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Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses

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Automatisierte Medienanalyse

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as if the 10 and you have to tip the what and present to you today is the 1st of the big projects which consist of building model and the numerical simulations to study music loudly that sentences so the 1st step is about as undertaken any easier than in the past such kind of wouldn't want to go to small OK so all this is the 1st president of short overview of synaptic transmission that Atkin consonants is conditional on the program and then managed UBS undertaken uses Alaska so the scientists maybe you and knows what it is Is a structure not very well known to be in there is a functioning that permit to transmit analytical signal from the 1 the presented to you on to another person takes a women electrical signal rights mentioned potential rent here and it triggers the opening of the Baltic state of constant and which of the blue China's on understood the picture and this will prevent the entry of consumer finance in the terminal the orange dots and discussed can go to bind to specific receptors the organized on Dr. musicals about physical although 1 one-shot just opposed to the right and it may find those about there's a goal and the specific receptors on the physical it would trigger the meanings of which was begun in the Senate declared and then it could the combined to the pink recent also specific was it often with leaders and the chemical cascade and everything will prevent the I mean creates a miniature gold signal in the percentage of so it's a very complex phenomenon and just to very interested in what's happening in the press and the ball went out which comes from my and also the consumption and have to find the very small receptor located at the doctor visit became so just because you on the spot says about physical are attached to the membrane from not press which is a complex of potatoes and onions not complex you have receptors for the customer to the judgment of the Bloomington and the views and beliefs if you got some like fall 8 finds the receptors then the same thing as a good will fuse with the membrane momentum that is equal to the rent and then everything will start for the prosecution
so the here that we did it got some ideas on how best to bring that use freely in the 10 0 lead we know the particles that customers are charged particles that we will make this and the 1st step and that Mexico's justice fanned tensions with the plan can hear you understand in Green Bay London planes in and the binding on this not complex is where the brawn article will find was arrested in a confined here so this is our mother of these items finding the complex find this month here which is the center of the centenarians and of the Independence High .period between the physical pain get sold we are not interested in the time and in the field stamp of the project the probability that Lions starting from this channel will find this small so I represent not only has undertaken a users you for these numbers could find so that now escape program we have here it is the following evident article is a described by a statistic equation eggs .period sequels square root of 2 D at W . efficient radiation from the party candidate about his white notes and the 1st time entering being the main hero make a bomb which represent the main interested in as few as a small hole in red isn't winning this picture is given by this for the 1st time that the article fine the main again about good is reflected in work on the border of the main except under its nose sold so we are interested in the majors passage on to the city and them which is you and we know it's a very well known it's Dean that Disney investors this time following the submission of them extraordinary mental problems which is here at Indianapolis in Europe coalminers wildly as division coefficient and equal 0 is a classical reflection the bonhomie and you equals 0 it's a classical absorption absorption and the Red Sea sold going to do to try to find asymptotic an analysis of the of the site
OK so those are the 1st 3rd we can little blue ceiling going this is the man that its invariant irritation around the axis of the time here trees vary easy to see and according to the equation we have uh we know that these 4 men is independent of the time if we we consider the cynical coordinates around them so we can uh just study in agreement on problems in the main only got adjusted to the demands of prediction of the domain of the tables in and so on this menacing blue His the ruling the red sphere is here that the red the arc of this small as soon as there is now just signals repair and the equation becomes the following equation where are you recognize here the bastion in single coordinate the isn't there so I'm now in into D the main with into the program which is equivalent to the problem we have unisys as well but I put the division edition right and that we have reflection of the blue black and green onerous is and absorption of the segment the are interested in gas and that takes off you when it's done which is the length of the thing and a goes very small goes to the reserves 1 from the rest of the month so the
prominent here is that we have a similarity because when it's in those 2 0 the point here is not regular soap 2 the singular this singularity for read we will have to look at the problem of the similarity that it prevents us to use a classical many which are for example the Green functions under this domain because we love the order of the Green functions in its analysis singularity this depends the main we don't have access to this Delaware which is very classical is matching hasn't thinks so we try to find a solution the other cost me the whole we to find a solution in the domain we try to match and then we can obtain something that's here because of the job which is not possible as well so the idea is to dismantle arrives the similarity and we are using conformal laps so he here because we have a tendency because we need to use investment which comes very easy when you stop to think about it because it was transformed this domain into the maintain looming area here because that they most maddening principle this the agenda and new owing to borrow Strickland and you notice that there small hole here in red is going to restrict line here and another maps putting the spheres circle in 2 straight lines and Strickland to circles so indirectly from there the whole here is not spare time it's not a simple model Co but the readiness of the circle is 1 of 2 air base which is here the In the absence of out of the whole unleash you maybe don't remember
because I didn't tell you this before hair-raising although screwed up it's going it's a simple computations so
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solve this equation will now use scanning property so it's getting the heart and soul
we put the zinc I called Best squared to Hardage the square root adopting that's look which means that Will
which means that we are going not thinking it our interests in the region very close to the hole get very close to the responded so my setting
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so we concluded that it is not among the main force pastime to a smaller rival located between 2 attendance for and we could show that these investors Chinese Constance outside of the monetary area as an adjustment to its and he's wearing these those that these investors stand well approximated by a person process so this is the result of the world was already known so it's meaning that we can we can consider that the removal of these particles to the small hole is personal and those the 1st of the mission that will offer the arrival is an exponential this is very interesting because you think this analysis in further development of the project that I don't have time to present here we could compute as well the probabilities where particles stops inside the here because periods we have the investors to go to the hold when you are far from the whole because we said it's because usually means we are far what's happening when your clothes the problem is that still the program so using the same kind of analysis what we have here we could compute the probability to reach this year and that escaping the and it's the same kind of computation and using this we could build a model of the active zone which is a place where physical are located and the constant channel located as well to investigate the influence of the position of the channels on the clothing on physical not planning of this included strikes at under stability which it poverty to have diffusion the British have I am about coming to this physical on arts and using this week could built and 1 of them the Senate determine how much bigger wizard the whole of stuff we have over there but the fact that these investors Chinese person and is really what is important here in our study because if you want to monitor the presenting coming now and you have a Brenham particle in Uganda were enhancing relations if you aren't very simple not that simple because of the men is not that firm that OK you can do it but you would wait for hours because of the very small hole you here and because of that there very long time you have to find the small holes the fact that it's a process allows you to use standing is terrorism to say OK it's personnel and I can at least use for what's happening because it's constant in doesn't of the positions of independent of back and that's what we did in the following of this project and I wanted to show you this because it's a very said about anything is there he said going after that because we could show that the 1st Boston is independent of the position of the studies pursuant to this work was published in the scientific togetherness relations I want to send just might proviso that development and my mates and organizer of this conference for the opportunity to present my work to thinking if the land and some of across the board president of the community the 1st Standing approximately 2 because of this because it doesn't have the position they didn't happen when you start so it's fair to say that you have that meaning the violence is the same as it's well approximated any other questions probably not in the sense that he was
Lineares Funktional
Impuls
Physikalismus
Güte der Anpassung
Gebäude <Mathematik>
Komplex <Algebra>
Arithmetisches Mittel
Konstante
Skalarprodukt
Algebraische Struktur
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Reduktionsverfahren
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Radikal <Mathematik>
Projektive Ebene
Optimierung
Widerspruchsfreiheit
Numerisches Modell
Ebene
Unterring
Länge
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Zahlenbereich
Gleichungssystem
Fortsetzung <Mathematik>
Kartesische Koordinaten
Zeitbereich
Division
Computeranimation
Kreisbogen
Topologie
Temperaturstrahlung
Prognoseverfahren
Kugel
Dean-Zahl
Wurzel <Mathematik>
Optimierung
Stochastische Abhängigkeit
Analysis
Beobachtungsstudie
Statistik
Oval
Grothendieck-Topologie
Stochastische Abhängigkeit
Zeitbereich
Klassische Physik
Koordinaten
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Zeitbereich
Computeranimation
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Kugel
Flächeninhalt
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Stochastische Abhängigkeit
Gerade
Normalvektor
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Numerisches Modell
Arithmetisches Mittel
Wärmeausdehnung
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Regulärer Graph
Leistung <Physik>
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Zeitbereich
Optimierung
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Computeranimation
Wärmeausdehnung
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Zentrische Streckung
Regulärer Graph
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Gleichungssystem
Zeitbereich
Wurzel <Mathematik>
Ordnung <Mathematik>
Term
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Ortsoperator
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Parametersystem
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Erweiterung
Approximation
Amenable Gruppe
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Numerisches Modell
Forcing
Flächeninhalt
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Numerisches Modell

Metadaten

Formale Metadaten

Titel Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses
Serientitel Les Probabilités de Demain
Teil 09
Anzahl der Teile 17
Autor Guerrier, Claire
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/20262
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2016
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract Claire Guerrier - Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses Synaptic microdomains are underlying fundamental and yet not completely understood functions, such as learning and memory, breathing, sleeping, and many more. Motivated by understanding and analyzing these neuronal structures, we built a model to study vesicular release at synapses. As a first step, we computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. The method relies on Möbius conformal transformation applied to the Laplace equation. We also estimated, when the particle starts inside a boundary layer near the hole, the splitting probability to reach the hole before leaving the boundary layer, which is also expressed using a mixed boundary-value Laplace equation. Using these results, we developed model equations and their corresponding stochastic simulations to study vesicular release at neuronal synapses, taking into account their specific geometry.

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