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8)
Does neuroscience have a logic? - Limitations of brain and
machine information processing
Principal organiser: Dr. Jose Luis Perez Velazquez
Assistant
Professor, Department of Paediatrics and Institute of Medical
Science, University of Toronto
Associate Scientist, Neuroscience and Mental Health Programme,
Brain & Behaviour Centre
Hospital for Sick Children Research Institute
Luis
Garcia Dominguez
Neuroscience and Mental Health Programme, Brain
& Behaviour Centre, Hospital for Sick Children
Summary
One of the main goals of neuroscience is to understand consciousness,
and of particular interest is the question of self-consciousness.
This scheme contains the implicit assumption that brain states
(or some specific cognitive states) like the "self"
can be reached. But is this so? Are all brain states reachable
and/or observable? Some aspects of neuroscience research have
developed in close parallel to some aspects of mathematical
research. Specifically, the view of mathematics as a consistent
and complete system of logic, and the demise of this programme
by the works of K. Gödel and A. Turing, ran in parallel
to the notions of a deterministic nervous system function through
classical Cartesian reflexes, a viewpoint that not many neuroscientists
would adopt today. Thus, some results in mathematical logic
can offer insight to the neuroscientists involved in seeking
answers to these questions that are at the forefront of neuroscientific
research these days. Along these lines, issues to be discussed
in the symposium could be the limitations imposed by certain
results in (meta)mathematics, and the queries relating complexity
measures to neuronal activity and its relation to behaviour:
if brain is complex, what kind of complexity is applicable to
it? Many words have been devoted to discuss whether some of
the aforementioned mathematical results reveal something about
the brain and brain information processing associated with the
sense of self and consciousness, and our plan is to gather workers
in several disciplines (mathematics, logic, philosophy, and
neuroscience) that could express their opinions and, perhaps,
find an (approximate) answer to some of those queries.
Speakers and Abstracts
Information
Processing Limits on Generating Neuroanatomy
Christopher Cherniak, University of Maryland
An apparent paradox is emerging regarding models of brain-wiring:
Available connectivity in, e.g., cerebrum, is stringently
limited; yet deployment of the interconnections attains fine
grained optimization, sometimes without detectable limits.
Neuroconnectivity architecture sometimes shows virtually perfect
network optimization, rather than just network satisficing.
Such connection cost-minimization problems are a major hurdle
of microcircuit design, and are known to be NP-complete. How
does biology effectively solve them? Briefly, some anomalies
of the computational realm seem to be exploited; for instance,
some "butterfly effects". This line of thought suggests
extensions to the Anthropic Principle of cosmology, that is,
further possible constraints on models of a brain-friendly
Universe in which our intelligence can arise.
The
Logic of Neuroscience and Goedel's incompleteness theorems
Jeff Buechner, Rutgers University-Newark and The Saul Kripke
Center, CUNY, The Graduate Center
If neuroscience has a logic, then if it is strong enough to
express arithmetic, it is subject to the Goedel incompleteness
theorems. Distinguish between the logic of neurological processes
and the logic of mental processes that are dependent upon
(in some way: either reducible to or supervenient upon) those
neurological processes. There are various possibilities: the
logic(s) of mental processes and neurological processes are
subject to the Goedel theorems, neither are, or one is while
the other is not. I argue that even if the logic of either
is subject to the Goedel theorems, that there is a way out.
This has to do with the connection between mathematical certainty
and the Goedel incompleteness theorems, one little recognized
by logicians, mathematicians, philosophers, neuroscientists,
cognitive scientists.
Rumbling
about Brain Noise
AR McIntosh, PhD, Rotman Research Institute - Baycrest Centre
When
we measure brain dynamics, noise is often considered as
a nuisance variable that needs to be factored out of the
equation. However, given the brain is almost always active,
it is quite likely that this "noise" may serve
a vital role in normal function. Following from the perspective
of stochastic resonance, local noise fluctuations are key
in extracting relevant signal from the barrage of noisy
input. At a network level, optimal noise would facilitate
the transmission of information between neural elements.
Ongoing noise fluctuations, which may be captured in the
oft observed "resting-state" network, would thus
sculpt the moment-to-moment response of the network. From
a developmental perspective, the emergence of optimal noise
can be related to structural changes in myelin and synaptic
density, resulting in a paradoxical increase in measured
noise as the system matures. So too, as the system ages
and brain structures deteriorate, the noise profile is similarly
changed having broad, and seemingly unrelated, behavioural
effects. Thus, in addition to a connectivity structure that
can be characterized in terms of optimal small world properties,
the tuning of internal noise may be a second factor that
produces a system with optimal capacity for information
segregation and integration – in other words, optimal
complexity.
Nonliner
Cable-like Properties of Microtubules and Their Potential
for Neuronal Processing
Jack
Tuszynski, University of Alberta
Recently,
it has become apparent that neurons may utilize microtubules
(MT) networks in cognitive processing via associated proteins
(MAPs), including MAP-tau and MAP2, in such neuronal processes
as learning and memory (Kaech et al., PNAS 98:7086-7092, 2001).
MTs are also linked to the regulation of a number of ion channels,
thus contributing to the electrical activity of excitable
cells. Hence, MTs may play a role in the processing of electrical
signals within the cell. Cytoskeletal alterations may reflect
changes of neural circuits in response to learning and experience,
and they must involve highly dynamic regulatory mechanisms.
Little is known, however about the intrinsic electrical properties
of MTs, and in particular as to how these electrical properties
are modulated. We recently reported novel features of MTs
in solution (Priel et al., Biophys. J. 90:4639-4643, 2006).
Namely, MTs behave as bio-molecular transistors capable of
amplifying electrical signals. In that report, we used taxol-stabilized,
polymerized tubulin, which were electrically manipulated with
a modified dual "patch-clamp" setup. Our data provided
the first direct experimental proof that MTs sustain novel
biomolecular transistor capabilities, which likely play a
yet unknown role in cell function.
To elucidate the electrodynamic properties of MTs and gain
insight into the regulatory role that MTs play in cellular
activity, we shall present a model intended to explain the
ionic conductive properties of an MT based on a nonlinear
electrical circuit, which mimics the behavior of an MT in
solution. Using the theory of polyelectrolytes for ionic condensation
along the stretch of a polymer, we assess that the cylindrical
volume of depleted ions outside the ionic cloud surrounding
the MT serves as an electrical shield. Hence, we expect this
cloud to act as a dielectric medium between the two providing
both resistive and capacitive components for the MT dimers.
The inductive component is due to the MT's helical structure
that should induce a helical ionic flow in a solenoidal manner.
There are a number of potential biological implications for
a MT-based electrical device, e.g., MT-supported phenomena
such as fast axonal transport. Interestingly, while axonal
MTs are highly polarized, the MTs in dendrites have both plus
and minus ends pointing outward. It is entirely possible that
electrical amplification may provide a novel means for directionality
in MTs. It has been postulated that electrical sorting may
be suitable mechanism of vesicle trafficking. Thus electrical
amplification by MTs, can provide novel means for explaining
relevant cellular features in neuronal function, and likely
other aspects of cell biology at large.
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