the brain of each and every one of you is composed of hundreds of billions of
is composed of hundreds of billions of
is composed of hundreds of billions of neurons also called nerve cells and
neurons also called nerve cells and
neurons also called nerve cells and hundreds of trillions of synapses
hundreds of trillions of synapses
hundreds of trillions of synapses through which an electrical current
through which an electrical current
through which an electrical current flows between the neurons in reaction to
flows between the neurons in reaction to
flows between the neurons in reaction to a stimulus from the outside a wave of
a stimulus from the outside a wave of
a stimulus from the outside a wave of electrical activity traverses this
electrical activity traverses this
electrical activity traverses this network as the brain processes
network as the brain processes
network as the brain processes information the hidden structure in this
information the hidden structure in this
information the hidden structure in this dynamic tapestry has only recently come
dynamic tapestry has only recently come
dynamic tapestry has only recently come to light thanks to the mathematical
to light thanks to the mathematical
to light thanks to the mathematical tools of algebraic topology which is my
tools of algebraic topology which is my
tools of algebraic topology which is my mathematical field during the next 15
mathematical field during the next 15
mathematical field during the next 15 minutes I’m going to guide you on a
minutes I’m going to guide you on a
minutes I’m going to guide you on a mathematical mystery tour of our new
mathematical mystery tour of our new
mathematical mystery tour of our new vision of how the brain functions
vision of how the brain functions
vision of how the brain functions what is connection is to this
what is connection is to this
what is connection is to this constellation of points and lines and
constellation of points and lines and
constellation of points and lines and shapes in the image behind me and how it
shapes in the image behind me and how it
shapes in the image behind me and how it accelerates the development of the new
accelerates the development of the new
accelerates the development of the new field of digital neuroscience with
field of digital neuroscience with
field of digital neuroscience with important implications for our
important implications for our
important implications for our understanding of brain pathologies and
understanding of brain pathologies and
understanding of brain pathologies and for the creation of new drugs to be able
for the creation of new drugs to be able
for the creation of new drugs to be able to test new drugs in a digital
to test new drugs in a digital
to test new drugs in a digital environment and also for the
environment and also for the
environment and also for the amplification of artificial intelligence
amplification of artificial intelligence
amplification of artificial intelligence and machine learning about which you’ve
and machine learning about which you’ve
and machine learning about which you’ve already heard a lot today so the
already heard a lot today so the
already heard a lot today so the research I’m going to be talking to you
research I’m going to be talking to you
research I’m going to be talking to you about is actually related to the brain
about is actually related to the brain
about is actually related to the brain of a rat rather than the brain of a
of a rat rather than the brain of a
of a rat rather than the brain of a human and you might think that that’s
human and you might think that that’s
human and you might think that that’s sort of cheating because the brain of a
sort of cheating because the brain of a
sort of cheating because the brain of a rat is much smaller than that of a human
rat is much smaller than that of a human
rat is much smaller than that of a human as we see here but there are a lot of
as we see here but there are a lot of
as we see here but there are a lot of resemblances nevertheless the structure
resemblances nevertheless the structure
resemblances nevertheless the structure of a brain of a rat is still complex and
of a brain of a rat is still complex and
of a brain of a rat is still complex and despite its small size it’s the
despite its small size it’s the
despite its small size it’s the structure of its neocortex that part of
structure of its neocortex that part of
structure of its neocortex that part of the brain that’s responsible for higher
the brain that’s responsible for higher
the brain that’s responsible for higher functions for sight for hearing for
functions for sight for hearing for
functions for sight for hearing for language in the case of humans for
language in the case of humans for
language in the case of humans for cognition in general is very similar
cognition in general is very similar
cognition in general is very similar between a rat and a human so if we
between a rat and a human so if we
between a rat and a human so if we understand things about the structure of
understand things about the structure of
understand things about the structure of the brain of a rat we will also have
the brain of a rat we will also have
the brain of a rat we will also have learned a lot about the structure of the
learned a lot about the structure of the
learned a lot about the structure of the brain of humans so let’s look more
brain of humans so let’s look more
brain of humans so let’s look more closely at the structure of a brain of a
closely at the structure of a brain of a
closely at the structure of a brain of a rat despite its small size it wears only
rat despite its small size it wears only
rat despite its small size it wears only to ground
to ground
to ground as opposed to 1.2 kilograms for the
as opposed to 1.2 kilograms for the
as opposed to 1.2 kilograms for the brain of a human it has still composed
brain of a human it has still composed
brain of a human it has still composed of hundreds of millions of neurons
of hundreds of millions of neurons
of hundreds of millions of neurons connected by hundreds of billions of
connected by hundreds of billions of
connected by hundreds of billions of synapses so if we’re going to actually
synapses so if we’re going to actually
synapses so if we’re going to actually study this brain and what we’d like to
study this brain and what we’d like to
study this brain and what we’d like to do really is to build some sort of
do really is to build some sort of
do really is to build some sort of digital model of it some computer model
digital model of it some computer model
digital model of it some computer model that it seems like we need a huge amount
that it seems like we need a huge amount
that it seems like we need a huge amount of data in order to go about modeling
of data in order to go about modeling
of data in order to go about modeling this it’s such a big data problem with
this it’s such a big data problem with
this it’s such a big data problem with capital letters big that it’s really not
capital letters big that it’s really not
capital letters big that it’s really not manageable with our current tools not
manageable with our current tools not
manageable with our current tools not only that even collecting the data
only that even collecting the data
only that even collecting the data itself is an impossible problem there’s
itself is an impossible problem there’s
itself is an impossible problem there’s too much data to collect so what can we
too much data to collect so what can we
too much data to collect so what can we do well because the brain is in fact
do well because the brain is in fact
do well because the brain is in fact highly structured we don’t need to make
highly structured we don’t need to make
highly structured we don’t need to make all the measurements in order to create
all the measurements in order to create
all the measurements in order to create this model it’s enough in fact just to
this model it’s enough in fact just to
this model it’s enough in fact just to make a few measurements well chosen and
make a few measurements well chosen and
make a few measurements well chosen and then to construct the model based on
then to construct the model based on
then to construct the model based on that taking advantage of this degree
that taking advantage of this degree
that taking advantage of this degree high degree of organization of the brain
high degree of organization of the brain
high degree of organization of the brain so if we’re going to talk about building
so if we’re going to talk about building
so if we’re going to talk about building a model of the brain we need to talk
a model of the brain we need to talk
a model of the brain we need to talk about what the building blocks are the
about what the building blocks are the
about what the building blocks are the building blocks of the brain and
building blocks of the brain and
building blocks of the brain and therefore of the model for the brain
therefore of the model for the brain
therefore of the model for the brain that we’re going to be talking about are
that we’re going to be talking about are
that we’re going to be talking about are neurons so what is neuron a neuron is
neurons so what is neuron a neuron is
neurons so what is neuron a neuron is the basic processing unit of the brain
the basic processing unit of the brain
the basic processing unit of the brain and they come in many flavors both in
and they come in many flavors both in
and they come in many flavors both in terms of their shapes and in terms of
terms of their shapes and in terms of
terms of their shapes and in terms of their response to electrical stimulus
their response to electrical stimulus
their response to electrical stimulus there are electrical activity because
there are electrical activity because
there are electrical activity because they communicate via electricity now in
they communicate via electricity now in
they communicate via electricity now in the digital reconstruction I’m going to
the digital reconstruction I’m going to
the digital reconstruction I’m going to be talking about which is built by the
be talking about which is built by the
be talking about which is built by the Blue Brain Project at EPFL
Blue Brain Project at EPFL
Blue Brain Project at EPFL they take as input data these neurons
they take as input data these neurons
they take as input data these neurons and they’re particularly interested in
and they’re particularly interested in
and they’re particularly interested in studying was called the somatosensory
studying was called the somatosensory
studying was called the somatosensory cortex of the brain so it’s part of this
cortex of the brain so it’s part of this
cortex of the brain so it’s part of this neocortex it’s roughly here we’re
neocortex it’s roughly here we’re
neocortex it’s roughly here we’re talking about humans and it has to do
talking about humans and it has to do
talking about humans and it has to do with the primary processing of sensory
with the primary processing of sensory
with the primary processing of sensory information touch sight hearing taste
information touch sight hearing taste
information touch sight hearing taste and so on so when the signals first
and so on so when the signals first
and so on so when the signals first arrive in the brain that’s where they’re
arrive in the brain that’s where they’re
arrive in the brain that’s where they’re processed and so we want or the Blue
processed and so we want or the Blue
processed and so we want or the Blue Brain Project wanted to reconstruct this
Brain Project wanted to reconstruct this
Brain Project wanted to reconstruct this part of the brain the input data for
part of the brain the input data for
part of the brain the input data for this reconstruction consists
this reconstruction consists
this reconstruction consists of hundreds and thousands of care
of hundreds and thousands of care
of hundreds and thousands of care painstakingly obtained microscopy images
painstakingly obtained microscopy images
painstakingly obtained microscopy images of all kinds of different neurons that
of all kinds of different neurons that
of all kinds of different neurons that show up in the somatosensory cortex
show up in the somatosensory cortex
show up in the somatosensory cortex there are in fact 55 different types
there are in fact 55 different types
there are in fact 55 different types based on shape and so they took samples
based on shape and so they took samples
based on shape and so they took samples of the 55 different types gathered the
of the 55 different types gathered the
of the 55 different types gathered the data in laboratory and use that as input
data in laboratory and use that as input
data in laboratory and use that as input but we’re going to talk not only about
but we’re going to talk not only about
but we’re going to talk not only about the structure of the brain but also its
the structure of the brain but also its
the structure of the brain but also its function it’s active because your brain
function it’s active because your brain
function it’s active because your brain you your not your brain is actually
you your not your brain is actually
you your not your brain is actually doing things right you hope so anyway
doing things right you hope so anyway
doing things right you hope so anyway and so you need to understand his
and so you need to understand his
and so you need to understand his activity and for that you need to know
activity and for that you need to know
activity and for that you need to know something about the electrical behavior
something about the electrical behavior
something about the electrical behavior of these neurons so they were also very
of these neurons so they were also very
of these neurons so they were also very intricate complex experiments carried
intricate complex experiments carried
intricate complex experiments carried out in laboratories to measure the
out in laboratories to measure the
out in laboratories to measure the electrical response of neurons to
electrical response of neurons to
electrical response of neurons to different stimuli and that is also input
different stimuli and that is also input
different stimuli and that is also input data for this model given this input
data for this model given this input
data for this model given this input data it was run through a supercomputer
data it was run through a supercomputer
data it was run through a supercomputer which is based here in Ticino actually I
which is based here in Ticino actually I
which is based here in Ticino actually I think even in Lugano the blue-jean
think even in Lugano the blue-jean
think even in Lugano the blue-jean computer which reconstructs the model
computer which reconstructs the model
computer which reconstructs the model and so we end up with a model that shows
and so we end up with a model that shows
and so we end up with a model that shows how all these neurons are connected i
how all these neurons are connected i
how all these neurons are connected i have luck to work with a fantastic
have luck to work with a fantastic
have luck to work with a fantastic visualization team at the Blue Brain
visualization team at the Blue Brain
visualization team at the Blue Brain Project who created this image of a
Project who created this image of a
Project who created this image of a couple of neurons and how they’re
couple of neurons and how they’re
couple of neurons and how they’re communicating to each other so the sort
communicating to each other so the sort
communicating to each other so the sort of blobs you see are the sohma’s or cell
of blobs you see are the sohma’s or cell
of blobs you see are the sohma’s or cell bodies of the neurons which are their
bodies of the neurons which are their
bodies of the neurons which are their primary processing units the sort of
primary processing units the sort of
primary processing units the sort of tendrils you see are the axons and
tendrils you see are the axons and
tendrils you see are the axons and dendrites of the neurons which are the
dendrites of the neurons which are the
dendrites of the neurons which are the sort of the communication wires so
sort of the communication wires so
sort of the communication wires so signal flows through a neuron from its
signal flows through a neuron from its
signal flows through a neuron from its dendrites into the soma and then out
dendrites into the soma and then out
dendrites into the soma and then out through the axon the sort of bright
through the axon the sort of bright
through the axon the sort of bright spots that you see okay there are touch
spots that you see okay there are touch
spots that you see okay there are touch points between the axon the one neuron
points between the axon the one neuron
points between the axon the one neuron and the dendrite of the next those are
and the dendrite of the next those are
and the dendrite of the next those are the synapses where you see electrical
the synapses where you see electrical
the synapses where you see electrical activity happening synapses act as sort
activity happening synapses act as sort
activity happening synapses act as sort of valves electricity flows in one
of valves electricity flows in one
of valves electricity flows in one direction through the synapse from the
direction through the synapse from the
direction through the synapse from the axon of one neuron called the
axon of one neuron called the
axon of one neuron called the presynaptic neuron to the dendrite of a
presynaptic neuron to the dendrite of a
presynaptic neuron to the dendrite of a second neuron called the postsynaptic
second neuron called the postsynaptic
second neuron called the postsynaptic neuron so we need this basic lesson in
neuron so we need this basic lesson in
neuron so we need this basic lesson in neuroscience in order to understand the
neuroscience in order to understand the
neuroscience in order to understand the construction of the model and then how
construction of the model and then how
construction of the model and then how we’re going to go about simplifying it
we’re going to go about simplifying it
we’re going to go about simplifying it afterwards so what we’re going to do is
afterwards so what we’re going to do is
afterwards so what we’re going to do is how to come up with some sort of
how to come up with some sort of
how to come up with some sort of geometric abstraction abstract
geometric abstraction abstract
geometric abstraction abstract representation of this network of
representation of this network of
representation of this network of neurons and it’s this mathematical
neurons and it’s this mathematical
neurons and it’s this mathematical abstraction you’re going to be able to
abstraction you’re going to be able to
abstraction you’re going to be able to study to quantify it to be able to say
study to quantify it to be able to say
study to quantify it to be able to say more about the structure of the brain
more about the structure of the brain
more about the structure of the brain and what the role of that structure is
and what the role of that structure is
and what the role of that structure is for the function of the brain so in more
for the function of the brain so in more
for the function of the brain so in more detail before we talk about those
detail before we talk about those
detail before we talk about those mathematical models let’s talk more
mathematical models let’s talk more
mathematical models let’s talk more about how the blue brain model of the
about how the blue brain model of the
about how the blue brain model of the brain is constructed what the scientists
brain is constructed what the scientists
brain is constructed what the scientists do is they’re looking at us what you
do is they’re looking at us what you
do is they’re looking at us what you could think of as a sort of core sample
could think of as a sort of core sample
could think of as a sort of core sample of the somatosensory cortex so this you
of the somatosensory cortex so this you
of the somatosensory cortex so this you know you sort of would imagine
know you sort of would imagine
know you sort of would imagine drilling down into somatosensory cortex
drilling down into somatosensory cortex
drilling down into somatosensory cortex you take a little core sample that’s
you take a little core sample that’s
you take a little core sample that’s only about two millimeters high and
only about two millimeters high and
only about two millimeters high and about half a millimeter in diameter and
about half a millimeter in diameter and
about half a millimeter in diameter and this core sample like an archaeological
this core sample like an archaeological
this core sample like an archaeological core sample for example has different
core sample for example has different
core sample for example has different layers there are six different layers
layers there are six different layers
layers there are six different layers and a lot is known about how many
and a lot is known about how many
and a lot is known about how many neurons of which type you will find in
neurons of which type you will find in
neurons of which type you will find in each layer roughly where there should be
each layer roughly where there should be
each layer roughly where there should be so the algorithm that they designed
so the algorithm that they designed
so the algorithm that they designed that’s run through the supercomputer
that’s run through the supercomputer
that’s run through the supercomputer here positions
here positions
here positions different kinds of neurons in the
different kinds of neurons in the
different kinds of neurons in the different layers according to this
different layers according to this
different layers according to this biological rule of thumb not only that
biological rule of thumb not only that
biological rule of thumb not only that since diversity is so important in
since diversity is so important in
since diversity is so important in nature in many ways it’s important to
nature in many ways it’s important to
nature in many ways it’s important to come of diversity of shapes of the
come of diversity of shapes of the
come of diversity of shapes of the neurons so the shapes that are extract
neurons so the shapes that are extract
neurons so the shapes that are extract from microscopy also tweaked a little
from microscopy also tweaked a little
from microscopy also tweaked a little bit so that you get a wide palette of
bit so that you get a wide palette of
bit so that you get a wide palette of different shapes of neurons that go into
different shapes of neurons that go into
different shapes of neurons that go into this process then the final stage is to
this process then the final stage is to
this process then the final stage is to figure out where their neurons are
figure out where their neurons are
figure out where their neurons are connecting together they have to be able
connecting together they have to be able
connecting together they have to be able to pass a signal from one to the other
to pass a signal from one to the other
to pass a signal from one to the other we have to figure out where the synapses
we have to figure out where the synapses
we have to figure out where the synapses are and so that’s the next step in the
are and so that’s the next step in the
are and so that’s the next step in the process which is actually a complicated
process which is actually a complicated
process which is actually a complicated four step algorithm of which I will
four step algorithm of which I will
four step algorithm of which I will spare you the details today so at the
spare you the details today so at the
spare you the details today so at the end of this anatomical process one ends
end of this anatomical process one ends
end of this anatomical process one ends up with what we call the microcircuit so
up with what we call the microcircuit so
up with what we call the microcircuit so it’s a digital representation of this
it’s a digital representation of this
it’s a digital representation of this part of the somatosensory cortex with
part of the somatosensory cortex with
part of the somatosensory cortex with its six layers 31,000 neurons connected
its six layers 31,000 neurons connected
its six layers 31,000 neurons connected by 37 million simpson OPS’s and we see
by 37 million simpson OPS’s and we see
by 37 million simpson OPS’s and we see these beautiful layers and they have we
these beautiful layers and they have we
these beautiful layers and they have we have different types of neurons that are
have different types of neurons that are
have different types of neurons that are the excitatory neurons which are
the excitatory neurons which are
the excitatory neurons which are boosting the signal and getting the
boosting the signal and getting the
boosting the signal and getting the party more excited and then you have the
party more excited and then you have the
party more excited and then you have the police neurons whoa
police neurons whoa
police neurons whoa well the inhibitory neurons who show up
well the inhibitory neurons who show up
well the inhibitory neurons who show up at the party and say turn down the
at the party and say turn down the
at the party and say turn down the volume please because you’ll have these
volume please because you’ll have these
volume please because you’ll have these both kind of notes because otherwise
both kind of notes because otherwise
both kind of notes because otherwise things would get kind of out of control
things would get kind of out of control
things would get kind of out of control so we can make this simulation or can
so we can make this simulation or can
so we can make this simulation or can build this digital reconstruction and
build this digital reconstruction and
build this digital reconstruction and this tells us about the structure of
this tells us about the structure of
this tells us about the structure of this part of the brain of the rat but
this part of the brain of the rat but
this part of the brain of the rat but what we really care about is its
what we really care about is its
what we really care about is its function how it becomes active so for
function how it becomes active so for
function how it becomes active so for that we need to integrate into this
that we need to integrate into this
that we need to integrate into this model physiological information
model physiological information
model physiological information responds to electrical stimuli and
responds to electrical stimuli and
responds to electrical stimuli and that’s where this other experimental
that’s where this other experimental
that’s where this other experimental data comes in and so what the modelers
data comes in and so what the modelers
data comes in and so what the modelers do is they include information about all
do is they include information about all
do is they include information about all the possible electrical reactions of
the possible electrical reactions of
the possible electrical reactions of different types of neurons to input
different types of neurons to input
different types of neurons to input stimuli even neurons of the same shape
stimuli even neurons of the same shape
stimuli even neurons of the same shape may have different electrical behaviors
may have different electrical behaviors
may have different electrical behaviors then they take into account the fact
then they take into account the fact
then they take into account the fact that synapses have come in many many
that synapses have come in many many
that synapses have come in many many many different flavors and they built
many different flavors and they built
many different flavors and they built that into it as well once that has been
that into it as well once that has been
that into it as well once that has been built into the model you actually have a
built into the model you actually have a
built into the model you actually have a circuit they can react to input stimuli
circuit they can react to input stimuli
circuit they can react to input stimuli you can patch a bunch of these together
you can patch a bunch of these together
you can patch a bunch of these together and have a biologically remarkably
and have a biologically remarkably
and have a biologically remarkably accurate model of a piece of neural
accurate model of a piece of neural
accurate model of a piece of neural tissue when which you can perform
tissue when which you can perform
tissue when which you can perform experiments by inputting different kinds
experiments by inputting different kinds
experiments by inputting different kinds of stimuli this is an example of what it
of stimuli this is an example of what it
of stimuli this is an example of what it looks like when you input stimuli to one
looks like when you input stimuli to one
looks like when you input stimuli to one of these virtual pieces of neural tissue
of these virtual pieces of neural tissue
of these virtual pieces of neural tissue you see this electrical activity that is
you see this electrical activity that is
you see this electrical activity that is spreading you have a sort of beautiful
spreading you have a sort of beautiful
spreading you have a sort of beautiful tapestry of sort of random spiking
tapestry of sort of random spiking
tapestry of sort of random spiking that’s going on so these electrical
that’s going on so these electrical
that’s going on so these electrical discharges we see are called spikes by
discharges we see are called spikes by
discharges we see are called spikes by the neuroscientists and you see the sort
the neuroscientists and you see the sort
the neuroscientists and you see the sort of wave of activity spreading across
of wave of activity spreading across
of wave of activity spreading across this network and you’d really like to
this network and you’d really like to
this network and you’d really like to understand it looks very random you
understand it looks very random you
understand it looks very random you can’t walk how can we describe how can
can’t walk how can we describe how can
can’t walk how can we describe how can we quantify how can we characterize this
we quantify how can we characterize this
we quantify how can we characterize this behavior when this beautiful wave of
behavior when this beautiful wave of
behavior when this beautiful wave of electricity sweeps across there what
electricity sweeps across there what
electricity sweeps across there what exactly is going on so for that we need
exactly is going on so for that we need
exactly is going on so for that we need new mathematical tools so if we look at
new mathematical tools so if we look at
new mathematical tools so if we look at this network of neurons again another
this network of neurons again another
this network of neurons again another beautiful visualization by the team at
beautiful visualization by the team at
beautiful visualization by the team at Blue Brain you can say well what sort of
Blue Brain you can say well what sort of
Blue Brain you can say well what sort of mathematical structures are hidden the
mathematical structures are hidden the
mathematical structures are hidden the thicket of connections in this neural
thicket of connections in this neural
thicket of connections in this neural network or through what sort of filter
network or through what sort of filter
network or through what sort of filter should one look in order to discern
should one look in order to discern
should one look in order to discern what’s going on and that’s where my my
what’s going on and that’s where my my
what’s going on and that’s where my my kind of mathematics algebraic topology
kind of mathematics algebraic topology
kind of mathematics algebraic topology is going to come into play
is going to come into play
is going to come into play but before that let’s talk about what we
but before that let’s talk about what we
but before that let’s talk about what we need to think about how we can abstract
need to think about how we can abstract
need to think about how we can abstract this representation of the circuit in
this representation of the circuit in
this representation of the circuit in order to even apply any kind of
order to even apply any kind of
order to even apply any kind of mathematics to it so in order to get
mathematics to it so in order to get
mathematics to it so in order to get here today if you’re not from Lugano you
here today if you’re not from Lugano you
here today if you’re not from Lugano you probably needed a map of Lugano in order
probably needed a map of Lugano in order
probably needed a map of Lugano in order to find the lock so that means that
to find the lock so that means that
to find the lock so that means that you’re used to thinking about an
you’re used to thinking about an
you’re used to thinking about an abstract representation of a real
abstract representation of a real
abstract representation of a real complex object if you look at a map of
complex object if you look at a map of
complex object if you look at a map of Lugano it’s telling you the essential
Lugano it’s telling you the essential
Lugano it’s telling you the essential information you need to know about
information you need to know about
information you need to know about Nagano in order to get from here to
Nagano in order to get from here to
Nagano in order to get from here to there but it doesn’t tell you everything
there but it doesn’t tell you everything
there but it doesn’t tell you everything about Nagano we’re gonna do the same
about Nagano we’re gonna do the same
about Nagano we’re gonna do the same sort of abstract representation of this
sort of abstract representation of this
sort of abstract representation of this circuit of neurons in order to be able
circuit of neurons in order to be able
circuit of neurons in order to be able to reduce this problem something we can
to reduce this problem something we can
to reduce this problem something we can actually study so this is about
actually study so this is about
actually study so this is about connectivity how are neurons connected
connectivity how are neurons connected
connectivity how are neurons connected together and how many ways because you
together and how many ways because you
together and how many ways because you could have sort of sequences of neurons
could have sort of sequences of neurons
could have sort of sequences of neurons that are all connected together by
that are all connected together by
that are all connected together by synapses but you could have many
synapses but you could have many
synapses but you could have many different patterns paths of synapses
different patterns paths of synapses
different patterns paths of synapses they would get you from one to another
they would get you from one to another
they would get you from one to another that’s the sort of question we’re
that’s the sort of question we’re
that’s the sort of question we’re interested in studying so in order to do
interested in studying so in order to do
interested in studying so in order to do this we’re going to talk about the
this we’re going to talk about the
this we’re going to talk about the topologist version of the map of Lugano
topologist version of the map of Lugano
topologist version of the map of Lugano we’re going to represent neuron just by
we’re going to represent neuron just by
we’re going to represent neuron just by a dot so it’s something zero dimensional
a dot so it’s something zero dimensional
a dot so it’s something zero dimensional a mathematician would say a dot then a
a mathematician would say a dot then a
a mathematician would say a dot then a connection between two neurons is gonna
connection between two neurons is gonna
connection between two neurons is gonna be represented by something
be represented by something
be represented by something one-dimensional a little line segment
one-dimensional a little line segment
one-dimensional a little line segment going from one to the other and since as
going from one to the other and since as
going from one to the other and since as I said the synapses are unidirectional
I said the synapses are unidirectional
I said the synapses are unidirectional they act like valves electricity flows
they act like valves electricity flows
they act like valves electricity flows in one direction we put a little arrow
in one direction we put a little arrow
in one direction we put a little arrow on the edge to indicate the flow
on the edge to indicate the flow
on the edge to indicate the flow information like this so that’s how
information like this so that’s how
information like this so that’s how we’re going to be representing
we’re going to be representing
we’re going to be representing connections between neurons but
connections between neurons but
connections between neurons but sometimes you’re going to get a whole
sometimes you’re going to get a whole
sometimes you’re going to get a whole bunch of neurons that are working
bunch of neurons that are working
bunch of neurons that are working together a family of neurons that are
together a family of neurons that are
together a family of neurons that are connected together and they’re forming
connected together and they’re forming
connected together and they’re forming what we call directed sympathies that’s
what we call directed sympathies that’s
what we call directed sympathies that’s our fancy word for these sorts of
our fancy word for these sorts of
our fancy word for these sorts of especially important connectivity
especially important connectivity
especially important connectivity structures so for the in the case of the
structures so for the in the case of the
structures so for the in the case of the three neurons the three dots that are
three neurons the three dots that are
three neurons the three dots that are represented there that are all connected
represented there that are all connected
represented there that are all connected we’re looking at a family of neurons
we’re looking at a family of neurons
we’re looking at a family of neurons that are all connected together in such
that are all connected together in such
that are all connected together in such a way that they’re working together to
a way that they’re working together to
a way that they’re working together to force the flow of information from an
force the flow of information from an
force the flow of information from an input to an output that are labeled
input to an output that are labeled
input to an output that are labeled they’re a source and then a sink
they’re a source and then a sink
they’re a source and then a sink in the case of the 3d object then we
in the case of the 3d object then we
in the case of the 3d object then we have four different neurons that are all
have four different neurons that are all
have four different neurons that are all working together in a family to ensure
working together in a family to ensure
working together in a family to ensure the flow of information from the source
the flow of information from the source
the flow of information from the source to the sink there’s always there’s a
to the sink there’s always there’s a
to the sink there’s always there’s a unambiguous flow of information in one
unambiguous flow of information in one
unambiguous flow of information in one direction and these go even higher
direction and these go even higher
direction and these go even higher dimensions we can even talk about
dimensions we can even talk about
dimensions we can even talk about four-dimensional things which a little
four-dimensional things which a little
four-dimensional things which a little hard to represent on a flat screen but
hard to represent on a flat screen but
hard to represent on a flat screen but this is the idea that we would have five
this is the idea that we would have five
this is the idea that we would have five neurons they were all working together
neurons they were all working together
neurons they were all working together to encourage the flow of information
to encourage the flow of information
to encourage the flow of information from source to sink and what our
from source to sink and what our
from source to sink and what our experiences have shown is that the
experiences have shown is that the
experiences have shown is that the higher the dimension of a simplex like
higher the dimension of a simplex like
higher the dimension of a simplex like this the more highly coordinate of the
this the more highly coordinate of the
this the more highly coordinate of the electrical behavior of the neurons is
electrical behavior of the neurons is
electrical behavior of the neurons is this shows that it really takes a team
this shows that it really takes a team
this shows that it really takes a team to work together towards the same target
to work together towards the same target
to work together towards the same target and then you can really boost the signal
and then you can really boost the signal
and then you can really boost the signal this has really come out very clearly in
this has really come out very clearly in
this has really come out very clearly in our experiments so these are important
our experiments so these are important
our experiments so these are important things to study now when you give the
things to study now when you give the
things to study now when you give the child a collection of blocks we can
child a collection of blocks we can
child a collection of blocks we can think of these directives simplices
think of these directives simplices
think of these directives simplices blocks they’re going to take the blocks
blocks they’re going to take the blocks
blocks they’re going to take the blocks and build more complex structures a
and build more complex structures a
and build more complex structures a castle for example from the blocks the
castle for example from the blocks the
castle for example from the blocks the important features of the castle are
important features of the castle are
important features of the castle are going to be its windows its rooms its
going to be its windows its rooms its
going to be its windows its rooms its doors and such and similarly when we
doors and such and similarly when we
doors and such and similarly when we look at the network of neurons the
look at the network of neurons the
look at the network of neurons the directed simplices that we see that a
directed simplices that we see that a
directed simplices that we see that a network of neurons also build complex
network of neurons also build complex
network of neurons also build complex structures that have important features
structures that have important features
structures that have important features that look like windows and rooms and so
that look like windows and rooms and so
that look like windows and rooms and so on so for example from a bunch of one
on so for example from a bunch of one
on so for example from a bunch of one dimensional simplices you can build
dimensional simplices you can build
dimensional simplices you can build together something that looks like a
together something that looks like a
together something that looks like a window do you think of that as a cavity
window do you think of that as a cavity
window do you think of that as a cavity in a more general language we can also
in a more general language we can also
in a more general language we can also do this in higher dimensions we can take
do this in higher dimensions we can take
do this in higher dimensions we can take what we call these two dimensional
what we call these two dimensional
what we call these two dimensional simplices each of which is built from
simplices each of which is built from
simplices each of which is built from three neurons which you can think of as
three neurons which you can think of as
three neurons which you can think of as triangular blocks if you ache eight take
triangular blocks if you ache eight take
triangular blocks if you ache eight take eight of these triangular blocks and you
eight of these triangular blocks and you
eight of these triangular blocks and you glue them together along the edges you
glue them together along the edges you
glue them together along the edges you can build a nice box which is hollow on
can build a nice box which is hollow on
can build a nice box which is hollow on the inside so this is another notion of
the inside so this is another notion of
the inside so this is another notion of a cavity and these works in higher and
a cavity and these works in higher and
a cavity and these works in higher and higher dimensions as well now remember
higher dimensions as well now remember
higher dimensions as well now remember these dimensions are not sort of real in
these dimensions are not sort of real in
these dimensions are not sort of real in some sense these are geometric
some sense these are geometric
some sense these are geometric representations of the structures in the
representations of the structures in the
representations of the structures in the neural network so how many of these
neural network so how many of these
neural network so how many of these things are there in the network the
things are there in the network the
things are there in the network the microcircuitry built and are there more
microcircuitry built and are there more
microcircuitry built and are there more than you would see in a random circuit
than you would see in a random circuit
than you would see in a random circuit turns out they the answer is yes what
turns out they the answer is yes what
turns out they the answer is yes what this graph is showing us if we look at
this graph is showing us if we look at
this graph is showing us if we look at the blue curve
the blue curve
the blue curve it tells us the number of simplices of
it tells us the number of simplices of
it tells us the number of simplices of different dimensions that we find in the
different dimensions that we find in the
different dimensions that we find in the blue brain microcircuit and we said that
blue brain microcircuit and we said that
blue brain microcircuit and we said that tens of millions of two dimensional
tens of millions of two dimensional
tens of millions of two dimensional three dimensional simplices millions of
three dimensional simplices millions of
three dimensional simplices millions of four dimensional simplices and you can’t
four dimensional simplices and you can’t
four dimensional simplices and you can’t see it on this graph but they’re
see it on this graph but they’re
see it on this graph but they’re actually lots of five six and seven
actually lots of five six and seven
actually lots of five six and seven dimensional simplices which means you
dimensional simplices which means you
dimensional simplices which means you have up to eight neurons that are all
have up to eight neurons that are all
have up to eight neurons that are all working together to amplify the signal
working together to amplify the signal
working together to amplify the signal and to send it along moving average the
and to send it along moving average the
and to send it along moving average the green curve for example which is just a
green curve for example which is just a
green curve for example which is just a randomly connected network we see it’s
randomly connected network we see it’s
randomly connected network we see it’s much less complex so that the biology is
much less complex so that the biology is
much less complex so that the biology is giving us complexity in this structure
giving us complexity in this structure
giving us complexity in this structure which is important we need that
which is important we need that
which is important we need that complexity in order to be for the brain
complexity in order to be for the brain
complexity in order to be for the brain to function properly what we see here is
to function properly what we see here is
to function properly what we see here is what’s actually going on with activity
what’s actually going on with activity
what’s actually going on with activity we’re measuring activity now and the
we’re measuring activity now and the
we’re measuring activity now and the video that’s turning on the Left is
video that’s turning on the Left is
video that’s turning on the Left is showing us little snapshots of activity
showing us little snapshots of activity
showing us little snapshots of activity in the network the line segments that
in the network the line segments that
in the network the line segments that you see are actually connections that
you see are actually connections that
you see are actually connections that are active during that particular
are active during that particular
are active during that particular snapshot which gives us in each case for
snapshot which gives us in each case for
snapshot which gives us in each case for each of these snapshots a little sub
each of these snapshots a little sub
each of these snapshots a little sub network to analyze in the same way what
network to analyze in the same way what
network to analyze in the same way what the curves are showing us is the
the curves are showing us is the
the curves are showing us is the reaction of the whole network to stimuli
reaction of the whole network to stimuli
reaction of the whole network to stimuli to three different stimuli and we see
to three different stimuli and we see
to three different stimuli and we see that what happens is there are
that what happens is there are
that what happens is there are one-dimensional structures that appear
one-dimensional structures that appear
one-dimensional structures that appear and then as these ones the mental
and then as these ones the mental
and then as these ones the mental structures these one-dimensional
structures these one-dimensional
structures these one-dimensional cavities like windows are starting to
cavities like windows are starting to
cavities like windows are starting to disappear there are three-dimensional
disappear there are three-dimensional
disappear there are three-dimensional ones that come up then it regions are
ones that come up then it regions are
ones that come up then it regions are sort of a combination at which point it
sort of a combination at which point it
sort of a combination at which point it collapses so as the brain is processing
collapses so as the brain is processing
collapses so as the brain is processing information it’s creating sort of
information it’s creating sort of
information it’s creating sort of virtual sandcastles that are
virtual sandcastles that are
virtual sandcastles that are increasingly complex and then all of a
increasingly complex and then all of a
increasingly complex and then all of a sudden it Rives at the end of
sudden it Rives at the end of
sudden it Rives at the end of information processing and the whole
information processing and the whole
information processing and the whole thing washes away like a wave washing a
thing washes away like a wave washing a
thing washes away like a wave washing a sandcastle off the beach so what can we
sandcastle off the beach so what can we
sandcastle off the beach so what can we say about the future of digital
say about the future of digital
say about the future of digital neuroscience algebraic topology has
neuroscience algebraic topology has
neuroscience algebraic topology has given us the tools to discern the hidden
given us the tools to discern the hidden
given us the tools to discern the hidden structure in the brain and in its
structure in the brain and in its
structure in the brain and in its function and understand how the shape of
function and understand how the shape of
function and understand how the shape of the structure shapes its function so we
the structure shapes its function so we
the structure shapes its function so we need to push this further and see maybe
need to push this further and see maybe
need to push this further and see maybe what happens as we start learning in the
what happens as we start learning in the
what happens as we start learning in the brain on the other hand we can now now
brain on the other hand we can now now
brain on the other hand we can now now that we know something about normals
that we know something about normals
that we know something about normals function should look like we can start
function should look like we can start
function should look like we can start to say what is malfunctioning going to
to say what is malfunctioning going to
to say what is malfunctioning going to look like how can we characterize a
look like how can we characterize a
look like how can we characterize a brain that’s not functioning properly so
brain that’s not functioning properly so
brain that’s not functioning properly so this should give us a tool
this should give us a tool
this should give us a tool better understand brain pathologies we
better understand brain pathologies we
better understand brain pathologies we can also as I said test drugs on here
can also as I said test drugs on here
can also as I said test drugs on here and now that we’ve learned more about
and now that we’ve learned more about
and now that we’ve learned more about which structures in a network leads to
which structures in a network leads to
which structures in a network leads to better function then we may be weak
better function then we may be weak
better function then we may be weak there people who are doing artificial
there people who are doing artificial
there people who are doing artificial intelligence and machine learning can
intelligence and machine learning can
intelligence and machine learning can use this knowledge to amplify their
use this knowledge to amplify their
use this knowledge to amplify their artificial neural networks the future of
artificial neural networks the future of
artificial neural networks the future of digital neuroscience is bright and I
digital neuroscience is bright and I
digital neuroscience is bright and I strongly encourage young people who love
strongly encourage young people who love
strongly encourage young people who love mathematics and who are passionate about
mathematics and who are passionate about
mathematics and who are passionate about the brain and want to curious about how
the brain and want to curious about how
the brain and want to curious about how it functions to consider a digital
it functions to consider a digital
it functions to consider a digital neuroscience as their profession for the
neuroscience as their profession for the
neuroscience as their profession for the future thank you very much
future thank you very much
future thank you very much [Applause]
”
Be First to Comment