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Hvad er et neuralt netværk egentlig?

Kunstige neurale net (Artificial Neural Networks – ANN) generelt, og dybe net specielt er tidens hotte område inden for kunstig intelligens. Man har opnået mange gode resultater med denne teknik (f.eks. spille go, beskrive billeder, og oversætte sprog).

Men hvordan fungerer de egentlig? Jeg skal prøve at give en meget kort beskrivelse af det. Før vi kan tale om hvad dybe (kunstige) neurale net er kan vi starte med at se på hvad de basale dele af et kunstigt neural net er.

Biologiske neurale net

Kunstige neurale net er inspireret af biologisk neurale net som vi kender fra hjerner i alle dyr på jorden. I det abstraktionsniveau som er nyttigt her består et neutralt net af neuroner, axoner og dendritter. En neuron er en nervecelle som kan behandle strømsignaler som kommer ind via dendritter og sende nye elektriske signaler ud via axoner (se figur 1). Jeg skal ikke gå nærmere ind på den ionudveksling som muliggøre dette. Men blot henvise interesserede læsere til at slå det op. Den engelske udgave af wikipedia har en udmærket artikel her. Det er meget interessant, og uhyre meget mere kompliceret end man skulle tro.

Illustration: Privatfoto

Figur 1: Neuron

Kunstige neurale net

Et kunstigt neuralt net modellere kunstige neurale net på det abstraktionsniveau som indeholder neuroner, axoner og dendritter. Det er fundamentalt en graf (typisk en ikke-cyklisk rette graf) hvor kanterne svarer til axoner og dendritter (i kunstige neurale net skelner man ikke), og noderne svarer til neuroner (se figur). Hver kant har en vægt tilknyttet som bestemmer hvor meget hver værdi skal vægtes med.

Hver node har en aktiveringsfunktion som typisk summerer værdierne på de kanter som peger ind i noden (dendritter) og aktiverer de kanter som peger ud af noden (axoner), givet at en eller anden tærskelværdi er overskredet.

Figur 2: Neuralt net

Men et kunstigt neuralt net (og et biologisk) er ikke noget værd uden en måde at få det til at lære noget på. Dette er fundamentet for alle maskinlæringsmetoder: det at træne en model til at lave beslutninger.

Læring i neurale net

Lidt mere formelt er idéen bag maskinlæring generelt er at der findes en funktion som mapper inputværdier til outputværdier (I et ANN findes input værdierne på inputnoderne og outputværdien på outputnoderne). Hvis man kender denne funktion er man færdig og kan gå hjem. Hvis ikke, kan man bruge en maskinlæringsalgoritme til at lære den.

Kort fortalt fremsætter sådan en algoritme en hypotese om denne funktion som man så kan gå at teste. Hvis fejlen er for stor justerer man sin algoritme (lærer). Dette blive man ved med indtil fejlen er tilstrækkelig lille; eller at hypotesen er tilstrækkelig tæt på den virkelige funktion, om man vil. Dette kaldes overvåget læring (supervised learning). Denne fremgangsmåde kræver naturligvis at vi har nogle eksempler på kendte mappinger mellem input- og outputværdier.

En ANN er i princippet sådan en (stor) funktion hvor præcisionen er afhængig af alle vægtene. Den underliggende idé er at man kan justere vægtene på kanterne med en værdi som er afhængig af fejlen nettet producerer. Den bedst kendte måde at gøre dette på er ved at bruge backpropagation.

Meget simpelt går backpropagation ud på at man præsentere en ANN for noget input. Det kan f.eks. være et billede man ønsker at klassificere. Så propagerer man værdier ned igennem nettet. Nu kan man sammenligne det output som nettet giver med det man ved det skal være (husk dette er overvåget læring). Hvis svaret ikke er perfekt kan man propagerer fejlen tilbage og ændre vægtene i kanterne. Dette bliver man ved med indtil fejlen er tilstrækkelig lille. Hvis man er interesseret i mange flere detaljer er dette et godt sted.

Når man har kørt sin backpropagation på sit træningssæt er man klar til at verificere nettet på en testsæt. Det er essentielt at man holder disse to sæt adskilte. Ellers løber man nemt risikoen for at overtræne på et subsæt af verden (overfitting) og derved midste enhver generaliserbarhed. Hvis testen er god kan man gå i produktion.

Dette var en ultra kort, og ikke specielt teknisk introduktion til kunstige neurale net. For de specielt interesserede er der rigtig meget litteratur tilgængelig. De engelske wikipedia-sider er ganske udmærkeder. Ellers kan jeg anbefale Rojas' fremragende bog Neural Networks - A Systematic Introduction. Den er ikke helt ny men er stadigvæk en af de bedste.

Næste gang skal vi kigge på de dybe net.

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Svar på:

Kunstige neurale net er inspireret af biologisk neurale net som vi kender fra hjerner i alle dyr på jorden. I det abstraktionsniveau som er nyttigt her består et neutralt net af neuroner, axoner og dendritter.

Astrocytter "regerer" i vores hjerne?:

RIKEN. (2016, April 25). Change in the brain: Astrocytes finally getting the recognition they deserve. ScienceDaily:
Citat: "...
Until recently, synaptic strength was thought to change only at synapses of active presynaptic neurons. Now, RIKEN scientists have shown that the truth is more complicated, and more interesting.
...
"We have found an active mechanism that helps to increase variation in synaptic strength," explains lead scientist Yukiko Goda, "and surprisingly, it comes from astrocytes, which have previously been thought to play mostly passive roles in the brain."
..."

University of Gothenburg. (2012, August 24). Astrocytes control the generation of new neurons from neural stem cells. ScienceDaily.

September 27, 2012, scitechdaily.com: Study Suggests that Astrocytes are Critically Important for Processing Sensory Information:
Citat: "...
The findings, published this week in the online edition of the Proceedings of the National Academy of Sciences, are the latest in a growing body of evidence suggesting that astrocytes are critically important for processing sensory information, says Mriganka Sur, the Paul E. and Lilah Newton Professor of Neuroscience at MIT and senior author of the paper.
[]
Sur’s lab has been studying astrocytes for about five years, as part of a longstanding interest in revealing the functions of different cell types in the cortex. The star-shaped cells were first discovered and named 150 years ago, but since then, “it’s been a mystery what they do,” says Sur, who is a member of MIT’s Picower Institute for Learning and Memory and director of the Simons Center for the Social Brain at MIT.
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“If you are paying attention to something, which causes this release of acetylcholine, that leads to a long-lasting memory of that stimulus. If you remove the astrocytes, that doesn’t happen,” Sur says.
..."

October 10, 2014, scitechdaily.com: Previously Unknown Mechanism Repairs Brain after Stroke:
Citat: "...
The researchers have shown that following an induced stroke in mice, support cells, so-called astrocytes, start to form nerve cells in the injured part of the brain. Using genetic methods to map the fate of the cells, the scientists could demonstrate that astrocytes in this area formed immature nerve cells, which then developed into mature nerve cells.
..."

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Ja, det er meget kompliceret. Jeg vil gå så langt som at sige at det er helt fantastisk kompliceret. Heldigvis kan man tillade sig et meget simplere abstraktionsniveau når man blot har en computationelmodel som er inspireret af biologien. Men tak for referencerne. Nu har jeg lidt læsestof til weekenden.

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Ja, det er meget kompliceret. Jeg vil gå så langt som at sige at det er helt fantastisk kompliceret. Heldigvis kan man tillade sig et meget simplere abstraktionsniveau når man blot har en computationelmodel som er inspireret af biologien. Men tak for referencerne. Nu har jeg lidt læsestof til weekenden.

Lidt mere om astrocytter:

12. januar 2014, videnskab.dk: Overraskende studie: Skal hjernen tænkes helt om? Vores følelser og tanker er muligvis ikke kun styret af hjernens nerveceller, antyder en ny undersøgelse. Studiet åbner en ny dør ind til, hvordan hjernen og sindet fungerer, mener danske forskere:
Citat: "...
»Vores undersøgelse peger på, at man ikke længere kan studere, hvordan hjernen skaber mentale funktioner uden at tage astrocytterne med i beregningerne,« siger Barbara Lykke Lind, postdoc på Institut for Neurovidenskab og Farmakologi ved Københavns Universitet.
...
Astrocytter har endda langt mere komplekse forbindelser til hinanden end neuronerne.
..."

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Nogle andre interessante indlæg om neuroner:

Re: Rigtig intelligens, kræver kvantefysik.

fx:

University Of Southern California. (2004, June 16). Gray Matters: New Clues Into How Neurons Process Information. ScienceDaily:
Citat: "...
"It's amazing that after a hundred years of modern neuroscience research, we still don't know the basic information processing functions of a neuron," said Bartlett Mel.
...
"We show that the cell significantly violates that rule," Mel said.
The team found that the summation of information within an individual neuron depends on where the inputs occur, relative to each other, on the surface of the cell.
..."

University Of California - Los Angeles (2004, December 14). UCLA Neuroscientist Gains Insights Into Human Brain From Study Of Marine Snail. ScienceDaily:
Citat: "...
"Our work implies that the brain mechanisms for forming these kinds of associations might be extremely similar in snails and higher organisms. People may think invertebrates are not very sophisticated, but we don't appreciate just how complicated their nervous systems are, and how complex their behaviors are.
[]
We don't fully understand even very simple kinds of learning in these animals."
..."

University College London. (2010, August 13). Single neurons can detect sequences. ScienceDaily:
Citat: "...
Surprisingly, they found that each sequence produced a different response, even when it was delivered to a single dendrite. Furthermore, using theoretical modelling, they were able to show that the likelihood that two sequences can be distinguished from each other is remarkably high.
..."

Hjerneforskning - Mikrotubuli.

11. december 2013, videnskab.dk: Orme husker uden hjerner:
Citat: "...
En særlig art af fladorme kan ikke alene overleve at få hugget hovedet af, de kan også gro et nyt. Og nu er det tilmed bevist, at det nye hoved kan huske, hvad det gamle lærte. Det fører til nye spekulationer om, hvor vores bevidsthed egentlig sidder.
..."

Hjernen er plastisk i en grad, så man har svært ved at tro det.

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Nutidens bedste analyseinstrumenter kan gå hjem og vugge - de bliver basket af banen af vores øres ekstraordinære gode ulineare signalbehandling. Det samme gælder selvfølgelig nutidens AI og robotters signalbehandling.

De fleste forskere undgår ulinear analyse fordi det er for kompliceret.

Jan 31, 2013, physicsworld.com: Human hearing is highly nonlinear:
Citat: "...
People can simultaneously identify the pitch and timing of a sound signal much more precisely than allowed by conventional linear analysis. [f.eks. wavelet transformation og link ] That is the conclusion of a study of human subjects done by physicists in the US. The findings are not just of theoretical interest but could potentially lead to better software for speech recognition and sonar.
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Oppenheim and Magnasco discovered that the accuracy with which the volunteers determined pitch and timing simultaneously was usually much better, on average, than the Gabor limit. In one case, subjects beat the Gabor limit for the product of frequency and time uncertainty by a factor of 50, clearly implying their brains were using a nonlinear algorithm.
...
Mike Lewicki, a computational neuroscientist at Case Western Reserve University in Ohio, says the research is "a nice demonstration that our perceptual system is doing complex things – which, of course, people have always known – but this is a nice quantitative demonstration by which, even at the most basic level, using the most straightforward stimuli, you can demonstrate that the auditory system is doing something quite remarkable".
..."

University of California - San Diego (2010, July 5). Our brains are more like birds' than we thought. ScienceDaily:
Citat: "...
In the latest research, they used modern, sophisticated imaging technologies, including a highly sensitive tracer, to map a region of the chicken brain (part of the telencephalon) that is similar to the mammalian auditory cortex. Both regions handle listening duties. They discovered that the avian cortical region was also composed of laminated layers of cells linked by narrow, radial columns of different types of cells with extensive interconnections that form microcircuits that are virtually identical to those found in the mammalian cortex.
The findings indicate that laminar and columnar properties of the neocortex are not unique to mammals, and may in fact have evolved from cells and circuits in much more ancient vertebrates.
..."

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Fri vilje?

11 Apr 2006, arxiv.org: The Free Will Theorem, JOHN CONWAY AND SIMON KOCHEN:
Citat: "...
Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know
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It is hard to take science seriously in a universe that in fact controls all the choices experimenters think they make.
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It is also hard to take seriously the arguments of those who according to their own beliefs [!] are deterministic automata!
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The authors strongly believe, [!] however, that there is a way our brains prevent some of this cancellation, so allowing us to integrate what remains and producing our own free will.
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Einstein could not bring himself to believe that “God plays dice with the world,” but perhaps we could reconcile him to the idea that “God lets the world run free.”
..."

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Albert-Ludwigs-Universität Freiburg. (2010, September 10). Neurons: Faster than thought and able to multiply. ScienceDaily:
Citat: "...
Not only does this theory explain why nerve cells process information much faster than previously thought. It also became clear that neurons do more than just add up pulses: In the decisive moments, they actually multiply. The availability of this mathematical operation, write the scientists, finally explains how the brain is able to execute complex computations. [?]
..."

Northwestern University. (2011, February 19). Conventional wisdom of how neurons operate challenged: Axons can work in reverse. ScienceDaily:
Citat: "...
"Signals can travel from the end of the axon toward the cell body, when it typically is the other way around. We were amazed to see this."
...
He and his colleagues first discovered individual nerve cells can fire off signals even in the absence of electrical stimulations in the cell body or dendrites. It's not always stimulus in, immediate action potential out.
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"The axons are talking to each other, but it's a complete mystery as to how it works," Spruston said. "The next big question is: how widespread is this behavior? Is this an oddity or does in happen in lots of neurons? We don't think it's rare, so it's important for us to understand under what conditions it occurs and how this happens."
..."

Charité - Universitätsmedizin Berlin. (2012, June 22). Information flow in the brain is not a 'one-way street'. ScienceDaily:
Citat: "...
They discovered that signals can also be initiated in axons, i.e. outside the cell body.
..."

American Society for Cell Biology. (2009, December 11). Fruit fly neuron can reprogram itself after injury. ScienceDaily:
Citat: "...
When the researchers used a laser to cut off the entire axon of the Drosophila neuron, the supposedly stable dendritic microtubules burst into action, essentially deconstructing and rebuilding the entire dendritic microtubule cytoskeleton.
..."

Yale University. (2006, April 13). Brain Communicates In Analog And Digital Modes Simultaneously. ScienceDaily:
Citat: "...
This means that the waveform generated in the receiving neuron is not just determined by the digital pattern of action potentials generated, but also by the analog waveform occurring in the sending neuron.
..."

Salk Institute for Biological Studies (2013, April 10). Despite what you may think, your brain is a mathematical genius: How visual system automatically adapts to new environments. ScienceDaily:
Citat: "...
"It's as if the brain's on a budget; if it devotes 70 percent here, then it can only devote 30 percent there," says Gepshtein. "When the adaptation happens, if now you're attuned to high speeds, you'll be able to see faster moving things that you couldn't see before, but as a result of allocating resources to that stimulus, you lose sensitivity to other things, which may or may not be familiar."
..."

University College London. (2010, August 13). Single neurons can detect sequences. ScienceDaily:
Citat: "...
Surprisingly, they found that each sequence produced a different response, even when it was delivered to a single dendrite. Furthermore, using theoretical modelling, they were able to show that the likelihood that two sequences can be distinguished from each other is remarkably high.
..."

Northwestern University. (2012, December 5). Workings of the brain: After 100 years, understanding the electrical role of dendritic spines. ScienceDaily:
Citat: "...
"This research conclusively shows that dendritic spines respond to and process synaptic inputs not just chemically, but also electrically," said William Kath
..."

University of North Carolina School of Medicine. (2013, October 27). Neuroscientists discover new 'mini-neural computer' in the brain. ScienceDaily:
Citat: "...
"All the data pointed to the same conclusion," Smith said. "The dendrites are not passive integrators of sensory-driven input; they seem to be a computational unit as well."
..."

University College London - UCL. (2013, October 27). Smart neurons: Single neuronal dendrites can perform computations. ScienceDaily:
Citat: "...Dendrites thus act as miniature computing devices for detecting and amplifying specific types of input...."

Durham University (2009, June 17). Common Fish Species Has 'Human' Ability To Learn. ScienceDaily:
Citat: "...
The sticklebacks [Hundestejler] can compare the behaviour of other sticklebacks with their own experience and make choices that lead to better food supplies, according to the study by St Andrews and Durham universities.
...
"But our results suggest brain size isn't everything when it comes to the capacity for social learning."
...
Co-author Professor Kevin Laland from the School of Biology at St Andrews University added: "Nine-spined sticklebacks may be the geniuses of the fish world.
..."

University At Buffalo (2003, December 2). New Research Finds Some Animals Know Their Cognitive Limits. ScienceDaily:
Citat: "...
The researchers have shown that the monkeys and the dolphin used the "uncertain" response in a pattern that is essentially identical to the pattern with which uncertain humans use it.
...
They apparently know when they know and when they don't know, he adds.
..."

San Francisco State University (2009, October 2). Consciousness Is The Brain's Wi-Fi, Resolving Competing Requests, Study Suggests. ScienceDaily:
Citat: "...
"If the brain is like a set of computers that control different tasks, consciousness is the Wi-Fi network that allows different parts of the brain to talk to each other and decide which action 'wins' and is carried out," said San Francisco State University Assistant Professor of Psychology Ezequiel Morsella, lead author of the study.
...
The results demonstrated that merely preparing to perform an incompatible action, for example preparing to move simultaneously left and right, triggered stronger changes in awareness than preparing to perform a compatible action or experiencing a conflict that does not engage the muscles that move our bodies. Participants rated changes in their awareness on an eight-point scale and reported an average rating of 4.5 when mentally preparing to perform an incompatible action and an average rating of two for compatible actions.
The findings support a new theory developed by Morsella which predicts that the primary role of consciousness is to bring together competing demands on skeletal muscle. Morsella's theory also proposes that consciousness allows individuals to adapt their actions in the future, for example wearing an oven mitt to hold a hot dish.
The results give credence to an interesting idea that 'thinking is for doing,' a framework psychologists are using to explore the link among consciousness, perception and action. "Our findings add to the growing body of evidence that when you prepare to perform two competing actions you prime the same areas of the brain associated with carrying out that same action," Morsella said.
..."

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KTH The Royal Institute of Technology (2013, September 16). Feeling small: Fingers can detect nano-scale wrinkles even on a seemingly smooth surface. ScienceDaily:
Citat: "...
"This means that, if your finger was the size of the Earth, you could feel the difference between houses from cars," Rutland says. "That is one of the most enjoyable aspects of this research. We discovered that a human being can feel a bump corresponding to the size of a very large molecule."
...
The smallest pattern that could be distinguished from the non-patterned surface had grooves with a wavelength of 760 nanometres and an amplitude of only 13 nanometres.
..."

16. januar 2009, computerworld.dk: Forsker: Kunstig intelligens er stadig på babystadiet:
Citat: "...
Hollywood-versionen af intelligente robotter med kunstig intelligens vil dog aldrig komme i nærheden af virkelighedens mekaniske fumlegøjer, der på nuværende tidspunkt knap kan gå opad en trappe uden at vælte.
...
robot-forsker Manuela Veloso fra Carnegie Mellon Universitet i den amerikanske by Pittsburgh.
...
Den portugisiske robot-forsker er med over 200 videnskabelige artikler en sværvægter inden for kunstig intelligens-forskningen, hvor hun har specialiseret sig i fysiske robotter.
..."

6. aug 2010, ing.dk: Menneskehjernen vinder overraskende over udbredt algoritme:
Citat: "...
Computeren mangler overblik
...
[ Horisont-effekten: ]
»Computerprogrammet kan ende i en situation, hvor den finder en ’lokal minimal’ energikonserverende struktur, mens den aldrig kommer frem til det globale energiminimum, dvs. den globalt set bedste struktur,« siger Ole Nørregaard Jensen.
..."

DOE/Los Alamos National Laboratory. (2008, March 12). Insect's Sensory Data Tells A New Story About Neural Networks. ScienceDaily:
Citat: "...
"In this system, the motion-sensitive neurons emit spikes very often and very precisely," said Nemenman. "Historically, people have observed a lot more random spike intervals. This research is a departure from the traditional understanding in that we see that the precision of spike timing that carries information about the fly's rotation is a factor of ten higher than even the most daring previous estimates."
...
"This may be one of the main reasons why artificial neural networks do not perform anywhere comparable to a mammalian visual brain," said Nemenman
..."

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Næste gang skal vi kigge på de dybe net.

Det bliver også interessant at læse om de dybe net.

Hvis du evt. kan belyse hvordan deep learning er bedre end tolags ANN ville det være godt, da jeg synes at have lært at tolags ANN (med eet hidden layer), kan fitte enhver funktion. "Hvad skal vi så med dybe net :-)" Det er dog mange år siden jeg lærte og arbejdede med ANN.

PS: "Input-laget" regner jeg ikke som et lag, men blot som en "holdeplads" for input-værdierne. De ægte lag har et lag af kunstige output-neuroner med tilhørende input-vægte.

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Hvis hjernen var så simpel, at vi mennesker kunne forstå den, ville vi være så dumme, at vi ikke kunne.

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October 10, 2014, scitechdaily.com: Previously Unknown Mechanism Repairs Brain after Stroke:
Citat: "...
The researchers have shown that following an induced stroke in mice, support cells, so-called astrocytes, start to form nerve cells in the injured part of the brain. Using genetic methods to map the fate of the cells, the scientists could demonstrate that astrocytes in this area formed immature nerve cells, which then developed into mature nerve cells.
..."

Friske/nye neuroner rider på motor-proteiner via mikrotubuli-"motorvejene", når de migrerer til rette sted i hjernen:

Drexel University. (2016, May 17). Study shows how neurons reach their final destinations: With a boost from motor proteins, sliding microtubules give nerve cells a smoother ride.. ScienceDaily.

Efter motorvejsturen metamorfer den nye neuron sig til det givne "miljø":

November 10, 2015, Neurons Can Be Changed from One Type Into Another from Within the Brain:
Citat: "...
“What we’ve shown here is that not only neurons can be dramatically changed from one type into another from within the brain,” said Arlotta, who is also an associate member of the Stanley Center for Psychiatric Disease at the Broad Institute of Harvard and M.I.T., but also that “neighboring neurons recognize the reprogrammed cells as different and adapt by changing how they communicate with them.”
..."

Howard Hughes Medical Institute. (2015, October 1). Single neuron may carry over 1,000 mutations. ScienceDaily:
Citat: "...
The majority of these mutations appear to arise while genes are in active use, after brain development is complete.
...
What they found was that every neuron's genome was unique. Each had more than 1,000 point mutations (mutations that alter a single letter of the genetic code), and only a few mutations appeared in more than one cell. What's more, the nature of the variation was not quite what the scientists had expected.
"We expected these mutations to look like cancer mutations," Walsh says, explaining that cancer mutations tend to arise when DNA is imperfectly copied in preparation for cell division, "but in fact they have a unique signature all their own. The mutations that occur in the brain mostly seem to occur when the cells are expressing their genes.
...
In fact, the scientists found, a particular neuron might be more closely related to a cell in the heart than to a neighboring neuron.
..."

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Cell Press. (2016, May 19). Antibiotics that kill gut bacteria also stop growth of new brain cells. ScienceDaily:
Citat: "...
"We found prolonged antibiotic treatment might impact brain function," says senior author Susanne Asu Wolf of the Max-Delbrueck-Center for Molecular Medicine in Berlin, Germany. "But probiotics and exercise can balance brain plasticity and should be considered as a real treatment option."
..."

Får man lavere IQ og EQ fx af at anvende tandpasta med bakteriedræbende stoffer som fx triclosan?:

03.05.2016, Disse fem tandpastaer indeholder problematisk kemi. 32 tandpastaer er blevet gransket af Forbrugerrådet Tænk Kemi:
Citat: "...
Blandt de 32 tandpastaer var der én, der indeholdt det bakteriedræbende konserveringsmiddel triclosan
..."

Bliver fisk og mus "dummere" af at indtage triclosan?:

August 14, 2012, cbsnews.com: Antibacterial agent Triclosan shown to hinder muscle movement in mice, fish: Citat: "...
restrict muscle contractions in mice and fish, leading researchers to ponder what the results can mean for humans.
...
Triclosan is an antibacterial chemical that is found in many household items and throughout the environment
...
We were very surprised that triclosan essentially impaired ECC in both cardiac muscle cells and skeletal muscle cells...It did so at relatively low concentrations and relatively quickly."
..."

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University of California - San Diego. (2015, October 21). Biologists discover bacteria communicate like neurons in the brain. ScienceDaily:
Citat: "...
Biologists have discovered that bacteria -- often viewed as lowly, solitary creatures -- are actually quite sophisticated in their social interactions and communicate with one another through similar electrical signaling mechanisms as neurons in the human brain.
..."

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