Travis Mills describes himself as "just a guy who had a bad day at work."
During a routine patrol in an Afghan village on April 10, 2012, Mills put down his 80-pound backpack and set off an improvised explosive device that left him as one of only five surviving quadruple amputees from the war on terrorism.
"I'm not going to make it," Mills recalls telling Sgt. Daniel Bateson, one of the medics who immediately responded. "‘Leave me, and go save my guys.' And he told me, ‘With all due respect, Sgt. Mills, shut up. Let me do my job.'"
The wounds he tried desperately to treat were so severe that Bateson remembers thinking, "Nobody lives after this."
Mills, however, isn't just anybody. Not only did he survive, he has flourished, drawing on his winsome personality, leadership skills and inspirational message to help fellow veterans dealing with severe physical injuries and post-traumatic stress disorder.
BORN TO LEAD
Growing up in his small hometown of Vassar, Mich., Mills excelled in football, baseball and basketball. In the book "Tough As They Come," his high school football coach remembers Mills as a gifted athlete.
"His junior year, Travis and his friends got into weightlifting and powerlifting and went to all the football camps," Vince Leveille writes. "That year, we won the conference championship and made the playoffs for the first time ever. Travis' work ethic motivated everybody. Everybody got stronger because Travis was their leader."
Mills went on to college but started to feel pulled in a new direction. After returning home to Vassar, he met with military recruiters and found what seemed to be missing in his life.
"Joining the military felt like joining a sports team," Mills writes. "With the military came camaraderie. The job itself took a lot of drive. I was an adrenaline junkie, and it seemed like a big adventure."
He did basic training at Fort Benning, Ga., and was assigned to the 82nd Airborne Division at Fort Bragg, N.C. After two tours in Afghanistan, he began his third in early 2012.
The assignment wasn't unlike the previous ones: work with Afghan government officials to help them provide their own security. But this time Mills and his unit were deployed to the dangerous Maiwand district in Kandahar province.
On top of that, Mills was leaving behind his wife, Kelsey, and their 5-month-old daughter, Chloe. The 6-foot-3-inch, 240-pound soldier told them goodbye Feb. 23, 2012, wrappping his arms around them for the last time.
On the eve of that third deployment, Mills felt uneasy. "I don't know if I'm coming back from this one," he recalls telling a fellow soldier.
BRUNT OF THE BLAST
That "bad day at work" was supposed to be a day off for Mills and his unit. But an informant's tip changed everything.
Mills, the weapons squad leader, suited up and headed out to investigate with two dozen soldiers and an ordnance disposal team. He instructed his team to secure a perimeter around an abandoned Afghan army post they believed the Taliban was using to make explosives. As the soldiers began their work, Mills' backpack detonated the IED, which blew off his right arm and leg and badly injured his remaining two limbs.
"My left hand was still there, tattered up, so the first thing I did was radio my lieutenant and tell him I was hit," Mills says. "I told him we needed some help and a medic came rushing up, tourniquets everywhere. The medics fixed me up and got me on the helicopter. There were two others who got hurt with me, and we flew to the hospital. I was calm and awake the whole time. Got to the operating table, and I told them to quit touching me and to leave me alone because I was fine."
Though Mills was the most severely wounded, he was more worried about his men while en route to the military hospital in Kandahar. Shane Waite, one of the flight medics, sent a message to Kelsey about her husband.
"His face was dirty and there was dust in his eyes, but he never shed a tear," Waite writes. "I replay a moment in my mind when he looked at another wounded soldier and winked to reassure him that all would be OK."
The medical team at Kandahar sedated Mills during the immediate surgeries and recovery period. His left arm and left leg had to be removed, leaving him a quadruple amputee. Doctors woke up Mills on April 14 – his 25th birthday. Three days later, he arrived at Walter Reed National Military Medical Center in Bethesda, Md., for more surgeries.
Kelsey, her parents and Travis' parents took turns staying at his bedside. Mills wouldn't talk to Kelsey for two days. On the third day, he told her "to take Chloe, my little girl who was only 6 months old, and the money in the account, and go. There was no reason for her to put up with this. This isn't who she married. I lost everything, I thought. Thankfully, she gave me the confidence and strength to keep going."
Still, those first few days at Walter Reed were extremely difficult. Mills questioned whether or not he wanted to live. He slept most of the time; his waking hours were brutal.
Amputees often report feeling a sensation of intense burning in the areas of their missing limbs. The patient's brain interprets the misfiring of an amputated nerve ending as pain. Usually, medication and/or electrical stimulation can alleviate it. Mills says treatment felt like he "was being filleted alive."
Nothing eased his pain. So doctors put him in a ketamine coma – a procedure likened to rebooting the body like a computer, so rare it has been performed fewer than three dozen times.
Five days later, Mills woke and began experiencing wild hallucinations – marauding with Genghis Khan, chatting with Kramer from the TV show "Seinfeld" and playing in the National Hockey League – mixed with fits of screaming. Eventually, though, he came out of it. No more pain. No more hallucinations. No more wanting to die.
He realized the worst was over and glanced at a plaque on his nightstand. A verse that once angered him now gave him comfort:
"Be strong and courageous. Do not be afraid; do not be discouraged, for the Lord your God will be with you wherever you go." – Joshua 1:9
Before the ketamine treatment, Mills wanted to call it quits. "Who would open jars for Kelsey?" he wondered. But he didn't give up, thanks to family, friends, various community organizations and his own indomitable spirit.
When Mills returned home to Michigan for a visit, the men and women of American Legion Post 400 in Richfield were waiting for him.
"The Legion was the first organization to reach out to my parents and ask what they could do to help," says Mills, now a post member. "They found out I was coming home for my first time, knowing I was in a wheelchair and that I didn't have any legs yet to be able to walk up and down stairs or in and out of the house. The Legion helped put a ramp on the house so I could get inside to be with my family."
The Richfield post also put on dinners to raise money to help the Mills family pay for renovations to their home. "They are always calling to see if there is anything else they can do," Mills says. "It's just great to know that people are out there who want to help in situations like this. I wasn't really planning to lose my arms and legs, but it happens, I guess."
About four weeks after the explosion, Mills received his first prosthetic hand and began learning how to control it. "Then, seven weeks in, I got to put my legs on for the first time and walk, which is pretty fast. Then it was next step, next step, next step, and I was able to fully recover within 19 months. I was able to drive, shower, dress myself, feed myself, things like that. Back to pretty much everyday normal life, as much as I could get."
Mills worked hard at his physical therapy – hip flexors, core work, walking and pulling weight – and occupational therapy, which included picking up items and shaving his face.
Nowadays, Mills snowboards, kayaks, canoes and rides a gravity bike. "It's fun to get back out there and know that I can still do things with my daughter, which is more important to me than anything in the world," he says. "I love the things I can do with my daughter, like take a Polaris Ranger through the trails."
Mills' passion for outdoor activities and his desire to give back, as well as his recovery experience at Water Reed, were catalysts for his initiative to create a camp for wounded veterans.
While undergoing rehabilitation in an apartment at the military medical center, Mills spent time visiting patients in their hospital rooms, giving them hope, encouragement and even a chuckle or two. He realized early on how crucial it was for his wife to be at his side while he adjusted to his life-altering injuries. So when it was Mills' turn to motivate others, he assembled a support team – sometimes bringing along Kelsey and Chloe, or other wounded veterans – to comfort those who did not have family or friends on site.
That was only the beginning. Mills says he was inspired by the assistance he received from the Legion and others in the immediate aftermath of his "bad day at work."
"When I first got blown up and was in the hospital, all these people came to see me and wanted to help out by donating money to me," he recalls. "I just felt like with all the good out there, I should take that money and donate it back to something else. What better way than to build a veterans camp?"
The Travis Mills Foundation sponsors weeklong camps for wounded servicemembers and their families, where they participate in archery, horseback riding, tubing, bass fishing and trail riding. Of course, everything in the camp – including the zip line – is designed with the severely injured in mind.
Taylor Morris, a Navy veteran and quadruple amputee, was injured about a month after Mills lost his limbs. The two bonded at Walter Reed. Morris says the camps have helped him as he continues to recover.
"We did boating, fishing, swimming, kayaking and a bunch of golfing, and had campfires every night," he says. "One of the camps had a ropes course up in the trees that was pretty fun, a confidence-builder."
For Morris and others like him, the camps offer far more than achieving physical success.
"Fellowship is an important part of it," he says. "That's not just limited to other veterans. I think the people who were in that situation maybe understand a little better some of the things you are going through."
Morris' wife, Danielle, appreciates that the camps include the whole family. "I think it is great that Travis is building it on the basis of both supporting military personnel as well as their families," she says. "I also think it's great that he's focusing on past wars as well. So many others served before this generation, and it's important for them to connect as well."
A PERMANENT HOME
Last year, Mills' foundation purchased the former Elizabeth Arden estate in the Mount Vernon-Rome area of Maine as a site for a permanent facility. It is undergoing renovation and is expected to be ready in 2017.
"It will be 100 percent handicap accessible and will cater to veterans who are wounded," Mills says. "It will branch out to guys with PTSD, traumatic brain injury and other kinds of injuries, but right now we are focusing on amputation and spinal cord injuries from neck and waist down. We are going to be set up for anything and everything so we can show these guys and their families a great time."
The plan is to host between six and 10 families each week throughout the summer and then expand into winter camps. In addition to the physical activities offered at previous camps, the new site will have a spa and dedicated areas for arts and crafts. In time, Mills envisions American Legion posts sending groups of members for weeklong retreats.
"I want them to take away memories with their families and have a great time," Mills says of camp participants. "I want them to take away a network of people they can call and talk to – (people) who are going through any situation they might have. I want people to go away from this camp knowing there are people out there who care and honor their sacrifice. I want them to really focus on themselves and see that they can accomplish great things."
While Mills' story of perseverance serves as inspiration to military members and civilians throughout the nation, his source of motivation is closer to home.
"My daughter is always going to help me succeed," he says. "Whether I fail at first, she will never see me (give up and) quit. I want these guys, women and their families to know they can still be together having a great time. Their life isn't over. Just because they are wounded doesn't change the fact that they are still functioning members of their family and the society around them."
Henry Howard is deputy director of The American Legion's Media and Communications Division.Show Full Article
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En théorie des automates, le lemme d'Arden est un résultat concernant les langages rationnels.
Il décrit les solutions de l'équation :
où et sont deux langages formels et est une inconnue. Le lemme d'Arden s'utilise notamment dans la méthode des équations linéaires gauches qui permet de calculer le langage reconnu par un automate fini donné.
Le lemme est nommé d'après Dean N. Arden qui l'a décrit en 1961. C'est maintenant un résultat que l’on retrouve dans de nombreux manuels ou supports de cours.
Énoncé[modifier | modifier le code]
On peut voir l'équation comme la définition récursive d'un langage : un mot de ce langage est soit dans , soit formé d'un mot dans suivi d'un autre mot du langage, et on peut interpréter la solution comme une définition itérative : un mot est formé d'une suite de mots dans , puis d'un mot final dans .
Exemples[modifier | modifier le code]
- L'équation , où et sont des lettres, a l'unique solution .
Preuve[modifier | modifier le code]
1. Le langage est solution. En effet, on a :
2. Le langage est la plus petite solution. Soit en effet une autre solution. Alors on a : . En continuant à remplacer par , on obtient pour tout l'équation
ce qui montre que contient tous les , donc .
3. Si ne contient pas , alors cette solution est la seule. Soit en effet une autre solution. On sait déjà que contient . Par ailleurs, on a pour tout l'équation
Soit un mot de de longueur . Il appartient alors au membre droit de l'équation, mais il n'est pas dans parce que tout mot de ce langage a longueur au moins (puisque tout mot de contient au moins une lettre). Donc le mot appartient à un autre langage de l'union, donc à Ceci prouve que est contenu dans , donc l'égalité .
Application[modifier | modifier le code]
Le lemme d'Arden permet, par la résolution d'un système d'équation par substitution, de déterminer le langage reconnu par un automate fini. On procède comme dans la méthode d'élimination de Gauss : on exprime une variable en fonction des autres, on la remplace par cette expression, on résout le système à une variable de moins, et on explicite la valeur de la variable éliminée.
Soit un automate fini sur un alphabet . Pour chaque état , soit le langage reconnu à partir de l'état , c'est-à-dire le langage reconnu en prenant pour état initial. On pose enfin . Ce sont les étiquettes de transition de à . On a alors :
L'application du lemme d'Arden permet alors d'éliminer une à une les inconnues des équations de la forme précédente, et d'obtenir une expression explicite des et notamment des qui permettent de déterminer le langage reconnu par l'automate .
Exemple[modifier | modifier le code]
L'automate ci-contre donne le système d'équations :
Le lemme d'Arden donne
En injectant cette expression de dans l'expression précédente de et en factorisant, on obtient
et par application du lemme d'Arden,
Notes et références[modifier | modifier le code]
Référence[modifier | modifier le code]
Bibliographie[modifier | modifier le code]
- Olivier Carton, Langages formels, calculabilité et complexité, Vuibert, (ISBN 978-2-7117-2077-4, présentation en ligne)
- (en)John E. Hopcroft, Rajeev Motwani et Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, , 3e éd.(ISBN 978-0-32146225-1)
- Jacques Sakarovitch, Éléments de théorie des automates [« Elements of Automata Theory »], Cambridge University Press, (ISBN 9780521844253)
Liens externes[modifier | modifier le code]
- ↑(en) Dean N. Arden, « Delayed-logic and finite-state machines », dans 2nd Annual Symposium on Switching Circuit Theory and Logical Design, (FOCS), Detroit, Michigan, USA, IEEE Computer Society, 17-20 octobre 1961 (DOI 10.1109/FOCS.1961.13), p. 133-151.