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Email: leslielove@house.mi.gov
S-689 House Office Building
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Meet Leslie
Map Of House District 10
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D010 News / Committee / Bio - Leslie Love
State Representative Leslie Love is serving her third term representing the 10th House District, which comprises Redford Charter Township and a portion of northwest Detroit. Previously, Love served on the Workforce and Talent Development (Democratic Vice Chair), Transportation and Infrastructure, Regulatory Reform, Commerce and Trade, and Financial Services committees.
In addition to her committee assignments, Love has served as the Democratic Caucus vice chair, 2nd vice chair and chaplain for the Michigan Legislative Black Caucus, treasurer of the Progressive Women's Legislative Caucus, and on the Greater Wayne County Caucus.
In the first year of her first term, Love was the first woman, first African-American and first freshman representative in her caucus to introduce legislation that was signed into law as a public act (PA 68). Currently, she has more public acts than any other African-American Representative currently serving. Additionally, she has numerous House resolutions adopted, has introduced and co-sponsored numerous bills, and passed several bill amendments. Love has sponsored legislation on several significant bill packages, including the bipartisan Sexual Assault, Drivers' Responsibility, Juvenile Justice Reform and End of Life bill packages; Civil Rights bill package, Michigan Credit Union Act package, Pay Equity and Reproductive Rights packages.
Love was appointed to serve on the MiSTEM Advisory Council, a group of business, K-12 and higher education and philanthropic leaders dedicated to helping make Michigan a world leader in STEM (Science, Technology, Engineering and Math) education, Michigan Legislative Council, and was selected as a fellow to the, highly competitive, Council of State Government-Bowhay Institute for Legislative Leadership Development.
Known for her passionate floor speeches, Love made headlines when she led the charge informing voters about auto insurance reform in 2018 and Proposal 1, Michigan's road funding ballot initiative in 2015. She was also an outspoken opponent to eliminating straight-ticket voting, repealing prevailing wage and subversion of eliminating the sub-minimum wage.
To date, Love secured over $500,000 in appropriations for her district, making significant contributions to South Redford and Redford Union school district for technology enhancements and equipment. In addition, she has worked to help improve the community, helping secure funds for the Viola Liuzzo Park Association and O'Hair Neighborhood Association in Detroit for revitalization and community service programming, including $60,000 to Redford Township Junior Athletic Association for after-school youth sports.
As her slogan goes, "Always on the job. Always in the Community," and Love's commitment to and love for the district is evident by the plethora of ways in which she engages the community, including holding Coffee Hours, Legislative Updates, After Work with the Rep Dinners, community leader discussions, town halls and more.
Before her election to office, Love was the director of theatre operations and adjunct professor at Marygrove College for 12 years. She was a professor for Wayne County Community College District as well. In her spare time, she pursued her avocation as an actor, playwright, and stand-up comedian.
Love was born and raised in Michigan. She grew up in Detroit, attended Detroit Public Schools and graduated from Cooley High School. She earned a bachelor of arts from Siena Heights University, a master of fine arts from Wayne State University and a master of arts in human resources management from Marygrove College.
Michigan Wildlife Council Unveils Photo Mosaic Exhibit
Love on passage of expungement package of bills
Camilleri, Manoogian Look to Create Election Day Holidays
Love on the passing of former Congressman John Conyers
Love on package to support, protect Michigan workers
Love on closure of strip club in her district
Love on plan to crack down on companies committing payroll fraud
Appropriations subcommittee - Joint Capital Outlay - Democratic Vice Chair
Appropriations subcommittee - Transportation
Appropriations subcommittee - Health and Human Services


Gant Chinos deserve a place in every man's wardrobe. They are the ultimate in smart casual, meaning you can wear them for almost any occasion. Chinos fall brilliantly between the casual nature of denim and the formality of suit trousers. Effortlessly transforming from day to night occasions and with its military heritage and iconic traditional khaki colour, chinos are available in a huge variety of fabric, cut and colour. Check out the range of must-have GANT chinos at EJ Menswear.
Getting the right fit for your chinos couldn't be easier. They sit at a mid-rise waist, lower than suit trousers and similar to a pair of jeans. The traditional cut was a slim-fit, but now chinos are available in straight, skinny and tapered fits too.
The length is up to you. You can wear them how you want to, whether that's the classic ankle length or rolled up at the bottom. This is a look that works well if you're ditching the socks or want to show off some hi-top trainers.
Ever wondered where chinos get their name from? They started life as military trousers and began to be called chinos during the Spanish American War of 1898. Chino comes from the Spanish word for China, as the original fabric the trousers were made from was cotton twill, which came from China.
The trousers became official uniform of the U.S Army in the early 20th century and were a familiar sight during the world wars. Thanks to their versatility and comfort, military men continued wearing them after their service. They soon became associated with the Ivy League, becoming a famous symbol of the new 'preppy' look during the 1950s. The style was soon picked up by premium American lifestyle brand GANT.
Get your new chinos from EJ Menswear today for weekend casual and for a laid-back job paired with an Oxford shirt and brogues. Perfect for spring and summer, whether you're enjoying boat drinks, dining out or just fancy a change from the denim!


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Motorsports & Automotive
Thread starter Paul Jeffrey
f1 car launch formula one grand prix lewis hamilton mercedes mercedes w10 vatteri bottas
F1 2019 Car Launch: Mercedes W10
The most successful team of the hybrid turbo era have revealed their new car - welcome to the world the Mercedes-AMG Petronas W10.
Looking set to defend their 2018 Drivers and Constructors World Championship with an unchanged line-up of newly minted five-time World Champion Lewis Hamilton once again alongside Finnish team-mate Valtteri Bottas, Mercedes have revealed the new W10 at Silverstone earlier today - taking the opportunity to not only show off the new car, but to record some initial laps at the British circuit ahead of shipping out for pre-season testing later this month.
Much like Red Bull, Mercedes have taken the opportunity to shake down the new car under filming conditions at the home of the British Grand Prix, using specially fitted Pirelli tyres and keeping running under 100km, in a bid to perform last minute system checks and ensure no initial teething troubles crop up with the new machine prior to serious running taking place over at Barcelona in just a few days time.
"The 2019 season will be a new challenge for all of us," said Toto Wolff, Team Principal & CEO. "The regulations have changed quite substantially. We have to start from scratch, we need to prove ourselves again – against our own expectations and against our competitors. We start the season with zero points, so we're taking nothing for granted and there's absolutely no feeling of entitlement to be at the front. In fact, with the regulation change for the new season, every team can have a shot at the title and we're seeing all of them as a potential threat."
"Regulation changes are both opportunity and threat," said Technical Director James Allison. "They are an opportunity because all the old assumptions about what you need to have to be quick are swept away and, if you are fleet of foot and smart in dealing with that, you can do better than all the other teams that are tackling the same change. They are a threat because if you are not as smart and you didn't see how to make the most of these new regulations, then you'll certainly suffer in the coming season. But they are always exhilarating because you have that sharp sense of anxiety that you might not be doing enough but equally the thrill and excitement of looking forward to finding out."
The new car obviously takes advantage of the latest technical regulations, however perhaps most notable is a very nice new take on the traditional Silver Arrows colour scheme, Mercedes coming out with a refreshed design that looks very neat and impressive on the new car - one of my favourite designs revealed so far!
To check out when the next cars are set to be revealed, and how to watch it all unfold live, check out THIS LINK.
For more from the world of Formula One, head over to the RaceDepartment Formula One sub forum and join in with fellow fans of the top level of open wheel motorsport.
Like what we do at RaceDepartment? Follow us on Social Media!
Paul Jeffrey
RaceDepartment Editor-in-Chief, occasional YouTuber, commentator and broadcaster, with a passion for motorsport on both the real and virtual racetrack.
Reactions: Frank Lehmann, asehauDLM, BLAK1978 and 2 others
Gopher04
delicousmuffin
In my opinion the first good looking Mercedes F1 car since 2013 and probably my favourite of their F1 liveries. This might actually be my favourite livery of 2019. If someone told me that a few weeks ago I really wouldn't have believed them.
Diabolikpt
the car looks awesome the only thing is it needed a bit more black coming from the back
Koen Verlinde
They said that 2019 cars would look very different from 2018. Well I must be blind cause I ain't seeing any significant difference.
If quizzes are quizzical then what are tests?
I'm with @Gopher04
BigMike8
SimRacing 604
I like it! It's not flashy or a bold change, but I think it's a nice looking car. It blends the Halo well
NewOne0
A little disappointing that they lied about the camouflage to create some fake hype, but besides that, the subtle changes make the car look way better than it did all these last years. Imo, this is the best version of their "standard" livery that they kept since 2011. Still not as good as the 2010er livery tho.
Very good, almost like 2018 but the profile is a bit lower (see the comparison on the twotter website). Front wing isn't much different though, surprisingly.
Botass first to try it - hopefully a better performance for the finn this year.
Enagee
Some cars are just look too busy with their liveries you cant see the shape of the car ......This look simple and clean , you can see the air flow . Mclaren and Ferrari will be most interesting to see.
Very niiiice.
paracletus said:
Showing results for twitter website
Search instead for twotter website
Michel Forest
Great livery. And the design of that car looks really FAST... I'm « afraid » we are in for yet another dominant season by Mercedes. Plus, they will run a brand new engine... Ouch! Ferrari better step up their game in 2019.
Cheesenium
Definitely the best car so far.
farjam
the McLaren is ready too:
Alpha Romeo nose and frontwing:
farjam said:
So the livery is less dark and tyres too? Hard work from the designer. lol
Frankly i can't see the difference (same for Renault).
ZuneGuy
Simplicity and beauty - It looks like a race car. I'm looking forward to seeing Lewis throw this bad boy around.

redpajama_set_name: RedPajamaCommonCrawl


This is a certification for a expert menber of the Art committee-wester paiting of international culture & Arts federation in concordance with art.2-7 of the Regulations of International Culture & Arts Federation.
This certificate is awarded to Ariel Cavarro Avila who has participated in "the 3rd International Environment Exhibition - The earth I love" in korea.
Rodriguez Muñoz, Yony Percy (yony2010@hotmail.com) - Todos los derechos reservados, 2015.


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Red Deer resident Vince Jackman stands beside one of the 105 decorated Christmas trees in his home at 42 Comfort Close Thursday. To raise money for the Central Alberta Humane Society, Jackman and his partner are inviting Red Deerians over Dec. 9th to see the trees and leave a donation. Robin Grant/Red Deer Express
One hundred and five trees of Christmas
Red Deer couple decorated 105 Christmas trees to raise money for the Central Alberta Humane Society
Robin Grant
You'll likely hum O Christmas Tree at least once this holiday season – imagine doing that 105 times.
That's the number of big, small and medium sized trees crammed into one Red Deer couple's home in a bid to raise money for the local Humane Society.
Every year during the holiday season, Red Deer residents Vince Jackman and Tom Kereluk decorate more uniquely themed Christmas trees than you can keep track of.
"We have some that are plaid themed, some are Halloween-inspired, Asian themed, angels, Star Wars and Harry Potter," Jackman said.
Jackman has always been passionate about Christmas, he said. As he got older, he wanted to give back. The fundraising effort started 13 years ago.
As part of the fundraising, the couple holds a party at their home at the end of November. He said his partner bakes elaborate cheesecakes and they invite friends and family over who donate money to the cause.
Jackman even has a tree for his little chihuahua, Sophie, who passed away last year.
As an homage to Sophie, he said this year's fundraising effort was named after her.
"Her tree is filled with photos of her throughout her life of 11 years," he said. "She was a princess for sure."
On Dec. 9th, the couple is holding the last open house from 1 to 4 p.m. They are inviting residents to come over and see the trees. All they ask is for a donation to the Central Alberta Humane Society.
All the trees fit in their home at 42 Comfort Close.
"There are little and big trees," he said. "A designer tree by Alfred Sung, a tree of designer labels and perfume and cologne bottles.
"You have all those cologne bottles and perfume bottles and you never know what to do with them besides throw them out, so we thought, let's make a tree out of them. So that one is all blinged-out."
There are trees for everyone. Jackman said they won their Harry Potter tree at an auction last year. There is a Gay Pride tree and a tree that belonged to Jackman's grandmother.
Many of the themes were inspired by gifts he and Kereluk received over the years.
"We have one tree where our nieces and nephews have made ornaments for us every Christmas," he said. "It's a tree of what they have given us over the years."
He said as a not-for-profit, the Central Alberta Humane Society does not receive any government funding. It relies solely on donations and fundraising. He encourages people gifting pets to get them from shelters.
"Animals get the short end of the stick when it comes to being disposed of, so it's very dear to our heart so we all continue to do what we can and host these parties and make it bigger and better every year to raise money so that the animals that our shelter deals with will go to good homes and get the lives that they deserve."
So far, Jackman has raised $4,000. He is hoping to make it to $5,000.
"Everyone is welcome," he said. "Please come and enjoy and spread the Christmas cheer."
Nuit Blanche Red Deer looking to make a comeback in 2019
Tips for managing diabetes over the Christmas season


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Federal judge Bill Pryor's history in gay-pornography, like a ghost that won't go away, rears its head again with the emergence of nudie photograph No. 4
Bill Pryor No. 1, with special guest
(From Metro Weekly)
Bill Pryor, the fiercely anti-LGBT federal judge who almost became Donald Trump's nominee to the U.S. Supreme Court (SCOTUS), has a gay-porn past that keeps on giving.
We broke the story in September 2013 of Pryor's appearance at badpuppy.com, a Cocoa, Florida-based site that has grown to become a "super store" of gay-porn images. Less than one week after the story broke, and became somewhat of a viral Web sensation, deputies from Shelby County, Alabama, started making regular appearances (in twos and threes, with multiple vehicles) on our property. Less than a month after that, Deputy Chris Blevins entered our basement garage (without showing a warrant, stating he had a warrant, or stating his purpose for being on the premises) and beat me up, doused me with pepper spray, and hauled me to the Shelby County Jail for a five-month stay.
That's the price you pay for reporting accurately and forcefully about judicial and political corruption -- most of it Republican based -- in a Deep Red state. And you thought the First Amendment protected your rights to free speech and a free press.
I unearthed gay-porn photo No. 1 and broke the original story with old-fashioned, shoe-leather journalism. But the story has not ended there. We are blessed with a bunch of dedicated and sharp-eyed readers, and they have found other nudie photos of Pryor, part of a gallery that reportedly included eight to 12 images.
Bill Pryor No. 2
Readers helped us publish gay-porn photo No. 2 on March 22, 2017. That's the one featuring a youthful Pryor, then an undergraduate at Northeast Louisiana University (now the University of Louisiana Monroe, ULM), straddling a block of wood -- he's got wood, get it?
Photo No. 3, again dug up by enterprising readers, ran on April 5, 2017. It featured Pryor holding what we thought was a gourd, with a male face drawn on it. This seemed to mark a major step forward in artistic expression for the future federal judge. A helpful reader informed us that Pryor actually was holding a coconut, not a gourd. (See, I told you we had smart readers.)
Now, Legal Schnauzer readers have struck again, helping ensure that gay-porn photo No. 4 would land in our laps. (Isn't teamwork fun?) I never dreamed that we would wind up with a full, or almost full, gallery to Bill Pryor's nudie oeuvre. But at the rate our readers are digging things up, I think we might just make it -- and it might not take too much longer.
(Note: Redacted versions of photos 1-3 are published within this post. Links to NSFW versions of the photos, plus an amusing meme about Trump's one-time infatuation with Pryor, are at the end of this post.)
Photo No. 4 has appeared at three tumblr sites, that we know of: (Warning: All three links contain explicit images.)
* Oldies But Hotties!
* Vintage Gay
* Who's a Big Boy?
Our plans are to run photo No. 4 later this week. While this story undeniably has titillating qualities -- or perhaps "prickly qualities" would be a more accurate term -- there is serious junk going on beneath the surface. (He said "junk" . . . uh huh . . . uh huh.)
Multiple press reports during the 2016 presidential campaign indicated Pryor was the favorite to be Trump's choice for SCOTUS. Those reports picked up steam when U.S. Sen. Jeff Sessions (R-AL), long a champion of Pryor's career (perhaps because of the pair's deeply personal attachment), became the first major political figure to jump on the Trump Train -- eventually being named attorney general and lying during his confirmation hearings about meetings with a Russian ambassador.
"Mr. Coconut"
Why did Pryor's SCOTUS hopes sink into the depths, with the seat eventually going to Neil Gorsuch, of Colorado? We addressed that issue in a recent post, titled "Did Legal Schnauzer reporting on his nude photos at the badpuppy.com gay-pornography Web site cost Alabama's Bill Pryor a seat on the U.S. Supreme Court?" From that post:
Alabama federal judge Bill Pryor came in no better than third last night in the race to become Donald Trump's first (and, hopefully, only) nominee to the U.S. Supreme Court. That was quite a fall for a candidate who widely was considered the front-runner just a few weeks ago. And that raises this question: Did our reporting here at Legal Schnauzer about Pryor's ties to 1990s gay pornography cost him a lifetime appointment on the nation's highest court?
I don't know the answer to that question, and I admit that even raising it sounds like I'm tooting my own horn. (Perhaps that's because I am tooting my own horn.) But a number of intelligent people I like and admire -- a doctor, a retired lawyer, my wife -- have told me in recent days they thought Pryor's fading prospects were directly related to our reports about his nudie photos that appeared at badpuppy.com in the 1990s. The hypocrisy, my friends and loved ones said, of an ardently anti-gay rights judge appearing at a gay-porn Web site (in photos taken during his college days in the 1980s), would be too much for the Trump administration to stomach.
Here's more:
The conventional wisdom holds that Pryor's star fell because Team Trump was concerned his controversial statements about abortion rights, gay rights, privacy, and other hot-button cultural issues would make it difficult to get him confirmed. That might be the case, but such a scenario suggests reasonable, rational, and deliberate thought -- and we've seen no sign that exists in the Trump White House.
So, did Legal Schnauzer cause Pryor's downfall? (Hah! Sorry, couldn't contain myself.) Well, my friends and loved ones say they've seen signs that our reports about Pryor's BadPuppy days have made their way into conservative circles. And that, they say, spelled doom for Pryor, especially in the homophobic environment of the modern GOP.
For now, we don't know for sure what caused Pryor's slide, even though Jeff Sessions surely was whispering sweet nothings about his "boy toy" into the head Cheeto's ears. Heck, Pryor might even be resurrected for a future SCOTUS seat if Trump and Sessions can avoid being indicted long enough.
But here's the key point: At the rate our readers are digging up gay-porn photos of Pryor, we might have a full set before long. You can't say much positive about the Trump administration in its first 100 days, but there is this: The "Gang That Couldn't Shoot Straight" does appear to be somewhat Web savvy. Mr. Orange himself is the diabolical prince of Twitter, so it's hard to imagine that word of Pryor's adventures in homo-erotica have not reached 1600 Pennsylvania Avenue -- assuming Trump is ever there.
Will our readers ensure that Bill Pryor's judicial career goes into a deep, quiet slumber? Looks to me like they are well on their way.
From The Sword
Oh man, this makes my week. Can't wait for the photo behind Door No. 4
Message for Bill Pryor: Make tumblr your friend. Hah!
The story all along has been that the Pryor gallery included 8-12 images. Well, we're now up to 4 -- and counting. The story seems to be playing out just as it was written.
You have to wonder about a guy who poses for these pictures and turns out to be ardently against the rights of gay people. Peculiar. Classic self-hatred?
To 8.18 am
It is classic Republican hypocrisy. I guess for most of them it is "Do as I say" not "Do as I do" They all claim strict Christian observance but it is mostly a cover. The louder they shout their love of God and Christ the more you can be certain they are corrupt to their core!
Maybe Billy didn't have much to be proud of back in the day, other than that big schlong.
Pryor is Catholic, and if he's the product of warped Catholicism, that probably explains a lot.
What I see in those pictures is an exhibitionist, and I don't think those tendencies go away. I know I wouldn't leave my grandson alone with Pryor for a million bucks.
The meme of Schlump over Pryor's schlong is hilarious. Can't stop laughing.
Got to give Pryor credit for being well hung. Must make him feel good in the locker room.
Wish you could put up a jackpot to reward readers who find Pryor photos.
I would love to do that. Wish I had the cash to do that.
Pryor should be impeached because there is no question he failed to enclose these embarrassing photos that are in his background.
That really is the big question: Did Pryor lie to Congress? I asked Pryor about that in an email, and he refused to answer.
I'd say the chances are 99.99 percent that he lied under oath to Congress.
Snopes seems to disagree with you.
http://www.snopes.com/william-pryor-nude/
You are late to the game about Snopes. You also are off about their finding. "Unproven" simply means they couldn't prove it, one way or another. That's because they didn't do any legwork. Their finding should have been "we're too lazy to figure out what's going on."
Here is my analysis of Snopes piece, which I wrote roughly six months ago:
http://legalschnauzer.blogspot.com/2016/11/snopescom-famed-web-fact-checking-site.html
Daily Mail wrote a rather unflattering piece about Snopes a few months ago:
http://www.dailymail.co.uk/news/article-4042194/Facebook-fact-checker-arbitrate-fake-news-accused-defrauding-website-pay-prostitutes-staff-includes-escort-porn-star-Vice-Vixen-domme.html
Thanks for sharing. There is a lot of dicey stuff out there about Snopes; I'm not sure what is true and what isn't. I do give them credit for building a nice audience.
@11:08 simply has no understanding of how Snopes works. A finding of "unproven" doesnt' mean the story is false. It means they couldn't prove it true or false, and in this case, they simply didn't try very hard. Also, their analysis included a number of glaring errors of their own.
I was glad to have attention for the story, and it shows how widespread my reporting on the subject has become. But they did zippo to disprove the story, didn't even come close.
We have a misunderstanding here. This is not the post about photo No. 4. This is a post about photo No. 4 coming later this week. It's a post setting the stage for No. 4.
I ran links to the sites where No. 4 was found to give readers an idea where it was found. No one is asking readers to shift through hundreds, or thousands, of photos to find Bill Pryor. I will be producing the Pryor photo later this week. Here is the key information from the post, which perhaps you missed:
"Photo No. 4 has appeared at three tumblr sites, that we know of: (Warning: All three links contain explicit images.)
Our plans are to run photo No. 4 later this week."
really liked the new picture of Trump, it just says so much.
He may try to anoint Pryor at a later date, but right now his appointee to the health position in cabinet is anti choice. its a nice start for these compulsory pregnancy people, who wish to control women and their bodies. Guess the new T.V. series based on Margret Atwood's book, The Handmaids Tale, is timely,.
this should be a lesson to young people as to why you should not put your whole life on computer and/or in pictures.
A contest would be nice, for "best" picture of a Supreme Court Judge.
Q: What has three legs and can be useful for taking sharp, clear photographs?
A: Bill Pryor
Hah! Good one.
Maybe the judge needs a new nickname -- Bill "Tripod" Pryor.
Congratulations. You continue to engage in baseless character assassination.
Accurate reporting = "baseless character assassination"
Hah, good one.
I will put up some cash for the complete collection of photos or the magazine or magazines in which they appeared.


text:
Museum-Piece
K O S O V O R A I L W A Y S M U S E U M
The Museum as an institution preserves evidences of our culture, of the past, and the slow evolution in eternal searching of rail worker for the splendid as irreplaceable precondition, of society, humanism, today and the railway of tomorrow.
This publication dedicated to the museum of Kosovo Railways, is one of the strongest means for notification of broader public with the content and real value of this small treasure of Kosovo Railways history and culture.
This, simultaneously is a strong mean to recover the non confidence caused by de-recognition of the role and importance of Kosovo Railways. In the end, these are works of benefactors – rail workers faithful to art giving pleasure to esthetics, whereas to ease further studies to experts of this traffic domain in our country.
Kosovo Railways Museum is unique amongst national museums in Kosovo. The initiative for establishment – construction of this institution came spontaneously in September 2006 and ended on 24 August 2007 when the solemn inauguration took place in the presence of Kosovo Railways workers and many guests from Kosovo Government, UNMIK and KFOR invited.
Kosovo Railways workers used the offered possibility and gathered collections exposed in this Museum, which can be seen by a broader public. Alignment of exhibits has been performed basing on the determined professional criteria.
Kosovo Railways workers, unit for MVH in Kaçanik and Fushe Kosove, workshop for maintenance of wagons and service of SS TK and EN equipments in Fushe Kosove, during 2006 up to 24 August 2007, collected books, manuscripts, tools, stamps, old and nowadays pictures of railway transport which they disposed in the Kosovo Railways Museum.
Today, has been realized the aim that in a terrific and elegant edition »Kosovo Railways Museum« with its existing collections, illustrated with pictures and short descriptions, has its doors open for researchers with acute taste, which in this museum shall find the source of esthetic pleasure. Viewing it from the historic aspect, the museum in a sense is an appropriate depot for gathering, adjustment and preservation of this collection for successors, all what has not disappeared on the occasion of extinction of many collections and the past. Museum is a sort of shelter for old collections that people and events have separated them with force from their natural environment and left them aside – without respective environment. For this, professional services of the museum are engaged to ensure preservation, renewal and best placement of these technical tools and to protect them from the events of time.
Usually, in this time of "war" for existence, come out few difficulties as well. Modern times, indifferent "visitors" and with no good intention, with their actions, maybe unintentionally cause no measurable damages of historic values and of the past of Kosovo Railways.
Opposite these facts exist positive requests for education and development of culture domain in Kosovo Railways. Thus idea came out for establishment – construction of Kosovo Railways museum, in logical manner, even though many problems and many works remain uncompleted. For this, should think Kosovo Railways workers and the readers of this manual for Kosovo Railways Museum.
Connections that result between the observer and the existing collection present only the admiration towards the visual view and necessary clearing, therefore for the visitor to consider these experiences relevant for himself and the time Kosovo Railways are passing through.
Kosovo Railways Museum enters amongst the corresponding museums in our country for preservation of valuable heritages of the past and obligation for care, preservation, protection and enrichment with new values.
For your curiosity, this Museum, in organized and individual manner is being visited mainly by preschool children, elementary and secondary schools, students and representatives of KFOR and international visitors.


text:
\section{Introduction}
This paper deals with the question: what can be inferred from an unknown constrained linear system on the basis of state measurements? A similar question, for unconstrained systems, has recently led to the development of the \textit{informativity framework} in \cite{vanWaarde2020}. The observation at the center of this framework is that we can only conclude that the unknown system has a given property if \textit{all} systems compatible with the measurements have this property. In the context of linear systems this has lead to, among others, results for analysis problems in \cite{Eising2020c} and control problems in \cite{vanWaarde2020c,Trentelman2020}. Parallel to the work performed within this framework, similar analysis problems are addressed in \cite{Koch2020}, while control problems are addressed in \cite{DePersis2020,Berberich2020}.

In contrast to this earlier work, we will be focusing on conically constrained linear systems. Such conic constraints often arise naturally in modeling, taking the form of e.g. nonnegativity constraints on the input or states. Specifically, we will be looking at the class of difference inclusions of the form
\[ x_{k+1} \in H(x_k)\]
where $H:\mathbb{R}^n\rightrightarrows \mathbb{R}^n$ is a convex process, that is, a set-valued map whose graph is a convex cone. It it straightforward to show that any conically constrained linear system can be written as such a system and vice versa. Such difference inclusions arise naturally in many different contexts, including chemical reaction networks \cite{Angeli:09}, von Neumann-Gale economic growth models \cite{makarov:77} and cable-suspended robots \cite{j37,oh:05-2}. Lastly, as shown in e.g. \cite{Frankowska:87,Aubin:84}, difference inclusions of convex processes can be used as meaningful approximations of more complex set-valued maps.

The many applications of convex processes have led to interest in the analysis of such systems. In particular, this paper will consider the system-theoretic properties of reachability and null-controllability. For a given convex process, tests for these properties have been developed in terms of spectral conditions. First among these were the characterizations of reachability and null-controllability in \cite{AFO:86,PD:94}. However, the aforementioned characterizations only regard \textit{strict} (nonempty everywhere) convex processes, which limits the applicability for our goals. In \cite{ReachNullc:19} both of these results are generalized to work for a class of nonstrict convex processes. These characterizations of \cite{ReachNullc:19} will be fundamental in our investigation of informativity. In this paper, we will be interested in analysing whether these system-theoretic properties hold for \textit{all} convex processes compatible with measured data. Specifically, the data we consider will consist of exact measurements of the state. This means that we leave studies involving measurement noise or partial state measurements as future extensions.

Apart from the aforementioned work, some results in data-driven analysis and control should be mentioned. With regard to unconstrained linear systems \cite{Park2009} analyses stability of an input/output system using time series data. The works \cite{Wang2011,Liu2014,Niu2017,Zhou2018} deal with data-based controllability and observability analysis. Lastly, many methods arising from Model Predictive Control (MPC) are well suited to constrained systems. For an overview of such methods, we refer to \cite{Mayne:00,Mayne2014}. More specifically, MPC has recently been brought into a data-based context in \cite{Piga2018,Coulson2019}.

The contribution of this paper is threefold:
\begin{enumerate}
	\item We expand the informativity framework of \cite{vanWaarde2020} towards the class of convex processes. This framework will naturally lead to the formulation of a number of problems. In particular, we will illustrate the framework by resolving the problems of informativity for reachability and null-controllability.
	\item We develop explicit tools to manipulate and perform analysis on convex processes with a polyhedral graph. Assuming polyhedrality will allow us to represent convex processes and the conditions required for reachability and null-controllability in a convenient way.
	\item Lastly, we note the fact that polyhedral convex processes naturally arise from the aforementioned informativity problems with finite measurements. This allows us to combine the previous points to formulate tests \textit{on measured state data} to conclude that all convex processes consistent with the data are reachable or null-controllable.
\end{enumerate}

This paper is organized as follows: We begin in Section~\ref{sec:cp} with definitions of convex process and reachability and null-controllability. After this, Section~\ref{sec:prob} introduces informativity and formally states the problem we will consider in this paper. In Section~\ref{sec:prelim cp}, we will present some known results regarding the analysis of convex processes, which will be applied in Section~\ref{sec:inf} to our problem. We finalize the paper with conclusions in Section~\ref{sec:conc}.
\vspace{-0.5em}
\section{Convex processes}\label{sec:cp}

Given convex sets $\calS,\calT\subseteq\mathbb{R}^n$ and scalar $\rho\in\R$ we define the sum and scalar multiplication of sets as:
\[ \calS+\calT := \{s+t \mid s\in\calS, t\in\calT\}, \quad \rho \calS := \{\rho s \mid s\in\calS\}. \]
We denote the closure of $\calS$ by $\cl\calS$. A \textit{convex cone} is a nonempty convex set that is closed under nonnegative scalar multiplication.

A \textit{set-valued map}, denoted $H:\R^n\rightrightarrows \R^n$ is a map taking elements of $\mathbb{R}^n$ to subsets of $\mathbb{R}^n$. It is called a {\em convex process\/}, {\em closed convex process\/} or {\em linear process\/} if its graph
\[ \graph H := \{(x,y)\in \R^n\times \R^n \mid y\in H(x)\}\]
is a convex cone, closed convex cone or subspace, respectively.

The \textit{domain} and \textit{image} of $H$ are defined as $\dom H= \{x\in \R^n\mid H(x)\neq \emptyset \}$ and $\im H = \{y\in \R^n : \exists\, x \textrm{ s.t. } y\in H(x)\}$. If $\dom H=\R^n$, we say that $H$ is \textit{strict}.

In this paper we consider systems described by a \textit{difference inclusion} of the form
\vspace{-0.5em}\begin{equation}\label{eq:diffinc} x_{k+1} \in H(x_k)
\end{equation}
where $H:\R^n\rightrightarrows \R^n$ is a convex process. Our main motivation for considering this class of systems is the fact that this class of systems captures the behavior of all linear systems with convex conic constraints. This will be made explicit in the following example.

\begin{example}\label{ex:linear cons}
	Consider states $x_k$ in $\mathbb{R}^n$ and inputs $u_k\in \mathbb{R}^m$. Let $A$ and $B$ be linear maps of appropriate dimensions and let $\calC\subseteq\mathbb{R}^{n+m}$ be a convex cone. Consider the linear system with conic constraints given by:
	\begin{equation}\label{eq:cons system}
	x_{k+1}= Ax_k +Bu_k, \quad\begin{bmatrix} x_k \\ u_k \end{bmatrix} \in \calC.
	\end{equation}
	Note that this description can be applied to any combination of input, state and output constraints.

	We can describe the dynamics of \eqref{eq:cons system} by the difference inclusion~\eqref{eq:diffinc} with the convex process $H$ defined by:
	\[  H(x) := \left\lbrace Ax+Bu \,\middle\vert\,  \begin{bmatrix} x \\ u \end{bmatrix} \in \calC \right\rbrace. \]
	This reveals that we can study the properties of conically constrained linear systems by studying convex processes, without any loss of generality.
\end{example}

Next, we define a number of sets associated with the difference inclusion \eqref{eq:diffinc}. A $q$\textit{-step trajectory} is a (finite) sequence $x_0,\ldots,x_q$ such that \eqref{eq:diffinc} holds for all $k<q$. We define the $q$\textit{-step behavior} as:
\[ \mathfrak{B}_q(H) := \left\lbrace (x_k)_{k=0}^q \in (\mathbb{R}^n)^{q+1}\mid (x_k) \textrm{ satisfies } (\ref{eq:diffinc})\right\rbrace . \]
Using this, we define the \textit{reachable} and \textit{null-controllable} sets by:
\bse\label{eq:reach null def}
\begin{align*}
\!\!\calR(H) &\!:=\! \big\lbrace \xi \mid \exists q, (x_k)_{k=0}^q \in\mathfrak{B}_q(H) \textrm{ s.t. } x_0=0, x_q=\xi \big\rbrace, \\
\!\!\!\calN(H) &\!:=\! \big\lbrace \xi \mid \exists q, (x_k)_{k=0}^q \in\mathfrak{B}_q(H)\textrm{ s.t. } x_0=\xi, x_q=0 \big\rbrace.
\end{align*}
\ese
We say that a point $\xi\in\mathbb{R}^n$ is \textit{reachable} if $\xi\in\calR(H)$. That is, there exists a $q$-step trajectory from the origin to $\xi$. Similarly, we say a point $\xi\in\mathbb{R}^n$ is \textit{null-controllable} if $\xi\in\calN(H)$.

By a \textit{trajectory} of \eqref{eq:diffinc}, we mean a sequence $(x_k)_{k\in\N }$ such that \eqref{eq:diffinc} holds for all $k\geq 0$. The \textit{behavior} is the set of all trajectories:
\[ \mathfrak{B}(H) := \left\lbrace (x_k) \in (\mathbb{R}^n)^\mathbb{N}\mid (x_k) \textrm{ is a trajectory of } \eqref{eq:diffinc}\right\rbrace . \]

The set of \textit{feasible} states of the difference inclusion \eqref{eq:diffinc} is the set of states from which a trajectory emanates:
\[ \mathcal{F}(H) := \left\lbrace\xi \mid \exists (x_k)\in \mathfrak{B}(H) \textrm{ with } x_0=\xi \right\rbrace.\]
Clearly, if $H$ is a convex process, then $\calF(H)$ is a convex cone.

It is important to stress that in general not every point in the state space is feasible: In Example~\ref{ex:linear cons}, if we consider a point $x_0$ for which no $u_0$ satisfies the constraints, we have that $H(x_0)=\emptyset$. This means that $x_0$ is not a feasbile point. As there is no need to reach or control states that violate the constraints, we say the system \eqref{eq:diffinc} is \textit{reachable} or \textit{null-controllable} if every feasible state is reachable or null-controllable respectively. In terms of the previously defined sets, these can be written as $\calF(H)\subseteq\calR(H)$ and $\calF(H)\subseteq\calN(H)$ respectively.

It is important to note that, as is the case for discrete-time linear systems, reachability and null-controllability are not equivalent notions.
\vspace{-0.5em}\section{Problem formulation}\label{sec:prob}
In this paper we are interested in analyzing the properties of an unknown system based on measurements performed on it. We will assume that the system under consideration is given by
\vspace{-0.5em}\[ x_{k+1} \in H_s(x_k)\]
where $H_s$ is an unknown convex process. However, we do have access to a number of exact state measurements corresponding to ($q-$step) trajectories of $H_s$. It is clear to see that we can view a single $q-$step trajectory as $q$ separate $1-$step trajectories. Therefore, without loss of generality, we assume that we measure single steps. That is, we are given a finite number of pairs $(x_k,y_k)\in \graph H_s$, with $k=0,\ldots, T$

Suppose that we are interested in characterizing reachability of $H_s$. As $H_s$ is unknown, it is indistinguishable from all other convex processes that could have generated the measurements. Therefore, we may only conclude that $H_s$ is reachable if \textit{all} convex processes that are compatible with the data are reachable. This motivates the following definition. Let $\Sigma$ denote the set of all convex processes $H:\mathbb{R}^n\rightrightarrows\mathbb{R}^n$ and let $\calD\subseteq\mathbb{R}^n\times \mathbb{R}^n$ be a finite set of measurements. Define the set of all convex processes compatible with these measurements by:
\begin{equation}\label{eq:sigma D} \Sigma_\calD := \{ H\in\Sigma \mid \calD\subseteq\graph H\}. \end{equation}
Recall that, in order to characterize whether $H_s$ is reachable, we require all convex processes compatible with the measurements to be reachable. As such, we say that the data $\calD$ are \textit{informative for reachability} if every $H\in\Sigma_\calD$ is reachable. In a similar way we define \textit{informativity for null-controllability}.

Note that informativity is fundamentally a property of the data and the system class, but \textit{not} of the system $H_s$. This leads to the following problem formulation:

\begin{problem}\label{prob: prob}
	Provide necessary and sufficient conditions on the data $\calD$ under which the data are informative for reachability or null-controllability.
\end{problem}
\begin{remark}
	Following Example~\ref{ex:linear cons}, it is clear that all convex processes consistent with the data are reachable if and only if all conically constrained linear systems consistent with the data are reachable. As these problems are equivalent we will only focus on formulations in terms of convex processes in the remainder of this paper.
\end{remark}
It should be noted that, in certain cases, the informativity problem can be resolved trivially, as shown by the following example.
\begin{example}
	Let $n=1$, and assume that we measure the 2-step trajectory given by $x_0=0,$ $x_1=1,$ and $x_2=-1$. Then we have $\calD = \left\lbrace (0,1), (1,-1)\right\rbrace$.

	Note that nonnegative scalar multiples of these measurements are also (finite step) trajectories of any convex process in $\Sigma_\calD$. As such, it is clear that for any $\alpha,\beta\geq 0$ we have 2-step trajectories $y_0=0$, $y_1=\alpha$, $y_2=-\alpha$ and $z_0=0$, $z_1=0$, $z_2=\beta$. Furthermore, the sum of two such 2-step trajectories is one as well. Therefore $(0,\alpha,\beta-\alpha)\in\mathfrak{B}_2(H)$ for any $H$ consistent with the data. As such, $\calR(H)=\mathbb{R}$ for any $H\in\Sigma_\calD$.
\end{example}
In general, however, resolving the problem is not this straightforward. To be precise, it is made difficult by two things. First of all, apart from trivial examples, the set $\Sigma_\calD$ contains infinitely many convex processes. As such, it is usually not possible to take an approach based on identification. In addition, there may \textit{not} exist $q$ for a convex process $H$ such that
\[\!\!\calR(H) \!:=\! \big\lbrace \xi \mid \exists (x_k)_{k=0}^q \in\mathfrak{B}_q(H) \textrm{ s.t. } x_0=0, x_q=\xi \big\rbrace.\]
Therefore, testing whether a given convex process is reachable or null-controllable is a nontrivial problem in itself (see e.g. \cite{AFO:86,ReachNullc:19}).
\vspace{-1em}\section{Analysis of convex processes}\label{sec:prelim cp}
By definition a convex cone $\calC$ is closed under \textit{conic combinations}: If $c_1,...,c_\ell\in\calC$ then
\[ \sum_{i=1}^\ell \alpha_ic_i \in \calC \quad \forall \alpha_i\geq 0. \]
The set of all conic combinations of a set $\calS$ is called the \textit{conic hull} and is denoted by $\cone  \calS $. If there exists a finite set $\calS$ such that $\calC = \cone\calS$ we say that $\calC$ is \textit{finitely generated} or \textit{polyhedral}. We denote the set of vectors of length $\ell$ with nonnegative and nonpositive elements by $\mathbb{R}_+^\ell$ and $\mathbb{R}_-^\ell$ respectively. Then, if $M\in\mathbb{R}^{k\times \ell}$ and $\calS$ is the set of columns of $M$, we have that
\vspace{-0.5em}\begin{equation}\label{eq:conic hull rep} \cone \calS = M\mathbb{R}^\ell_+.\end{equation}

For a nonempty set $\calC\subseteq \R^n $, we define the \textit{negative} and \textit{positive polar cone}, respectively,
\begin{align*}
\calC^- &:= \{ y\in\R^n \mid \langle x,y\rangle\leq 0 \hspace{1em} \forall x\in \calC\}, \\
\calC^+ &:= \{ y\in\R^n \mid \langle x,y\rangle\geq 0 \hspace{1em} \forall x\in \calC\}.
\end{align*}
Given sets $\calC$ and $\calS$, we have that $(\calC^-)^-=\cl(\cone\calC)$, and:
\begin{equation}\label{eq:dual sum} (\calC+\calS)^-  =\calC^-\cap \calS^-, \quad (\calC\cap\calS)^- = \cl (\calC^-+\calS^-). \end{equation}
Let $A$ be a linear map and let $\bullet^{-1}$ denotes the inverse image, that is, $A^{-1}\calC^- = \{ x \mid Ax\in \calC^-\}$. Then if $\calC$ is a convex cone  we have that (see e.g. \cite[Theorem 2.4.3]{Aubin:90}):
\begin{equation}\label{eq:dual and linear map}(A^\top\calC)^- = A^{-1} \calC^-.\end{equation}
The aforementioned properties also hold for the positive polar cone.

Let $H:\mathbb{R}^n\rightrightarrows\mathbb{R}^n$ be a convex process. We define \textit{negative} and \textit{positive dual} processes $H^-$ and $H^+$ of $H$ as follows:
\begin{subequations}
	\begin{align} \label{eq:def of dual}
	p\in H^-(q) &\iff \langle p,x\rangle\geq \langle q,y\rangle\quad \forall\, (x,y)\in\gr(H),  \\
	p\in H^+(q) & \iff \langle p,x\rangle\leq \langle q,y\rangle\quad \forall\, (x,y)\in\gr(H).
	\end{align}
\end{subequations}

Note that $H^+(q)= -H^-(-q)$ for all $q$. If $H$ is a closed convex process, we know that $(H^+)^- = H$ and
\begin{equation}\label{eq:H(0) to domain} H(0)=(\dom H^+)^+=(\dom H^-)^-.\end{equation}
It is straightforward to check that
\begin{equation}\label{eq:dual in graphs} \graph(H^-) \!=\! \begin{bmatrix} 0 &\!\! I_n \\ -I_n &\!\! 0 \end{bmatrix} \left(\graph H\right)^-\!, \graph(H^+)\!=\! \begin{bmatrix} 0 &\!\! I_n \\ -I_n &\!\! 0 \end{bmatrix} \left(\graph H\right)^+\!\!. \end{equation}
For a convex cone $ \calC\subseteq\R^n$, we define $\lin(\calC) =-\calC\cap \calC$ and $\Lin(\calC)=\calC-\calC$. We can now define two linear processes $L_-$ and $L_+$ associated with $H$ by
\begin{equation}\label{eq:def of L- and L+}
\graph(L_-):=\lin\big(\gr(H)\big)\textrm{ and } \graph(L_+):=\Lin\big(\graph(H)\big).
\end{equation}
By definition, we therefore have
\begin{equation}\label{eq:lh-+}
\graph(L_-)\subseteq\graph(H)\subseteq\graph(L_+).
\end{equation}
It is clear that $L_-$ and $L_+$ are, respectively, the largest and the smallest (with respect to the graph inclusion) linear processes satisfying \eqref{eq:lh-+}. We call $L_-$ and $L_+$, respectively, the minimal and maximal linear processes associated with $H$. If $H$ is not clear from context, we write $L_-(H)$ and $L_+(H)$ in order to avoid confusion.

If $L$ is a linear process it is clear that the negative and positive dual processes are equal, which allows us to denote it by $L^\bot:=L^- =L^+$. In fact, the minimal and maximal linear processes associated with a convex process enjoy the following additional properties:
\begin{subequations}\label{eq:L(H) vs L(H+-)}
	\begin{align}
	&L_-(H^-)=L_-(H^+)=L_+^\bot, \\
	&L_+(H^-)=L_+(H^+)=L_-^\bot.
	\end{align}
\end{subequations}
For the reachable and null-controllable sets of $L_-$ and $L_+$ we use the following shorthand notation:
\begin{align*}
\calR_- := \calR(L_-), \quad &\calR_+:= \calR(L_+). \\
\calN_- := \calN(L_-), \quad &\calN_+:= \calN(L_+).
\end{align*}

We denote the image of a set $\calS$ under a convex process $H$ by $H(\calS) := \{ y\in\mathbb{R}^n \mid \exists x\in \calS \textrm{ s.t. } y\in H(x)\}$. A direct consequence of this definition is that
\begin{equation}\label{eq:H(S) in graph} H(\calS) = \begin{bmatrix} 0 & I_n \end{bmatrix} \big( \gr(H) \cap \left(\calS\times\mathbb{R}^n\right)\big). \end{equation}
We can define powers of convex processes, by taking $H^0$ equal to the identity map, and letting for $q\geq 0$:
\[H^{q+1}(x) := H(H^{q}(x)) \quad \forall x\in \mathbb{R}^n. \]
We can define the inverse of a convex process by $H^{-1}(y)=\{ x \mid y\in H(x)\}$. Note that this is always defined as a set-valued map. For higher negative powers of $H$ we use the shorthand: $H^{-n}(x) = (H^{-1})^n(x)$.

Let $L:\mathbb{R}^n\rightrightarrows\mathbb{R}^n$ be a linear process, then we know that $\calF(L)= L^{-n}(\mathbb{R}^n)$ and $\calR(L)= L^n(0)$. In addition
\begin{subequations}\label{eq:LorthRF}
	\begin{gather}
	\calF(L^\bot) = \calR(L)^\bot, \\
	\calR(L^\bot) = \calF(L)^\bot.
	\end{gather}
\end{subequations}

We will characterize reachability in terms of spectral conditions. For this we require one more definition: A real number $\lambda$ and vector $\xi\in\R^n\setminus\{0\} $ form an \textit{eigenpair} of $H$ if $\lambda\xi\in H(\xi)$. In this case $\lambda$ is called an \textit{eigenvalue} and $\xi$ is called an \textit{eigenvector} of $H$.

In the following, we will need the assumption:
\begin{equation}\label{eq:reach assump} \dom H +\calR_- =\R^n. \end{equation}
As proven in \cite[Thm. 1, Lem. 7]{ReachNullc:19}, we can characterize reachability in terms of eigenvalues of the dual process.

\begin{theorem}\label{thm:cp reach}
	Let $H$ be a convex process such that \eqref{eq:reach assump} holds. Then, the following are equivalent:
	\begin{enumerate}
		\item $H$ is reachable.
		\item $\calR(H)=\R^n$.
		\item $\calR_+=\R^n$ and $H^{-}$ has no nonnegative eigenvalues.
	\end{enumerate}
\end{theorem}
We now move towards null-controllability. It is tempting to think that null-controllability of $H$ is equivalent to reachability of $H^{-1}$. However, while indeed it is true that $\calR(H^{-1})=\calN(H)$, we do not necessarily have that $\calF(H^{-1}) = \calF(H)$.

As such, we require a characterization of null-controllability. This will be done under slightly more restrictive assumptions than Theorem~\ref{thm:cp reach}. To be precise, we will assume both \eqref{eq:reach assump} and
\begin{equation}\label{eq:nullc assump}
	\calR_+ = \im H+\calN_-=\R^n.
\end{equation}
The following was proven in \cite[Thm. 2, Lem. 9]{ReachNullc:19}:
\begin{theorem}\label{thm:nullc}
	Let $H$ be a convex process such that \eqref{eq:reach assump} and \eqref{eq:nullc assump} hold. Then, the following are equivalent:
	\begin{enumerate}
		\item $H$ is null-controllable.
		\item $\calN(H)-\calR(H)=\mathbb{R}^n$.
		\item $H^{-}$ has no positive eigenvalues.
	\end{enumerate}
\end{theorem}

The following shows why we require separate tests for these two properties.
\begin{example}
	Recall that, as is the case for discrete time linear systems, a convex process can be null-controllable without being reachable. As a simple example consider the convex process given by:
	\[ \graph H := \mathbb{R}\times \{0\}. \]
	On the other hand, we know that reachability implies null-controllability for discrete time linear systems. For general convex processes this is not the case. As an example, let:
	\[ \graph G := \{ (x,y) \mid 0\leq x\leq y \}. \]
	Note that $\calR(G)=\mathbb{R}_+=\calF(G)$, and therefore $G$ is reachable. As any trajectory of $G$ is a non-decreasing sequence, $G$ is clearly not null-controllable. This means that in general tests for reachability can not be employed to obtain results for null-controllability.
\end{example}

These two theorems allow us to check for reachability and null-controllability without explicitly determining $\calR(H)$ or $\calN(H)$. This will be central in resolving Problem~\ref{prob: prob} in the next section.
\vspace{-0.5em}\section{Informativity for convex processes}\label{sec:inf}
We turn our attention to the context of informativity. Let $\calD\subseteq\mathbb{R}^n\times \mathbb{R}^n$ be a finite set of measurements. We define the \textit{most powerful unfalsified process}, $H_\calD$, by:
\[ \graph H_\calD := \cone \calD. \]
By definition we see that $H_\calD\in\Sigma_\calD$ and $\graph H_\calD \subseteq \graph H$ if and only if $H\in\Sigma_\calD$. Our goal is to find conditions on $\calD$ under which every $H\in\Sigma_\calD$ is reachable or null-controllable. we start with the following theorem:

\begin{theorem}\label{thm:reach iff Rn}
	Suppose that \eqref{eq:reach assump} holds for $H_\calD$. Then $H_\calD$ is reachable if and only if every $H\in\Sigma_\calD$ is reachable.
\end{theorem}
\BP Note that $H_\calD\in\Sigma_\calD$. Therefore the `if' part is immediate. For the `only if' part, assume that $H_\calD$ is reachable. By Theorem~\ref{thm:cp reach}, we have that $\calR(H_\calD)=\mathbb{R}^n$. Now let $H$ be a convex process such that $\graph H_\calD \subseteq \graph H$. As any $q-$step trajectory of $H_\calD$ is one of $H$, it is immediate that $\calR(H_\calD)\subseteq\calR(H)$. Therefore $\calR(H)=\mathbb{R}^n$. This implies that $H$ is reachable. \EP
\vspace{-1em}\begin{remark}\label{rem:r not rn}
It is important to stress that a convex process $H$ is defined to be reachable if $\calF(H)\subseteq\calR(H)$. Therefore a nonstrict convex process $H$ can be reachable whilst $\calR(H)\neq \mathbb{R}^n$. Now let $\graph H\subseteq \graph G$. Note that we may \textit{not} conclude reachability of $G$ from reachability of $H$ in general. As an example, let $\graph H = \{0\}$. This convex process is reachable, and its graph is contained in the graph of any other convex process, which are not necessarily reachable.
\end{remark}

Next, we study null-controllability. It is clear that the reasoning of Remark~\ref{rem:r not rn} also applies to null-controllability. This leads to an important point of contrast between Theorem~\ref{thm:cp reach} and Theorem~\ref{thm:nullc}: Under the conditions of the latter the convex process $H$ can be null-controllable even if $\calN(H)\neq \mathbb{R}^n$.

\begin{theorem}\label{thm:nullc stab iff Rn}
	Suppose that \eqref{eq:reach assump} and \eqref{eq:nullc assump} hold for $H_\calD$. Then, $H_\calD$ is null-controllable if and only if every $H\in\Sigma_\calD$ is null-controllable.
\end{theorem}
\BP Again the `if' part is immediate. For the `only if' part, assume that $H_\calD$ is null-controllable. Let $H$ be a convex process such that $\graph H_\calD \subseteq \graph H$. As in the proof of Theorem~\ref{thm:reach iff Rn}, we see that $\calR(H_\calD)\subseteq\calR(H)$ and $\calN(H_\calD)\subseteq\calN(H)$. This implies that
\[ \mathbb{R}^n= \calN(H_\calD)-\calR(H_\calD) \subseteq \calN(H)-\calR(H).\]

Note that we also have $\graph L_-(H_\calD) \subseteq \graph L_-(H)$ and $\graph L_+(H_\calD) \subseteq \graph L_+(H)$. Therefore, it is clear that \eqref{eq:reach assump} and \eqref{eq:nullc assump} hold for $H$. This implies that $H$ is null-controllable. \EP
\vspace{-0.5em}
The question rests whether we can provide simple tests for reachability and null-controllability of $H_\calD$ in terms of the data $\calD$. In order to resolve this, we will begin by giving two equivalent representations of $H_\calD$.

Denote $T= |\calD|$ and $\calD = \{(x_t,y_t): t=1,\ldots,T\}$. We define the matrices $X,Y\in\mathbb{R}^{n\times T}$ by taking:
\[X:= \bbm x_1 & x_2 & \cdots & x_T \ebm,\quad Y := \bbm y_1 & y_2 & \cdots & y_T \ebm.\]
Since $\cone\calD$ is a convex cone, we have that $\calD^+=(\cone \calD)^+$. As $\calD$ is a finite set, we have that $\cone\calD$ and $\calD^+$ are polyhedral cones. This means that there exists $\ell\in\mathbb{N}$ and $\eta_1,\ldots,\eta_{\ell}\in\mathbb{R}^{2n}$, such that $\calD^+=\cone\{\eta_1,\ldots,\eta_{\ell}\}$. We can now define matrices $Z,W\in\mathbb{R}^{\ell\times n}$ by the following partition:
\[ \begin{bmatrix} Z & -W \end{bmatrix} := \begin{bmatrix} \eta_1  &\ldots & \eta_{\ell} \end{bmatrix}^\top. \]
As $\cone \calD $ is closed, it is equal to $(\calD^+)^+$. Recall that $\graph H_\calD = \cone \calD$. Therefore, we can use \eqref{eq:conic hull rep} to represent $H_\calD$ in the following ways:
\begin{equation}\label{eq:reps of HD} \graph H_\calD \!=\! \begin{bmatrix} X \\ Y \end{bmatrix} \mathbb{R}_+^T=\! \left\lbrace (x,y) \mid \begin{bmatrix} Z & \!-W \end{bmatrix} \begin{bmatrix} x\\y\end{bmatrix} \in \mathbb{R}_+^{\ell} \right\rbrace.\end{equation}

Immediately, we see that
\[ \dom H_\calD = X\mathbb{R}_+^T \qand  \im H_\calD= Y\mathbb{R}_+^T.\]
Using \eqref{eq:reps of HD} we can express the minimal and maximal linear processes of $H_\calD$ as follows:
\vspace{-0.5em}\begin{align*}
\graph L_-(H_\calD) &= \ker \begin{bmatrix} Z & -W \end{bmatrix}, \\
\graph L_+(H_\calD) &= \im \begin{bmatrix} X \\ Y \end{bmatrix}.
\end{align*}
For the characterizations of reachability and null-controllability in Theorem~\ref{thm:cp reach} and Theorem~\ref{thm:nullc} respectively, we need the reachable and null-controllable sets of $L_+$ and $L_-$. In order to characterize these in terms of the data $\calD$, we first look at the image of a set under these linear processes. For a given set $\calS\subseteq \mathbb{R}^n$ we can apply \eqref{eq:H(S) in graph} to verify that:
\begin{align*}
L_-(H_\calD)(\calS) &= W^{-1}Z\calS, \\
L_+(H_\calD)(\calS) &= YX^{-1}\calS.
\end{align*}
Recall that for a linear process $L$ the reachable set is \textit{finitely determined} and $\calR(L)=L^n(0)$. Combining the above with some slight abuse of notation, we can write:
\begin{align*}
\calR(L_-(H_\calD)) &= (W^{-1}Z)^n\{0\}, \\
\calR(L_+(H_\calD)) &= (YX^{-1})^n\{0\}.
\end{align*}
This characterizes the reachable sets of $L_-(H_\calD)$ and $L_+(H_\calD)$ using subspace algorithms with at most $n$ steps. Following the same reasoning with negative powers, we obtain that:
\begin{align*}
\calN(L_-(H_\calD)) &= (Z^{-1}W)^n\{0\},  \\
\calN(L_+(H_\calD)) &= (XY^{-1})^n\{0\}.
\end{align*}

We now shift our focus to the negative dual of $H_\calD$, and show that it can be represented in terms of $X$ and $Y$ or $Z$ and $W$ as well.

By \eqref{eq:dual in graphs} and the first representation of \eqref{eq:reps of HD} we have that:
\[ \graph(H^-_\calD) = \begin{bmatrix} 0 & I_n \\ -I_n & 0 \end{bmatrix} \left(\begin{bmatrix} X \\ Y \end{bmatrix} \mathbb{R}_+^T \right)^-. \]
By \eqref{eq:dual and linear map} this implies that:
\[ \graph(H^-_\calD) \!=\! \begin{bmatrix} 0 &\! I_n \\ -I_n &\! 0 \end{bmatrix}\!\!\begin{bmatrix} X^\top &\!\! Y^\top \end{bmatrix}^{-1}\!\mathbb{R}_-^T=\!\begin{bmatrix} Y^\top &\!\!-X^\top \end{bmatrix}^{-1}\!\mathbb{R}_-^T. \]
Similarly, we can begin from \eqref{eq:dual in graphs} and the second representation in \eqref{eq:reps of HD} instead. As such, we can conclude that the negative dual of $H_\calD$ satisfies:
\[ \graph(H_\calD^-) \!=\! \begin{bmatrix} W^\top \\Z^\top \end{bmatrix}\mathbb{R}_+^\ell =\! \left\lbrace (x,y) \mid \begin{bmatrix} Y^\top &\! -X^\top \end{bmatrix} \begin{bmatrix} x\\y\end{bmatrix} \in \mathbb{R}_-^T \right\rbrace.\]

Then, we have that $\lambda$ and $\xi$ form an eigenpair of $H_\calD^-$ if and only if $\xi\neq 0$ and $\xi^\top(Y -\lambda X) \leq 0$.

We can now combine the previous discussion with Theorem~\ref{thm:cp reach} and Theorem~\ref{thm:reach iff Rn} to obtain the following characterization of informativity for reachability in terms of data:
\begin{theorem}\label{thm:inf reach}
	Let $\calD\subseteq\mathbb{R}^n\times \mathbb{R}^n$ be a finite set. Suppose that \[X\mathbb{R}_+^T+(W^{-1}Z)^n\{0\}=\mathbb{R}^n. \]
	Then, $\calD$ is informative for reachability if and only if $(YX^{-1})^n\{0\}=\mathbb{R}^n$ and for all $\lambda\geq 0:$
	\[ \xi^\top(Y -\lambda X) \leq 0 \implies \xi = 0. \]
\end{theorem}
\begin{remark}
	Note that $(YX^{-1})^n\{0\}=\mathbb{R}^n$ implies that $\calR(L)=\mathbb{R}^n$ for all \textit{linear processes} $L$ such that $\calD \subseteq \graph L$. That is, all such linear processes are reachable.
\end{remark}

\begin{example}
	Let $n=2$ and suppose that we measure the following $4-$step trajectory:
	\[ x_0 \!=\! \begin{bmatrix} 0 \\ 0 \end{bmatrix}\!, x_1\!=\!  \begin{bmatrix} 1 \\ 0 \end{bmatrix}\!, x_2\!=\!  \begin{bmatrix} 0 \\ 1 \end{bmatrix}\!, x_3\!=\!  \begin{bmatrix} 0 \\ -1 \end{bmatrix}\!, x_4\!=\!  \begin{bmatrix} -1 \\ 0 \end{bmatrix}. \]
	If we define $X$ and $Y$ as before, we get
	\[ X= \begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{bmatrix}, \quad Y= \begin{bmatrix} 1 & 0 & 0 &-1 \\  0 & 1 & -1&0\end{bmatrix}.\]
	We can use these to find $Z$ and $W$:
	\[\begin{bmatrix} Z & -W \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & -1\end{bmatrix}. \]
	First, note that $X\mathbb{R}^4_+ = \mathbb{R}_+ \times \mathbb{R}$ and $(W^{-1}Z)^2\{0\} = \mathbb{R}\times \{0\}$. Therefore, we can now use Theorem~\ref{thm:inf reach} to check for informativity.

	Now, it is straightforward to verify that $(YX^{-1})^2\{0\}=\mathbb{R}^2$. Lastly, let $\lambda \geq 0$ and  \[\begin{bmatrix} \xi_1 & \xi_2 \end{bmatrix}\begin{bmatrix}  1 & -\lambda  & 0 & -1 \\ 0 & 1 & -1-\lambda  & \lambda \end{bmatrix} \leq 0.\]
	By direct inspection, it is clear that this implies that
	\[ \xi_1\leq 0, \quad \xi_2 \leq \lambda \xi_1, \quad 0 \leq (1+\lambda)\xi_2, \quad \lambda \xi_2 \leq \xi_1.\]
	These inequalities show that for any $\lambda \geq 0$ we have that $\xi_1=\xi_2=0$. This proves that $\calD$ is informative for reachability.
\end{example}

In a similar fashion we can apply our discussion to Theorem~\ref{thm:nullc} and Theorem~\ref{thm:nullc stab iff Rn} to obtain a characterization of informativity for null-controllability.

\begin{theorem}\label{thm:inf null-c}
	Let $\calD\subseteq\mathbb{R}^n\times \mathbb{R}^n$ be a finite set. Suppose that
\[X\mathbb{R}_+^T+(W^{-1}Z)^n\{0\} =\mathbb{R}^n \]
and
\[(YX^{-1})^n\{0\}=Y\mathbb{R}_+^T+(Z^{-1}W)^n\{0\}= \mathbb{R}^n.\]
Then $\calD$ is informative for null-controllability if and only if for all $\lambda> 0:$
\[ \xi^\top(Y -\lambda X) \leq 0 \implies \xi = 0. \]
\end{theorem}

\begin{remark}
	If $H$ is a convex process whose graph is polyhedral, we can always find a finite set $\calD$ such that $H=H_\calD$. This means that the results of Theorem~\ref{thm:inf reach} and Theorem~\ref{thm:inf null-c} can be applied to any polyhedral convex process without loss of generality.
\end{remark}

\vspace{-0.5em}\section{Conclusions}\label{sec:conc}
In this paper, we have resolved a number of informativity problems for conically constrained linear systems. This means that we have formulated conditions on finite, exact, state measurements under which we can test whether the measured system is reachable or null-controllable. The resulting tests take the convenient form of subspace inclusions and spectral conditions.

Future work includes extending the ideas in this paper towards the more general class of linear systems with convex constraints. It is easy to see that these systems can be viewed as difference inclusions of convex set-valued maps. Similar to the approach in this paper, we can define the smallest set-valued map consistent with the data by taking the convex hull instead of the conic hull. As such, a characterization of reachability for such systems will lead to informativity results for this class of systems. Another direction of future work is investigating informativity for the analysis of other properties and for control. Interesting problems are for example dissipativity or feedback stabilization. Resolving such a problem would require formulating characterizations for a given convex process to have the aforementioned properties. Lastly, this paper considers only exact measurements of the state. However, many realistic scenarios will involve noisy measurements. Incorporating noisy data within this framework will lead to interesting informativity problems.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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text:
Q: TensorFlow: How do I generate a dataset from two arrays? I've been trying to generate a custom dataset from two arrays. One with the shape (128,128,6) (satellite data with 6 channels), and the other with the shape (128,128,1) (binary mask). I have been using the function tf.data.Dataset.from_tensor_slices:
train_dataset = tf.data.Dataset.from_tensor_slices((train_raster, train_mask))

What I get is this:
<PrefetchDataset element_spec=(TensorSpec(shape=(128, 128, 6), dtype=tf.float32, name=None), TensorSpec(shape=(128, 128, 1), dtype=tf.float32, name=None))>

However, when I try to run this through my model I get this error:
ValueError ValueError: `Shapes (None, 128, 128, 1) and (None, 2) are incompatible

(None, 2) since my output is one of 2 classes.
In a tutorial I've seen the dataset as <PrefetchDataset shapes: ((None, 128, 128, 3), (None, 128, 128, 1)), types: (tf.float32, tf.float32)>. Is there a difference, and if so, how do I fix it? It seems like only one of the two tensors is being run through the model, but I don't quite understand why.
Model definition:
model = tf.keras.Sequential([
tf.keras.layers.Conv2D(32, (3,3), padding='same', activation=tf.nn.relu, input_shape=(128, 128, 6)), tf.keras.layers.MaxPooling2D((2, 2), strides=2),
tf.keras.layers.Conv2D(64, (3,3), padding='same', activation=tf.nn.relu),
tf.keras.layers.MaxPooling2D((2, 2), strides=2),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(128, activation=tf.nn.relu),
tf.keras.layers.Dense(2, activation=tf.nn.sigmoid)
])

A: Adding @Kaveh comments in the answer section for the benefit of the community as this fixed the user's issue. (Thank you @Kaveh)

I can guess that your last layer outputs 2 neurons (for binary mask).
But since you have specified an array with the shape (128,128,1) in
your dataset, it leads to an error. If you just passed the
train_dataset to your model, it considers the first part of tuple
(first array) as input and the second array (128,128,1) as your labels
If you print your model summary, you will see your model output is
just two numbers (None,2). But you need output as (128,128,1). So,
your dataset is ok. You need to modify your model architecture. For
example an architecture like U-Net.

redpajama_set_name: RedPajamaStackExchange


Take the road less traveled! Maui Mall is excited to invite those extreme off-road lovers to show off their most beloved trail blazer on Friday April 20, 2018 from 5:30PM-8PM.
This showcase event benefiting Maui Food Bank is an opportunity for the Maui community to get together and talk story about their lifted truck, mud-fueled dirt bike, customized rock-crawler, and cooler than classic motorcycle.
Maui Food Bank will be accepting canned food donations at the registration table in place of a standard vehicle entry fee. The event is free to the public and is keiki friendly. Donations will be accepted all night for any member of the community that wants to contribute.
Those wishing to enter their vehicle in the showcase must sign up online. The link can be found on the Maui Mall events page on Facebook. Spaces are limited. Vehicles can begin parking at 4:30PM at the Kaahumanu Avenue/ DMV Parking lot of Maui Mall.


Opening Reception: Friday, Oct. 16 5 to 9 p.m.
Closing Reception: Friday, Nov. 20 5 to 9 p.m.
We are proud to present Dana Depew's first major solo show in Cleveland in over three years. Experience recent sculptural, two-dimensional and video-based works produced from reclaimed and found objects. "Assholes and Elbows" refers to working hard at a task. It originated in farm work. If a group of field hands is busy and bent over picking crops, then a supervisor looking out over the group would see nothing but "assholes and elbows."
"I grew up on a farm in Medina, Ohio with eight siblings. There were always daily chores and tasks we each had to do. My father would always say 'Get out there and do your chores and all I want to see is assholes and elbows.'"


This post has just saved me a huge amount of faffing. It's a great idea tying the Oookstar to the Trailstar! I shall now go and have a play.
Glad to be of use :-) It does make a big difference. I wish I'd thought of it sooner.
Hi-Tec Owaka sandals aren't available in the US. Do you know the weight (UK site doesn't list it)?
Hi-Tec GT Strap is the only sandal available in the US, at 269g.
Which model (weight) of Inov-8 Terroc do you wear?
Thanks for the gear list.
My size 9 Owaka's weigh 562 grams. The Terrocs I have are the 330 model.
562 grams per sandal or for the pair?
Thanks for this post, there are some great recommendations here. First read this when I started updating my ancient gear for a long backpack. My kit list is resembling yours a bit now! The Rab Myriad jacket, Trailstar and Caldera Ti-Tri stove have been a revelation. Wouldn't be without a windshirt now either.
What colour is your Trailstar? It looks green but I note this isn't an option. Is it the grey? Interesting post btw.
Thanks David. My Trailstar is grey.
Useful post thanks. I am thinking of taking my Trailstar on this year's TGO Challenge (despite me being a lanky old thing), rather tha my Scarp 1. I was interested in the second photo of this post. You appear to have changed the 'standard' guying arrangement for the TS door which might make it easier to change the door when the wind shifts. Have you now got a short guy at each TS attachment point and then a single detached piece of cord to run from the door trekking pole to the ground rather than one long guy on the 'normal' door panel? If so how do you attach the short guy to the front trekking pole - ie just with a knot or do you have some other system? I was wondering about having a short cord loop and mini carabiner to slip around the top of the trekking pole and then to fasten the short guy from the shelter and the long guy to the ground into the carabiner. Hope this query makes sense!
Hi David, all I've done is add a second guyline to the front trekking pole as this makes it more stable. I simply loop the guyline over the pole handle. The other guyline, which is tied to the Trailstar, is just wrapped a few times around the pole handle. Your carabiner idea sounds good.
Some great info chris thanks for the help.
I want to mountain bike the route that you walked so would like to know if you think this may be possible?
Such as the best and worst terrain and if you think this may be possible ?
I notice you had a Paramo Katmai Light shirt.
How good is it in the Scottish weather and does it smell after a while.
I usually use Icebreaker tops to mitigate the odour.
Just looking for a change.
Sandy, the Katmai Light was fine on the Watershed walk. I wore it every day and it never smelt much though it did look pretty awful due to sweat stains at times!
Great article! In the past, I've done several long distance 2 week walks but b&b'd all the way. I'm interested in giving backpacking/tenting a try on a few 2 week routes with LEJOG in mind for the long-term goal sometime within the next 5 years. Thank you for the great list of items!


IDAHO FALLS — Jokes about laser hair removal, an appendectomy, and massage therapy are only scratching the surface when it comes to Steve Soelberg's comedic act.
Soelberg, a Seattle native who's been seen on viral VidAngel Dry Bar Comedy videos, will be performing locally April 4.
Soelberg's performance is separate from the Dry Bar tour but will keep to its PG style. Soelberg describes himself as a comic who's also clean.
"I'm pretty excited to be part of hopefully starting a good, long tradition of doing good standup in Idaho Falls," Soelberg says.
He says it's not his first time performing in eastern Idaho, but it is his first time performing in the Downtown Event Center's comedy club setting.
The DEC is a new venue headlining comics, including ones known from Dry Bar like Alex Velluto and Cory Michaelis. Soelberg and his other Dry Bar counterparts are some of the first comedians to participate in the new comedy lineup at the event center.
Soelberg recently performed in Rexburg opening for Ashton native and Netflix's "Happy Face" comedian Ryan Hamilton last fall.
"It's good to do stuff that you know works well," Soelberg says.
Soelberg got his start a decade ago when he invited his friends to watch him perform at an open mic night. He says his first performance was well received, but his second one — not so much.
Despite the lack of success on his second go, Soelberg was addicted to getting laughs.
You can catch some of Soelberg's performances online through Dry Bar Comedy, or find his special on Amazon Prime.
Get tickets to the performance here.


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Tucked away from the road in this small group of four sits this striking stand alone three bedroom, two bathroom villa. This circa 2001 property boasts a large living, separate meals, kitchen and large outdoor entertaining area. The Three bedrooms are all complete with built in robes and complimented by two well appointed bathrooms. The kitchen is complete with gas cook top and dishwasher. Ducted air conditioning will keep you cool throughout the summer months. The large double garage is with generous storage area.
Be quick to inspect this property as is it priced to sell. Call Richard Lyster on 0488 681 361.


Small plastic sphere which, on impact, splits to release contents.
Can contain a number of different irritants / compounds such as: hot PAVA powder, marking projectiles, water-filled projectiles, and scented powder (for training). Also available as a glass breaking solid nylon projectile.


These Felt Cat Bookmarks are a quick and easy craft for kids that can be made in just 15 minutes, and they're a great way to use up leftover felt scraps! Customize your kitty bookmark to look like your favorite feline friend!
My two younger boys share a deep love for two things – reading and CATS – so when they asked me to come up with a kids craft project idea for them one rainy day, I knew that these felt cat bookmarks would be a huge hit! Better yet, they can be made in under 15 minutes using just a few basic craft supplies!
I admit that I'm not the greatest at cutting felt shapes out by hand, but luckily my Cricut Maker machine cuts felt like a dream! I quickly cut out four felt cats to serve as the base of their bookmarks (you'll need two pieces for each bookmark).
Use the low-temperature glue gun to create a ring with the elastic, overlapping the ends by around 1″. Allow to cool.
Glue the felt cat to the elastic, making sure to cover the seam. Glue the second felt cat to the opposite side of the elastic.
Use felt glue to adhere the edges of the felt cats together.
Use felt glue along with felt scraps, googly eyes, rhinestones, etc. to embellish the cat bookmarks.
My kids liked the way that the googly eyes looked more than felt eyes, so that's what they went with, and they used acrylic paint to add the mouths and some sparkle to the whiskers.
Super cute and easy peasy!
The kids are loving their felt cat bookmarks, and my youngest is saving his special new bookmark for use ONLY in his favorite Garfield comic books!
Don't forget to check out these other great felt projects that can be made in under 15 minutes – just click the graphic above!
Pin the Cat Bookmark Craft for Kids for Later!
These may be the cutest thing ever!!
These cat bookmarks are super adorable!


After more than 60 years in business, Wilmette Jewelers closed its doors for business back in January. At the time, owner Gayle Inbinder expressed her hope that she could find the right buyer for the property—someone who shared the family-based values that the long-time jewelry store had always been known for.
Soon after, she found that right buyer in Bella Cosa Jewelers.
Located at 1149 Wilmette Avenue, the new location of Bella Cosa Jewelers opened in mid-November and Molfese says he is eager to greet many new customers during the always-bustling holiday season.
"The holidays are the time of year where shoppers are looking for that perfect gift, so I'm excited that many people will be coming in to see the new jewelry store in town," he says.
Of course, Bella Cosa Jewelers have long considered the North Shore as home to an important segment of their existing customer base, with many of them travelling to Bella Cosa's Willowbrook location for their fine jewelry needs throughout the years.
Bella Cosa has long been known to carry a large selection of GIA graded loose diamonds, beautiful fine jewelry, and gemstone jewelry including prestigious lines such as Tacori, Simon G., Jack Kelege and Tag Heuer However, Wilmette's Bella Cosa Jewelers will be a bit different from the Willowbrook store.
It's this inviting feeling that has always been part of the success of Bella Cosa, which is a family business.
And yes, Bella Cosa not only values their customers, but the community in which they work.
Bella Cosa Jewelers is located at 1149 Wilmette Avenue in Wilmette. For more information, visit mybella.com.


Saturday, June 16th, the Moon begins the day void-of-course in Cancer but soon enters Leo, the sign that rules children, at 2:21 AM and is no longer void-of-course.
Moon square Neptune, 4:45 AM: This is perfect aspect to sleep through. If you have to get up early, you will need more caffeine than usual.
Moon conjunct Venus, 7:14 AM: A perfect morning to indulge in what makes us happen and feel satisfied! We feel closer to our loved ones. A good morning for a breakfast meeting for networking.
Moon opposes Mars, 4:18 PM: You are feeling a need for adventure and the need to express the real you! We are open about our feelings. We are very protective about those we love. Tempers are short, and we may feel challenged if other push their point of view too strongly. A good time for a work out!


One of the best views in Bay Ridge! Annapolis to Eastern Shore! Steps to sandy beach! Kitchen w/corian, hardwoods, stainless appliances, wine cooler. Private rear gardens & in-ground pool w/ guest house beyond! A total of 2, 376 sq ft of finished space, 3 BR & 2.5 baths in main house. Rear parking accessed from Byrd Lane for additional vehicles!


text:
Israel tears love apart
Amjad Ayman Yaghi The Electronic Intifada 21 November 2018
Married couples are being forced to live separately because of the restrictions Israel has forced on Palestinians.
Ashraf Amra APA images
The only way that Moamen Asad Bashir could live with his wife was to flee Gaza.
Moamen married Nermeen Hamdan in Hebron five years ago. The couple had met in Ramallah – another city in the occupied West Bank – where Moamen worked as a carpenter and Nermeen as a teacher.
In June 2015, Moamen returned home to Gaza for his mother's funeral. Afterwards he made multiple applications to cross the Erez checkpoint, which separates Gaza and Israel. But the Israeli authorities refused to give him a permit.
Forced to live apart from his wife and children in the West Bank, he also lost his job in a Ramallah furniture factory because he couldn't return to it.
It wasn't until February this year that Moamen and Nermeen were reunited. They now live in Brussels, with their two daughters, Yumna, 5, and Ayah, 4.
Reaching the Belgian capital proved arduous. Moamen first traveled through Rafah, the crossing between Gaza and Egypt, and then on to Turkey. He was smuggled into western Europe. The people smuggler who arranged his trip charged him almost $3,000. Nermeen and their children flew to Brussels from Jordan.
"I was extremely distressed," said Moamen by Skype. "The Israeli occupation wouldn't let me see my wife. I decided to emigrate after all the doors were closed in my face."
Ahmad Shaheen is in a similar situation. A plumber from Gaza, Ahmad has been married to Nisreen Abu Arab for eight years. She and their four children live in the West Bank city of Nablus; Ahmad has been prevented from joining them.
Two years ago, Ahmad left Nablus for Gaza as his mother was severely ill.
Two months after his return to Gaza, Ahmad set about returning to Nablus. He has still not been able to leave Gaza. All his applications to travel via Erez have either been turned down – with Israel citing "security" reasons – or elicited no response.
"Our rights are enshrined in international conventions and yet we can't see our wives," he said. "That is the most basic of rights. Today, I am thinking of emigrating not because I don't love my homeland and the Palestinian cause but because I want to live with my family and raise my children."
Ahmad's mother has died since he came back to Gaza. She never once met her grandchildren from Nablus face-to-face.
Israel has routinely blocked Palestinians from traveling through Erez in recent times.
Between January and August this year, Israel permitted an average of 9,000 Palestinians to exit Gaza via Erez per month. Before the second intifada began in September 2000, the average number of Palestinians allowed to leave through Erez each month exceeded half a million.
Israel's harsh policies on travel are – in some cases – preventing couples from getting married.
Manal has given up hope that she will be able to wed her beloved Nayif.
The couple, whose last names are not included to protect their privacy, met following Israel's 2014 attack on Gaza. Nayif, who lives in Ramallah, traveled to Gaza at that time to visit his mother. During the trip, he and Manal fell in love.
Nayif subsequently went back to Ramallah but Manal remains in Gaza. She, too, has been refused permission to cross the Erez checkpoint.
Danger?
In Palestinian tradition, a couple registers their marriage contract before their engagement begins. As Manal and Nayif have taken that step but cannot formally go ahead with their wedding and live together, they are now considered divorced.
"My dreams and our love story have been killed by the occupation," Manal said. "I don't know if I or our marriage presented any danger to them. My only offense is that I lived in Gaza."
Fadel Ashour, a Gaza-based psychiatrist, said that Israel's policies have a marked effect on mental health. People who are forced to separate from their spouses can end up feeling disconnected from society at large, he added. Emotional healing is difficult to achieve amid the stress of life in Gaza.
"These cases are like birds kept alone in a cage," Ashour said. "Maybe the cure for them is to go outside Gaza, change where they live and get married again. But these solutions cannot be attained while Gaza remains under siege."
Ahed, another man from Gaza, went to live in Bethlehem during 2009. As well as finding work in one of Bethlehem's sweet shops, he met his wife-to-be Dunia in the West Bank city.
The couple wed in 2014. For the next two years, they lived in Bethlehem. Ahed went back to Gaza in 2016 for his father's funeral. Israel then denied him permission to leave the territory via Erez.
With no prospect of them being able to reunite, Dunia and Ahed divorced in July this year. The couple have a son, though Ahed has never seen him in person. Dunia was pregnant at the time Ahed went to Gaza for his father's funeral.
"I feel pain every evening," said Ahed. "The occupation has claimed that it cannot give me a permit for security reasons. I don't know if that is based on the truth. How do they judge that I am such a danger that they won't allow me see my family?"
Amjad Ayman Yaghi is a journalist based in Gaza.
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Fadel Ashour
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Amjad Ayman Yaghi 24 December 2020
20 years on still no justice for Muhammad al-Dura
Amjad Ayman Yaghi 30 November 2020
Rising above racism
Amjad Ayman Yaghi 23 October 2020
Israeli military court refuses to release Ahed Tamimi
Tamara Nassar 17 January 2018
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Our Conveyancing Calendar provides a basic time-line for the legal process for home transfers in England and Wales.
We have provided this in the form of a flow chart which sets out the basic and usual way in which a conveyancing transaction runs from beginning to end.
We try to explain the normal procedures that are undertaken when dealing with any property transaction and what you are require to do.
arrange for independent survey i.e. full structural or homebuyers report if required.
Please note that the above time scales are a guide only. Completing a property purchase can be done much quicker if everything is in place to proceed. Sometimes matters do not proceed quite according to plan, particularly if there is a chain involved however we will communicate with all parties involved to try and achieve as smooth a transaction as possible. The most important thing to effect a smooth and timely completion is for all parties to carry out their responsibilities without any delays.
The process for Buying and Selling Residential Property in England and Wales is known as Conveyancing. This process is usually undertaken on behalf of clients by a Solicitor or Conveyancer.
The process is briefly set out below.
The charges made by the relevant authorities to process the necessary Searches required to protect them and any Lender.
The charges made by H M Land Registry to register them as the new owner of the property.
Government Stamp Duty Land Tax, if applicable.
If the property is leasehold, the freeholders charge to register them as the new owner.
Our fee for any extra work that they may authorise us to carry out for them.
The actual amount of these expenses will depend upon the purchase price of the property and its location.
We will need to ask the clients to provide us with a payment on account, to cover the various Search fees. We will collect the remainder of the expenses from them later, generally before contracts are exchanged.
On receipt of the payment on account, we will carry out all necessary searches. In every purchase, we will carry out a Local Search and a Drainage Water Search. Depending on where the property is situated, it may also be necessary to carry out other searches, such as a Coal Mining Search.
The owner of a property may have to pay for decontamination of land, even if he was not originally responsible for the contaminating activity. We will, therefore, make an environmental search on behalf of the clients in order to check this and other environmental matters. We are not, however, professionally qualified to interpret the contents of the results of such search. If the clients decide not to take advice from someone who is suitably qualified, then we will complete the purchase at your own risk as regards these matters.
As soon as we have details of the solicitors acting for the Seller, we will write to them to request the draft contract and the title documents.
On receipt of the purchase documents from the Seller's solicitors, we will approve the contract and investigate and confirm the seller's ownership of the property and prepare the purchase Transfer Deed.
We then raise relevant Pre-Contract enquiries with the Seller's solicitors. The Client will have inspected the property and should let us know as soon as possible if there are any aspects they would like clarified, or extra enquiries raised. If they do not inform us of any of these matters, we will not be able to investigate them. For example, there may be someone in occupation of the property who is not the owner; the boundaries may appear to have been altered or there may be physical defects. These matters are generally covered within our initial client questionnaire.
If it appears that any works have been carried out to the Property which may have required Planning Permission or Building Regulations consent then the client should discuss this with their surveyor and then advise us, as further investigations may be needed. Works needing Planning Permission may include extensions; new buildings (such as conservatories) and loft conversions. Many works will not require such permission provided they are within certain size and position guidelines. Building Regulations consent is generally needed for internal alterations including removal of structural walls and chimney breasts, creation of through living rooms by removal of the dividing wall and installation of bathrooms.
Where the clients have applied to a Lender for a Mortgage Loan. By the time that they receive the written loan offer, the Lender should also have sent us a copy, together with our instructions and the mortgage literature. We will then advise them on the contents of the offer including any special conditions that the lender requires to be satisfied before the lender will release the monies to us, we will then arrange for the clients to sign the mortgage documentation.
When all preliminary matters have been dealt with, we will send the clients our Purchase Report, which will contain copies of any important documents, a plan of the property and details of any relevant restrictions on your use of the property.
On exchange of contracts the clients are required to pay a non-refundable deposit to the Seller. This figure is normally 10% of the purchase price, although the Seller will often accept less if the buyers are obtaining a mortgage loan in excess of 90% of the purchase price.
We will also at this stage send a completion statement to the client detailing the funds we require to complete. This will include all expenses as detailed above and will allow a credit for the advance payment for searches. Please note we will not be in a position to exchange contracts until these funds have been paid in and cleared through our Bank. Where the property which the client is buying is Leasehold or where we for example the clients are buying a new build property the figures may be subject to some variation and a further definitive statement will be sent immediately prior to completion setting out the exact details.
Exchange of Contracts then takes place and the agreed date for completion is inserted in the contract. The client is then contractually bound to buy the property and will be able to move in as from the completion date. Please note that adequate buildings insurance cover must be in place as from the date of exchange. If the clients have not agreed with their Lender that they are insuring via them this insurance will be the clients' responsibility.
After exchange and before completion we carry out final searches, which will include a bankruptcy search against each of the buyers.
We will ask the Lender to arrange for our bank account to be credited with the mortgage loan monies one working day before the completion date. Although this will involve interest being charged by your Lender for one extra day, this step will ensure that we are able to protect the client against the practical and financial consequences of any delay on the day of completion. It will also ensure an early completion and release of the keys on the day.
We suggest that a few days before completion, the client contacts the Seller to arrange the handing over of the keys. The usual arrangement is that the Seller will leave the keys at the estate agents for the client to collect on the day of completion.
We strongly recommend, as a security precaution, that all clients arrange for the locks to be changed once they move in. This is because it is impossible to say, with any certainty, how many sets of keys have been produced in the past, and to whom they may have been given.
We will deal with the payment of Stamp Duty and the registration of Title at the Land Registry. The registration process will usually be completed within 4-6 weeks.
When the registration process is complete, the Land Registry will supply a Title information Document (TID), which confirms the clients ownership of the property. This will then be sent to the Lender for them to retain. Any Deeds which are not required by the Lender will be sent to the client unless they instruct us to store them for safe-keeping. We will send the client a copy of the TID, for their records, showing them as the new registered owner.
Property held in joint names can be held in one of two ways.
This is where the joint owners are all equally entitled to the property.
When one of the owners dies, that person's interest in the property passes automatically to the surviving owner(s). If, therefore, there are two joint owners and one of them dies, the other becomes solely entitled to the property.
A Joint Tenant cannot deal with his/her "share" of the property in a Will – it cannot pass to anyone other than the surviving owners.
Do not be confused by the term "tenant" this has nothing to do with "tenants" in the ordinary meaning of the word.
Under this arrangement the property is held by the joint owners in specific proportions, which may or may not be equal. There might for example, be two owners each owning a half interest in the property, or three owners having a 20%, 40% and 40 % share respectively.
If one of the joint owners dies that person's interest does NOT pass automatically to the surviving joint owners, but would form part of his/her estate and will pass according to that person's Will or under the rules of intestacy.
A joint owner could, therefore, make a Will leaving his/her share to the other owner(s) or leaving it to someone else altogether.
When the property is held in this way, it is essential to have a Declaration of Trust either in the deeds or separately which states the proportions owned by each of the joint owners.
It is necessary when purchasing a property in joint names to decide whether the property should be owned as Joint Tenants or as Tenants in Common. This decision need not be permanent as it is possible to change from one form of ownership to the other. Please note that severing a joint tenancy (i.e. converting to tenants in common) can be done without the consent of the joint owner(s). One person can instigate it and the other(s) do not have to agree for it to be effective.
If the joint owners are not entitled to equal proportions of the value of the property then they should not hold the property as Joint Tenants, unless they wish to become entitled to equal proportions.
If the joint owners do not wish their interest to pass automatically on their death to the other joint owner(s) they should not hold as Joint Tenants, but as Tenants in Common. There may be personal and/or tax reasons for this.