A patient is reported with psychological change characterised by impaired concentration and thought projection, followed by both severe anxiety and depression, starting after three weeks on high dose methysergide. The acute problem settled slowly after methysergide withdrawal and is likely to represent an unusual and serious side effect of that drug.
To date, there have been relatively few reports of psychiatric side effects of methysergide,5–7 even though this molecule is known "on the street" as a substitute for LSD5 and has been used for a very long time in clinical practice. To highlight this issue in neurological practice at a time of renewed interest in the side effects of ergot related medicines,8 we describe a patient who developed an adverse psychiatric reaction following the administration of methysergide.
A 22 year old male law student started taking methysergide as prophylactic treatment for chronic cluster headache.9 His past medical history included childhood counselling and transient psychiatric symptoms while on corticosteroid treatment for his cluster headache.
Methysergide was prescribed as initially at a dose of 1 mg daily with a slow increment over seven weeks up to 12 mg a day. During that period, the patient reported a reduction in both the frequency and the severity of headaches. Three weeks after the does of 12 mg/day was started he developed temporal and spatial perceptual disturbances. Objects began to look out of proportion and his sense of time was altered. He had déjà vu, a sense of depersonalisation, and the conviction of being able to broadcast his thoughts, as well as the belief that the telephone could read his mind. A sense of incredible insecurity and anxiety overwhelmed him, and feelings of extreme apathy and anhedonia developed. He could not study and was despondent. Methysergide treatment was discontinued and verapamil started. At the same time, for the psychiatric disturbances, he was given olanzapine, then risperidone, and later mirtazapine. All these psychiatric medicines were eventually stopped because he had no improvement.
Three months after methysergide was stopped, a psychiatrist diagnosed a severe depressive episode and at about that time the hallucinations started to settle. At a follow up visit nine months after stopping methysergide, the family reported a significant improvement in his condition but noted that he still experienced uncontrollable feelings of insecurity and anxiety. The patient requested the presence of the family during his clinic visits and preferred his parents to answer questions, as speaking increased his anxiety. Remarkably, when he did speak he expressed the view that despite the dramatic side effects he was happy that he had been treated with methysergide as the cluster headache attacks had been so dreadful that he was pleased to have had relief from them.
We report a patient with psychological change characterised by impaired concentration and thought projection, followed by both severe anxiety and depression starting after three weeks on high dose methysergide. The acute problem settled slowly after methysergide withdrawal and is likely to represent an unusual and worrisome side effect of that drug. It is notable that the patient and his family still felt that the methysergide was, on balance, a useful treatment of his chronic cluster headache.
Persyko5 described a migraine patient who developed, after a single dose of 2 mg methysergide, extreme agitation, impaired concentration, bizarre behaviour, hyperacusia, and loss of self control followed by depression. Wilcox7 described a patient who developed, after 6 mg of methysergide, anxiety, a sense of depersonalisation, and a subjective feeling that colours seemed intolerably vivid. Skorzewska and Lal6 reported that a second 2 mg dose of methysergide induced a florid, transient psychosis in a patient with a family history of schizophrenia. Thirteen years later the same patient developed a major depression. In a series of 57 migraineurs, Hale and Reed10 found that discontinuation of methysergide was necessary in nine because of severe psychiatric reactions; psychosis, nightmares, and hallucinations were noted.
In our patient there was a close temporal relation between methysergide treatment and syndrome onset, and a partial overall clinical improvement following drug withdrawal. Both features are indicative of a methysergide induced reaction. Additionally, this patient had already had psychiatric symptoms with corticosteroids, which suggests an underlying predisposition. Consistent with this premise, Mendels11 reported worsening of psychotic symptoms in schizophrenic patients following methysergide administration.
There are several possible mechanisms by which methysergide might produce psychiatric symptoms, although much of the pharmacology is somewhat old so this aspect must to some extent be speculative. Dopaminergic or serotonergic agonist activity would both be candidate mechanisms. Important pharmacological effects of methysergide are blockade of 5HT2 receptors, even if it is not a pure antagonist, and some agonist activity at various 5HT1 receptor subtypes.3 Methysergide has partial agonist activity at certain dopamine receptors.12 It is a congener of LSD and has structural similarities with it. It is well known that LSD is a complete or partial agonist of different 5HT receptors12 and its hallucinogenic effect is probably mediated by an action on 5HT2A receptor subtypes.13–15 The effect on our patient was rather long lasting, and well beyond the pharmacological effect of the drug, which is consistent with the hypothesis that it triggered an underlying psychiatric predisposition. Given the complexity of the serotonergic system and its interaction with multiple neurotransmitter systems it is perhaps surprising that more patients have not been reported with psychiatric side effects of methysergide.
Our experience, and that already reported, suggests that patients with a predisposition to psychiatric morbidity, and particularly those who have had psychiatric side effects on other treatments, are less than ideal candidates for methysergide. It remains a remarkably useful drug, especially in cluster headache, and when used with caution has stood the test of time.
Berde B, Schild HO. Ergot alkaloids and related compounds. In: Born GVR, Eichler O, Farah A, et al, eds. Handbook of experimental pharmacology, vol 49. Berlin: Springer-Verlag, 1978.
Sanders-Bush E, Mayer SE. 5-Hydroxytryptamine (serotonin) receptor agonist and antagonists. In: Hardman JG, Limbird LE, Molinoff PB, et al, eds. Goodman and Gillman's The pharmacological basis of therapeutics. 9th ed. New York: McGraw-Hill, 1995:249–63.
Fish B, Campbell M, Shapiro T, Floyd A. Schizophrenic children treated with methysergide (Sansert). J Nerv Ment Dis1969;30:534–40.
Persyko I . Psychiatric adverse reactions to methysergide. J Nerv Ment Dis1972;154:299–230.
Skorzewska A, Lal S. Methysergide-induced psychosis: case report with long-term follow-up. Neuropsychobiology1989;22:125–7.
Wilcox JA. Psychoactive properties of methysergide. J Psychoact Drugs1987;19:387–8.
Rascol O, Pathak A, Bagheri H, et al. New concerns about old drugs: valvular heart disease on ergot derivative dopamine agonists as an exemplary situation of pharmacovigilance. Move Disord 2004;19:611–13.
Headache Classification Committee. The International Headache Society. The international classification of headache disorders. Cephalalgia2004;24 (suppl 1) :1–160.
Hale AR, Reed AF. Prophylaxis of frequent vascular headache with methysergide. Am J Med Sci1962;243:92–8.
Mendels J . The effect of methysergide (an antiserotonin agent) on schizophrenia: a preliminary report. Am J Psychiatry1967;124:849–52.
Roth BL, Meltzer HY. The role of serotonin in schizophrenia. In: Bloom FE, Kupfer DJ, eds. Psychopharmacology – the fourth generation of progress. New York: Raven Press, 1995:1215–27.
Aghajanian GK, Marek GJ. Serotonin model of schizophrenia: emerging role of glutamate mechanisms. Brain Res Rev2000;31:302–12.
Heym J, Jacobs BL. Serotonergic mechanisms of hallucinogenic drug effects. Monogr Neural Sci1987;13:55–81.
Glennon RA. Do classical hallucinogens act as 5-HT2 agonists or antagonists? Neuropsychopharmacology 1990;3:509–17.
This article was withdrawn by the publisher.


Another guest appearance by my coworker Bob! I have such a weird work situation; most of my coworkers are located in Madison, WI. Bob comes in two, maybe three times a week, and Tomoko comes in when the whales let her. So I'm mostly alone, but I see Bob the most. So you see Bob the most, too!
I drew two comics today! This is the second! I'm starting a Discord channel for creative friends to hang out in. Please leave a comment if you're interested in joining and I'll send you an invite! I'm calling the channel Internet Touchery because, y'know, connecting through the internet. But like, not really connecting. It's like touching without touching; touchery.
Click here for today's bonus panel!
EDIT: Miracles do happen! I updated Blue Circus (nsfw) last night! It's just something small, but I explain more there. Click it to check it!
on May 1, 2018 and modified on August 13, 2018.
I'm creative sometimes. I would like to join this Discord.
The discord is decidedly disinterested in a daveless designation. D'invited!


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Валентин Петрович Пургин (1914 – 1940), с истинско име Владимир Петрович Голубенко, е единственият в историята мошеник, съумял с измама да добие званието "Герой на Съветския съюз".

Биография
Голубенко е роден през 1914 в Урал в семейство на работници. Остава с незавършено основно образование.

Заради кражба е осъден за първи път през 1933 г. Отново е осъден – за кражба, мошеничество и фалшификация, през 1937 г. Изпратен е в изправително-трудовия лагер "Дмитровлаг" край гр. Дмитров, Московска област, откъдето съумява да избяга. Голубенко, с откраднат паспорт на името на Валентин Петрович Пургин, преминава в нелегалност.

Пургин попада в Свердловск, където постъпва във Военно-транспортната академия, става кореспондент на железничарския вестник "Путёвка". Пургин обогатява фалшивата си самоличност, набавяйки си документи за завършено средно образование, академична справка и завидна атестация от началника на Свердловската академия.

Така подготвен, Пургин е готов за Москва. В столицата първоначално работи в редакцията на вестник "Гудок", но след запознанство и сближаване с Полетаев, редактор на "Комсомольская правда", Пургин е назначен в органа на Комсомола без проверка. През 1939 г. вече е заместник-началник на военния отдел в редакцията и създава около себе си ореол на тайнственност, намеквайки за връзки с НКВД и появявайки се пред колегите си закичен с военния орден "Червено знаме", в действителност откраднат.

През 1939 г. в качеството му на военен кореспондент Пургин е командирован в Далечния изток, за да отразява въоръжения граничен конфликт между СССР и Япония при Монголия. През есента в редакцията пристига съобщение, че Пургин е ранен в битка при Халхин Гол и бере душа в болница в Иркутск. Шумът около него е предизвикан с фалшиви епикризи, но го довежда обратно в редакцията, където го чака орден "Ленин". В края на 1939 г. Пургин става кандидат-член ВКП (б) с препоръки от отдавнашни членове на комунистическата партия.

В началото на Съветско-финландската война (1939 – 1940) Пургин е изпратен на фронта със звание младши командир. През януари 1940 г. изпраща в редакцията съобщение, че е изпратен по секретна задача в Ленинград, поради което няма да може да кореспондира. Пургин се готви в действителност за бягство на Запад, а междувременно пилее командировъчните стредства в гуляи. Войната с Финландия обаче приключва с порой от държавни награди за победителите-червеноармейци. Пургин фалшифицира официална бланка на 39-а дивизия, с която предлага себе си за такава награда. Отчитайки позитивите на чистото му минало и предишните му награди на 21 април 1940 г., с указ му е присвоено най-висшето държавно звание "Герой на Съветския съюз". Указът е публикуван във в. "Комсомольская правда" заедно с очерк за военните му подвизи, докато самият Пургин отдъхва в Сочи със съпругата си Лидия Бокашова.

Радостта е кратка, тъй като фотографията, публикувана в същия този очерк, спомага за разкриването на фалшивата самоличност на Валентин Пургин от свидетели. Владимир Голубенко е арестуван, напълно е разобличен и е осъден на смърт чрез разстрел, а наградният указ е отменен.

Източници

Външни препратки
 "Трибунал для героев", книга
 "Загадка Пургина", журнал "Журналист", № 6, 2003 г.

-
Съветски военни кореспонденти
Лагеристи в ГУЛАГ
Руски престъпници
Руски журналисти
Съветско право
Членове на КПСС
Починали в Москва
Убити журналисти
Псевдоними

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P2 have been learning about estimation in Maths. They are also going to start rehearsing for our annual school nativity.
P2 have been learning about the Victorian times. They are going on a trip to the Victorian school.
They love their new pretend tool bench. They have drilled, hammered and pierced.
Primary 2 have also had visitors every Tuesday. The visitors have been teaching them some music. They are enjoying it so far!
P2 have been playing outside with Loose Parts. They also have a toy kitchen outside. They love to make meals and pretend that they made a masterpiece. They hope that they can become little chefs!


Ways to live a blessed Life!
We learned that God has blessed all of us by giving us one blessing after another.
What steps should we take to live a blessed life?
1. Receive God's blessing through Christ.
2. Celebrate God's blessing in worship.
3. Expect God's blessing by faith.
4. Share God's blessing with others.
Everything that we have is because of the grace of God.
To be blessed. I don't know of any human being who doesn't desire to live a blessed life. And because God is really sweet to us, he made sure to include His recipe for a blessed life right there in His instruction book.
Let's look at Joshua where we met some VIBP's (Very Important Blessed People).
In Joshua 1, Moses is gone and Joshua is the new leader. Previously, the Reubenites, Gadites, and the half-tribe of Manasseh asked Moses for permission to go ahead and settle just east of the Promised Land.
The time had come for the rest of God's people to cross over and claim the promise. The Reubenites, Gadites, and the half-tribe of Manasseh could have just said, "Good luck guys! Buh bye!" They were all settled in and set.
But that's not what God's people do.
God's people are ever on guard ready to serve and support each other. The R's, G's, and 1/2M's left the comfort of their already established homes to do whatever it took to help the rest of God's people claim their rightful place and settle across the Jordan River.
They committed themselves to Joshua, their trusted leader. They made an easy transition from following Moses to following Joshua because they knew both men were appointed and anointed by God.
We have to pause and ask ourselves, Are you willing to do whatever it takes to serve God and support His people? Are you willing to put our own comfort aside to help others have the same opportunity?
The book of Joshua continues by telling the story of the Israelites' victorious journey into the Promised Land. In chapter 22, Joshua stands before those fighting men once again. He commended them for their valiant efforts and told them it was now time to enjoy the fruit of their labor. Everyone was settled and ready to enjoy the long-awaited promise of a land flowing with milk and honey.
But before he sent them on their way, he gave them a solemn warning.
Being blessed is a dangerous place to be. If we get too comfy, we'll let down our guard and give the evil one lots of little cracks through which to sneak.
So what's the recipe for a blessed life?
1. Love the Lord your God: Our love for God should be so intense that we can't bear to not be in His presence. We need to learn to truly love Jesus. What is meant by loving Jesus is having a relationship with Him. God wants you to lean on Him with everything.
2. Walk in all His ways: Blessed people walk in sync with God at all times…no lagging behind or rushing ahead. Understand what is true worship.
3. Obey His commands: This is where the whenever, wherever, and whatever comes in. We should have NO limits to our obedience. NO reservations. NO wavering. Trust in God.
God blesses those who trust, believe, and expect His blessings. We must consistently have faith.
4. Hold fast to Him: When you think of holding on to God, what picture comes to your mind? Do you picture someone hanging onto the side of a cliff with white knuckles shaking? I'll tell you what I picture. I picture a little child in Daddy's arms with arms wrapped tight around his neck and head rested securely on his shoulder. Daddy's big arms are doing the heavy-duty holding.
5. Serve Him will all your heart and soul: Just as the fighting men left their homes to take on the important mission of claiming the promised land, we all have a mission. Christians should never be bored! No coasting through life. No half-hearted effort. No sitting around waiting for someone else to do it. Bless others and God will bless you.
We are all God's children. What we know about our Lord is available to others. God is pleased when we share what we have with others. Life is a cycle. As we give to others, God gives to us.
Some recipe, huh? No obscure ingredients, no fancy slicing and dicing, no marinating for hours.
Love Him, walk with Him, obey Him, hold onto Him, serve Him…and be blessed.


Rep. Adam Schiff, chairman of the House Intelligence Committee, told CBS Face the Nation on Sunday that Special Counsel Robert Mueller "can't indict the president." Schiff and Republican Congressman Jim Jordan said Mueller's investigation into Russia's role in the 2016 U.S. election, now in the hands of Attorney General William Barr, should be made public. Rough Cut (no reporter narration).


text:
Call-In: 866-801-8255 SiriusXM | Urban View Channel 126 Nationally 6am – 10am ET weekdays.
Madison Speaks
Judge Robert L. Wilkins
Home > Books > Judge Robert L. Wilkins
The Long Road to Hard Truth: The 100-Year Mission to Establish the National Museum of African American History and Culture
Author: Judge Robert L. Wilkins
Genres: Civil Rights, Education, Historical
In Long Road to Hard Truth: The 100 Year Mission to Create the National Museum of African American History and Culture, Robert L. Wilkins tells the story of how his curiosity about why there wasn't a national museum dedicated to African American history and culture became an obsession-eventually leading him to quit his job as an attorney when his wife was seven months pregnant with their second child, and make it his mission to help the museum become a reality.
My Life on the Courts
My Life on the Courts is the candid memoir of an African American federal judge that chronicles his journey through the courts and out of the depths of depression.
Grace Will Lead Us Home: The Charleston Church Massacre and the Hard, Inspiring Journey to Forgiveness
A deeply moving work of narrative nonfiction on the tragic shootings at the Mother Emanuel AME church in Charleston, South Carolina from Pulitzer Prize-winning journalist Jennifer Berry Hawes.
Joe Madison Responds to President Trump's Racist Tweets
Stephen A. Smith - The Republican Party Doesn't Look Like Me
2019 Talkers Heavy 100
Mistaken Identity, "Your Biological Father Is Someone Else."
"That Should Wake Them Up" Radio Host Proposes TSA Workers Have Mass Sickout in Atlanta After Super Bowl
Joe on Morning Joe on MLK Day – Discussing Dr. Kings Legacy
The Family Of Dick Gregory Presents: "A BENEFIT TRIBUTE TO Lillian Gregory"
Joe on the Go
SiriusXM | Urban View Channel 126 Nationally 6am – 10am ET weekdays.
Phone: Call-In: 866-801-8255
E-mail: Listen to the Black Eagle on SiriusXM | Urban View Channel 126 Nationally 6am - 10am ET weekdays.
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Joe on the Go!
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text:
Tony Snow Out Jeff Gannon In as White House Press Secretary
Washington, DC (APE) – in a stunning move today it was announced that the anticipated replacement of outgoing press secretary Scott McClellan with Fox TV news commentator Tony Snow had been scrubbed. The White House today announced that instead, effective immediately, the new press secretary would be controversial independent journalist Jeff Gannon.
It was revealed that after a rigorous security check, Snow had been found to have voiced a number of anti-administration sentiments in the past through his duties with Fox news. In the past, Snow had accused the Bush administration of "losing control of the federal budget", "becoming something of an embarrassment", being "more eager to please than lead", and looking "impotent". According to White House sources, these aspersions were, "but the tip of the iceberg".
Fox news, upon hearing of the allegations reportedly has immediately suspended Snow pending further investigation by Fox security.
In a hastily arranged press conference, Jeff Gannon was introduced as the successor to Scott McClellan. Gannon stated that he was happy to be on board with the president in this capacity and look forward to developing deeper relationships with many in the White House.
"What can I say," Gannon stated, "President Bush rewards loyalty. I have to be honest, it really feels good to me to be on top again." Gannon became a controversial figure about a year ago when it was revealed that his journalism credentials were virtually nonexistent while being allowed access to the White House press pool. It was further revealed that his true name was James Guckert and that prior to his work as a reporter for "Talon News" he had dabbled in online gay Marine pornography.
Gannon stated that he was looking forward to bringing new life to the administration's chronically sagging polls. He stated that he is toying with the idea of forming a White House staff softball team to improve morale. "I was a pretty darned good catcher in my day," he joked with the press in attendance.
White House Introduces Its Version of Monopoly: Iraqopoly
Tom Cruise Diagnosed with Postpartum Depression
Google's Caffeine Enhanced Search Engine much faster than Regular Google
How Many US Troops Are In Iraq? More Than You Think
Republicans regain footing, nothing bad happened this afternoon
President Bush starts White House on fire while burning the Constitution
Chupacabra DNA Testing Results Partially Human!
Larry Craig Makes Constitutional Argument : Airport bathroom sex is protected Right
US Military Gunships Pound Targets in Washington D.C!
Trump Calls in New Plumber to Fix White House Leaks!
Bush Orders Arrest of Bob Woodward, Author of State of Denial
Karl Rove Awarded Presidential Medal of Freedom For Defending Identity of Valerie Plame


Looking for outdoor dining in Saratoga Springs during the spring, summer and fall? Take in the scenery while enjoying your meal. Find popular patio dining spots at your favorite Saratoga restaurants below!
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Discussion in 'US West Standard - Ladder' started by Jerais, Jul 26, 2010.
Looking for a Jah rune to complete an Enigma here. I've got a Sur and some Ists to offer, let me know what you guys are wanting for one!
Also, looking for a 15% Ed MP to put this puppy in.
Quick Done Deal. Got an offer from Buka. TY man.


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Q: I need to prove that A is Lebesgue-measurable I'm struggling with this measure theory problem. It says:

Let $B$ be a Lebesgue-measurable set, with $m(B)<\infty$ and
$A\subset B$. Prove that $A$ is Lebesgue-measurable if and only if
$m(B)=m$* $(A)+m$* $(B\backslash A)$. ($m$ is the measure application
and $m$*$ $ the exterior measure application in $\Bbb R$).

The implication $A$ is Lebesgue-measurable $\longrightarrow$ $m(B)=m$* $(A)+m$* $(B\backslash A)$ is easy, because if $A$ is Lebesgue-measurable, then $m$* $(F)=m$* $(F\cap A)+m$* $(F\backslash A), \forall F\subseteq \Bbb R$.
I have problems with the reverse implication. The problem gives a hint: "you can use that, if $A\subseteq \Bbb R, m$* $(A)<\infty$, then $\exists B$ Lebesgue-measurable with $A\subseteq B$ that verifies $m(B)=m$* $(A)$".

A: As the hint says, there exists $E$ measurable with $A\subset E$ and $m^*(A)=m(E)$. From this we get that we can replace $B$ by $B\cap E$ in
$$\tag1
m(B)=m^*(A)+m^*(B\cap A^c).
$$
Indeed,
$$\tag2
m(E)=m^*(A)\leq m(B\cap E)\leq m(E),
$$
so $m(E)=m(B\cap E)$. Then
\begin{align}
m^*(A)+m^*(B\cap E\cap A^c)
&=m^*(A)+m^*(B\cap A^c\cap E)+m^*(B\cap A^c\cap E^c)\\[0.25cm]&\ \ \ \ \ \ \ \ \ \ \ \ \ \ -m^*(B\cap A^c\cap E^c)\\[0.3cm]
&=m^*(A)+m^*(B\cap A^c)-m^*(B\cap A^c\cap E^c)\\[0.3cm]
&=m^*(B)-m^*(B\cap A^c\cap E^c)\\[0.3cm]
&=m^*(B)-m^*(B\cap  E^c)\\[0.3cm]
&=m(B\cap (B\cap E^c)^c)\\[0.3cm]
&=m(B\cap E)=m^*(A).
\end{align}
So we have $m^*(B\cap E\cap A^c)=0$.
Now,  for any $F$, \begin{align}
m^*(F\cap A)+m^*(F\cap A^c)
&\leq m^*(F\cap  B\cap E)+m^*(F\cap ((B\cap E)^c\cup (B\cap E)\setminus A) )\\[0.3cm]
&\leq m^*(F\cap  B\cap E)+m^*(F\cap (B\cap E)^c)+m^*(F\cap B\cap E\cap A^c)\\[0.3cm]
&\leq m^*(F\cap  B\cap E)+m^*(F\cap (B\cap E)^c)+m^*( B\cap E\cap A^c)\\[0.3cm]
&=m^*(F\cap  B\cap E)+m^*(F\cap (B\cap E)^c)\\[0.3cm]
&=m^*(F).
\end{align}

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text:
Home » Health Problems » New urine dipstick test detects cause of disease that blinds millions
New urine dipstick test detects cause of disease that blinds millions
Scientists at Scripps Research have developed a urine diagnostic to detect the parasitic worms that cause river blindness, also called onchocerciasis, a tropical disease that afflicts 18 to 120 million people worldwide.
Described in the journal ACS Infectious Diseases, the new, non-invasive test may provide an inexpensive method of determining in real time whether a person has an infection, which would give public health officials and doctors critical information for tracking outbreaks and treating current infections.
"River blindness affects individuals both in Africa and Latin America, and because many of these endemic regions are difficult to access, what is needed in the field is an inexpensive point-of-care means to monitor the disease," says Kim Janda, Ph.D., the Ely R. Callaway Jr. Professor of Chemistry and member of the Skaggs Institute for Chemical Biology at Scripps Research.
River blindness is a filarial disease, like elephantiasis, and occurs when the parasitic worm Onchocerca volvulus takes up residence in the skin. Adult worms pump out babies (microfilaria) at an alarming rate, which are ultimately re-spread by blackfly bites. The microfilariae can migrate to the eye and die, releasing toxins and causing inflammation. People with the disease will slowly go blind without medical intervention.
Janda says onchocerciasis monitoring and evaluation are especially necessary steps for people leading elimination efforts. To know if these efforts are working, doctors need to be able to show when disease transmission has been interrupted. The current gold standard for detecting the parasitic worms is a "skin snip" biopsy. However, snips are generally insensitive indicators of infection, and the sensitivity of the skin snip decreases as the density of microfilaria in the skin decreases. Other tests cannot distinguish between past and current infections.
Currently, onchocerciasis elimination programs rely primarily on mass drug administration of the therapy Ivermectin to suppress and eventually eliminate transmission of Onchocerca volvulus. Yet, without a means to evaluate if an infection is ongoing, it's hard to assess if prevention efforts are working—and if it's safe for people to stop taking medication.
The new lateral flow assay took over 10 years to develop, but it is now ready for manufacturing and testing in the field. The key to the assay's success was in the making of designer antibodies to detect a unique biomarker that only shows up when a human host has metabolized a worm neurotransmitter called tyramine. Humans then secrete this biomarker in urine.
A negative on the "dipstick" test shows a colored line in the test. Got the parasite? The test would show no lines.
Unlike the skin snip biopsy, Janda says this non-invasive test is the first to use a metabolite produced by adult worms. Moreover, the dipstick's inexpensive design, coupled with smartphone apps, would offer automatic image processing, which ultimately could translate to address critical gaps in the surveillance and treatment of river blindness.
Tagged blinds, cause, detects, dipstick, disease, millions, new, of, test, that, urine
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Allana Ferguson Wants The NRL To Create A Women's Rugby League Comp
Mung beans: Health benefits, nutrition, and recipe tips
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Eating walnuts may help fight breast cancer: Study


text:
package tweetharvest

import (
	"errors"
	"net/http"
	"strings"
	"sync"
	"time"

	"golang.org/x/net/context"
	"golang.org/x/net/html"

	"github.com/ChimeraCoder/anaconda"
	"google.golang.org/appengine"
	"google.golang.org/appengine/datastore"
	"google.golang.org/appengine/log"
	"google.golang.org/appengine/urlfetch"
)

//Reducer is an instance of an HTTP server
type Reducer struct {
	c context.Context
}

//Constans are used to standardize strings used for data access from the Datastore.
const tweetScoreKind string = "TweetScore"
const scoreKey string = "Scores"
const scoreKeyID string = "default_scorestore"

//ServeHTTP is an Handler for Process requests.  It serves as the reduce function of
// the system, creating a score, for each of the addresses found in tweets.
func (reduce Reducer) ServeHTTP(writer http.ResponseWriter, request *http.Request) {
	reduce.c = appengine.NewContext(request)
	log.Infof(reduce.c, "Starting Reduce Processing.")

	//Wait group keeps the process open until all go routines are complete inc to 1 for
	// the calculatenewScores routines
	var wg sync.WaitGroup
	wg.Add(1)

	//tweets is a channel for holding TweetIDs
	tweets := make(chan *anaconda.Tweet)
	go reduce.queryForTweets(tweets, &wg)

	//Hold until updateDatastore is compelete
	wg.Wait()
	writer.WriteHeader(http.StatusOK)
}

func (reduce Reducer) queryForTweets(out chan<- *anaconda.Tweet, wg *sync.WaitGroup) {
	defer wg.Done()
	//lastProcess := reduce.getLastProcessedTweet()

}
func (reduce Reducer) calculateNewScores(out chan<- *TweetScore, wg *sync.WaitGroup) {
	log.Infof(reduce.c, "Calculating New Scores")

	//Tell the wait group that the method is done when it completes.
	defer wg.Done()

	//Score map holds a mapping of addresses to their scores.
	score := make(map[string]*TweetScore)

	//Get all new tweets since the last time the reduce process was run than range over
	// those tweets.
	tweets := GetAllNewTweets(reduce.getLastProcessedTweet(), reduce.c)
	for _, data := range tweets {

		//If the map does not contain a key for this address, create a new value and add
		// it to the map.
		if score[data.Address] == nil {
			score[data.Address] = &TweetScore{
				Address: data.Address,
				Query:   data.Query,
			}
		}

		//Update the score, LastAvtive, and TweetIDs data with the current tweet
		score[data.Address].Score = score[data.Address].Score + data.getScore()
		score[data.Address].LastActive, _ = data.CreatedAtTime()
		score[data.Address].TweetIDs = append(score[data.Address].TweetIDs, data.Id)
	}

	//Range over the map and output the values into the channel for further processing
	for _, data := range score {
		log.Infof(reduce.c, "Calculate: Address: %v\tScore: %v", data.Address, data.Score)
		out <- data
	}
	//Close the channel to indicate that there is no more data
	close(out)
}

//updateDataStoreScore is a method that updates or creates records in the datastore with
// with the contents of the a TweetScore struct
func (reduce Reducer) updateDataStoreScore(score TweetScore, wg *sync.WaitGroup) {
	//At the end of the method close the score
	defer wg.Done()

	//Get the existing score for this address from the datastore.
	//log.Infof(reduce.c, "Pulling existing score for address: %v", score.Address)
	q := datastore.NewQuery(tweetScoreKind).
		Filter("Address =", score.Address).
		Ancestor(getTweetScoreKey(reduce.c))

	iterator := q.Run(reduce.c)

	oldScore := &TweetScore{}
	key, err := iterator.Next(oldScore)
	if err != nil && err == datastore.Done {
		//log.Infof(reduce.c, "No old score exists for this address.")
		//No old score exists, so we just add the new one

		oldScore.Title, err = reduce.
			getTitle(score.Address)
		if err != nil {
			log.Infof(reduce.c, "Failed to GET address: %v \n\t%v", score.Address, err.Error())
		}
		oldScore.Address = score.Address
		oldScore.LastActive = score.LastActive
		oldScore.Score = score.Score
		oldScore.TweetIDs = score.TweetIDs
		oldScore.Query = score.Query

		//Create a new key
		key = datastore.NewIncompleteKey(reduce.c, tweetScoreKind, getTweetScoreKey(reduce.c))
	} else {
		//We have an old score, increment the score, add new TweetIDs, and update LastActive
		//log.Infof(reduce.c, "Old score for this address is: %v", oldScore.Score)
		oldScore = &TweetScore{Score: score.Score,
			LastActive: score.LastActive,
			TweetIDs:   score.TweetIDs,
		}
	}

	//log.Infof(reduce.c, "Writing to database: %v\t%v", oldScore.Address, oldScore.Score)
	datastore.Put(reduce.c, key, oldScore)
}

//getTitle retrives the content of an address then sends the body to the scraper
// to in order to find the title which is returnted to the user.
func (reduce Reducer) getTitle(address string) (string, error) {
	client := urlfetch.Client(reduce.c)
	resp, err := client.Get(address)

	if err != nil {
		return "", err
	}
	return reduce.scrapeTitle(resp)
}

//scrapeTitle parses through an HTML document to find the <title> tag then get
// the content of that tag and return it to the user.
func (reduce Reducer) scrapeTitle(resp *http.Response) (string, error) {
	defer resp.Body.Close()

	if strings.ToLower(resp.Header.Get("Content-Type")) != "text/html; charset=utf-8" {
		message := "Wrong content type.  Recieved: " + resp.Header.Get("Content-Type") + " from " + resp.Request.URL.String()
		log.Infof(reduce.c, message)
		return "", errors.New(message)
	}

	tokenizer := html.NewTokenizer(resp.Body)
	var titleIsNext bool
	for {
		token := tokenizer.Next()
		switch {
		case token == html.ErrorToken:
			log.Infof(reduce.c, "Hit the end of the doc without finding title.")
			return "", errors.New("Unable to find title tag in " + resp.Request.URL.String())
		case token == html.StartTagToken:
			tag := tokenizer.Token()
			isTitle := tag.Data == "title"

			if isTitle {
				titleIsNext = true
			}
		case titleIsNext && token == html.TextToken:
			title := tokenizer.Token().Data
			log.Infof(reduce.c, "Pulled title: %v", title)
			return title, nil
		}
	}
}

//getLastProcessedTweet gets the last date that any score was active,
// which should be the date of the last processed tweet
func (reduce Reducer) getLastProcessedTweet() time.Time {
	//Get a single value from the datastore with the newest date
	q := datastore.NewQuery(tweetScoreKind).
		Project("LastActive").
		Order("-LastActive").Limit(1)

	i := q.Run(reduce.c)

	score := &TweetScore{}
	_, err := i.Next(score)
	if err != nil {
		//If there is no date (I.E. this is the first time we have run this process) return
		// a date of one day prior, to keep processing size under control.
		log.Infof(reduce.c, "Could not find last processed tweet date, returning one day ago")
		return time.Now().AddDate(0, 0, -1)
	}
	//log.Infof(reduce.c, "Last tweet scored is dated: %v", score.LastActive)
	return score.LastActive
}

//getTweetScoreKey returns the same key every time so that all TweetScore entites have
// a common Ancestor
func getTweetScoreKey(c context.Context) *datastore.Key {
	// The string "default_guestbook" here could be varied to have multiple guestbooks.
	return datastore.NewKey(c, scoreKey, scoreKeyID, 0, nil)
}

redpajama_set_name: RedPajamaGithub


Arrangements can be made for weddings. Please call the church and speak with the Priest.
In keeping with the tradition of the Anglican church, both adults and infant children are baptized. Baptisms take place at Sunday services.
Please discuss arrangements with the Priest.
Note: Every Wednesday during the season of Lent there is a 12:05 pm service and a 7:30 pm service.


Very impressed by the quality of the B1 Hosel Boring Fixture. More a piece of art. Almost a shame to use it. Thanks again!
I've been in the golf business my entire working life and do all of my own club repair work. I wouldn't use anything but a Mitchell Angle Machine on my clubs. The quality is second to none and the machines are truly the industry standard!
I use my Mitchell angle machine to check the specs on my Titliest T-MB irons. Mitchell and especially its founder are the BEST!
Due to the warm weather, we have been busy in the shop. Mitchell Golf is the best and only equipment I will ever use. Thanks!


text:
Q: can i set a Windows.print from chrome to a IE modal? I am trying to execute a windows.print () using js from a chrome browser to open a modal in IE and execute that function. It's possible?
This is executed from the web using a button that calls this function.
Here I draw my idea

A: Short answer: This is generally not possible
Slightly less short answer: If you control the machine(s) this should work on, you can do something similar (no modal, but an IE window/tab) with a custom protocol handler. See here: Open Internet Explorer from Chrome using a protocol handler (ie:url)


Drupal GDPR Module - Exploration of a suite of Drupal specific GDPR tools to help achieve compatibility.
A live demo of the GDPR module and how it can be used by site builders, developers and Data Protection Officers to achieve GDPR compatibility. We will be focusing on the GDPR consent tools and the GDPR field settings that enable a site owner to easily response to subject access requests and requests for erasure.
We (FreelyGive) have been working on a suite of GDPR tools in collaboration with BRAINSUM as a result of our experience working with native Drupal CRM. In this talk I will demonstrate the tools we have built, some of the rationale behind why we built them like that and how to use them.
A dashboard for end users to request "Right to access" and "Right to be forgotten"
A specific take on handling the backup and restore process where some individuals have asked to be forgotten.


We're proud to serve the greater Lafayette area with a wide selection of Lawn & Garden Supplies, Pet Supplies, Birdhouses and Feeders, Gloves, Boots, Pesticides and Cajun Injectors!
Paul Chastant opened a small Purina Feed Store in 1933. Chastant Bros. is now a 3rd generation, family-owned and operated store. We have grown into a complete farm store serving the needs of the local agricultural community, and offering a full line of products and services for those in the farming industry, as well as those seeking home improvement.
We are proud to serve the greater Lafayette area including New Iberia, Obelousas, Franklin, Beaux Bridge, Abbeville, Melville, and Crowley. Chastant Bros. carries a wide selection of lawn & garden supplies, birdhouses & feeders, pet supplies, gloves and boots, pesticides and Cajun Injectors. Chastant Brothers is also one of the largest Pecan buyers in the area. Not only do we sell Pecans, bring them in and we'll crack them for you too!
Chastant Bros delivers bulk fertilizer to any destination within a 50 mile radius. Stop by or give us a call for any additional information on our products and services.


text:
Sports Notebook
Wrangler News
Home News Briefs 3 Cronkite grads among candidates for award recognizing best U.S. public-relations campaigns
3 Cronkite grads among candidates for award recognizing best U.S. public-relations campaigns
Wrangler News Staff
Their careers may have only recently started, but three graduates of the Public Relations Lab at ASU's Walter Cronkite School of Journalism and Mass Communications already have achieved a major milestone.
The grads, Cassidy Olson, Rachel Steingard and Samantha Womer, comprise the creative team being credited with developing a community-wide, educational approach to curbing underage drinking. The campaign has been nominated for honors as part of a PR News Platinum Awards Competition honoring top public-relations initiatives by corporations, agencies and nonprofits worldwide.
The team was led by Dr. Fran Matera, the PR Lab's faculty adviser.
Tempe Coalition, a partnership between Tempe Community Council and the city of Tempe, launched the campaign, titled 21 or Too Young, with the help of the Cronkite school in December 2011.
The campaign included public service announcements in theaters, billboards, community events, wristbands and pledges.
Awards will be announced Sept. 14 in New York City.
Sign up for our e-edition here!
© Wrangler News
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Welcome to The Wrangler Community!
Think Local. Read Local.


Lauren Goodger found herself the subject of a comedy sketch earlier this week at a London clothes store.
The Only Way Is Essex star was hoping to pick up some dresses in the exclusive store when she overheard 'Kate Middleton' talking about her impending nuptials on the phone.
And things went from bad to worse when Kate called her over asking advice on what she should do because she had feelings for another man - Prince Harry!
Lauren was trying on a dress in the changing room when she heard Kate talking about the wedding to a friend, admitting she was 'crapping it' about her big day.
'Kate' is heard saying: 'I want my life back. Am I really doing the right thing? I just don't know if being a princess will make up for it.
Kate then asked if anybody is there, to which Lauren, who is engaged to fellow TOWIE star Mark Wright, heads over to the changing room curtain to give some agony aunt advice.
But then Kate lets Lauren in to her real dilemma - the fact that she is trying to decide between Prince William and Prince Harry, admitting: 'I'm torn between two men. It's not just another guy, it's Harry.
Struggling to hide her giggles at the unexpected conversation topic, Lauren then replied: 'Oh my god, I think I want to give you a hug and stuff. I wouldn't feel ashamed if that's the way you feel.
The sketch, set up by entertainment channel Comedy Central, was then revealed to be a set up as 'Prince William' burst through the changing room to pick up his princess.
Following the reveal, Lauren then sent a text message to fiancé Mark Wright telling him she had met the real Kate Middleton and they had been invited to the big day.


text:
A two-time Peabody Award-winner, Radiolab is an investigation told through sounds and stories, and centered around one big idea. In the Radiolab world, information sounds like music and science and culture collide. Hosted by Jad Abumrad and Robert Krulwich, the show is designed for listeners who demand skepticism, but appreciate wonder. WNYC Studios is a listener-supported producer of other leading podcasts including On the Media, Snap Judgment, Death, Sex & Money, Nancy and Here's the Thing with Alec Baldwin. © WNYC Studios
https://www.wnycstudios.org/podcasts/radiolab/projects/podcasts
Science & Medicine Natural Sciences
link to the podcast (with twitter card)
Embed code for the latest episode (iframe)
G: Problem Space
In the first episode of G, Radiolab's miniseries on intelligence, we went back to the 1970s to meet a group of Black parents who put the IQ test on trial. The lawsuit, Larry P v Riles, ended with a ban on IQ tests for all Black students in the state of California, a ban that's still in place today. This week, we meet the families in California dealing with that ban forty years later. Families the ban was designed to protect, but who now say it discriminates against their children. How much have IQ tests changed since the 70s? And can they be used for good? We talk to the people responsible for designing the most widely used modern IQ test, and along the way, we find out that at the very same moment the IQ test was being put on trial in California, on the other side of the country, it was being used to solve one of the biggest public health problems of the 20th century.This episode was reported and produced by Pat Walters, Rachael Cusick and Jad Abumrad, with production help from Bethel Habte.Music by Alex Overington. Fact-checking by Diane Kelly.Special thanks to Lee Romney, Moira Gunn and Tech Nation, and Lee Rosevere for his song All the Answers. Radiolab's "G" is supported in part by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
link to the episode (with twitter card)
Embed code (iframe)
Embed code (javascript)
fyydify! link
14 June 2019 42m


While a night in front of the idiot box watching Lost or Prison Break may provide sufficient intellectual stimulation for people like Mr. O'Shea or Miss Le Breton, I personally have a slightly higher cultural taste. With that in mind I headed off to the Grand Theatre this evening to see a stage show of the hit BBC Radio 4 show "I'm Sorry I Haven't A Clue" of which I am a big fan.
The show featured most of the long running members of the radio show with Humphrey Lyttelton taking on his role as the chairman, Colin Sell at the piano and Graeme Garden, Tim Brooke-Taylor and Barry Cryer making up the original contestants with Jeremy Hardy taking the place of the now late Willie Rushton.
The Grand was rennovated a year or two ago adding in air conditioning and better seats as well as restoring it's fabulous beauty. Once you add to that a very funny show and you have a winning night out. Most of the best rounds from the show appeared including one song to the tune of another, sound charades and of course, Mornington Crescent.
All in all, an enjoyable night out.
Is it really so hard to publish current information on a website?
Having just got off the phone from Argos who have lost my order (not the order contents but actually any record of the order ever being made) I headed off to Tesco's website to find out when they are open as today is a bank holiday. But they have actually taken the information off! Last time I was on there I could find out all about the holiday opening hours but it's not available anymore. They've done away with the "when is Tesco open this week" section and replaced it with standard static opening times text.
This was something I was thinking about earlier with regards to the union. Would it be so hard for them to have a page listing what is open when? They occasionally publish the term time and non-term time opening hours on each page for the shop or bar but it's never in any kind of easily accessible fashion. Nor is it usually that accurate.
Things like when the union closes for the day. This never appears on the website. They have a sign on the front door saying "closed." The website still claims The Old Bar is open. Still claims The Terrace is open till 12:30. Has no information on Extras out of term time opening hours. It has no information on when The ARC is open, when the cash office is open, hell, when the union building itself is open.
Is it really so much to ask for a bit of current information?
It's August 27th! In 5 days it will be September. Where did summer go?
I still have loads of unsolved items on my to do list. My room is still a tip (not that it will be a major issue once I move out as it will all move out with me and I can sort it then). My server still isn't working. The network in the house still isn't setup properly.
I don't know what the situation is really. Will I have more time during term time? I work 50-60 hour weeks at the moment. When term time starts again I'll go back up to anywhere from 60-80 hour weeks so will I really have more time to solve things?
Do you know how much money I got in my last pay cheque? £370! 12 out of the 14 days of that pay period I worked and all I came away with was £370. I think I must have been raped by tax because I was on over £400 pre-tax before my last shift.
All in all I'm realising how much of a bad shape my overdraft is in. Once my credit cards are paid off it's going to take 4 or 5 weeks to clear it on full time pay and I have about 3 weeks left. While I still have my student loan to come in, I have rent going out and I got hit by a massive phone bill from when I was sorting out our BT line and internet for the house.
Still hopefully I should be able to generate some kind of decent pay cheque next time. At the moment I need to pick up some more shifts to fill my days off but I made a good start today – I clocked into work at 05:45 in the morning and I've just got home now. Open closes for the win.
Doing a random search I suddenly stumbled upon the fact that Worfolk.org was available for registration. Confirming that it was indeed available (I didn't want to get my hopes up as someone has been sat on it for a while) I snapped it up with great pleasure. It's currently just redirecting to Worfolk.biz but at least now it's under my control.
Unfortunately there are still squatters sat on the .com and .net.
The beta version of ChrisWorfolk.com v3 is now available for your viewing pleasure. It's a lot clearer than the current site and easier to read and it uses a nicer URLs. There are a few issues with it at the moment, mainly that it has only been tested in Firefox so far and suffers from some issues when displaying in Internet Explorer.
Currently my VPS is going down every 10-15 minutes! Neither me nor my host can work out what is going on.
The end result is, after continued problems with my VPS I've ordered a new one with ServInt. I am going to be migrating a lot of my important sites over to that and then those remain will ever stay on my current VPS or will me migrated over to a new VPS with PowerVPS and the old one cancelled depending on whether I can stabilise it or not.
I think I've finally found the reason why all my dialog boxes and default fonts on my laptop have started to look strange – I have 8 fonts left on my computer.
I thought it a little wierd when I went into PowerPoint today and I only had a very small choice of fonts. Then when opening up the source files for some posters I had done I was informed the fonts were missing by a different application. I checked the system folder which contains fonts and it looked fine. But when I tried to copy them to my desktop I got an error and all but 8 of them disappeared. Weird.
To be honest, I never thought I would really use the backups I made of my font files. OCD for the win.
The Scottish National Party have recently outlined plans or a referendum on independence. You can read the news report on BBC News.
Alex Salmond talked about the Scottish people needing to work out what kind of a country they want to be. But of course – they aren't a country! You're not. You're a region of the UK. Just like England.
To be honest, I don't see what the case is for breaking up the UK, which is what we are talking about here. Maybe there is a good case, if so please outline it to me. But at the moment it just seems we have nothing to gain and a lot to lose.
It's not like the UK is the biggest country in the world. Making it a little bit smaller isn't going to help that. How about things like the United Nations? Presumably we would have seperate representation then and presumably the U.K. would remain on the U.N. Security Council whereas Scotland would not. How would things like advertising work if Scotland changed their VAT rate? How will border control work? Policing? These are mostly small problems. But there would be millions of them to solve.
I'd be interested to see what everyone else thinks of such plans.
I finally got round to replacing my MP3 player on Saturday getting an 80GB iPod video. As I have previously mentioned, I installed Rockbox on the device so I didn't have to use iTunes and spent most of Saturday loading as much of my music collection onto it as I could fit.
So far it's pretty good. It's easy enough to use once I get used to it although I end up struggling to decide what to listen to :D. The interface is a bit small given the size of the screen and I haven't worked out how to make it bigger yet (if indeed it is possible). Battery life is awful as expected, I have to charge it up every few days (or every day if in heavy yse) but I wasn't expecting anything better from a rechargeable battery.


There have been rumors of Motorola making a new Android tablet device that will have a 4:3 aspect ratio, like the iPad.
If a company's domain registrations are any indication of what's in store, then Motorola's next tablet may be called: Kore.
On Wednesday August 3, Motorola registered five new domain names centered around the word "Kore". These appear to be the company's first domain registrations in months.
The names include MotorolaKore.com, KoreMotorola.com, Moto-kore.com, MotoKore.com, and Motorola-Kore.com.
Registrar Name….: CORPORATE DOMAINS, INC.


text:
#ifndef QOEMBED_RICH_H
#define QOEMBED_RICH_H

#include "qoembed_global.h"
#include "response.h"

namespace qoembed {

class RichPrivate;

class QOEMBEDSHARED_EXPORT Rich : public Response
{
public:
    Rich();
    Rich(const Rich &other);
    ~Rich();

    Rich &operator=(const Rich &rhs);

    virtual QString render() const;

    void setHtml(const QString &html);
    QString html() const;

    void setWidth(unsigned width);
    unsigned width() const;

    void setHeight(unsigned height);
    unsigned height() const;

private:
    RichPrivate *d;
};

} // namespace qoembed

#endif // QOEMBED_RICH_H


text:
\section{Introduction}

Normal form theory is one of the most effective tools for the local study of nonlinear dynamical systems. The basic idea is to use permissible transformations and obtain a simplified vector field. Transformations are permissible that preserve certain dynamical features of the original system. The space of all permissible transformations form a group and acts on vector fields like an action of a group on a vector space. Consider a set of vector fields generated by the group acting on a given vector field. Then, the infinite level normal form of the vector field is to find a unique representative from this set. Thereby, the computation of infinite level normal forms is an important tool for classification of vector fields. The uniqueness of a normal form computation is determined by the (infinite) level of normal form through an specifically chosen normal form style and costyle. The level of a normal form assesses the remaining spectral data at our disposal in the permissible transformation space for further simplification of the system while a normal form style and costyle makes a unique choice for the normal form vector field in each level of normal form computation, see \eg \cite{baiderchurch,Gazor,GazorYuSpec,MurdBook,Sanders03}. Therefore, the infinite level normal form is sometimes called the simplest normal form or unique normal form when a normal form style have already been fixed. When a system has some symmetries, it is important that its normal form would preserve the symmetries. Although there are research results on the simplest normal forms of symmetric systems but they are considerably less than the existing results on normal forms without symmetry. There are several reasons for this. The first difficulty is to recognize the symmetries and then, to find the group of transformations preserving the symmetries. Therefore, one is also concerned with the space of the symmetric vector fields invariant under the group action. This needs a good understanding on the algebraic interactions of the symmetric and nonsymmetric vector fields with the transformation groups. Once all these are successfully accomplished, in most cases the normal form computation is more difficult in systems with symmetry than in systems without symmetry.

\pagestyle{myheadings}
\markright{{\footnotesize {\it M. Gazor, F. Mokhtari and J. A. Sanders
\hspace{2.3in} {\it Hopf-Zero singularity}}}}

Normal form decomposition of a nonsymmetric vector field into two symmetric vector fields can have many important potential applications.
For example Eulerian and Hamiltonian vector fields are two important families of vector fields. Therefore, the study of their dynamics is important. Normal form decomposition of arbitrary vector fields into Eulerian (nonconservative or dissipative) and Hamiltonian (conservative) vector fields are also important in both theory and applications. Wiggins \cite[Chapter 33]{Wiggins} remarks that transforming a system into an integrable Hamiltonian system plus a nonconservative perturbation facilitates ``a wealth of techniques for the global analysis of nonlinear dynamical systems such as Melnikov theory, perturbation theory for normally hyperbolic invariant manifolds, and Kolmogorov, Arnold, and Moser (KAM) theory''. Furthermore, Palaci\(\acute{\hbox{a}}\)n \cite{PalacChaos05} indicated that such kind of decomposition can be used in developing an ODE solver. For example using the obtained scalar function as the integral of a piece of the vector field in an ODE solver, can enhance its efficiency. These signify the importance of developing methods for such kind of decomposition.
Recently, some researchers have paid attention to this theory and have made important contributions to the subject, see \eg [3, 4, 7, 8, 18, 23--27, 29, 32].
Furthermore, the dynamics of a system may sometimes be analyzed by dynamics of its components. For example, an advection-diffusion model consists of advection terms and diffusion terms and its dynamics is well understood as a combination/competition of the dynamics associated with the advection and diffusion terms, see \eg \cite[Section 5.5]{Logan}. Therefore, the study of each components of a decomposed vector field may help to better understand the dynamics of the full system as a combined dynamics or as a competing behavior between its components. Thus, it is important to individually deal with the cases that the vector field is a quasi-Eulerian, or is a conservative vector field, see \cite{GazorMoazeni,GazorMokhtari1st}. In this paper a vector field is called {\em conservative} when it has a first integral and is called {\em nonconservative} when it does not have any first integral.

This paper deals with the nonconservative family of our upcoming results on such decomposition for Hopf-Zero singular vector fields.  Systems with Hopf-Zero singularity are important in applications.
There are several important research results on the simplest normal forms of Hopf-Zero singularity, see \cite{AlgabaHopfZ,ChenHopfZ03,ChenHopfZ,YuHopfZero}. However, there does not seem to exist any result on such kind of normal form decomposition for Hopf-Zero singularity. Although the Hamiltonian vector fields (symplectic structures) require an even dimensionality, the decomposition idea still can work. Indeed we instead work with conservative and nonconservative family of vector fields, see \cite{GazorMokhtari}. In this paper we are concerned with the study of nonconservative family. Indeed, we consider the family of Hopf-Zero singularities given by
\ba\label{Eq1}
v= z\ddy-y\ddz+ v_{[2]},
\ea where
\ba
v_{[2]}:=f(x, y^2+z^2)E,\quad E:=x\ddx+\frac{1}{2}y\ddy+\frac{1}{2}z\ddz,
\ea and \(f\) is a formal power series function and without constant terms. Any result in this direction also helps in a better understanding of the more complicated algebraic structures involved in the three dimensional nilpotent singularities. In this paper the coefficients are taken from a field \(\f\) of characteristic zero, see \cite{Sanders03} where the coefficients are taken from a local ring containing the rational numbers. Since \(E\) is a quasi-Eulerian vector field, \(v_{[2]}\) is called a formal quasi-Eulerian vector field, that is a nonconservative vector field. The reader should note that this family of vector fields are indeed the classical (first level) normal form of a very much larger family of vector fields.
This, however, is independent from \cite{GazorMokhtari} and basically refers to an essentially separate problem. Our normal form computation is to use a transformation group that preserves the Eulerian structure and it would only simplify the function \(f.\) However, our results in \cite{GazorMokhtari} work with the bigger group, that is, the set of all near-identity transformations and may create conservative terms into the normal form system. Indeed, the quasi-Eulerian vector field \(E\) is defined such that its generated family would form a Lie algebra.

This paper is organized as follows. Section \ref{sec2} introduces a family of nonconservative vector fields that is a Lie algebra and presents a general notations for normal form computations. The simplest normal forms and orbital normal forms of this family of vector fields with non-zero quadratic part are obtained in Sections \ref{secNF} and \ref{secONF}, respectively. In Section \ref{secPNF} we prove that under certain technical conditions multi-parameter nonconservative perturbations of the vector field \(v\) given by Equation (\ref{Eq1}) can be transformed into
\ba\label{FinalPNF0}
w^{(\infty)}= z\ddy-y\ddz+ g(x, y^2+z^2, \mu)E,
\ea where \(g(x,R,\mu)=x+\beta^0_1R+\sum^{r}_{i=0}R^{i}\mu_i+\beta^0_r R^{r}\) for a \(r\geq2.\)

\section{Nonconservative vector fields and notations}\label{sec2}

This section presents the necessary Lie algebra structure and notations that we need for normal form computations in the following sections.

\begin{defn} Define
\ba\label{Eul}
E^l_k&:=& x^{l+1}(y^2+z^2)^{k-l}\ddx+ \frac{1}{2} x^{l}
{(y^2+z^2)}^{k-l}y\ddy+\frac{1}{2} x^l{(y^2+z^2)}^{k-l}z\ddz,
(0\leq{l}\leq{k}).\quad
\ea Since \(E^l_k= x^{l}(y^2+z^2)^{k-l}E\) and \(E\) is a quasi-Eulerian vector field, we call \(E^l_k\) a quasi-Eulerian vector fields. Then define
\be\label{Lie}
\E:= \Span\Big\{\sum\beta^l_{k} E^l_k \;|\; \beta^l_{k}\in \f, {l+k\geq 1}, k\geq l\Big\}. \ee Let \(\Theta^0_0:= z\ddy-y\ddz.\) Therefore, the vector field given by Equation (\ref{Eq1}) can be represented by an element of \(\Theta^0_0+\E.\)
\end{defn} The following theorem follows from a straightforward computation.
\begin{thm}\label{iso} The vector space \(\{a\Theta^0_0+v|a\in \f, v\in\E\}\) is a Lie algebra with the following structure constants:
\bas\label{aa}
{[E^l_k, E^{m}_{n}]}&=& (n-k)E^{l+m}_{k+n},
\\
{[E_k^l, \Theta^0_0]}&=&0,
\eas for any \(l,k,m,n\in \NZ:=\N\cup\{0\}.\)
\end{thm}
\begin{proof} The space \(\E\) is a Lie algebra by the Lie bracket \([v,w]:= fE(g)E-gE(f)E\) for any \(v= f(x, y^2+z^2)E,w= g(x, y^2+z^2)E\in \E\) and \(E\) is considered as a differential operator acting on functions, see \cite[Page 2]{DumortierBook} and \cite{GazorMokhtari}. The structure constants follow from the fact that \(x^{l}(y^2+z^2)^{k-l}\) is an \(E\)-eigenfunction with eigenvalue \(k.\)
\end{proof} Note that one may consider the ring generated by polynomials \(x^{l}(y^2+z^2)^{k-l}.\) Then, it forms a Lie algebra; the Lie bracket of two eigenfunctions is given by their product multiplied with the substraction of their eigenvalues. Thus, normal form computations can be implemented on a computer algebra system using scalar valued functions rather than using vector fields. This enhances the efficiency of the computer program. The space \(\{a\Theta^0_0+v|a\in \f, v\in\E\}\) is indeed a Lie subalgebra of all the classical normal forms of Hopf-Zero singularity, see \eg \cite{AlgabaHopfZ,ChenHopfZ03,ChenHopfZ,MurdBook}.
\begin{thm}  There does not exist any first integral for any nonzero \(v\in \E,\) \ie any \(v\in \E\) is a non-conservative vector field.
\end{thm}

\bpr
Suppose that \(f=\sum_{m,n,k}\alpha_{m,n,k} x^my^nz^k\) is a first integral for \(gE\in \E\) where the function \(g\) is nonzero.
Then, \( f_x\dot{x}+ f_y\dot{y}+ f_z\dot{z}=
0
\) implies \(\alpha_{m,n,k}=0\) for all \(m,n,k\in \NZ,\) \ie \(f=0.\)
This completes the proof.
\epr

Now we briefly present a general framework on how to obtain the simplest (orbital and parametric) normal form of a vector field, for more detailed information, terminology and background material see \cite{GazorYuSpec}. Let \(\E=\sum^\infty_{i=0} \E_i\) be a graded Lie algebra, \ie \([v_i,v_j]\in \E_{i+j}\) for any \(v_i\in \E_i\) and \(v_j\in\E_j\). The sub-indices \(i\) for spaces (not element indices, of course) in this paper refer to the homogenous spaces of grade \(i\) according to the associated grading. Recall that a style of a normal form is a rule to choose a unique complement space to a subspace of \(\E.\) Assume a normal form style is given and \(A= \sum^\infty_{i=1}A_i\) is the graded vector space of all generators associated with the permissible transformations (in \cite{GazorYuSpec} this is denoted by \(A^0\)). The space \(A\) acts linearly on \(\E.\) This action is denoted by \(*\) and it preserves the grading structures, \ie \(A_i*\E_j\subseteq \E_{i+j}\) for any \(i, j.\)
\begin{rem}
The action \(*\) is the initially linear map of the associated near-identity permissible transformations generated by elements of \(A\), see \cite{GazorYuSpec} for more detailed discussion.
\end{rem}
The space \(A\) and its associated action \(*\) are different for the normal form, orbital normal form and parametric normal form of vector fields. Therefore, we will explicitly define these accordingly in the following three sections. Let \(v=\sum^\infty_{i=0}v_i\) and inductively define
\be
d^{n,1}: A_n\rightarrow\E_n, \quad \hbox{ by } d^{n,1}(Y_n):= Y_n*v_0 \hbox{ for } Y_n\in A_n,
\ee and
\be
d^{n,k}: A_n\times \ker(d^{n-1,k-1})\rightarrow\E_n \quad (\hbox{for any } k\leq n),
\ee given by \(d^{n,k}(Y_{n}, Y_{n-1}, \ldots, Y_{n-k+1}):= \sum^{k-1}_{i=0} Y_{n-i}*v_i,\) where
\bes (Y_{n-1}, Y_{n-2}, \ldots, Y_{n-k+1})\in \ker(d^{n-1,k-1}).\ees
For any \(k>n,\) let \(d^{n,k}:=d^{n,n}.\)
Note that \((Y_{n-1}, Y_{n-2}, \ldots, Y_{n-k+1})\in \ker(d^{n-1,k-1})\) if and only if
\be\sum^{j}_{i=0} Y_{n+i-j-1}*v_{j-i}=0\ee for any \(j=0, 1, \ldots,k, \) see also \cite{wlhj}. Let
\(\RC^{n,k}:= \IM (d^{n,k}).\) Then, there exist the complement subspaces \(\C^{n,k}\) such that
\be
\RC^{n,k}\oplus \C^{n,k}=\E_n
\ee follows the normal form style. We call \(d^{n,k}\) the \(k\)-th level state map.
If \(v_i\in \C^{n,k}\) for any natural number \(n,\) we say that \(v=\sum v_i\) is in the \(k\)-th level extended partial normal form (see \cite{Mord04} for the original definition and ideas) and when \(v_i\in \C^{i,i}\) for any natural number \(i,\) \(v\) is said to be in the infinite level (orbital or parametric) normal form. Notice that the domain of the map \(d^{n,k}\) has \(k\)-components. However, the first component does not play any role in our normal form computation, since \(\Theta^0_0\) is the zero grade of the system and we have \([\E, \Theta^0_0]=0\) in Section \ref{secNF}, and in Sections \ref{secONF} and \ref{secPNF} the linear part \(\Theta^0_0\) is first removed before normal form computation. Thus, we omit the first component and we only have \((k-1)\)-components in the domain of the map \(d^{n,k},\) \ie \(d^{n,k}(Y_{n-1}, \ldots, Y_{n-k+1})= \sum^{k-1}_{i=1} Y_{n-i}*v_i.\)

\begin{thm}\label{LNF}
There always exist a sequence of permissible transformations transforming a vector field into its \(k\)-th (or infinite) level extended partial normal form.
\end{thm}
\bpr
The proof follows from \cite[Theorem 4.4]{GazorYuSpec}.
\epr

In this paper, we also discuss the symmetry group of the infinite level normal forms. The symmetry group of a vector field is a subgroup of the permissible transformations such that the infinite level normal form \(v^{(\infty)}\) is invariant under the symmetry group acting on \(v^{(\infty)}\). This symmetry group is generated by the infinite level co-normal form space. The infinite level co-normal form space is a subspace, say \(B,\) of the space of permissible transformation generators \(A\) in which \(B*v^{(\infty)}=0\) and can be computed through the normal form computation.

\section{The simplest normal forms }\label{secNF}

In this section we obtain the simplest normal form of vector fields given by Equation (\ref{Eq1}) with nonzero quadratic terms, \ie
\be\label{E0}
v^{(1)}:= \Theta^0_0+ \beta^1_1 E^1_1 + \cdots\in \Theta^0_0+\E,
\ee where \(\beta^1_1\neq0.\) Define the grading function \(\delta \) for the space \(\E\) by
\bas
\delta(E^l_k)&:=& 2k-l \quad \hbox{ and } \quad \delta(\Theta^0_0)=0.
\eas Then, \(\delta(E^l_k)\geq k.\) For simplicity of notation \(\delta\) or \(\delta_\alpha\) is used for all gradings in this paper.

\begin{lem}\label{seclev}
There exists a formal near identity transformation that sends the vector field \(v\) given by Equation (\ref{E0}) into the second level extended partial normal form
\ba\label{secNFE}
v^{(2)}=\Theta^0_0+\beta^1_1 E^1_1+\beta^0_{1}E^0_1+\beta^2_2E^2_2+\beta^1_2E^1_2+\sum^\infty_{k=2}\beta^0_kE^0_k,
\ea where \(\beta^1_1\) is not changed.

\end{lem}
\bpr Define \(A:= \sum^\infty_{i=1}\E_i.\) Since \([E^l_k, E^{1}_{1}]= -(k-1)E^{l+1}_{k+1},\) a complement space to the image of \(d^{n,2}\) is \(\Span \{E^0_{2k}\}\) for any \(n=2k>3,\) \(\Span \{E^1_{2}\}\) for \(n=3,\) and \(\Span \{E^2_{2}, E^0_{1}\}\) for \(n=2.\)
\epr

The reader should note that in this paper the notation \(\beta^l_k\) for coefficients are not changed as they are updated in the normal form computation.

\begin{thm}\label{SNF} There exists a natural number \(r\) and a
formal near identity transformation sending \(v^{(2)}\) given by equation (\ref{secNFE}) into one of the following \((2r+2)\)-th level extended partial normal forms:
\be\label{2n2f}
v^{(2r+2)}= \Theta^0_0+\beta^1_1 E^1_1+\beta^0_{1}E^0_1+\beta^2_2E^2_2+\beta^1_2E^1_2+ \beta^0_rE^0_r +\sum^\infty_{k=r+2}\beta^0_kE^0_k \quad(\hbox{for } r\geq 2),
\ee
or
\be\label{2n2s}
v^{(2r+2)}= \Theta^0_0+\beta^1_1 E^1_1+\beta^0_{1}E^0_1+\beta^2_2E^2_2+\beta^1_2E^1_2+ \beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)E^0_2+ \beta^0_rE^0_r +\sum^\infty_{k=r+2}\beta^0_kE^0_k,
\ee where \(\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)\neq0\)  and \(r>2.\)
Furthermore, \(v^{(2r+2)}=v^{(\infty)},\) and for \(\beta^0_r\neq 0\) there is no non-trivial symmetry in the symmetry group for \(v^{(\infty)}\).
\end{thm}
\bpr
Consider the vector field \(v^{(2)}\) obtained in Lemma \ref{seclev}. Denote
\bes\mathcal{E}_{0,k+1}:=\Big(0,\ldots,0,(\beta^1_2-\beta^0_1\beta^2_2)E^0_2,\beta^2_2E^1_2,E^0_1,0\Big)\ees
and \bes\mathcal{E}_{1,k+2}:=\Big(0, \ldots, 0, \big(\beta^0_2-\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)\big)E^0_2, (\beta^1_2-\beta^0_1\beta^2_2)E^1_2, \beta^2_2E^2_2, E^1_1\Big),\ees
where the number of zeros is \((k-3)\)-times for any \(k\geq 3.\)
Then, we have
\bas
\ker(d^{5,5})= \Span \{\mathcal{E}_{0,5}\}.
\eas

In the case that \(\beta^0_2-\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)\neq 0,\) we have
\bes d^{6,6}(\mathcal{E}_{0,6})=\big(\beta^0_2-\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)\big) E^0_3\in \IM d^{6,6}
\hbox{ and } d^{6,6}(\mathcal{E}_{1,6})=\beta^0_1\big(\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2)-\beta^0_2\big) E^0_3.\ees
Then,  \(\beta^0_1\mathcal{E}_{0,6}+\mathcal{E}_{1,6
\in \ker d^{6,6}.\) Let \(r:=2,\) and hence the \(6\)-th level extended partial normal form is given by Equation (\ref{2n2f}).

For \(\beta^0_2=\beta^0_1(\beta^1_2-\beta^0_1\beta^2_2),\) let \(r:= \min \{k\,|\; \beta^0_k\neq 0 \hbox{ for } k>2\}.\)
When \(\beta^0_k= 0\) for all \(k>1,\) the choice \(r:=2\) trivially completes the proof. Thus, we can assume that \(\beta^0_r\neq 0\) and \(r\) is finite. Therefore, \(\ker d^{k,k}=\Span \{\mathcal{E}_{0,k}, \mathcal{E}_{1,k}\}\) for any \(6\leq k\leq 2r+1,\)
\bas
d^{2r+2,2r+2}(\mathcal{E}_{0,2r+2})=(r-1)\beta^0_{r}E^0_{r+1}
& \hbox{ and } &
d^{2r+2,2r+2}(\mathcal{E}_{1,2r+2})={-(r-1)\beta^0_{r}\beta^0_1E^0_{r+1}}.
\eas Thereby, \bes E^0_{r+1}\in \IM d^{2r+2,2r+2} \hbox{ and } \ker d^{2r+2,2r+2}=\Span\{\mathcal{E}_{2r+2}\},\ees where \(\mathcal{E}_{2r+2}:=\beta^0_1\mathcal{E}_{0,2r+2}+ \mathcal{E}_{1,2r+2}.\)
Hence, \(\ker d^{k,k}=\Span\{\mathcal{E}_{k}\}\) for \(k\geq2r+2\) is one dimensional. Identify \(\mathcal{E}_{k}\) with an element in \(\E,\) then \(\mathcal{E}_{k}\) converges to the infinite level normal form vector field in the filtration topology when \(k\) approaches infinity, see \cite{GazorYu,GazorYuFormal}. This proves that the simplest normal form computation does not produce any non-trivial symmetry for the normal form system. The proof is complete by Theorem \ref{LNF}.
\epr

\section{The simplest orbital normal form}\label{secONF}

In this section, we obtain the simplest orbital normal form of \(v\) given by Equation (\ref{E0}).
Let \(Z^m_n:= x^my^{n-m}\) for \(m\leq n, m, n\in \N,\) and \(Z^0_0:=1.\)
Then,
\bas
\RM:= \Span \Big\{\sum_{n\geq m\geq 0} a^m_nZ^m_n| a^m_n\in \f, n\neq 0\Big\}
\eas
is the space associated with time rescaling generators, \ie \(\f[[x, y]]= \RM\oplus \f.\) The time rescaling computation is governed by a module structure, see \eg \cite{GazorYuSpec}.
Thus, the structure constants for the ring \(\RM\) and the \(\RM\)-module \(\E\) are given by
\ba
Z^m_nZ^l_k:=Z^{m+l}_{n+k} &\hbox{ and }&  Z^m_n E^l_k:= E^{m+l}_{n+k}.
\ea Furthermore, let
\be
r:= \min \{k|\beta^0_{k}\neq0\}.
\ee A grading function is defined by \(\delta(Z^l_k):= 2k-l\) and thus, \(\RM= \sum^\infty_{i=1}\RM_i.\) Define \(A_i:=\E_i\times \RM_i\) for any \(i\geq 1,\) \(A:= \sum^\infty_{i=1}A_i.\) Here \(A\) is a graded vector space according to \cite{GazorYuFormal,GazorYuSpec} and denotes the set of all formal sums \(\sum^\infty_{i=1}(v_i, T_i),\) where \(v_i\in \E_i\) and \(T_i\in \RM_i\). The action of \(A\) on \(\E\) is given by \((S,T)*v:=[S,v]+Tv\) for any \((S, T)\in A\) and \(v\in \E.\)

\begin{thm}\label{inftThmONF}
There exists a natural number \(r\) such that the vector field \(v\in \Theta^0_0+\E\) with nonzero quadratic part can be transformed into the simplest orbital normal form
\bas\label{inftONF}
v^{(\infty)}&=&\Theta^0_0+ E^1_1+\beta^0_{1}E^0_1+\beta^0_r E^0_r, \ \hbox{ for any }
r\geq2.
\eas Furthermore, the symmetry group of the vector field \(v^{(\infty)}\) is not finitely generated. When \(\beta^0_r\neq 0\) the symmetry group has no non-trivial symmetry from the group of permissible changes of state variables.
\end{thm}
\bpr We first remove the linear part \(\Theta^0_0\) from the system with a linear change of state variable \([x,y,z]:=exp\big((Z\ddY-Y\ddZ)t\big)[X,Y,Z],\) that sends the new variables \([X,Y,Z]\) into the old variables, see also \cite[Proof of Lemma 5.3.6]{MurdBook}. Therefore, we may assume \(v:=E^1_1+\ldots\in \E.\) Since \bes d^{2,2}(0,Z^1_1)= -\beta^2_2E^2_{2}\in \IM d^{2,2}\hbox{ and } d^{3,2}(0,Z^0_1) =-(\beta^1_2-\beta^2_2\beta^0_1) E^1_{2}\in \IM d^{3,2},\ees both terms of \(E^2_{2}\) and \(E^1_{2}\) are eliminated from the second level extended partial orbital normal form, \ie \(v^{(2)}= E^1_1+\sum^\infty_{k=1}\beta^0_k E^0_k.\) Now let \(r:=\min \{k| \beta^0_k\neq0, k>1\}.\) (In case \(r\) is not finite, an arbitrary choice for \(r>1\) trivially completes the proof.)
Denote \bes \ZS^0_{m,k+2}:= \big(0,\ldots,0, Z^0_m, \frac{-1}{(1-m)}E^0_m\big)\ees where the number of zeros is
\(2k\)-times for \(k\geq 1\). Then,
\be\label{2rl}
\ZS^0_{m,3}= \Big(0,0, Z^0_m, \frac{-1}{(1-m)}E^0_m\Big)\in \ker d^{2m+2,3}\hbox{ and }
d^{2m+2r,2r+1}(\ZS^0_{m,r})=\frac{r-1}{m-1}\beta^0_r E^0_{m+r},
\ee
for any \(m\geq 1.\)
By Theorem \ref{LNF} there exist transformations that send the vector field \(v\) into the infinite level orbital normal form \(u:=E^1_1+\beta^0_{1}E^0_1+\beta^0_r E^0_r\in \E\) for some \(r\geq2, \beta^0_1, \beta^1_r\in \f.\)
For any \(Z^l_k\) (\(l\geq 1, k\geq 2)\) there exists a nonzero state solution \(S\in \mathscr{S}\) and a time solution \(T\in \ta\) such that \((T, S)*u=-Z^l_ku. \) Therefore, the symmetry group for \(u\) is not finitely generated. Now the linear change of state variable \([x,y,z]:=exp\big((Y\ddZ-Z\ddY)t\big)[X,Y,Z]\) puts the linear part \(\Theta^0_0\) back into the normal form system, \ie \(v^{(\infty)}\) in Equation (\ref{inftONF}) is obtained. The composition of this map with the symmetry group associated with \(u\) results in a symmetry group for \(v^{(\infty)}.\) The rest of the proof follows Theorem \ref{SNF}.
\epr

\section{Parametric normal form}\label{secPNF}

This section is concerned about parametric normal form of a non-degenerate multi-parameter nonconservative perturbation \(w(\mu)\) (will be defined bellow) of the vector field \(v\) given by Equation (\ref{Eq1}), see also \cite{GaoPNF,GazorYuSpec,Mord08}. Define
\be\label{LieP}
\mathscr{S}:= \Span\Big\{\sum\beta^l_{k,\mathbf{m}} E^l_k\mu^\mathbf{m}| \beta^l_{k,\mathbf{m}}\in \f\Big\}, \ee where
the summation is over \(\mathbf{m}\in \NZ^q, \) \({l+k\geq 0},\) \(k\geq l,\) \(\mu:= (\mu_1, \mu_2, \ldots, \mu_q), |\mathbf{m}|=\sum^q_{j=1}m_j\geq 0, \beta^0_{0,\0}=0,\) and \(\mu^\mathbf{m}:= \mu_1^{m_1}\ldots\mu_q^{m_q}.\) We similarly define the parametric time space \(\ta\) such that \(\f[[x,y,\mu]]=\ta\oplus \f,\) and the space \(\PM\) as the space of all formal power series in terms of parameters \(\mu\in \f^q\) without constant term,
\ie \(\f[[\mu]]^q=\PM\oplus \f^q.\) The algebraic structures are naturally extended from nonparametric to the parametric cases,
see \eg \cite{GazorYuFormal,GazorYuSpec}. For \(\mathbf{m}=(m_1, \ldots, m_q)\in \NZ^q\) and \(\alpha=(\alpha_1, \ldots, \alpha_q)\in \N^q,\)
let \(\alpha\cdot\m:=\sum^q_{j=1}\alpha_jm_j.\) Then, define the grading function by
\bes
\delta_\alpha(E^l_k\mu^\mathbf{m}):= 2k-l+\alpha\cdot\mathbf{m}, \delta_\alpha(Z^l_k\mu^\mathbf{m}):= 2k-l+\alpha\cdot \m,\hbox{ and }
\delta_\alpha(\mu^\mathbf{m}):=\alpha\cdot \m.\ees
Define \bes A_i:= \mathscr{S}_i\times\PM_i\times \ta_i,\; A:=\sum^\infty_{i=1} A_i, \hbox{ and } (S, P, T)*v:= D_\mu (v)P+ Tv+[S, v]\ees for any \((S, P, T)\in A.\) The perturbation of the system is considered to be within the space of \(\mathscr{S},\) \ie \(w(\mu)\in \Theta^0_0+\mathscr{S}\). We call any vector field
\be\label{pv} w(\mu)\in \Theta^0_0+ \mathscr{S}\ee
a multi-parameter nonconservative perturbation of the vector field \(v\) given by Equation (\ref{Eq1}), when \(w(0)=v.\) Similar to the previous section, we remove the linear part \(\Theta^0_0\) from the vector field with a linear change of state variable. Since \(w_0=0,\) the first component of the map \(d^{n,k}\) is omitted, \eg the map
\be
d^{n,2}: A_{n-1}\rightarrow\E_n,
\ee is defined by \(d^{n,2}(Y_{n-1})= Y_{n-1}*v_1 \hbox{ for any } Y_n\in A_n.\) Since \(\beta^1_{1,\mathbf{0}}\neq 0,\) through a time rescaling we may assume that \(\beta^1_{1,\mathbf{0}} =1,\) \ie \(w=\sum^\infty_{i=1}w_i,\) \(w_1=E^1_1\) and \(w_i= \sum \beta^l_{k,\mathbf{m}} E^l_k\mu^\mathbf{m}\) with the summation over \(l, k, \mathbf{m}\in \NZ^q,\) \(i=2k-l+\alpha\cdot\mathbf{m}\) for any \(i>1.\)

\begin{lem} Any multi-parameter nonconservative parametric perturbation of a vector field given by equation (\ref{Eq1}) can be transformed to the second level extended partial  parametric normal form of \(w^{(2)}\) given by
\be\label{sec}
w^{(2)}= E^1_1+ \sum_{k\geq 0, |\mathbf{m}|\geq 0} \beta^0_{k, \mathbf{m}}E^0_k \mu^{\mathbf{m}} \quad (\beta^0_{0,\0}=0).
\ee
\end{lem}
\bpr Let \(\alpha:=(1,\ldots,1).\) Since \bes D_\mu v_1=0,\, [E^l_k,E^1_1]= (1-k)E^{l+1}_{k+1},\,
Z^0_0E^1_1= E^1_1, \, Z^0_1E^1_1= E^1_2, \,\hbox{ and } Z^1_1E^1_1= E^2_2,\ees for any \(N\geq 2\) we have
\be\IM d^{N,2}= \Span \{E^l_k\mu^{\mathbf{m}}\,| \hbox{ for any } l\geq 1, k\geq l, \hbox{ where } N= 2k-l+|\mathbf{m}|\}.\ee
Thereby, \(\NC^{N,2}= \Span\{E^0_k\mu^{\mathbf{m}}\,|\; N= 2k+|\mathbf{m}|\}\)  for any \(N\geq 2.\)
\epr
Consider the second level extended partial parametric normal form \(w^{(2)}\) given by Equation (\ref{sec}). Let \(r:=\min \{k\,|\; \beta^0_{k,\mathbf{0}}\neq0, k>1\}.\) For the rest of this paper, we assume that there exists \(\beta^0_{k,\mathbf{0}}\neq0\) for a \(k>1,\) \ie \(r\) is finite. Define a \((r+1)\times q\) matrix
\be
A:= (a_{ij}), \hbox{ where } a_{ij}:= \beta^0_{i-1,e_j} \hbox{ and } e_j \hbox{ denotes the } j\hbox{-th standard basis of } \f^q.
\ee

\noindent Then, we call a parametric vector field \(w(\mu)\in \Theta^0_0+\mathscr{S}\) a non-degenerate multi-parameter nonconservative perturbation of the vector field \(v\) if \(v=w(\mathbf{0}),\) and \(\rank(A)= r+1\) when \(w(\mu)\) is transformed into \(w^{(2)}\) given by Equation (\ref{sec}). When this condition is satisfied, through an invertible linear change of parameters we can transform the vector field \(w^{(2)}\) into
\be\label{secT}
\tilde{w}^{(2)}= E^1_1+ \sum^r_{k=1}\beta^0_{k,\mathbf{0}}E^0_k+ \sum^r_{k=0}E^0_k \mu_{k+1}+ \sum_{r\geq k\geq 0, |\mathbf{m}|\geq 2} \beta^0_{k, \mathbf{m}}E^0_k\mu^{\mathbf{m}} + \sum_{k> r, |\mathbf{m}|\geq 0} \beta^0_{k, \mathbf{m}}E^0_k \mu^{\mathbf{m}},
\ee
\ie \(a_{ij}=0\) if \(i\neq j,\) and \(a_{ii}=1.\) Now we update the grading weight vector \(\alpha\) by \(\alpha_i:=2(r-i+1).\) Therefore, \(\delta_\alpha(E^0_k \mu_{k+1})= 2r\) for any \(0\leq k\leq r.\)

\begin{lem} \label{SPNF}Let \(w(\mu)\) be a non-degenerate multi-parameter nonconservative perturbation of the vector field \(v\) governed by Equation (\ref{Eq1}). Then, there exist a natural number \(r\) and a sequence of permissible transformations such that they transform \(w\) into its \((2r+1)\)-th level extended partial parametric normal form
\be
w^{(2r+1)}= E^1_1+ \beta_{1}E^0_1+ \beta_{r}E^0_r+ \sum^r_{k=0} E^0_k \mu_{k+1} \quad (\beta^0_{r,\mathbf{0}}\neq 0).
\ee Furthermore, \(w^{(\infty)}=w^{(2r+1)}.\) The symmetry group of \(w^{(\infty)}\) is not finitely generated, yet it has no non-trivial symmetry from the group of permissible changes of state variables.
\end{lem}

\bpr Without loss of generality we assume that  \(w\) is transformed into \(\tilde{w}^{(2)}\) given by Equation \ref{secT} and \(\beta^0_{r,0}\neq0\).
By Equation (\ref{2rl}), we have
\bes E^0_{m+r}\mu^\mathbf{m}\in \IM d^{2m+2r+\alpha\cdot\mathbf{m}, 2r+1} \ \hbox{ for any } m\geq 1.\ees Furthermore, the condition \(\rank(A)=r+1\) implies that \bes E^0_k\mu^\mathbf{m}\in \IM d^{2k+\alpha\cdot\mathbf{m}, 2r+1} \ \hbox{ for any } |\mathbf{m}|\geq 2 \hbox{ and } 0\leq k\leq r.\ees Theorem \ref{LNF} implies that there exist transformations such that \(w^{(2)}\) can be transformed into \(w^{(2r+1)}\) as desired. Since \(w^{(2r+1)}\) does not have any term of grade higher than \(2r,\) we have \(w^{(\infty)}=w^{(2r+1)}.\) The uniqueness of \(w^{(\infty)}\) together with an argument similar to the proof of Theorem \ref{inftThmONF} complete the proof.
\epr
A linear change of state variables creates the linear part \(\Theta^0_0\) back into the infinite level normal form system. This together with Lemma \ref{SPNF} proves the following theorem.
\begin{thm}\label{PNF} Let the hypothesis of Lemma \ref{SPNF} hold. Then, there is a sequence of permissible transformation transforming the system generated by \(w(\mu)\) into the infinite level normal form system
\ba\label{FinalPNF}
{\dot{x}}&=&x g(x,\rho,\mu), \quad {\dot{\rho}}=\frac{1}{2}\rho g(x,\rho,\mu), \quad \dot{\theta}=1,
\ea where \(g(x,\rho, \mu)=x+\beta_1\rho^{2}+\sum^{r}_{k=0}\rho^{2k}\mu_{k+1}+\beta_r \rho^{2r},\) \(\beta_r\neq0\) and \(r\geq2.\)
\end{thm}

The following theorem sheds light to the dynamics of the infinite level parametric normal form system.
\begin{thm}\label{bifur} Consider the infinite level parametric normal form system in Theorem \ref{PNF}. Then, the surface \(\rho^2=c|x|,\) for any nonnegative constant \(c\), is an invariant manifold of solutions for the system. Furthermore, the surface \(x=-\beta_1\rho^{2}-\sum^{r}_{k=0}\rho^{2k}\mu_{k+1}-\beta_r \rho^{2r}\) is an invariant manifold of limit cycles for the parametric system; except that it includes the origin as a fixed point. This implies that any point outside the later invariant surface, approaches a limit cycle or the origin through the surface \(\rho^2=c|x|\) for an appropriate constant \(c.\)
\end{thm}
\bpr By Equation (\ref{Eul}) we have \(\frac{1}{2}\rho\dot{x}= x\dot{\rho}\) and thus, \(\rho^2=c|x|\) is an invariant set for the system.
The rest of the proof follows from Theorem \ref{PNF}.
\epr

Now we present an example and find its parametric normal form.
\begin{exm} Consider the system governed by
\bas
\dot{x}&=& 2x\mu_1+2x^2(a+\mu_{1}+\mu_{2})+2x(y^2+z^2)(b+\mu_{2})+2x^3(c+{\mu_{1}}^2+{\mu_2}^2)+ 2x(y^2+z^2)^2\mu_3
\\&&+ 2ex^4+2x^2(y^2+z^2)(d+\mu_{1}^2),
\\
\dot{y}&=&z+y\mu_1+xy(a+\mu_{1}+\mu_{2})+y(y^2+z^2)(b+\mu_{2})+x^2y(c+{\mu_2}^2)+ y(y^2+z^2)^2\mu_3
\\&&+ex^3y+xy(y^2+z^2)(d+\mu_{1}^2),
\\
\dot{z}&=&-y+z\mu_1+xz(a+\mu_{1}+\mu_{2})+z(y^2+z^2)(b+\mu_{2})+x^2z(c+{\mu_2}^2)+ z(y^2+z^2)^2\mu_3
\\&&+ex^3z+xz(y^2+z^2)(d+\mu_{1}^2).
\eas where \(ab(da-cb)\neq 0.\) Then (using a Maple program) we obtain its parametric normal form given by
\bas
\dot{x}&=& 2x g(x, y^2+z^2, \mu),
\\
\dot{y}&=&z+y g(x, y^2+z^2, \mu),
\\
\dot{z}&=&-y+z g(x, y^2+z^2, \mu),
\eas where \(g(x, R, \mu):=\mu_1+(\beta_1+\mu_2)R+(\beta_2+\mu_3) R^{2},\) \(\beta_1=\frac{b}{a}\) and \(\beta_2=\frac{b(da-cb)}{a^3}.\)

\end{exm}

redpajama_set_name: RedPajamaArXiv


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text:
Digital, Booking Sites
Airbnb's CTO on the Battle for New York and IPO Rumours
The next six months will be interesting for the rental upstart, and fascinating to watch from the outside. Can it find a balance with regulators and can it keep the user growth momentum going?
At yesterday's TechCrunch Disrupt Berlin conference, TechCrunch writer Ryan Lawler interviewed Airbnb CTO and co-founder Nathan Blecharczyk about the service's rapid growth over the last year and the challenges that it is facing in large markets like New York City and San Francisco.
But Blecharczyk first used the event to announce a change to Airbnb's search functionality, making it easier for users to compare photos of rentals while also looking at a map of their destination. The CTO called it a solution to Airbnb's "unique search problem" of giving the user a map and photos at the same time.
Early on, Blecharczyk also confirmed a widely circulated yet unconfirmed report that Airbnb raised a large investment from PayPal founder Peter Thiel last fall. "We did raise money a year ago from Peter Thiel's Founder Fund," Blecharczyk told Lawler. "$200 million." He denied that Mark Zuckerberg was part of that round.
More About Airbnb:
Airbnb Is Fighting to Make Sharing Legal in New York, But It Already Is
Airbnb Vs. New York City: The Defining Fight of the Sharing Economy
What HomeAway Can Teach Airbnb About Getting Along With Cities
Lawler pressed Blecharczyk on Airbnb's regulation hurdles. The CTO blamed the troubles on Airbnb's innovative powers more than anything else. "What we're doing hadn't been envisioned before," he said. "Previously there were were people and there were businesses and there were rules for both. In the sharing economy those are merging."
Read more about what collaborative consumption and the sharing economy mean to the future of travel.
Buy the Report
Blecharczyk returned often to the concept of "dialog" with states and municipalities. "We have to have a dialog," he said more than once in reference to laws that seek to limit the types of rentals on the site. In response to Lawler's question about the New York State Attorney General's request for user data, Blecharczyk explained that the state was after information about just the largest users of Airbnb, likely for tax purposes.
"With the Attorney General in New York we see eye-to-eye on a lot of facts. They're concerned about a few users that are quite large that have over 100 properties. We understand you may not want users with that many properties on our service," he said. "He asked for data not just on those users but all users. We didn't think that was appropriate"
Lawler pressed him on just removing the biggest offenders, which are clearly in violation of the state law, to which Blecharczyk said, "We would love to have a dialog with the city and realize where to draw the line. There are a lot of interesting side cases in there."
Blecharczyk addressed competition in Europe, specifically Wimdu, an Airbnb clone that the original considered buying last summer. "We did not share the same values that Wimdu is about," Blecharczyk said, referring to Wimdu as "mercenary" and Airbnb as "missionary."
The continent is central to Airbnb's strategy. Of the roughly 500,000 listings available on the service, approximately 300,000 are in Europe, Blecharczyk said. He explained how Airbnb was helping people hit by the economic crisis make ends meet.
"People are having trouble holding on to their homes and we're providing a tool to help them," he said. "We're empowering people to take their future into their own hands."
As for Airbnb's future, Blecharczyk said a quick IPO isn't the goal, nor is acquisition.
"We have a very big vision and it don't think we could do that as a subsidiary of another company," he said. "We are very well financed. I don't anticipate the need to do [an IPO] any time soon."
View the full interview here:
Tags: airbnb, sharing, techcrunch
Photo Credit: Airbnb CTO and co-founder Nathan Blecharczyk. TechCrunch Disrupt
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Passionate about photography. Photographs tell a story.
No Small Wonder Why I am passionate about Photography: Photographs freeze a moment.
It is no small wonder why I am hooked on the process of photography. Photographs tell a story. The story of our lives can be captured through photography. Photographs physically freeze action and deliver a slice of a moment. Once my finger is released from the shutter, an image is frozen forever. Birth, growth, nature, action, destruction, chaos and splendor are etched by way of photography. Photographs create memories, emotions, documentation, history and permanency.
I created the collage below, knitting together more than 30 elements, symbolizing historical and real events in the town of Natick, Massachusetts in metro-west Boston. So many of us engage in the art of photography. Photographs connect generations passed to the future. Fleeting moments are preserved. Light, and the absence of it, are factors affecting photography. Photographs are transformed as light either augments or diminishes.
It is no small wonder why my eyes are trained to survey life and events surrounding me. I specialize in Aerial photography. Natural light is the only light available or appropriate for pictures taken at 1,000 ft and above.
I'm grateful to my paying customers, who create opportunities for me to engage in what I love, photography. Photographs are used to demonstrate completion of tasks, used for marketing products, both on the web and for publication. I am hired to capture aerial views of estates for sales purposes. On a more personal side, photographs are shared as gifts, keepsakes and souvenirs for generations past and future.
And finally, it is no small wonder that I commit to offer my personal best through the art of photography. Photographs are the best physical means to reflect our world, our people, our widlife, our faith and our rich natural resources.


On Monday we will announce some big news for this football club and a chance for everyone – club, players, supporters and the town – to come together and stand Shoulder to Shoulder for Stevenage.
After more than 6 years since we first stated our ambition to build a new North Stand at the Lamex Stadium, it is finally going to happen, and you can be a part of it.
Full announcement to come on Monday – keep your eyes peeled.


Sure the party was great and seeing the family was wonderful! But what a mess! We understand that this may not be the best for your carpet. Foggs Carpet Cleaning is here to help your family to recover from the mess.
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We would also recommend calling and scheduling a cleaning now. Why? So that you can make sure that all that food and drink that made its way into your floors doesn't sit for long. Foggs can help you get things off to a good start for a new year. Contact us today!
Cleaning Tips: How to clean up that family holiday mess!