K, Kato H, Tsutsumi K, Mizukawa S, Yabe S, Seki H, Akimoto Y, Uchida D, Tomoda T, Yamamoto N, Horiguchi S, Okada H.
Acta Med Okayama. 2016 Aug;70(4):313-6.


Every year during the Oscar telecast, there's that moment when a buzzworthy young actor goes to the podium and mentions that recently she had the honor of hosting the Academy's Scientific and Technical Awards. Then, the producers cut to footage of that event, which features people you don't recognize winning for things you don't understand. The whole thing sounds very technical — and also, admittedly, rather boring.
Attend what's known more informally as the Sci-Tech Awards and you get a much different, warmer impression. Although the evening lacks the star power of the Academy Awards, it's easy to argue that Sci-Tech's honorees are more crucial to the foundation of modern-day filmmaking. A movie star can be a fleeting commodity. The innovations celebrated at the Sci-Tech Awards can define how millions of moviegoers experience films.
Part awards show, part insider soirée, the Sci-Tech Awards exude a chummy air as like-minded individuals talk shop in tuxedos at the elegant Beverly Wilshire Hotel ballroom. Where directors and actors may not have even gone to college, this room is filled with engineers and PhDs. They're not the sort who normally receive such public accolades. As Tom Lianza said when receiving his award for co-developing the HP DreamColor LP2480zx Professional Display, "I really don't know what to say — I'm a color scientist."
You know their work. You just don't know you do.
At the Sci-Tech Awards, acceptance speeches give shout-outs to HP, not agents — largely because these people don't have agents. If editors, cinematographers and other film craftspeople are dismissively identified as "below the line" talents, Sci-Tech winners are under the radar, practically invisible. You know their work. You just don't know you do.
The evening was hosted by Miles Teller and Margot Robbie, two great young actors who split the difference between polite formality — they dutifully introduced each award and detailed its recipients' significance — and lighthearted, smartass irreverence. While discussing "voxels," the elements that make up a virtual three-dimensional space, Teller used the word so many times in his presentation that the Whiplash star finally proposed that the audience take a drink every time someone said voxels, which quickly became the night's official running joke. Later, while presenting an award to Ken Museth, Peter Cucka, and Mihai Aldén for creating OpenVDB, an open-source tool for storing and manipulating voxels, The Wolf of Wall Street's Robbie came down with a case of the giggles, unable to continue. Apologizing while laughing, she explained that the term OpenVDB just felt filthy. "I don't know why it sounds so sexual to me," she exclaimed. Perhaps someone had had too many voxels.
Saturday night's recipients were sometimes honored for the most specialized of achievements. Michael Sechrest, Chris King, and Greg Croft were recognized for their work on SpeedTree Cinema, a software that produces digital forests in films like Noah. (The technology had started as a process in video games.) Marco Revelant, Alasdair Coull, and Shane Cooper received an award for Barbershop, a program focusing on the animation of individual hairs for characters in the Hobbit films and Dawn of the Planet of the Apes. These are the sort of feats that may seem insignificant to the common viewer, but in an era of year-round blockbusters, the demand for gorgeous artificial worlds is skyrocketing.
That said, there remained a playful tension between old-school Hollywood glamour and the cutting edge of filmic technology. Ron Fedkiw, a winner for developing Industrial Light & Magic's PhysBAM Destruction System, which has helped level cities (virtually) in movies like Pacific Rim, came to the podium and announced, "Mr. Fantastic gave me my award," alluding to Teller's role in the forthcoming Fantastic Four reboot. At most events, photogenic talents like Teller and Robbie are the main attraction, but on Saturday they were merely game sports struggling to tread water in a sea of brainiacs. At one point in the evening, Robbie, while wrestling with a particularly complicated explanation for one of the technical awards, took a moment to address the audience, tartly asking if we noticed that, "I have all the hard things to say." Teller, not missing a beat, responded, "I'm the eye candy."
A performance didn't elicit the greatest audience response. A chip did.
And one of the evening's two Oscar statutes went to Dr. Larry Hornbeck, who in 1987 invented the digital micromirror that's used in TI's DLP projectors, which helped end the era of film projectors in theaters. Receiving a standing ovation, Hornbeck — in his early 70s and looking grandfatherly with his glasses and receding hairline — took to the podium and held aloft a digital micromirror, or DLP chip. "Who would have ever believed … that this would change the way that the world sees new cinema?" That prompted a few random ecstatic whoops. In the land of the Sci-Tech Awards, a performance didn't elicit the greatest audience response. A chip did.
The Academy Awards ceremony that will be held February 22 will include snippets from Saturday's event. (During a photo shoot of all the evening's recipients at the close of the night, a photographer advised the gathered honorees to smile. "Remember," he said, "this is for the main show!") But the films vying for Oscars aren't so far removed from the innovations and transformations celebrated this evening. As Scientific and Technical Awards Chairman Richard Edlund assured the crowd at the beginning of the night, "They wouldn't be able to make movies without us."


The good thing where movies are right now is that studios that finance independent classic arms are allowing films to get made that five years ago no one would have made. Do you think they would have made Brokeback Mountain 10 years ago? Do you think Capote could have gotten off the ground five years ago? I think that studios are allowing their classic divisions to really take risks. To hire new directors and give new people chances, new writers chances. I think it�s a tremendously powerful revolution.
I think we are eventually going to get to a point where the audience is going to want to make a choice: to go to a movie theater and let the movie just roll over them, and they walk out having felt that a confident filmmaker told them a really good story and that�s really satisfying. But also in the future there is going to be a movie theater that allows the audience to be active members in the story-telling process. And I think the audiences who are flocking to video games, which is an interactive experience, are going to want to interact with movies as they play in real time. And there will be room for both. There will be stories that allow the audience to determine the outcome. Some day in the not too distant future you'll be able to go to a movie and the movie will be all around you. The movie will be over your head, it will be a 360 degrees around you, even be a little bit under you, and you will be in your seat with hand controls where you can rotate your seat, lean back, lean forward, have complete control over your seat to be able to keep up with all the imagery that is going to take you on a mind-blowing journey. I see that kind of experience without losing narrative.
Cell phones play a huge role in diminishing returns in the movies because you can do so much with your cell phones. You can talk on it, you can play games on it, you can watch TV on it, you can watch film clips on it, you can organize your life with it, you can text messages. Cell phones tend to bring us more inside of our lives whereas movies offer a chance to escape, so there are two competing forces. One force is very old — from nickelodeons to silent movies to talkies to cinemascope to cinerama to IMAX. The other venue is the gadgets that sort of anchor us in one place and eat up the hours in our day, that makes us wait for the DVD.
The great thing about 3D special effects, computerized effects, is that now we can pretty much do anything our imaginations tell us. That's one of the greatest tools I've ever had in my professional life — being able to imagine a dinosaur and a real dinosaur is walking though our artificial jungle. Right now technology cannot say no to our imaginations. That�s a great thing for audiences and for filmmakers, and it's one of the happier notes that I've observed over the last decade. The only danger is when the technological tools become the whole point of making the movie, as opposed to a great story with great characters. When we become infatuated with the tools that can do anything and we forget the story, that's when we get in trouble. And in the end the audience calls us on it. I appreciate the fact that we can all get carried away with the special effects because they are fun; they are fun for the filmmakers, they are fun for audiences. This is a burgeoning technology and we are all bound to overindulge in it and make some mistakes, but I think we all get back to telling a good story. If you look at some of the movies that came out this year, there were a couple special effects extravaganzas, but I think the movies that hit people closest to their hearts were films that dealt with morality and conscience and intolerance. None of [the best picture nominees] had special effects and this was an exceptional year in that sense. But it was also a year that brought us the last Star Wars,, one of the best Batman ever made; it brought us Narnia, the great King Kong, and I got a chance to squeeze War of the Worlds in there, where I worked very hard not to allow the special effects to upstage the characters in the movie.


Social media success is not about bashing out as much content as you can and waiting for the results to roll in. It might have worked at the dawn of social media when the competition was low, but I promise you, it's not going to work today.
A successful social media strategy demands you to sharpen your ears and be willing to use social listening. Social media is called social for a reason. It's not a one-way conversation. If social listening is not part of your strategy, you are doomed to fail. Or if you are lucky- just slow you down.
While social listening is crucial to a successful social media strategy, there are marketers who ignore it, don't know what it is, or is doing it wrong.
Therefore, in this article, I'll tell you everything you need to know about social listening, why it's important for your brand, and how to successfully implement it into your social media strategy.
Many people don't know what it is. And it makes me drop a tear, because social listening plays an important role in your customer relationships, and how you take care of your audience.
If you don't know what social listening is, don't worry, though! It's never too late to learn.
My initial plan with the answer to this question was to write what social listening is, but I've come to the realization that it's even more important to tell you what it is not because there are lots of confusion around social listening. Of course, I'll answer the initial question as well:).
Social listening is not the same thing as social media monitoring. It's understandable that these two get mixed up because they're similar in some ways, but there are a few key differences that separate the two.
Second of all, social listening is not just looking at your comments or mentions. It's so much more than that. Social listening is about extracting key information from what people say about you and to you on social media. and then taking that information and taking action based on the things you've learned.
Things are being said about your brand outside of the comments and mentions of your brand, so not paying attention to them would be missing out on valuable, key information that will allow you to get a deeper insight into your audience's thoughts and opinions about you.
Highly valuable information and insights, but without a mention of the brand.
There's a key difference between social media monitoring and social listening, and that is that monitoring only gathers information and listens to what people are saying, and includes a simple reply, letting them know you're trying to solve their issue.
But social listening is so much more than that. It takes the information into consideration and gets analyzed and reflected on. Instead of trying to solve the problems when they appear, it goes to the bottom of the reasons why the problems appear in the first place. This will present you with a bigger picture and a greater understanding of your brand and how your audience perceives it.
Social listening is the process of monitoring social media channels for mentions of your brand, competitors, product, and then analyzing and reflecting on that information – and then taking appropriate action, that will solve the root of the matter rather than just paint the ugly spot.
The purpose of using social listening is to get a better understanding of what people think about you, what they think is good, and what they think is bad. But if you just listen to what people have to say, but then don't do anything about the problems and pain points they're facing with your brand, what's the point of social listening?
There are many benefits and reasons you should use social listening, but summarized, without social listening, you're basically operating your business in the dark. If you aren't listening to what your audience has to say – the people who are most close to your business, potentially even using your product or service every day, you're missing out on tons of valuable information and insights from them. This means feedback and tips on things that you can do better.
And from inside the company, identifying flaws with yourself and your own business can be difficult, and that's why your customers are so valuable because they tell you their opinion and thoughts – but if you don't listen to it, it just shows that you don't care about them.
Your business probably has a social media strategy by now, but if it doesn't, now is the time to create one. And make sure that social listening is part of it. Learning what people say about you us vital to any brand for determining the success of your social media strategy, but if you never take the time to listen to the problems people have, you'll believe that your strategy is flawlessly fine-tuned to perfection – which never is the case.
Listening will also allow you to understand which social platforms are most effective for you, and it will tell you what platforms people are talking most about you. As a result, social listening will save you both time and money, because every time you make a mistake as a brand, it is costing you money – and a ton of time to make things right.
As a brand, you always want to measure results with your marketing efforts – and social media is no different. Social listening allows you to evaluate the current state of your social media presence, but it will also allow you to measure the results of your short-term tactics and efforts, and measure both quantitative and qualitative metrics.
The quantitative metric is as simple as looking at how many people are talking about your brand, and quality is looking at the sentiment of conversation, and more focusing on what people are saying rather than seeing that they are saying something.
Conversations including the Keyword "Pepsi" on Twitter. Keeping track of conversations around your brand will allow you to understand what people are saying and thinking about you.
Because, a disgruntled and angry customer is a brand mention, but just because it increases your number of mentions around your brand doesn't mean that it is positive. – It can be though – if you are able to respond to them and solve their issue, but this is also the reason why qualitative and quantitative are important – because using only one won't tell the full picture.
How well do you think you know your audience?
If the answer was yes, do you think you know your customers, or is a guess?
In fact, according to a new study by IBM, nearly 80% of consumers stated that brands really don't know them.
Knowing your audience is vital for knowing what content to share, what personality and tone you should use that resonate best with them, how you should interact with them and much more.
If you don't know them, you'll have a hard time connecting with them, and this creates difficulties in getting them to trust you, and considering the fact that trust is the single most important thing to driving a sale, you might be deep out in the water.
Wendy's is the most famous example of a brand that has found their brand personality on social media. They combine sassiness with an edgy personality that can be seen as controversial – but their target audience loves it.
Think about it: if your audience doesn't trust your brand, will they buy from you? Probably not. Luckily, social listening will help you turn this around and provide key information about your audience, letting you get a better understanding of who they are, and get to know them more thoroughly – leading to a long-lasting relationship and real trust establishment.
People are talking about your brand, but if you aren't there to meet them – whether an angry mention or a positive one, you won't have an opportunity to build your relationships with them, get to know them better, and ultimately increase their trust in you.
Your competition may or may not be using social listening, but if they're serious, they are. But the truth is that only a few are doing it correctly, and this leaves an opportunity for you to shine.
Normally, most brands only come to social monitoring, and responding to their customers who are complaining and trying to find a solution, but by going one step further, and using social listening and taking appropriate action on a very foundational level, you can become the first in your industry to address the problems that everyone in your industry are facing – no matter if they are customers or competitors of yours.
When monitoring what is being said by looking at relevant keywords and conversations, stories will unfold, and you will surely start seeing patterns of people who are having conversations where they are talking about issues they are having with products and brands in your industry – yourself included.
Taking this information and changing the way your brand works or how your product is developed will show your audience (and your competitors' audience) that you are listening to what people are saying, and also show that you are better than your competitors, thus leaving you in the spotlight.
Brand reputation is extremely important in this day and age, and if you aren't on your toes, things can go bad really quickly as information is exchanged in a heartbeat on social media.
Today, you aren't the one that is deciding your brand's reputation. Instead, your customers are the ones who are determining conversation about you, and if you don't take the time to listen to the conversations, you're putting your brand at a great risk.
By taking help of the power of social listening, you can identify potential threats and conversations where you can see an undertone of anger and complaints about your brand, and then ameliorate the situation before it escalates and harms your business on a bigger level.of your brand.
Now it's time to start executing, and before you do, you need to know what you should actually listen for.
When using social media listening, a lot of focus will go towards keywords when looking for conversations about and around your brand.
You also want to look at common misspellings of the keywords above.
If you, for example, search for a misspelled hashtag of "CocaCola" in hashtags on Instagram, you will notice that there is a lot of them. And this means that Coca-Cola is missing out on valuable information if they aren't actively looking for these types of keywords.
Over 32 thousand posts! That's a staggering amount and tons of information that can be extracted from them.
If you're just looking at the conversations about your brand and not taking action, you're working with social media monitoring, not social listening as mentioned earlier.
Social listening is so much more than gathering information and gaining an understanding of your audience and what they think of you. It is also so much more than taking the time to respond to the angry/disgruntled customers and the people who have faced an issue with your brand or products.
That's what your customer service do, and by working actively with social listening, you can minimize the messages that your customer service receives because you've already identified and put in solutions to the most common problems that your audience is facing.
This is a principle that goes for everything in life, and it is based on the fact that it is better to solve the real problem so that it doesn't happen again, rather than dealing with the issues it created.
If your roof is leaking, what is best? To put a bucket where the water drops or to actually fix the leakage?
With social listening, you cannot draw conclusions from one two or three observations. You need to allow time to show patterns in the things your audience is saying about you.
Dealing with the issues that your real problems create isn't a long-term strategy, and by using social listening, you identify the real problems and then take appropriate actions so that people aren't facing them again. It is better to put in resources and solutions to the real problems rather than wasting efforts on making your angry customers happy again.


text:
Q: How to swap elements in different list and different size Pandas? I have a dataframe df1. The dataframe has one column named 'Path'. Each row has a list. They are like this:
Path
____________________
[OAK, PHX, MIA, FLL, PBG]
[OAK, SEA, FLL, PBG]
[OAK, LAS, ORD, FLL, PBG]
[OAK, DFW, FLL, PBG]
...

I wish to swap the second and third value of each odd row with the corresponding second and third values of the next row (even row), and then swap each pair individually. In the input example from above, the values PHX, MIA from the first row should be swapped with the values SEA, FLL from the second row, and then inverted.
Path
____________________
[OAK, PHX, MIA, FLL, PBG]
[OAK, SEA, FLL, PBG]

# Swap 2nd and 3rd value between rows

Path
____________________
[OAK, SEA, FLL, FLL, PBG]
[OAK, PHX, MIA, PBG]

# Swap 2nd and 3rd value in all rows
Path
____________________
[OAK, FLL, SEA, FLL, PBG]
[OAK, MIA, PHX, PBG]

The result should be something like this:
Path
____________________
[OAK, FLL, SEA, FLL, PBG]
[OAK, MIA, PHX, PBG]
[OAK, FLL, DFW, FLL, PBG]
[OAK, ORD, LAS, PBG]
....

How can I do it with Python?

A: out = df['Path'].apply(lambda x : pd.Series(x)  )

dfLength = len(df)
if dfLength%2==0:
    oddIndex = list(range(0,dfLength-1, 2))
    evenIndex = list(range(1, dfLength,2))
else:
    oddIndex = list(range(0,dfLength, 2))
    evenIndex = list(range(1, dfLength,2))

#Swapping odd-even rows
oddData = out.iloc[oddIndex][[1,2]].copy()
evenData = out.iloc[evenIndex][[1,2]].copy()

out.iloc[oddIndex, [1,2]] = evenData.values
out.iloc[evenIndex, [1,2]] = oddData.values

#Swapping columns 2 & 3
col2 = out.loc[:,1].copy()
col3 = out.loc[:,2].copy()

out.loc[:,1] = col3.values
out.loc[:,2] = col2.values

Final output would look like
     0    1    2    3    4
0  OAK  FLL  SEA  FLL  PBG
1  OAK  MIA  PHX  PBG  NaN
2  OAK  FLL  DFW  FLL  PBG
3  OAK  ORD  LAS  PBG  NaN

If you want the output as a list,
out.apply(lambda x : list(x.dropna().values), axis = 1)

0    [OAK, PHX, MIA, FLL, PBG]
1         [OAK, SEA, FLL, PBG]
2    [OAK, LAS, ORD, FLL, PBG]
3         [OAK, DFW, FLL, PBG]
4         [OAK, DFW, FLL, PBG]

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Home Chevron icon It indicates an expandable section or menu, or sometimes previous / next navigation options. Media
Comedian Hannah Gadsby tore into Netflix's 'amoral algorithm cult' after its co-CEO defended releasing Chappelle's new special
Travis Clark
Gadsby.
Comedian Hannah Gadsby, who won an Emmy for a Netflix special, lambasted the company's co-CEO.
Co-CEO Ted Sarandos referenced Gadsby in a memo to staff defending Dave Chappelle's new special.
Some Netflix employees and talent have criticized the special, in which Chappelle makes transphobic comments.
Comedian Hannah Gadsby tore into Netflix co-CEO Ted Sarandos in an Instagram post on Friday, after Sarandos wrote a memo to staff, which referenced her, defending Dave Chappelle's controversial new standup special.
"Now I have to deal with even more of the hate and anger that Dave Chappelle's fans like to unleash on me every time Dave gets 20 million dollars to process his emotionally stunted partial word view," Gadsby wrote. "You didn't pay me nearly enough to deal with the real world consequences of the hate speech dog whistling you refuse to acknowledge, Ted."
Gadsby has two standup specials on Netflix, including "Nanette," for which she won an Emmy.
Sarandos defended Chappelle and Netflix's decision to release his new special, "The Closer," in an all-staff memo this week after employees began speaking out against the special, as reported by multiple outlets including Variety and The Hollywood Reporter. The Netflix trans employee resource group is planning a company-wide walkout next week.
"We are working hard to ensure marginalized communities aren't defined by a single story," Sarandos wrote in part. "So we have 'Sex Education,' 'Orange is the New Black,' 'Control Z,' Hannah Gadsby and Dave Chappelle all on Netflix. Key to this is increasing diversity on the content team itself."
"The Closer" is Chappelle's sixth and perhaps final Netflix special. The comedian struck a three-special deal in 2016 with Netflix worth $60 million, The New York Post reported at the time, but it's unclear if he was paid more for the additional specials.
In "The Closer," Chappelle makes transphobic comments and defends "Harry Potter" author JK Rowling by exclaiming "Team TERF!," which stands for trans exclusionary radical feminist, a term Rowling has referred to herself as.
Gadsby isn't the first person with content on Netflix who has spoken out against the streamer over the special.
Jaclyn Moore, who is trans and is an executive producer on Netflix's "Dear White People," said that she wouldn't work with the company "as long as they continue to put out and profit from blatantly and dangerously transphobic content."
Below is Gadsby's full post:
"Hey Ted Sarandos! Just a quick note to let you know that I would prefer if you didn't drag my name into your mess. Now I have to deal with even more of the hate and anger that Dave Chappelle's fans like to unleash on me every time Dave gets 20 million dollars to process his emotionally stunted partial word view. You didn't pay me nearly enough to deal with the real world consequences of the hate speech dog whistling you refuse to acknowledge, Ted. Fuck you and your amoral algorithm cult … I do shits with more back bone than you. That's just a joke! I definitely didn't cross a line because there isn't one."
Disclosure: Mathias Döpfner, CEO of Business Insider's parent company, Axel Springer, is a Netflix board member.
NOW WATCH: Netflix copycats are changing the streaming game and making viewers pay the price
More: Netflix Hannah Gadsby Streaming Ted Sarandos