ChapterPDF Available

Circuital and Developmental Explanations for the Cortex

Authors:

Abstract

The cerebral cortex manifests a paradox, which puzzles researchers since early neuroscience: despite a strikingly uniform structure, the functional repertoire of the cortex is incredibly vast. The purpose of this work is to analyze the phenomenon of the apparent clash between uniformity and variety of functions, and to pinpoint the sort of explanations that this phenomenon requests. A possible resolution of this paradox has been proposed several times in terms of a basic neural circuit so successful to underlie all cortical functions. Circuital models have the virtue of belonging to the mechanistic framework of explanation, and have greatly improved the understanding of computational properties of the cortex. However, they all fall short of explaining the contrast between uniformity and multiplicity of functions in the cortex. One reason for this failure is in neglecting the developmental aspect of the cortex, the most likely source of variation in functions. In biology, developmental explanations are receiving increasing attention, but are often contrasted with mech-anistic ones. I contend that, in the case at hand, the explanandum of the development differs from the ones usually found in developmental biology, and developmental aspects in the cortex can be taken into account within a mechanistic explanation.
Chapter 3
Circuital and Developmental Explanations for
the Cortex
Alessio Plebe
Abstract The cerebral cortex manifests a paradox, which puzzles researchers since
early neuroscience: despite a strikingly uniform structure, the functional repertoire of
the cortex is incredibly vast. The purpose of this work is to analyze the phenomenon
of the apparent clash between uniformity and variety of functions, and to pinpoint
the sort of explanations that this phenomenon requests. A possible resolution of
this paradox has been proposed several times in terms of a basic neural circuit so
successful to underlie all cortical functions. Circuital models have the virtue of be-
longing to the mechanistic framework of explanation, and have greatly improved the
understanding of computational properties of the cortex. However, they all fall short
of explaining the contrast between uniformity and multiplicity of functions in the
cortex. One reason for this failure is in neglecting the developmental aspect of the
cortex, the most likely source of variation in functions. In biology, developmental
explanations are receiving increasing attention, but are often contrasted with mech-
anistic ones. I contend that, in the case at hand, the explanandum of the development
differs from the ones usually found in developmental biology, and developmental
aspects in the cortex can be taken into account within a mechanistic explanation.
Key words: cerebral cortex; canonical circuit; developmental explanation; mecha-
nistic explanation
Alessio Plebe
Department of Cognitive Science
University of Messina, Italy
e-mail: aplebe@unime.it
1
2 Alessio Plebe
3.1 Introduction
It is well agreed upon that the mammalian neocortex is the site of processes en-
abling higher cognition from consciousness to symbolic reasoning and, for humans,
language (Miller et al, 2002; Fuster, 2008; Noack, 2012). Why the particular way
neurons are combined in the cortex makes such a difference with respect to the rest
of the brain is still, after a century of research, largely unknown. Edinger (1904) was
one of the first to rank mammals as the most intelligent animals, in virtue of the brand
new layered brain equipment introduced by nature. Although current comparative
cognition has weakened this intellectual superiority, the cortex is still considered to
be the crowning achievement of brain evolution, and the quest for an understanding
of its computational properties is among the most prominent and yet unresolved
issues in neuroscience.
This chapter addresses one of the most puzzling facts of the cortex: the clash
between the strikingly uniform structure of the cortex, and the breadth of its functional
repertoire. This paradox will be spelled out precisely in §3.2 and the consistency of
its premises will be assessed. Such paradox has been often cited by neuroscientists as
the motivation for searching a fundamental circuit responsible for the computational
power of the cortex, often called “canonical circuit” (Plebe, 2018).
How these circuits are conceived, and their achievements, will be discussed
in §3.3. This is currently the mainstream line of research on the cortex, which
extends up to the large-scale brain simulation projects (Markram et al, 2015). An
epistemological virtue of the circuital direction of research is that canonical models
may broadly qualify as mechanistic. However, they all fall short of explaining the
contrast between uniformity and multiplicity of functions in the cortex. The main
reason is that circuital models neglect the developmental aspect of the cortex, which
is of paramount importance in the diversification of functions across cortical areas.
Development is not just crucial for the early diversification of cortical functions, it
is an everyday business for the cortex, as detailed in §3.2.2.
Developmental explanation in biology is anything but new (Waddington, 1957;
Gottlieb, 1971), however it remained marginal until recently. Today developmentally
oriented explanations and epigenetics have become mainstream (Baedke, 2018),
stirring a growing philosophical debate on the explanatory standards in biology.
Several philosophers have claimed that developmental explanations are distinct and
irreducible to mechanistic explanations (Mc Manus, 2012; Parkkinen, 2014). How-
ever, as discussed in §3.4, the standard cases these philosophers have in mind are
quite different from the case of the cortex, which seems to fit well into a multi-level
mechanistic explanation.
Even if research on combining developmental mechanisms with basic cortical cir-
cuits is still marginal with respect to the mainstream research, examples of proposals
in this direction are described in §3.5. These models may qualify as mechanistic
sketch, even if incomplete.
3 Circuital and Developmental Explanations for the Cortex 3
3.2 Explanandum and explanations for the cortex
In a first approximation much of the research on the cerebral cortex aims at progress-
ing in some way the answer to the question “how does the cortex work?”.
To answer this general question, among the contributions that may broadly qualify
as mechanistic, one can include the identification of the layered structure of the cortex
and, within it, the structure of specific classes of neurons with their interconnections
(Ramón y Cajal, 1891; Lorente de Nó, 1938; Braak, 1980; Nieuwenhuys, 1994).
Since much of the activity in the cortex is electrical, a privileged path to an answer
to the general question might be the search of some fundamental structure in the
cortex processing electrical signals. This is the kind of explanation sought by the
“canonical circuits” research effort (Plebe, 2018) that will be shortly summarized in
§3.3.
However, the mammalian cortex is a very special part of the brain and requires
explanations to peculiar sorts of phenomena. I argue that the most compelling phe-
nomenon is the combination of the following two facts:
P1the cortex is remarkably uniform;
P2the cortex is the main site of a bewilderingly variety of functions.
The clash between uniformity in structure and variability in the performed func-
tions is echoed by many neuroscientists when writing about the cortex, I collected
here just few quotations:
The mammalian cerebral neocortex can learn to perform a wide variety of tasks, yet its
structure is strikingly uniform. It is natural to wonder whether this uniformity reflects the
use of rather few underlying methods of organizing information (Marr, 1970, p.163)
The apparent uniformity of the neocortex has given rise to the speculation that [. . . ] is
designed to perform the same basic operation, or ‘computation’ as it is now fashionable to
call it. [. . . ] The tempting notion is then that nature’s laboratory has hit on a process that
enables it to use the same machinery for very different ends. If this attractive view is correct,
the $64000 question is then: what is the cortex doing with its inputs?
(Martin, 1988, p.639–640)
Neurobiological studies have shown that cortical circuits have a distinctive modular and lam-
inar structure, with stereotypical connections between neurons that are repeated throughout
many cortical areas. It has been conjectured that these stereotypical canonical microcircuits
are [. . . ] advantageous for generic computational operations that are carried out throughout
the neocortex (Haeusler et al, 2009, p.73)
The neocortex is the brain structure most commonly believed to give us our unique cognitive
abilities. Yet the cellular organization of the neocortex is broadly similar not only between
species but also between cortical areas. (Harris and Shepherd, 2015, p.170)
The cerebral cortex performs a wide range of cognitive tasks in mammals [. . . ] Yet it pro-
cesses these diverse tasks with what appears to be a remarkably uniform, primarily six-layer
architecture [. . . ] This has long suggested the idea that a piece of six-layer cortex with a sur-
face area on the order of a square millimeter constitutes a fundamental cortical ’processing
unit’
4 Alessio Plebe
(Miller, 2016, p.75)
Before discussing what sort of explanation this paradox requires, let me scrutinize
propositions P1and P2and check if they really lead to a paradox. Premise P2
is quite straightforward, there is ample evidence of the array of heterogeneous
functions engaging the cortex. One may require to provide a working definition
of “function” as used in proposition P2, being a notoriously ambiguous notion in
philosophy. Regarding the cortex, “function” can be cast as etiological function
in a realistic account (Wright, 1976), as capacities of its components (Cummins,
1975), as cognitive capacities deriving from its activities (Young et al, 2000), or
as mathematical mapping between incoming and outgoing signals (Rathkopf, 2013;
Burnston, 2016). However, for the current purposes, it is easy to verify the cortex’s
involvement in a multitude of functions under all accounts of the term “function”
just listed.
3.2.1 Is the cortex uniform?
Premise P1is more controversial than P2. The issue of uniformity gave birth to
two opposing parties in neuroscience: the “lumpers” and the “splitters” (Carlo and
Stevens, 2013, p.1488). The former find the idea of uniformity exciting and puzzling,
whereas the latter believe that every cortical area is unique in structure. One notable
radical example in the “splitters’ party is found in Marcus et al (2014, p.551–552):
“What would it mean for thecortex to be diverse rather than uniform? One possibility
is that neuroscience’s quarry should be not a single canonical circuit”. Marcus and
co-workers solve the paradox by denying premise P1: the diversity of functions in
the cortex is simply explained by diverse structures.
I take that the question, as formulated in the title of this section, cannot get a sharp
answer because is ill-posed. There is no suitable metrics for quantitatively assessing
uniformity in general. For example, the cortex is certainly not uniform down to the
molecular level like a metal plate. Moreover, there are obvious diversification in the
two layers of the cortex engaged in the main extracortical communication. The fourth
layer is the main target of thalamocortical projections, therefore it is well developed
in primary sensorial areas. For the opposite reason the fifth layer is mainly populated
by pyramidal cells projecting into the basal ganglia or directly to the corticospinal
tract, therefore is highly developed in all motor areas. The different extent of layers IV
and V has been used by von Economo and Koskinas (1925) for a broad classification
of the cortex into granular, typical of sensorial areas rich of spiny stellate neurons
fed by thalamic fibers, and agranular, with few spiny stellate cells, such as the motor
areas. However, apart from the density of extracortical connections in layers IV
and V, the laminar structure and the intracortical connectivity remain similar even
between granular and agranular areas.
3 Circuital and Developmental Explanations for the Cortex 5
I think that for the purpose of the present discussion, the issue of uniformity is man-
ageable in a relativistic perspective, confronting the available data on uniformity/dis-
uniformity across the entire cortex, with the variations in neuroanatomical structure
in the rest of the brain. By using a relativistic account of uniformity, experimental
evidences seem to speak in favor of P1, as I will show.
The most important and investigated kind of uniformity is the regular repetition
of the radial profile of the cortex, which can be grouped into six distinct layers,
as first observed by Berlin (1858) and detailed by early neuroscientists such as
Ramón y Cajal (1906); Brodmann (1909); Vogt and Vogt (1919); von Economo
and Koskinas (1925). In a first attempt to assess the uniformity of the cortex on a
quantitative basis, Rockel et al (1980) counted the number of cells through the entire
thickness of the cortex in most of the major cortical areas in monkeys, humans,
and several other mammals. This count has been found to be surprisingly constant
for the different areas and the different species, with about 110 neurons in cortical
sections of 30µmin diameter. The only exception is always to be found in the primary
visual cortex, with a count of about 270 neurons. Their observations have been the
subject of a fierce debate for over 30 years, with doubts raised concerning whether
their experimental methods were technically flawed (Rakic, 2008), and other studies
reporting twofold or even threefold variation in neural density across the entire
cortex (Herculano-Houzel et al, 2008). Recently Carlo and Stevens (2013) replicated
the direct count performed by Rockel and coworkers, with modern stereological
methods, and confirmed the same uniformity of count.
Additional neurophysiological features of the cortex were compared by Karbowski
(2014) across species and regions. Again, he found remarkable invariance in a number
of neuroanatomical measures. The length of postsynaptic density, the thick part of
the postsynaptic membrane hosting neurotransmitter receptors, has a mean value of
0.38µmfor the entire human cortex, with a standard deviation of only 0.04µm. The
synaptic density has a mean of 5×1011cm3with a standard deviation as small as
0.3. The ratio of excitatory to inhibitory synapses is highly invariant even across
species, with an average of 0.83 and a standard deviation of 0.03.
In addition to the qualitative and statistical uniformity of the radial organization,
there is a further uniformity in the cortex due to the periodical replication of a small
cylindrical structure. The so-called columnar organization of the cortex was first
suggested by von Economo and Koskinas (1925) and by Lorente de Nó (1938). It
has been first demonstrated by Mountcastle (1957) in the somatic sensory cortex,
where in vertical cylinders all neurons respond to the same single stimulation of
cutaneous receptors. Few years later Hubel and Wiesel (1959) discovered a columnar
organization in the primary visual cortex. A related concept was introduced by Rakic
(1995), the “ontogenetic column”, a vertical stack of cells, divided by glial septa,
generated during the embryonic migration of neurons into the cortical plate. This
column is smaller in diameter compared to those of Mountcastle and Hubel and
Wiesel. To what extent the columnar organization is ubiquitous in the cortex is
an open question. For Horton and Adams (2005) there are too many and diverse
concepts under the umbrella of “cortical column”, for being a unifying principle of
the cortical structure. Still, there is a widespread view that columnar organization
6 Alessio Plebe
is a fundamental feature of the cortex, even if not homogeneous and common to all
areas (Rockland, 2011; Kaas, 2012; Molnár, 2013; Rothschild and Mizrahi, 2015;
Casanova and Opris, 2015)
The dimensions along which self-similarity of the cortex can be evaluated, here
briefly summarized, lean toward a judgment of uniformity when compared with
how the rest of the brain is organized. There are, indeed, other parts of the brain
with a laminar structure, the most relevant is the cerebellum. In fact the cerebellum
is organized like a small brain, with an outer laminated “cortex” surrounding its
deep non-laminated nuclei, and the cerebellar cortex is as uniform as the cerebral
cortex (Ito, 1984). The difference is that the cerebellar cortex has three layers, with
a population of cells different from that of the cortex. Moreover, the cerebellum is
much more narrow in scope than the cerebral cortex, being involved mostly in the
regulation of movements and in some forms of motor learning. Most of the other
parts of the brain lack any laminar structure, still there are several alternative forms of
patterning of local circuits. For example, part of the ventral striatum is characterized
by the alternation of striosomes and matrisomes, with the former rich of cholinergic
and dopaminergic transmission, and the latter impoverished in these substances
(Graybiel, 1984). A second example of a typical small circuital module in the brain
is the glomerulus, spherical aggregation of neurons with the entire synaptic structure
contained within a single glial sheath. The glomerulus is a prominent component of
the olfactory bulb (Treloar et al, 2002), and is found also in the lateral geniculate
nucleus of the thalamus (Sherman and Guillery, 2006) and in the cerebellum (Ito,
1984), not in the cerebral cortex.
In summary, the number of neuroanatomical regularities of the cortex, unique
with respect to the rest of the brain, allow to consider the cortex – at least – uniform
enough to rise surprise and sense of anomaly when joining premise P1and P2.
3.2.2 Plasticity in the cortex
Having established that the premises P1and P2hold, the phenomenon of the para-
doxical coexisting uniformity and functional diversification of the cortex still lacks
an explanation. In my opinion, the weakness of the mainstream research on mech-
anistic cortical canonical models is in overlooking the developmental dimension of
the cortical circuits. The focus is almost entirely on the mature circuits and functions,
neglecting the enormous capacity of the cortex to mold its computational functions
in response to patterns of input.
This key feature belongs to the phenomena collected under the term neural
plasticity, which in fact comes in several different forms (Berlucchi and Buchtel,
2009) and has been investigated under a variety of perspectives. A still dominant
perspective is the reorganization of the nervous system after injuries and strokes
(Lövdén et al, 2010; Fuchs and Flügge, 2014), other streams of research focus on
memory formation (Squire and Kandel, 1999; Bontempi et al, 2007). A first account
3 Circuital and Developmental Explanations for the Cortex 7
of plasticity as occurring in the cortex was in the landmark paper of Buonomano and
Merzenich (1998), who distinguished three levels of plasticity:
1. synaptic plasticity, addressing changes at single synapse level;
2. cellular conditioning, addressing changes at single neuron level;
3. representational plasticity, addressing changes in distributed neural responses
participating to specific domains of representations.
Their taxonomy was related to the different methodologies of analysis, for exam-
ple synaptic plasticity studies were generally conducted in slice preparations, while
experiments on representational plasticity were conducted inducing peripheral den-
nervation or intensive behavioral training. For the purpose of the current discussion,
we can adopt a similar, but more specific classification into:
1. synaptic plasticity, addressing changes at single synapse level;
2. intracortical map plasticity, addressing internal changes at the level of a single
cortical map;
3. intercortical map plasticity, addressing changes on a scale larger than a single
cortical map.
The term “map” as used in “cortical map” can be regarded as synonymous of
the more popular “area”. The parcellation of the cortex into a mosaic of spatially
contiguous areas is a long sought enterprise in neuroscience, which proved to be
extremely challenging (Drury et al, 1996; Nieuwenhuys, 2013; Glasser et al, 2016).
It is not difficult to imagine that the main difficulty boils down in the uniformity of
the cortex, which lacks the sharp boundaries in neurobiological properties proper
to other parts of the brain. Even at the level of genetic expression, the boundaries
in functional characteristics across cortical areas do not correspond to any sharp
transition in the graded expressions of the transcription factors in the progenitors
zones (O’Leary et al, 2007, 2013). Genetic expression across the entire cortex is
highly homogeneous, with the exception of the visual area V1, in contrast to sharp
and complex differential relationships between extracortical brain areas (Hawrylycz
et al, 2012).
The use of “map” instead of “area” has the advantage of implicitly adopting a
parcellation policy more suited for the cortex: a lawful relation between the surface
of the cortex and a relevant aspect of the representational structure. First introduced
by Mountcastle (1957) for the somatosensory cortex, a cortical map is defined by
the continuous map on the surface of the cortex isomorphic to the somatic sensorial
space. In fact, cortical maps can be rigorously identified for all sensory and motor
areas, but in higher areas the represented domain has a complicated and mostly
unknown topological structure, which makes a systematic mapping on the cortical
surface difficult.
Synaptic plasticity is not different from that in the rest of the brain, and in-
volves the known mechanisms of long-term potentiation (LTP), long-term depres-
sion (LTD) and spike-timing-dependent plasticity (STDP) (Markram et al, 1997;
Feldman, 2000). Intracortical map plasticity is easier to be observed in maps of the
sensorial cortex, where it is responsible, for example, of perceptual learning (Fahle
8 Alessio Plebe
and Poggio, 2002; Weinberger, 2007), the long-term enhanced performance on a
perceptual task as result of repeated experiences. While perceptual learning is an
everyday business, intracortical map plasticity is responsible for the main early di-
versification of cortical functions, driven by spontaneous neural activity (Khazipov
and Buzsáki, 2010; Zhang et al, 2011). Intercortical map plasticity induces modi-
fications on a scale larger than a single map afferent. Typical case is the abnormal
developments in primary cortical areas: when following the loss of sensory inputs,
neurons become responsive to sensory modalities different from their original one
(Karlen et al, 2010).
The most striking examples of modal plasticity are the famous rewiring experi-
ments, in which retinal axons of ferrets are connected at birth to the medial geniculate
nucleus, which relay the signals to A1 instead of V1. This abnormal connectivity
induced a functional reorganization of A1, which enabled visual behavior in the
animals (Roe et al, 1987, 1990). A main question raised by this visual perception
is how the transformation in A1 occurs. Either A1 and V1 are so similar that the
change in sensory input has not been so significant, or intercortical map plasticity is
powerful enough to mold the A1 small-scale circuitry to function, partially, as V1.
Gao and Pallas (1999) gave a precise answer, demonstrating that A1 deeply changes
its normal organization across a major tonotopic axis, into a periodical, symmetrical
array of orientation-tuned clusters of neurons, resembling that of V1.
It is possible now to clarify what sort of explanation we are after, when we face
the paradox of the cortex. The mainstream research on canonical circuits attempts to
elaborate the following sort of explanation:
P1the cortex is remarkably uniform;
P2the cortex is the main site of a bewilderingly variety of functions.
EC
there must be a canonical circuit common all over the cortex, able
to perform many different functions.
Explanations of the sort EC, with suffix Cfor “circuit”, are doomed to failure, as I
will argue in §3.3. If the set of premises is enforced with plasticity, a different sort
of explanation can be offered:
P1the cortex is remarkably uniform;
P2the cortex is the main site of a bewilderingly variety of functions.
P3the cortex is characterized by a remarkable plasticity.
ED
there must be a strategy common all over the cortex, which enables
a basic circuit to gradually change and develop a wide variety of
functions, depending on the input patterns.
where in EDthe suffix Dis for “circuital-developmental”. Sketches of this sort of
explanation will be discussed in §3.5.
3 Circuital and Developmental Explanations for the Cortex 9
3.3 Circuital explanations
Most of the achievements in characterizing cortical mechanisms derives from the
circuital perspective. The origin of circuital perspective is in the blending of electri-
cal and electronic engineering with neurophysiology around half of the last century,
and such perspective (Brazier, 1961; Rose and Abi-Rached, 2013). A paradigmatic
case of the impact electrical engineering has in the field of neuroscience is the cable
equation, first derived by Lord Kelvin for the design of the transatlantic telegraph
cable (Thomson Kelvin, 1855), later adapted by Wilfrid Rall (1957) to neural mem-
brane potentials. The same basic equation is at the heart of the NEURON simulator
(Hines and Carnevale, 1997), adopted in the current largest brain simulation projects.
The circuit equivalent to the cable equation is used as a model of the electrical
behavior of dendrites and axons of single neurons. It inherits the exact abstraction
assumed in electrical engineering as network of idealized quantized components of
very few types (batteries, resistors, inductors, capacitors), connected by ideal perfect
conductor lines, and as node connections obeying the laws of Kirchhoff (1845).
A similar set of assumptions is implicitly assumed in the microcircuits proposed to
explain the cortex. The most influential of such circuits is the “canonical microcircuit
of the cortex”, formulated by Douglas et al (1989). Exactly like in the cable equation
model, this cortical microcircuit inherits the main assumption of electrical circuits,
approximating the electromagnetic field into a finite set of attributes that does not
depend on the position of elements in physical space (Paynter and Beaman, 1991).
However, unlike the cable equation, the elements in the canonical microcircuit of
the cortex are not standard electrical components but “neurons”, abstracted in three
classes. One class corresponds to the combination of superficial pyramidal neurons
in layers II and III, and spiny stellate in layer IV projecting to them. The second class
encompasses deep pyramidal population of layer V and VI, and a third class includes
generic GABA-receptor inhibitory cells. The circuit made of these three virtual
neural units was implemented in a computational model, using rate-encoding of the
outputs of the three units. The effect of outputs on connected units was computed
as a change in membrane potential after a transmission delay. The output of each
unit was a thresholded hyperbolic function of the average membrane potential, after
a constant time relaxation. The tuning and later validation of the model was derived
by intracellular recordings in the cat visual cortex (area 17), using a technique also
borrowed from electrical engineering: pulse stimulation.
Electrode recordings were in response to electrical pulses in range 0.2–0.4 msec
stimulating the optic radiation above the lateral geniculate nucleus. The main ad-
vantage was the availability of standard engineering system analysis tools for the
evaluation of the responses. In addition, pulse stimulation is agnostic with respect to
the many different natural stimuli to different cortical areas, thus making the canon-
ical circuit general. Once the model was tuned, it was able to produce simulated
responses to pulse signals in good agreement with the measured cortical responses.
Later on, Douglas et al (2004) confirmed the validity of their canonical model, with
minor revisions to the relative strengths of the connections. The dominant excitation
is now provided by intracortical connections between pyramidal neurons, so that
10 Alessio Plebe
even a relatively weak thalamic input can be greatly amplified. Even if inhibition
is relatively weak, by modulating the recurrent excitation it may play an important
role.
Circuits are abstractions aimed at isolating the main components of a system and
their reciprocal electrical connections, seemingly providing a typical mechanistic
explanation. In addition, the circuit of Douglas and Martin is complemented with a
computational counterpart. Neurocomputational models, under certain conditions,
are forms of mechanism with their own explanatory power (Piccinini, 2015). One
adopted criterion for ascertaining which models give mechanistic explanation of the
modeled system, is the 3M (model-mechanism-mapping) constraint (Kaplan, 2011;
Kaplan and Craver, 2011):
A model of a target phenomenon explains that phenomenon to the extent that (a) the variables
in the model correspond to identifiable components, activities, and organizational features
of the target mechanism that produces, maintains, or underlies the phenomenon, and (b) the
(perhaps mathematical) dependencies posited among these (perhaps mathematical) variables
in the model correspond to causal relations among the components of the target mechanism.
This constraint does not work as a logical binary condition, in fact complete
mechanistic models of neural behavior are unrealistic. The constraint is perfectly
compatible with incomplete models, where details are omitted either for reasons of
computational tractability or because these details are still unknown.
The idealizations of the model are in terms of population: the three elements
in the model of Douglas et al. represent populations of certain categories of real
neurons. Therefore, constraint (a) of 3M, “the variables in the model correspond
to identifiable components [. . . ] of the target mechanism”, is not met, or at least
with large approximation. Note that this approximation is different from the issue
of the amount of details included in a model. It is not a matter of excluding details,
in the case of the canonical circuits units are clearly not physical single cells, their
extension in the cortex is not specified, nor the number and locations of cells on
which the population of cells is averaged as a single abstract unit.
The same group of Douglas and Martin worked for overcoming this issue con-
structing a more comprehensive microcircuit template of the cortex, using sophis-
ticated statistical experimental data. Binzegger et al (2004) used three-dimensional
cell reconstruction on a sample of primary visual cortex, and analyzed the laminar
pattern of synaptic boutons of 39 reconstructed neurons. The average number of
synapses formed between neurons in different layers was estimated using an en-
hanced version of a simple rule due to (Peters and Payne, 1993). In its simplest form,
this rule states that the synapses from a given type of presynaptic neuron distribute
evenly over the population of potential postsynaptic cells in the same cortical layer.
In the refined version more details are taken into account, for example the fact
that chandelier cells form synapses with pyramidal cells only. The final result is not a
circuit any more, rather a graph of synaptic connections between every type of cells,
in five layers (layer II and III are joined together), having as edges the estimated
proportion of synapses. A different way of deriving a statistical canonical circuit of
the cortex is by using cellular recordings instead of cell morphology.
3 Circuital and Developmental Explanations for the Cortex 11
Thomson et al (2002) used paired recording – the simultaneous continuous mea-
surement of electrical potentials from presynaptic and postsynaptic sites – obtaining
about 1000 recordings on a variety of cortical neurons in several layers. Haeusler
and Maass (2007) used these data to assemble a statistical circuit made of 6 virtual
cell types, corresponding to excitatory or inhibitory populations of cells distributed
into layers II/III, IV, and V. This graph can include two types of edges: probability
of connections, as in Binzegger et al., but also average strengths of connections.
Haeusler & Maass implemented a network of about 500 single compartment neu-
rons, with proportion of connections matching those of the graph, and performed a
series of computational tasks, such as classifying two different sequences of spikes.
The performances were compared with the same task executed by networks with the
same number and type of neurons, but without the layered structure and the propor-
tions of connections derived by real cortical data. Haeusler et al (2009) implemented
within the same neural simulation the statistical graph of Binzegger et al., in order to
compare the two models, with very similar performances. A different simulator was
developed (Potjans and Diesmann, 2014) based on the combined data of Binzegger
et al. and Thomson et al., giving better accuracy in predicting certain experimental
findings like spontaneous firing rates, but no performances on computational tasks
were evaluated.
The most advanced cortical circuit derived from statistical cytology and con-
nectivity data has been developed within the Human Brain Project (Markram et al,
2015). It reproduces a volume of 0.3mm3of the rat somatosensory cortex with 31
thousands neurons and 37 million synapses. This microcircuitry is able to reproduce
activities and several response properties recorded in vitro and in vivo experiments.
However, even in the most advanced and refined form, explanations of the sort EC
(see §3.2) tell little, if nothing, about the paradox of the cortex expresses in premises
P1and P2. The main reason hinges upon neglecting premise P3, upon addressing
a static adult configuration only, discarding the development of synaptic connection
in relation to the type of input patters. In the simulations of Haeusler & Maass, all
synaptic strengths are necessarily equal to the statistical average derived by the data.
If, for example, the synaptic strengths in the circuit corresponding to one orientation-
selective column in the primary cortex were all substituted with their mean value,
the column would loose its selectivity, missing entirely its computational function.
Consider the rewiring experiment described in §3.2, if an explanation of kind EC
were to hold, then we may expect the following two cases:
1. A1 in the rewired ferrets would continue to perform its tonotopic function forever,
a useless function with the new connectivity;
2. the microcircuit in A1 would be versatile enough to immediately switch from the
tonotopic function to orientation selectivity, triggered by the new input.
Neither of these cases occurred. Instead, intracortical map plasticity was powerful
enough to mold A1 small-scale circuitry to function, partially, as V1. A1 deeply
changed its normal organization across a major tonotopic axis, into a periodical,
symmetrical array of orientation-tuned clusters of neurons, resembling that of V1.
Using optical imaging Sharma et al (2000) compared the patterns of horizontal
12 Alessio Plebe
connections in V1, normal A1 and rewired A1. While in normal A1 this pattern is
elongated anteroposteriorly along the isofrequency axis, in rewired A1 the field of
connections is wider, very patchy and elongated mediolaterally. This pattern is very
similar to the field of horizontal connections in V1.
The explanatory limits of ECcan be well interpreted in the light of timescales,
following Marom (2010). Canonical circuits are abstracted over a highly simplified
temporal manifold, which takes care of one or just few short timescales, neglecting
slower timescales at which important circuital adaptations take place.
3.4 Developmental explanations in biology
As mentioned in the Introduction, developmental explanations deserve their own
place in biology. One of the earlier contributions to the developmental perspective
in biology is found in the work of Conrad Hal Waddington (1957), who used to
conceive an animal as a “developmental system”. This idea blended with epigenet-
ics, which become an empirically testable field through the innovative experimental
research carried out by Gilbert Gottlieb (1971). He carefully worked in identify-
ing developmental conditions that allow the capacity of ducklings to identify their
maternal call, in particular the necessary auditory perceptual experiences during
hatching. Eventually, Ford and Lerner (1992) set a systematic research agenda for
developmental explanations in biology, proposing the “Developmental System The-
ory”, in which epigenetics and biological development processes are linked to ideas
coming from system theory and cybernetics. In fact, until recently concepts from
developmental system theory and epigenetics were not picked up by mainstream
biology, dominated by genetics. Today epigenetics and developmental system theory
are among the most booming fields in biology (Griffiths and Tabery, 2013; Baedke,
2018). As a consequence, the relevance and validity of mechanistic explanations in
developmental biological phenomena has become the topic of fervent discussions.
Mc Manus (2012) has argued that developmental phenomena cannot be accom-
modate within the mechanistic framework. Among the reasons, during development
it seems impossible to maintain a basic principle held in mechanistic explanations,
the mutual manipulation (Craver, 2007, p.153). This principle establishes a sort of
symmetry between the possibility to manipulate a part of the system and observing
changes in some of its activities, and the possibility to produce globally similar
changes and observe variations in one of its constitutive parts. Clearly, in a develop-
mental phenomenon it is almost impossible to manipulate the final form of the system
and observe changes in its initial constituents. For Ylikoski (2013) developmental
explanations are not fully unrelated with mechanistic explanations, they combine
in one some properties of causal explanations and other properties of mechanistic
explanations. Causal explanations typically address changes of a system in time,
seeking what triggers a specific change. Conversely, mechanistic explanations do not
take time into account, and seek parts and relations between parts that empower a
system with a causal capacity. A developmental explanation involves both time and
3 Circuital and Developmental Explanations for the Cortex 13
changes in the causal capacity of a system. However, Parkkinen (2014) contends
that in most cases the focus of development is not just in how the causal capacities
of a system have changed in time, rather in the formation of novel constituents.
A textbook example is the formation of a segmented body plan starting from the
embryo. For this reason, Parkkinen is less compliant than Ylikoski in seeing a con-
tinuity between developmental and mechanistic explanations, and more in line with
McManus. A different criticism on the possibility of developmental processes to be
included in mechanistic explanations is raised by Brigandt (2015), based on the use
of mathematical models. An important methodology in the study of the develop-
ment of morphological structures is given by mathematical models, mostly based on
reaction-diffusion equations. Brigant argues that, since mechanistic explanations are
usually contrasted to mathematical explanations, the former are not appropriate for
explaining biological processes such as morphological structures development.
The issue appears relevant in explaining how the cortex works, because such
explanation involves mathematical models, as seen in §3.3 and as proposed in §3.5.
However, the separation drawn by Brigandt between mechanistic and mathematical
explanations is somehow too sharp. It is correct that for Craver (2007) that certain
mathematical models are just predictive and not explanatory, as reported by Brigandt,
but this is the case for certain mathematical models. As seen in §3.3, there are
criteria for discriminating between mathematical models with pure predictive scope
and those that explain.
Most of the discussions of the philosophy of developmental explanations in bi-
ology targets phenomena that are different from the issue of cortical plasticity. The
most common domains of development in biology focus on specific segments of
ontogeny, such as the period from fertilization to birth in embryology, or from birth
to the adult form of the organism (Minelli and Pradeu, 2014). Developmental as-
pects in the cortex are not just limited to specific periods in ontogenesis, they are
constitutive of the everyday working of the cortex. Development is in action, for
example, every time a new mental concept is acquired, or an existing one is refined
(Plebe and Mazzone, 2016). Recent brain imaging techniques have demonstrated
subtle changes in cortical microconnectivity in tasks such as learning about the Mi-
croraptor zhaoianus1(Bauer and Just, 2015), new names of flowers (Hofstetter et al,
2017), or the structure of organic compounds (Just and Keller, 2019).
A discussion close to the case at hand is provided by (Craver and Darden, 2013,
pp.171–174) about LTP. First, LTP is one of the major forms of neural plasticity,
therefore directly relevant to the cortex too. But most of all, Craver and Darden relate
the basic mechanism that explains LTP with other higher level phenomena which
depend on LTP, or depend on intermediate phenomena depending on LTP. In other
words, development becomes integrated in a multi-level mechanistic explanation. In
the example given by Craver and Darden, the mechanism at lower level concerns the
phenomena of the activation of NMDA receptors in the postsynaptic cell and the
chain of biochemical activities triggered by calcium ions that flow into the cell when
NMDA receptors open. The level immediately above is the mechanism inducing the
1a four-winged dinosaur bird species
14 Alessio Plebe
strengthening of the synaptic connection between a presynaptic and a postsynaptic
cell, in which the main constituents are the phenomena and activities of the level
below. A next level is the formation of place cells in the hippocampus (O’Keefe
and Recce, 1993), which are the basis of spatial cognition. The higher level is the
exploration of a mouse in an environment (for example, a controlled Morris water
maze), capturing visual cues that trigger the generation of place cells, through LTP
plasticity.
This example shares aspects with the account of development needed to complete
an explanation of the cortex, in particular the stratification in levels. The lowest level
encompasses the same NMDA mechanism found in LTP plasticity, supplemented by
other mechanisms of plasticity, as those reviewed in §3.2. The highest level is one
of the meaningful functions performed by a cortical area, such as visual or auditory
processing, at a mature stage of its development. Possible ways of linking the lowest
and the highest levels are discussed in the next section.
3.5 Developmental explanations for the cortex
The circuital approach for studying the cortex is dominating current mainstream
computational neuroscience (Haeusler et al, 2009; Markram et al, 2015). There are,
however, several strands of research that address developmental explanations. In this
section I will first provide a brief historical survey of this research, followed by
two examples of developmental explanation for the cortex, described in some more
detail.
3.5.1 Modeling cortical plasticity
Several theoretical models have been proposed for cortical plasticity. One of the first,
and most influential, was based on the mathematical framework of self-organization,
a unified mathematical treatment of natural phenomena where a global ordering
emerges from complex local interactions (Ashby, 1947; Haken, 1978; Kauffman,
1993). The first attempts to use the mathematical framework of self-organization for
describing neural phenomena are attributed to von der Malsburg (1973); Willshaw
and von der Malsburg (1976), who addressed the organization of maps in the visual
cortex. There are three key mechanisms in cortical circuits that match with the
premises of self-organization:
1. small signal fluctuations might be amplified, an effect highlighted in the canonical
circuits described in §3.3;
2. there is cooperation between fluctuations, in that excitatory lateral connections
tend to favor the firing of other connected neurons, and LTP reinforces synapses
of neurons that fire frequently in synchrony;
3 Circuital and Developmental Explanations for the Cortex 15
3. there is competition as well, with the static part captured by computations like
divisive normalization (Kouh and Poggio, 2008), and the additional dynamics
caused by synaptic homeostasis, which compensates for the gain in contribution
from more active cells, by lowering the synaptic efficiency of other afferent cells.
In the cortical model devised by von der Malsburg the activity xiof each neuron i
was computed by the following system of differential equations:
txi(t)=αixi(t)+Õ
j∈L i
wij fxj(t)+Õ
j∈A i
wi j aj(t)(3.1)
f(xi(t))=(xi(t) − θiif xi(t)> θi
0otherwise (3.2)
where Liis the set of cortical neurons with lateral connections to the cell i, and
Aiis the set of all afferent axons, each carrying a signal a(t).wij are the synaptic
efficiencies between cell presynaptic jand postsynaptic i, and are modified by an
amount proportional to the presynaptic and postsynaptic signals, in the case of
coincidences of activity. Periodically all wi j leading to the same cortical cell iare
renormalized, resulting in competition, in that some synapses are increased at the
expense of others. The source of afferents, in such process of self-organization, can
be the external scene seen by the eyes, but also spontaneous activity generated by the
brain itself (Mastronarde, 1983). Equations like those in (3.1), explain different kinds
of organization in the visual system ranging from retinotopy, ocular dominance, to
orientation sensitivity (von der Malsburg, 1995).
From then on, several further theoretical models have been proposed on how the
cortex can develop functions using the basic synaptic plasticity mechanisms (Elia-
smith and Anderson, 2003; Deco and Rolls, 2004; Ursino and La Cara, 2004). Here
I will give details on just one theoretical model, and show how this model succeed
in explaining aspects of the functions performed in cortical areas V1 and V2, as the
result of development. The model is based on a formulation of self-organization,
simpler than that of von der Malsburg, called LISSOM (Laterally Interconnected
Synergetically Self-Organizing Map) (Sirosh and Miikkulainen, 1997; Miikkulainen
et al, 2005) evolved in the Topographica neural simulator (Bednar, 2009, 2014).
3.5.2 The LISSOM architecture
The basic equation of the LISSOM describes the activation level xiof a neuron iat
a certain time step k:
x(k)
i=fγAai·vi+γEei·x(k1)
iγHhi·x(k1)
i(3.3)
The vector fields vi,ei,xiare circular areas of radius rAfor afferents, rEfor excitatory
connections, rHfor inhibitory connections. The vector aiis the receptive field of the
16 Alessio Plebe
unit i. Vectors eiand hiare composed by all connection strengths of the excitatory or
inhibitory neurons projecting to i. The scalars γA,γE,γH, are constants modulating
the contribution of afferents, excitatory, inhibitory and backward projections. The
function fis a non linear monotonic function, which details will be given next, kis
the time step in the recursive procedure.
All connection strengths adapt according to the general Hebbian principle, and
include a normalization mechanism that counterbalances the overall increase of
connections of the pure Hebbian rule. Here is the equation for the changes in afferent
synapses:
arA,i=arA,i+ηAxivrA,i
arA,i+ηAxivrA,iarA,i(3.4)
where ηAare the learning rates , and k · k are the L1-norm. The formulation in (3.3)
takes into account the following key features of cortical circuits:
1. the intercortical connections of inhibitory and excitatory types;
2. the afferent connections, of thalamic nature or incoming from lower cortical areas;
3. the organization on two dimensions of neural coding;
4. the reinforcement of synaptic efficiency by Hebbian learning;
5. homeostatic compensation of neural excitability.
In modeling how the cortex develops purposeful and efficient functions a crucial
aspect in need of explanation is how to reconcile adaptivity on one side, and robust-
ness and stability on the other side. Adaptivity is the key to construct connections
implementing functions, driven by environment and internal experiences, but the
sensitivity to changes in input patterns exposes to destabilizing forces, as seen in
§3.2. Stevens et al (2013) addressed this issue using Topographica, in the case of
orientation maps development in the primary visual cortex. There is large empirical
evidence for the robustness and stability of this development in several mammals
and against several differences in visual experiences, see references in the paper
from Stevens and co-workers. The most complete and direct evidence for robustness
derives from studies on ferrets, with orientation maps recorded using chronic optical
imaging at different ages (Chapman et al, 1996), showing how the earliest measur-
able maps are similar in form to the eventual adult map. Many computational models
of orientation map development have been proposed (Goodhill, 2007), but no model
previous to Stevens et al. has been shown to develop with robustness and stability.
The key for developing robust and adaptive orientation maps in the model of
Stevens et al. is in the nonlinear function fof equation (3.3), expressed as a piecewise
linear function with threshold θ:
f(z)=
1when z>1+θ
zθwhen θ < z<1+θ
0otherwise
(3.5)
The threshold adapts according with the neural activation level x:
θ(k)=θ(k)+λ(¯xµ)(3.6)
3 Circuital and Developmental Explanations for the Cortex 17
Fig. 3.1 Examples of V1 subunit interactions in the neural responses in area V2 of the model by
Plebe (2012). In gray scale the level of activation of a single V2 neuron in the model, when in the
receptive fields of the two V1 subunits two oriented bars are presented. The orientation of the two
bars are the axes of the plots.
where ¯xis a smoothed exponential average in time of the activation level x, and λand
µare fixed parameters. This computation implements the biological mechanism of
neural intrinsic homeostatic adaptation (Turrigiano and Nelson, 2004). The model
learns in a first stage from synthetic noisy disks, which simulate internal retinal
waves of the prenatal phase, followed by real natural images. The results of the
orientation maps in the model, taken at iterations steps between 2000 and 10000,
closely resemble the orientation maps in ferrets measured at postnatal days age from
P33 up to P42.
Most computational models of the cortex focus on the primary perceptual areas,
especially V1, for which features of the neuron receptive fields are well documented.
However, the most valuable functions of the cortex rely on a hierarchical computa-
tional strategy in which circuits at later levels in the hierarchy combine inputs from
earlier levels building more complex responses. Thus, a model that nurtures canon-
ical hopes, is required to explain how higher areas of the cortex build complexity
upon lower areas. A suitable case to explore is in the secondary visual cortex, V2, as
it receives most of its input from the well understood primary visual area. In addition,
recently responses of neurons in V2 have been the object of several investigations (Ito
and Komatsu, 2004; Anzai et al, 2007; Hegdé and Van Essen, 2007). The model by
Plebe (2012) investigated computationally the complex responses in V2 as resulting
from V1 inputs. The model was based on two Topographica layers corresponding to
V1 and V2, in each one the neurons are ruled by equation (3.3), with V2 receiving
afferent from V1, and backprojecting to V1 as well.
The model was able to reproduce the sensitivity to angles, as measured by Ito
and Komatsu (2004), and also the subtle dependencies of V2 neurons from subunits
in V1 belonging to their receptive fields, found by Anzai et al (2007). The contour
plots in Fig. 3.1 reveal the mechanics of the selectivity to angles in neurons of V2,
as depending from nonlinear interactions between two V1 subunits in its receptive
fields. The plots are obtained by presenting simultaneously in the retina two oriented
bars, centered withing the two receptive fields of the two V1 subunits, and measuring
the response in the model V2 unit for every combination of the two orientations. It can
18 Alessio Plebe
be seen that there are peaks of response to specific combinations of orientation, but
there are also areas in the two orientations space with an inhibitory effect, as resulting
from the empirical study of Anzai et al (2007). The complex responses in V2 were
not implicit in the model definition, they result from development, achieved by a first
stage of experience with simple noisy elongated patterns, followed by more complex
patterns like corners and crosses. Thus, the model provides a preliminary insight
of how complexity in cortical responses emerges from development (Riesenhuber,
2012).
3.5.3 What the developmental models have explained
We can summarize the achievements of the two LISSOM-based models as follows:
the first model is able to reproduce the orientation selectivity in V1, developed
by exposure to plausible visual experiences;
the first model exhibits the kind of balance between adaptivity and robustness in
the development of orientation maps recorded in case studies;
the second model is able to reproduce the sensitivity to angles on V2, as depending
from nonlinear interactions between V1 subunits.
Turning back to the main issue of explaining the paradox of the cortex, defined in
§3.2, shall we claim that models like Topographica are giving explanations of the sort
ED? Probably not, at least not yet, because the coverage of phenomena successfully
explained so far by the models is limited with respect to the wide range of functions
in the cortex that a canonical model has the burden to explain. However, I deem
this kind of models as the most promising road toward ED. There are two distinct
computational aspects of these models that potentially may apply all over the cortex:
1. a stereotyped essential sketch of the constituents of a cortical response, both in a
initial or a mature stage, in equation (3.3)
2. a stereotyped essential sketch of the etiology of a cortical response, by its history
of experiences, given in equation (3.4)
The computation in point 1. describes the behavior of an abstract LISSOM unit
as dependent from all its intracortical and extracortical connections. Therefore, it
is not anchored to a specific circuital sketch, as in explanations of the kind EC.
There might be a sort of resemblance with the idea of “canonical computations”, the
mathematical operations most often carried out across different areas in the cortex.
According to this idea, the general applicability of these operations makes the cortex
powerful and flexible (Kouh and Poggio, 2008; Carandini and Heeger, 2012). It is
out of the scope of this paper to discuss canonical computations, suffice it to say that
they identify specific operations, such as divisive normalization or maximization.
This is not the case of equation (3.3) of the LISSOM model.
The computation in point 2. is not anchored to a specific circuital sketch, either.
A specific instance of Topographica model, like the two here described, relies on a
3 Circuital and Developmental Explanations for the Cortex 19
simulated cortical map, which circuital structure is not modified during development.
The consequences of LISSOM equation (3.4) are at the level of intracortical map
plasticity, which suffice to produce mature functions in the simulated experiments.
Both points 1. and 2. contribute in an explanation that might qualify as mecha-
nistic sketch, while including development effects. As seen in the previous section,
several philosophers have defended, to various degrees, the autonomy of develop-
mental explanations as distinct and irreducible to mechanistic explanations in biology
(Mc Manus, 2012; Ylikoski, 2013; Parkkinen, 2014; Brigandt, 2015). However, the
class of biological phenomena these philosopher take into consideration are much
different from the problem of the cortex here addressed. By contrast, the phenomenon
of LTP analyzed by Craver and Darden (2013), which is more relevant for the case
at hand, can be well explained within a multi-level mechanistic framework.
In the models described in this section, the lower level corresponds to synaptic
plasticity, in the taxonomy suggested in §3.2. This level is not the target of the
explanation, therefore it is synthesized in equation (3.4), without unfolding its details.
The main level is the intracortical map plasticity, described in the LISSOM equations
(3.3) in conjunction with (3.4). The higher level is the phenomenon of orientation
selectivity in V1 in the model of Stevens et al., and the selectivity to angles in
V2 by combinations of V1 subunit responses in the model of Plebe. The models
can be assumed as mechanistic sketches (Craver, 2007, p.114), with most of the
mathematical variables corresponding to identifiable components or activities in
the cortex, even if at a coarse level. For example, the threshold θin equation (3.6)
corresponds to the regulation of firing rates in biological V1 in dependence of the
average activity. The details of how it is implemented in real neurons (by changing
the number and distribution of ion channels) is left out in the model.
3.6 Conclusions
In this chapter we have analyzed the search of an explanation of why the cortex is at
the same time so uniform and so diversified in functions. This enterprise is justified
only if the premise of uniformity is true, and our review of the current knowledge
suggests that it is the case. Most proposals addressing this issue have followed a
circuital strategy, trying to distill a fundamental circuital arrangement of cells in the
cortex – often called “canonical” – at the heart of its computational power. Despite
the enormous progress brought by this body of research, the answer to the paradox
of the cortex is still, disappointingly, inconclusive. One reason is that all canonical
solutions proposed so far have overlooked the dimension of cortical development due
to plasticity, which is the main source of its computational flexibility, as supported
from the reviewed evidences. Thus, a successful road towards a canonical explana-
tion of the cortex paradox should be better construed as a mixed explanation of both
the constituents essential for its computational power, and the developmental account
of how cortical maps achieve their mature functions. There are several sketches of
models following this direction, we provided details of two cases. Should this direc-
20 Alessio Plebe
tion loose the epistemological advantage of a mechanistic format of explanation, that
canonical circuits have to some degree? Probably not, for the development compo-
nents too it would be possible to establish correspondences between mathematical
elements of the models and neurophysiological correlates. Therefore, it is possible to
qualify certain models of the cortex that include development as, at least, incomplete
mechanistic sketches.
References
Anzai A, Peng X, Van Essen DC (2007) Neurons in monkey visual area V2 encode combinations
of orientations. Nature Neuroscience 10:1313ŋ–1321
Ashby WR (1947) Principles of the self-organizing dynamic system. The Journal of general psy-
chology 37:125–128
Baedke J (2018) Above the gene, beyond biology: toward a philosophy of epigenetics. Pittsburgh
University Press, Pittsburgh (PA)
Bauer AJ, Just MA (2015) Monitoring the growth of the neural representations of new animal
concepts. Human Brain Mapping 36:3213–3226
Bednar JA (2009) Topographica: Building and analyzing map-level simulations from Python,
C/C++, MATLAB, NEST, or NEURON components. Frontiers in Neuroinformatics 3:8
Bednar JA (2014) Topographica. In: Jaeger D, Jung R (eds) Encyclopedia of Computational Neu-
roscience, Springer-Verlag, Berlin, pp 1–5
Berlin R (1858) Beitrag zur structurlehre der grosshirnwindungen. PhD thesis, Medicinischen
Fakultät zu Erlangen
Berlucchi G, Buchtel H (2009) Neuronal plasticity: historical roots and evolution of meaning.
Nature Reviews Neuroscience 192:307–319
Binzegger T, Douglas RJ, Martin KA (2004) A quantitative map of the circuit of cat primary visual
cortex. Journal of Neuroscience 24:8441–8453
Blumberg MS, Freeman JH, Robinson S (eds) (2010) Oxford Handbook of Developmental Behav-
ioral Neuroscience. Oxford University Press, Oxford (UK)
Bontempi B, Silva A, Christen Y (eds) (2007) Memories: Molecules and Circuits. Springer-Verlag,
Berlin
Braak H (1980) Architectonics of the human telencephalic cortex. Springer-Verlag, Berlin
Brazier M (1961) A history of the electrical activity of the brain: The first half-century. Macmillan,
New York
Brigandt I (2015) Evolutionary developmental biology and the limits of philosophical accounts
of mechanistic explanation. In: Braillard PA, Malaterre C (eds) Explanation in Biology – An
Enquiry into the Diversity of Explanatory Patterns in the Life Sciences, Springer-Verlag, Berlin,
pp 135–173
Brodmann K (1909) Vergleichende Lokalisationslehre der Grosshirmrinde. Barth, Leipzig
Buonomano DV, Merzenich MM (1998) Cortical plasticity: From synapses to maps. Annual Review
of Neuroscience 21:149–186
Burnston DC (2016) Computational neuroscience and localized neural function. Synthese
193:3741–3762
Carandini M, Heeger D (2012) Normalization as a canonical neural computation. Nature Reviews
Neuroscience 13:51–62
Carlo CN, Stevens CF (2013) Structural uniformity of neocortex, revisited. Proceedings of the
Natural Academy of Science USA 110:719–725
Casanova MF, Opris I (eds) (2015) Recent Advances on the Modular Organization of the Cortex.
Springer-Verlag, Berlin
3 Circuital and Developmental Explanations for the Cortex 21
Chapman B, Stryker MP, Bonhoeffer T (1996) Development of orientation preference maps in
ferret primary visual cortex. Journal of Neuroscience 16:6443–6453
Craver CF (2007) Explaining the brain: mechanisms and the mosaic unity of neuroscience. Oxford
University Press, Oxford (UK)
Craver CF, Darden L (2013) In Search of Mechanisms: Discoveries across the Life Sciences.
University of Chicago Press, Chicago (IL)
Cummins R (1975) Functional analysis. Journal of Philosophy 72:741–765
Deco G, Rolls E (2004) A neurodynamical cortical model of visual attention and invariant object
recognition. Vision Research 44:621–642
Douglas RJ, Martin KA, Whitteridge D (1989) A canonical microcircuit for neocortex. Neural
Computation 1:480–488
Douglas RJ, Markram H, Martin K (2004) Neocortex. In: Shepherd GM (ed) The Synaptic Orga-
nization of the Brain, Oxford University Press, Oxford (UK), pp 499–558, 5th Edition
Drury HA, Van Essen DC, Anderson C, Lee C, CooganT, Lewis JW (1996) Computerized mappings
of the cerebral cortex: A multiresolution flattening method and a surface-based coordinate
system. Journal of Cognitive Neuroscience 8:1–28
Edinger L (1904) Vorlesungen über den Bau der nervösen Zentralorgane des Menschen und der
Tiere. Vogel, Leipzig (DE)
Eliasmith C, Anderson CH (2003) Neural Engineering Computation, Representation, and Dynamics
in Neurobiological Systems. MIT Press, Cambridge (MA)
Fahle M, Poggio T (eds) (2002) Perceptual Learning. MIT Press, Cambridge (MA)
Feldman DE (2000) Timing-based LPT and LTD at vertical inputs to layer II/III pyramidal cells in
rat barrel cortex. Neuron 27:45–56
Ford DH, Lerner RM (1992) Developmental systems theory: An integrative approach. Sage Publi-
cations, Newbury Park (CA)
Fuchs E, Flügge G (2014) Adult neuroplasticity: More than 40 years of research. Neural Plasticity
2014:ID541870
Fuster JM (2008) The Prefrontal Cortex. Academic Press, New York, fourth edition
Gao WJ, Pallas S (1999) Cross-modal reorganization of horizontal connectivity in auditory cortex
without altering thalamocortical projections. Journal of Neuroscience 19:7940–7950
Glasser MF, Coalson TS, Robinson EC, , Hacker CD, Harwell J, Yacoub E, Ugurbil K, Andersson
J, Beckmann CF, , Jenkinson M, Smith SM, Essen DCV (2016) A multi-modal parcellation of
human cerebral cortex. Nature 536:171–182
Goodhill GJ (2007) Contributions of theoretical modeling to the understanding of neural map
development. Neuron 56:301–311
Gottlieb G (1971) Development of species identification in birds: An inquiry into the prenatal
determinants of perception. Chicago University Press, Chicago (IL)
Graybiel AM (1984) Correspondence between the dopamine islands and striosomes of the mam-
malian striatum. Neuroscience 13:1157–1187
Griffiths PE, Tabery J (2013) Developmental systems theory: What does it explain, and how does
it explain it? Advances in Child Development and Behavior, vol 44, JAI, Berlin, pp 65–94
Haeusler S, Maass W (2007) A statistical analysis of information-processing properties of lamina-
specific cortical microcircuit models. Cerebral Cortex 17:149–162
Haeusler S, Schuch K, Maass W (2009) Motif distribution, dynamical properties, and computational
performance of two data-based cortical microcircuit templates. Journal of Physiology – Paris
21:1229–1243
Haken H (1978) Synergetics – An Introduction, Nonequilibrium Phase Transitions and Self-
Organization in Physics, Chemistry and Biology, 2nd edn. Springer-Verlag, Berlin
Harris KD, Shepherd GM (2015) The neocortical circuit: themes and variations. Nature Neuro-
science 18:170–181
Hawrylycz MJ, Lein ES, Guillozet-Bongaarts AL, Shen EH, et al (2012) An anatomically compre-
hensive atlas of the adult human brain transcriptome. Nature 489:391–399
Hegdé J, Van Essen DC (2007) A comparative study of shape representation in macaque visual
areas V2 and V4. Cerebral Cortex 17:1100–1116
22 Alessio Plebe
Herculano-Houzel S, Collins CE, Wong P, Kaas JH, Lent R (2008) The basic nonuniformity of the
cerebral cortex. Proceedings of the Natural Academy of Science USA 34:12593–ŋ12598
Hines M, Carnevale N (1997) The NEURON simulation environment. Neural Computation 9:1179–
1209
Hofstetter S, Friedmann N, Assaf Y (2017) Rapid language-related plasticity: microstructural
changes in the cortex after a short session of new word learning. Brain Structure and Function
222:1231–1241
Horton JC, Adams DL (2005) The cortical column: a structure without a function. Philosophical
transactions of the Royal Society B 360:837–862
Hubel D, Wiesel T (1959) Receptive fields of single neurones in the cat’s striate cortex. Journal of
Physiology 148:574–591
Ito M (1984) The cerebellum and neural control. Raven Press, New York
Ito M, Komatsu H (2004) Representation of angles embedded within contour stimuli in area V2 of
macaque monkeys. Journal of Neuroscience 24:3313–3324
Just MA, Keller TA (2019) Converging measures of neural change at the microstructural, informa-
tional, and cortical network levels in the hippocampus during the learning of the structure of
organic compounds. Brain Structure and Function https://doi.org/10.1007/s00429-019-01838-
4:1–13
Kaas JH (2012) Evolution of columns, modules, and domains in the neocortex of primates. Pro-
ceedings of the Natural Academy of Science USA 109:10655–10660
Kaplan DM (2011) Explanation and description in computational neuroscience. Synthese 183:339–
373
Kaplan DM, Craver CF (2011) Towards a mechanistic philosophy of neuroscience. In: French S,
Saatsi J (eds) Continuum Companion to the Philosophy of Science, Continuum Press, London,
pp 268–292
Karbowski J (2014) Constancy and trade-offs in the neuroanatomical and metabolic design of the
cerebral cortex. Frontiers in Neural Circuits 8:9
Karlen SJ, Hunt DL, Krubitzer L (2010) Cross-modal plasticity in the mammalian neocortex. In:
Blumberg et al (2010), pp 357–374
Kauffman SA (1993) The origins of order – Self-Organization and Selection in Evolution. Oxford
University Press, Oxford (UK)
Khazipov R, Buzsáki G (2010) Early patterns of electrical activity in the developing cortex. In:
Blumberg et al (2010), pp 161–177
Kirchhoff G (1845) Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesonere
durch eine kreisförmige. Poggendorff’s Annalen der Physik und Chemie 64:487–514
Kouh M, Poggio T (2008) A canonical neural circuit for cortical nonlinear operations. Neural
Computation 20:1427–1451
Lorente de Nó R (1938) Architectonics and structure of the cerebral cortex. In: Fulton J (ed)
Physiology of the nervous system, Oxford University Press, Oxford (UK), pp 291–330
Lövdén M, Bäckman L, Lindenberger U, Schaefer S, Schmiedek F (2010) A theoretical framework
for the study of adult cognitive plasticity. Psychological Bulletin 136:659 – 676
Marcus GF, Marblestone A, Dean T (2014) The atoms of neural computation. Science 346:551–552
Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coinci-
dence of postsynaptic APs and EPSPs. Science 275:213–215
Markram H, Muller E, Ramaswamy S, et al MWR (2015) Reconstruction and simulation of
neocortical microcircuitry. Cell 163:456–492
Marom S (2010) Neural timescales or lack thereof. Progress in Neurobiology 90:16–28
Marr D (1970) A theory for cerebral neocortex. Proceedings of the Royal Society of London B
176:161–234
Martin KAC (1988) The Wellcome Prize lecture – from single cells to simple circuits in the cerebral
cortex. Quarterly Journal of Experimental Physiology 73:637–702
Mastronarde DN (1983) Correlated firing of retinal ganglion cells: I. spontaneously active inputs
in X- and Y-cells. Journal of Neuroscience 14:409–441
3 Circuital and Developmental Explanations for the Cortex 23
Mc Manus F (2012) Development and mechanistic explanation. Studies in History and Philosophy
of Biological and Biomedical Sciences 43:532–541
Miikkulainen R, Bednar J, Choe Y, Sirosh J (2005) Computational maps in the visual cortex.
Springer-Science, New York
Miller EK, Freedman DJ, Wallis JD (2002) The prefrontal cortex: Categories, concepts and cogni-
tion. Philosophical Transactions: Biological Sciences 357:1123–1136
Miller KD (2016) Canonical computations of cerebral cortex. Current Opinion in Neurobiology
37:75–84
Minelli A, Pradeu T (2014) Theories of development in biology - problems and perspectives. In:
Minelli A, Pradeu T (eds) Towards a Theory of Development, Oxford University Press, Oxford
(UK), pp 1–14
Molnár Z (2013) Cortical columns. In: Rubenstein JLR, Rakic P (eds) Comprehensive develop-
mental neuroscience: neural circuit development and function in the healthy and diseased brain,
Academic Press, New York, pp 109–129
Mountcastle V (1957) Modality and topographic properties of single neurons in cats somatic
sensory cortex. Journal of Neurophysiology 20:408–434
Nieuwenhuys R (1994) The neocortex. Anatomy and Embryology 190:307–337
Nieuwenhuys R (2013) The myeloarchitectonic studies on the human cerebral cortex of the Vogt-
Vogt school, and their significance for the interpretation of functional neuroimaging data. Brain
Structure and Function 218:303–352
Noack RA (2012) Solving the “human problem”: The frontal feedback model. Consciousness and
Cognition 21:1043ŋ–1067
O’Keefe J, Recce M (1993) Phase relationship between hippocampal place units and the EEG theta
rhytm. Hippocampus 3:317–330
O’Leary DD, Chou SJ, Sahara S (2007) Area patterning of the mammalian cortex. Neuron 56:252–
269
O’Leary DD, Stocker A, Zembrzycki A (2013) Area patterning of the mammalian cortex. In:
Rubenstein JLR, Rakic P (eds) Comprehensive developmental neuroscience: Patterning and
Cell Type Specification in the Developing CNS and PNS, Academic Press, New York, pp 61–85
Parkkinen VP (2014) Developmental explanation. In: Galavotti MC, Dieks D, Gonzalez WJ, Hart-
mann S, Uebel T, Weber M (eds) New Directions in the Philosophy of Science, Springer-Verlag,
Berlin, pp 157–172
Paynter H, Beaman JJ (1991) On the fall and rise of the circuit concept. Journal of the Franklin
Institute 328:525–534
Peters A, Payne BR (1993) Numerical relationships between geniculocortical afferents and pyra-
midal cell modules in cat primary visual cortex. Cerebral Cortex 64:467–478
Piccinini G (2015) Physical Computation: A Mechanistic Account. Oxford University Press, Oxford
(UK)
Plebe A (2012) A model of the response of visual area V2 to combinations of orientations. Network:
Computation in Neural Systems 23:105–122
Plebe A (2018) The search of “canonical” explanations for the cerebral cortex. History and Philos-
ophy of the Life Sciences 40:40–76
Plebe A, Mazzone M (2016) Neural plasticity and concepts ontogeny. Synthese 193:3889–3929
Potjans TC, Diesmann M (2014) The cell-type specific cortical microcircuit: Relating structure and
activity in a full-scale spiking network model. Cerebral Cortex 24:785ŋ–806
Rakic P (1995) Radial versus tangential migration of neuronal clones in the developing cerebral
cortex. Proceedings of the Natural Academy of Science USA 92:323–ŋ327
Rakic P (2008) Confusing cortical columns. Proceedings of the Natural Academy of Science USA
34:12099–ŋ12100
Rall W (1957) Membrane time constant of motoneurons. Science 126:454
Ramón y Cajal S (1891) On the structure of the cerebral cortex in certain mammals. La Cellule
7:125–176
Ramón y Cajal S (1906) In: DeFelipe J, Jones EG (eds) Cajal on the Cerebral Cortex: an Annotated
Translation of the Complete Writings, Oxford University Press, Oxford (UK), 1988
24 Alessio Plebe
Rathkopf CA (2013) Localization and intrinsic function. Philosophy of Science 80:1–21
Riesenhuber M (2012) Getting a handle on how the brain generates complexity. Network: Compu-
tation in Neural Systems 23:123–127
Rockel A, Hiorns R, Powell T (1980) The basic uniformity in structure of the neocortex. Brain
103:221–244
Rockland KS (2011) Five points on columns. Frontiers in Neuroanatomy 4:Article 22
Roe AW, Garraghty P, Sur M (1987) Retinotectal W cell plasticity: experimentally induced retinal
projections to auditory thalamus in ferrets. Soc Neurosci Abst 13:1023
Roe AW, Garraghty P, Esguerra M, Sur M (1990) A map of visual space induced in primary auditory
cortex. Science 250:818–820
Rose N, Abi-Rached JM (2013) Neuro: The New Brain Sciences and the Management of the Mind.
Princeton University Press, Princeton (NJ)
Rothschild G, Mizrahi A (2015) Global order and local disorder in brain maps. Annual Review of
Neuroscience 38:247–268
Sharma J, Angelucci A, Sur M (2000) Induction of visual orientation modules in auditory cortex.
Nature 404:841–847
Sherman SM, Guillery RW (2006) Exploring the thalamus and its role in cortical function. MIT
Press, Cambridge (MA)
Sirosh J, Miikkulainen R (1997) Topographic receptive fields and patterned lateral interaction in a
self-organizing model of the primary visual cortex. Neural Computation 9:577–594
Squire L, Kandel E (1999) Memory: from Mind to Molecules. Scientific American Library, New
York
Stevens JLR, Law JS, Antolik J, Bednar JA (2013) Mechanisms for stable, robust, and adaptive
development of orientation maps in the primary visual cortex. JNS 33:15747–15766
Thomson AM, West DC, Wang Y, Bannister P (2002) Synaptic connections and small circuits
involving excitatory and inhibitory neurons in layers 2-5 of adult rat and cat neocortex: Triple
intracellular recordings and biocytin labelling in vitro. Cerebral Cortex 12:936–953
Thomson Kelvin W (1855) On the theory of the electric telegraph. Proceedings of the Royal Society
of London 7:382–399
Treloar HB, Feinstein P, Mombaerts P, Greer CA (2002) Specificity of glomerular targeting by
olfactory sensory axons. Journal of Neuroscience 22:2469–2477
Turrigiano GG, Nelson SB (2004) Homeostatic plasticity in the developing nervous system. Nature
Reviews Neuroscience 391:892–896
Ursino M, La Cara GE (2004) Comparison of different models of orientation selectivity based on
distinct intracortical inhibition rules. Vision Research 44:1641–1658
Vogt C, Vogt O (1919) Allgemeine Ergebnisse unserer Hirnforschung. Journal Psychol Neurol
25:279–461
von der Malsburg C (1973) Self-organization of orientation sensitive cells in the striate cortex.
Kybernetic 14:85–100
von der Malsburg C (1995) Network self-organization in the ontogenesis of the mammalian visual
system. In: Zornetzer SF, Davis J, Lau C, McKenna T (eds) An Introduction to Neural and
Electronic Networks, Academic Press, New York, pp 447–462, (Second Edition)
von Economo C, Koskinas GN (1925) Die Cytoarchitektonik der Hirnrinde des erwachsenen
Menschen. Springer-Verlag, Berlin
Waddington CH (1957) The strategy of the genes: A discussion of some aspects of theoretical
biology. George Allen and Unwin, London
Weinberger NM (2007) Associative representational plasticity in the auditory cortex: A synthesis
of two disciplines. Learning and Memory 14:1–16
Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by
self-organization. Proceedings of the Royal Society of London B194:431–445
Wright L (1976) Teleological Explanations. University of California Press, Berkeley (CA)
Ylikoski P (2013) Causal and constitutive explanation compared. Erkenntnis 2:277–297
Young MP, Hilgetag CC, Scannell JW (2000) On imputing function to structure from the behavioural
effects of brain lesions. Philosophical transactions of the Royal Society B 355:147–161
3 Circuital and Developmental Explanations for the Cortex 25
Zhang J, Ackman J, Xu HP, Crair MC (2011) Visual map development depends on the temporal
pattern of binocular activity in mice. Nature Neuroscience 71:1141–1152
Chapter
The cerebral cortex manifests a feature that puzzles researchers since early neuroscience: the functional repertoire of the cortex is incredibly vast despite its strikingly uniform structure. This work analyzes the phenomenon of the apparent clash between uniformity and variety of functions, and it pinpoints the sort of explanations that this phenomenon requests. A possible resolution of this tension has been proposed several times in terms of a basic neural circuit so successful to underlie all cortical functions. Circuital models have the virtue of belonging to the mechanistic framework of explanation, and they have greatly improved the understanding of computational properties of the cortex. However, they all lack explanations of the contrast between uniformity and multiplicity of functions in the cortex. A reason for this failure is neglecting the developmental aspect of the cortex, the most likely source of variation in functions. In biology, developmental explanations are receiving increasing attention, but they are often contrasted with the mechanistic ones. I contend that, in the case at hand, the explanandum of the development differs from the ones usually found in developmental biology, and developmental aspects in the cortex can be taken into account within a mechanistic explanation.
Article
Full-text available
Human brain imaging revealed that the brain can undergo structural plasticity following new learning experiences. Most magnetic resonance imaging (MRI) uncovered morphometric alternation in cortical density after the long-term training of weeks to months. A recent diffusion tensor imaging (DTI) study has found changes in diffusion indices after 2 h of training, primarily in the hippocampus. However, whether a short learning experience can induce microstructural changes in the neocortex is still unclear. Here, we used diffusion MRI, a method sensitive to tissue microstructure, to study cortical plasticity. To attain cortical involvement, we used a short language task (under 1 h) of introducing new lexical items (flower names) to the lexicon. We have found significant changes in diffusivity in cortical regions involved in language and reading (inferior frontal gyrus, middle temporal gyrus, and inferior parietal lobule). In addition, the difference in the values of diffusivity correlated with the lexical learning rate in the task. Moreover, significant changes were found in white matter tracts near the cortex, and the extent of change correlated with behavioral measures of lexical learning rate. These findings provide first evidence of short-term cortical plasticity in the human brain after a short language learning task. It seems that short training of less than an hour of high cognitive demand can induce microstructural changes in the cortex, suggesting a rapid time scale of neuroplasticity and providing additional evidence of the power of MRI to investigate the temporal and spatial progressions of this process.
Article
Full-text available
Neural plasticity has been invoked as a powerful argument against nativism. However, there is a line of argument, which is well exemplified by Pinker (2002) and more recently by Laurence and Margolis (2015a) with respect to concept na-tivism, according to which even extreme cases of plasticity show important innate constraints, so that one should rather speak of " constrained plasticity ". According to this view, cortical areas are not really equipotential, they perform instead different kinds of computation, follow essentially different learning rules, or have a fixed internal structure acting as a filter for specific categories of inputs. We intend to analyze this argument, in the light of a review of current neuroscientific literature on plasticity. Our conclusion is that Laurence and Margolis are right in their appeal to innate constraints on connectivity – a thesis that is nowadays welcome to both na-tivists (Mahon and Caramazza, 2011) and non-nativists (Pulvermüller et al, 2014) – but there is little support for their claim of further innate differentiation between and within cortical areas. As we will show, there is instead strong evidence that the cortex is characterized by the indefinite repetition of substantially identical computational units, giving rise in any of its portions to Hebbian, input-dependent plasticity. Although this is entirely compatible with the existence of innate constraints on the brain's connectivity, the cerebral cortex architecture based on a multiplicity of maps correlating with one another has important computational consequences, a point that has been underestimated by traditional connectionist approaches.
Article
Full-text available
In this paper I criticize a view of functional localization in neuroscience, which I call “computational absolutism” (CA). “Absolutism” in general is the view that each part of the brain should be given a single, univocal function ascription. Traditional varieties of absolutism posit that each part of the brain processes a particular type of information and/or performs a specific task. These function attributions are currently beset by physiological evidence which seems to suggest that brain areas are multifunctional—that they process distinct information and perform different tasks depending on context. Many theorists take this contextual variation as inimical to successful localization, and claim that we can avoid it by changing our functional descriptions to computational descriptions. The idea is that we can have highly generalizable and predictive functional theories if we can discover a single computation performed by each area regardless of the specific context in which it operates. I argue, drawing on computational models of perceptual area MT, that this computational version of absolutism fails to come through on its promises. In MT, the modeling field has not produced a univocal computational description, but instead a plurality of models analyzing different aspects of MT function. Moreover, CA cannot appeal to theoretical unification to solve this problem, since highly general models, on their own, neither explain nor predict what MT does in any particular context. I close by offering a perspective on neural modeling inspired by Nancy Cartwright’s and Margaret Morrison’s views of modeling in the physical sciences.
Book
First published in 1957, this essential classic work bridged the gap between analytical and theoretical biology, thus setting the insights of the former in a context which more sensitively reflects the ambiguities surrounding many of its core concepts and objectives. Specifically, these five essays are concerned with some of the major problems of classical biology:the precise character of biological organisation, the processes which generate it, and the specifics of evolution. With regard to these issues, some thinkers suggest that biological organisms are not merely distinguishable from inanimate ‘things’ in terms of complexity, but are in fact radically different qualitatively: they exemplify some constitutive principle which is not elsewhere manifested. It is the desire to bring such ideas into conformity with our understanding of analytical biology which unifies these essays. They explore the contours of a conceptual framework sufficiently wide to embrace all aspects of living systems.
Book
Stuart Kauffman here presents a brilliant new paradigm for evolutionary biology, one that extends the basic concepts of Darwinian evolution to accommodate recent findings and perspectives from the fields of biology, physics, chemistry and mathematics. The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of self-organization: the spontaneous emergence of order widely observed throughout nature. Kauffman here argues that self-organization plays an important role in the emergence of life itself and may play as fundamental a role in shaping life's subsequent evolution as does the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt remain poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems, contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biological science itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences.
Article
Understanding the amazingly complex human cerebral cortex requires a map (or parcellation) of its major subdivisions, known as cortical areas. Making an accurate areal map has been a century-old objective in neuroscience. Using multi-modal magnetic resonance images from the Human Connectome Project (HCP) and an objective semi-automated neuroanatomical approach, we delineated 180 areas per hemisphere bounded by sharp changes in cortical architecture, function, connectivity, and/or topography in a precisely aligned group average of 210 healthy young adults. We characterized 97 new areas and 83 areas previously reported using post-mortem microscopy or other specialized study-specific approaches. To enable automated delineation and identification of these areas in new HCP subjects and in future studies, we trained a machine-learning classifier to recognize the multi-modal 'fingerprint' of each cortical area. This classifier detected the presence of 96.6% of the cortical areas in new subjects, replicated the group parcellation, and could correctly locate areas in individuals with atypical parcellations. The freely available parcellation and classifier will enable substantially improved neuroanatomical precision for studies of the structural and functional organization of human cerebral cortex and its variation across individuals and in development, aging, and disease.
Book
This book articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Six desiderata to be satisfied by an account of concrete computation are set out: 1) objectivity; 2) explanation; 3) the right things compute; 4) the wrong things don’t compute; 5) miscomputation is explained; and 6) taxonomy. The book discusses previous accounts of computation and argues that the mechanistic account satisfies the desiderata better than competing accounts. Many kinds of computation are explicated, such as digital vs. analog, serial vs. parallel, neural network computation, program-controlled computation, and more. The book argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected as trivial insofar as true; false insofar as nontrivial. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended. A hypercomputer is a system that yields the values of a Turing-uncomputable function. If a genuine hypercomputer were physically constructible and reliable, it would refute the modest Physical Church-Turing Thesis. Proposed counterexamples to the Physical Church-Turing thesis are still far from falsifying it, however, because they have not been shown to be physically constructible and reliable.